A novel joint sparse regularization model to structural damage identification by the generalized fused lasso penalty

Abstract

The sparse regularization (SReg) model is widely used for structural damage identification by employing the sparsity peculiarity of the structural damage. The conventional SReg model often separately conducts damage identification on each measurement, while ignores the utilization of the similarity information among different measurements. In this paper, we propose a novel joint sparse regularization model for structural damage identification. In detail, combined with the sparsity of the structural damage by the conventional SReg model, our model employs the similarity of different measurements to further improve the damage identification performance, which is realized by the generalized fused lasso penalty. Numerical simulations on the six-bay planar truss structure and experimental studies on the cantilever beam structure illustrate that the damage identification accuracy of our model is promoted 3.59% and 20.75% than the conventional SReg one, respectively.

A joint fraction function regularization model for the structural damage identification

“…Therefore, in the experimental study, the sparse regularization parameter β of the above two models is the same as the numerical study in this paper (i.e., β 2 ½0:005; 1). For the Joint-SReg model, since the experimental data is the same as the paper Li et al (2023c), the sparse regularization parameter β of the model can be selected by referencing the paper Li et al (2023c) (i.e., β = 0.0085). Figure 7 shows the comparison among the damage identification results estimated by the Joint-Fra-Reg model, the Joint-SReg model, the Fra-Reg model and the true damage, which are represented by Joint-Fra-Reg, Joint-SReg, Fra-Reg and True Damage, respectively.…”

“…Firstly, in this numerical study, the L -curve criterion is applied to select the optimal sparsity regularization parameter β in damage scenario 1 for the joint fraction function regularization model (10), joint sparse regularization model (Li et al, 2023c) and fraction function regularization model (Li et al, 2023b), respectively Hou et al (2018b); Yao et al (2011). Then the selected parameter was substituted into the corresponding model.…”

“…In fact, the fraction function regularizer can mitigate the drawback of the l 1 -norm regularizer by controlling the severity of the penalties and characterizes the sparsity of the structural damages better, which is more consistent with the spatial sparsity of actual structural damages. Moreover, the similarity among different measurements of the same modal parameter of the structure in a short time has been proved to be useful in the paper Li et al (2023c), where the similarity among different measurements is utilized through a data fusion technique to improve the accuracy of damage identification.…”

A fraction function regularization model for the structural damage identification

“…Although frequencies can be obtained handily and accurately, they are ordinarily insensitive to local damage, which usually causes the false damage localization. Based on the fact that mode shapes involve spatial information and are more sensitive to local damage, many studies employ both natural frequencies and mode shapes for damage identification (Hou et al, 2017(Hou et al, , 2021Chen and Yu, 2019;Li et al, 2022). Moreover, the l 1 regularization method is introduced to accurately identify sparse coefficient solution in Chen et al (2022), and the paper Hou et al (2018) studies the parameter selection method of the l 1 regularization model to further improve the damage identification accuracy.…”

Substructural damage identification using autoregressive moving average with exogenous inputs model and sparse regularization

“…Subsequently, sparse regularization was introduced into structural damage detection (Chen et al, 2021). Compared with the commonly used Tikhonov regularization, the damage identification accuracy is improved considerably when sparse regularization is used (Li et al, 2022).…”