Robust Mass Damper Design using Stochastic Simulation

Mass dampers (for example, TMDs or TLCDs) are widely used for suppression of structural vibrations. Their design is based on the adjustment of their parameters, referred to herein as design variables, to the dynamic characteristics of the coupled damper-structure system. Uncertainty in the parameters of the model considered for the system significantly influences the effectiveness of this design. Prior knowledge about the system is quantified in this study by specifying probability distributions for the uncertain model parameters. The objective function for optimal design is chosen to be maximization of the systems reliability against failure, an appropriate concept for applications that involve uncertainty. Failure is defined to be exceedance of limit states for some of the systems response quantities that are important. Stochastic simulation is used to evaluate the systems response to efficiently address the high complexity that exists in many applications of mass dampers and to overcome the limitations related to analytical approximations when there are non-linearities (e.g associated with TLCDs or base-isolated civil structures) or when there is a need to consider transient response. The use of stochastic simulation for the calculation of the objective function, however, significantly increases the computational cost for the required optimization with respect to the design variables. An efficient approach is proposed for this task. It combines two algorithms suggested for simulation-based optimization: the Stochastic Subset Optimization, for identification of a set that icludes the design variables, and the Simultaneous Perturbation Stochastic Averaging with common random numbers, for pinpointing the optimal solution inside the identified set. Examples are presented that show the efficiency of the proposed design for cases with model uncertainty. The suggested techniques have applications to a large variety of excitations and simple or complex systems