Reliability-Based Design Using Two-Stage Stochastic Optimization with a Treatment of Model Prediction Errors

Design problems that involve optimization of the reliability of engineering systems are the focus of this paper. Methodologies are discussed applicable to problems that involve nonlinear systems and a large number of uncertain parameters specifying the system and excitation models. To address the complexity of these problems, stochastic simulation is considered for evaluation of the system reliability. An innovative approach, called stochastic subset optimization (SSO), is discussed for performing a sensitivity analysis with respect to the design variables of the problem as well as the uncertain model parameters. In a small number of iterations, SSO converges to a smaller subset of the original design space that has high plausibility of containing the optimal design variables and that consists of near-optimal designs. For higher accuracy, an appropriate stochastic optimization algorithm may then be used to pinpoint the optimal design variables within this subset. This produces an efficient two-stage framework for optimal reliability design. Topics related to the combination of the two different stages for overall enhanced efficiency are discussed. An example is presented that illustrates the effectiveness of the proposed two-stage methodology for a challenging dynamic reliability problem. Also, a study is performed of the influence on the optimal design decisions of the prediction error of the system model, which is introduced because no model makes perfect predictions of the system response