A non-probabilistic time-variant reliable control method for structural vibration suppression problems with interval uncertainties

•Non-probabilistic time-variant reliability-based optimization method is presented.•Time-varying UQ analysis achieved by the interval mathematics is conducted.•Novel reliability index for the safety estimation of the active control is defined. Active control techniques are necessary to structural vibration problems and thus studies of controller design are particularly important in mechanical dynamic engineering. Because parametric deviations due to inherent nature or external excitation are inevitable and can severely influence the final performance of real control systems, optimal active control considering uncertainty is gradually becoming a major concern in modern theory fields. In this paper, a novel non-probabilistic time-variant reliability-based optimization (NTRBO) strategy is presented for closed-loop controller design of vibration reduction issues. First, boundary rules and auto-correlation characteristics of controlled responses are confirmed based on the state-space transformation and the interval process approach. Then, enlightened by models of the first passage and the safety factor (SF), a new definition of the time-variant reliability measurement is provided. As keys to construct the optimal controller, weighing matrices in the Riccati equation are finally determined by solving the developed NTRBO model. The validity and the feasibility of the proposed methodology are demonstrated by several example applications, and the results reveal that uncertainty factors in optimal active control can be addressed from a new time-variant reliability perspective.