Non-probabilistic stability reliability measure for active vibration control system with interval parameters

A systematic non-probabilistic reliability analysis procedure for structural vibration active control system with unknown-but-bounded parameters is proposed. The state-space representation of active vibration control system with uncertain parameters is presented. Compared with the robust control theory, which is always over-conservative, the reliability-based analysis method is more suitable to deal with uncertain problem. Stability is the core of the closed-loop feedback control system design, so stability criterion is adopted to act as the limited state function for reliability analysis. The uncertain parameters without enough samples are modeled as interval variables. Interval perturbation method is employed to estimate the interval bounds of eigenvalues, which can be used to characterize the stability of the closed-loop active control system. Formulation of defining the reliability of active control system based on stability is discussed. A novel non-probabilistic reliability measurement index is discussed and used to determine the probability of the stability based on the area ratio. The feasibility and efficiency of the proposed method are demonstrated by two numerical examples.