應用近場與遠場麥克風陣列於 工具機噪音源識別

Noise source identification for machine tools using nearfield and farfield microphone arrays

陳勁誠(Ching-Cheng Chen)

指導教授 ： 白明憲

國立清華大學/工學院/動力機械工程學系/博士(2013年)

https://doi.org/10.6843/NTHU.2013.00015

摘要

本論文提出利用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。遠場聲學影像的演算法包括延遲和相加法、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以及方向。結果顯示多重信號分類法在定位噪音源位置上可以得到高解析度的影像。在近場陣列訊號處理中，一種來自離散單層位能方程式的稱作間接等效聲源法，和另一種來自離散赫姆茲積分方程式的稱作直接等效聲源法。在上述兩種等效聲源法的使用上，撤退距離與元素平均面積參數的選取是非常重要的。文中將透過黃金分割搜索法和模擬退火法去最佳化間接與直接等效聲源法的參數。透過基於狀態空間的遞迴運算，本文採用基於卡爾曼濾波器的狀態觀測器和基於粒子濾波狀態估計器去替代直接的逆運算。狀態觀測器和估計器能夠適應性的追踪聲場的動態變化，即使是存在噪音和擾動的環境下。
借助數學編程系統的方法下可以實現波束合成器的最佳權重係數和麥克風陣列的逆運算濾波器。其中遠場和近場麥克風陣列的問題可以被套用到壓縮取樣和凸優化的架構上。凸優化技術被有效的應用於波束形成器的設計，聲場的重建，聲源分離和模態分析在近場和遠場麥克風陣列中。如何設計能夠承受系統誤差的最佳化波束形成器在實際的應用上一直是一個關鍵問題。一般系統的誤差定義如下：如傳感器的不一致性、傳感器位置誤差和指向性誤差。本文從統計的角度檢驗了系統誤差對波束形成器性能的影響。由於在實際的應用中麥克風的數量是有限的，本文提出幾種聲場內插的技術，其中包含基於等效聲源法的內插法、欠定的等效聲源法、直接的基底函數法和基於基底函數的內插法。這些方法將會與直接的等效聲源法作比較。在基於基底函數法中，平面與球面波函數都被用來重建近場聲全息圖於不同的幾何聲源形狀。直接的基底函數法和基於基底函數的內插法採用壓縮取樣的技術進行內插。對於使用稀疏陣列的配置上，上述幾種聲場內插的技術能夠有效的強化聲場影像的解析度。透過模擬和實驗的結果，所提出的遠場及近場麥克風陣列方法被證明能夠有效地識別聲源在實際的案例中，包括木箱實驗，非接觸式模態分析和工具機實驗。

關鍵字

噪音源識別 ； 聲場可視化 ； 波束成形

並列摘要

Farfield and nearfield microphone arrays are proposed for noise source identification (NSI) and sound field visualization (SFV). Farfield acoustic imaging algorithms including the delay and sum (DAS) algorithm, the minimum variance distortionless response (MVDR) algorithm and the multiple signal classification (MUSIC) algorithm are employed to estimate direction of arrival (DOA). Results show that the MUSIC algorithm can attain the highest resolution of localizing sound sources positions. In the nearefield array signal processing, one formulation derived from discretizing the simple layer potential is termed the indirect equivalent source model (ESM)-based nearfield acoustical holography (NAH), while another formulation derived from discretizing the Kirchhoff-Helmholtz integral equation is termed the direct ESM-based NAH. In the use of ESM NAH, the choice of parameters including retract distance and average area of element is of vital importance. These parameters are optimized, with the aid of the golden section search and parabolic interpolation (GSS-PI) algorithm and the simulated annealing (SA) algorithm, for the direct and indirect ESM formulations. Instead of directly solving the inverse problem, the forward problem is solved in a recursive manner akin to the approach adopted by using recursive Wiener filtering. The approaches proposed are based on a state-space formulation employing the Kalman filter-based state observer and particle filter-based state estimator. The state observer and estimator are adaptive in nature and capable of tracking dynamic variation of sound field, even in the presence of noises and perturbations.
Optimum weighting coefficients and inverse filters for microphone arrays can be accomplished, with the aid of a systematic methodology of mathematical programming. Both farfield and nearfield array problems are formulated in terms of compressive sampling (CS) and convex optimization (CVX) formalisms. CVX is applied to beamformer design, pressure field reconstruction, source separation and modal analysis with satisfactory performance in both nearfield and farfield microphone arrays. Design of optimal beamformers that withstand system errors such as channel mismatch, sensor position error, and pointing error has been a key issue in real-world applications of arrays. This thesis also examines the effects of system errors on beamformer performance from a statistical perspective. In practical applications where only patch array with scarce sensors are available, the ESM-based interpolation (ESM-IP), under-determined ESM (UD-ESM), direct basis function model (D-BFM) and BFM-based interpolation (BFM-IP) are proposed to reconstruct source velocity with sound filed interpolation. These methods were compared with the direct ESM (D-ESM) method. In the BFM-based NAH, basis functions including planar and spherical wave functions are used. CS is exploited in the BFM-IP and the D-BFM in light of CVX method. It is desirable to enhance the image resolution based on a sparse array configuration. As indicated by the simulation and experiment results, the proposed technique proved effective in identifying sources of many practical examples, including wooden box experiment, noncontact modal analysis of plate and machine tools.

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