以特徵系統實現演算法分析聲場之模態參數

模態分析（modal analysis, MA）在結構力學及振動學是很重要的一項技術，但由於其模態的高複雜度卻鮮少應用於聲學領域中。在本篇論文裡，我們從狀態空間的觀點將一封閉環境聲場建立數學模型，提出的方法為特徵系統實現演算法（eigensystem realization algorithm, ERA），將房間聲場建立單輸入多輸出（single-input-multiple-output, SIMO）的線性系統。接著利用特徵值分解把此系統轉換至模態空間且求得在量測點上的模態參數，如共振頻率、阻尼係數、共振模態等。為了重建及解析出整個房間模態，我們提出了平面波分解（plane wave decomposition）以及壓縮感知（compressive sensing, CS）演算法將重建問題寫成欠定逆問題（undertermined inverse problem）並求得稀疏解。因此，對於任意一對的麥克風及聲源位置的模態即可由插值法求得，並且利用模態參數我們可重建房間脈衝響應（room impulse response, RIR），最後提出三種應用：流形學習（manifold learning）、聲源定位（source localization）及混響器（reverberator）。

關鍵字

模態分析；特徵系統實現演算法；平面波分解；壓縮感知

並列摘要

Modal analysis (MA) is an important technique in structure dynamics and vibration. In acoustics, MA is rarely investigated due to high modal density and complexity. In this paper, a novel approach of MA is proposed for enclosed acoustic field from a perspective of state-space formulation of control systems. The proposed technique is based on single-input-multiple-output (SIMO) state-space model established by using the eigensystem realization algorithm (ERA) for the room. Next, the realization is converted to a modal form from which natural frequencies, damping factors, and mode shapes can be identified. In order to reconstruct a sparse representation of mode shapes, plane-wave decomposition in conjunction with compressive sensing (CS) technique is exploited to formulate an underdetermined inverse problem. Therefore, mode shapes at any arbitrary source-receiver positions can be ＂interpolated＂ on the basis of the realized state space model. Room impulse responses (RIRs) can also be reconstructed with the implementation of theses predicted modal parameters. Finally, three application examples are presented: manifold learning, source localization, and reverberator.

並列關鍵字

Modal Analysis ； Eigensystem Realization Algorithm ； Plane-Wave Decomposition ； Compressive Sensing

國際替代計量

以特徵系統實現演算法分析聲場之模態參數

全文下載

主題瀏覽