A unified equivalent model of the l0 minimization model for structural damage identification

Sensitivity analysis-based structural damage identification can be transformed into solving the l0 minimization model (the original model) because damage typically occurs in a few sections or members especially at the early stage, making it spatially sparse. Many existing approximation models have a...

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Vydáno v:	Mechanical systems and signal processing Ročník 242
Hlavní autoři:	Song, Xueli, Ma, Xiao, Li, Rongpeng, Yi, Wen, Ma, Lingjuan, Zheng, Supei, Wang, Kaiming
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Ltd 01.01.2026
Témata:	Difference of convex functions algorithm Sensitivity analysis Sparsity base function minimization model Structural damage identification Unified equivalent model Structural damage identification Sparsity base function minimization model Difference of convex functions algorithm Unified equivalent model Sensitivity analysis
ISSN:	0888-3270
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Shrnutí:	Sensitivity analysis-based structural damage identification can be transformed into solving the l0 minimization model (the original model) because damage typically occurs in a few sections or members especially at the early stage, making it spatially sparse. Many existing approximation models have approximately solved the original model because it is NP-hard, by replacing the l0-norm with continuous sparsity-promoting functions, which inevitably reduces the accuracy of damage identification in theory. A unified nonconvex model, where sparsity base function fθ (θ>0 controls the tightness of approximation) replaces the l0-norm of the original model, is theoretically equivalent to the original model when parameter θ satisfies certain conditions. Inspired by this, this paper firstly proposes a unified equivalent model (named sparsity base function minimization model) for structural damage identification to theoretically eliminate the reduction of damage identification accuracy caused by approximately solving the original model. Secondly, a general optimization algorithm based on the Difference of Convex functions Algorithm and the Alternating Direction Method of Multipliers is designed to solve the proposed unified equivalent model, and a novel parameter selection strategy is proposed to select θ. Finally, the results of numerical simulations and experimental studies demonstrate that six specific forms of the proposed unified equivalent model outperform the l1 regularization model, the elastic net, and the l1/2 regularization model in terms of damage localization and quantification accuracy, respectively.
ISSN:	0888-3270
DOI:	10.1016/j.ymssp.2025.113621