Optimal Design of Uncertain Systems Under Stochastic Excitation

Abstract

The structural synthesis problem of uncertain linear systems subjected to uncertain loads is considered. Uncertain system parameters are modeled as random variables with a prescribed joint probability density function, whereas the loads are modeled as stochastic processes. Second-order probabilistic descriptors are combined with approximate extreme response theories to obtain reliability estimates for the systems. A multicriterion optimal design methodology, based on a preference aggregation rule, is used in this formulation. Optimization is carried out by generating and solving a sequence of explicit approximate problems. The uncertainty in system parameters is taken explicitly in the analysis, and its effect is investigated on the optimal design. It is shown that uncertainties are important because they can change the system reliability significantly. Therefore, in these cases, the effect of uncertainty in the model parameters must be considered explicitly during the design process. An example problem is presented to illustrate the performance of the proposed methodology.

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