Multi-parameter Tikhonov regularization-based OTPA with application to ship-radiated noise evaluation

The purpose of this study is to reduce the errors caused by the inversion of the transfer function (TF) matrix when evaluating ship-radiated noise by operational transfer path analysis. The singular value decomposition (SVD), generalized cross validation (GCV), and L-curve methods are separately introduced to evaluate the TF matrix, and the performances are compared. In order to overcome the shortcomings of the aforementioned methods and further reduce the errors, the optimized multi-parameter (M-P) Tikhonov regularization method based on the criterion of condition number is proposed to create an optimal regularization parameter to evaluate the TF matrix herein. The feasibility is verified with a double-layer cylindrical shell model experiment in Thousand Islets Lake. The obtained results indicate that the average error of M-P Tikhonov regularization is reduced by up to 0.38 dB compared with that of the L-curve, 0.68 dB compared with that of the GCV, and 1.34 dB compared with that of the SVD under various combinations of noise levels, which can provide guidance for ship-radiated noise evaluation in engineering applications.