Novel Method for Selection of Regularization Parameter in the Near-field Acoustic Holography

Abstract

Because of the ill-posedness of the near-field acoustic holography(NAH),the regularization method is required to stabilize the computational process of NAH.The regularization effect is related to how to select the parameter correctly and effectively.However the L-curve method commonly used for the selection of regularization parameters has the disadvantages of wrong selection and incorrect selection,which influences the application of NAH.For the purpose of solving the problems existed in the L-curve method,the (?)-curve method is introduced into the field of NAH,and the performance applied to NAH directly is analyzed on the basis of equivalent source method-based NAH.However,it is found out via investigations that the(?)-curve method in NAH also has the problem of wrong selection and is unable to choose the regularization parameter correctly.In order to select the parameter correctly and effectively,a novel method for selecting regularization parameters is proposed based on the original(?)-curve method,which can be called improved (?)-curve method.In the proposed method the regularization parameters are discretized linearly between the largest singular value and the smallest singular value,and the solution norm and the residual norm corresponding to these regularization parameters are also described in a linear coordinate instead of in a lg-lg coordinate,which are the two main differences compared with the L-curve and with the original(?)-curve method.In linear coordinate and using the linearly discretized regularization parameters,the solution norm is a monotonically decreasing function of the residual norm as the increase of the regularization parameter,moreover the curve is convex everywhere.So the regularization parameters can be selected correctly and effectively based on the improved(?)-curve method.Then a numerical simulation is done with a simply supported plate to verify the validity of the proposed method.Experiments with two actual sources,a clamped plate and the double speakers,are carried out to do a further demonstration.The simulation result as well as the experimental result shows that the improved(?)-curve method is efficacious and has some advantages over the L-curve method and the original(?)-curve method.The proposed novel method is able to avoid the problem of wrong selection and to select the regularization parameter correctly even if the curve is smooth.