Non-probabilistic time-variant reliability assessment (NTRA) for the active control of vibration systems with convex uncertainties.

Uncertainties, such as material dispersion, loading fluctuation and cognitive inconsistency, widely exist in active vibration control systems, and more importantly, the controller performance is generally sensitive to the parametric deviation. Thus, the uncertainty-oriented safety assessment for the controlled structure is of great significance in practical engineering. In view of the limitation of uncertain samples, a novel non-probabilistic time-variant reliability assessment (NTRA) approach, which combines the set-theoretical convex model and the first-passage method, is proposed for vibration suppression problems under the linear quadratic regulator (LQR) control scheme. Boundary rules and the time-dependency features of the controlled responses are first determined using the space-state transformation and the convex process theory. For safety reasons, a new time-variant reliability index is defined under the area-ratio principle, and its solution details are further discussed. Two engineering examples and one experimental case are presented to demonstrate the validity and applicability of the developed methodology.