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

Ruibiao Li,Wenjun Bu

doi:10.1063/5.0023867

Abstract

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.

Highlights

Ship-radiated noise refers to a multi-complex coupled noise source1 that is usually composed of mechanical,2 propeller,3 and hydrodynamic noise
The inverse condition is subject to limitations of the quantity of sensors and operational conditions, and an ill-condition matrix may lead to an unreliable transfer function (TF)
The core of that evaluating ship-radiated noise by operational transfer path analysis (OTPA) is to solve the TF matrix based on the training samples

Summary

Introduction

Ship-radiated noise refers to a multi-complex coupled noise source that is usually composed of mechanical, propeller, and hydrodynamic noise. Ship-radiated noise harms acoustic stealth and produces large amounts of pollution that affects marine organisms. ship-radiated noise evaluation in real-time can help on the control of vibration and noise, which is of great significance for improving comprehensive acoustic performance.6,7In the previous research of Guo et al. and Choi et al., operational transfer path analysis (OTPA) was used to evaluate shipradiated noise. OTPA is based on the “input response–transfer path–output response” model, which takes the self-noise and vibrational response of ships as the input response and the far-field radiated noise response as the output response. This model is widely used in the transmission of vibrational noise in mechanical systems, which focuses on solving problems such as the contribution of each noise source to the target through different transfer paths and structural load identification.. Subject to ship application conditions, the cross coupling between ship sources can lead to the inaccurate identification of transfer paths, which magnifies the estimated error of the TF by the SVD method. The measured input and output responses often include strong noise from the marine environment, which increases the estimated errors and instability of the TF. In addition, the inverse condition is subject to limitations of the quantity of sensors and operational conditions, and an ill-condition matrix may lead to an unreliable TF

Objectives

Results

Conclusion