基于 L-曲线参数优化的均匀声场重建算法

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。

Uniform sound field reconstruction algorithm based on L-curve parameter optimization

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.