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This paper discusses a probabilistic framework for performance assessment and optimal design of floor isolation systems for the protection of acceleration sensitive contents. A multi-objective formulation is considered for the optimization problem with the two competing objectives corresponding to (i) maximization of the level of protection offered to the sensitive content (acceleration reduction) and (ii) minimization of the demand for appropriate clearance to avoid collision to surrounding objects (floor displacement reduction). Uncertainties are addressed by characterizing these objectives in terms of the associated seismic risk, whereas a surrogate modeling approach is developed to evaluate this risk and support the design optimization. As an illustrative example, the design of a polynomial friction pendulum isolator system is presented. The formulation is demonstrated to efficiently provide design solutions with different performance levels across the considered competing objectives, offering a range of options for selecting the final protection system.

Probabilistic approaches for cost-effective design of fluid viscous dampers for seismic hazard mitigation are gaining increasing attention within the structural engineering community, especially in the context of retrofitting strategies. A systematic probabilistic framework is presented here for this purpose, optimizing the dampers in a multi-objective setting considering life-cycle cost criteria. The framework is based on an assembly-based vulnerability approach for the earthquake loss estimation that uses the nonlinear time-history response of the structure under given excitation to estimate damages in a detailed, component level. Characterization of the earthquake hazard through a stochastic ground motion model is considered in this context. The parameters of these models are connected to the regional seismicity characteristics through predictive relationships. Description of the uncertainty for those characteristics and for the predictive relationships, by appropriate probability models, leads then to a complete probabilistic description of the seismic hazard. The life-cycle repair cost is then quantified by its expected value over the space of the uncertain parameters for the structural system and the seismic excitation. Additionally, the upfront cost of the dampers is calculated based on their capacity required for the maximum credible earthquake, with the latter calculated to correspond to a certain probability of exceedance based on the established probabilistic description for the earthquake hazard. Because of the complexity of the adopted models, estimation of all necessary probabilistic quantities (expected repair cost and reference velocities) though stochastic (Monte Carlo) simulation is considered. The multi-objective problem is defined by considering the following two objectives: (a) minimization of the expected life-cycle cost composed of the combination of the upfront damper cost and the present value of future earthquakes losses, and (b) minimization of the probability that during the lifetime of the structure the repair cost for a single event will exceed a specific threshold, defined by the stakeholders of the structure. Since the latter is not influenced by the upfront damper cost these two ultimately correspond to competing objective (thus the multi-objective problem is well posed). To facilitate an efficient optimization for different threshold selections, and support their truly free choice from the system stakeholders, a innovative search technique is developed. This technique is based on calculation of the structural response (corresponding to the most computationally demanding task) only once, and not separately for each threshold defined. This approach similarly allows for an efficient optimization under different design scenarios corresponding to the seismic hazard. An illustrative example is presented that considers the retrofitting of a three story building with viscous dampers.