An adaptive scheme for reliability-based global design optimization: A Markov chain Monte Carlo approach

The reliability-based design of structural dynamic systems under stochastic excitation is presented. The design problem is formulated in terms of the global minimization of the system failure probability. The corresponding optimization problem is solved by an effective stochastic simulation scheme based on the transitional Markov chain Monte Carlo method. Although the scheme is quite general, is computationally very demanding due to the large number of reliability analyses required during the design process. To cope with this difficulty, an advanced simulation technique is combined with an adaptive surrogate model for estimating the failure probabilities. In particular, a kriging meta-model is selected in the present formulation. The algorithm generates a set of nearly optimal solutions uniformly distributed over a neighborhood of the optimal solution set. Such set can be used for exploration of the global sensitivity of the system reliability. Several illustrative examples are presented to investigate the applicability and effectiveness of the proposed design scheme.