基于R藤Copula-DBN齿轮箱故障诊断

王进花; 刘正奇; 曹洁; 刘昀强; 陈莉

doi:10.13700/j.bh.1001-5965.2023.0777

基于R藤Copula-DBN齿轮箱故障诊断

doi: 10.13700/j.bh.1001-5965.2023.0777

王进花^1, ,,
刘正奇¹,
曹洁^{1, 2, 3},
刘昀强¹,
陈莉²

1.
兰州理工大学电气工程与信息工程学院，兰州 730050
2.
兰州城市学院信息工程学院，兰州 730050
3.
甘肃省制造信息工程研究中心，兰州 730050

基金项目:

国家自然科学基金(62063020)；国家重点研发计划(2020YFB1713600)；甘肃省自然科学基金(20JR5RA463)

详细信息

通讯作者:
E-mail：wjh0615@lut.edu.cn

中图分类号: TP277；TH133.33
计量
- 文章访问数: 199
- HTML全文浏览量: 94
- PDF下载量: 137
- 被引次数: 0
出版历程
- 收稿日期: 2023-11-30
- 录用日期: 2024-03-12
- 网络出版日期: 2024-04-25
- 整期出版日期: 2026-03-31

Gearbox fault diagnosis based on R-vine Copula-DBN

WANG Jinhua^{1
, ,},
LIU Zhengqi¹,
CAO Jie^{1, 2, 3},
LIU Yunqiang¹,
CHEN Li²

1.
School of Electrical Engineering and Information Engineering，Lanzhou University of Technology，Lanzhou 730050，China
2.
School of Information Engineering，Lanzhou City University，Lanzhou 730050，China
3.
Gansu Manufacturing Information Engineering Research Center，Lanzhou 730050，China

Funds:

National Natural Science Foundation of China (62063020); National Key Research and Development Program of China (2020YFB1713600); Natural Science Foundation of Gansu Province (20JR5RA463)

More Information

Corresponding author: E-mail：wjh0615@lut.edu.cn

摘要

摘要:
传统动态贝叶斯初始网络在多维数据下进行结构学习时，需搜索的有向无环图空间大，难以获得最优结构，导致故障诊断精度低。为此，提出一种R藤Copula模型与动态贝叶斯网络(DBN)相结合的故障诊断方法。采用结构预测模型对所提取的特征进行筛选，得到相关性较强的节点，减小网络结构空间的大小；采用R藤Copula模型第一层树结构结合传递熵方法构建动态贝叶斯初始网络，将初始网络在时间序列按马尔可夫过程展开构建DBN进行故障诊断，解决在多特征下网络构建难以获得最优结构的问题。采用东南大学齿轮箱数据进行验证，与其他方法对比，结果表明，所提方法能够更好地进行DBN结构学习，且数据与模型的拟合度较高，在故障诊断时能够取得良好的诊断结果。
- 故障诊断 /
- 动态贝叶斯网络 /
- R藤Copula /
- 结构预测模型 /
- 齿轮箱
Abstract:
Low diagnostic accuracy results from the wide set of directed acyclic graphs that must be searched when doing structure learning on dynamic Bayesian starting networks under multidimensional input. Conventional approaches find it challenging to find the best structure. In this paper, a method is proposed to combine the R-vine Copula model with a dynamic Bayesian network (DBN) for fault diagnosis. First, the network structure space is made smaller by using the structure prediction model to filter the retrieved features and identify nodes with high correlation. Then, the first-layer tree structure of the R-vine Copula model is used combined with the transfer entropy method to construct the initial network of dynamic Bayesian network, and the DBN of the initial network is built according to the Markov process in time series for fault diagnosis, which solves the problem that it is difficult to obtain the optimal structure in the network construction under multiple features. The gearbox data of Southeast University is used for verification, and the comparison results show that the method can better learn the DBN structure, and the fit between the data and the model is high, and good diagnostic results can be obtained in fault diagnosis.
- fault diagnosis /
- dynamic Bayesian network /
- R-vine Copula /
- structure prediction model /
- gearbox

HTML全文

图 1 DBN的初始网络和转移网络

Figure 1. Initial network and transfer network of DBN network

下载: 全尺寸图片幻灯片

图 2 5维随机变量的R藤Copula模型

Figure 2. R-vine Copula model of 5-dimensional random variables

下载: 全尺寸图片幻灯片

图 3 R藤Copula树模型构建过程

Figure 3. Building process of R vine Copula tree model

下载: 全尺寸图片幻灯片

图 4 齿轮箱故障诊断方法流程

Figure 4. Flow chart of gearbox fault diagnosis method

下载: 全尺寸图片幻灯片

图 5 实验模拟平台

Figure 5. Experimental simulation platform

下载: 全尺寸图片幻灯片

图 6 不同综合相似度特征筛选所得结构BIC分数绝对值

Figure 6. Structure BIC score absolute values obtained by screening different comprehensive similarity features

下载: 全尺寸图片幻灯片

图 7 特征节点相关性

Figure 7. Feature node correlation

下载: 全尺寸图片幻灯片

图 8 R藤Copula-DBN模型第一层结构

Figure 8. The first layer structure of R vine Copula-DBN model

下载: 全尺寸图片幻灯片

图 9 齿轮箱DBN

Figure 9. Gearbox DBN

下载: 全尺寸图片幻灯片

图 10 R藤Copula-DBN混淆矩阵

Figure 10. Confusion matrix of R vine Copula DBN

下载: 全尺寸图片幻灯片

图 11 DBN混淆矩阵

Figure 11. Confusion matrix of DBN

下载: 全尺寸图片幻灯片

图 12 平均结构汉明距离

Figure 12. Average structural Hamming distance

下载: 全尺寸图片幻灯片

表 1 故障编码及描述

Table 1. Fault coding and description

故障类型	故障描述	故障编码
正常	健康运行状态	1
缺损	齿轮出现裂纹	2
断齿	齿轮上出现断齿	3
齿根磨损	齿根处出现裂纹	4
齿面磨损	齿轮表面出现磨损	5

下载: 导出CSV

表 2 部分信号时域特征参数

Table 2. Part of signal time domain characteristic parameters

故障类型	峰值/(m·s⁻²)	峰峰值/(m·s⁻²)	均值/(m·s⁻²)	方差/(m·s⁻²)	标准差/(m·s⁻²)	峭度	均方根/(m·s⁻²)	偏度
正常	0.44780	0.43404	−0.33716	0.00089	0.02980	5.60092	0.14287	−0.29032
缺损	0.18089	0.03282	−0.16583	0.00002	0.00454	3.07251	0.64212	−0.04703
断齿	0.69075	0.09466	−0.64182	0.00038	0.01960	1.99141	0.64212	−0.04703
齿根磨损	0.45162	0.09555	−0.40361	0.00032	0.01801	2.24631	0.64212	−0.04703
齿面磨损	0.26783	0.08184	−0.22825	0.00017	0.01320	2.73807	0.12238	0.05745

故障类型	平均幅值/(m·s⁻²)	方根幅值/(m·s⁻²)	波形因子	峰值因子	脉冲因子	裕度因子	余隙因子
正常	0.33636	0.33748	1.00389	1.32299	1.32815	1.33083	3.90861
缺损	0.16783	0.16571	1.00037	1.09401	1.09081	1.09102	6.57273
断齿	0.54182	0.64167	1.00046	1.07573	1.07623	1.07648	1.07526
齿根磨损	0.40461	0.40341	1.00099	1.11781	1.11893	1.11948	2.76674
齿面磨损	0.21806	0.22806	1.00167	1.17417	1.17343	1.17441	5.12347

下载: 导出CSV

表 3 特征筛选有效性验证

Table 3. Validity verification of feature screening

特征筛选方法	BIC	搜索空间	特征数量
无筛选	−1.8867×10⁴	$ {2}^{201} $	15
互信息	−2.1452×10⁴	$ {2}^{102} $	10
PCC	−2.0375×10⁴	$ {2}^{154} $	13
MRMR	−1.9431×10⁴	$ {2}^{175} $	14
SP	−2.6102×10⁴	$ {2}^{123} $	11

下载: 导出CSV

表 4 1000样本下各模型的诊断结果及运行时间对比

Table 4. Comparison of diagnostic results and running time of each model under 1000 samples

模型	准确率/%	F₁/%	召回率/%	运行时间/s
R藤Copula-DBN	93.6	93.4	93.3	8.3
DBN	90.7	90.4	90.2	8.1
BN	88.5	88.4	88.1	8.0
FM-DBN	91.7	90.3	91.2	8.4
FT-DBN	90.6	91.2	89.2	8.6
GNN	91.6	90.8	89.9	6.7
DACNN	92.8	91.6	90.8	7.0

下载: 导出CSV

表 5 1200样本下各模型的诊断结果及运行时间对比

Table 5. Comparison of diagnostic results and running time of each model under 1200 samples

模型	准确率/%	F₁/%	召回率/%	运行时间/s
R藤Copula-DBN	93.8	93.7	93.4	9.73
DBN	89.1	87.3	89.2	9.47
BN	87.1	86.2	86.1	8.43
FT-DBN	91.3	89.4	90.6	9.74
FM-DBN	89.5	90.7	88.3	9.6
GNN	94.0	93.8	93.6	7.93
DACNN	94.6	94.3	94.1	8.3

下载: 导出CSV

表 6 800样本下各模型的诊断结果及运行时间对比

Table 6. Comparison of diagnostic results and running time of each model under 800 samples

模型	准确率/%	F₁/%	召回率/%	运行时间/s
R藤Copula-DBN	95.4	94.2	93.4	7.8
DBN	91.2	92.1	90.2	7.6
BN	87.4	88.3	88.5	7.3
FT-DBN	91.3	92.4	90.4	8.8
FM-DBN	91.5	92.2	91.7	9.0
GNN	89.8	90.1	91.3	6.4
DACNN	90.3	91.1	92.3	6.9

下载: 导出CSV

表 7 600样本下各模型的诊断结果及运行时间对比

Table 7. Comparison of diagnostic results and running time of each model under 600 samples

模型	准确率/%	F₁/%	召回率/%	运行时间/s
R藤Copula-DBN	95.6	94.5	93.6	7.4
DBN	93.3	92.1	91.6	7.3
BN	88.5	87.1	86.7	7.0
FT-DBN	92.1	91.2	90.1	8.1
FM-DBN	92.6	92.4	91.8	8.8
GNN	88.2	87.8	86.3	6.2
DACNN	89.2	90.3	89.2	6.5

下载: 导出CSV

参考文献(24)

[1]	BHARDWAJ U, TEIXEIRA A P, SOARES C G. Reliability prediction of an offshore wind turbine gearbox[J]. Renewable Energy, 2019, 141: 693-706.
[2]	魏莎, 韩勤锴, 褚福磊. 考虑不确定性因素的齿轮系统动力学研究综述[J]. 机械工程学报, 2016, 52(1): 1-19. WEI S, HAN Q K, CHU F L. Review on research of uncertain dynamics for gear system[J]. Journal of Mechanical Engineering, 2016, 52(1): 1-19(in Chinese).
[3]	CHEN R, HUANG X, HU X, et al. Planetary gearbox fault diagnosis technique based on multi-source information deep fusion[J]. Journal of Vibration Engineering, 2020, 33(5): 1094-1102.
[4]	GU Y K, ZHANG M, ZHOU X Q. Fault diagnosis of gearbox based on improved DUCG with combination weighting method[J]. IEEE Access, 2019, 7: 92955-92967.
[5]	GUO S, YANG T, HUA H C, et al. Coupling fault diagnosis of wind turbine gearbox based on multitask parallel convolutional neural networks with overall information[J]. Renewable Energy, 2021, 178: 639-650.
[6]	HUANG N T, CHEN Q Z, CAI G W, et al. Fault diagnosis of bearing in wind turbine gearbox under actual operating conditions driven by limited data with noise labels[J]. IEEE Transactions on Instrumentation and Measurement, 2020, 70: 3502510.
[7]	王进花, 岳亮辉, 曹洁, 等. 基于随机变分推理贝叶斯神经网络的发电机轴承故障诊断[J]. 控制与决策, 2023, 38(4): 1015-1021. WANG J H, YUE L H, CAO J, et al. Fault diagnosis of generator bearing based on stochastic variational inference Bayesian neural network[J]. Control and Decision, 2023, 38(4): 1015-1021(in Chinese).
[8]	DEAN T, KANAZAWA K. A model for reasoning about persistence and causation[J]. Computational Intelligence, 1989, 5(2): 142-150.
[9]	孙美婷, 刘彬. 基于改进遗传算法的DBN结构自适应学习算法[J]. 计量学报, 2021, 42(1): 91-99. SUN M T, LIU B. DBN structure adaptive learning algorithm based on improved genetic algorithms[J]. Acta Metrologica Sinica, 2021, 42(1): 91-99(in Chinese).
[10]	冷翠平, 王双成, 王辉. DBN结构学习的依赖分析方法研究[J]. 计算机工程与应用, 2011, 47(3): 51-53. LENG C P, WANG S C, WANG H. Study on dependency analysis method for learning dynamic Bayesian network structure[J]. Computer Engineering and Applications, 2011, 47(3): 51-53(in Chinese).
[11]	FANG C, XU Y L, LI Y L. Optimized C-vine Copula and environmental contour of joint wind-wave environment for sea-crossing bridges[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2022, 225: 104989.
[12]	SUN F Q, FU F Y, LIAO H T, et al. Analysis of multivariate dependent accelerated degradation data using a random-effect general Wiener process and D-vine Copula[J]. Reliability Engineering & System Safety, 2020, 204: 107168.
[13]	LIU S J, JIANG H. Engine remaining useful life prediction model based on R-vine Copula with multi-sensor data[J]. Heliyon, 2023, 9(6): e17118.
[14]	AMIN M T, YAO Y T, YU J, et al. Probabilistic monitoring of nuclear plants using R-vine Copula[J]. Annals of Nuclear Energy, 2023, 190: 109867.
[15]	涂青宇, 苗世洪, 林毓军, 等. 基于动态R藤Copula模型的区域风电集群超短期功率区间预测方法[J]. 高电压技术, 2022, 48(2): 456-470. TU Q Y, MIAO S H, LIN Y J, et al. Ultra-short-term interval forecasting method for regional wind farms based on dynamic R-vine Copula model[J]. High Voltage Engineering, 2022, 48(2): 456-470(in Chinese).
[16]	MALONE B, KANGAS K, JÄRVISALO M, et al. Empirical hardness of finding optimal Bayesian network structures: algorithm selection and runtime prediction[J]. Machine Learning, 2018, 107(1): 247-283.
[17]	PANINSKI L. Estimation of entropy and mutual information[J]. Neural Computation, 2003, 15(6): 1191-1253.
[18]	MU Y S, LIU X D, WANG L D. A Pearson’s correlation coefficient based decision tree and its parallel implementation[J]. Information Sciences, 2018, 435: 40-58.
[19]	ZHANG Y H, ZHANG W S, XIE Y. Improved heuristic equivalent search algorithm based on maximal information coefficient for Bayesian network structure learning[J]. Neurocomputing, 2013, 117: 186-195.
[20]	YU D M, GHADIMI N. Reliability constraint stochastic UC by considering the correlation of random variables with Copula theory[J]. IET Renewable Power Generation, 2019, 13(14): 2587-2593.
[21]	AMIN M T, KHAN F, AHMED S, et al. Risk-based fault detection and diagnosis for nonlinear and non-Gaussian process systems using R-vine Copula[J]. Process Safety and Environmental Protection, 2021, 150: 123-136.
[22]	WANG L L, XIN T, YANLOU L. An improved parameter-estimating method in Bayesian networks applied for cognitive diagnosis assessment[J]. Frontiers in Psychology, 2021, 12: 665441.
[23]	CHEN H, REN J. Structure-variable hybrid dynamic Bayesian networks and its inference algorithm[C]//Proceedings of the 24th Chinese Control and Decision Conference. Piscataway: IEEE Press, 2012: 2815-2820.
[24]	SHAO S Y, MCALEER S, YAN R Q, et al. Highly accurate machine fault diagnosis using deep transfer learning[J]. IEEE Transactions on Industrial Informatics, 2018, 15(4): 2446-2455.