Stochastic System Design Optimization using Stochastic Simulation

Engineering design in the presence of uncertainties often involves optimization problems that include as objective function the expected value of a system performance measure, such as expected life-cycle cost or failure probability. For complex systems, this expected value can rarely be evaluated analytically. In this study, it is calculated using stochastic simulation techniques which allow explicit consideration of nonlinear characteristics of the system and excitation models, as well as complex failure modes. At the same time, though, these techniques involve an unavoidable estimation error and significant computational cost which make the associated optimization challenging. An efficient framework, consisting of two stages, is presented here for such optimal system design problems. The first stage implements a novel approach, called Stochastic Subset Optimization, for iteratively identifying a subset of the original design space that has high plausibility of containing the optimal design variables. The second stage adopts some stochastic optimization algorithm to pinpoint, if needed, the optimal design variables within that subset. Topics related to the combination of the two different stages for overall enhanced efficiency are discussed. An illustrative example is presented that shows the efficiency of the proposed methodology; it considers the retrofitting of a four-story structure with viscous dampers. The minimization of the expected lifetime cost is adopted as the design objective. The expected cost associated with damage caused by future earthquakes is calculated by stochastic simulation using a realistic probabilistic model for the structure and the ground motion