Game theory-based maximum likelihood method for finite-element-model updating of civil engineering structures

Finite element modelling is performed to numerically predict the behaviour of civil engineering structures. Due to the different assumptions adopted during the modelling phase, this initial model does not always reflect adequately the actual structural behaviour. In this context, the results of experimental structural dynamic properties can be used to improve initial numerical model via the implementation of the so-called finite element model updating method. After this process, the updated model better reflects the actual structural behaviour. Due to its simplicity, for practical engineering applications, the updating process is usually performed consid- ering the maximum likelihood method. According to this approach, the updating problem may be formulated as the combination of two sub-problems: (i) a bi-objective optimization sub-problem; and (ii) a decision-making sub-problem. The bi-objective function is usually defined in terms of the residuals between the experimental and numerical modal properties. As optimization method, nature-inspired computational algorithms have been usually considered due to their high efficiency to cope with non-linear optimization problems. Despite this extensive use, this method presents two main limitations: (i) the high simulation time required to compute the Pareto optimal front; and (ii) the necessity of solving a subsequent decision making problem (the selection of the best solution among the different elements of the Pareto front). In order to overcome these limitations, in this paper game theory has been adopted as computational tool to improve the performance of the updating process. For this purpose, the updating problem has been re-formulated as a game theory problem considering three different game models: (i) non-cooperative; (ii) cooperative; and (iii) evolutionary. Finally, the performance of proposal has been assessed when it is implemented for the model updating of a laboratory footbridge. As result of this study, game theory has been shown up as efficient tool to improve the performance of the updating process under the maximum likelihood method since it allows a direct estimation of the solution reducing the simulation time without compromising the accuracy of the result.