Design and sensitivity analysis of dynamical systems subjected to stochastic loading

The paper presents an efficient procedure which allows to carry out reliability-based optimization of linear systems subjected to stochastic loading. The optimization problem is replaced by a sequence of approximate explicit sub-optimization problems that are solved in an efficient manner. Approximation concepts are used to construct high quality approximations of dynamic responses during the optimization process. The approximations are combined with efficient simulation methods to generate explicit approximations of reliability measures in terms of the design variables. The number of dynamic analyses required for the convergence of the design process is reduced dramatically. An efficient sensitivity analysis with respect to the optimization variables and general system parameters becomes possible with the proposed formulation. The sensitivity is evaluated by considering the behavior of the design when the parameters vary within a bounded region. The analysis can identify the degree of robustness of the final design with respect to variations of selected system parameters. A numerical example in terms of a 26-story reinforced concrete building under stochastic earthquake excitation exemplifies the proposed methodology.