Tradeoff analysis of non-linear dynamical systems under stochastic excitation

An efficient methodology to carry out multi-objective optimization of non-linear structural systems under stochastic excitation is presented. Specifically, an efficient determination of particular Pareto or non-inferior solutions is implemented. Pareto solutions are obtained by compromise programming which is based on the minimization of the distance between the point that contains the individual optima of each of the objective functions and the Pareto set. The response of the structural system is characterized in terms of the first two statistical moments of the response process, i.e. the mean and variance. An efficient sensitivity analysis of non-inferior solutions with respect to the design variables becomes possible with the proposed formulation. Such information is used for decision making and tradeoff analysis. The compromise programming problem is solved by an efficient procedure that combines a local statistical linearization approach, modal analysis, global approximation concepts, and a sequential optimization scheme. Numerical results show that the total number of stochastic analyses required during the multi-objective optimization process is in general very small. Hence, different compromise solutions including the design that best represents the outcome that the designer considers potentially satisfactory are obtained in an efficient manner. In this way, the analyst can conduct a decision-making analysis through an efficient interactive procedure.