臺灣博碩士論文加值系統

本論文提出遠場及近場麥克風陣列來識別噪音源的位置及聲場可視化。在遠場麥克風陣列中，稀疏且隨機配置的麥克風陣列已知可以用來傳遞遠場的影像而不會產生鬼葉瓣的問題。在最佳化麥克風的配置中，全域最佳化技術包括蒙地卡羅法、模擬退火法和內部方格蒙地卡羅法被用來有效率地尋找最佳的麥克風配置。模擬結果顯示出要避免鬼葉瓣的出現，隨機配置麥克風是必要的。而結合模擬退火法和蒙地卡羅法的方法可以有效率的找到一個令人滿意的配置，這個配置能得到傑出的波束圖和相對較均勻的麥克風分布。在到達方向的估測中，平面波的聲源被視為球面波。遠場聲學影像的方法包括延遲和相加法、時間反轉法、單進多出等效聲源反逆濾波法、最小變異無失真響應法和多重信號分類法被用來估測聲源位置。結果顯示多重信號分類法在定位噪音源位置上可得到最佳的結果。在近場麥克風陣列中，提出近場等效音源影像(Nearfield Equivalence Source Imaging, NESI)來識別噪音源的位置及強度。NESI是在時間面上設計,它除了可以應用在穩態噪音源上亦可應用在非穩定噪音源上。利用最小均方最佳化來設計出多通道反逆濾器。調整化被利用來仰制不足解模型相稱的不好條件值。設計的參數如:麥克風陣列的孔徑、麥克風的間距、焦點的間距及量測距離都會明顯地影嚮到聲場影像解析度的結果。重建距離的選定是依據傳遞矩陣的條件值大小來決定。並且利用窗口矩陣的設計來成功地解決在邊界上失焦的問題。此外，本論文使用撤退焦點表面法來避免在重建聲場表面上的奇異問題。並使用&;#40644;金比例法來求得最佳的撤退距離（虛擬聲源面及重建面之間的距離）。在結果中發現，在平面活塞聲源中最佳的撤退距離為0.4到0.5倍的麥克風間距及在球面活塞聲源中最佳的撤退距離為0.8到1.7倍的麥克風間距。近場等效聲源成像法利用多通道反算濾波器可重建數個聲學變數，包含聲壓、粒子速度、主動聲強及聲功率。而當可供使用的麥克風數量不足時，可運用虛擬麥克風技巧裡的內插及外插方法分別增加解析度及減低邊緣效應。使用高效率之狀態空間最小化獲得技術來實現多通道反逆濾器。經由最佳化計算，最佳的近場麥克風配置為等間距之麥克風置配。根據模擬及實際聲源(個人電腦、空氣壓縮機、速克&;#36921;及非接觸式模態測式)測試結果,本論文所提出的NESI技術可以有效地去識別出噪音源的位置及強度。

Farfield and nearfield microphone arrays are proposed for noise source identification (NSI) and sound field visualization (SFV). In farfield array, arrays with sparse and random microphone deployment are known to be capable of delivering high quality far-field images without grating lobes. In the optimal deployment of microphone arrays, global optimization techniques including the simulated annealing (SA) algorithm and the intra-block Monte Carlo (IBMC) algorithm are exploited to find the optimal microphone positions efficiently. In direction of arrival (DOA) estimation, the planar wave sources are assumed to be spherical wave sources in this thesis. Farfield acoustic imaging algorithms including the delay and sum (DAS) algorithm, the time reversal (TR) algorithm, the single input multiple output equivalent source inverse filtering (SIMO-ESIF) algorithm, the Minimum variance distortionless response (MVDR) algorithm and the multiple signal classification (MUSIC) algorithm are employed to estimate DOA. Results show that the MUSIC algorithm can attain the highest resolution of localizing sound sources positions. In narfield array, a nearfield equivalence source imaging (NESI) technique is proposed to identify locations and strengths of noise sources. The NESI is based on the time-domain formulation that applies not only to stationary but also a transient noise. Multichannel inverse filters are designed using the least-square optimization. Regularization is employed to mitigate the ill-posedness inherent in the model-matching problem. Window design can also be incorporated into the inverse filters to overcome defocusing problems when the distance of reconstruction (DOR) is large or when the number of microphones is less than that of the focal points. As a basic form of the equivalent source method (ESM) applied to nearfield acoustical holography (NAH) problems, discrete monopoles are utilized to represent the sound field of interest. When setting up the virtual source distribution, it is vital to maintain a “retreat distance” (RD) between the virtual sources and the actual source surface such that reconstruction would not suffer from singularity problems. However, one cannot increase the distance without bound because of the ill-posedness inherent in the reconstruction process with large distance. How to reach the best compromise between the reconstruction errors induced by the point source singularity and the reconstruction ill-posedness is an interesting problem in its own right. This thesis revisits this issue, with the aid of an optimization algorithm based on the golden section search (GSS) and parabolic interpolation. The results revealed that the RD appropriate for the ESM ranged from 0.4 to 0.5 times the spacing for the planar piston, while from 0.8 to 1.7 times average spacing for the spherical piston. Acoustical variable including sound pressure, particle velocity, active intensity and sound power are calculated by using multichannel regularized inverse filters. In practical applications in which only patch array with scarce sensors are available, a virtual microphone approach is employed to ameliorate edge effects using extrapolation and to improve imaging resolution using interpolation. The multichannel inverse filters are implemented in light of a highly efficient state-space minimal realization technique. A special kind of beam pattern and cost function definition is used for the multiple-input-multiple-output (MIMO) imaging problem. A striking result was also obtained that random deployment presents no particular benefit in nearfield imaging and the optimal configuration is the uniform array. As indicated by the simulation and experiment results, the proposed technique proved effective in identifying sources of many kinds, including broadband, narrowband, stationary, and transient sources.

摘 要 I
ABSTRACT III
誌 謝 VI
TABLE OF CONTENTS VII
LIST OF TABLES XI
LIST OF FIGURES XIII
CHAPTER 1. INTRODUCTION 1
1.1 Background and motivation: problem statement 1
1.2 Review of prior arts: approaches for noise identification problems 4
1.3 Organization of the thesis 7
CHAPTER 2. THEORETICAL PRELIMINARIES OF ACOUSTICS 10
2.1 Fundamentals of acoustics 10
2.2 Sound field representation using basis function expansion 18
2.3 Sound field representation using Helmholtz integral equation 23
2.4 Inverse problems and ill-posedness 42
CHAPTER 3. THEORETICAL PRELIMINARIES OF SIGNAL PROCESSING 44
3.1 Linear algebra basics 44
3.2 Digital signal processing basics 47
3.3 Array signal processing basics 69
3.4 Optimization algorithms 75
CHAPTER 4. FARFIELD ARRAY SIGNAL PROCESSING ALGORITHMS 86
4.1 Low-resolution algorithms 86
4.1.1 Delay and sum beamformer 86
4.1.2 Time reversal beamformer 91
4.1.3 SIMO-ESIF algorithm 94
4.1.4 Optimal array: cost functions, Rayleigh’s quotient 97
4.1.5 Choice of farfield array parameters 121
4.2 High-resolution algorithms 123
4.2.1 Minimum variance distortionless response (MVDR) 123
4.2.2 Multiple signal classification (MUSIC) 125
4.2.3 Choice of parameters: Akaike information criterion (AIC) 127
4.3 Comparison of the farfield algorithms 130
CHAPTER 5. NEARFIELD ARRAY SIGNAL PROCESSING ALGORITHMS 146
5.1 Fourier NAH 146
5.2 BEM-based NAH (IBEM): direct and indirect formulations 151
5.2.1 Direct IBEM Formulation 151
5.2.2 Indirect IBEM Formulation 161
5.3 Equivalent source method (ESM) 163
5.3.1 Direct ESM 165
5.3.2 Indirect ESM 168
5.3.3 Nearfield Equivalent Source Imaging (NESI) 173
5.3.4 Kalman filter-based algorithm 177
5.3.5 Choice of nearfield array parameters 184
5.4 Comparison of the nearfield algorithms 188
CHAPTER 6. PRACTICAL IMPLEMENTATIONS 191
6.1 Inverse filter design 191
6.1.1 Model matching: ill-posedness and regularization 191
6.1.2 Window design 193
6.1.3 Parameter choice methods (PCM) 196
6.2 Multi-channel fast filtering 200
6.2.1 The time-domain processing 203
6.2.2 The frequency-domain processing 203
6.2.3 Comparison of filtering approaches 207
6.3 Post-processing 210
6.3.1 Acoustic variables: p, u, I, W 210
6.3.2 Miscellaneous processing items 212
6.4 Choice of distance of reconstruction and lattice spacing 219
6.5 Virtual microphone technique: field interpolation and extrapolation 220
6.6 Choice of retreat distance (RD) 224
6.6.1 Integral approximation error vs. reconstruction ill-posedness 224
6.6.2 Determination of RD: Golden Section Search (GSS) 225
6.7 Optimization of sensor deployment: uniform vs. random array 242
6.7.1 Optimal nearfield array: cost functions 242
6.7.2 Optimizing farfield sensor deployment 247
6.7.3 Optimizing nearfield sensor deployment 263
6.8 System integration and experimental arrangement 276
CHAPTER 7. APPLICATION EXAMPLES 279
7.1 Scooter: transient sources 281
7.2 Compressor 290
7.3 IT equipment 295
7.4 Wooden box 299
7.5 Non-contact modal analysis 303
7.6 Other applications of the ESM 311
CHAPTER 8. CONCLUSIONS 313
REFERENCES 316
ABBREVIATIONS 325
PUBLICATIONS 328

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