Reliability-based-design-optimization of base isolated buildings considering stochastic system parameters subjected to random earthquakes

Base isolation (BI) is established as an effective control strategy for improving seismic performance of structures. The studies on performance of BI system under stochastic earthquake load are notable. However, most of the studies consider system parameters as deterministic and the optimal isolator characteristics are obtained accordingly. A major limitation of such deterministic approach is that the uncertainties in the performance related decision variables cannot be included in the parameters optimization process. But, the safety of a BI system can be significantly affected due to uncertainty in the system parameters. The present study deals with the Reliability-Based-Design-Optimization (RBDO) of BI system to mitigate seismic vibration effects considering system parameter uncertainty. With the aid of matrix perturbation theory and first order Taylor series expansion, the concept of total probability theory is used to evaluate the unconditional response of structures under parameter uncertainty. For this, the conditional second order information of responses is obtained in the random vibration framework. Subsequently, the unconditional failure probability of the primary structure is used as the objective function in order to obtain the optimum parameters of the isolator. The proposed design is tolerant to the uncertainty and provides estimate of the enhanced risk unforeseen in the deterministic system. A multistoried building frame isolated by Lead-Rubber-Bearing (LRB) is taken up for numerical illustration and to elucidate the effect of parameter uncertainty on the optimum performance of BI system.