基于不确定理论的退化数据分析方法

doi:10.3969/j.issn.1001-506X.2020.12.31

摘要/Abstract

摘要：

作为可靠性领域传统的数学工具，概率论难以解决现代可靠性工程面临的难题。本文以不确定理论在退化数据分析中的应用为切入点,阐述了不确定理论的基本公理、运算法则与不确定统计方法,给出了基于确信可靠性理论的可靠性建模思路,提出了不确定失效阈值情形下的退化数据分析与可靠性建模方法。利用时变不确定正态分布建立产品的退化方程,根据专家知识建立失效阈值的不确定分布进而构建裕量方程,最终根据度量方程推导出产品可靠性模型。使用不确定统计中的极大似然估计法与假设检验法解决参数估计与模型验证问题。案例分析说明如果不考虑失效阈值的不确定性,会造成可靠性评估结果较大偏差。研究表明不确定理论适合处理退化数据分析中的不确定性难题,具有广阔的应用前景。

关键词: 不确定理论, 确信可靠性, 不确定正态分布, 失效阈值, 退化数据

Abstract:

As a traditional mathematical tool in reliability field, the probability theory is not applicable to solve the problem that modern reliability engineering encounters with. Taking the application of the uncertainty theory in degraded data analysis as the entry point, the fundamental axioms, operational rules and statistical methods of the uncertainty theory are expounded, and the reliability modeling guideline based on the brief reliability theory is provided. The methods of degraded data analysis and reliability modeling considering uncertain failure threshold is proposed. The degradation equation is established by adopting the time-varying uncertain normal distribution, and the uncertainty distribution of the failure threshold is constructed according to the expert's knowledge, so as to obtain the margin equation of the product. Finally, the reliability model is deduced based on the measurement equation. The problems of parameter estimation and model verification are solved by using the maximum likelihood estimation method and hypothesis test method of uncertain statistics, respectively. The case study shows that the reliability assessment results will obviously deviate if the uncertainty of failure threshold is not considered. The research indicates that the uncertainty theory is suitable to deal with the uncertainty problems in degradation data analysis and has a broad application prospect.

Key words: uncertainty theory, brief reliability, uncertain normal distribution, failure threshold, degradation data

中图分类号:

TB114.3

王浩伟, 康锐. 基于不确定理论的退化数据分析方法[J]. 系统工程与电子技术, 2020, 42(12): 2924-2930.

Haowei WANG, Rui KANG. Method of analyzing degradation data based on the uncertainty theory[J]. Systems Engineering and Electronics, 2020, 42(12): 2924-2930.

图/表 10

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序号	测量时刻t_{i, j}/h
序号	0.25	0.50	0.75	1.00	1.25	1.50	1.75	2.00	2.25	2.50	2.75	3.00	3.25	3.50	3.75	4.00
1	0.47	0.93	2.11	2.72	3.51	4.34	4.91	5.48	5.99	6.72	7.13	8.00	8.92	9.49	9.87	10.94
2	0.71	1.22	1.90	2.30	2.87	3.75	4.42	4.99	5.51	6.07	6.64	7.16	7.78	8.42	8.91	9.28
3	0.71	1.17	1.73	1.99	2.53	2.97	3.30	3.94	4.16	4.45	4.89	5.27	5.69	6.02	6.45	6.88
4	0.27	0.61	1.11	1.77	2.06	2.58	2.99	3.38	4.05	4.63	5.24	5.62	6.04	6.32	7.10	7.59
5	0.36	1.39	1.95	2.86	3.46	3.81	4.53	5.35	5.92	6.71	7.70	8.61	9.15	9.95	10.49	11.01
6	0.46	1.07	1.42	1.77	2.11	2.40	2.78	3.02	3.29	3.75	4.16	4.76	5.16	5.46	5.81	6.24
7	0.51	0.93	1.57	1.96	2.59	3.29	3.61	4.11	4.60	4.91	5.34	5.84	6.40	6.84	7.20	7.88
8	0.41	1.49	2.38	3.00	3.84	4.50	5.25	6.26	7.05	7.80	8.32	8.93	9.55	10.45	11.28	12.21
9	0.44	1.00	1.57	1.96	2.51	2.84	3.47	4.01	4.51	4.80	5.20	5.66	6.20	6.54	6.96	7.42
10	0.51	0.83	1.29	1.52	1.91	2.27	2.78	3.42	3.78	4.11	4.38	4.63	5.38	5.84	6.16	6.62

接受域边界	t_{i, j}/h
接受域边界	0.25	0.50	0.75	1.00	1.25	1.50	1.75	2.00	2.25	2.50	2.75	3.00	3.25	3.50	3.75	4.00
Φ_{t_{i, j}}^-1(0.05)	0.22	0.44	0.66	0.88	1.10	1.32	1.54	1.77	1.99	2.21	2.43	2.65	2.87	3.09	3.31	3.53
Φ_{t_{i, j}}^-1(0.95)	0.93	1.86	2.80	3.73	4.66	5.59	6.53	7.46	8.39	9.32	10.26	11.19	12.12	13.05	13.99	14.92

测量序号	各测量时刻退化数据在各分布类型下的p值
测量序号	正态分布	对数正态分布	威布尔分布
1	0.255	0.516	0.225
2	0.970	0.897	0.952
3	0.990	0.990	0.979
4	0.178	0.347	0.153
5	0.370	0.571	0.329
6	0.649	0.788	0.593
7	0.347	0.455	0.328
8	0.485	0.658	0.466
9	0.583	0.817	0.546
10	0.267	0.461	0.262
11	0.281	0.453	0.269
12	0.169	0.301	0.157
13	0.106	0.196	0.094
14	0.100	0.180	0.097
15	0.164	0.286	0.161
16	0.159	0.307	0.152

序号	对数均值	对数标准差
1	-0.761	0.275
2	0.033	0.248
3	0.508	0.221
4	0.758	0.217
5	0.981	0.228
6	1.160	0.231
7	1.311	0.224
8	1.455	0.228
9	1.561	0.227
10	1.659	0.230
11	1.749	0.228
12	1.837	0.230
13	1.925	0.220
14	1.993	0.228
15	2.057	0.224
16	2.127	0.225

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