Structural optimization of linear dynamical systems under stochastic excitation: a moving reliability database approach

A method to carry out structural synthesis of deterministic linear dynamical systems under stochastic excitation is introduced. The structural optimization problem is written as a nonlinear mathematical programming problem with reliability constraints. Probability that design conditions are satisfied within a given time period is used as a measure of system reliability. The solution of the original optimization problem is replaced by the solution of a sequence of approximate sub-optimization problems. An explicit approximation of the system reliability in terms of the design variables is constructed in each sub-optimization problem. The approximations are locally adjusted to a reliability database, which is obtained by an efficient importance sampling technique. Each approximate optimization problem is solved in an efficient manner due to the availability of the system reliability in explicit form. Numerical examples are presented to illustrate the performance and efficiency of the proposed methodology.