Reliability-based Optimal Design by Efficient Stochastic Simulation

Reliability-based design requires the optimization of the probability of failure, over the admissible space for the design variables. This probability can rarely be evaluated analytically and so it is often calculated using stochastic simulation techniques, which involve an unavoidable estimation error and significant computational cost. These features make efficient reliability-based optimal design a challenging task, especially for dynamic problems with stochastic excitation, where the models used are typically complex. A new method called Stochastic Subset Optimization is proposed here for iteratively identifying sub-regions for the optimal design variables within the original design space. An augmented reliability problem is formulated where the design variables are artificially considered as uncertain and Markov Chain Monte Carlo simulation is implemented in order to draw samples of them that lead to failure. In each iteration, a set with high probability of containing the optimal design parameters is identified using a single reliability analysis. Statistical properties for the identification and stopping criteria for the iterative approach are discussed. The set optimization can be combined with any stochastic search optimization algorithm for enhanced overall efficiency. Simultaneous-perturbation stochastic approximation with common random numbers is used in this study for this purpose and a complete framework for efficient reliability-based optimization is discussed. An illustrative example is presented that shows the efficiency of the proposed methodology