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.

Li, R.; Bu, W., and Xu, R., 2020. Research on ship-radiated noise evaluation and experimental verification based on OTPA optimized by operating condition clustering. In: Liu, X. and Zhao, L. (eds.), Today's Modern Coastal Society: Technical and Sociological Aspects of Coastal Research. Journal of Coastal Research, Special Issue No. 111, pp. 326–330. Coconut Creek (Florida), ISSN 0749-0208.In terms of evaluating ship-radiated noise with operational transfer path analysis (OTPA), discordance occurs between the operating conditions and the linear system requirement of OTPA because of large dispersion between operating conditions, which leads to obvious estimated errors amid several frequency bands. Therefore, OTPA, which is optimized by operating condition clustering, is proposed to mitigate the errors; that is, all operating conditions are classified into several classes by the k-means method based on weighted principal-component analysis. Next, the operating conditions belonging to the same class that are similar to one other but maintain independence are taken as the input of OTPA. By this means, the nonlinear input question of OTPA can be solved. The feasibility of optimized OTPA is verified by a reduced-scale cabin experiment in Thousand Islet Lake. The obtained results indicate that the average cumulative error yielded by optimized OTPA is reduced by up to 1.79 dB compared with traditional OTPA. In addition, the average maximum absolute error is reduced by up to 6 dB. Furthermore, the statistical analysis of errors verifies the effectiveness and stability of optimized OTPA. Optimized OTPA can provide guidance for radiated noise evaluation in practical engineering applications, which is of importance for reducing ship-radiated noise pollution of the marine environment.