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

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 method. In the ETSPM, the subinterval perturbation method 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, 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.

Rough Set Analysis of the Heat Conduction in the Steam Pipe

During the analysis of stability heat conduction in the composite pipes, firstly, when the heat equation contained fuzzy and random uncertain parameters, interval equations of the heat conduction are presented in the rough set. Secondly, the error expecting of heat conduction equation is presented. Finally, with upper (lower) approximation in rough set, a new method of the rough set analysis to deal with the stability heat conduction is presented.

A Method for Static Interval Analysis of Uncertain Structures with Interval Parameters

By representing the uncertain parameters as interval numbers, the static linear interval equations about the structural system were obtained in this paper by means of the finite element method. These equations are linear interval equations, for which some solution methods were discussed and a step-dividing method was presented. In this method, the independent uncertain parameters were given the discrete values within each interval, and the linear interval equations were changed into the corresponding certain ones. And then the boundaries of every interval solution components are determined by searching for the maximum and minimum values of the equation solutions. Some mathematical examples were used to examine the correctness and efficiency of the algorithm and which was applied to static interval analysis of engineering problems. Compared with other methods, the calculation results show that the algorithm of this paper is efficient and accurate.