Research on the Indirect Solution Optimization Regularization Method for Ship Mechanical Excitation Force

Yao, Zhenyu; Xu, Rongwu; Zhang, Jiarui; Peng, Tao; Li, Ruibiao

doi:10.3390/app151810238

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Open AccessArticle

Research on the Indirect Solution Optimization Regularization Method for Ship Mechanical Excitation Force

by

Zhenyu Yao

^*,

Rongwu Xu

,

Jiarui Zhang

,

Tao Peng

and

Ruibiao Li

Institute of Power Engineering, Naval University of Engineering, Wuhan 430033, China

^*

Author to whom correspondence should be addressed.

Appl. Sci. 2025, 15(18), 10238; https://doi.org/10.3390/app151810238

Submission received: 6 August 2025 / Revised: 9 September 2025 / Accepted: 17 September 2025 / Published: 19 September 2025

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The optimization regularization method proposed in this paper has achieved very good results in solving the indirect calculation problem of excitation force in the field of ships.

Abstract

Accurate identification of mechanical excitation forces is of great significance for the control of ship radiated noise and structural design. Currently, the identification of excitation forces mostly relies on indirect calculations, which suffer from ill-conditioned problems. Regularization correction is one of the main means to solve this problem. Although regularization methods have been widely developed, their application in the field of ships is relatively rare. Currently, the commonly used methods are truncation singular values and Givonov regularization methods. This paper starts from the practical application of ships and addresses the problem of poor correction effect of traditional regularization methods. Two optimized regularization methods, quasi-optimal discriminant criterion and B-spline interpolation function method, are proposed. These methods are verified through simulations and experiments. The results of the scaled model experiments show that compared with using the L-curve alone, the Q-O method reduces the regularization error by 29%, while the BL curve improves the robustness by 38% under a 15 dB noise condition.

Keywords: Ill-posed problem; regularization; quasi-optimality criterion; B-spline interpolation

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MDPI and ACS Style

Yao, Z.; Xu, R.; Zhang, J.; Peng, T.; Li, R. Research on the Indirect Solution Optimization Regularization Method for Ship Mechanical Excitation Force. Appl. Sci. 2025, 15, 10238. https://doi.org/10.3390/app151810238

AMA Style

Yao Z, Xu R, Zhang J, Peng T, Li R. Research on the Indirect Solution Optimization Regularization Method for Ship Mechanical Excitation Force. Applied Sciences. 2025; 15(18):10238. https://doi.org/10.3390/app151810238

Chicago/Turabian Style

Yao, Zhenyu, Rongwu Xu, Jiarui Zhang, Tao Peng, and Ruibiao Li. 2025. "Research on the Indirect Solution Optimization Regularization Method for Ship Mechanical Excitation Force" Applied Sciences 15, no. 18: 10238. https://doi.org/10.3390/app151810238

APA Style

Yao, Z., Xu, R., Zhang, J., Peng, T., & Li, R. (2025). Research on the Indirect Solution Optimization Regularization Method for Ship Mechanical Excitation Force. Applied Sciences, 15(18), 10238. https://doi.org/10.3390/app151810238

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Research on the Indirect Solution Optimization Regularization Method for Ship Mechanical Excitation Force

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