钒电池核心部件可靠性模型参数估计分析

doi:10.19799/j.cnki.2095-4239.2024.1209

储能科学与技术 ›› 2025, Vol. 14 ›› Issue (6): 2524-2531.doi: 10.19799/j.cnki.2095-4239.2024.1209

钒电池核心部件可靠性模型参数估计分析

徐航¹(), 史小虎², 余龙海², 孙彦招³, 王友¹()

^1.湖北文理学院机械工程学院，湖北襄阳 441053
^2.大力储能技术湖北有限责任公司，湖北襄阳 441035
^3.湖北文理学院汽车与交通工程学院，湖北襄阳 441053

收稿日期:2024-12-19 修回日期:2025-01-07 出版日期:2025-06-28 发布日期:2025-06-27
通讯作者: 王友 E-mail:1769280663@qq.com;wyslllo@sina.com
作者简介:徐航（1997—），男，硕士研究生，研究方向为数字化设计及数值模拟，E-mail：1769280663@qq.com；
基金资助:
湖北省自然科学基金联合基金项目(2023AFD036)

Parameter-estimation analyses of reliability models for the core components of a vanadium-redox-flow battery

Hang XU¹(), Xiaohu SHI², Longhai YU², Yanzhao SUN³, You WANG¹()

^1.School of Mechanical Engineering, Hubei University of Arts and Sciences, Xiangyang 441053, Hubei, China
^2.Dali Energy Storage Technology Hubei Co. , Ltd. , Xiangyang 441035, Hubei, China
^3.School of Automobile and Transportation Engineering, Hubei University of Arts and Sciences, Xiangyang 441053, Hubei, China

Received:2024-12-19 Revised:2025-01-07 Online:2025-06-28 Published:2025-06-27
Contact: You WANG E-mail:1769280663@qq.com;wyslllo@sina.com

摘要/Abstract

摘要：

可靠性设计是钒电池电堆开发过程中的重要组成部分，对储能系统的安全性和经济性具有决定性作用。本工作以液流框、双极板为研究对象，建立了基于对数正态分布、二参数和三参数Weibull分布模型的钒电池核心部件可靠性模型，阐明了基于极大似然估计法和GM(1，1)方法的参数估计法，以K-S检验法和均方根误差(RMSE)为评价指标，探讨了分布模型和参数估计方法对可靠性预测结果的影响。结果表明：液流框可靠性模型的拟合优度最小值为0.89，说明采用两种参数估计方法获得的可靠性模型全部通过拟合优度检验；进一步地，可靠性模型的均方根误差最小值为0.22，说明基于GM(1，1)方法的二参数分布模型最适宜于表达液流框的可靠性模型。双极板可靠性模型的拟合优度最小值为0.03，说明极大似然估计法不适用于开展三参数Weibull分布参数估计；进一步地，可靠性模型的均方根误差最小值为0.16，说明基于GM(1，1)方法的二参数分布模型是能精确表达双极板的可靠性模型。研究结果对钒电池核心部件及系统的可靠性设计与优化具有理论指导意义。

关键词: 钒电池, 可靠性, 概率分布模型, K-S检验, 均方根误差

Abstract:

Reliability design is an important aspect of the development of vanadium-battery stacks, and it plays a decisive role in the safety and economy of energy-storage systems. Taking the liquid-flow frame and bipolar plate as the research objects, this study establishes reliability models for the core components of vanadium batteries based on the lognormal distribution and on two-parameter and three-parameter Weibull-distribution models. Parameter-estimation in this study is based on the maximum-likelihood estimation method and the GM (1,1) method. The K-S test and the root-mean-square error (RMSE) were adopted as evaluation indicators for exploring the influence of the distribution model and the parameter-estimation method on the reliability of the predictions. The results show that the minimum goodness-of-fit for the liquid-flow-frame reliability model is 0.89, indicating that the reliability models obtained using the two-parameter-estimation methods all pass the goodness-of-fit test. Further, the minimum RMSE of the reliability model is 0.22, which indicates that the two-parameter distribution model based on the GM (1,1) method is the most suitable reliability model for the liquid-flow frame. The minimum goodness-of-fit of the bipolar plate reliability model is 0.03, which indicates that the maximum-likelihood estimation method is not suitable for estimating the parameters of the three-parameter Weibull-distribution. Further, the minimum RMSE of the reliability model is 0.16, which indicates that the two-parameter distribution model based on the GM (1,1) method is the most accurate reliability model for the bipolar plate. These research results have theoretical guiding significance for the reliability design and optimization of vanadium-battery core components and systems.

Key words: vanadium battery, reliability, probability distribution model, K-S test, RMSE

中图分类号:

TB 114.3

徐航, 史小虎, 余龙海, 孙彦招, 王友. 钒电池核心部件可靠性模型参数估计分析[J]. 储能科学与技术, 2025, 14(6): 2524-2531.

Hang XU, Xiaohu SHI, Longhai YU, Yanzhao SUN, You WANG. Parameter-estimation analyses of reliability models for the core components of a vanadium-redox-flow battery[J]. Energy Storage Science and Technology, 2025, 14(6): 2524-2531.

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试样序号	失效概率P	液流框	双极板
试样序号	失效概率P	拉伸强度/MPa
1	0.05	43.00	15.79
2	0.10	44.38	15.80
3	0.15	45.12	15.95
4	0.20	45.42	16.01
5	0.25	45.88	16.25
6	0.30	45.95	16.42
7	0.35	46.12	16.82
8	0.40	46.50	16.86
9	0.45	46.82	16.90
10	0.50	47.10	16.97
11	0.55	47.35	17.05
12	0.60	47.59	17.08
13	0.65	47.82	17.20
14	0.70	48.31	17.26
15	0.75	49.46	17.38
16	0.80	49.58	17.41
17	0.85	49.84	18.10
18	0.90	50.01	18.11
19	0.95	50.10	18.35

钒电池部件	参数估计方法	对数正态分布	二参数Weibull分布	三参数Weibull分布
液流框	MLE	0.98	0.93	0.95
液流框	GM	0.98	0.89	0.99

双极板	MLE	0.84	0.72	0.03
双极板	GM	0.84	0.79	0.78

钒电池部件	参数估计方法	对数正态分布		二参数Weibull分布		三参数Weibull分布
钒电池部件	参数估计方法	μ	σ	β	λ	β	λ	γ
液流框	MLE	3.85	0.04	27.41	48.04	4.08	7.60	40.23
液流框	GM	3.85	0.04	28.38	48.03	7.33	14.64	33.36

双极板	MLE	2.83	0.05	23.84	17.29	—	—	—
双极板	GM	2.83	0.05	25.68	17.28	2.78	2.40	14.81

钒电池部件	参数估计方法	对数正态分布		二参数Weibull分布		三参数Weibull分布
钒电池部件	参数估计方法	μ	σ	β	λ	β	λ	γ
液流框	MLE	[3.83,3.88]	[0.03,0.06]	[15.06,39.74]	[26.44,69.64]	[4.03,4.13]	[6.74,8.47]	[38.59,41.88]
液流框	GM	[3.83,3.88]	[0.03,0.06]	[15.62,41.15]	[26.43,69.62]	[6.92,7.73]	[8.06,21.22]	[27.18,39.53]

双极板	MLE	[2.81,2.85]	[0.03,0.06]	[13.12,34.56]	[9.52,25.09]	—	—	—
双极板	GM	[2.81,2.85]	[0.03,0.06]	[14.13,37.22]	[9.51,25.05]	[2.39,3.17]	[1.32,3.48]	[13.84,15.77]

钒电池部件	参数估计方法	对数正态分布		二参数Weibull分布		三参数Weibull分布
钒电池部件	参数估计方法	μ	σ	β	λ	β	λ	γ
液流框	MLE	0.05	0.030	24.68	43.20	0.10	1.73	3.29
液流框	GM	0.05	0.030	25.52	43.19	0.81	13.16	12.35

双极板	MLE	0.04	0.030	21.44	15.57	—	—	—
双极板	GM	0.04	0.030	23.09	15.54	0.78	2.16	1.93

钒电池核心部件可靠性模型参数估计分析

Parameter-estimation analyses of reliability models for the core components of a vanadium-redox-flow battery

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钒电池部件	期望和方差	对数正态分布		二参数Weibull分布		三参数Weibull分布
钒电池部件	期望和方差	MLE	GM	MLE	GM	MLE	GM
液流框	E	47.13	47.13	47.09	47.11	47.13	47.08
液流框	V	3.96	3.96	4.61	4.31	3.61	4.88

双极板	E	16.93	16.93	16.90	16.92	—	—
双极板	V	0.59	0.59	0.78	0.68	2.02	0.69

钒电池部件	参数估计方法	对数正态分布	二参数Weibull分布	三参数Weibull分布
液流框	MLE	47.03	47.03	47.02
液流框	GM	487.29	0.22	47.03

双极板	MLE	16.58	16.60	—
双极板	GM	40.10	0.16	16.60

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