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研究生: 許瑋仁
Hsu, Wei-Jen
論文名稱: 基於壓縮感知與等效聲源法之聲學陣列成像技術發展
Development of Acoustic Holography for Microphone Array Based on Compressive Sensing and Equivalent Source Method
指導教授: 吳柏賢
Wu, Bo-Hsien
學位類別: 碩士
Master
系所名稱: 工學院 - 系統及船舶機電工程學系
Department of Systems and Naval Mechatronic Engineering
論文出版年: 2024
畢業學年度: 112
語文別: 中文
論文頁數: 96
中文關鍵詞: 聲學檢測聲場重建壓縮感知等效聲源法
外文關鍵詞: Acoustic Detection, Sound Field Reconstruction, Compressive Sensing, Equivalent Source Method
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  • 近場聲音成像量測是一種聲音視覺化的聲學檢測技術,近場量測可測得由物體輻射出的消逝波,相較於遠場聲學成像具有更高的空間解析度。本研究以等效聲源法為理論基礎,並導入壓縮感知技術於聲學反算問題中,目標在提升近場聲音成像量測的聲場重建性能,研究中透過模擬與實驗驗證該方法的可行性。在數值模擬方面,討論了陣列形狀對於性能的影響,包括等間隔方形陣列與非等間隔螺旋陣列,同時對多種聲學預估方法進行比較,例如最小平方法、壓縮感知—最小能量法以及壓縮感知—最小範數法,在數種聲源之數值模擬結果中,最小範數法搭配螺旋陣列效果最佳,在單極子、偶極子以及直線四極子聲源中,其平均聲壓誤差較最小能量法搭配方形陣列分別低約21.33%、16.69% 以及24.67%。在平板聲源的數值模擬中,雖然誤差僅有大約5.85%,但仍能夠顯示出使用螺旋陣列以及最小範數法的優勢。在實驗階段,本研究構建了一組96通道的螺旋麥克風陣列,並針對不同類型的聲源模型(如單揚聲器、雙揚聲器、平板振動聲源)進行量測與驗證,結果顯示螺旋陣列設計結合壓縮感知技術確實可有效提升聲場重建的準確性,其中又以最小範數法之壓縮感知具有最佳的聲場重建性能。

    Near-field acoustic holography(NAH) is an acoustic detection technology that visualizes sound, capturing the evanescent waves radiated by objects in the near field, which offers higher spatial resolution compared to far-field acoustic holography. This study is based on the equivalent source method and incorporates the compressive sensing technique in the acoustical inversion problem, aiming to enhance the sound field reconstruction performance in NAH. The feasibility of this method is verified through simulations and experiments. In numerical simulations, the effects of array shape on performance are discussed, including square array and pseudo-randomly spiral array. Several equivalent source estimation methods are compared, such as the least squares method(LSM), minimum energy method of the compressive sensing(CS-l_2), and minimum norm method of the compressive sensing(CS-l_1). The numerical simulation results for several sound sources indicate that the CS-l_1 combined with a spiral array yields the best results, with errors approximately 60% lower than the Least Squares Method combined with a square array. In the experimental, a 96-channel spiral microphone array was constructed and verified for different types of sound source models(e.g., single loudspeaker, dual loudspeaker, and plate vibration source). The results show that the spiral array design, combined with compressive sensing techniques, effectively improves the accuracy of sound field reconstruction, with the CS-l_1 yielding the best performance in sound field reconstruction.

    摘要 2 Extended Abstract 3 INTRODUCTION 4 ACOUSTIC RECONSTRUCTION METHODS 5 Equivalent Source Method 6 Equivalent Source Estimation Method 8 Experimental Validation 9 RESULTS AND DISCUSSION 10 誌謝 12 目錄 14 表目錄 18 圖目錄 19 符號對照表 22 一、導論 23 1.1 研究動機與目的 23 1.2 文獻回顧 24 二、聲學理論 27 2.1 荷姆霍茲方程式 27 2.1.1 狀態方程式 27 2.1.2 動量方程式 28 2.1.3 連續方程式 30 2.1.4 線性波動方程式 31 2.1.5 荷姆霍茲方程式 32 2.2 近場聲音成像法 33 2.2.1 等效聲源法 33 2.2.2 最小平方法 36 2.2.3 壓縮感知 37 三、聲音成像模擬 40 3.1 麥克風陣列設計 40 3.1.1 方形麥克風陣列 40 3.1.2 偽隨機螺旋陣列 40 3.2 測試聲源模型介紹 42 3.2.1 單極子聲源 42 3.2.2 偶極子聲源 43 3.2.3 直線四極子聲源 44 3.2.4 平板聲源 44 3.3 模擬配置 46 3.3.1 模擬過程與步驟 46 3.3.2模擬雜訊與訊噪比 49 3.4 模擬結果 51 3.4.1 最小平方法之侷限性探討 51 3.4.2 單極子聲源模擬結果與討論 53 3.4.3 偶極子聲源模擬結果與討論 56 3.4.4 直線四極子聲源模擬結果與比較 59 3.4.5 平板聲源模擬結果與比較 63 四、聲音成像實驗 69 4.1 數位式麥克風陣列設計 69 4.1.1 數位麥克風 70 4.1.2 串接型梳狀積分濾波器 71 4.1.3 濾波器參數選用 74 4.2 單揚聲器實驗 76 4.2.1 實驗場景設計 76 4.2.2 實驗結果分析與討論 76 4.3 雙揚聲器實驗 79 4.3.1 實驗場景設計 79 4.3.2 實驗結果分析與討論 81 4.4 平板振動聲源實驗 85 4.4.1 實驗場景設計 85 4.4.2 平板振動模態 87 4.4.3 實驗結果分析與討論 89 五、結論與未來展望 91 5.1 研究結論 91 5.2 未來展望 92 參考文獻 93

    [1] J. D. Maynard, E. G. Williams, and Y. Lee, “Nearfield acoustic holography: I. Theory of generalized holography and the development of NAH,” J. Acoust. Soc. Am., vol. 78, no. 4, pp. 1395–1413, Oct. 1985.
    [2] P. M. Morse, H. Feshbach, and E. L. Hill, “Methods of theoretical Physics,” American Journal of Physics, vol. 22, no. 6, pp. 410–413, Sep. 1954.
    [3] E. Fernandez-Grande, A. Xenaki, and P. Gerstoft, “A sparse equivalent source method for near-field acoustic holography,” The Journal of the Acoustical Society of America, vol. 141, no. 1, pp. 532–542, Jan. 2017.
    [4] Z. Prime and C. Doolan, “A comparison of popular beamforming arrays,” Proc. ACOUSTICS, 2013.
    [5] L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, “Fundamentals of Acoustics, 4th Edition,” ISBN 0-471-84789-5. Wiley-VCH, 1999.
    [6] A. M. Pasqual, “A patch near-field acoustical holography procedure based on a generalized discrete Fourier series,” Mechanical Systems and Signal Processing, vol. 90, pp. 285–297, Jun. 2017.
    [7] E. G. Williams and J. A. Mann, “Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography,” The Journal of the Acoustical Society of America, vol. 108, no. 4, pp. 1373–1373, Oct. 2000.
    [8] Per Christian Hansen, Discrete Inverse Problems. 2010.
    [9] S. Boyd and L. Vandenberghe, Convex Optimization. 2004.
    [10] M. Donadio, “CIC Filter Introduction,” 2000.
    [11] A. V. Oppenheim and R. W. Schafer, Discrete-Time signal Processing. 1989.
    [12] M. Bellanger, "Multirate digital signal processing," in IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 32, no. 4, pp. 941-941, August 1984.
    [13] 許哲維, 基於FPGA平台與數位麥克風陣列之聲學相機實現, 碩士論文, 逢甲大學, 台中, 台灣, 2016.
    [14] F. Duvigneau, S. Koch, R. Orszulik, E. Woschke, and U. Gabbert, “About the Vibration Modes of Square Plate-like Structures,” vol. 36, no. 3, pp. 180–189, Jan. 2016.
    [15] J. B. Fahnline and G. H. Koopmann, “A numerical solution for the general radiation problem based on the combined methods of superposition and singular-value decomposition,” The Journal of the Acoustical Society of America, vol. 90, no. 5, pp. 2808-2819, Nov. 1991.
    [16] Y. Zhang and N. Xiang, “The Use of Equivalent Source Method in Computational Acoustics,” J. Vib. Control, vol. 22, no. 19, Oct. 2016.
    [17] J. Arteaga, “Improved source reconstruction in Fourier-based Near-field acoustic holography applied to small aperture,” Journal of Sound and Vibration, vol. 331, no. 7, pp. 1622-1635, Mar. 2012.
    [18] J. Hald, “Scaling of plane-wave functions in statistically optimized near-field acoustic holography,” The Journal of the Acoustical Society of America, vol. 136, no. 5, pp. 2687-2696, 2014.
    [19] A. T. Wall, K. L. Gee, and T. B. Neilsen, “Multisource statistically optimized near-field acoustical holography,” The Journal of the Acoustical Society of America, vol. 137, no. 2, pp. 963-975, Feb. 2015.
    [20] Y.-B. Zhang, F. Jacobsen, C.-X. Bi, and X.-Z. Chen, “Near field acoustic holography based on the equivalent source method and pressure-velocity transducers,” The Journal of the Acoustical Society of America, vol. 126, no. 3, pp. 1257–1263, Sep. 2009.
    [21] G. Chardon, L. Daudet, A. Peillot, F. Ollivier, N. Bertin, and R. Gribonval, “Near-field acoustic holography using sparse regularization and compressive sampling principles,” The Journal of the Acoustical Society of America, vol. 132, no. 3, pp. 1521–1534, Sep. 2012.
    [22] K. Chelliah, G. Raman, and R. T. Muehleisen, “An experimental comparison of various methods of nearfield acoustic holography,” Journal of Sound and Vibration, vol. 403, 2017.
    [23] Brüel & Kjær, “Spatial Transformation of Sound Fields (STSF),” Brüel & Kjær Technical Review, no. 1, 1986.
    [24] J. R. Underbrink, “Circularly symmetric, zero redundancy, planar array having broad frequency range applications,” U.S. Patent no. 6,205,224, 2001.
    [25] D. Tan, Z. Chu, and G. Wu, “Robust reconstruction of equivalent source method based near-field acoustic holography using an alternative regularization parameter determination approach,” The Journal of the Acoustical Society of America, vol. 146, no. 1, pp. EL34–EL38, Jul. 2019.
    [26] E. G. Williams, “Regularization methods for near-field acoustical holography,” The Journal of the Acoustical Society of America, vol. 110, no. 4, pp. 1976–1988, Oct. 2001.

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