Reliability evaluation and control for wideband noise-excited viscoelastic systems

• The reliability for wideband noise-excited viscoelastic systems is investigated.
• A procedure is proposed and proves to be accurate and efficient.
• The viscoelasticity improves the system reliability.
• The quasi-optimal bounded control for maximizing reliability is derived.
• The control strategy is illustrated to be effective.

Reliability of first-passage type for wideband noise-excited viscoelastic systems and the quasi-optimal bounded control strategy for maximizing system reliability are investigated. The viscoelastic term is approximately replaced by equivalent damping and stiffness separately. By using the stochastic averaging method based on the generalized harmonic functions, the averaged Itô stochastic differential equation is obtained for the system amplitude. The associated backward Kolmogorov equation is derived and solved to obtain the system reliability. By applying the dynamic programming principle to the averaged system, the quasi-optimal bounded control is devised by maximizing system reliability. The application of the proposed analytical procedures and the effectiveness of the control strategy are illustrated through one example.