Page 124 - 《应用声学》2020年第1期

第 39 卷 第 1 期 Vol. 39, No. 1
2020 年 1 月 Journal of Applied Acoustics January, 2020

⋄ 研究报告 ⋄

基于L-曲线参数优化的均匀声场重建算法

张 旭 1 赵洪亮 2† 程希光 1 裴景春 2

(1 山东科技大学电子信息工程学院 青岛 266590)
(2 山东科技大学电气与自动化工程学院 青岛 266590)

摘要：为了得到最小二乘法声场重建问题的稳定解，通常需要引入 Tikhonov 正则化方法。然而正则化程度取
决于正则化参数的选择。针对这一问题，提出了一种基于 L-曲线法参数选择的均匀声场重建算法。该算法根
据重建误差与扬声器功率计算得到 L-曲线，该曲线上曲率最大的点所对应的参数值作为 Tikhonov 正则化参
数的选值。确定正则化参数后可进一步得到扬声器权系数以及重建均匀声场。针对不同正则化参数取值方法，
对控制区域进行均匀声场重建以及重建性能仿真。仿真结果及实验表明，L-曲线法实现了重建误差与扬声器
驱动信号功率之间的平衡。
关键词：声场重建；L-曲线法；Tikhonov 正则化参数；最小二乘法
中图法分类号: O422.2 文献标识码: A 文章编号: 1000-310X(2020)01-0120-08
DOI: 10.11684/j.issn.1000-310X.2020.01.015

Uniform sound field reproduction algorithm based on L-curve parameter

optimization

ZHANG Xu 1 ZHAO Hongliang 2 CHENG Xiguang 1 PEI Jingchun 2

(1 College of Electronic and Information Engineering, Shandong University of Science and Technology, Qingdao 266590, China)
(2 College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China)

Abstract: Tikhonov regularization method is a common method to solve the ill-posed problem in sound field
reproduction with stable solutions. However, the degree of regularization depends on the proper selection of
regularization parameters. To solve this problem, a uniform sound field reproduction algorithm based on L-
curve parameter selection is proposed. This method plots the L-curve according to the norm of reproduction
error versus the norm of the loudspeaker power. The point with the largest curvature on this curve is selected
as the Tikhonov regularization parameter. After determining the regularization parameters, the loudspeaker
power coefficients can be obtained and hence the uniform sound field can be reproduced. A simulation study is
performed to reproduce the sound field of the controlled area with different regularization parameters and the
reproductive performance is evaluated. The simulation and experiment results show that the L-curve method
achieves a balance between the reproduction error and the power of the loudspeaker driving signal.
Keywords: Sound field reconstruction; L-curve method; Tikhonov regularization parameters; Least squares
method

2019-05-05 收稿; 2019-11-28 定稿
作者简介: 张旭 (1995– ), 女, 山东济南人, 硕士研究生, 研究方向: 信号与信息处理。
† 通信作者 E-mail: zhl6401p@126.com