Stochastic optimal design of nonlinear viscous dampers for large-scale structures subjected to non-stationary seismic excitations based on dimension-reduced explicit method

Nonlinear fluid viscous dampers have been widely used in energy-dissipation structures. This paper is devoted to the stochastic optimal design of viscous dampers for large-scale structures under non-stationary random seismic excitations. The optimization problem is formulated as the minimization of the standard deviation of a target displacement component subjected to the constraint on the standard deviations of damping forces of viscous dampers, and the method of moving asymptotes (MMA), a gradient-based optimization method, is employed to solve the optimization problem involved. An effective dimension-reduced explicit method is first proposed for fast nonlinear time-history analysis of structural responses and the corresponding sensitivity analysis with respect to the parameters of viscous dampers, in which only a small number of degrees of freedom associated with the viscous dampers need to be considered in the iteration scheme, leading to extremely low computational cost in the nonlinear analysis. Then the proposed dimension-reduced explicit method is further used to conduct sample analyses with high efficiency in Monte-Carlo simulation (MCS) so as to obtain the statistical moments of critical responses and the relevant moment sensitivities required in the process of optimal design. To demonstrate the feasibility of the proposed method, the stochastic optimal design of viscous dampers is carried out for a large-scale suspension bridge with a main span of 1688 m, and the mean peak values of critical responses with the optimal parameters of viscous dampers are finally obtained for the design purpose of the bridge.