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Robust optimum design of base isolation system in seismic vibration control of structures under uncertain bounded system parameters

The optimum design of a base isolation (BI) system in the framework of total probability theory cannot be applied in many real situations when the required detailed information about the uncertain parameters are limited and the maximum possible ranges of variations are only known and can be modeled as an uncertain but bounded type. The interval analysis based bounded design optimization usually applied in such cases are the worst case measures and unsuitable for practical design. Moreover, such a design method does not consider the variation of the performance of an isolated system due to uncertainty and may not correspond to an optimum design yielding maximum performance with its minimum dispersion. The robust optimization requiring only the bounds on the magnitude of the uncertain parameters will be a viable alternative in such situations. The present study deals with the robust optimization of BI system for seismic vibration mitigation of structures characterized by bounded uncertain parameters. The robust optimization is performed by using a two-criteria equivalent optimization problem, where the weighted sum of the nominal value of the maximum root mean square acceleration of the superstructure and its dispersion is optimized. The bounded design optimization is also performed to demonstrate the effectiveness of the proposed robust optimization approach. A five-storied building frame with attached isolator elucidates the effectiveness and importance of the proposed design approach by comparing the present robust optimization results with the results obtained by the bounded design optimization procedure.