Two-dimensional extreme distribution for estimating mechanism reliability under large variance
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Two-dimensional extreme distribution for estimating mechanism reliability under large variance Zhi-Hua Wang1,2 • Zhong-Lai Wang1,2
•
Shui Yu1,2
Received: 20 October 2019 / Revised: 5 December 2019 / Accepted: 26 May 2020 Ó Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The effective estimation of the operational reliability of mechanism is a significant challenge in engineering practices, especially when the variance of uncertain factors becomes large. Addressing this challenge, a novel mechanism reliability method via a two-dimensional extreme distribution is investigated in the paper. The time-variant reliability problem for the mechanism is first transformed to the time-invariant system reliability problem by constructing the two-dimensional extreme distribution. The joint probability density functions (JPDFs), including random expansion points and extreme motion errors, are then obtained by combining the kernel density estimation (KDE) method and the copula function. Finally, a multidimensional integration is performed to calculate the system time-invariant reliability. Two cases are investigated to demonstrate the effectiveness of the presented method. Keywords Time-variant reliability Great variance Twodimensional Extreme distribution Kernel density estimation (KDE) Multidimensional Integration
& Zhong-Lai Wang [email protected] 1
School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
2
Center for System Reliability and Safety, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
1 Introduction Mechanisms, as important components in mechatronic systems, are designed to achieve the desired performance under working conditions. However, the actual mechanism outputs usually fluctuate around the desired performance because of the uncertainties from the design, manufacturing, assembling and operational processes [1–3]. The corresponding random errors necessitate reliability analysis of the mechanism to ensure operational safety [4]. Mechanism reliability is basically defined as the probability that the outputted performance of a mechanism with uncertainties falls inside the acceptable error boundaries [5]. Since stochastic degradation, time-dependent stochastic working conditions, and stochastic motion exist in the mechanism, the outputted performance is time-varying and uncertain, and the theory of random process can be employed for reliability analysis [6–8]. Some instantaneous reliability analysis methods have been proposed to perform reliability analysis at a given time point. For example, Wang et al. [9] developed a hybrid dimension reduction method to predict mechanism reliability, including the uncertainty of the joint clearance. Zhao and Ono [10] proposed an eigenvalue dimension reduction approach for mechanism reliability. However, the instantaneous reliability cannot indicate the operational sa
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