An Efficient Polynomial Chaos Method for Stiffness Analysis of Air Spring Considering Uncertainties

Traditional methods for stiffness analysis of the air spring are based on deterministic assumption that the parameters are fixed. However, uncertainties have widely existed, and the mechanic property of the air spring is very sensitive to these uncertainties. To model the uncertainties in the air spring, the interval/random variables models are introduced. For response analysis of the interval/random variables models of the air spring system, a new unified orthogonal polynomial expansion method, named as sparse quadrature-based interval and random moment arbitrary polynomial chaos method (SQ-IRMAPC), is proposed. In SQ-IRMAPC, the response of the acoustic system related to both interval and random variables is approximated by the moment-based arbitrary orthogonal polynomial expansion. To efficiently calculate the coefficient of the interval and random orthogonal polynomial expansion, the sparse quadrature is introduced. The proposed SQ-IRMAPC was employed to analyze the mechanic performance of an air spring with interval and/or random variables, and its effectiveness has been demonstrated by fully comparing it with the most recently proposed orthogonal polynomial-based interval and random analysis method.

Sparse quadrature for high-dimensional integration with Gaussian measure

In this work we analyze the dimension-independent convergence property of an abstract sparse quadrature scheme for numerical integration of functions of high-dimensional parameters with Gaussian measure. Under certain assumptions on the exactness and boundedness of univariate quadrature rules as well as on the regularity assumptions on the parametric functions with respect to the parameters, we prove that the convergence of the sparse quadrature error is independent of the number of the parameter dimensions. Moreover, we propose both an a priori and an a posteriori schemes for the construction of a practical sparse quadrature rule and perform numerical experiments to demonstrate their dimension-independent convergence rates.