Reliability and sensitivity analysis for bearings considering the correlation of multiple failure modes by mixed Copula function

Wang, Xingang; Wang, Bingxiang; Chang, Miaoxin; Li, Lei

doi:10.1177/1748006x19876137

Cited by 5 publications

(7 citation statements)

References 35 publications

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“…When calculating the reliability of a specific mechanical system, the multivariate Gauss Copula function [29]and the Archimedes Copula function are usually selected to deal with the correlation problem.…”

Section: B Reliability Model Of Series Mechanical Systemmentioning

confidence: 99%

Dynamic Reliability Evaluation of High-Speed Train Gearbox Based on Copula Function

Liu

Chen

2022

IEEE Access

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As a key component of the high-speed train transmission system, the reliability of the gearbox directly affects the reliability and driving safety of the high-speed train. Taking the key parts in the gearbox: driving gear, driven gear, gearbox housing and bearing as the research object, the dynamic reliability of the gearbox is evaluated. First, combined with classical stress-strength interference theory, the number of stochastic loads is regarded as a Poisson process, and the strength degradation is described by the Gamma process, the Gamma strength degradation parameter of each part is determined from the part material or the part's P-S-N curve, and the reliability model of each key part of the gearbox is obtained. Second, the gearbox is regarded as a series system, and the Gumbel Copula function is introduced to deal with the nonlinear correlation between different parts and between different failure modes of the same part. The nesting relationship of the Copula function is determined, the parameter values of the Gumbel Copula function are determined based on the kernel density estimation and maximum likelihood estimation method, so as to establish the dynamic reliability model of the gearbox system and realize the evaluation of the dynamic reliability of the gearbox. The evaluation results show that the method for evaluating the reliability of high-speed train gearboxes is in line with engineering practice. The evaluation method has practical significance for the reliability check, optimization design and dynamic tracking of the gearbox reliability during the service period of the high-speed train gearbox.

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Section: B Reliability Model Of Series Mechanical Systemmentioning

confidence: 99%

Dynamic Reliability Evaluation of High-Speed Train Gearbox Based on Copula Function

Liu

Chen

2022

IEEE Access

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“…Solving the maximum point of the formula (25), the maximum likelihood estimation value 􏽢 θ of the unknown parameters θ in the copula function can be obtained as 1.…”

Section: Copula Function Eorymentioning

confidence: 99%

“…When calculating the reliability of a specific mechanical system, the multivariate Gaussian Copula function [25] and the Archimedes Copula function are usually selected to deal with the correlation problem.…”

Section: Reliability Model Of the Series Mechanical Systemmentioning

confidence: 99%

Dynamic Fatigue Analysis of High-Speed Trains Gearbox Using Copula Function

Liu

Chen

et al. 2022

Mathematical Problems in Engineering

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As a key component of the transmission system of high-speed trains, the reliability of gearbox is crucial to the overall reliability and driving safety of high-speed trains. In this work, a comprehensive reliability model for the key parts of the gearbox including the driving and driven gears, bearings, and gearbox housing is developed, which combines the strength degradation parameters obtained by P-S-N curves of the corresponding material, and a stress-strength interference model based on the Poisson distribution of random stress and the Wiener strength degradation process. Further, a nested Copula function reliability model of the gearbox series system is developed using the binary Frank Copula function considering the correlation of failures of different parts and different failure modes. This model realizes the dynamic reliability analysis of the gearbox under different failure modes. The reliability analysis of the key parts of the gearbox and the gearbox series system of high-speed train achieved with this model are in line with the engineering practice. This method enables dynamic tracking and monitoring of gearbox reliability during the service life of high-speed train.

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“…In addition, since it is difficult to accurately describe the complex correlation among multiple failure modes using a single join model, several researchers thus attempted to construct mixed copula functions to provide a better description. [37][38][39] Wang et al 38 applied the Clayton copula, Gumbel copula, and Frank copula to establish a reliability model for a rolling bearing. Jiang et al 39 established a mixed copula model using the linear weighting method in the structural reliability analysis.…”

Section: Introductionmentioning

confidence: 99%

A mixed-copula-based integral method for reliability analysis of a novel multi-functional rescue end-effector

Wang

Xia

Wang

et al. 2023

Advances in Mechanical Engineering

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To improve the performance of a conventional rescue equipment, we designed a novel multi-functional rescue end-effector comprising a separation mechanism and a grasping mechanism. The failure causes of the separation mechanism are analyzed, and three main failure modes are determined. Meanwhile, their performance functions are established as well. To solve the complex correlations among multiple failure modes, a novel mixed copula function that can capture the upper and lower tail dependencies simultaneously is proposed, which comprises the Gumbel copula and the Clayton copula. Further, a novel procedure that adopts the non-parametric kernel density estimation (NKDE) technique to estimate the probability density function (PDF) and the cumulative distribution function (CDF) for each performance function of the separation mechanism is proposed. The parameters of the mixed copula function are estimated using the method of maximum likelihood estimation. Subsequently, to further study the separation mechanism’s reliability during working, a time-variant parameter estimation method is introduced to build the time-variant mixed copula function. Finally, both the reliability and time-variant reliability of the separation mechanism are analyzed via the proposed integral methods. Comparisons with other analysis schemes show that the proposed integral method is not only effective but also efficient in analyzing the reliability of our target mechanism.

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Reliability and sensitivity analysis for bearings considering the correlation of multiple failure modes by mixed Copula function

Cited by 5 publications

References 35 publications

Dynamic Reliability Evaluation of High-Speed Train Gearbox Based on Copula Function

Dynamic Reliability Evaluation of High-Speed Train Gearbox Based on Copula Function

Dynamic Fatigue Analysis of High-Speed Trains Gearbox Using Copula Function

A mixed-copula-based integral method for reliability analysis of a novel multi-functional rescue end-effector

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