Performance measures and optimal design of linear structural systems under stochastic stationary excitation

The optimal design of linear structural systems under stochastic, stationary dynamic excitation is discussed. Several measures are considered for quantification of the stochastic performance, including the standard H2H2 and multi-objective H2H2 measures related to the second-order statistics of the response, as well as a measure related to first-passage system reliability. Of these, first-passage reliability is the performance measure most closely aligned with the design of Civil Engineering structures, but it is also the least analytically-tractable. This paper discusses the evaluation and optimization of these performance measures, including an efficient approximation to first-passage reliability, and examines the degree to which the optimal structural design, and its reliability, vary when the optimization is carried out under these different measures. For the reliability-optimal design, the effect of the spatial and temporal correlation of multiple out-crossing events is investigated. An example is presented, which considers the optimal configuration of viscous dampers for protection of a five storey structure under earthquake excitation.