基于二元维纳过程的小样本齿轮泵可靠寿命预测

摘要/Abstract

摘要： 提出了一种基于二元维纳过程的小样本齿轮泵可靠寿命预测方法。利用具有随机效应的维纳过程建立齿轮泵容积效率和总效率退化过程模型，表征了齿轮泵退化特征随时间的波动性和个体差异性。基于赤池信息量准则（AIC）筛选了合适的Copula函数来描述两个退化特征之间的相关关系。建立了二元退化模型，采用马尔可夫链蒙特卡罗（MCMC）方法进行了模型未知参数识别。针对齿轮泵性能退化试验通常是小样本的特点，利用Bootstrap抽样方法对表征个体差异的参数进行了再抽样估计。最后通过齿轮泵性能退化试验实现了可靠寿命预测，验证了所提方法的有效性与准确性。试验结果表明，齿轮泵性能退化过程中两个特征存在非线性相关关系，考虑相关关系的可靠寿命预测较单一特征预测结果更保守，且受最先达到失效阈值的性能特征影响更大。

关键词: 二元维纳过程, 寿命预测, 性能退化, 齿轮泵

Abstract: One kind of Q-precentile life prediction method for gear pumps with small sample sizes was proposed based on bivariate Wiener process.The degradation processes of volume efficiency and total efficiency for gear pumps were modeled by Wiener process with random effects, and the fluctuation of gear pump performance characteristics with time and individual differences were characterized.The appropriate Copula function was selected to describe the correlation between the two degradation performance characteristics based on Akaike information criterion(AIC). A bivariate degradation model was established and the unknown parameters of the model were estimated by Markov chain Monte Carlo(MCMC) method. The Bootstrap sampling method was used to re-sample the parameters representing individual differences by considering the facts that the performance degradation test of gear pumps was usually a small sample size. Finally, through gear pump performance degradation tests, the Q-precentile life prediction was realized, and the validity and accuracy of the proposed method were verified.The testing results show that there is a non-linear correlation between the two characteristics in the degradation processes. Q-precentile life prediction considering correlation is more conservative than single feature prediction, and is more affected by the performance characteristics that first reach the failure threshold.

Key words: bivariate Wiener process, life prediction, performance degradation, gear pump

中图分类号:

TH17

刘小平1,2;郭斌1,2;崔德军1,2;吴振宇1,2;张立杰1,2. 基于二元维纳过程的小样本齿轮泵可靠寿命预测[J]. 中国机械工程.

LIU Xiaoping1,2;GUO Bin1,2;CUI Dejun1,2;WU Zhenyu1,2;ZHANG Lijie1,2. Q-precentile Life Prediction Based on Bivariate Wiener Process for Gear Pumps with Small Sample Sizes[J]. China Mechanical Engineering.

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