Modeling Multibody Systems with Uncertainties. Part I: Theoretical and Computational Aspects
Modeling Multibody Systems with Uncertainties. Part I: Theoretical and Computational Aspects
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DOI：
10.1007/s11044-006-9007-5
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发表时间：
2006-06
影响因子：
3.4
通讯作者：
Adrian Sandu;C. Sandu;M. Ahmadian
中科院分区：
文献类型：
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作者：
Adrian Sandu;C. Sandu;M. Ahmadian
本研究探讨了利用广义多项式混沌理论对存在参数不确定性和外部不确定性的复杂非线性多体动力学系统进行建模。多项式混沌框架之所以被选择，是因为它为工程系统的大型、非线性多体模型提供了一种有效的计算方法，其中不确定参数的数量相对较少，而不确定性的大小可能非常大(例如，车辆-土壤相互作用)。该方法可以量化不确定度在时间域和频域的分布，并使多体系统的仿真结果具有“误差条”。本研究的第一部分介绍了多项式混沌方法的理论和计算方面。同时考虑了多体动力学的无约束公式和约束公式。直接随机配置法是一种比传统Galerkin法更便宜的方法。证明了随机配置法与随机响应面方法是等价的。我们证明了多维基函数被构造为一维基函数的张量积，并讨论了多项式和三角非线性的处理。参数不确定性用有限支撑概率密度来建模。随机强迫用截断的卡尔胡宁-洛夫展开式离散。配套论文《具有不确定性的多体动力学系统建模》。第二部分：数值应用“说明了所建议的方法在选定的一组测试问题上的使用。总体结论是，尽管多项式混沌有其局限性，但对于具有不确定性的多体系统的仿真是一种有效的方法。
This study explores the use of generalized polynomial chaos theory for modeling complex nonlinear multibody dynamic systems in the presence of parametric and external uncertainty. The polynomial chaos framework has been chosen because it offers an efficient computational approach for the large, nonlinear multibody models of engineering systems of interest, where the number of uncertain parameters is relatively small, while the magnitude of uncertainties can be very large (e.g., vehicle-soil interaction). The proposed methodology allows the quantification of uncertainty distributions in both time and frequency domains, and enables the simulations of multibody systems to produce results with “error bars”. The first part of this study presents the theoretical and computational aspects of the polynomial chaos methodology. Both unconstrained and constrained formulations of multibody dynamics are considered. Direct stochastic collocation is proposed as less expensive alternative to the traditional Galerkin approach. It is established that stochastic collocation is equivalent to a stochastic response surface approach. We show that multi-dimensional basis functions are constructed as tensor products of one-dimensional basis functions and discuss the treatment of polynomial and trigonometric nonlinearities. Parametric uncertainties are modeled by finite-support probability densities. Stochastic forcings are discretized using truncated Karhunen-Loeve expansions. The companion paper “Modeling Multibody Dynamic Systems With Uncertainties. Part II: Numerical Applications” illustrates the use of the proposed methodology on a selected set of test problems. The overall conclusion is that despite its limitations, polynomial chaos is a powerful approach for the simulation of multibody systems with uncertainties.