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Active noise control: a case study

(in lingua inglese)

Scopo del progetto è l’attenuazione del rumore prodotto da due ventole ad alta velocità, per il raffreddamento di un dispositivo di Digital Video Broadcasting - Terrestrial. E' stato necessario adottare una metodologia di controllo attivo del rumore (ANC) implementata in hardware: essa utilizza sensori ed attuatori elettroacustici per la generazione di un segnale di cancellazione, atto ad attenuare il disturbo in una zona di quiete. ostruzione di un modello che consenta di esprimere la potenza, misurata in un punto, come la somma di quelle generate da un numero predefinito di sorgenti ideali, localizzate in prossimità del dispositivo. Tale modello viene calcolato per le ventole grazie ad acquisizioni acustiche su una griglia tridimensionale di punti; similmente, la procedura viene adottata anche per ricostruire il modello dell’attuatore.

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Articoli tecnico scientifici o articoli contenenti case history
Tesi di Laurea, Politecnico di Milano, Anno Accademico 2011-2012

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Estratto del testo
POLITECNICO DI MILANO Scuola di Ingegneria dell''Informazione POLO TERRITORIALE DI COMO Master of Science in Computer Engineering Active Noise Control: a case study Supervisor: Prof. Fabio Salice
Assistant Supervisor: Prof. Luigi Piroddi
Master Graduation Thesis by: Giacomo Laita Student Id. number: 754404 Academic Year 2011 / 2012 POLITECNICO DI MILANO Scuola di Ingegneria dell''Informazione POLO TERRITORIALE DI COMO Corso di Laurea Specialistica in Ingegneria Informatica Controllo Attivo del Rumore: un caso di studio Relatore: Prof. Fabio Salice
Correlatore: Prof. Luigi Piroddi
Tesi di laurea di: Giacomo Laita Matricola: 754404 Anno Accademico 2011 / 2012 ''Engineering is the art of giving a rigorous meaning to the word enough' Contents List of Figures 12 List of Tables 14 List of Algorithms 16 Introduction 19 1 Active Noise Control 24 1.1 Algorithms for ANC . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.2 Operative principles . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.3 ANC concept extension . . . . . . . . . . . . . . . . . . . . . . . . 31 2 The Literature 33 2.1 Duct arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2 Fan improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.3 Fan modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.4 Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.4.1 Applications examples . . . . . . . . . . . . . . . . . . . . . 65 2.5 Summary and key ideas . . . . . . . . . . . . . . . . . . . . . . . . 76 3 The proposed method 78 4 Measurements and Modeling 85 4.1 Experiment setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.2 DVB-T device power model . . . . . . . . . . . . . . . . . . . . . . 90 4.2.1 Data preprocessing . . . . . . . . . . . . . . . . . . . . . . 96 4.2.2 Power model . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.2.3 Results and Model selection . . . . . . . . . . . . . . . . . . 109 4.3 Speaker power model . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.4 Model matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7 5 Concluding remarks 130 5.1 Method evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.2 Further developments . . . . . . . . . . . . . . . . . . . . . . . . . 131 Bibliography 134 List of Figures 1 Device under study, kindly provided by SY.E.S. . . . . . . . . . . . . . . . 20 2 A Basic ANC scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.1 Destructive interference example . . . . . . . . . . . . . . . . . . . . . . 25 1.2 LMS block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.3 FxLMS block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.4 One dimensional duct section . . . . . . . . . . . . . . . . . . . . . . . 28 1.5 Example of the superposition principle . . . . . . . . . . . . . . . . . . . 30 2.1 Dual ANC system setup . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2 SPL vs. air'ow of a fan with and without the duct . . . . . . . . . . . . . . 34 2.3 Narrow band noise spectrum with ANC system o' and on . . . . . . . . . . 35 2.4 Acoustic system used . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.5 Implementation results of the fan noise power spectrum . . . . . . . . . . . 36 2.6 A dipole source in a side branch resonator . . . . . . . . . . . . . . . . . . 37 2.7 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.8 Frequency spectra of ventilating fan noise and residual noise at error microphone
position; with switched o' ANC system (thick lines) and with switched on ANC
system (thin lines); black lines for the SBR secondary source and gray lines for
the classical monopole source . . . . . . . . . . . . . . . . . . . . . . . 38 2.9 On-axis far-field sound-pressure level from the shaken fan unit relative to the BPF
tonal sound-pressure level radiated by the same fan in free-delivery operation. The
independent variable is the apparent electrical power supplied to the mechanical
shaker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.10 Directivity condition analysis . . . . . . . . . . . . . . . . . . . . . . . . 40 2.11 Experimental setup used to demonstrate active fan noise control . . . . . . . . 40 2.12 Spectra of the fan sound-pressure level sensed at the error sensor position, when the controller is on and o' . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.13 Sound power level reduction in a ba'ed axial-'ow fan as a function of frequency (dB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.14 Sound-pressure level directivity patterns measured for the ba'ed fan with the small 'ow obstruction in position, with and without the ANC in operation . . . 42 2.15 ANC with magnetic bearings . . . . . . . . . . . . . . . . . . . . . . . . 43 2.16 Schematic of a centrifugal fan noise testing facility . . . . . . . . . . . . . . 43 10 2.17 Close loop system: G yw is the duct model, Ga the bearing actuator, K the ANC controller and w the noise disturbance . . . . . . . . . . . . . . . . . . . 44 2.18 Magnetic bearings control system . . . . . . . . . . . . . . . . . . . . . 44 2.19 Block diagram of magnetic bearings system . . . . . . . . . . . . . . . . . 44 2.20 Block diagram of the ANC system: the reference signal x(n) is generated by a tachometer on the fan motor, u(n) is the noise control signal, y(n) is the
anti-noise one and d(n) is the radiated fan noise which depends on the BPF . . 45 2.21 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.22 Spectra of sound pressure level (76.5 Hz) . . . . . . . . . . . . . . . . . . 47 2.23 Spectra of sound pressure level (100 Hz) . . . . . . . . . . . . . . . . . . 47 2.24 Experimental setup to study the acoustic radiation, resulting from the rotor and the upstream obstruction . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.25 Picture of the rotor/stator arrangement . . . . . . . . . . . . . . . . . . . 48 2.26 Sound pressure spectrum with (black thick line) and without sinusoidal 'ow ob- struction (gray thin line) . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.27 Resonator location . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.28 Superposition of fan and resonator sources . . . . . . . . . . . . . . . . . 50 2.29 Mouth patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.30 Outer fan shroud with relevant dimensions (mm) . . . . . . . . . . . . . . 52 2.31 Blade passage frequency level, together with the level of each harmonic at half of the velocity loading condition . . . . . . . . . . . . . . . . . . . . . . 52 2.32 Mouth perforated patterns, tested in experimental noise reduction model . . . . 53 2.33 Blade tone SPL reductions with optimized resonator mouth perforation . . . . 53 2.34 Phase-locked loop block diagram . . . . . . . . . . . . . . . . . . . . . . 54 2.35 FFT spectrum of the pair of fan with dominant tone at 350 Hz . . . . . . . . 55 2.36 SPL comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.37 Sound measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.38 Sound power comparison . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.39 ANC system employing the input separation . . . . . . . . . . . . . . . . . 60 2.40 Acoustic measures of the di'erent components fans . . . . . . . . . . . . . 62 2.41 Fans and sensors location . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.42 Dynamic fan control: implementation . . . . . . . . . . . . . . . . . . . . 63 2.43 Dynamic fan control: control curve . . . . . . . . . . . . . . . . . . . . . 64 2.44 Control results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.45 Data projector (a) and controller block diagram (b) . . . . . . . . . . . . . 65 2.46 Pick-up microphone locations . . . . . . . . . . . . . . . . . . . . . . . 67 2.47 Controller block diagram, together with delay blocks relocated in series with transfer functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.48 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.49 The increase of the vent holes number . . . . . . . . . . . . . . . . . . . 69 2.50 Other modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.51 Noise spectrum comparison . . . . . . . . . . . . . . . . . . . . . . . . 71 2.52 Positions of the control sources . . . . . . . . . . . . . . . . . . . . . . 71 2.53 Frequency spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.54 Semicircular measurement boom . . . . . . . . . . . . . . . . . . . . . . 73 2.55 Error sensor location (round markers) . . . . . . . . . . . . . . . . . . . . 75 3.1 DVB-T module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.2 Power profiles comparison . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.3 Propagation of the attenuation point . . . . . . . . . . . . . . . . . . . . 83 4.1 Microphone characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.2 MM1 frequency response curve . . . . . . . . . . . . . . . . . . . . . . . 86 4.3 Device dimensions (mm) . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.4 Fans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.5 Example of the measurement setup . . . . . . . . . . . . . . . . . . . . . 90 4.6 Example of the measurement setup: zoomed detail . . . . . . . . . . . . . . 90 4.7 Schematic of the microphones position . . . . . . . . . . . . . . . . . . . 91 4.8 3D points disposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.9 Points dispositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.10 Points connections: global view . . . . . . . . . . . . . . . . . . . . . . 98 4.11 Points connections: upper view . . . . . . . . . . . . . . . . . . . . . . 99 4.12 Deleted points after the processing . . . . . . . . . . . . . . . . . . . . . 100
4.13 Fans noise: frequency analysis . . . . . . . . . . . . . . . . . . . . . . . 101
4.14 Device and ideal sources (upper view): the values indicate the strengths of the sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 4.15 Genelec 6010A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.16 Genelec 6010A: frequency response and polar pattern . . . . . . . . . . . . 116 4.17 Spherical coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.18 Measuring gear: loudspeaker . . . . . . . . . . . . . . . . . . . . . . . . 119
4.19 Loudspeaker model points (blue) and excluded ones (red) . . . . . . . . . . . 120
4.20 Loudspeaker acoustic center (red symbol) and ideal sources (blue points) . . . . 122
4.21 Device and loudspeakers placement after the matching procedure (di'erent views) 127 List of Tables 2.1 Test fans specifications . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.2 Performance comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.3 Frequency spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.1 Microphones array: distances between microphone one and the others . . . . . 92 4.2 SET-AC: sampling distances along z-axis (m) . . . . . . . . . . . . . . . . 92 4.3 SET-DOWN: sampling distances along y and z-axis (m) . . . . . . . . . . . 93 4.4 SET-UP: sampling distances along y and z-axis (m) . . . . . . . . . . . . . 93 4.5 Brute force approach: results . . . . . . . . . . . . . . . . . . . . . . . 109 4.6 Results for M = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.7 Heuristic approach results for M = 2 . . . . . . . . . . . . . . . . . . . . 110 4.8 Heuristic approach results for M = 3 . . . . . . . . . . . . . . . . . . . . 111 4.9 Heuristic algorithm: medians of the classes residues . . . . . . . . . . . . . 111 4.10 Heuristic algorithm: W CF results . . . . . . . . . . . . . . . . . . . . . 113
4.11 Final model information . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.12 Polar pattern test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.13 Microphones array: microphones distances (Loudspeaker case) . . . . . . . . 119
4.14 Sampling distances along z-axis, with array aligned with the x-axis (Loudspeaker) 120
4.15 Heuristic algorithm: WCF computation results (loudspeaker) . . . . . . . . . 121
4.16 Loudspeaker final model . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.17 DVB-T device: final model . . . . . . . . . . . . . . . . . . . . . . . . 123
4.18 Loudspeaker: final model . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.19 Heuristic algorithm: W CF computation results (Model matching) . . . . . . . 126
4.20 Matching first solution . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.21 Matching second solution . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.22 Matching: final solution . . . . . . . . . . . . . . . . . . . . . . . . . . 128 14 List of Algorithms 1 Points connection . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 2 Brute force algorithm: Core section . . . . . . . . . . . . . . . . . . 103 3 STD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4 Heuristic algorithm: Main . . . . . . . . . . . . . . . . . . . . . . . 105 5 Heuristic algorithm: HX . . . . . . . . . . . . . . . . . . . . . . . . 106 6 Heuristic algorithm: LMSHX . . . . . . . . . . . . . . . . . . . . . 107 7 Heuristic algorithm: LMSHZ . . . . . . . . . . . . . . . . . . . . . 108 8 Heuristic algorithm: SELECTION block . . . . . . . . . . . . . . . . 108 9 STD: Model matching . . . . . . . . . . . . . . . . . . . . . . . . . 125 Abstract The master thesis here presented is part of the project PIANO (the Italian acronym of ''low cost platforms for the active noise control') which was commissioned to
Politecnico di Milano in February 2011. The project goal is the attenuation of the noise produced by two high rotational cooling fans of a Digital Video Broadcasting - Terrestrial (DVB-T) device. In order to adopt a pervasive solution, it is necessary to employ a hardware- implemented Active Noise Control (ANC) methodology: this utilizes electro-acoustic
sensors and actuators to generate an anti-noise signal, whose aim is the cancellation
of the disturbance in a particular point in space (quiet zone). Nevertheless, the project specifications prohibit any structural modification of the device, with the exception of small microphones and loudspeakers installations,
provided that the cooling performance is not damaged. A dedicated study is needed
to built a robust method for defining the correct actuators number and positions, in
order to achieve the project goal as well as to extend the quiet zone. The description of the selected method is presented after a state of the art analysis: this method is based on the assumption that the power, measured in a point, could be
expressed as the sum of the ones generated by ideal sources located near the device. Once a 3D point grid is defined, acoustic measures on it allow the computation of the model for the two fans; then, the actuator one is obtained by adopting a similar
procedure. After that, the optimal number and positions of loudspeakers are derived itera- tively from the above models: hence, it is possible to have the best combination of
actuators to reproduce the original energy field. Sommario Il lavoro di tesi qui presentato è inserito all''interno del progetto PIANO (''PIAtta- forme a basso costo per il coNtrOllo attivo del rumore'), commisionato al Politecnico
di Milano nel Febbraio 2011. Scopo del progetto è l''attenuazione del rumore prodotto da due ventole ad al- ta velocità, per il ra'reddamento di un dispositivo di Digital Video Broadcasting ''
Terrestrial (DVB-T). Per poter rendere la soluzione pervasiva è necessario adottare una metodologia di controllo attivo del rumore (ANC) implementata in hardware: essa utilizza sensori
ed attuatori elettroacustici per la generazione di un segnale di cancellazione, atto ad
attenuare il disturbo in una particolare zona dello spazio, detta zona di quiete. Le specifiche di progetto, tuttavia, vietano qualsiasi modifica strutturale del dispo- sitivo ad eccezione dell''installazione di piccoli microfoni ed altoparlanti, purchè questi
non compromettano le prestazioni. Si è quindi costretti a sviluppare uno studio dedi-
cato alla costruzione di un metodo per definire il numero e le posizioni ottimali degli
attuatori, permettendo non solo di raggiungere l''obiettivo ma anche di estendere la
zona di quiete. Ad una prima parte che si focalizza sull''analisi dello stato dell''arte, segue la descri- zione del metodo adottato: esso si basa sulla costruzione di un modello che consenta
di esprimere la potenza, misurata in un punto, come la somma di quelle generate da
un numero predefinito di sorgenti ideali, localizzate in prossimità del dispositivo. Tale modello viene calcolato per le ventole grazie ad acquisizioni acustiche su una griglia tridimensionale di punti; similmente, la procedura viene adottata anche per
ricostruire il modello dell''attuatore. Dopo aver così ottenuto i modelli, si procede iterativamente per ricavare il nu- mero e la posizione ottima degli attuatori, in modo da riprodurre al meglio il profilo
energetico originale. Introduction The master thesis here presented is part of the research project PIANO, a broad research work which was commissioned to Politecnico di Milano and started in Febru-
ary 2011. The name is the Italian acronym of ''PIAttaforme a basso costo per il
coNtrOllo attivo del rumore', that can be translated as ''low cost platforms for the
active noise control': a brief explanation of what this project is related to is given in
the following. The PIANO project The PIANO project goal is the reduction of the noise emitted by two high perfor- mance cooling fans of a DVB-T (Digital Video Broadcasting Television) elaboration
system (Fig.1): this type of fan reaches high rotational speed, that aims at dissipat-
ing the high amount of heat released by the image processors, in order to keep the
computational performance requirements unchanged. (a) DVB-T device (b) Fan grid detail Figure 1: Device under study, kindly provided by SY.E.S. Furthermore, these devices are organized in racks and placed inside a closed room: it is easy to understand how much annoying the generated global noise can be for an
operator who has to work nearby. 20 The project specifications require to pursue the predetermined goal without modi- fying the device, while the addition of small sensors and actuators is allowed, provided
that it does not a'ect the cooling performance and the possibility of performing main-
tenance: thus, the noise reduction system must be embedded into the device. All
these restrictions forced the adoption of a hardware (FPGA) implemented ANC sys-
tem, while acoustic sensors and actuators, as microphones and loudspeakers, were
chosen. Figure 2: A Basic ANC scheme Brie'y, a basic ANC system, shown in Figure 2, has to sense and then elaborate a reference signal coming from the operating environment: in most of the cases, this
last signal is the same of the noise or a quantity related to it. By having this infor-
mation, the controller is able to generate the attenuation signal. Since the procedure
is designed to eliminate the disturbance in a well established area (quiet zone), an
error sensor needs to be placed there (even if this is not always possible): therefore,
its measures are used as performance hints and fed to the elaboration section. An
algorithm, typically an adaptive LMS (Least Mean Square) one, updates the coef-
ficients of a control filter whose output drives the canceling actuators, after being
properly manipulated: the filter weights the reference signal upon the performance
information given by the error sensor. Obviously, this thesis work does not cover the entire project: in fact, the ANC controller issue has already been discussed in [12] and [10]. The first paper presents an
exhaustive description of the algorithm choice: after having compared di'erent LMS
algorithmic solutions, the FxLMS (Filtered-x LSM) was the one adopted. The authors
describe also the translation of the general equations of the method into a hardware
language and the algorithm implementation on a FPGA board. [10] deals with the
hardware problems and the adopted solution to accomplish a good implementation
and a good computer-controller communication. Please, refer to the cited papers if
additional information is needed. Covered Topics The master thesis focuses its on the active noise control theory and its fundamen- tal acoustic phenomena, in order to provide a new solution for extending the quiet
zone. This goal is achieved through a smart positioning of sensors and actuators,
based on an energy modeling of the involved sources: this is an new perspective,
which should allow the improvement of the overall attenuation performance by ex-
ploiting the standard ANC components. The next chapter introduces a more detailed description of how an active noise control system works and what algorithms are usually employed, with particular at-
tention to the previously quoted FxLMS one. Chapter 2 is dedicated to a state of the art analysis, which aims at understanding if such a specific problem has already been addressed by the scientific community. After that, the work will proceed in Chapter 3 by illustrating the adopted method to extend the quiet zone. Chapter 4 will deal with the method implementation in
order to compute the fans model as well as the control source one: this chapter will
end with the matching between the two models and the analysis of the results. Chapter 1 Active Noise Control The information here presented is taken from two important literature sources, which are [26] and [20]: the following summary tries to supply the reader with the
knowledge necessary to understand the developments in the subsequent chapters. Acoustic noise is sound which is perceived as ''o'ensive' when heard [26]. Several di'erent types of sources can produce this kind of disturbance: for instance, large in-
dustrial equipments, household appliances, transportation equipments and electronic
devices. The growing attention to the problem, from both the legislative and the
acoustic comfort perspectives, has forced the scientific community to develop inno-
vative and cost-e'ective noise control strategies. The whole set of possible solutions can be divided into passive and active methods: the first category reduces the noise by absorbing it, through the employment of passive
structures like barriers, silencers, mu'ers and di'erent types of absorbing materials.
Although these systems have the ability of attenuating a broad range of frequencies,
they are large, costly and ine'ective at low frequencies. On the other side, the Active
Noise Control (ANC) employs electro-acoustic systems to cancel the unwanted noise
through the addition of sound, according to the superposition principle and three
physical mechanisms: destructive interference by way of creation of an anti-noise
signal (Fig.1.1), impedance coupling and acoustic energy absorption. The ''actors' of an ANC system, from a control systems perspective, are: ' the plant, i.e. the physical system to be controlled (the DVBT device in this case of study); ' the sensors, to sense the disturbance and to monitor how well the system is performing (microphones); ' the actuators, the devices which do the work of altering the plant response (loudspeakers); 24 Chapter 1. Active Noise Control 25 ' the controller, that is, the signal processor which tells the actuators what to do, on the basis of sensors'' signals and the knowledge of how the plant responds
to the actuators (FPGA). Figure 1.1: Destructive interference example Active control systems are able to operate at low frequencies, where passive meth- ods are ine'ective: moreover, the reduction is achieved without physical modification
or rearrangement of existing noise sources. Additional benefits also include: increased
material durability and fatigue life, lower operating cost, compact size and modularity. On the other hand, one of the major limitations of these systems is that the reduction of noise, in a localized specific region, has the unwanted side e'ect of
amplifying it elsewhere: in addition, the noise to attenuate needs to be measured
before it reaches the area of interest. Chapter 1. Active Noise Control 26 1.1 Algorithms for ANC Figure 1.2: LMS block diagram The most common adaptive algorithm is the Least Mean Square (Fig.1.2): it is able to identify a filter, whose a-priori impulse response h(n) is unknown, by the
approximation of a secondary filter, W (n). The convolution theorem states that d(n) = h(n) '' x(n) (1.1) and y(n) = w(n) T '' x(n) (1.2) with the algorithm filter weights estimation w(n) based on the previous values of
x(n), inside a predefined window w(n) = [w1(n), . . . , wL(n)] (1.3) x(n) = [x(n), . . . , x(n '' L '' 1)]T (1.4) In order to estimate the w(n), the function to minimize is simply J (n) = E | (d(n) '' y(n))2 | (1.5) The resolution uses the derivative operator and then sets to 0 the results to obtain
the following weights update rule wl(n + 1) = wl(n) + µx(n '' l)e(n), for l = 0, 1, . . . , L '' 1 (1.6) This simple algorithm has its own limitations, which are overcome by the FxLMS (Filtered-x LMS), as represented in Figure 1.3. The basic innovation is the introduction of the block function S(z), which de- scribes the e'ect produced on the attenuation signal by: ' DAC and ADC converters; ' amplifiers, speakers and microphones; 1.1. Algorithms for ANC Chapter 1. Active Noise Control 27 Figure 1.3: FxLMS block diagram ' the acoustic channel between the actuator and the cancellation area and the one between this area and the error microphone. The error equation changes by adding the secondary path estimation e(n) = d(n) '' (s(n) '' y(n)) (1.7) First of all, the secondary path needs to be estimated o'-line by injecting, for example,
a white noise into the loudspeaker in order to measure the path impulse response ' s(n). Since the error microphone signal is used to update the filter coe'cients, the
condition of no noise in the primary path should be satisfied. Hence, a first equation
for the weights update is built ' sl(n + 1) = ' sl(n) + µx(n '' l)e(n), for l = 0, 1, . . . , L '' 1 (1.8) Thus, the revised filter update equation becomes wl(n + 1) = wl(n) + µx'(n '' l)e(n) (1.9) x'(n '' l) = '''s(n) '' x(n) (1.10) The insertion of a further estimation block may cause an increasing of the error and, at the same time, instability may arise too. To avoid this, the gain µ must be
restrained and the phase error between s(n) and ' s(n) has not to exceed 90'. 1.1. Algorithms for ANC Chapter 1. Active Noise Control 28 1.2 Operative principles By looking at the standard ANC system in Figure 2 (see Introduction), it is evident that three major issues has to be solved: the position of the reference microphone,
the position of the error one and that of the canceling loudspeaker. The acoustic characteristics of the noise source and the environment are usually time varying; in addition, the frequency content, amplitude, phase and sound velocity
of the undesired noise are non-stationary. In order to overcome these variations,
the ANC system must be adaptive [21]: this means that a reference microphone
must sense an input signal, which should be highly correlated to the primary noise.
Moreover, this signal should be fed to the elaboration section, for generating the
anti-noise signal which has to reach the desired quiet zone before the disturbance
[26]. This issue involves the analysis of the bu'ering problem, which implies the
synchronization of the elaboration section in order to drive the secondary source with
the correct signal at the correct time (in relation to this project, [10] solved the
problem of signal bu'ering). The positioning of the reference sensor near the device, so that it is possible to acquire such a good reference signal, should not be a di'cult task. Moreover, the
faster the elaboration system is, the closer the secondary source can be placed to this
reference microphone, by paying attention to the possible interaction between the
noise and anti-noise signals (feedback problem). Considering the use of a small and
easily mountable actuator, the control source could be located in the proximity of the
device: however, the main problem still remains the location of the error microphone. Acoustically speaking, sound is a pressure wave traveling in a medium, at high speed too. The sound emitted from a source becomes less loud as it goes away from
its origin, because the initial energy is spread out over an increasingly large area. It''s
a well-known theory that, if a waveguide is present (like a duct), sound can travel
long distances without significant decay. Figure 1.4: One dimensional duct section 1.2. Operative principles Chapter 1. Active Noise Control 29 So, let''s focus our attention on image 1.4: a disturbance is passing through a control volume of a tube with cross-section S and length dx, whereas p and ρ denote
the pressure and density variation respectively. The 1-dimensional wave equation can
be described by using the mass and the momentum conservation laws: this equation
explains how the acoustic pressure 'uctuations behave with respect to time and space ''2p ''x2 '' ''2ρ ''t2 = 0 (1.11) If an adiabatic acoustic compression takes place, p = c2 0ρ and so ''2p ''x2 '' ''2p c2 0''t 2 = 0 (1.12) The last equation is linear and contains only di'erential operators: the solutions
are in the form of p(x, t) = f (t '' x/c0) for the forward traveling direction and p(x, t) = g(t + x/c0) for the backward one. The linearity involves also that the
superposition principle p(x, t) = p1(x, t) + p2(x, t) applies to the equation solutions
and, thus, the active noise control principle can be applied in practice. In fact, by
considering harmonic waves, the equation is reduced to p(x, t) = '' [ p(x)e j't] (1.13) = |A| cos('t '' kx + 'A) (1.14) where ' = 2'/T is the angular frequency and k = 2'/λ the wave number. The
superposition principle, considering harmonic waves traveling in the same positive
direction, can be expressed as p(x) = Ae'' jkx + Be''jkx (1.15) If an equal amplitude reverse phase sound wave can be generated, it ends with Ae''jkx
for the noise signal and ''Ae''jkx for the anti-noise one p(x) = Ae'' jkx '' Aejkx = 0 (1.16) Figure 1.5 expresses the relation above: the red line is the pressure emitted by the noise source, while the blue one is the pressure from the secondary source (e is the
position of the loudspeaker). The error microphone is placed where it''s desired that
the attenuation occurs (point L). By detecting the waves'' di'erence (Fig.1.5(a)), the
system is able to adjust the amplitude and phase of the control one to achieve the
complete attenuation of both sounds (Fig.1.5(b)). An important remark arises: the global attenuation can be obtained only if both waves generate a comparable pressure profile at the area of interest. This means that
the pressure must be uniform in a direction normal to the propagation one: if this
happens, the wave can be called plane waves. 1.2. Operative principles Chapter 1. Active Noise Control 30 (a) Starting situation (b) Operating point situation Figure 1.5: Example of the superposition principle The duct helps the attenuation process due to its ability of attenuating the prop- agation of high order modes, which quickly decay with the distance thereby allowing
the propagation of plane waves at sound speed: anyway, this case of study has no
duct and, as stated in the introduction, the project specifications clearly compel to
avoid the addition of hardware that could limit the operator work. The above dissertation is still valid if the condition of far field holds: this is the sound field in which sound pressure decreases inversely with the distance from
the source; it corresponds to a reduction of approximately 6 dB for each doubling
distance. The acoustic condition of far field can be expressed as dF arF ield ' λ = c0 f (1.17) which, considering low frequency disturbance, is equivalent to meters. This is a
problem, because it implies that the error microphone should be positioned inside the
forbidden region. 1.2. Operative principles Chapter 1. Active Noise Control 31 1.3 ANC concept extension In summary, the main limitations, imposed by the ANC on the project goal, are two: the placement of the error microphone in the forbidden region and the need of
extending the quiet zone to optimize the overall attenuation. This master thesis proposes its own solution, which involves the use of a standard noise control methodology, aided by experimental studies, in the direction of the
smart placement of sensors and actuators: in particular, the solution is based on the
mathematical modeling of both the noise generated by sources and the anti-noise by
the actuators. Once a model is available, it is possible to search the best loudspeakers
position to achieve the established goal. In order to develop such a method, it is important to carry out a state of the art analysis in order to understand if this problem has already been addressed by the
scientific community: hence, the next chapter is dedicated to this aim. 1.3. ANC concept extension Chapter 2 The Literature An initial state of the art analysis, which was carried forward until October 2012, is here presented. The investigation was aimed at understanding if this particular
kind of problem has been already addressed in research works and also how it has
been solved. The papers revision allows the definition of four majors classes of works,
which are described in the following; after that, a final and global evaluation is pro-
posed. 2.1 Duct arrangement As it was already stated, the standard ANC systems perform to the best of their ability if the problem is duct ''driven': so, it''s no accidental that a lot of jobs deal
with this type of issue. The use of a duct has the disadvantage of requiring extra volume and of con- taminating the system, but the acoustic field composition of fan and loudspeaker is
simplified and, by lining the duct with acoustic foam, the high frequency disturbances
are attenuated. These statements are underlined by [1], whose authors conclude that
the better the primary and secondary source directivity is in agreement, the better
the control is. [5] proposes a combination of passive and active noise control to at-
tenuate the noise produced by a 90 '90'20 mm fan positioned at the midpoint of a 440 mm-long duct, whose cross-section is designed to avoid obstructing the air'ow,
thereby not lowering the cooling performance. Each part has the same, but independent, ANC system running: the gear is composed by a loudspeaker, a reference microphone placed 3 cm away from the
center of the fan and an electronic controller Figure 2.1. 33 Chapter 2. The Literature 34 Figure 2.1: Dual ANC system setup The choice of the latter one relies on a Silentium''s S-Cube' controller running an FxLMS algorithm: an interlaced Echo Cancellation algorithm is added for taking care
of the echo issues, due to the fact that each microphone picks up signals from both
loudspeakers. After establishing the operating point of the fan (see [5] for further
details) the attenuation performance is evaluated. Figure 2.2: SPL vs. air'ow of a fan with and without the duct Figure 2.2 shows that the use of a duct passively attenuate the noise SPL, while the performance, see Figure 2.3, validates the proposed method in noise attenuation
at low frequencies. 2.1. Duct arrangement Chapter 2. The Literature 35 Figure 2.3: Narrow band noise spectrum with ANC system o' and on In their paper [33], Sebald and Veen explain that the adoption of a duct causes the air turbulence to contaminate, due to pressure 'uctuation, the reference microphone
measures and so to degrade the performance of a noise remover. A smart placement
of the microphone can help to overcome the problem: a most e'ective discrimination
can be achieved by placing the sensor parallel to the air 'ow. In [6] Fleming et al. introduce a new technique for controlling low-frequency reverberant sound-field without the need of a precise plant model. They state that
once the interaction between sound-fields, mechanical speaker and electromagnetic
transducer is known, a simple electrical impedance can be designed and connected to
the terminals of a loudspeaker in order to alter its dynamic and improve the dissipation
of the acoustic energy. The impedance is then connected to an electrical network,
which is designed on the electrical properties of the loudspeaker to make it emulating
the acoustic response of a Helmholtz resonator: in this way, highly resonant acoustic
modes can be attenuated. Due to the narrow-band nature of this type of resonators,
the obtained acoustic mitigation is highly dependent on the target acoustic resonance
frequencies. [9] plans an optimal internal model-based (IMB) controller in order to attenuate the noise coming from a rack server cooling fan: the aim is to reduce the periodic
acoustic disturbances in presence of a non-periodic ones. To accomplish this mission
the rack is mounted inside a duct lined with acoustical foam: four speakers are
connected in parallel and placed at the end of it near to the pick-up microphone 2.4. 2.1. Duct arrangement Chapter 2. The Literature 36 Figure 2.4: Acoustic system used The controller, after its design (see [9]) and the identification of the sensors and disturbance dynamics, is tuned to match the resonance modes of the system. The
results are shown in Figure 2.5 and a good attenuation is achieved, despite a little
amplification of sound near the first four harmonics due to the sensitivity of the IMC
Bode''s diagram. (a) IMB o' (b) IMB on Figure 2.5: Implementation results of the fan noise power spectrum 2.1. Duct arrangement Chapter 2. The Literature 37 [27] implements a feed-forward active noise control system which combines a single loudspeaker, that acts as a dipole secondary source, with a side branch resonator to
reduce the acoustic feedback. The basic idea is that two monopole sources, with
appropriate signal delay '0 = L/c0 (where L is the length of the side branch resonator
and c0 is the sound speed), form an unidirectional sound source in a duct if, and only if,
they have same amplitude but reverse phase: the sound generated on the back side of
the loudspeaker is used for acoustic feedback reduction. Literally speaking, the sound
formed on the other side (front of the loudspeaker), which propagates upstream,
is canceled by the sound generated on the rear side. An acoustical short circuit is
employed for acoustic feedback reduction and the side branch resonator (SBR) acts
like a transmission line for frequency response improvement of the secondary source
in band pass frequency range. Also dipole, as a typical loudspeaker is, can be used
for such a reduction: a lot of care has to be paid to the acoustic geometrical setup. Figure 2.6: A dipole source in a side branch resonator A simple analysis is performed on the various sound fields in the pipe (they are represented by the pi in Figure 2.6), with the purpose of finding their amplitude
coe'cients and determining the boundary conditions at the SBR openings (gray
points). It comes out to the authors'' attention that the shorter the side branch
resonator is, the higher is the central frequency of feedback reduction and the broader
its useful frequency range. Besides, the volume 'ow generated on the backside of the
loudspeaker cone is distributed across SBR cross section A2, while the 'ow at the
opposite is distributed in two directions of the main duct 2A1: as a consequence, the
sound pressure created in the upstream direction is proportional to 1/A1, whereas
the one in the downstream direction to 1/A1 + 1/A2. It can be pointed out that
the higher is the ratio A1/A2, the better is the feedback reduction. Hence, the first
scheme has to change as Figure 2.7 shows: the length of the SBR is shorter and the
cross section ration is set to 1. 2.1. Duct arrangement Chapter 2. The Literature 38 Figure 2.7: Experimental setup Measurements are performed and a pink noise excitation is fed to the system, in order to: ' find out the whole set of acoustic paths needed to apply the active noise re- duction algorithm FxLMS ; ' understand how the dumping material, inside the SBR, can a'ect the directivity of the secondary source. The application of this new method ensures a faster convergence and a lower level
of residual noise. If the SBR secondary source is switched o', attenuation can be
pursued despite a 3dB insertion loss, due to the dumping material: by the way, it
is fundamental for obtaining the directivity which is necessary to reach the wanted
feedback reduction (Fig.2.8). Figure 2.8: Frequency spectra of ventilating fan noise and residual noise at error microphone position; with switched o' ANC system (thick lines) and with switched on ANC system (thin lines); black lines for the SBR secondary source and gray lines for the classical monopole source 2.1. Duct arrangement Chapter 2. The Literature 39 2.2 Fan improvement Lauchle et al. [13] take under consideration the problem of attenuating a noise coming from a discrete-frequency axial-'ow fan and propose a very interesting and
innovative method. First of all, this type of fan radiates sound at the blade-passing
frequency (BPF), whose value is given by the number of fan blades multiplied by the
shaft speed: the predominant direction of radiation is 90' to the fan axis. The smart idea is to use the fan itself as an anti-noise source by connecting it to an electromagnetic shaker to generate controlled unsteady forces on the primary
source. If the shaken fan unit produces substantial radiation for a reasonable power input to the shaker and the fan noise directivity patterns (of the primary and secondary
sources) are identical, thus the method is implementable. Experiments show that the
first condition is satisfied by suppling 0.1 W to the shaker (Fig.2.9): furthermore, the
image suggests that the shaken fan can act as a crude loudspeaker, thereby being
suitable for ANC applications. Figure 2.9: On-axis far-field sound-pressure level from the shaken fan unit relative to the BPF tonal sound-pressure level radiated by the same fan in free-delivery operation. The independent variable is the apparent electrical power supplied to the mechanical shaker The second condition is verified thanks to the experimental setup showed in Figure 2.10(a): a movable microphone, placed in the free-field 1 meter far from the fan,
provides measurements every 5' for ba'ed and unba'ed axial 'ow fan units. Because
of the better pattern uniformity in the ba'ed case, as it is visible in Figure 2.10(b),
the performance of the ba'ed shaken fan in noise reduction is now taken into account:
an FxLMS algorithm is implemented and an optical tachometer is used as reference
sensor (Fig.2.11). 2.2. Fan improvement Chapter 2. The Literature 40 (a) Experimental setup for measur-
ing ba'ed fan directivity (b) Far-field directivity pattern Figure 2.10: Directivity condition analysis Figure 2.11: Experimental setup used to demonstrate active fan noise control 2.2. Fan improvement Chapter 2. The Literature 41 Figure 2.12: Spectra of the fan sound-pressure level sensed at the error sensor position, when the controller is on and o' Comparing the spectra (Fig.2.12), it is possible to note a reduction of 20 dB for what concerns the fundamental BPF tone, while 15 dB and 8 dB are, respectively,
the values for the second and third harmonics. This harmonics attenuation lowering is caused by to the less uniform fan directivity for higher BPF''s harmonics. Figure 2.13 allows the evaluation of the power radiated by
the fan with and without the activated controller: 13 dB and 8 dB are the reduction
of the fundamental and the first harmonic which are lower than the ones at the
microphone location. Figure 2.13: Sound power level reduction in a ba'ed axial-'ow fan as a function of frequency (dB) 2.2. Fan improvement Chapter 2. The Literature 42 Figure 2.14: Sound-pressure level directivity patterns measured for the ba'ed fan with the small 'ow obstruction in position, with and without the ANC in operation This is clearly visible in Figure 2.14, that highlights the obstruction created by the cylindrical rod, placed across the center of the fan during the experiment setup;
moreover, the same image shows how much good the attenuation is along the fan
axis. The authors also test the shaken fan in a last experiment: an empty desktop computer cabinet is placed on the planar ba'e over the fan, which moves air to the
case. The error microphone is positioned inside the cabinet, while a remote one is
located 1 meter far from there: this setup leads to a noise reduction of 21 dB at the
external position and 26 dB at the internal one. In conclusion, the new method demonstrates that the fan itself can act as an anti-noise source, avoiding the need of adding a separate secondary source. Lauchle''s concept is extended one step further by [18], [30], [17] and [29]: instead of connecting the fan to a shaker, the impeller is equipped with magnetic bearings
which support it and allow the fan blade to be actuated like an audio speaker, by
moving the impeller back and forth (Fig.2.15). Co-locating the disturbance produced by the impeller rotation and the attenuation signal from the vibration of the fan impeller has the advantage that both signals
enter the space in the same point. As [30] states, while trying to demonstrate the
e'ectiveness of the new approach in achieving broadband noise reduction, co-location
means also same path; this phrase can be better understood by looking at Figure 2.16,
which shows the testing gear: the same route length exists both from the anti-noise
source to the error microphone and from the disturbance to the same microphone. To build up a robust noise controller for accomplishing the previously quoted task 2.2. Fan improvement Chapter 2. The Literature 43 Figure 2.15: ANC with magnetic bearings of broadband noise attenuation, H'' control theory is adopted [29]. A first analysis shows that the fan impeller, supported by magnetic bearings both radially and axially,
generates a broadband and tonal noise, with significant tone at the rotation frequency
and at the blade pass frequency (BPF). The authors derive a state space model
(nominal plant) for the acoustic system in Figure 2.16: they start from an infinite
dimensional physical model by using a subspace algorithm on the system''s response
to a white noise signal (see [29] for details). The controller design is focused on
obtaining a feedback one, which reduces the gain of the close loop system regarding
the tone''s frequencies (Fig.2.17): based on the nominal plant, a single weighting
filter is chosen to shape the gain. This has to be greater than the one at BPF,
to achieve a significant roll o' at high frequency by avoiding an excessive spillover.
Subsequently, the controller is obtained by solving the RSP (Robust Stabilization
Problem) and the complexity is reduced via elimination of the pole/zero cancellation
and state reduction. Figure 2.16: Schematic of a centrifugal fan noise testing facility 2.2. Fan improvement Chapter 2. The Literature 44 Figure 2.17: Close loop system: G yw is the duct model, Ga the bearing actuator, K the ANC controller and w the noise disturbance As already mentioned, a real implementation of an improved magnetic bearings method is presented in [17]. Because of the bearings'' inherent instability, they require
a feedback controller (Fig.2.18) which stabilizes and maintains the rotor in a desired
position and, as a consequence, dictates the bearings'' dynamic characteristics. Figure 2.18: Magnetic bearings control system Despite the magnets are intended to maintain the rotor in a certain position (the rotor levitates in a nominal position), they can also be used to shake it and
to achieve sound control with no additional hardware requirements: the shaking
movement can be obtained by perturbing the rotor''s reference position signal u(t)
intentionally (Fig.2.19). Figure 2.19: Block diagram of magnetic bearings system 2.2. Fan improvement Chapter 2. The Literature 45 In particular, the force f (t) generated by the bearings electromagnets is a function of the rotor displacement z(t) and the winding current i(t), with constants ks as the
force-displacement factor and ki as the force-current one. The transfer function
(Gb(s)), which describes the interaction between bearings and rotor, is so governed
by Newton''s second law and by considering the rotor like a rigid body with mass m.
Hence, it follows f (t) = ksz(t) + kii(t) = m d2z(t) dt2 (2.1) Gb(s) = Z(s) I(s) = ki/m s2 '' (ks/m) (2.2) Ge(s) represents the transfer function for the coil dynamics: by stating that A is the power amplifier gain, L and R are respectively the coil inductance and resis-
tance and, recalling the equations for an electromagnetic coil, the transfer function
is expressed as Ge(s) = A/L s + (R/L) (2.3) The last transfer function, Gc(s), governs the controller position and it stabilizes the magnetic bearings: proportional-derivative (PD) and proportional-integral deriva-
tive (PID) laws are typically used, with constant Kp and Kd as the desired sti'ness
and damping, respectively. Gc(s) = R kiA [Kds + (Kp + ks)] (2.4) Figure 2.20: Block diagram of the ANC system: the reference signal x(n) is generated by a tachometer on the fan motor, u(n) is the noise control signal, y(n) is the anti-noise one and d(n) is the radiated fan noise which depends on the BPF 2.2. Fan improvement Chapter 2. The Literature 46 Figure 2.20 shows the block diagram of the ANC system which is used to drive the magnetic bearing sound actuator: a feed-forward approach is taken into consideration
and it is equipped with a FIR filter controller whose weights are updated by an FxLMS
algorithm. Figure 2.21: Experimental setup The experimental apparatus is visible in Figure 2.21 and it consists of a three- bladed fan connected to a servomotor by a 'exible link passing through the supporting
magnetic bearings. An error microphone is placed 36 cm in front of the outlet side
of the fan, with an 8 cm o'set from its rotational axis. Three experiments are performed in order to demonstrate if the proposed method is capable of generating a sound of su'ciently high amplitude and coherent frequency:
this sound should reduce the noise at the error microphone (feedback) and in other
points far from it (without the feedback information). Figure 2.22 shows the noise produced by the uncontrolled situation measured when the fan rotor runs at 2000 rpm: a spike at 100 Hz (corresponding to the BPF)
appears on the spectra. If the magnetic bearings are driven by a set of sinusoids (76.5
Hz) with the aim of vibrating the fan only in the axial direction, a spike appears at
the given frequency: this spike is the demonstration that the bearings are able to
produce sound at a specific frequency. 2.2. Fan improvement Chapter 2. The Literature 47 (a) Noise control o' (b) Noise control on Figure 2.22: Spectra of sound pressure level (76.5 Hz) Further experiments, whose aim is the 100 Hz spike removal (Fig.2.23), illustrate the viability of using magnetic bearings as a noise control actuator. By driving an
axial-'ow fan with a magnetic thrust bearing, the blade-rate tone of the fan is reduced
by 4 dB at the error microphone and by 3 dB at the points which are located at 180
cm far from the error microphone. (a) Noise control o' (b) Noise control Figure 2.23: Spectra of sound pressure level (100 Hz) Gérard et al., in their paper [3], provide an analytical tool to design 'ow control obstructions which destructively interfere with the primary tonal noise arising from
cooling fans. Trapezoidal and sinusoidal shapes are suitable for this type of job, since
they can control a tone without a'ecting its harmonics, which is an important issue in
the noise control field. The obstruction, as the authors state in [2], must be located so
that the secondary radiated sound has equal magnitude but opposite phase compared
with the primary noise: in addition, the obstruction should be ''location-adaptable'
to control non-stationary non-uniform 'ows. In [2] the experimental setup, which is
used to validate the thesis expressed in [3], is shown in Figure 2.24: an engine cooling 2.2. Fan improvement Chapter 2. The Literature 48 unit is installed in a rigid frame, while a sinusoidal obstruction, placed upstream, can
rotate and axially move forth and back. Figure 2.24: Experimental setup to study the acoustic radiation, resulting from the rotor and the upstream obstruction SPL measurements are done at a BPF of 290 Hz for trapezoidal, sinusoidal and cylindrical obstructions: results reveal that no attenuation is achieved when the ob-
structions is at the maximum axial distance between itself and the rotor. A second set of experiments is tuned to investigate the noise attenuation in the free field. The same setup gear is employed but data are collected with respect to
both the couple rotor/stator arrangement (Fig.2.25)(a)) and the rotor/stator plus
triangular obstruction, inserted between two vanes of the stator (Fig.2.25)(b)). (a) (b) Figure 2.25: Picture of the rotor/stator arrangement 2.2. Fan improvement Chapter 2. The Literature 49 An attenuation of 12.2 dB is achieved in the first case with a small enhancement of the BPF harmonics, thereby proving the frequency selectivity ability of the sinusoidal
obstruction. In the second case, same results (10 - 20 dB) are obtained, even if the
additional obstruction causes a slight increase of the broadband noise 'oor (Fig.2.26).
It has to be pointed out that this increase is so low to be neglect. (a) Case 1: upstream (b) Case 2 upstream Figure 2.26: Sound pressure spectrum with (black thick line) and without sinusoidal 'ow obstruction (gray thin line) 2.2. Fan improvement Chapter 2. The Literature 50 In [15], the idea is to cancel the axial fan blade tone noise through the use of an optimal tuned quarter wavelength resonators (Fig.2.27). Figure 2.27: Resonator location The resonator is excited when the tip of the blade passes by its perforated mouth, causing a periodic pressure generation: the changing of resonator''s length or mouth
opening can originate an out-of-phase condition with respect to the blade tone. In
particular, a quarter-wave resonator radiates as a monopole source, while axial fans
as dipole source. This resonator can be tuned to be 180'out-of-phase from the
downstream fan noise, in order to reduce the waveform on this side: of course, the
upstream waves are in phase and thus amplified (Fig.2.28). Figure 2.28: Superposition of fan and resonator sources 2.2. Fan improvement Chapter 2. The Literature 51 The amplitude of the resonator response depends on the number of resonators involved: furthermore, the perforated mouth is essential for maintaining an high level
of fan e'ciency so that an accurate investigation needs to be performed. The above
mentioned resonators are 152 mm long nylon tubes with a 60 ml syringe tube inside:
the perforated mouthpiece is accommodated at the open end while the close end
consists of a movable 127 mm long nylon plunger. The mouthpiece is a piece of a 5.1
mm thick aluminum with the same curvature of the inner radius of the fan shroud.
In order to fulfill the attenuation job, the resonator acoustic characteristics (i.e. the
impedance with respect to mouth porosity) must be known. Figure 2.29: Mouth patterns Di'erent resonator''s lengths and mouth patterns are tested (Fig.2.29) and the SPL vs. the resonator frequency response is measured by calibrated probes inside the
tube. Results highlight that a reduction in the open perforated area (pattern 1 to
6) causes a shift of the resonant frequency from 598 Hz to 320 Hz and a reduction
of the attenuation factor too: in addition, the resonator behavior approaches that
of the closed-closed tube type. This type of data is used to model the closed-end
resonator response as a function of the driving pressure by acoustic transmission line
theory: the resonator attenuation increases as the mouth porosity decreases. The
arrangement is tested thanks to the use of a fan facility: a 'uted duct, with upstream
and downstream anechoic termination and a 260 mm diameter ten blade automobile
radiator fan in the middle. The outer shroud (Fig.2.30) is made by Plexiglas rings glued together: it is de- signed to accommodate ten evenly spaced resonators around the fan''s perimeter,
corresponding to each blade. The resonator tubes are inserted into each of these
holes and fitted with plugs when they are not used to attenuate the noise. Tests
about di'erent loading fan conditions highlight that, at free-stream velocity of 3.2
m/s (by now it will be considered unchanged), the resonators have a negligible e'ect 2.2. Fan improvement Chapter 2. The Literature 52 Figure 2.30: Outer fan shroud with relevant dimensions (mm) on the fan performance: in addition, the SPL of the fundamental BPF varies depend-
ing on the fan load. The author suggests the need of characterizing the pressure,
generated on the surface of the shroud by the passing blades, to provide both the
tuning of the resonators and their anti-phase cancellation analysis. Figure 2.31: Blade passage frequency level, together with the level of each harmonic at half of the velocity loading condition Measurements are taken at each hole for three loading conditions: results in Figure 2.31 confirm that the peaks occur at the BPF with also the presence of higher
harmonics components. Furthermore, the phase analysis shows the existence of a
transition region at the blade passing one, which explains the significant di'erence 2.2. Fan improvement Chapter 2. The Literature 53 between upstream and downstream shroud pressures (180'). Figure 2.32: Mouth perforated patterns, tested in experimental noise reduction model Several mouth perforation patterns are tested to evaluate the best noise reduction attitude,by considering the operative fan velocity equals to half of the maximum one
(Fig.2.32). At the beginning, the first pattern is adopted to decide the optimal
resonator length to obtain the maximum upstream and downstream SPL reduction
(221 mm and 304 mm respectively). Taking into account the downstream case tune,
a 12 dB reduction at the BPF tone is achieved. Further experiments lead to the determination of the optimal perforation: pattern 7 reduces the tonal noise 8 dB more than the fully perforated one as well as the
harmonics (Fig.2.33). An increase of 4.7 dB occurs in the upstream direction but
without e'ect on the first harmonic. A detailed analysis reveals that a resonator,
mounted near the leading edge of the fan blade, is the most e'ective in attenuating
downstream SPLs and vice versa. In practice, since the most axial fans radiate more
strongly in one direction, the overall radiated noise reductions can be obtained by
reducing noise in the louder direction while the level, radiated in the other directions,
increases only slightly. Figure 2.33: Blade tone SPL reductions with optimized resonator mouth perforation 2.2. Fan improvement Chapter 2. The Literature 54 In relation to the cooling problem of servers, [31] presents an inexpensive method to reduce the noise dominant tone perception: a change in the thermal management
firmware or the adding of a micro-controller can lock the fans to a common frequency
and to a 180'out-of-phase situation; this condition should generate two waves which
can be destructively summed together. The experiments regard a pair of mu'n fans in a rack mountable system, whose dominant tone is in the range from 140 Hz to 490 Hz. The presence of a range
is justified by the fact that the dominant tone can be computed by multiplying the
number of blades of each fan by the number of rotation per second (in this case,
between 1200 and 4200 rpm based on a 1 to 9 V variable control input voltage,
which varies the speed). The real speed is measured by a tachometer and, because
of the noisy signal characteristics, a bandpass filter is implemented. Figure 2.34: Phase-locked loop block diagram The above measurements (frequency vs. control voltage) are used to design a phase locked loop (PLL, Fig.2.34) for locking fans to a constant phase. The general
strategy is to allow one fan to run freely (acting as reference) and to phase-lock the
other to the first one: this choice not only requires to control half of the sources but
it is also adaptive to every change that happens to the reference fan. The whole set of collected data is used for developing a mathematical Laplace- domain fan model, which is then converted into a phase model in order to control
that variable instead of the frequency. The PD (Phase Detector) block in Figure 2.34
represents a counting-type phase device, which has to find the di'erence between the
accumulated phases of the two fans; at the same time, it has to generate an output
signal representing the phase di'erence in radiants: a compensator, equipped with
an integrator able to absorb the DC component of the error signal, adjusts the trade
o' between the responsiveness to disturbance and the overall system stability. The fans under analysis are inside a chassis and a microphone is placed 25 cm far away, pointing to the blowers outputs: some experiments are performed considering
both the freely running unsynchronized pair of fans and the synchronized case with 2.2. Fan improvement Chapter 2. The Literature 55 (a) Unsynchronized pair of fans (b) Synchronized pair of fans with canceling tone Figure 2.35: FFT spectrum of the pair of fan with dominant tone at 350 Hz subtractive tones. Figure 2.35 shows the attenuation of the dominant tone at 345 Hz,
by a factor of 2.5. It needs to be pointed out that the optimal phase o'set must be
manually tuned at the operative location: this can be done by analyzing a real-time
spectrum of the activated system and seeking for the o'set that best reduces the
identified tonal component. 2.2. Fan improvement Chapter 2. The Literature 56 2.3 Fan modeling Centrifugal fans are commonly used in several applications to meet the heat cool- ing requirement: in addition, they are also chosen because they can generate a su'-
cient air'ow in accordance with the dimension limit. Besides the cooling performance,
having a low acoustic emission is important too: [32] takes into consideration a 80
mm-diameter backward-inclined centrifugal fan and supplies not only a numerical
analysis of the 'ow-field but also an e'cient noise prediction. The simulation is
done by using the a commercial software CFD - Fluent (please refer to the paper for
the adopted assumptions and boundary conditions). For what concerns the acoustic
noise evaluation, the authors show that the numerical simulation of a LES (Large
Eddy Simulation) turbulence model can well predict the acoustic behavior of the fan,
supplying useful information to the fan designer. It is recalled here that the noise produced by a fan can be thought as composed by a broadband part and a discrete part. In particular, the second one is a combination
of: ' a BPF frequency and its harmonics; ' a shaft frequency and its harmonics. The latter is the result of asymmetries, in the fan structure, which cause distortion in the 'ow field and low frequency range noise (anyway, very di'cult to attenuate).
Considering both the broadband and the discrete parts, new hybrid methods for the
numerical prediction of the sound field are available and they can achieve acceptable
results; in particular, they provide information helpful to study some acoustic e'ects
like eccentricity, which is usually a result of the slight positioning error of the fan
rotor. In [34], the additional aeroacoustic e'ect, produced by geometrical asymmetries, is taken under test. Furthermore, symmetric and asymmetric rotating fans are modeled
and analyzed: detailed information of the mathematical methods can be found in
[34]. The models of the two fans are similar: their di'erence only consists of the 0.45
mm distance between the geometric center and the rotating one of the asymmetric
fan. The SPL measurement is shown in Figure 2.36: it is clearly visible that the
asymmetry causes the noise to be on average of 5 dB greater than the other case:
thus, the first harmonic is 18 dB higher and the angular symmetry is broken. Any tiny eccentricities can bring large variation of sound frequency spectrum and it needs to be further studied in order to provide a more detailed and complete
information to the modeling procedure. Hence, the work of [34] can be an integration to the one of [32], because it supplies additional hints on how a fan can be better designed. 2.3. Fan modeling Chapter 2. The Literature 57 (a) Globally (b) Harmonically divided Figure 2.36: SPL comparison As stated beforehand, the cooling property of the 'ow created by a centrifugal fan is a basic requirement for most electronic devices such as desktop computers
and notebooks. On the other side, fans are the less reliable parts and their frequent
failures need to be addressed. Therefore, [24] proposes the study of the acoustic noise generated by two tandem tubeaxial fans, stacking in this configuration to solve the redundancy issues. Doubling
the fans brings to a corresponding doubling of the noise output produced, which has
to be added to that one deriving from the air'ow interaction. In order to quantify the
noise, the fans are suspended in a volume by rubber bands to eliminate any additional
source of noise, which could be present in a real electronic device enclosure: moreover,
the fans are bolted together so that no free movements are allowed and the spacing
between them is filled with washers. A PVC frame (Fig.2.37) is created as control
volume and its surfaces are orthogonally scanned to acquire the sound intensity, whose
sound power is then derived from in accordance with ISO 9614-2. Figure 2.37: Sound measurement setup 2.3. Fan modeling Chapter 2. The Literature 58 Di'erent types of fans are put under test (Tab.2.1) with the following configura- tions: 1. one fan; 2. two fans at di'erent distances from one another in a closed channel configura- tion; 3. same as above but now the channel is open to ambient. Fan Size (mm) No. of fan blades CFM@12 V I 120 '38 3 112 II 120 '38 7 110 III 80 '25 7 35 IV 60 '25 7 12 Table 2.1: Test fans specifications The analysis is divided in two sections that is, noise and air'ow measurements.
For what concerns the second one, which is not of main interest here, please refer directly to page 337 of [24], while the description of the noise measurements is now
further analyzed. It is important to remember that, by suspending the fan inside a
control volume, no noise-generating mechanisms are present: thus, if the separation
distance between the sources approaches the infinite, the air'ow interactions reach
a minimum and the radiated sound power becomes close to a theoretical reference
value. On the other side, the finite separation distance causes the measured power to
be greater than the theoretical one and this di'erence can be ascribed to the air'ow
in'uences: indeed, at zero distance the emission reaches the maximum. Figure 2.38 shows the sound power of Fan Type I and II: the straight line at the bottom of the left image represents the theoretical reference for a single fan sound
power, while the dotted line (in both images) is the reference for two fans; in addition,
the square marked line is associated with the open channel configuration, while the
remaining with the closed one. As it can be seen in Figure 2.38, the two channel configurations functions are similar and give close results for small separations, whereas the increase of the fans
distance cause greater sound power emission (quantifiable as 5 dB) by the closed
channel: anyway, the open channel configuration is 4 - 5 dB greater than the baseline
reference, indicating that an interaction between the two 'ows is present. 2.3. Fan modeling Chapter 2. The Literature 59 (a) Fan Type I (b) Fan Type II Figure 2.38: Sound power comparison The two images give also another information: the comparison of the sound power dependency on separation distance is weaker for Fan Type II, pointing out that also
the number of fan blades (3 in the first case, 7 in the other) plays a significant role
on noise emission. In summary, increasing the space between two fans can bring about a total sound power reduction of 5 dB because of less interactions between the two 'ows; moreover,
an open to ambient channel can help to further reduce the emission. It needs to be
pointed out that tests are performed considering an isolated fan: indeed, a study has
indicated that the noise emission of fan mounted inside a chassis is greater than the
emission which would be present with only a fan [16]. 2.3. Fan modeling Chapter 2. The Literature 60 2.4 Others This last category is created to grant access to those papers which can not be included into the previous sections. Furthermore the papers, here presented, deal
with real case of study applications and noise reduction techniques. The problem of the fan active noise control can be approached from di'erent perspectives: the attention can switch from the attenuation into the reduction of
emission or from the fan itself into its type of usage, in a way that the active noise
control becomes implicit without the use of additional sound sources. [11] proposes a parallel ANC system implementing the standard FxLMS algorithm. The key idea is to split the input signal into periodic and random components: in
fact, since periodic signals are perfectly predictable (through a FFT analysis), a perfect
anti-noise signal can be generated for them, resulting in a very high attenuation level. Figure 2.39: ANC system employing the input separation The Figure 2.39 shows the above stated idea: the input signal x(n) is separated into its periodic q(n) and stochastic v(n) components. These are fed to appropriate
ANC systems whose outputs are filtered by the transfer functions of the electrical
and acoustic path from the loudspeaker to the error microphone; then the outputs
are compared to the predicted noise coming from the sources to end with the error
signal, which allows the tuning of the system. Considering 'x the noise attenuation level of the input x(n), it can be written as the energy of the signal to cancel (ξd = ξd q + ξdv because of the independence of stochastic and deterministic parts), divided by the sum of the energies of the error in
its periodic (ξe q ) and random (ξev ) components. Assuming the perfect cancellation of the periodic part, the upper bound for the maximum noise attenuation level is: 'x = ξd ξe q + ξev = ξd q + ξdv ξe q + ξev '' ξd q + ξdv ξe v = 'v ( 1 + ξd q ξd v ) (2.5) 2.4. Others Chapter 2. The Literature 61 The better performance of the separation method is shown for di'erent numbers of tone in the below Table 2.2 Table 2.2: Performance comparison The separation principle is also used by [19] to propose an alternative algorithm for the attenuation of a periodic disturbance in the presence of a random one. The
authors develop a standard state-space model of the system and use a traditional LTI
controller as starting point to design an IMC controller, with two aims: tracking and
canceling a periodic disturbance and also coping it with the random one. The internal
model needs to capture the relevant properties of the unknown input microphones
signal: thus, a model of a periodic signal with time-variant frequency is required.
Considering that the estimation and rejection of the disturbance should be done
together, the frequency of the period must become a state: this produces a non-linear
state space equation (because of the presence of the state variable inside cosine and
sine), which forces the adoption of an Extended Kalman Predictor for the estimate
of states and frequencies. 2.4. Others Chapter 2. The Literature 62 The requirement of an active noise control system is bound to the need of elim- inating an annoying sound coming from a source: in [4], this source is a validation
platform cooling system (in the paper, two platforms are investigated but here only
one is discussed). A validation platform is a system used to test and debug new mi-
croprocessors and chip-sets. Because of the need of doing various tests even in critical
conditions, the combination of high cooling requirement and accessibility forces the
fans to reach very high rotational speed: considering that these platforms are open
system, this speed produces a noise able to reach a maximum of 85 dBA at 1 meter far
from the system. The authors analyze the problem from the perspective of reducing
the noise instead of attenuating it. First of all, individual component acoustic analysis
is performed: results highlight that the higher noise is associated with the memory
system (Fig.2.40), and therefore, they suggest implementing the fans management
on it. Figure 2.40: Acoustic measures of the di'erent components fans 2.4. Others Chapter 2. The Literature 63 The authors goal is to lower the rotational speed of the fans by maintaining the cooling requirement. Therefore, temperature sensors are needed but their placement
selection is critical, because they have to sense the worst temperature value: to do this
task, their are located near the heating sources, so that the temperature is registered
before the heat is dissipated by the fans (Fig.2.41). (a) (b) Figure 2.41: Fans and sensors location The real time dynamic fan-control implementation is shown below in Figure 2.42: when the components on the board are powered on, the ambient temperature rises
around the sensors, which send a signal to the micro-controller; the latter increases or
reduces the fans speed with respect to the input data, that is, the sensed temperature
and the control curve (Fig.2.43). Figure 2.42: Dynamic fan control: implementation 2.4. Others Chapter 2. The Literature 64 Figure 2.43: Dynamic fan control: control curve The RPM control curve, visible in Figure 2.44, allows to run the fans at di'erent speeds depending on the ambient temperature, by causing a reduction from 6 to
11 dBA with respect to the case of all 3 fans running at 100%. A further 4 dBA
reduction can be achieved if the fans guard is re-designed, because of the diminished
resistance to the air 'ow. Figure 2.44: Control results 2.4. Others Chapter 2. The Literature 65 2.4.1 Applications examples A feedforward based active noise controller is implemented by [28] on a NEC LT170 data projector: the system under consideration is shown below (Fig.2.45(a)). (a) (b) Figure 2.45: Data projector (a) and controller block diagram (b) A feedforward compensator F (q) is usually fed by the input signal u(t) coming from a pick-up microphone: its output drives the control speaker to attenuate the
noise disturbance η(t). The objective is the reduction of the performance index e(t), which represents the error signal. In particular, if the sound disturbance is not in'uenced by the
compensation one and the compensator is stable, the following stable map equation
can be written e(t) = W (q) [H(q) + G(q)F (q)] η(t) (2.6) It leads to the ideal compensator F (q) = '' H(q) G(q) (2.7) considering that the acoustic coupling minimization is obtained both by shielding the
pick-up microphone and by installing non-invasive small directional speakers at the
inlet and outlet grill. The ideal compensator assumes full-knowledge of the other transfer functions: this aspect involves that it is necessary to find an approximated solution through
an output error-based optimization. The block diagram (Fig.2.45(b)) and the error
Equation 2.6 help to understand that all the needed transfer functions depend on
both the microphones and the speakers positions. 2.4. Others Chapter 2. The Literature 66 Taking into account that the last ones are kept fixed and the error microphone is used only to test the attenuation performance (but it is not part of the ANC system),
the optimization procedure must carry on by evaluating the compensator for di'erent
pick-up microphone positions: the filter coe'cients θ define the degree of freedom
for the estimation of the compensator F (q, θ), which is subjected to min θ 1 N N '' t=1 e 2(t, θ) (2.8) In particular, signals u(t) and e(t) are measured for di'erent positions, with the feedforward compensation o' (e1(t) when F (q, θ) = 0) and, once again, with the
air-cooling system o' (e2(t)). The collected data can be used to solve the minimization problem and find the filter coe'cients (detailed computations can be found in [28], only the relevant steps
are reported here) e1(t) = H(q)u(t) (2.9) e2(t) = ''G(q) [u(t) + ν(t)] (2.10) e(t, θ) = e1(t) '' F (q, θ)es(t) '' F (q, θ)G(q)ν(t) (2.11) The performance, for a specific pick-up microphone position and considering an absence of noise on the input microphone, is evaluated taking into account VN (θ) := 1 N N '' t=1 ϵ 2(t, θ) (2.12) Hence, it can be derived that ' θ = min θ ''Rd VN (θ) (2.13) F (q, θ) = p ''1 '' k=0 θkq'' k (2.14) Operative setup highlights four possible pick-up microphone locations, as Figure 2.46 shows: (1) in proximity of the bulb, (2) in air 'ow, (3) in the central part
and (4) close to cooling fan. The previously described experiments are repeated
for each position, resulting in the following VN (' θ) values: (1) 1.4171 ' 10''4, (2) 1.7725 ' 10''4 (there is a lot of noise at the pick-up microphone), (3) 1.0421 ' 10''4 and (4) 1.7282 ' 10''4. By fixing the pick-up microphone on the third position and putting the error one 25 cm away from the inlet grid, measures of e1(t) and e2(t) are
gathered and used to estimate a low order IIR filter, which is then parameterized by
a 24th order FIR filter. 2.4. Others Chapter 2. The Literature 67 Figure 2.46: Pick-up microphone locations In their paper [25], Cordourier and Bustamante assert that the main source of continuous noise, generated by a personal computer, is normally the external cooling
fan; thus, a single-channel active noise control system with one reference signal (s(n)),
one control signal (q(n)) and one error signal (e(t) to minimize) is proposed. Figure 2.47: Controller block diagram, together with delay blocks relocated in series with transfer functions Figure 2.47 describes in detail the presented system: in particular, since a com- puter audio processing is implemented by bu'ering audio blocks on N samples, if
the assumption of periodic tonal disturbance is valid, this bu'ering delay can be
overcome. 2.4. Others Chapter 2. The Literature 68 Moreover, by considering that the internal delay due to signal conditioning (D) a'ects in the same way input and output stages, it follows that Ninput = D (2.15) Noutput = N + D (2.16) It implies to put two identical delay blocks of N +2D samples on both the feed-forward
and the feedback filters. Testing the system under analysis gives the results summarized in Figure 2.48(a): besides the overall 40 dB attenuation, it appears clear that the system can not elim-
inate the main tonal component at 1270 Hz. A further experiment (Fig.2.48(b)),
similar to the previous one but with the addition of a cellphone emitting a synthetic
tone at 700 Hz, shows that this last tonal component can be totally removed. (a) Laptop noise without control (upper left), with con-
trol (lower left) and noise reduction level (right) (b) Same experiment as above, except the adding of a 700
Hz sinusoid Figure 2.48: Results 2.4. Others Chapter 2. The Literature 69 Hence, the data can identify the inability of the system to attenuate a disturbance which is not strictly periodic: in conclusion, the paper asserts the uselessness of the
method for laptop cooling fan noise but, on the other side, its usefulness for periodic
case disturbances. A di'erent electronic device, a plasma display panel television (PDP-TV), is an- alyzed by [22] in order to achieve noise reduction and cooling performance improve-
ment. This kind of television employs cells of excited Xeon or Neon to create ultravi-
olet light based on a digital signal: this requires from 360 to 600 Watt power and so
fans are needed to maintain the temperature below the operating limit. The choice is
a 7 blades 120 mm diameter fan, which rotates at 1600 r.p.m. producing an overall
A-weighted Sound Pressure Level (OASPL) of 25 dB when unloaded. Without mod-
ifying the system, the noise attenuation can be accomplished through the increase of
the cooling performance, thereby allowing the r.p.m. reduction and so the noise, as
pointed out by [4]. (a) Original rear case (b) Modified rear case Figure 2.49: The increase of the vent holes number Hence, to reduce the 'ow-induced noise while maintaining the cooling perfor- mance, 'ow velocity measurements and visualizations with smoke are performed:
results reveal a strong concentration near corners also at low speed, provoking an
ine'cient operating point and noise because the 'ow does not intersect the fan. An equation which could describe the SPL of a fan system can be the following, with Kw as the specific noise level and Q as the system resistance (pressure rise in
the fan) SP L = Kw + 10 log Q + 20 log ''P (2.17) In order to reduce the system resistance, the authors propose: ' increasing the number of vent holes, by the modification of the TV rear case, obtaining a 1.7 dB reduction on the broadband noise (Fig.2.49); 2.4. Others Chapter 2. The Literature 70 ' installing a foam ring on the back of the case, to prevent the passing of second leakage 'ow between fan and rear case (Fig.2.50(a)); ' increasing the distance between fan and rear case through the rounding of the rear case (Fig.2.50(b)). (a) Foam ring duct extension (b) Rounded rear case Figure 2.50: Other modifications The previous ideas aim at reducing the broadband noise; for what concerns the discrete one (related to BPF), the authors discover that the removal of the strut,
attached to the display panel for avoiding its deformation due to heat, can help to
reduce the noise by 1 dB. If the whole set of proposed modifications is applied, a gain of 36% on the 'ow can be obtained: this performance surplus is exploitable to vary the fan r.p.pm. and
assess its e'ects on the noise (Fig.2.51). In particular, the mathematical connection
between r.p.m. and fan noise is described by SP L = SP Lref + 50 log ( RP M RP Mref ) (2.18) Final results show the possibility of decreasing the r.p.m. from 930 to 830: this means
to achieve a 6.3 dB noise reduction with even a 10% increased 'ow rate of the fan,
thereby improving the cooling performance of the system. 2.4. Others Chapter 2. The Literature 71 Figure 2.51: Noise spectrum comparison A very detailed and complete analysis on a 7 blades 80 mm diameter fan noise is performed by [14]: furthermore, the system under study is equipped with four
independent control sources, placed round the fan as visible in Figure 2.52 with a
fixed center-to-center distance of 60 mm (the loudspeakers are inserted into PVC
caps to prevent that a possible radiation inside the enclosure invalidates the reference
signal). Figure 2.52: Positions of the control sources 2.4. Others Chapter 2. The Literature 72 The authors select to maintain the fan at a fixed rotational speed, to emit the SPL shown in Figure 2.53(a) (measures are taken 1.3 meter away from the sources). The picture emphasizes the presence of BPF and well known harmonics, which are the elements to attenuate: because of this, a non-acoustic reference sensor, an
inexpensive infrared emitter-detector pair, is used only to track the passage frequency
of the blades. To correctly match the real harmonics of the system, the reference
signal is band-pass filtered: in addition, a further amplification step is necessary for
a proper analog-to-digital conversion (Fig.2.53(b)). (a) On-axis (b) Infrared post-processed signal Figure 2.53: Frequency spectrum The only sensor not yet analyzed is the error microphone: as stated for the refer- ence one, this kind of sensor could be a simple inexpensive electret-type microphone
placed 75-90 mm away from the source, depending on the active speaker configura-
tion selection (two high-definition error microphones are used during experiments).
Talking of configuration, the authors test the following ones: only a speaker, two
adjacent, two opposite, three and all four. The control algorithm is a standard FxLMS implemented on a DSP board and the performance is measured through 13 microphones, attached on a semi-circular boom
at equal angle increments (Fig.2.54). For each configuration, several trials are carried
out to measure frequency attenuation and fan directivity: Table 2.3 presents the
results, in terms of mean-square pressure reduction and standard deviation, averaged
over the eight best trials. 2.4. Others Chapter 2. The Literature 73 Figure 2.54: Semicircular measurement boom Table 2.3: Frequency spectrum 2.4. Others Chapter 2. The Literature 74 At first, fan''s radiation becomes less smooth and more directional as the frequency increases. For what concerns the noise SPL attenuation, it can be concluded that: ' the greatest BPF attenuation is achieved by the two adjacent channels con- figuration: in theory, the greatest should be the one with the whole set of
loudspeakers, but the poor frequency response at that frequency limits the
co-operation; ' the second harmonic, on the other side, confirms theoretical analysis which suggests the 4x4 configuration; it can be noticed that the 3x3 performs very
closely to the 4x4: this implies that the adding of the fourth source may benefit
from an increase of the source symmetry; ' same trend for the third and fourth harmonic; ' it must be observed that the adjacent configuration performs worse than the opposite one (i.e. loudspeaker coupling) for the third harmonic but better for
the fourth: this suggests that the number and locations of error microphones
have high in'uence on the attenuation performance; ' the use of inexpensive sensors for the reference (and error) signal does not compromise the final overall attenuation. The just analyzed fan is a standard cooling fan for desktop computer: [7] compares the performance of the previous ANC system with thta of a more compact one, which
employs a 60 mm diameter fan running at higher speed with loudspeaker of a proper
dimension. A theoretical discussion, whose subject regards two monopole sources
in near-field proximity with one another (details can be found in [7]), suggests the
definition of an optimal control source strength in order to obtain a minimum radiated
power WMIN WMIN = WMONO [ 1 '' ( sin kd kd ) 2 ] (2.19) with ' WMONO the power radiated by a single monopole source; ' k the acoustic wave number; ' d the separation distance between the sources (m). A quick analysis of the formula highlights that if kd ' ' the attenuation is null and also small values of kd lead to small attenuation: this could explain why the
addition of a fourth source gains little in sound attenuation with respect to the case
with 3. In [7] the primary focus is on the analysis of the four sources case, but the
three sources case is implemented too. 2.4. Others Chapter 2. The Literature 75 Figure 2.55: Error sensor location (round markers) As appears in [14], the positions of the error microphones have great impact on the attenuation performance. The placement could be optimized by finding the region
of greatest pressure attenuation when sound power radiation is minimized: in detail,
these are the positions far enough from the source to avoid low SNR and common to
the null contours for all frequencies of interest (Fig.2.55). Control sources are equally spaced around the fan within a 80 '80 mm2 area: the experimental gear is the same of [14], but 4 error microphones are used. Considering
a BPF of 600 Hz with the second harmonic at 1200 Hz and the third at 1800 Hz,
the SPR (Sound Power Reduction) achieved by the system is 14.5 dB, 16.6 dB and
9 dB respectively. To improve the compactness of the system the case with 3 symmetrically spaced control sources is analyzed. Besides a practical implementation problem connected to
the square geometry of commercial fans, the system is able to achieve a SPR of 14.8
dB, 15.7 dB and 8.5 dB for the three harmonics respectively: this little performance
reduction is not enough to reject the compacting procedure of the system. Taking into account both cases (four and three fans arrangements), an issue arises, that is the attenuation increase of the second harmonic with respect to the
BPF. Theoretically, an increase in frequency leads to an increase of kd, which should
decrease the performed attenuation. Further analysis reveal that the attenuation of
the BPF is near the broadband noise, suggesting that the latter limits the theoretically
achievable attenuation. 2.4. Others Chapter 2. The Literature 76 In conclusion, the proposed system shows good attenuation performance and so the substitution of the 80 mm case with the 60 mm one is possible and cheaper.
Moreover, the use of the 3 loudspeakers instead of 4 is feasible without lowering too
much the performance. 2.5 Summary and key ideas At the end of this literature digression, it is possible to summarize the key ideas proposed by the various authors for reducing the noise emitted by several devices
cooling fans: ' new algorithms can be developed to control the fans rotational speed in a smarter way: by installing temperature sensors near modules to cool, detailed
and precise information can be fed to the algorithm which can vary the fans
rotational speed with respect to the cooling requirement; ' advanced tools, for the study of the physical and acoustic parameter of a fan, can help the designer in the creation of items with higher performance and
lower cost; ' modifications on the fan itself or on the guard can reduce the resistance on the cooling 'ow, allowing a corresponding reduction of the fan speed because less
energy needs to be spent to dissipate the heat; ' the co-location of the noise and anti-noise sources permits the elimination of the noisy components when they are generated. Two examples can be recalled,
regarding the installation of resonators around the fan and the connection of
the fan structure to a shaker; ' if no mechanical modifications are allowed on the noise sources, standard ANC methods can help in noise reduction: an example is the duct driven approach,
which installs a duct to give to a standard ANC system the possibility of better
operating. It is also possible to place more loudspeakers around the fan, study-
ing di'erent positions and attenuation methods, for generating the anti-noise
wave and canceling the disturbance in a particular point in space. 2.5. Summary and key ideas Chapter 3 The proposed method The device under consideration is illustrated again in Figure 3.1: the project''s specifications state clearly that no components can be removed or modified. In the
picture, the fan grid was removed only to show the fans position and put in evidence
that the access to this area is very di'cult: thus, even if alterations were possible,
they would be very di'cult to realize. Figure 3.1: DVB-T module 78 Chapter 3. The proposed method 79 Having this limitation in mind, it appears clear that the whole set of fan/case modification hints, coming from the literature (see section 2.2), is not feasible in this
application. Further, there is not the possibility of interacting with the algorithm
which controls the fans speed, because it is tailored to application and optimized to
meet the cooling requirement needed by all electronic components. In the introduc-
tion, the choice made for the selection of the noise control algorithm has already been
explained: because of this choice, none of the literature proposals can be taken into
account. Hence the development of something di'erent is needed: to do that, it is impor- tant to understand more deeply what happens when two plane waves superimpose.
Section 1.2 emphasizes the principle, the superposition one, which permits active
noise control systems to operate and, furthermore, it is explained how adding a wave
to another one can produce a cancellation of both of them. If the waves are out-of-phase and have equal amplitude, during the superposition the resulting pressure is null: on the contrary, due to the energy conservation law,
their energies are summed together. To better understand the previous statement,
let''s consider the intensity of a plane wave, which can be computed as [8] I = p2 RM S
ρ0c (3.1) where I represents the sound intensity (measured in [W atts/m2]) or, rather, the
mean energy that passes through a unit of area, normal to the propagation direction. A deeper analysis highlights the meaning of the other variables: ρ is the 'uid density while c the sound speed. If the sound particles propagation is equivalent to
an adiabatic transformation governed by the equation (P /p0) = (ρ/ρ0)γ, the sound
speed is usually written as c = '' γRT0 (3.2) and so I = p2 RM S ρ0 '' γRT0 (3.3) where ' R is the molar gas constant; ' T0 is the static temperature (K); ' γ is the specific heat ratio. Since both waves propagate in the same 'uid at the same temperature, their intensities are proportional only to their pressure: however, their pressures are equal
because their amplitudes are the same. Finally, it can be stated that the two waves
have the same intensity over the entire area of attenuation. Chapter 3. The proposed method 80 Since the power of a plane wave is W = IS = Sp2 rms ρ0c (3.4) and the two waves not only have the same intensity but also propagate across the
same surface, they have the same power. All the information leads to the following conclusion, which represents an inter- esting hint to look at the problem: when the noise and anti-noise wave superimpose,
their energies are summed together; at the operating point, the ANC system is able
to lock these waves in amplitude and out-of-phase, achieving opposite pressures over
the area and, more important, the same power. Data could be exploited to solve the problem of the error microphone positioning and to obtain the best possible attenuation over a larger area. Hence, this master thesis proposes its own solution, which consists in obtaining two energy models (of noise and anti-noise sources), which can be matched them together to find the optimal number and positions of the latter for achieving the optimal attenuation over the largest possible area Figure 3.2: Power profiles comparison Before proceeding in the dissertation, let''s focus on Figure 3.2: the green area represents the restricted space region in which the placement of sensors and actuators
is allowed; in addition, the equal-energy curve of the noise (blue) and anti-noise (red)
signals are visible. The gray box indicates the fans location, while the black lines
define the device perimeter. In section 1.2 the problem of the placement of the
three major actors was discussed: now reference microphone''s, error microphone''s
and loudspeaker''s positions must be defined. Chapter 3. The proposed method 81 For what concerns the reference microphone, its positioning needs to allow the acquisition of a signal strictly related to the one to attenuate. So, a dedicated
search has to be accomplished in order to find the position of the sensor inside the
permitted area: more details could be supplied once the characteristics of the fans
noise are known. To characterize the energy profile of the noise sources (blue and red lines in Figure 3.2), a set of points inside the desired area of attenuation is chosen and a quantity,
strictly connected to the physical power, is measured for each of them: this quantity
can be defined as the global audio power of the signal si(t) through the equation Wi = 1 NSAMP LES NSAMP LES '' t=0 |si(t)|2 (3.5) Once the set of data is acquired, it is used to solve a mathematical system, which describes the measured Wi as the weighted sum of the powers generated by a finite
number of ideal sources, located in the proximity of the device. The model has not
the claim of physically characterizing the acoustic situation, but it should only define
in a linear way the power at di'erent points in space: since this variable decreases
proportionally to the square of the distance, it is described as Wi = M '' j=1 kj d2 ij for i = 1, · · · N (3.6) In particular, Wi is the measured quantity, d2 ij is the square of the euclidean dis- tance between the point i and the ideal source j, whose strength is defined by kj.
Considering N points and M sources, the model can be written in its matrix form W = AK = 
    a11 a12 · · · a1M a21 a22 · · · a2M .. . .. . . .. .. . aN1 aN2 · · · aNM 
    
    k1
k2 .. . kM 
    (3.7) with: ' W = [W1, . . . , WN ] T ' K = [k1, . . . , kM ] T ' aij = 1 d2 ij Given the points positions as well as the number and locations of the ideal sources, the best strength vector is found thanks to the LMS solving equation ' K = (A T A)''1AT W (3.8) Chapter 3. The proposed method 82 It appears clear that the last two input values (sources number and positions) are problem variables: since the model is supposed to be linear, one of them needs to
be transform into usable data. Hence, this can be done by means of a procedure
which iteratively defines a number of sources and their initial positions, to further
adjust their location by following the minimization of the cost function, which is
the relative residual percentage. So, for a certain combination of ideal sources with
defined positions, the cost function (i.e. residue) is the sum of the squared normalized
estimation error: R = N '' n=0 [ ' Wi '' Wi Wi ] 2 with ' Wi = [ai1, . . . , aiM ] ' K (3.9) Once the sources'' number and strengths (kj) are identified, a similar method is applied to the attenuation speakers and a model is computed. At this point, the two models allow the description of the profiles of fans and loudspeakers: the next steps are dedicated to define both their number and their
locations inside the constrained area and to adjust the strengths in order to reproduce
the first power field. Considering what has already been described, it is established
that the algorithm is able to attenuate the noise where the two profiles are the same,
once a steady state has taken place. Now, let''s suppose that the energy profiles are equal to those shown in Figure 3.3: of course, since the number of attenuation sources is limited and the model has low
complexity, it is not possible to reproduce perfectly the power profile. Nonetheless,
the loudspeakers positions can be chosen to be the best solution in order to reproduce
the fans profile. Chapter 3. The proposed method 83 Figure 3.3: Propagation of the attenuation point The black circles in Figure 3.3 represent the points where the energy profiles are identical: it is assured that, there, the algorithm can achieve perfect attenuation.
Furthermore, it can be stated that the error microphone could be placed in any of
these points, because the attenuation condition (equal amplitude and reverse phase),
imposed at that location, is equally transmitted to the other points (meanwhile, no
important ambient changes have to take place). Hence, if one of these points is inside
the allowed area, then the error microphone location is found: the more similar the
two power profiles are, the better the noise attenuation is in all points of the extended
area. The next chapter will be devoted to the exhaustive and clear explanation on how the energy profiles of fans and loudspeakers are obtained. Chapter 4 Measurements and Modeling The ending section of the previous chapter has underlined the need of a part which should describe both the experimental equipment for measurements and the
methodology, employed to compute the mathematical models from the acquired data.
In the following pages, the experimental setup is illustrated in order to list the complete
audio acquisition chain; after that, the chapter will focus on the specific description
of the path undertaken to model the fans and loudspeaker powers. Lastly, it will end
with the models matching, necessary to find the optimal number and positions of
secondary sources and extend the quiet zone. 85 Chapter 4. Measurements and Modeling 86 4.1 Experiment setup The data collection was entirely carried out at the Sound and Music Computing Laboratory (SMC Lab) of Politecnico di Milano - Polo Territoriale di Como, which
supplied the complete set of electro-acoustic devices. In particular, the laboratory
is equipped with a quasi-anechoic room (whose nickname is Minotauro), which is
completely upholstered with sound-absorbing panels. The room has poor absorption
for very low frequencies, but the performance increases above the 400 Hz and the
behavior becomes very similar to the one of a real anechoic chamber. This type
of environment permits to isolate the measurement gear from external noises, by
allowing a clean acquisition of the desired signals. The sound is sensed by using the professional condenser acquisition microphone beyerdynamic)))) MM1, shown in Figure 4.1(a). It is a very good device as both
the polar pattern (Fig.4.1(b)) and the frequency response curve confirm (Fig.4.2):
it is an omni-directional microphone with a quasi-perfect 'at frequency response.
These characteristics assure a perfect response to the input signal and the absence
of distortions: in addition, if a smart placement is adopted (inside the 300' '' 60' range), the attenuation produced on the sensed pressure is almost null. (a) MM1 microphone (b) MM1 polar pattern Figure 4.1: Microphone characteristics Figure 4.2: MM1 frequency response curve 4.1. Experiment setup Chapter 4. Measurements and Modeling 87 The signal coming from microphone is pre-amplified by a rack of Focusrite OctoPre LE', which allows the tune of the input gain: an important aspect to consider is that
this gain was kept constant for each acquisition session. So, it is possible to compare
the amplitude of the signals: as it has already been explained, the amplitude is the
fundamental variable which permits the computation of the chosen power indicator. At the end, the signal is sampled and digitally converted through a Lynix Aurora 16 interface: the sample frequency is Fs = 44100 Hz and the conversion is set to
a 16 bits range. This data stream is recorded and elaborated by the mathematical
software Matlab®. For what concerns the geometric positions of the sensors, all the measures refer to a point in the room which was designated as the origin: the bottom left corner
of the wall, since it is the nearest to the device. The origin is represented in Figure
4.3, together with the placement of the device inside the room. The geometric
dimensions and the distances between two points are measured through the use of
a laser rangefinder BOSCH GLM 80: the instrument is able to measure distances
greater than 5 cm, with a precision of one millimeter. By considering this reference system, the triple of coordinates (xp, yp, zp) of a generic measured point in space refers to: ' xp: distance from the upper part of the microphone body to the wall on the left of the device; ' yp: distance between the top of the microphone and the 'oor; ' zp: the same of xp, but the wall is the one behind the device. 4.1. Experiment setup Chapter 4. Measurements and Modeling 88 (a) Upper view (b) Front view Figure 4.3: Device dimensions (mm) 4.1. Experiment setup Chapter 4. Measurements and Modeling 89 Figure 4.4 presents a detailed view of the noise sources, that is, the two fans; they have a diameter of 8 cm and their centers are 10 cm far away from one another.
Even if the fans are supposed to rotate at the same speed in phase accordance,
unfortunately this is not true: indeed, by listening to the produced global sound, it
is easy to recognize a variable phase shift. Since the model does not analyze the
problem from the dynamic system perspective, but it takes into account the power
as an averaged computation, the shift is a no-issue for this particular case study. Figure 4.4: Fans After this initial description the next section will present the method employed for modeling the fans noise. 4.1. Experiment setup Chapter 4. Measurements and Modeling 90 4.2 DVB-T device power model Figure 4.5: Example of the measurement setup The data acquisition setup for the fans noise is shown in Figure 4.5 and a zoomed view is illustrated in Figure 4.6. The high rotational speed of the fans produces vibrations which are propagated to the support, in this case a table. To avoid the generation of undesired additional
noise, which can corrupt the measures, the device and the table are divided by an
acoustic absorbing layer (made of the same material of the panels which cover the
walls). Figure 4.6: Example of the measurement setup: zoomed detail 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 91 The model proposed in Chapter 3 is here recalled: Figure 4.7: Schematic of the microphones position Wi = M '' j=1 kj d2 ij for i = 1, · · · , N (4.1) Now let''s focus on on a particular case with only two
sources, s1 and s2, which have equal strength and distances
from a generic point P equal to ds 1P = 2ds2P . The model tells that the power contribution of the first source is only a quarter of the second one, because of the
presence of the square operator on the distance variable:
this means that the ability of a source to in'uence a point
varies with the inverse of the squared distance between
them. The design of the measurement grid must take into account this information: the space sampling granularity
needs to increase as the distance from the noise source
increases. From an operative point of view, a microphones array was assembled in order to both respect the previous sug-
gestion and design a simple acquisition procedure. A particular metal structure (see Fig.4.6 for a global view and Fig.4.7 for the schematic) was used, since it al-
lowed to place 13 microphones and maintain a regularity
in the measurement pattern. Two additional microphones,
namely microphone 1 and 15, were added to the others by
positioning two booms at the sides of the first mentioned
microphones array. Hence, the final measurement array is
composed by 15 microphones which are numbered from 1
(left) to 15 (right): Table 4.1 lists the cumulative distances
(with respect to the x axis) between the microphone ID-
1 and the one identified by the first column. During the
measures, it was tried to maintain the central microphone
(ID-8) aligned with the x-coordinate of the center between
fans. 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 92 Microphone ID Distance (cm) 2 15 3 25 4 30 5 35 6 40 7 42.5 8 45 9 47.5 10 50 11 55 12 60 13 65 14 75 15 90 Table 4.1: Microphones array: distances between microphone one and the others Furthermore, the granularity increase has to be valid also for axis y and z: let''s consider the center height of the fans (y0 = 85 cm) and the front depth of the grid
(z0 = 80.7 cm) as reference points. The dataset is composed by three groups of measures: SET-AC, SET-DOWN and SET-UP. For what concerns the first set (SET-AC), the array was moved only along z- axis by maintaining the height of the microphones aligned with y0: this implies eight
di'erent positioning for a total of 120 points; Table 4.2 summarizes the steps along
the z-axis (all values are referred to z0 and expressed in meters). Axis Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 z +0.05 +0.1 +0.2 +0.3 +0.45 +0.6 +0.8 +1 Table 4.2: SET-AC: sampling distances along z-axis (m) 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 93 SET-DOWN had the same pattern of the first, but the array was also lowered along y-axis: thus, the points positions are referred to y0 and z0 (Tab.4.3). It should
be noticed that it was not possible to lower the array beyond a certain limit, because
of the presence of microphones'' body, cables and the boom supporting the array. Axis Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 y -0.025 -0.025 -0.075 -0.075 -0.125 -0.175 -0.275 -0.525 z 0.05 0.1 0.2 0.3 0.45 0.6 0.8 1 Table 4.3: SET-DOWN: sampling distances along y and z-axis (m) Lastly, SET-UP operated similarly to the previous one, with the di'erence that the movement was along the positive direction of the y-axis (Tab.4.4): this third set
adds other 120 points, for a total amount of 360. Axis Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 y +0.05 +0.05 +0.15 +0.25 +0.30 +0.40 +0.50 +0.70 z 0.05 0.1 0.2 0.3 0.45 0.6 0.8 1 Table 4.4: SET-UP: sampling distances along y and z-axis (m) Moreover, eight di'erent positioning were used for every described SET and the real coordinates of the microphones were measured for each of the 24 moves. The
geometrical points information is collected into a matrix P360'3 whose rows define
the coordinates of each point in space: in particular, P(i, 1) is the x-coordinate of
point i, while P(i, 2) and P(i, 3) are the one of y- and z-axis respectively. A view of the space arrangement of the points with respect to the device is presented: in order to clearly understand the position of points in space, the following
graphs respect the room proportions. Figure 4.8 shows the 3D points disposition,
while Figure 4.9 presents a side view and an upper one respectively: points are
marked with color red, the device is indicated in green and the fan grid in black. Because of the need of statistically characterizing the measures, seven acquisition cycles were performed for each move: the device was turned on, the recording of 60
seconds activated and, when it was finished, the device was turned o' to allow the
re-positioning of the array. 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 94 Figure 4.8: 3D points disposition 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 95 (a) Side view (b) Upper view Figure 4.9: Points dispositions 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 96 4.2.1 Data preprocessing A relevant step to manage is the understanding of the data set reliability with respect to the chosen model: hence it is important to filter out data which could lead
to incorrect estimations. It has already been introduced that, for each point, seven acquisition cycles were conducted: thus, it''s possible to compute a vector composed of seven di'erent power
variables Wil = 1 60 '' F s 60 ''F s '' t=0 |sil(t)|2 (4.2) where i indicates the point and l the cycle: the vector is expressed by Wi = [Wi1 Wi2 Wi3 Wi4 Wi5 Wi6 Wi7] (4.3) Because of the high quality of the employed audio chain, the values of Wil were
very similar except for some rare cases, where the measures were clearly corrupted by
accidental external factors: the median operator was then applied on each vector to
achieve a reliable result, which was kept as the final power value. The obtained matrix W consists of 360 columns, which define the power variable for each point taken into consideration. By recalling the adopted model Wi = M '' j=1 kj d2 ij for i = 1, · · · N (4.4) it is easy to deduct that the data set would be good only if it re'ects the supposed
power decrease. From this perspective, an analysis was performed to verify the
reliability of the data set to the considered decay. This test aimed to find the points which can corrupt the model estimations: even though there are several ways of doing this, it was decided to operate graphically. The 3D points distribution was plotted and the power value corresponding to each point was assigned. Then, an algorithm (Alg.1) was created to connect points
whose values were defined, in a specific range, as a percentage of a reference value:
this operation had the goal of showing if there were points with similar power values
but located very far away from one another; this aspect surely would create an error
during the estimation. It is obvious that the higher the percentage, the larger the
set of connected points: this suggested keeping it lower and the value of 20% was
selected. 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 97 Algorithm 1 Points connection
Require: Data sorted for ascending values Define perc, the percentage for range acceptance
while Data vector not empty do ref ' data in first position range ' [(1 - perc) '' ref (1+ perc) '' ref] j ' 0 for i = 2 to end do if Data(i) inside range then CN(j) ' Data(i) j ' j + 1 end if end for
min ' minCN newref ' min newrange ' [(1 - perc) '' newref (1+ perc) '' newref] for i = find(Data = newref) to end do if Data(i) inside newrange then CN(j) ' Data(i) j ' j + 1 end if end for
Connect ref with each element of CN through a line
Delete all point be connected end while The result of this operation is shown in Figure 4.10 and 4.11: it is not easy to note, but an in-depth analysis reveals the presence of two classes of outer points: ' the first class is composed of elements located both at the limit of the mea- surement space and in the nearest device area. The behavior of the noise at
these points is not comparable, because it could be too strong or too weak for
correctly fitting the model; ' the second class comprises points distributed in the measurement space: there, the error is caused by measures corruptions due to microphone-to-microphone
interference or external factors (not shielded by the room). 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 98 Figure 4.10: Points connections: global view 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 99 Figure 4.11: Points connections: upper view In order to eliminate these points, the following procedure was designed: ' the distances values were computed for each point, with respect to the center between fans; ' the estimated power ' Wi was calculated; ' if the relative percentage error of the di'erence between the measured power and the estimated one was above 40%, the point was eliminated (the percentage
was chosen after several tests, not reported here). At the end of this procedure, the total amount of points was reduced from 360 to 293, which means that the eliminated points were 18.6% of the total: Figure 4.12
shows in red the deleted points. 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 100 Figure 4.12: Deleted points after the processing 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 101 Frequency analysis Before facing the modeling part, a simple frequency analysis was conducted for each acquisition cycle of every point, in order to characterize the
spectrum of the signal. The results confirm a frequency uniformity of the produced
field, because the same fundamental frequency was extracted. In particular, since
all the computations led to the same conclusion, only one picture describing the
frequencies distribution is here presented. Figure 4.13 shows the harmonic composition of the signal: the main components are the fundamental frequency at 1137 Hz and the first harmonic. Of course, the value on the y-axis changes depending on the closeness between the microphone and the source, but the relation between the harmonics is similar; the
presence of a little quantity of background noise is due to the air produced by the
fans, which can be removed only by switching o' the device. Figure 4.13: Fans noise: frequency analysis 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 102 4.2.2 Power model The model has already been introduced and explained in Chapter 3: its goal is to find out the best number, positions and strengths of ideal sources which can describe
the energy front created by the fans. Given the points positions as well as the number
and positions of the ideal sources, the best strength vector is found thanks to the
LMS solving equation ' K = (A T A)''1AT W (4.5) and the cost function for that particular combination is R = N '' n=0 [ ' Wi '' Wi Wi ] 2 with ' Wi = [ai1, . . . , aiM ] ' K (4.6) It''s clear that an iterative procedure is needed, because the decision factor can be computed only by defining the number and positions of sources. This means that
an heuristic procedure, starting from an initial sources arrangement, has to calculate
the cost function and then move the sources in order to minimize it. From an implementation point of view, some constraints were dictated: ' the y-position of the sources is fixed and equal to the height of the fan axis, which is y0 = 0.851 m; ' sources can freely be moved inside a predefined range of values for what con- cerns x- and z-axis (the discussion of this topic is intentionally postponed after
the algorithm description); ' sources can not overlap along x-axis, which means that, by numbering the sources from left to right, the number must remain ordered in an ascending
way. Before describing the heuristic algorithm, it must be pointed out that it has to be validated: therefore, a brute force algorithm was implemented to supply not only an
initial knowledge of the sources positions, but also a validation data set. 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 103 4.2.2.1 Brute force algorithm The brute force algorithm (Alg.2) defines a set of possible values (Xpos) of the x-coordinate: these have to belong to a predefined range and be separated from each
other by a step of δmin = 0.001 m; the same happens for the z-coordinate (Zpos)
too. Once Xpos and Zpos are defined, the matrices Xcomb and Zcomb are computed: they define the whole set of possible combinations between the corresponding vectors
elements; they have a number of rows equal to M (number of ideal sources) and a
number of columns equal to Lx = l2 x and Lz = l 2 z , that is, the square of the length of the respective origin vectors . Hence, a set of sources positions can be created by
taking the same column of both matrices (remember that the y-coordinate is fixed).
Of course, since the sources can not overlap along the x-axis, the matrix Xcomb has
to be filtered: the column which contains values sorted not in an ascending way must
be eliminated. After that, the algorithm can proceed as follows: Algorithm 2 Brute force algorithm: Core section
Require: Xcomb, Zcomb, M, W, N, P, Lx, Lz for i = 1 to Lx do Sx ' Xcomb(i, all) for j = 1 to Lz do Sz ' Zcomb(j, all) Rij ' STD(Sx, Sz, M, W, P) end for end for
Find indexes ib and jb of Rmin ' min(Rij) return Rmin The definition of ''STD' block is presented in Algorithm 3, which computes the value of the cost function R, given the sources positions. Algorithm 3 STD
Require: Sx, Sz, M, W, P for i = 1 to M do Compute the squared euclidean distances end for
Compute A ' K ' (AT A)''1AT W ' W ' A ' K Err ' (W '' ' W)/W R ' ErrT Err return R 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 104 Various simulations were conducted to find the correct initial intervals of x- and z-axis: to do that, the results of the brute force algorithm with di'erent input ranges
were evaluated. Results in Table 4.5 (see subsection 4.2.3) were obtained considering
the following values (m): 1.267 '' X '' 2.892 (4.7) 0.207 '' Z '' 1.407 The definition of Lx and Lz as ''squared length' clearly explains why the com- plexity of this type of algorithm is so high: in fact, the latter can be thought as
proportional to Lx ' Lz, because of the presence of the two nested for (see Alg.2). By considering the initial ranges and the accuracy of 1 mm, it is evident that the
number of operations to perform is huge: this allows to use this type of algorithm
only for a number of sources M ' 3. 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 105 4.2.2.2 Heuristic algorithm The heuristic algorithm reduces the computational burden of the previous brute force one: it starts from a defined sub-optimal solution and it iteratively finds new
sources positions by following the minimization of a cost function, which is, by the
way, the R already described. Concerning this case of study, the heuristic algorithm
is composed of di'erent functions which are illustrated in the following. At first, the ''Main' (Alg.4) takes the same parameters of the brute force algo- rithm: number of sources, power values, points coordinates and the range of x- and
z-axis. In order to move a sources set, it is necessary to define a starting position which also allows to compute the reference cost function value (R0). This starting position,
for each source, was randomly selected from the initial set of possible positions, built
up the Xpos and Zpos introduced in the last subsection (remember that y0 is fixed).
Let''s define the intervals limits as LX = [Xmax Xmin] (4.8) LZ = [Zmax Zmin] (4.9) Algorithm 4 Heuristic algorithm: Main
Require: Xpos, Zpos, M, W, N, P, maxITER, LX, LZ Xstart ' Take randomly M values from Xpos and sort them Zstart ' Take randomly M values from Zpos Rend ' 106, Xend ' Xstart, Zend ' Zstart while (IMPR > 0) and (iter < maxIter) do iter = iter + 1
for j = 1 to M do Xnew ' HX(Xstart, Zstart,M, W, N, P, j, LX) Znew ' HZ(Xnew, Zstart,M, W, N, P, j, LZ) end for
Compute Rnew ' STD(Xnew, Znew, M, W, P) Compute IMPR ' (R0 '' Rnew)/R0 if IMPR > 0 then Rend ' Rnew Xend ' Xnew Zend ' Znew end if end while
Save Rend, Xend, Zend By considering the random selection of the initial positions, the ''Main' can not be executed only once: it was chosen to run 200 cycles and save, for each of them, 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 106 the cost function value and the positions: after that, the minimum R was searched
and the resulting strengths and positions of sources were saved in an excel file; this
procedure was repeated 10 times for every class of sources (each value of M). The variable maxITER describes, as input parameter of the ''Main' (Alg.4), the maximum number of iterations of the while cycle: this limitation is needed to avoid
the waste of time resulting from iterations which lead to insignificant improvements
of the cost function. Since the average number of iterations was around 40, maxITER
was set equal to 50. Functions HX and HZ take the starting sources positions (defined as generic vectors X and Z) as input and iteratively move them one at a time, by evaluating if
the movement brings about an improvement or not. In particular, they first decide if
the source has to be moved in a positive or negative direction and then they call the
core functions of the method, which are recursive algorithms: the initial movement
is defined by the step δmin = 0.001 m. Algorithm 5 Heuristic algorithm: HX
Require: X, Z, M, W, N, P, j, LX Compute RSTART ' STD(X, Z, W, P) {Compute the new position of the jth- source under consideration}
XDX ' X(j) + δmin RDX ' STD(XDX, Z, M, W, P) XSX ' X(j) '' δmin RSX ' STD(XSX, Z, M, W, P) if RDX < RSX and RDX < RSTART then XNEW ' LMSHX(X, Z, M, W, N, P, j, LX, RSTART , δmin) else if RSX < RDX and RSX < RSTART then XNEW ' LMSHX(X, Z, M, W, N, P, j, LX, RSTART , δmin) else XNEW ' X end if
return
XNEW Since HX and HZ are identical except for the call of LMSHZ instead of LMSHX and the computation of the new positions on Z instead of X, only the former is
presented (Alg.5). LMSHX and LMSHZ represent the core functions of the entire method and they are illustrated in Algorithm 6 and Algorithm 7, respectively. In both algorithms,
the label ''SELECTION' refers to the code shown in Algorithm 8, only for writing
purposes. 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 107 Algorithm 6 Heuristic algorithm: LMSHX
Require: X, Z, M, W, N, P, j, LX, RSTART , δ posX ' X, Xnew ' posX(j) + δmin if Xnew inside LX then if M = 1 then res ' STD(Xnew, Z, M, W, P) if res < RSTART then RST ART ' res, posX(j) ' Xnew N ewX ' LMSHX(posX, Z, M, W, N, P, j, LX, RSTART , 2δ) else if |δ| = 0.001 then
N ewX ' X else N ewX ' LMSHX(X, Z, M, W, N, P, j, LX, RSTART , δ/2) end if end if
{First source on the left} else if j = 1 then if Xnew < X(2) then SELECTION else N ewX ' X end if
{Last source on right} else if j = M then if Xnew > posX(M-1) then SELECTION else N ewX ' X end if
{Generic source} else if N ewX > posX(M-1) and NewX < posX(M+1) then SELECTION else N ewX ' X end if else N ewX ' X end if
return
N ewX 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 108 Algorithm 7 Heuristic algorithm: LMSHZ Require: X, Z, M, W, N, P, j, LZ, RSTART , δ) posZ ' Z, Znew ' posZ(j) + δmin if Znew inside LZ then SELECTION else N ewZ ' Z end if Algorithm 8 Heuristic algorithm: SELECTION block posX(j) ' Xnew res ' STD(posX, Z, M, W, P) if res < RSTART then RST ART ' res N ewX ' LMSHX(posX, Z, M, W, N, P, j, LX, RSTART , 2δ) else if |δ| = 0.001 then N ewX ' X else N ewX ' LMSHX(X, Z, M, W, N, P, j, LX, RSTART , δ/2) end if end if As it can be clearly understood by the algorithms description, LMSHX and LMSHZ simply verify the compliance of the new position and recursively move the source with
growing step, until the cost function is minimized. If a move leads to the increase of
R, it is eliminated: the previous position is refreshed and a shorter step is adopted,
until the desired accuracy is reached. 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 109 4.2.3 Results and Model selection Table 4.5 reports the results produced by the brute force algorithm: #Sources R k(10''4) x(m) z(m) M=1 12.45 2.55 2.103 0.801 M=2 11.30 3.08 2.126 0.796 -0.486 2.302 0.753 M=3 10.77 13.9 2.116 0.751 -16.8 2.127 0.696 6.32 2.162 0.52 Table 4.5: Brute force approach: results In subsection 4.2.1 the data were filtered taking as reference point P0 = (Px 0 , Py0 , Pz0 ), the center between fans projected on their grid; this point is taken again as reference
and its coordinates are Px 0 = 2.092 m (4.10) Py 0 = 0.851 m Pz 0 = 0.807 m If the results are analyzed considering both the point P0 and Figure 4.4, it comes out that: ' M = 1: the source is positioned on the right of the center and slightly inside the case. This re'ects the fact that the two fans are not equal and so the
algorithm moves the power generation next to the biggest one, which is on the
right. Moreover, since the physical position of the fans is inside the device, the
z-coordinate of the ideal source re'ects this aspect: hence, the model has also
a correct physical meaning; ' M = 2: the above expressed concept is still valid: in fact both sources are placed on the right of P0, strictly inside the case; ' M = 3: the situation is comparable to the previous ones, with a better sources compaction. Despite these results are used only to validate the heuristic, they give a clear solving pattern: depending on the selected number of ideal sources, the model tries to
describe a global power distribution with one source and then it uses the remaining to
better define the di'erence between the two fans and shift the major power generation
over the source on the right. 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 110 The reader has surely noted the presence of negative values of strength (k): in relation to the specific case study this is not an error since the model has not the
claim to physically describe the situation, but it simply defines the power in a point. It must be pointed out that the heuristic algorithm results were preprocessed before comparing them with the previously described ones: in particular, since outliers
were present (with an estimated cost function ten times greater than the others,
probably due to a bad initial positions set), the adopted procedure for each class was: ' application of the median operator to the residues; ' elimination of the solutions whose residues were greater than the 120% of the median. Let''s now proceed with the comparison between the results of the brute force approach and the heuristic one concerning the first three classes, in order to evaluate
if the latter is reliable and if its results can be taken as the final ones. ' Class 1: both the algorithms produce the same values for all variables under consideration (strengths, positions and residues). This suggests that there is
only one global minimum of the cost function (Tab.4.6); #Sources R k(10''4) x(m) z(m) M=1 12.45 2.55 2.103 0.801 Table 4.6: Results for M = 1 ' Class 2: the results of the heuristic are presented in Table 4.7. #Sources R k(10''4) x(m) z(m) M=2 11.34 2.99 2.125 0.797 -0.387 2.31 0.761 Table 4.7: Heuristic approach results for M = 2 It is clear that this sources combination is very similar to the one proposed by
the brute force approach, since the residues are the same and the di'erence
between the sources positions is below the centimeter; 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 111 ' Class 3: Table 4.8 summarizes the results. #Sources R k(10''4) x(m) z(m) M=3 10.78 9.56 2.116 0.758 -17.2 2.139 0.662 1.10 2.166 0.561 Table 4.8: Heuristic approach results for M = 3 This time, despite the residues likeness, the sources positions are di'erent:
having the same modeling capacity with di'erent positions means that these
are equivalent; moreover, since the di'erences are limited, both the solutions
can be accepted. The analysis underlines the suitability of the heuristic algorithm: since it has a lower computational burden and its results are absolutely comparable to the optimal
ones of the brute force approach, it was chosen as the reference algorithm for this
case study. Hence, the selection of the final model is based on the heuristic results: due to the huge amount of them, a global discussion is presented in the following: ' the increase of the number of sources leads to a decrease of the cost function values, as visible in Table 4.9; #Sources R #Sources R M = 1 12.45 M = 6 8.18 M = 2 11.30 M = 7 7.53 M = 3 10.60 M = 8 7.31 M = 4 8.88 M = 9 7.12 M = 5 8.27 M = 10 6.88 Table 4.9: Heuristic algorithm: medians of the classes residues ' by looking at the various solutions inside a single class, it is possible to recognize that each one is composed of two di'erent types of sources, i.e. strong and
weak. If the strongest source (kmax) of every solution is taken and the other
sources with strength k ' kmax/10 are spotlighted, it comes out that: '' the weaker sources are placed inside the points volume far away from the device; 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 112 '' if the weaker sources are removed and the class is assigned again, the classes with M greater 6 tend to disappear while the class 3 polarizes
the results: it is composed only of sources behind the fans center, which
means that the model can perform better just modifying the energies
profiles, after they are created by the fans. This alteration is realized
through the insertion of weaker sources in the points volume; '' if the weaker sources are eliminated and the corresponding values of R are re-computed, a very high increase of the latter happens, suggesting
that this procedure can not be used to select the model but, in any case,
it gives useful hints on the model behavior. ' concerning the classes from 5 to 10, it is common to encounter sources with the same values of x-coordinate but di'erent values of z-coordinate (typically
one behind the center and one in the 'ux): this confirms the above emphasized
idea. In order to overcome these issues, it is necessary to create a value for describing how worthy a class would be if selected: this value must consider the complexity of
the corresponding class as well as its ability to reduce the residue. Therefore, the
named Worth Cost Function (W CF ) was inserted and computed by multiplying the
weight of the class (MWCF : higher the class, lower the value) by the weight of the
residue improvement (RWCF : lower the residue, greater the value). In particular, the
identification number of a class is defined as i, while Mmax = 10 is the greatest class,
Mmin = 1 the lowest and Ravg is the mean of the residues of a particular class (after
the outliers removal). Of course, the W CF has to be maximized MW CF = ( Mmax '' Mi Mmax '' Mmin ) (4.11) RW CF = ( Ravr max '' Ravg i Ravg max '' Ravg min ) (4.12) W CF = MW CF · RWCF (4.13) 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 113 The application of this new index allows the selection of the worthiest class to model the fans noise power: Table 4.10 reports the results, rounded to 2 decimal
places (after computations). #Sources Ravg MW CF RW CF W CF M = 1 12.45 1 0 0 M = 2 11.30 0.89 0.21 0.18 M = 3 10.53 0.78 0.34 0.27 M = 4 9.02 0.67 0.62 0.41 M = 5 8.29 0.56 0.75 0.41 M = 6 8.13 0.44 0.77 0.34 M = 7 7.62 0.33 0.87 0.29 M = 8 7.36 0.22 0.91 0.20 M = 9 7.16 0.11 0.95 0.11 M = 10 6.87 0 1 0 Table 4.10: Heuristic algorithm: W CF results By looking at the results, it can be pointed out that the classes 4 and 5 have the same W CF value and this involves that both are suitable for the current case study.
In Chapter 3, it was stated that the model has to describe in a simple way the fans
noise profile, in order to supply a linear method with low computational complexity.
Hence, this general way of thinking to the problem suggests the selection of class 4:
by deeper analyzing its solutions, it comes out that the 60% of them estimates the
sources at a particular position in space. For this reason, these solutions are chosen
to be the final result (Tab.4.11). Source ID s1 s2 s3 s4 k 7.52E-04 -9.35E-04 7.30E-06 5.51E-04 x(m) 2.116 2.145 2.224 2.246 y(m) 0.851 0.851 0.851 0.851 z(m) 0.764 0.659 1.171 0.371 Table 4.11: Final model information This particular solution gives a value R = 8.86, i.e. a mean percentage error of each point equal to Ri = 17%. Figure 4.14 shows the device together with the positions of the ideal sources. 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 114 Figure 4.14: Device and ideal sources (upper view): the values indicate the strengths of the sources 4.2. DVB-T device power model Chapter 4. Measurements and Modeling 115 4.3 Speaker power model Unlike the previous case, the computation of the anti-noise source model, i.e. a loudspeaker, requires to solve some additional problems, for instance the loudspeaker
selection and the decision on what signal should be fed to it in order for characterizing
its power model. It is important to underline that the volume knob of the speaker
was maintained at the same level (half of its dynamic) during all the experiments. Considering the case study, a small speaker would be the best choice: indeed, its dimensions would make it suitable to be embedded in the device without a'ecting the
cooling performance; however, such a speaker was not available and it was decided to
proceed with a Genelec® 6010A (Fig.4.15(a)). This is not a major issue, because this
master thesis proposes a method to enlarge the quiet zone: of course, a dedicated
study on how implementing the method should be accomplished. (a) Loudspeaker (b) Acoustic center Figure 4.15: Genelec 6010A 4.3. Speaker power model Chapter 4. Measurements and Modeling 116 The speaker user guide supplies useful information regarding its frequency response behavior, which is shown in Figure 4.16 together with its polar pattern: since the
frequency of interest is around 1 KHz, a zoomed view of that detail is inserted. Figure 4.16: Genelec 6010A: frequency response and polar pattern As visible, the value on the vertical axis is expressed in dBrA, that is, a standard dBA measure related to a reference one: because this was not supplied, a first analysis
needed to be carried out. Hence, a fonometer was positioned at the same height
of the speaker acoustic center PAC = [Px0 AC Py0AC Pz0AC ] = [2.302 1.099 0.809] (Fig.4.15(b)), but 1 meter far from it. A single sinusoid at 1137 Hz (the frequency of interest) was fed to the loudspeaker and di'erent amplitudes were tested: it was observed that a linear increase of the
input signal produced a linear variation on the output. Furthermore, by moving the
fonometer around the loudspeaker at the same height and distance from it, similar
values of output were recorded for the corresponding input amplitudes. 4.3. Speaker power model Chapter 4. Measurements and Modeling 117 Table 4.12 lists the measured values for amplitude equal to 0.2: Distance (m) Angle (') dBA 1 0 84 1 30 85.5 1 45 85 1 60 84.8 1 -30 85.3 1 -45 84.8 1 -45 84.7 Table 4.12: Polar pattern test Since the values are very similar and their di'erences are included in a range of 1.5 dB, it can be assumed that the information given by the frequency response scheme
(Fig.4.16) is reliable: the frequency under analysis is equally attenuated independently
of the measurement direction. Therefore, it is possible to state that, if a reference power of this frequency is de- fined, the attenuation on the acoustic plane is only due to the wave''s energy spreading
and so the model can be computed. Obviously, the loudspeaker characterization at
other frequencies would be mandatory if a precise model had to be built up: since
the model has not the claim to be that, the loudspeaker has been characterized at
the frequency of major interest, which, by the way, produces the most important con-
tribution to the power. Moreover, once it has been verified that a linear increase of
the input signal corresponds to a linear one at the measured output signal, the LMS
algorithm adjusts by itself the amplitude of the other harmonics, with a negligible
error for the case study and without mutually a'ecting the others. The model computation has to take into account the attenuation introduced by the loudspeaker: this can be done by adding a matrix which defines the attenuation, in
relation to the spherical position of the points with respect to the acoustic loudspeaker
center (AC). For simplicity''s sake, let''s consider this matrix as defined for every specific
frequency f of interest. The Loudspeaker Polar Matrix (LPMi(θi, 'i)) describes, for each measured point, the attenuation applied by the loudspeaker, considering the spherical coordinates
(Fig.4.17) of the point itself: this means that the original equation of the power at a
specific location Wi old = M '' j=1 kj d2 ij (4.14) needs to be modified by taking a new Wi new Wi new = Wiold · LP Mi(θ, ') · [θi 'i] T (4.15) 4.3. Speaker power model Chapter 4. Measurements and Modeling 118 Figure 4.17: Spherical coordinates where the vector [θi 'i] T indicates the spherical coordinates for each specific point (the radius is implicit in the model). Going back to the case study, it has to be pointed out that the LPM is unknown if a point is located outside the plane defined by the loudspeaker acoustic center:
hence, in order to move forward, the following reasoning was developed. The frequency under test does not experience any additional attenuation by the loudspeaker on the planar field: so, the matrix, for that particular frequency, can be
considered an identity as for all 'i and θ = 0. More important, it can be assumed
that the loudspeaker 3D polar behavior is equal to the plane one, that is, a point
characterized by (d, θi, ') is subjected to the same attenuation of a general one
(d, 0, '): thus, it is su'cient to acquire points in the plane to compute a model
where the measured power is produced by ideal sources. In addition, the matrix is
still present in the model equations but, for this specific frequency, it becomes an
identity and so Wi new = Wiold . E'ectively, a microphone was positioned at 1 meter far from the speaker''s acoustic center and the model power variable WR was measured, for di'erent input amplitudes,
to be employed as reference. Since the input gains of the pre-amplifiers were set equal
to the ones used during the acquisition of the device noise, the sinusoid at 1137 Hz
was amplified by a factor of 0.2 so that near field microphone saturation was avoided.
After that, several points inside the acoustic center plane were measured, in order to
gather a data set suitable for the computation of the loudspeaker model. 4.3. Speaker power model Chapter 4. Measurements and Modeling 119 Figure 4.18: Measuring gear: loudspeaker The measuring gear (Fig.4.18) has already been described in sections 4.1 and 4.2, so only the di'erences are listed: ' the loudspeaker was put on a piece of absorbing acoustic material, to avoid the generation of unwanted noise; ' the microphones array was composed of 13 microphones without the adding of the two side booms (Tab.4.13 reports the cumulative distances between the
microphone ID-1 and the others) Microphone ID Distance (cm) 2 10 3 15 4 20 5 25 6 27.5 7 30 8 32.5 9 35 10 40 11 45 12 50 13 60 Table 4.13: Microphones array: microphones distances (Loudspeaker case) ' the central microphone was aligned along the x-coordinate with the loudspeaker acoustic center and the array was moved from its initial position following the
increments on the z-axis with respect to Pz0 AC (Tab.4.14). The microphones array was then placed parallel to the z-axis and other two measure cycles were
conducted, with values of the x-coordinate around 1.4 and 3 meters. 4.3. Speaker power model Chapter 4. Measurements and Modeling 120 Axis Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 z +0.1 +0.2 +0.35 +0.45 +0.6 +0.75 1 Table 4.14: Sampling distances along z-axis, with array aligned with the x-axis (Loudspeaker) The median operator was applied to each set of measures in order to extract the power values; after that, the obtained set of data was normalized to WR and
preprocessed to remove the outliers (40%): Figure 4.19 shows the resulting points. Figure 4.19: Loudspeaker model points (blue) and excluded ones (red) 4.3. Speaker power model Chapter 4. Measurements and Modeling 121 The set of data was fed to the heuristic algorithm: since the scripts are the same, except for the initial ranges and the modification on the power computation, please
refer to subsection 4.2.2.2 (Alg.4 in particular); also the intervals are the same but
shifted at the acoustic center position Px0 AC '' 0.6 '' X '' Px0AC + 0.6 (4.16) Pz0 AC '' 0.5 '' Z '' Pz0AC + 0.5 (4.17) The results from the heuristic algorithm are organized in 10 classes each of 10 elements: being mindful of the procedure adopted in the previous section, the result
of the W CF computation are listed in Table 4.15. #Sources Ravg MW CF RW CF W CF 1 2.77 1 0 0 2 2.23 0.89 0.26 0.23 3 1.20 0.78 0.77 0.6 4 1.06 0.67 0.83 0.56 5 0.98 0.56 0.88 0.47 6 0.91 0.44 0.91 0.4 7 0.87 0.33 0.93 0.31 8 0.81 0.22 0.96 0.21 9 0.76 0.11 0.98 0.11 10 0.72 0 1 0 Table 4.15: Heuristic algorithm: WCF computation results (loudspeaker) Thanks to its W CF value, class 3 is the final choice for the loudspeaker model (Tab.4.16): by considering the set of solutions of this class, the 70% of them locates
the sources in very similar positions, with di'erences of a millimeter. Source ID l1 l2 l3 k -4.03E-01 2.13E+00 -1.28E+00 x(m) 2.118 2.261 2.35 y(m) 1.099 1.099 1.099 z(m) 0.81 0.743 0.666 Table 4.16: Loudspeaker final model Figure 4.20 shows the position of the acoustic center of the loudspeaker together with the ideal sources of the model: for each source the strength is also indicated. 4.3. Speaker power model Chapter 4. Measurements and Modeling 122 Figure 4.20: Loudspeaker acoustic center (red symbol) and ideal sources (blue points) 4.3. Speaker power model Chapter 4. Measurements and Modeling 123 4.4 Model matching This last section deals with the model matching, which aims at finding the number, positions and strengths of the control sources, in order to extend the quiet zone and
improve the attenuation performance. The final models for the DVB-T device (Tab.4.17) and the loudspeaker (Tab.4.18) are reported below, to refresh the work done until now: in addition, once these models
are known, their makers are no more important and, for example, the loudspeaker
model can be thought as originated by an actuator suitable for this case study. Source ID s1 s2 s3 s4 k 7.52E-04 -9.35E-04 7.30E-06 5.51E-04 x(m) 2.116 2.145 2.224 2.246 y(m) 0.851 0.851 0.851 0.851 z(m) 0.764 0.659 1.171 0.371 Table 4.17: DVB-T device: final model Source ID l1 l2 l3 k -4.03E-01 2.13E+00 -1.28E+00 x(m) 2.118 2.261 2.35 y(m) 1.099 1.099 1.099 z(m) 0.81 0.743 0.666 Table 4.18: Loudspeaker: final model The matching procedure has to move a definite number of loudspeakers inside a specific region and, at the same time, to adjust the strengths of their modeling
sources in order to reproduce the power field generated by the fans model. In order
to supply a general and simple method, this operation can be done by exploiting the
developed algorithms, through the integration of few code changes. The original model states that a power quantity Wi, measured in a particular point, is the sum of the powers generated by ideal sources Wi = M '' j=1 kj d2 ij for i = 1, · · · N (4.18) where dij is the distance between point i and the ideal source j. In order to match the two models, it was decided to let the fans model generate W: ' the 293 points used to compute the fans model are taken into consideration and their coordinates become the ones of the matching point set; 4.4. Model matching Chapter 4. Measurements and Modeling 124 ' since the positions of the DVB-T model sources are known, the distances from them to the matching set can be computed: it has to be underlined that also
the ki are known and so, by calling AM the matrix of the distances coe'cients
dij'' 2, the values of the power at those particular points (W Mi ) become WM = AM KDV B''T (4.19) WM represents the new data set for solving the matching problem. The position of the loudspeaker acoustic center is defined by PAC = [2.302 1.099 0.809]: the distance row vector DLi contains the di'erence, for each coordinate, between this
center and the position of the ith-ideal source (of course, since the y-coordinate was
fixed, the distance value is 0). DL i = [PACx '' xsi 0 PAC z '' zsi] for i = 1, 2, 3 (4.20) The formula allows to define the di'erence matrix DS DS = [DL 1 ; DL 2 ; DL 3 ] (4.21) The usage of this matrix is simple: indeed, to find the best loudspeaker posi- tion, the heuristic algorithm (see subsection 4.2.2.2) is employed, even if this time it
moves the acoustic center and not the ideal sources. Once a position of the AC is
found (called ACP ), the positions of the loudspeaker model sources (S1, S2, S3) are
obtained as Si = ACP '' DS(i, all) (4.22) and the matrix A can be calculated for each source-point couple. Anyway, the main problem remains how to combine the positions selection with the strengths one: thus, it was necessary to modify the computational block defined
by the Algorithm 3 (see subsection 4.2.2.1), whose job was the computation of the
cost function R: to do it, that algorithm had to obtain the strengths vector by
inverting the A matrix ' K = (A T A)''1AT W (4.23) Here a smart modification has to be applied. Since each loudspeaker is modeled with 3 sources, its strength becomes a vector of 3 components: this means that
a modification of the loudspeaker strength involves the modification of the entire
vector, so that the components vary in a corresponding manner. Let''s now neatly proceed by listing step by step the sequence of blocks needed to match the two models: 4.4. Model matching Chapter 4. Measurements and Modeling 125 ' the main section of the heuristic algorithm (Alg.4) was run 10 times for each class Mi, with initial ranges so defined (m) 1.755 '' X '' 2.213 (4.24) 0.801 '' Z '' 1.301 Even if, concerning z-axis, this is an area greater than the one in which the
actuators placement is allowed, it was decided to tune the algorithm on it to
further evaluate the solutions; ' the other algorithms, dealing with the heuristic approach, remain the same, ex- cept for the 3. For more details, please refer to subsection 4.2.2.2 (in particular,
Alg.5, 6, 7 and 8). The new computational block is now defined: let KAMP be the column vector of the loudspeaker model source strengths, ACx the coordinates of the M loudspeaker
centers along x-axis and ACz the ones along the z-axis. Algorithm 9 STD: Model matching
Require: ACx, ACz, M, WM, P for i = 1 to M do sourceX(1+(3(i-1)) to 3i) ' ACx(i) '' DS(all, 1) sourceZ(1+(3(i-1)) to 3i) ' ACz(i) '' DS(all, 3) end for
for
j = 1 to 3M do Compute squared euclidean distances considering sourceX and sourceZ end for
Compute A ' KOP T ' (AT A)''1AT WM for i = 1 to M do ' Ktemp ' ' KOP T (1 + (3(i '' 1)) to 3i) '' ' (KT AM P KAM P ) ''1K AM P ' Ktemp KNEW (1 + (3(i '' 1)) to 3i) ' ''KAMP end for ' W ' AKNEW Err ' (W '' ' WM)/WM R ' ErrT Err return R This method allows the computation of the best strengths of the di'erent sources, considering both the hints supplied by the original algorithm and the constraints
imposed by the model. The W CF was then calculated and Table 4.19 presents the results after the median operator filtering. 4.4. Model matching Chapter 4. Measurements and Modeling 126 #Sources (3M) Ravg MW CF RW CF W CF 3 96.47 1 0 0 6 40.34 0.89 0.69 0.61 9 39.54 0.78 0.70 0.54 12 29.44 0.67 0.82 0.55 15 31.55 0.56 0.80 0.44 18 16.89 0.44 0.97 0.43 21 19.83 0.33 0.94 0.31 24 24.68 0.22 0.88 0.20 27 14.84 0.11 1 0.11 30 17.43 0 0.97 0 Table 4.19: Heuristic algorithm: W CF computation results (Model matching) First of all, it can be noticed that the residues do not always decrease with the increase of the involved sources: this can be ascribed to both the applied ranges
limitation and the need to vary the strengths of the triple of sources. Anyway, the worthy cost function suggests class 2 should be selected, which means two loudspeakers for a total of six ideal sources. A deeper analysis of the
class'' solutions underlines the presence of two sets of possible speakers locations,
which are presented in Table 4.20 and Table 4.20 (strengths are not listed): R 48.57 x(m) 1.92 2.148 y(m) 0.851 0.851 z(m) 0.802 0.817 Table 4.20: Matching first solution R 34.85 x(m) 1.964 2.139 y(m) 0.851 0.851 z(m) 0.941 0.813 Table 4.21: Matching second solution 4.4. Model matching Chapter 4. Measurements and Modeling 127 The second solution has a lower residue, but the value of the first loudspeaker z-coordinate is too high: in fact, it would force the actuator positioning at 14 cm
away from the device; this would go against the project specification, since it could
prevent the possibility of performing maintenance. Because of that, solution number
1 represents the final choice: Figure 4.21 shows the device (in green) together with
the two loudspeakers (red dots), while Table 4.22 proposes again the solution with
the addition of the strengths vectors for each speaker. Figure 4.21: Device and loudspeakers placement after the matching procedure (di'erent views) 4.4. Model matching Chapter 4. Measurements and Modeling 128 Source k x(m) y(m) z(m) SPKR 1 5.74E-06 1.92 0.851 0.802 -3.00E-05 1.83E-05 SPKR 2 -1.70E-06 2.148 0.851 0.817 9.17E-06 -5.5E-06 Table 4.22: Matching: final solution It can be said that the strengths related to the loudspeakers can be expressed by dividing a certain k with respect to the original one, which leads to KSP KR 1 = ''1.42 ' 10''05 (4.25) KSP KR 2 = 4.30 ' 10''06 (4.26) This final matching solution presents a residue of 48.57, which is the sum of the squared normalized error over all the 293 points, by leading to an average di'erence
of 40% between the two power profiles at each point. Despite this result could seem not very good, it must be pointed out that the project goal was the extension of the quiet zone: hence, the method supplies infor-
mation on how well the algorithm performs during attenuation. Placing the error
microphone at the desired attenuation location leads to a perfect attenuation at that
zone, a similar one in the neighborhood and an average of 60% elsewhere. On the
other side, if the error microphone is placed inside the allowed region, the method
confirms the attenuation ability: indeed, it is known that a perfect attenuation can
be achieved, where the energies are the same while, where the power profiles are
di'erent there will be a certain amount of attenuation (estimated as an average of
60% of the total, since the profiles di'erence is equal to 40%). 4.4. Model matching Chapter 5 Concluding remarks 5.1 Method evaluation The master thesis here presented deals with the tuning of an active noise control method on a case study represented by a DVB-T device, whose cooling fans produce
a very annoying noise with fundamental frequency equal to 1137 Hz. The aims are
the attenuation of this noise and, at the same time, the extension of the quiet zone:
this are accomplished by finding the best position of the control sources. The project specifications require to attenuate the noise without modifying the device, while the addition of small sensors and actuators is allowed, provided that it
does not a'ect the cooling performance and the possibility of performing maintenance:
thus, the noise reduction system must be embedded into the device. In order to achieve these purposes, the master thesis proposes to model the noise power (emitted by the fans and measured in particular points i) as the weighted
sum of the powers generated by a finite number (M) of ideal sources, located in the
proximity of the device: Wi = M '' j=1 kj d2 ij for i = 1, · · · N (5.1) where Wi is a measured quantity describing the average fans power emission, d2 ij is the square of the euclidean distance between the point i and the ideal source j, whose
strength is defined by kj. This idea is based on the knowledge that a standard active
noise control algorithm is able to carry out a perfect attenuation when two planar
waves have same pressure over the area of interest, which means also same power
profile. 130 Chapter 5. Concluding remarks 131 The acquisition of a grid of points permits the calculation of that model for the DVB-T device (M1), that is, the identification of the ideal sources characteristics
which better describe the fans power generation. Then the same methodology is
employed to extract a power model (M2) of an anti-noise source, a loudspeaker. Once these models are obtained, the attenuation problem can be disconnected from the study case and it becomes: finding the best combination of the elements of
M2 which better reproduces the profile defined by M1. Hence, an iterative procedure
is assembled to compute the best number, positions and strengths of actuators, in
order to replicate the power profile originated by the noise. The matching procedure
points out the presence of a set of solutions which confirms the suitability of the
method for its specific purpose: the similarity of the power profiles highlights the
method ability to well characterize the positioning of the control sources. Despite this, the identified solution su'ers for some implementation issues, since it suggests the loudspeaker placement inside the fans grid: to overcome this hurdle
during the enactment of the solution it is necessary to study if a slight shift of the
couple of sources produces an acceptable decrease of the attenuation performance. 5.2 Further developments The development of the master thesis underlines possible improvements, which can be so summarized: ' extension of the model for considering also the variation along the y-axis; ' development of the control source model using a suitable loudspeaker, i.e. a piezoelectric one, with a detailed analysis of its 3D polar pattern in order to have
complete information: indeed, the latter permits the definition of an accurate
model which can better match the one of the fans; ' positioning of the reference and error microphones: the former can be placed wherever a signal, strictly related to the noise to attenuate, can be sensed.
Concerning the second one, a deeper analysis should be performed to find the
x-, y- and z-coordinates in which the matching is optimal: if such a position
is found inside the permitted area, therefore, it will be the location of the
microphone; ' change of the model by considering a dynamic one: this describes the power of a point also from a time perspective, to allow the tracing of the phase shifting
experienced by the two fans; ' implementation of a reliable hardware solution for the case study: a hardware board (which embeds the controller, the DAC and the ADC) must be developed 5.2. Further developments Chapter 5. Concluding remarks 132 and a further analysis on the proposed solution needs to be pursued, to identify
if the placement of a small loudspeaker inside the fans grid can allow the
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3rd International Conference on, pages 728 '' 731, May 2011. Acknowledgements I would like to thank: Rinaldo Mazzoni of SY.E.S. for supplying the DVB-T device; prof. Fabio Salice and prof. Luigi Piroddi for the professionalism, the patience and
the availability demonstrated in these months;prof. Augusto Sarti for making the
laboratory gear available to me; Salvo Daniele Valente, Fabio Antonacci and Lucio
Bianchi for aiding me during the acquisition sessions; all of my friends and the ''World
Domination Company & Friends' ©; my family, for the economic and moral support which allowed me to start a long time ago these academic studies which are now
going to end; Rossana, my beloved girlfriend, for everything and more, for accompanying me and helping me to the end, for being at my side today and tomorrow. 138

Document Outline

List of Figures List of Tables List of Algorithms Introduction Active Noise Control Algorithms for ANC Operative principles ANC concept extension The Literature Duct arrangement Fan improvement Fan modeling Others Applications examples Summary and key ideas The proposed method Measurements and Modeling Experiment setup DVB-T device power model Data preprocessing Power model Results and Model selection Speaker power model Model matching Concluding remarks Method evaluation Further developments Bibliography


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