Stochastic optimization of uncertain viscous dampers for energy-dissipation structures under random seismic excitations

•An effective analysis framework is proposed for stochastic optimization of nonlinear viscous dampers for energy-dissipation structures.•Both random seismic excitations and uncertain damper parameters are considered in the stochastic optimization framework.•The repetitive nonlinear time-history response and sensitivity analyses involved in MCS are conducted using the efficient explicit time-domain method.•The present approach is applied to the stochastic optimal design of nonlinear viscous dampers installed on a suspension bridge.