Combined active learning Kriging with optimal saturation nonlinear vibration control for uncertain systems with both aleatory and epistemic uncertainties

This paper addresses the vibration control problems of uncertain systems with both random and multidimen-sional parallelepiped (MP) convex variables by uniting the optimal saturation nonlinear control (OSNC) and an active learning Kriging (ALK) method. This method can be named ALK-MP-OSNC. The dynamic equations of the controlled systems can be written in ODE forms, and the functions containing saturation nonlinearities on the right side of each of ODE equation can be approximately replaced via using the Kriging model. The efficiency of the Kriging model can be improved through combining the differential evolution (DE) global optimal algorithm with the distance constraint condition. A three-pendulum system, a satellite motion and a moving-mass beam system are employed to demonstrate the performance of the improved ALK-MP-OSNC. Results indicates that the proposed method can efficiently drive the uncertain pendulum system to a chaotic behavior and the other two uncertain systems to a periodic motion. The efficiency and the accuracy of the proposed method can be researched through comparing with the original ALK and the Monte Carlo simulation. In conclusion, the proposed method can be applied to complex engineering fields such as aerospace engineering, civil engineering, ocean engineering, and space deployable engineering.