New approaches in reliability based optimization of tuned mass damper in presence of uncertain bounded parameters

Abstract

This work deals with control of vibrating structures using tuned mass damper (TMD) in presence of uncertain bounded structural parameters. The adopted optimization strategy of the TMD parameters is the reliability based optimization (RBO) where the failure probability, approximated with the classical Rice’s formula, is related to the primary structure displacement. In presence of uncertain bounded structural parameters it is convenient to describe them using intervals. Consequently, the optimized failure probability is also defined over an interval.In this paper a continuous-optimization nested loop method (CONLM) is presented to provide the exact range of the optimum TMD parameters and their corresponding failure probabilities. The CONLM is time consuming; in this context an approximation method using the monotonicity-based extension method (MBEM) with box splitting is also proposed. Therefore, the initial non-deterministic optimization problem can be transformed into two independent deterministic sub-problems involving discrete-optimization nested loop rather than the continuous-optimization nested loop used in the CONLM. The effectiveness and robustness of the presented optimum bounds of the TMD parameters are investigated and a performance index is introduced. The numerical results obtained with a one degree of freedom and a multi-degree of freedom systems subject to different seismic motions have shown the efficiency of the proposed methods, even with high level of uncertainties. Besides, the good robustness of the TMD device when it is exactly tuned on the optimum TMD parameters corresponding to the deterministic structural parameters has been proven.