Reliability-based performance optimization of TMD for vibration control of structures with uncertainty in parameters and excitation

Recent development of system identification using Bayesian models or stochastic filtering provides probabilistic descriptions (i.e., probability density function or statistical parameters like mean and variance) of the identified model parameters (e.g., mass, stiffness, and damping). Optimal design of passive controllers for these systems whose parameters are uncertain has remained an open problem. With this in view, the present study aims to develop numerical solution scheme for the optimal design of tuned mass damper (TMD) operating in uncertain environment. Deterministic design of TMD in these cases suffers detuning as the system parameters are random. Thus, a reliability-based design optimization (RBDO) scheme is presented in this paper for better performance of the TMD when exposed to uncertainties. To solve the RBDO problem, response surface methodology is used along with the moving least squares technique. Dual response surfaces are used for separate handling of optimization and reliability analysis. First response surface performs optimization of the design variables of TMD, while the second response surfaces are used for the estimation of the statistical properties like mean and variance to satisfy the constrained conditions. Numerical analysis is presented to show the effectiveness of the proposed algorithm for RBDO of single degree of freedom-TMD system as a proof of concept. The proposed meta-model-based algorithm can be applied for the optimal design of controller for large structures where conventional technique may face difficulty to handle both optimization and uncertainty quantification simultaneously. Copyright (C) 2016 John Wiley & Sons, Ltd.