Framework for Robust Design Optimization of Tuned Mass Dampers by Stochastic Subset Optimization

This study is focused on robust design optimization (RDO) of the tuned mass dampers (TMDs), which are widely used as a passive vibration controller in structural systems. The performance of the TMDs designed under the implicit assumption that all relevant system parameters (such as loading and structural characteristics) are deterministic is greatly affected by the inevitable inherent uncertainties in the system parameters. In this regard, a framework is proposed for the RDO of TMDs to determine its optimal solution which is less sensitive to system parameter variability. RDO is defined as a multi-objective optimization problem that aims to minimize the mean and variance of the performance function. In the case of multiple TMDs, the proposed framework uniquely avoids the presumption of their mass distribution, number, and placement location. In the proposed RDO framework, an augmented formulation is adopted wherein the design parameters are artificially introduced as uncertain variables with some prescribed probability density function (PDF) over the design space. The resulting optimization problem is solved using the stochastic subset optimization (SSO) and KN, a direct search optimization method. The effectiveness of the proposed framework is studied by analyzing four illustrative examples involving a single TMD attached to a single-degree-of-freedom (SDOF) structure, a single TMD attached to a multiple-degree-of-freedom (MDOF) structure, multiple TMDs attached to an MDOF structure, and an 80-story structure equipped with multiple TMDs.