Uncertain reduced-order modeling via balanced truncation for structural dynamic systems with interval parameters

摘要

To well retain the uncertainty characteristics of the original complex system during the model reduction process, a balanced truncation-based model reduction method for uncertain structural dynamic systems with interval parameters is proposed in this paper. Three different interval propagation analysis approaches, i.e., the first-order interval Taylor series expansion method, the interval vertex approach and the interval collocation method are employed to approximately estimate the lower and upper bounds of the system matrices, the Hankel singular values and the responses of the original system as well as the reduced-order model. The major characteristic of the proposed model reduction method is that the reduced-order model obtained in this way is also as uncertain as the original model. The proposed methods are applied in the reduced-order modeling of a fourth-order single-input-single-output linear time-invariant system and a mass-spring-damper vibration system with interval parameters, and the applicability and accuracy of the methods are demonstrated by considering different uncertainty levels. Results also indicate that the proposed method can provide a more robust and reasonable approximation of the original uncertain system compared with conventional deterministic model reduction approaches. model reduction; interval uncertainties; interval collocation method; interval vertex theorem; first-order interval Taylor series expansion.