Interval Uncertainty Quantification for the Dynamics of Multibody Systems Combing Bivariate Chebyshev Polynomials with Local Mean Decomposition

Abstract

Interval quantification for multibody systems can provide an accurate dynamic prediction and a robust reliability design. In order to achieve a robust numerical model, multiple interval uncertain parameters should be considered in the uncertainty propagation of multibody systems. The response bounds obtained by the bivariate Chebyshev method (BCM) present an intensive deterioration with the increase of time history in the interval dynamic analysis. To circumvent this problem, a novel method that combines the bivariate Chebyshev polynomial and local mean decomposition (BC-LMD) is proposed in this paper. First, the multicomponent response of the system was decomposed into the sum of several mono-component responses and a residual response, and the corresponding amplitude and phase of the mono-component were obtained. Then, the bivariate function decomposition was performed on the multi-dimensional amplitude, phase, and residual to transform a high-dimensional problem into several one-dimensional and two-dimensional problems. Subsequently, a low order Chebyshev polynomial can be used to construct surrogate models for the multi-dimensional amplitude, phase, and residual responses. Then, the entire coupling surrogate model of the system can be established, and the response bounds of the system can be enveloped. Illustrative examples of a slider-crank mechanism and a double pendulum are presented to demonstrate the effectiveness of the proposed method. The numerical results indicate that, compared to the BCM, BC-LMD can present a tight envelope in the long time-dependent dynamic analysis under multiple interval parameters.

Transformation of Mathematical Model for Complex Object in Form of Interval Difference Equations to a Differential Equation

“…At the same time, advantages of obtaining mathematical model based on its identification using interval data are obvious, since the very process of model identification is solving an optimization problem using universal and welldeveloped methods [26][27][28][29][30]. One more advantage of such approach is that built mathematical models take into account errors in data on the base of application of interval data analysis [31][32][33][34]. In this case, mathematical model is built in the form of a difference equation, which ensures the calculation of object characteristic estimates in the form of numerical intervals [21,34,35].…”

“…One more advantage of such approach is that built mathematical models take into account errors in data on the base of application of interval data analysis [31][32][33][34]. In this case, mathematical model is built in the form of a difference equation, which ensures the calculation of object characteristic estimates in the form of numerical intervals [21,34,35]. It should be noted that optimization task of identification of such model is quite complex from mathematical point of view.…”