Evaluation Method of Fault Diagnosability Based on Recursive Plot and Tensor Decomposition

doi:10.12382/bgxb.2021.0790

Abstract

Abstract:

Diagnosability reflects the difficulty of diagnosing system faults, so diagnosability evaluation of the system is a prerequisite for fault diagnosis. Taking the signals of test points into consideration, a fault diagnosability evaluation method based on a recurrence plot and tensor decomposition is proposed. The phase space reconstruction technique is used to graphically represent the signals of measured points in different states to form a recurrence plot. Features are extracted through analyzing the recurrence plot, which are then regarded as the original signal features. Through tensor decomposition, the similarity between signal features in different states is calculated as a basic measure of fault diagnosis difficulty. Simulation experiments show that, compared with the previous D-matrix diagnosability evaluation method that only considers the system model, the newly proposed method has effectiveness and objectivity.

Key words: fault diagnosability evaluation, recurrence plot, tensor decomposition, phase space reconstruction

LÜ Jiapeng, SHI Xianjun, NIE Xinhua, QIN Yufeng, LONG Yufeng. Evaluation Method of Fault Diagnosability Based on Recursive Plot and Tensor Decomposition[J]. Acta Armamentarii, 2023, 44(3): 763-772.

Figures/Tables 15

References 25

[1]	朱敏, 许爱强, 许晴, 等. 基于改进多层核超限学习机的模拟电路故障诊断[J]. 兵工学报, 2021, 42(2): 356-369. doi: 10.3969/j.issn.1000-1093.2021.02.013
	ZHU M, XU A Q, XU Q, et al. Fault diagnosis of analog circuit based on improved multilayer kernel extreme learning machine[J]. Acta Armamentarii, 2021, 42(2): 356-369. (in Chinese)
[2]	郭伟超, 赵怀山, 李成, 等. 基于小波包能量谱与主成分分析的轴承故障特征增强诊断方法[J]. 兵工学报, 2019, 40(11): 2370-2377. doi: 10.3969/j.issn.1000-1093.2019.11.022
	GUO W C, ZHAO H S, LI C, et al. Fault feature enhancement method for rolling bearing fault diagnosis based on wavelet packet energy spectrum and principal component analysis[J]. Acta Armamentarii, 2019, 40(11): 2370-2377. (in Chinese)
[3]	王大轶, 符方舟, 刘成瑞, 等. 控制系统可诊断性的内涵与研究综述[J]. 自动化学报, 2018, 44(9): 1537-1553.
	WANG D Y, FU F Z, LIU C R, et al. Connotation and research status of diagnosability of control systems: a review[J]. Acta Automatica Sinica, 2018, 44(9): 1537-1553. (in Chinese)
[4]	李文博, 王大轶, 刘成瑞. 卫星姿态控制系统的故障可诊断性评价研究[J]. 空间控制技术与应用, 2014, 40(5): 8-13.
	LI W B, WANG D Y, LIU C R. Evaluating fault diagnosability of satellite attitude control system[J]. Aerospace Control and Application, 2014, 40(5): 8-13. (in Chinese)
[5]	ERIKSSON D, FRISK E, KRYSANDER M. A method for quantitative fault diagnosability analysis of stochastic linear descriptor models[J]. Automatica, 2013, 49(6): 1591-600. doi: 10.1016/j.automatica.2013.02.045 URL
[6]	LIN L X, WANG Q, HE B W, et al. Evaluation of fault diagnosability for nonlinear uncertain system with multiple faults occuring simutaneously[J]. Journal of Systems Engineering and Electronics, 2020, 31(3): 634- 646. doi: 10.23919/JSEE.5971804 URL
[7]	PENG X F, LIN L X, ZHONG X Y, et al. Methods for fault diagnosability analysis of a calss of affine nonlinear systems[J]. Mathematical Problems in Engineering, 2015: 409184.
[8]	ZHAO D, AHN C K, PASZKE W, et al. Fault diagnosability analysis of two-dimensional linear discrete systems[J]. IEEE Transactions on Automatic Control, 2021, 66(2): 826 -832. doi: 10.1109/TAC.9 URL
[9]	李文博, 王大轶, 刘成瑞. 一类非线性系统的故障可诊断性量化评价方法[J]. 宇航学报, 2015, 36(4): 455-462.
	LI W B, WANG D Y, LIU C R. An approach to fault diagnosability quantitative evaluation for a class of nonlinear systems[J]. Journal of Astronautics, 2015, 36(4): 455-462. (in Chinese)
[10]	李文博, 王大轶, 刘成瑞. 动态系统实际故障可诊断性的量化评价研究[J]. 自动化学报, 2015, 41(3): 497-507.
	LI W B, WANG D Y, LIU C R. Quantitative evaluation of actual fault diagnosability for dynamic systems[J]. Acta Automatica Sinica, 2015, 41(3): 497-507. (in Chinese)
[11]	LIU J, HUA Y Z, LI Q D, et al. Fault diagnosability qualitative analysis of spacecraft based on temporal fault signature matrix[C]// Proceedings of 2016 IEEE Chinese Guidance, Navigation and Control Conference. London, UK:IEEE, 2016: 1496-500.
[12]	MEKKI T, TRIKI S, KAMOUN A. A qualitative approach to single fault isolation in switching systems[C]//Proceedings of the 14th International Conference on Science and Techniques of Automatic Control & Computer Engineering. London, UK:IEEE, 2013: 220-4.
[13]	LI B C, WANG H G, MU L Y, et al. A configuration design method for a redundant inertial navigation system based on diagnosability analysis[J]. Measurement Science and Technology, 2020, 32(2): 025111. doi: 10.1088/1361-6501/abbdf0
[14]	FU F Z, WANG D Y, LI W B, et al. Data-driven fault identifiability analysis for discrete-time dynamic systems[J]. International Journal of Systems Science, 2020, 51(2): 402-412.
[15]	DUNIA R, QIN S J. Subspace approach to multidimensional fault identification and reconstruction[J]. AIChE Journal, 1998, 44(8): 1813-1831. doi: 10.1002/(ISSN)1547-5905 URL
[16]	YUE H H, QIN S J. Reconstruction-based fault identification using a combined index[J]. Industrial & Engineering Chemistry Research, 2001, 40(20): 4403-4414. doi: 10.1021/ie000141+ URL
[17]	刘文静, 刘成瑞, 王南华, 等. 定量与定性相结合的动量轮故障可诊断性评价[J]. 中国空间科学技术, 2011, 31(4): 54-63.
	LIU W J, LIU C R, WANG N H, et al. Quantitative and qualitative model based fault diagnosability evaluation of momentum wheel[J]. Chinese Space Science and Technology, 2011, 31(4): 54-63. (in Chinese)
[18]	吕琛, 马剑, 刘红梅, 等. 基于认知计算与几何空间变换的故障诊断与预测[M]. 北京: 国防工业出版社, 2021.
	LÜ C, MA J, LIU H M, et al. Fault diagnosis and prognostics based on cognitive computing and geometric space transformation[M]. Beijing: National Defense Industry Press, 2021. (in Chinese)
[19]	化永朝, 李清东, 任章, 等. 连续系统故障可诊断性评价方法综述[J]. 控制与决策, 2016, 31(12): 2113-2121.
	HUA Y Z, LI Q D, REN Z, et al. Overview of fault diagnosability evaluation methods for continuous systems[J]. Control and Decision, 2016, 31(12): 2113-2121. (in Chinese)
[20]	符方舟, 王大轶, 李文博. 复杂动态系统的实际非完全失效故障的可诊断性评估[J]. 自动化学报, 2017, 43(11): 1941-1949.
	FU F Z, WANG D Y, LI W B. Quantitative evaluation of actual loe fault diagnosability for dynamic systems[J]. Acta Automatica Sinica, 2017, 43(11): 1941-1949. (in Chinese)
[21]	LIU Q Y, WANG Z D, ZHANG J F, et al. Necessary and sufficient conditions for fault diagnosability of linear open- and closed-loop stochastic systems under sensor and actuator faults[J]. IEEE Transactions on Automatic Control, 2022, 67(8): 4178- 4185. doi: 10.1109/TAC.2021.3108587 URL
[22]	刘文静, 李文博, 张秀云, 等. 基于图论的深空探测航天器故障可诊断性评价[J]. 控制理论与应用, 2019, 36(12): 2074-2084.
	LIU W J, LI W B, ZHANG X Y, et al. Fault diagnosability evaluation of deep space exploration spacecraft based on graph theory[J]. Control Theory & Applications, 2019, 36(12): 2074-2084. (in Chinese)
[23]	李巍华, 张小丽, 严如强. 复杂机电系统智能故障诊断与健康评估[M]. 北京: 国防工业出版社, 2021.
	LI W H, ZHANG X L, YAN R Q. Intellifent fault diagnosis and health assessment for complex electro-mechanical systems[M]. Beijing: National Defense Industry Press, 2021. (in Chinese)
[24]	BORZOU A, YOUSEFI R, SADYGOV R G. Another look at matrix correlations[J]. Bioinformatics, 2019, 35(22): 4748-4753. doi: 10.1093/bioinformatics/btz281 pmid: 31081021
[25]	刘成瑞, 刘文静, 王南华, 等. 基于相关性模型的液浮陀螺可诊断性分析方法[J]. 空间控制技术与应用, 2013, 39(1): 10-4, 22.
	LIU C R, LIU W J, WANG N H, et al. Fault diagnosability analysis method based on dependency model for liquid-floated gyros[J]. Aerospace Control and Application, 2013, 39(1): 10-4, 22. (in Chinese)

指标	计算方法	物理含义
递归率	$RR=\frac{\sum\limits_{i=1}^{{{N}_{m}}}{\sum\limits_{j=1}^{{{N}_{m}}}{{{R}_{ij}}}}}{N_{m}^{2}}$	描述了递归图中递归点的密度，反映了一个特定状态出现的概率
确定性	$DET=\frac{\sum\limits_{l={{l}_{\min }}}^{{{l}_{\max }}}{lp(l)}}{\sum\limits_{i=1}^{{{N}_{m}}}{\sum\limits_{j=1}^{{{N}_{m}}}{{{R}_{ij}}}}}$	描述了对角线结构的递归点数与所有递归点数的比例，反映了系统的可预测性
层流性	$LAM=\frac{\sum\limits_{v={{v}_{\min }}}^{{{v}_{\max }}}{vp(v)}}{\sum\limits_{v=1}^{{{v}_{\max }}}{vp(v)}}$	描述了递归图中垂直线结构的递归点数量，反映了系统的间歇性和层次性
递归熵	$ENTER = -\sum_{l=l_{\min }}^{N_{m}} p(l) \ln p(l)$	基于对角线长度频率分布的香农熵，描述了动力学系统种确定性结构和复杂度，反映了系统的动力学信息量或随机性程度

指标	计算方法	物理含义
递归率	$RR=\frac{\sum\limits_{i=1}^{{{N}_{m}}}{\sum\limits_{j=1}^{{{N}_{m}}}{{{R}_{ij}}}}}{N_{m}^{2}}$	描述了递归图中递归点的密度，反映了一个特定状态出现的概率
确定性	$DET=\frac{\sum\limits_{l={{l}_{\min }}}^{{{l}_{\max }}}{lp(l)}}{\sum\limits_{i=1}^{{{N}_{m}}}{\sum\limits_{j=1}^{{{N}_{m}}}{{{R}_{ij}}}}}$	描述了对角线结构的递归点数与所有递归点数的比例，反映了系统的可预测性
层流性	$LAM=\frac{\sum\limits_{v={{v}_{\min }}}^{{{v}_{\max }}}{vp(v)}}{\sum\limits_{v=1}^{{{v}_{\max }}}{vp(v)}}$	描述了递归图中垂直线结构的递归点数量，反映了系统的间歇性和层次性
递归熵	$ENTER = -\sum_{l=l_{\min }}^{N_{m}} p(l) \ln p(l)$	基于对角线长度频率分布的香农熵，描述了动力学系统种确定性结构和复杂度，反映了系统的动力学信息量或随机性程度

故障	释义
f₀	正常状态
f₁	电阻R₁开路
f₂	电阻R₃开路
f₃	电容C₁被击穿
f₄	电容C₁漏电

故障	释义
f₀	正常状态
f₁	电阻R₁开路
f₂	电阻R₃开路
f₃	电容C₁被击穿
f₄	电容C₁漏电

故障	f₀	f₁	f₂	f₃	f₄
f₀	0	0.017 8	0.101 0	0.386 3	0.039 2
f₁	0.017 8	0	0.056 0	0.182 1	0.006 6
f₂	0.101 0	0.056 0	0	0.164 9	0.025 2
f₃	0.386 3	0.182 1	0.164 9	0	0.142 7
f₄	0.039 2	0.006 6	0.025 2	0.142 7	0