近场声全息正则化方法比较

Comparison of Regularization Methods of Nearfield Acoustic Holography

为了正确选择正则化方法,在基于边界元方法的近场声全息理论基础上,分析了截断奇异值法和Tikhonov正则化方法的异同点,阐述了通过曲率求解L曲线拐角点的基本原理,并将L曲线准则和广义交叉检验法应用于截断奇异值正则化方法最优截断点的选取.通过数值仿真表明,利用L曲线最大曲率点可以有效地确定L曲线最优正则化参数位置;在基于边界元法的共形平面近场声全息中,当信噪比为60 dB时,4种组合正则化方法在1 000 Hz频率点处分辨距离能达到42 mm.最后,比较研究了4种组合正则化方法的重构精度和稳健性.

The selection of regularization methods is the key issue on the boundary element method （ BEM ）-based nearfield acoustic holography （ NAH ）. The characteristics of the truncated singular value decomposition （ TSVD ） method and standard Tikhonov regularization method were discussed respectively. The L-curve criterion and the generalized cross validation （ GCV ） method were both employed to attain the optimal regularization parameters for Tikhonov and TSVD regularization method. Furthermore, the maximum curvature of L-curve is used to determine the regularization parameter of the L-curve criterion. A numerical simulation of a speaker is taken as an example. The numerical results demonstrate the validity of the maximum curvature of L-curve applied in L-curve criterion. It can also be concluded that a signal noise ratio （ SNR ） of about 60 dB would lead to the resolution distance of 42 mm at the frequency of 1 000 Hz. Finally, the accuracy and limitation of four combined regularization methods are investigated.