Abstract
To manage the state estimation and fault-diagnosis problem of linear discrete uncertain systems with time delay, a state estimation and fault-diagnosis algorithm based on an improved zonotopic Kalman filter is proposed under the assumption that the process interference and measurement noise of the systems are unknown but bounded. First, zonotopes are used to contain the nonzero initial conditions of the system with time delay, and an optimal zonotopic Kalman filter is designed by using an iterative replacement method to determine the relationship between the current time and the delayed time. Subsequently, the optimal observer gain of the optimal zonotopic Kalman filter is designed by minimizing the size of the zonotopic sets to estimate the state sets. Next, the fault occurrence is detected by determining whether the true output value of the system is within the upper and lower bounds of the estimated output value, and the fault identification process is completed by the matching probability of the fault type. Finally, the fault-diagnosis of a numerical system, and the pitch system of a wind turbine are used as examples to demonstrate the effectiveness and feasibility of the proposed method for systems with time delay by analyzing the fault diagnosis results. A comparison with a normal fault-matching method indicates that the proposed fault-diagnosis algorithm is more rapid in fault identification.
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C. Edwards and S. Simani, “Fault diagnosis and fault-tolerant control in aerospace systems,” International Journal of Robust and Nonlinear Control, vol. 29, no. 16, pp. 5291–5292, November 2019.
Q. H. Zhang, “Adaptive Kalman filter for actuator fault diagnosis,” Automatica, vol. 93, pp. 333–342, July 2018.
Y. J. Wang, J. Q. Tian, Z. H. Chen, and X. T. Liu, “Model based insulation fault diagnosis for lithium-ion battery pack in electric vehicles,” Measurement, vol. 131, pp. 443–451, January 2019.
Y. Zhao and Y. Shen, “Distributed event-triggered state estimation and fault detection of nonlinear stochastic systems” Journal of the Franklin Institute-Engineering and Applied Mathematics, vol. 356, no. 17, pp. 10335–10354, November 2019.
H. R. Hwang, B. S. Kim, T. H. Cho, and I. S. Lee, “Implementation of a fault diagnosis system using neural networks for solar panel,” International Journal of Control, Automation, and Systems, vol. 17, no. 4, pp. 1050–1058, April 2019.
K. Verbert, R. Babuska, and B. De Schutter, “Bayesian and Dempster-Shafer reasoning for knowledge-based fault diagnosis-A comparative study,” Engineering Applications of Artificial Intelligence, vol. 60, pp. 136–150, April 2017.
H. Talhaoui, A. Menacer, A. Kessal, and A. Tarek, “Experimental diagnosis of broken rotor bars fault in induction machine based on Hilbert and discrete wavelet transforms,” International Journal of Advanced Manufacturing Technology, vol. 95, no. 1–4, pp. 1399–1408, March 2018.
N. T. Truong, T. I. Seo, and S. D. Nguyen, “Bearing fault online identification based on ANFIS,” International Journal of Control, Automation, and Systems, vol. 19, no. 4, pp. 1703–1714, April 2021.
J. Y. Gong, B. Jiang, and Q. K. Shen, “Distributed-observer-based fault tolerant control design for nonlinear multi-agent systems” International Journal of Control, Automation, and Systems, vol. 17, no. 12, pp. 3149–3157, December 2019.
Q. K. Shen, B. Jiang, and P. Shi, “Adaptive fault tolerant control against actuator faults” International Journal of Adaptive Control and Signal Processing, vol. 31, no. 2, pp. 147–162, February 2017.
R. Khan, P. Williams, P. Riseborough, A. Rao, and R. Hill, “Fault detection and identification-A filter investigation,” International Journal of Robust and Nonlinear Control, vol. 28, no. 5, pp. 1852–1870, March 2018.
F. Naseri, H. Samet, T. Ghanbari, and E. Farjah, “Power transformer differential protection based on least squares algorithm with extended kernel,” IET Science Measurement & Technology, vol. 13, no. 8, pp. 1102–1110, October 2019.
N. D. Peric, R. Paulen, M. E. Villanueva, and B. Chachuat, “Set-membership nonlinear regression approach to parameter estimation,” IET Science Measurement & Technology, vol. 70, pp. 80–95, October 2018.
M. Casini, A. Garulli, and A. Vicino, “A linear programming approach to online set membership parameter estimation for linear regression models,” International Journal of Adaptive Control and Signal Processing, vol. 31, no. 3, pp. 360–378, March 2017.
Y. Wang, Z. H. Wang, V. Puig, and G. Cembrano, “Zonotopic set-membership state estimation for discrete-time descriptor LPV systems,” IEEE Transactions on Automatic Control, vol. 64, no. 5, pp. 2092–2099, May 2019.
M. Pourasghar, V. Puig, and C. Ocampo-Martinez, “Interval observer versus set-membership approaches for fault detection in uncertain systems using zonotopes,” International Journal of Advanced Manufacturing Technology, vol. 29, no. 10, pp. 2819–2843, July 2019.
M. Buciakowski, M. Witczak, V. Puig, D. Rotondo, F. Nejjari, and J. Korbicz, “A bounded-error approach to simultaneous state and actuator fault estimation for a class of nonlinear systems,” Journal of Process Control, vol. 52, pp. 14–25, April 2017.
J. Wang, J. D. Wang, and M. Zhou, “On-line auxiliary input signal design for active fault detection and isolation based on set-membership and moving window techniques,” International Journal of Control, Automation, and Systems, vol. 17, no. 11, pp. 2796–2806, November 2019.
D. Y. Chen, N. Yang, J. Hu, and J. H. Du, “Resilient set-membership state estimation for uncertain complex networks with sensor saturation under round-robin protocol,” International Journal of Control, Automation, and Systems, vol. 17, no. 12, pp. 3035–3046, December 2019.
J. T. Li, Z. H. Wang, Y. Shen, and M. Rodrigues, “Zonotopic fault detection observer for linear parameter-varying descriptor systems,” International Journal of Robust and Nonlinear Control, vol. 29, no. 11, pp. 3426–3445, July 2019.
D. Rotondo, F. Nejjari, V. Puig, and J. Blesa, “Model reference FTC for LPV systems using virtual actuators and set-membership fault estimation,” International Journal of Robust and Nonlinear Control, vol. 25, no. 5, pp. 735–760, March 2015.
J. C. Hu and B. C. Ding, “An efficient offline implementation for output feedback min-max MPC,” International Journal of Robust and Nonlinear Control, vol. 29, no. 2, pp. 492–506, January 2018.
V. T. H. Le, C. Stoica, T. Alamo, E. F. Camacho, and D. Dumur, “Zonotopic guaranteed state estimation for uncertain systems,” Automatica, vol. 49, no. 11, pp. 3418–3424, November 2013.
C. Combastel, “Zonotopes and Kalman observers: Gain optimality under distinct uncertainty paradigms and robust convergence,” Automatica, vol. 55, pp. 265–273, May 2015.
W. H. Zhang, Z. H. Wang, S. H. Guo, and Y. Shen, “Interval estimation of sensor fault based on zonotopic Kalman filter,” International Journal of Control, vol. 94, no. 6, pp. 1641–1650, September 2019.
M. Pourasghar, C. Combastel, V. Puig, and C. Ocampo-Martinez, “FD-ZKF: A zonotopic Kalman filter optimizing fault detection rather than state estimation,” Journal of Process Control, vol. 73, pp. 89–102, January 2019.
H. Y. Shi, P. Li, J. T. Cao, C. L. Su, and J. X. Yu, “Robust fuzzy predictive control for discrete-time systems with interval time-varying delays and unknown disturbances,” IEEE Transactions on Fuzzy Systems, vol. 28, no. 7, pp. 1504–1516, July 2020.
Y. Zhao, J. Wang, F. Yan, and Y. Shen, “Adaptive sliding mode fault-tolerant control for type-2 fuzzy systems with distributed delays” Information Sciences, vol. 473, pp. 227–238, January 2019.
R. M. Yang, F. Y. Zang, L. Y. Sun, P. Zhou, and B. H. Zhang, “Finite-time adaptive robust control of nonlinear time-delay uncertain systems with disturbance,” International Journal of Robust and Nonlinear Control, vol. 29, no. 4, pp. 919–934, March 2019.
P. P. Yang, Y. Tang, M. D. Yan, and X. Zhu, “Consensus based control algorithm for nnonlinear vehicle platoons in the presence of time delay,” International Journal of Control, Automation, and Systems, vol. 17, no. 3, pp. 752–764, March 2019.
J. H. Yook, I. H. Kim, M. S. Han, and Y. I. Son, “Robustness improvement of DC motor speed control using communication disturbance observer under uncertain time delay,” Electronics Letters, vol. 53, no. 6, pp. 389–391, March 2017.
Z. H. Zhang, Z. H. Wang, W. T. Tang, Z. G. Feng, and Y. Shen, “Zonotopic reachable set estimation for linear discrete-time systems with time delay,” International Journal of Robust and Nonlinear Control, vol. 30, no. 14, pp. 5542–5558, July 2020.
F. Q. You, H. Li, Y. W. Zhang, and S. P. Guan, “A novel sensor fault diagnosis approach for time-varying delay systems with non-linear uncertainty,” Transactions of the Institute of Measurement and Control, vol. 39, no. 7, pp. 1114–1120, July 2017.
X. Y. Tong, W. C. Lian, and H. B. Wang, “A novel online multi-section weighed fault matching and detecting algorithm based on wide-area information,” Journal of Electrical Engineering & Technology, vol. 12, no. 6, pp. 2118–2126, November 2017.
Y. Wang, Z. H. Wang, V. Puig, and G. Cembrano, “Zonotopic fault estimation filter design for discrete-time descriptor systems,” IFAC-PapersOnLine, vol. 50, no. 1, pp. 5055–5060, July 2017.
L. I. Gliga, B. D. Ciubotaru, H. Chafouk, D. Popescu, and C. Lupu, “Fault diagnosis of a direct drive wind turbine using a bank of Goertzel filters,” Proc. of the 6th International Conference on Control, Decision and Information Technologies, pp. 1729–1734, September 2019.
M. Rahnavard, M. Ayati, M. R. H. Yazdi, and M. Mousavi, “Finite time estimation of actuator faults, states, and aerodynamic load of a realistic wind turbine,” Renewable Energy, vol. 130, pp. 256–267, January 2019.
D. H. Wu, W. Liu, J. Song, and Y. X. Shen, “Fault estimation and fault-tolerant control of wind turbines using the SDW-LSI algorithm,” IEEE Access, vol. 4, pp. 7223–7231, 2016.
L. Xu, W. L. Xiong, A. Alsaedi, and T. Hayat, “Hierarchical parameter estimation for the frequency response based on the dynamical window data,” International Journal of Control, Automation, and Systems, vol. 16, no. 4, pp. 1756–1764, August 2018.
Z. Y. Wang, Y. Wang, and Z. C. Ji, “A novel two-stage estimation algorithm for nonlinear Hammerstein-Wiener systems from noisy input and output data,” Journal of the Franklin Institute-Engineering and Applied Mathematics, vol. 354, no. 4, pp. 1937–1944, March 2017.
Y. Wang, H. Pu, P. Shi, C. K. Ahn, and J. Luo. “Sliding mode control for singularly perturbed Markov jump descriptor systems with nonlinear perturbation,” Automatica, vol. 127, p. 109515, May 2021.
J. Cheng, Y. Shan, J. Cao, J. H. Park, “Nonstationary control for T-S fuzzy Markovian switching systems with variable quantization density,” IEEE Transactions on Fuzzy Systems, vol. 29, no. 6, pp. 1375–1385, June 2021.
W. Zhou, J. Fu, H. Yan, X. Du, Y. Wang, and H. Zhou, “Event-triggered approximate optimal path-following control for unmanned surface vehicles with state constraints,” IEEE Transactions on Neural Networks and Learning Systems, pp. 1–15, July 2021. DOI: https://doi.org/10.1109/TNNLS.2021.3090054
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This work is supported in part by the the National Key Research and Development Program of China (2020YFB1710600), the Jiangsu Science and Technology Association Young Science and Technology Talents Lifting Project (TJ-2021-006) and the National Natural Science Foundation of China (61973138).
Zi-Xing Liu received her B.Sc. degree in automation from Jiangnan University, Jiangsu, China in 2019, and is currently pursuing an M.S. degree in Jiangnan University, Jiangsu, China. Her research interests include set-membership estimation and fault diagnosis.
Zi-Yun Wang received his B.Sc. degree in electronic information engineering from Jiangnan University in 2010 and a Ph.D. degree in control science and engineering from Jiangnan University in 2015. His research interests include system modeling and state estimation for practical industrial application.
Yan Wang received her Ph.D. degree in control science and engineering from Nanjing University of Science and Technology in 2006. Her research interests include system modeling and optimal scheduling.
Zhi-Cheng Ji received his Ph.D. degree in power electronics and power drives from China University of Mining and Technology in 2004. His research interests include nonlinear control, adaptive control, and system identification.
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Liu, ZX., Wang, ZY., Wang, Y. et al. Optimal Zonotopic Kalman Filter-based State Estimation and Fault-diagnosis Algorithm for Linear Discrete-time System with Time Delay. Int. J. Control Autom. Syst. 20, 1757–1771 (2022). https://doi.org/10.1007/s12555-021-0267-x
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DOI: https://doi.org/10.1007/s12555-021-0267-x