A Kriging Approach for the Probability of Failure Minimization in FTMD Design

Abstract

This paper aims at presenting an efficient approach for the optimal design of friction tunned mass damper (FTMD) devices under uncertainties. The objective function of the optimization problem is the maximization of structural reliability, which is approximated here as an out-crossing problem. The solution of the equations of motion of the FTMD system leads to a nonlinear dynamical problem, which coupled with the time dependent reliability problem, requires a substantial computational effort. An additional complexity is that the design of a multiple FTMD system is nonlinear and leads to a multimodal optimization problem. In order to address the issues of computational cost and multi-modality, an Efficient Global Optimization (EGO) method with Expected Improvement as infill criterion is employed. The results showed that the EGO was able to successfully provide the optimum solution of the FTMD design under uncertainty within a reasonable computational effort. For example, using only 80 points, the EGO algorithm was able to consistently find the optimum solution for all the cases analyzed in this paper. One aspect that is worth to be highlighted is that these results were obtained in problems with a relatively high stochastic dimension, e.g. over 30 random variables.