Determining the Best Pareto-solution in a Multi-Objective Approach for Model Updating

Abstract

<p>Using a multi-objective optimization algorithm avoid the use of weighting factors to balance the different residuals in a finite element model updating procedure under the maximum likelihood method. By using this approach, the fittest model is not unique and a set of solutions that form a curve, so-called Pareto optimal front, is obtained. Within this paper, first a review of the state of the art on the criteria used to determine the most adequate model among all the solutions of the Pareto front is presented. Subsequently, a case study of a real footbridge is considered. A finite element model of the footbridge is updated based on its experimental modal parameters. The Non- Dominated Sorting Genetic Algorithm is used to obtain the Pareto front. Since all the solutions in the Pareto front are non-dominated, the selection of the best candidate requires a reasonable criterion. Herein, different procedures to select the best updated model are discussed.</p>

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“…Hence, a subsequent decision making problem must be addressed in order to select the best solution among the different elements of the Pareto front. Among the different criteria provided in literature (Infantes et al, 2019), the normal boundary intersection (NBI) method has been considered herein (Deb and Gupta, 2011).…”

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“…The method for obtaining a smart representation of solutions from Pareto fronts was used. In the proposed method, multi-objective Pareto front topology optimization is based on the weighted sum method for each criterion [39]. For the analyzed criteria, the relationship was assumed (14):…”

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“…advantage that it is not necessary to define the weights of the residuals, it has a clear drawback, a subsequent decision-making problem must be solved to select the best solution among the set of possible solutions (the so-called Pareto front) provided by the optimization algorithm. In order to solve this decision-making problem, the normal boundary intersection (NBI) method has been considered herein [24] among the different criteria provide in literature [25].…”