Discrete Robust Design Optimization of Stochastic Dynamical Systems

In this paper attention is directed to the reliability-based optimization of uncertain structural systems under stochastic excitation involving discrete sizing type of design variables. The reliability-based optimization problem is formulated as the minimization of an objective function subject to multiple reliability constraints. The probability that design conditions are satisfied within a given time interval is used as a measure of system reliability. The objective function and the reliability constraints are approximated by using a hybrid form of linear and reciprocal approximations. The approximations are combined with an efficient sensitivity analysis to generate explicit expressions of the reliability constraints in terms of the design variables. The explicit approximate primal problems are solved by an appropriate discrete optimization scheme. A numerical example showing the efficiency and effectiveness of the approach reported herein is presented.