Evidence-theory-based kinematic uncertainty analysis of a dual crane system with epistemic uncertainty

蒙特卡罗方法 运动学 泰勒级数 摄动(天文学) 数学 区间算术 区间(图论) 应用数学 微扰理论(量子力学) 不确定度量化 算法 数学分析 统计 物理 经典力学 组合数学 量子力学 有界函数
作者
Bin Zhou,Bin Zi,Yiming Zeng,Weidong Zhu
出处
期刊:Journal of Computing and Information Science in Engineering [ASM International]
卷期号:22 (2)
标识
DOI:10.1115/1.4052005
摘要

Abstract An evidence-theory-based interval perturbation method (ETIPM) and an evidence-theory-based subinterval perturbation method (ETSPM) are presented for the kinematic uncertainty analysis of a dual cranes system (DCS) with epistemic uncertainty. A multiple evidence variable (MEV) model that consists of evidence variables with focal elements (FEs) and basic probability assignments (BPAs) is constructed. Based on the evidence theory, an evidence-based kinematic equilibrium equation with the MEV model is equivalently transformed to several interval equations. In the ETIPM, the bounds of the luffing angular vector (LAV) with respect to every joint FE are calculated by integrating the first-order Taylor series expansion and interval algorithm. The bounds of the expectation and variance of the LAV and corresponding BPAs are calculated by using the evidence-based uncertainty quantification (UQ) method. In the ETSPM, the subinterval perturbation method (SIPM) is introduced to decompose original FE into several small subintervals. By comparing results yielded by the ETIPM and ETSPM with those by the evidence theory-based Monte Carlo method (ETMCM), numerical examples show that the accuracy and computational time of the ETSPM are higher than those of the ETIPM, and the accuracy of the ETIPM and ETSPM can be significantly improved with the increase of the number of FEs and subintervals.

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