Structural finite element model updating optimization based on game theory

Abstract

To describe the behaviour of civil engineering structures numerically, the finite element model is usually used. The obtained numerical model can be used for various purposes, such as damage detection, establishment of structural health monitoring, prediction of structural life and so on. During numerical modelling, various assumptions and idealizations are introduced into the model, which means that the developed numerical model may not reflect the actual structural behaviour. To solve this problem, the numerical model is updated based on the results obtained as a part of its experimental investigation. These results may be displacements, stresses, structural dynamic properties, or data and results obtained as a part of the structural health monitoring (SHM). Most often, the finite element model updating is performed using the experimentally obtained structural dynamic parameters according to the maximum likelihood method. The mentioned maximum likelihood method is based on the transformation of the finite element model updating problem into an optimization problem. It consists in minimizing the objective function (single or multiobjective) using an optimization algorithm. In this paper, the basics of the potential of solving the FEMU optimization problem by applying the game theory are presented. First, the advantages and disadvantages of defining the FEMU optimization problem using single and multi-objective functions and existing optimization algorithms are highlighted. To show the capabilities of game theory in solving optimization problems, the different game models and their solution strategies are analyzed.