(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.

Articoli tecnico scientifici o articoli contenenti case history

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Estratto del testo

Assistant Supervisor: Prof. Luigi Piroddi

Correlatore: Prof. Luigi Piroddi

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

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

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.

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.

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.

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.

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.

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

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

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

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

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.

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

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

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

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

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.

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

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

a11 a12 · · · a1M a21 a22 · · · a2M .. . .. . . .. .. . aN1 aN2 · · · aNM

k1

k2 .. . kM

(3.7) with: '

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.

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

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

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

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

the coordinates of each point in space: in particular,

point i, while

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

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

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

Delete all point be connected

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

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

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

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

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:

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

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)

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.

XDX ' X(j) + δmin RDX ' STD(XDX, Z, M,

return

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

return

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

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 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;

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

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

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

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

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

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.

for

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

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.

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

achievement of the cooling requirement. 5.2. Further developments

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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

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