分段确定性马尔可夫过程的疲劳裂纹增长预测应用
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- 英文论文题名：Application of Piecewise Deterministic Markov Process Model on Prediction of Fatigue Crack Growth
- 论文作者：姜学鹏 ; 洪贝 ; 丁海强 ; 乔勇军
- 英文论文作者：Jiang Xuepeng ; Hong Bei ; Ding Haiqiang ; Qiao Yongjun ; Naval Aeronautical and Astronautical University
- 年：2016
- 作者机构：海军航空工程学院;
- 论文关键词：分段确定性马尔可夫过程 ; 疲劳裂纹增长 ; Fredholm方程 ; 可靠性分析 ; 首达时
- 英文论文关键词：piecewise deterministic Markov process ; fatigue crack growth ; fredholm equation ; degradation failure ; first passage tim
- 会议召开时间：2016-10-31
- 会议录名称：探索 创新 交流（第7集）——第七届中国航空学会青年科技论坛文集（上册）
- 英文会议录名称：Discovery,Innovation and Communication——Proceedings of 7th CSAA Science and Technology Youth Forum
- 语种：中文
- 分类号：V231
- 学会代码：ZGHU
- 会议名称：探索 创新 交流（第7集）——第七届中国航空学会青年科技论坛
- 会议地点：中国广东中山
- 主办单位：中国航空学会
- 学会名称：中国航空学会
- 页数：5
- 文件大小：252k
- 原文格式：O
- 会议级别：全国
摘要
分段确定性的马尔可夫过程(PDMP)是扩散过程的一种替换物,它实质上给出了是确定性运动和随机跳跃混合物的任意随机过程的表示,因而PDMP的样本轨迹能够包括确定性的退化过程和偶然的外伤性事件。在本研究中发现该过程到达一个确定性阈值的首达时的拉普拉斯变换满足Fredholm方程,通过指数快速收敛Neumann级数给出了此方程的解。将PDMP引入到具有退化的可靠性分析中,通过疲劳裂纹增长分析,研究了基于PDMP实行退化建模的可行性。
Piecewise Deterministic Markov Processes(PDMP) is an alternative to diffusion processes.It virtually gives a representation of any stochastic process being the mixture of deterministic motions and random jumps.Hence,the sample paths of PDMP contain deterministic degradation process and accidental traumatic events.The Laplace transform of the first crossing time of a fixed threshold by the process is shown to satisfy a Fredholm equation of second kind.Solution to this equation is given by exponentially fast converging Neumann series.The PDMP is introduced into reliability analysis of product with degradation.With the analysis of fatigue crack growth data,the feasibility of degradation modeling based on PDMP is studied.
Piecewise Deterministic Markov Processes(PDMP) is an alternative to diffusion processes.It virtually gives a representation of any stochastic process being the mixture of deterministic motions and random jumps.Hence,the sample paths of PDMP contain deterministic degradation process and accidental traumatic events.The Laplace transform of the first crossing time of a fixed threshold by the process is shown to satisfy a Fredholm equation of second kind.Solution to this equation is given by exponentially fast converging Neumann series.The PDMP is introduced into reliability analysis of product with degradation.With the analysis of fatigue crack growth data,the feasibility of degradation modeling based on PDMP is studied.
引文
[1]K Borovkova,A Novikov.On a Piece-Wise Deterministic Markov Process Model.Statistics&Probability Letters,2001,53:421-428.
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[7]Shunqin Li,Wansheng Tang,Chao Zhang.Poisson Process with Fuzzy Time-Dependent Intensity.ICIC 2006,LNAI4114:786-797,Springer-Verlag Berlin Heidelberg,2006.
[2]Julien Chiquet,Nikolaos Limnios.Estimating Stochastic Dynamical Systems Driven by a Continuous-Time Jump Markov Process.Methodol Comput Appl Probab,2006(8):431-447.
[3]吴波,祁向荣,江征风,等.基于多失效模式的轴承滚动体可靠性模型[J].轴承,2005(9):21-24.
[4]Wenbiao Zhao,E.A.Elsayed,An Accelerated Life Testing Model Involving Performance Degradation,RAMS,2004:324-329.
[5]Wenjian Li and Hoang Pham,Reliability Modeling of MultiState Degraded Systems with Multi-Competing Failures and Random Shocks[J].IEEE Transactions on Reliability,2005,54(2):297-303.
[6]J Lawless and M Crowder.Covariates and Random Effects in a Gamma Process Model with Application to Degradation and Failure[J].Lifetime Data Analysis,2004,10;213-227.
[7]Shunqin Li,Wansheng Tang,Chao Zhang.Poisson Process with Fuzzy Time-Dependent Intensity.ICIC 2006,LNAI4114:786-797,Springer-Verlag Berlin Heidelberg,2006.