Collaborative multi-objective design strategy of number and placement for structural vibration suppression components with correlated and bounded uncertainties

The optimization of structural vibration suppression components is of great significance to the active control of vibration and sound. For the active vibration control system with correlated and bounded uncertainty, this paper proposes a collaborative design strategy for the number and placement of structural vibration suppression components. The uncertainty is quantified as an interval parameter. The interval analysis of the active vibration control system is realized by the convex sets-based method. Analyzing the controllability and observability of the system, the Gramian criteria for the placement of structural vibration suppression components can be obtained. By propagating uncertainty based on convex sets, the bounds of eigenvalues for the Gramian criteria can be obtained. To optimize the number and placement of structural vibration suppression components, a collaborative design strategy is developed. This strategy first optimizes the number by comparing the Pareto Front with different component counts. On this basis, the multi-objective robust optimization for placement of component method is implemented by considering the interval and radius of the performance index. The feasibility of the collaborative multi-objective design strategy is demonstrated by two examples.