A Probabilistic Structural Damage Identification Method with a Generic Non-Convex Penalty

Rongpeng Li, Wen Yi, Fengdan Wang, Yuzhu Xiao, Qingtian Deng, Xinbo Li () and Xueli Song ()
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Rongpeng Li: School of Sciences, Chang’an University, Xi’an 710064, China
Wen Yi: School of Sciences, Chang’an University, Xi’an 710064, China
Fengdan Wang: School of Sciences, Chang’an University, Xi’an 710064, China
Yuzhu Xiao: School of Sciences, Chang’an University, Xi’an 710064, China
Qingtian Deng: School of Sciences, Chang’an University, Xi’an 710064, China
Xinbo Li: School of Sciences, Chang’an University, Xi’an 710064, China
Xueli Song: School of Sciences, Chang’an University, Xi’an 710064, China

Mathematics, 2024, vol. 12, issue 8, 1-17

Abstract: Due to the advantage that the non-convex penalty accurately characterizes the sparsity of structural damage, various models based on non-convex penalties have been effectively utilized to the field of structural damage identification. However, these models generally ignore the influence of the uncertainty on the damage identification, which inevitably reduces the accuracy of damage identification. To improve the damage identification accuracy, a probabilistic structural damage identification method with a generic non-convex penalty is proposed, where the uncertainty corresponding to each mode is quantified using the separate Gaussian distribution. The proposed model is estimated via the iteratively reweighted least squares optimization algorithm according to the maximum likelihood principle. The numerical and experimental results illustrate that the proposed method improves the damage identification accuracy by 3.98% and 7.25% compared to the original model, respectively.

Keywords: damage identification; model updating; non-convex function penalty; uncertainty; sparsity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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