Fault Isolability Evaluation Based on Zonotope
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摘要: 针对包含幅值有界而分布形式未知的故障及输入干扰项的线性离散系统, 提出了一种新的系统故障可分离性的量化评价方法. 故障可分离性是故障可诊断性中的重要部分, 针对现有方法中基于方向相似度的故障可分离性评价方法存在的不足加以补充, 提出了利用中心对称多胞体对故障可分离性进行分析, 将中心对称多胞体集合转化为多面体的表示形式, 以达到对故障可分离性量化评价的目的, 同时给出了具体评价原理和评价指标. 最后, 通过数值仿真算例, 验证了该方法的有效性和优越性.Abstract: This paper proposes a new quantitative evaluation method for fault isolability of the linear discrete systems subject to faults and input disturbances which are bounded but with unknown distributions. Fault isolability evaluation is an important part of fault diagnosis. In order to improve the existing direction similarity-based method, we propose a new fault isolability method via using zonotopes. To achieve the quantitative evaluation of fault isolability, zonotopes are converted into polytopes. Specific evaluation principles and indices are provided. Finally, numerical examples demonstrate the effectiveness and advantages of the proposed method.
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Key words:
- Dynamic system /
- zonotope /
- fault isolability /
- directional similarity
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图 1 各个故障模式组合下系统输出结果
Fig. 1 System output results under the combination of various fault modes
表 1 基于方向相似度可分离性评价结果
$(s=5)$ Table 1 Fault isolability evaluation results based on directional similarity
$(s=5)$ 次数 评价结果 次数 评价结果 次数 评价结果 1 0.0977 6 0.7662 11 0.9239 2 0.7345 7 0.0191 12 0.3114 3 0.1380 8 0.7235 13 0.6323 4 0.4580 9 0.1939 14 0.3153 5 0.2760 10 0.4178 15 0.2760 
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表 2 基于方向相似度可分离性评价结果
$(s=500)$ Table 2 Fault isolability evaluation results based on directional similarity
$(s=500)$ 次数 评价结果 次数 评价结果 次数 评价结果 1 0.6481 6 0.6836 11 0.6811 2 0.6480 7 0.6885 12 0.6734 3 0.6380 8 0.6654 13 0.6559 4 0.6294 9 0.6294 14 0.6289 5 0.6698 10 0.6168 15 0.6610
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表 3 数据分散程度评价
Table 3 Evaluation of data dispersion
窗口长度 极差($R$) 标准差($\sigma$) 窗口长度 极差($R$) 标准差($\sigma$) 5 0.9128 0.2577 225 0.1669 0.0349 10 0.7519 0.1758 250 0.1335 0.0297 50 0.3501 0.0882 375 0.1213 0.0278 100 0.2941 0.0604 450 0.0914 0.0259 175 0.1898 0.0514 500 0.0718 0.0226
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表 4 基于方向相似度可分离性评价结果(
$s=500$ )Table 4 Fault isolability evaluation results based on directional similarity (
$s=500$ )故障 $f_{1}$ $f_{2}$ $f_{3}$ $f_{4}$ $f_{1}$ NULL 1.0000 0.9236 0.4780 $f_{2}$ 1.0000 NULL 0.9236 0.4780 $f_{3}$ 0.9236 0.9236 NULL 0.6411 $f_{4}$ 0.4780 0.4780 0.6411 NULL
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表 5 基于中心对称多胞体可分离性评价结果(
$s=500$ )Table 5 Fault isolability evaluation results based on Zonotope (
$s=500$ )故障 $f_{1}$ $f_{2}$ $f_{3}$ $f_{4}$ $f_1$ NULL 1.0000 0.4464 0.1508 $f_2$ 1.0000 NULL 0.4463 0.1508 $f_3$ 0.4463 0.4463 NULL 0.3380 $f_4$ 0.1508 0.1508 0.3380 NULL
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表 6 基于中心对称多胞体可分离性评价结果(
$s=5$ )Table 6 Fault isolability evaluation results based on Zonotope (
$s=5$ )故障 $f_{1}$ $f_{2}$ $f_{3}$ $f_{4}$ $f_1$ NULL 1.0000 0.3665 0.2961 $f_2$ 1.0000 NULL 0.3665 0.2961 $f_3$ 0.3665 0.3665 NULL 0.3645 $f_4$ 0.2961 0.2961 0.3645 NULL
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[1] Chen J, Patton R J. Robust model-based fault diagnosis for dynamic systems. Springer Science & Business Media, 2012 [2] Wang Z H, Shi P, Lim C C. H-/H∞ fault detection observer in finite frequency domain for linear parameter-varying descriptor systems. Automatica, 2017, 86: 38−45 [3] 汤文涛, 王振华, 王烨, 沈毅. 基于未知输入集员滤波器的不确定系统故障诊断. 自动化学报, 2018, 44(9): 1717−1724Tang Wen-Tao, Wang Zhen-Hua, Wang Ye, Shen Yi. Fault diagnosis for uncertain systems based on unknown input set-membership filters. Acta Automatica Sinica, 2018, 44(9): 1717−1724 [4] 张柯, 姜斌. 基于故障诊断观测器的输出反馈容错控制设计. 自动化学报, 2010, 36(2): 274−281Zhang Ke, Jiang Bin. Fault diagnosis observer-based output feedback fault tolerant control design. Acta Automatica Sinica, 2010, 36(2): 274−281 [5] 冯建文, 孙黎, 刘金龙. 波音737-8事故简析. 航空动力, 2019, (02): 50−55Feng Jan-Wen, Sun Li, Liu Jin-Long. Brief analysis of the boeing 737-8 crashes. Aerospace Power, 2019, (02): 50−55 [6] 周东华, 刘洋, 何潇. 闭环系统故障诊断技术综述. 自动化学报, 2013, 39(11): 1933−1943Zhou Dong-Hua, Liu Yang, He Xiao. Review on fault diagnosis techniques for closed-loop systems. Acta Automatica Sinica, 2013, 39(11): 1933−1943 [7] Zhang J C, Zhu F L, Karimi H R, Wang F N. Observer-based sliding mode control for T-S fuzzy descriptor systems with time delay. IEEE Transactions on Fuzzy Systems, 2019, 27(10): 2009−2023 [8] 王大轶, 符方舟, 刘成瑞, 李文博, 刘文静, 何英姿, 邢琰. 控制系统可诊断性的内涵与研究综述. 自动化学报, 2018, 44(9): 1537−1553Wang Da-Yi, Fu Fang-Zhou, Liu Cheng-Rui, Li Wen-Bo, Liu Wen-Jing, He Ying-Zi, Xing Yan. Connotation and research status of diagnosability of control systems: a review. Acta Automatica Sinica, 2018, 44(9): 1537−1553 [9] Han W, Wang Z, Shen Y. H-/L∞ fault detection observer for linear parameter-varying systems with parametric uncertainty. International Journal of Robust and Nonlinear Control, 2019, 29(10): 2912−2926 [10] Li X H, Zhu F L, Xu L Y. Actuator and sensor fault reconstructions for uncertain Lipschitz nonlinear systems based on H∞ observers. Asian Journal of Control, 2015, 17(6): 2206−2217 [11] 张文瀚, 王振华, 沈毅. 基于鲁棒正不变集的传感器故障区间估计. 自动化学报, DOI: 10.16383/j.aas.c180504Zhang Wen-Han, Wang Zhen-Hua, Shen Yi. Interval estimation for sensor fault based on robust positive invariant. Acta Automatica Sinica, DOI: 10.16383/j.aas.c180504 [12] Tang W, Wang Z, Shen Y. Fault detection and isolation for discrete-time descriptor systems based on H-/L∞ observer and zonotopic residual evaluation. International Journal of Control, 2018: 1−12 [13] Wang Z H, Shen Y, Zhang X L. Actuator fault estimation for a class of nonlinear descriptor systems. International Journal of Systems Science, 2014, 45(3): 487−496 [14] IEEE STD 1522-2004. IEEE Trial—Use Standard for Testa- bility and Diagnosability Characteristics and Metrics. Pis-cataway, NJ: IEEE Standards Press, 2004. [15] 郭其一, 黄世泽. 非线性系统存在过程扰动时故障可分离研究. 同济大学学报(自然科学版), 2017, 45(08): 1183−1190 doi: 10.11908/j.issn.0253-374x.2017.08.012Guo Qi-Yi, Huang Shi-Ze. Study on the condition of separable fault of serial nonlinear system under the process noise. Journal of Tongji University (Natural Science), 2017, 45(08): 1183−1190 doi: 10.11908/j.issn.0253-374x.2017.08.012 [16] 姜斌, 冒泽慧, 杨浩, 等. 控制系统的故障诊断与故障调节. 北京: 国防工业出版社, 2009. 1-6Jiang Bin, Mao Ze-Hui, Yang Hao, et al. Fault diagnosis and fault accommodation for control systems. Beijing: National Defense Industry Press, 2009. 1−6 [17] 李晗, 萧德云. 基于数据驱动的故障诊断方法综述. 控制与决策, 2011, 26(1): 1−9Li Han, Xiao De-Yun. Survey on data driven fault diagnosis methods. Control and Decision, 2011, 26(1): 1−9 [18] Yue H H, Qin S J. Reconstruction-based fault identification using a combined index. Industrial and Engineering Chemistry Research, 2001, 40(20): 4403−4414 [19] Hua Y Z, Li Q D, Ren Z, Liu C R. A data driven method for quantitative fault diagnosability evaluation. In: Proceedings of the 2016 Chinese Control and Decision Conference. Yinchuan, China: IEEE, 2016. 1890−1894 [20] Zhang K, Jiang B, Shi P. Observer-based fault estimation and accomodation for dynamic systems. Springer, 2012 [21] Zhong M, Song Y, Ding S X. Parity space-based fault detection for linear discrete time-varying systems with unknown input. Automatica, 2015, 59: 120−126 [22] Zhang X, Zhu F, Guo S. Actuator fault detection for uncertain systems based on the combination of the interval observer and asymptotical reduced-order observer. International Journal of Control, 2019, (1): 1−20 [23] 李岳炀, 钟麦英. 具有多测量数据包丢失的线性离散时变系统故障检测滤波器设计. 自动化学报, 2015, 41(9): 1638−1648Li Yue-Yang, Zhong Mai-Ying. Fault detection filter design for linear discrete time-varying systems with multiple packet dropouts. Acta Automatica Sinnica, 2015, 41(9): 1638−1648 [24] Eguchi S, Copas J. Interpreting Kullback-Leibler divergence with the Neyman-Pearson lemma. Journal of Multivariate Analysis, 2006, 97(9): 2034−2040 [25] Eriksson D, Frisk E, Krysander M. A method for quantitative fault diagnosability analysis of stochastic linear descriptor models. Automatica, 2013, 49(6): 1591−1600 [26] 蒋栋年, 李炜, 王君, 孙晓静. 基于故障可诊断性量化评价的传感器优化配置方法研究. 自动化学报, 2018, 44(6): 1128−1137Jiang Dong-Nian, Li Wei, Wang Jun, Sun Xiao-Jing. Research on sensor optimal placement method using quantitative evaluation of fault diagnosability. Acta Automatica Sinica, 2018, 44(6): 1128−1137 [27] Eriksson D, Frisk E, Krysander M. A method for quantitative fault diagnosability analysis of stochastic linear descriptor models. Automatica, 2013, 49(6): 1591−1600 [28] 李文博, 王大轶, 刘成瑞. 基于方向相似度的航天器控制系统故障可诊断性评价研究. 中国控制会议, 2014.Li Wen-Bo, Wang Da-Yi, Liu Cheng-Rui. Fault diagnosability evaluation for spacecraft control systems via direction similarity. Chinese Control Conference, 2014. [29] Shen Q K, Jiang B, Shi P. Active fault-tolerant control against actuator fault and performance analysis of the effect of time delay due to fault diagnosis. International Journal of Control Automation and Systems, 2017, 15(2): 537−546 [30] Ben-Israel A, Greville T N E. Generalized inverses: theory and applications. Springer Science & Business Media, 2003 [31] Matias, Taupin, M -L. Mathematical methods of statistics. Journal of Political Economy, 1946, 53(4): 431−450 [32] 李佶桃, 王振华, 沈毅. 线性离散系统的有限频域集员故障检测观测器设计. 自动化学报, DOI: 10.16383/j.aas.c170725Li Ji-Tao, Wang Zhen-Hua, Shen Yi. Set-membership fault detection observer design in finite-frequency domain for linear discrete-time system. Acta Automatica Sinica, DOI: 10.16383/j.aas.c170725 [33] Combastel C. An Extended Zonotopic and Gaussian Kalman Filter(EZGKF) merging set-membership and stochastic paradigms: Toward non-linear filtering and fault detection. Annual Reviews in Control, 2016, 42: 232−243 [34] Combastel C. Zonotopes and Kalman observers: Gain optimality under distinct uncertainty paradigms and robust convergence. Automatica, 2015, 55: 265−273 [35] Matthias A, Olaf S, Martin B. Computing reachable sets of hybrid systems using a combination of zonotopes and polytopes. Nonlinear Analysis–Hybrid Systems, 2010, 4(2): 233−249 [36] Ziegler G M. Lectures on Polytopes. Lectures on polytopes, 1995 [37] Gover E, Krikorian N. Determinants and the volumes of parallelotopes and zonotopes. Linear Algebra & Its Applications, 2010, 433(1): 28−40 -
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