A new APSO-SPC method for parameter identification problem with uncertainty caused by random measurement errors

Peng Zhong; Xuanlong Wu; Li Zhu; Aohao Yang; Peng Zhong; Xuanlong Wu; Li Zhu; Aohao Yang

doi:10.3934/math.2025179

AIMS Mathematics

2025, Volume 10, Issue 2: 3848-3865. doi: 10.3934/math.2025179

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A new APSO-SPC method for parameter identification problem with uncertainty caused by random measurement errors

State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian 116024, China

Received: 03 November 2024 Revised: 29 December 2024 Accepted: 15 January 2025 Published: 26 February 2025
MSC : 68T20, 91G60

In parameter identification problem, errors are common in measurement data, resulting in uncertainty in the identified parameters. Traditional deterministic methods cannot address this uncertainty. A novel approach, which integrates an advanced particle swarm optimization algorithm (APSO) and the stochastic perturbation collocation method (SPC), is proposed to address this issue, called APSO-SPC for short. The APSO algorithm improves the heterogeneous comprehensive learning particle swarm optimization algorithm (HCLPSO) based on the dynamic evolution sequence (DES), improving computational efficiency for each deterministic parameter identification process. Furthermore, the SPC method accurately estimates the means and standard deviations of uncertain parameters. Three numerical examples demonstrate the accuracy and efficiency of the APSO-SPC method in assessing parameter uncertainties caused by random measurement errors.
Citation: Peng Zhong, Xuanlong Wu, Li Zhu, Aohao Yang. A new APSO-SPC method for parameter identification problem with uncertainty caused by random measurement errors[J]. AIMS Mathematics, 2025, 10(2): 3848-3865. doi: 10.3934/math.2025179

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Abstract

In parameter identification problem, errors are common in measurement data, resulting in uncertainty in the identified parameters. Traditional deterministic methods cannot address this uncertainty. A novel approach, which integrates an advanced particle swarm optimization algorithm (APSO) and the stochastic perturbation collocation method (SPC), is proposed to address this issue, called APSO-SPC for short. The APSO algorithm improves the heterogeneous comprehensive learning particle swarm optimization algorithm (HCLPSO) based on the dynamic evolution sequence (DES), improving computational efficiency for each deterministic parameter identification process. Furthermore, the SPC method accurately estimates the means and standard deviations of uncertain parameters. Three numerical examples demonstrate the accuracy and efficiency of the APSO-SPC method in assessing parameter uncertainties caused by random measurement errors.

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