本論文實現麥克風隨機排列陣列的遠場聲源定位和分離的兩個階段。麥克風陣列的位置分佈以模擬退火（Simulated annealing, SA）法優化設計，麥克風各點的位置以高斯分佈的方式隨機取點，繪製遠場波束圖 (Beam-pattern) 並尋求最大旁瓣 (maximum sidelobe) 的最小化。兩階段的演算法皆以球面波模型的基礎進行推導。在定位階段，先以延遲總和方法（Delay and sum, DAS）定出大致的聲源位置區域，接著使用參數估測方法使定位更加精確。在分離階段中，聲源振幅可以藉由麥克風接收到的聲壓與聲源傳遞至麥克風的傳遞矩陣之間的反矩陣問題求得。而當聲源的數量小於麥克風時則形成超定問題 (overdetermined problem)，可以透過提可諾夫正規化(Tikhonov Regularization, TIKR)求解，而假設的聲源數量大於麥克風，可以將定位後的轉向矩陣進行增廣而形成未定問題 (underdetermined problem)，進而使用壓縮感知 (Compressive sensing) 技術分離聲源。此外，聲學參數如聲壓、粒子速度、平均聲強及聲功率皆可以等效聲源法 (Equivalent source method, ESM) 計算出來，本論文以模擬與實驗驗證此演算法的可行性。

A farfield random array is implemented for sound source identification. Microphone positions are optimized, with the aid of the simulated annealing (SA) method as a supervised Monte Carlo approach, random samples of sensor position are drawn from Gaussian distribution to minimize the sidelobe maximum of the farfield beam-pattern. A two-stage localization and separation algorithm is devised on the basis of the equivalent source model (ESM). In the localization stage, the active source regions are located by using the delay-and-sum (DAS) method, followed by a parametric array localization procedure that is capable of locating sources with improved resolution. In the separation stage, source amplitude extraction is achieved by formulating an inverse problem based on the steering matrix relating the sound pressures received by the microphones and the source amplitudes. The number of sources is selected to be less than the number of microphones to render an overdetermined problem which can be solved by using the Tikhonov regularization (TIKR). Alternatively, the separation problem can be augmented into an underdetermined problem which can be solved using the compressive sensing (CS) technique. Furthermore, the acoustic variables including sound pressure, particle velocity, sound intensity, and sound power can be estimated based on ESM. Numerical and experimental results are presented to validate the proposed technique.

摘 要 i
ABSTRACT ii
誌 謝 iii
TABLE OF CONTENTS iv
LIST OF TABLES vi
LIST OF FIGURES vii
Chapter 1 INTRODUCTION 1
Chapter 2 RANDOM ARRAY MODELING AND DESIGN 5
2.1 Farfield array model 5
2.2 Optimizing array sensor deployment 5
Chapter 3 STAGE 1: SOURCE LOCALIZATION 12
3.1 Deterministic maximum likelihood (DML) estimation 12
3.2 Stochastic maximum likelihood (SML) estimation 13
3.3 Weighted subspace fitting (WSF) estimation 14
3.4 Parameter estimation in conjunction with SA optimization 15
Chapter 4 STAGE 2: SOURCE SIGNAL SEPARATION 17
4.1 Tikhonov regularization (TIKR) 17
4.2 Compressive sensing (CS) 18
4.3 Post processing for acoustic variables 19
4.4 Procedure of the two-stage algorithm 20
Chapter 5 NUMERICAL AND EXPERIMENTAL VALIDATION 23
5.1 Simulation of two monopole sources 23
5.2 Verification of sound power estimation 24
5.3 Two sources scenario 24
5.3.1 Audio sources 24
5.3.2 Practical sources 25
5.4 Subjective test 26
Chapter 6 CONCLUSIONS 46
REFERENCES 47

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