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

Abstract

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.