Efficient reliability-based design optimization of dynamic linear systems subjected to filtered white-noise inputs

Abstract

This paper presents a reliability-based design optimization methodology for dynamic linear structural systems, subjected to filtered white-noise excitations. A novel double-loop approach is proposed, where both inner and outer optimization problems are efficiently solved using gradient-based algorithms, combining a specifically-tailored adjoint method for the sensitivity analyses, while the reliability analyses are carried out using the first-order-reliability-method (FORM). Key to the proposed approach is that the mean-square of the responses of interest is efficiently evaluated via the Lyapunov equations, which leads to faster and more efficient reliability-based designs. The application of the methodology is demonstrated in three examples in which control systems are optimized. First, a serviceability limit-state function is considered for a footbridge subjected to crowd load excitation. The footbridge vibrations are controlled by viscous dampers and tuned-mass dampers. Second, a limit-state function is considered for a bending moment frame, undergoing a seismic event. The interstorey drifts of the frame are controlled one time by viscous dampers and another time by tuned-mass-dampers. Third, a large benchmark frame is optimized. Verification of the probability of failure achieved via the first-order-reliability-method is performed using Monte Carlo simulations (MCS), showing good agreement between the two methods. A clear resemblance is shown between optimal design achieved via zero-order method, although with significantly reduced computational cost.