A multi‐objective framework for finite element model updating using incomplete modal measurements

Abstract

Summary Finite element (FE) model updating in multi‐objective framework helps for better understanding of overall performance in updating (under various variations of weightages assigned to basic components of the objective function) along with providing scope for better judgmental selection. A FE model updating in multi‐objective framework is proposed with no requirement of repeated eigen‐solution along with avoiding repeated possibilities of incurring mode‐pairing error (by adopting an existing framework of system mode shape). Two multi‐objective optimization techniques are adopted: (a) weighted sum and (b) adaptive weighted sum methods. Moreover, a possible single best solution out of the Pareto front is identified based on minimum modal distance value and compared with Gibbs sampling technique (without mode‐matching). Two examples with multiple damage cases utilized in validating the proposed approach are as follows: (a) simulated example (ASCE benchmark structure) and (b) experimental example (four storied shear frame laboratory structure). It is observed that the proposed multi‐objective framework has performed well in FE model updating in case of both simulated and experimental cases. Additionally, a connection (directly relating the multi‐objective weights and error variances) is established between the proposed updating methodology and an existing Bayesian updating methodology to facilitate the probabilistic damage detection in Bayesian framework. Moreover, selection of an appropriate solution (out of the Pareto front) having suitable values of multi‐objective weights facilitates to estimate the suitable values of error variances (based on the proposed connection), consequently enabling an efficient Bayesian FE model updating without requirement of any assumption of error variances.

A fraction function regularization model for the structural damage identification

“…The structural damage identification methods have been extensively researched in recent years. Among them, vibration-based methods are intensively interested because of their easy operation and non-destructive nature (Hou and Xia, 2020; Debnath and Das, 2021; Chen et al, 2019; Wang et al, 2021; Zhu et al, 2014) The basic idea of these methods is that the vibration characteristics (such as modal frequencies and mode shapes) of the structure will change when the damage occurs (Cui et al, 2018a; Wang et al, 2021). Model updating is a widely utilized way in vibration-based damage identification methods.…”

A joint fraction function regularization model for the structural damage identification

“…At present, there are many commonly used damage identification methods, such as manual visual damage identification methods (Kim et al, 2017), vibration-based damage identification methods, and image-based damage identification methods (Gao and Mosalam, 2018). Among them, vibration-based methods have been extensively studied because of their advantages of identifying internal structural damages without destruction (Hou and Xia, 2020;Debnath and Das, 2021;Goyal and Pabla, 2016;Chen, et al, 2023b). The vibration-based methods include model updating method (Mottershead and Friswell, 1993) and dynamic fingerprint method (Sun et al, 2019), among which, the model updating method (Sun et al, 2013;Xu et al, 2012;Chatzi and Smyth, 2009) has become one of the main methods for structural damage identification due to its strong interpretability and operability.…”