Fault estimation based on ensemble unscented Kalman filter for a class of nonlinear systems with multiplicative fault. (English) Zbl 1483.93662
Summary: In this paper, a method for fault estimation with a multiplicative model in a nonlinear system by the unscented Kalman filter is introduced. The faults appear in the form of component, sensor, and actuator in the system equations. By using the augmented method, a fault signal will be as state variable of the system, the system dynamic equations are rewritten to represent a fault as a state variable. The existence of nonlinear equations in the presence of system noises results in an identical non-Gaussian noise, which leads to the difficulty in solving the problem of fault estimation with the unscented Kalman filter. Therefore, a filter combining a Gaussian mixture model (GMM) and the augmented ensemble unscented Kalman filter (AEnUKF) is designed to estimate the fault in this class of nonlinear systems. Suitable conditions and assumptions are appointed to guarantee the convergence of the estimation error. Next, the performance of the proposed method is evaluated by simulating a bioreactor system. The results of the simulation for the multiplicative fault estimation demonstrated performance by the AEnUKF-GMM algorithm better than the AUKF in the presence of non-Gaussian noise.
Keywords:
fault estimation; multiplicative fault; non-Gaussian noise; unscented Kalman filter; augment; Gaussian mixture modelReferences:
| [1] | Alizadeh, T.; Barzegari, S., Fault tolerant control of electromagnetic suspension system with simultaneous sensor and actuator faults, 1-6 (2015) |
| [2] | Armaou, A.; Demetriou, M. A., Robust detection and accommodation of incipient component and actuator faults in nonlinear distributed processes, AIChE Journal, 54, 10, 2651-2662 (2008) · doi:10.1002/aic.11539 |
| [3] | Behzad, H.; Sadrnia, M. A.; Darabi, A.; Ramezani, A., A fault diagnosis approach for electrical induction motors via energetic based scheme (2017) |
| [4] | Bessaoudi, T.; Hmida, F. B.; Hsieh, C.-S., Robust state and fault estimation for nonlinear stochastic systems with unknown disturbances, 1699-1704 (2017) |
| [5] | Bishop, G.; Welch, G., An introduction to the kalman filter, Proc of SIGGRAPH, Course, 8(27599-23175), 41 (2001) · doi:http://132.206.230.228/e761/SIGGRAPH2001_CoursePack_08.pdf |
| [6] | Blanke, M.; Kinnaert, M.; Lunze, J.; Staroswiecki, M.; Schröder, J., Diagnosis and fault-tolerant control (Vol. 2) (2006), Springer · Zbl 1126.93004 |
| [7] | Brahim, I. H.; Mehdi, D.; Chaabane, M., Robust fault detection for uncertain T-S fuzzy system with unmeasurable premise variables: Descriptor approach, International Journal of Fuzzy Systems, 20, 2, 416-425 (2018) · doi:10.1007/s40815-017-0344-8 |
| [8] | Candy, J. V., Bayesian signal processing: Classical, modern, and particle filtering methods (2016), John Wiley & Sons |
| [9] | Daum, F., Nonlinear filters: Beyond the Kalman filter, IEEE Aerospace and Electronic Systems Magazine, 20, 8, 57-69 (2005) · doi:10.1109/MAES.2005.1499276 |
| [10] | Dempster, A. P.; Laird, N. M.; Rubin, D. B., Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society: Series B (Methodological), 39, 1, 1-22 (1977) · Zbl 0364.62022 · doi:10.1111/j.2517-6161.1977.tb01600.x |
| [11] | Ding, B.; Fang, H., Multi-faults detection and estimation for nonlinear stochastic system based on particle filter and hypothesis test, International Journal of Systems Science, 47, 16, 3812-3821 (2016) · Zbl 1346.93355 · doi:10.1080/00207721.2015.1126381 |
| [12] | Ding, B.; Fang, H., Fault prediction for nonlinear stochastic system with incipient faults based on particle filter and nonlinear regression, ISA Transactions, 68, 327-334 (2017) · doi:10.1016/j.isatra.2017.03.018 |
| [13] | Du, M.; Scott, J.; Mhaskar, P., Actuator and sensor fault isolation of nonlinear process systems, Chemical Engineering Science, 104, 294-303 (2013) · doi:10.1016/j.ces.2013.08.009 |
| [14] | Gao, C.; Duan, G., Robust adaptive fault estimation for a class of nonlinear systems subject to multiplicative faults, Circuits, Systems, and Signal Processing, 31, 6, 2035-2046 (2012) · Zbl 1269.93111 · doi:10.1007/s00034-012-9434-x |
| [15] | Gao, C.; Duan, G., Fault diagnosis and fault tolerant control for nonlinear satellite attitude control systems, Aerospace Science and Technology, 33, 1, 9-15 (2014) · doi:10.1016/j.ast.2013.12.011 |
| [16] | Georg, S.; Schulte, H., Actuator fault diagnosis and fault-tolerant control of wind turbines using a Takagi-Sugeno sliding mode observer, 516-522 (2013) |
| [17] | Govaers, F.; Koch, W.; Willett, P., Gaussian-mixture based ensemble Kalman filter (2015) |
| [18] | Gu, Y.; Yang, G. H., Sensor fault estimation for Lipschitz nonlinear systems in finite-frequency domain, International Journal of Systems Science, 48, 12, 2622-2632 (2017) · Zbl 1372.93083 · doi:10.1080/00207721.2017.1334099 |
| [19] | Hmida, F. B.; Khémiri, K.; Ragot, J.; Gossa, M., Three-stage Kalman filter for state and fault estimation of linear stochastic systems with unknown inputs, Journal of the Franklin Institute, 349, 7, 2369-2388 (2012) · Zbl 1287.93090 · doi:10.1016/j.jfranklin.2012.05.004 |
| [20] | Ishihara, S.; Yamakita, M., Unscented Gaussian sum filtering for interval constrained nonlinear systems (2009) |
| [21] | Jianjun, Y.; Jianqiu, Z.; Zesen, Z., Gaussian sum PHD filtering algorithm for nonlinear non-Gaussian models, Chinese Journal of Aeronautics, 21, 4, 341-351 (2008) · doi:10.1016/S1000-9361(08)60045-X |
| [22] | Jin, X., Adaptive fault tolerant control for a class of multi-input multi-output nonlinear systems with both sensor and actuator faults, International Journal of Adaptive Control and Signal Processing, 31, 10, 1418-1427 (2017) · Zbl 1376.93034 · doi:10.1002/acs.2775 |
| [23] | Kamal, E.; Aitouche, A.; Bayart, M., A fuzzy approach for actuator fault-tolerant control of wind Energy Conversion systems (2011) · Zbl 1254.93119 |
| [24] | Karami, M.; Wang, L., Fault detection and diagnosis for nonlinear systems: A new adaptive Gaussian mixture modeling approach, Energy and Buildings, 166, 477-488 (2018) · doi:10.1016/j.enbuild.2018.02.032 |
| [25] | Keller, J.-Y.; Darouach, M., Two-stage Kalman estimator with unknown exogenous inputs, Automatica, 35, 2, 339-342 (1999) · Zbl 0937.93049 · doi:10.1016/S0005-1098(98)00194-0 |
| [26] | Khalil, H. K., Nonlinear systems (2002), Upper Saddle River · Zbl 1003.34002 |
| [27] | Lewis, F. L., Optimal estimation: with an introduction to stochastic control theory (1986), John Wiley & Sons · Zbl 0665.93065 |
| [28] | Li, W.; Jia, Y., Distributed consensus filtering for discrete-time nonlinear systems with non-Gaussian noise, Signal Processing, 92, 10, 2464-2470 (2012) · doi:10.1016/j.sigpro.2012.03.009 |
| [29] | Ling-Ling, F.; Yong-Duan, S., Fault-tolerant control and disturbance attenuation of a class of nonlinear systems with actuator and component failures, Acta Automatica Sinica, 37, 5, 623-628 (2011) · doi:10.1016/S1874-1029(11)60206-1 |
| [30] | Liu, Z.; Chan, S.-C.; Wu, H.-C.; Wu, J., Bayesian unscented Kalman filter for state estimation of nonlinear and non-Gaussian systems (2016) |
| [31] | McLachlan, G. J.; Krishnan, T., The EM algorithm and extensions (Vol. 382) (2007), John Wiley & Sons |
| [32] | Nagy, A. M.; Mourot, G.; Marx, B.; Ragot, J.; Schutz, G., Systematic multimodeling methodology applied to an activated sludge reactor model, Industrial & Engineering Chemistry Research, 49, 6, 2790-2799 (2010) · doi:10.1021/ie8017687 |
| [33] | O’neil, P. V., Advanced engineering mathematics (2011), Cengage learning |
| [34] | Papoulis, A.; Pillai, S. U., Probability, random variables, and stochastic processes (2002), Tata McGraw-Hill Education |
| [35] | Rahimi, A.; Kumar, K. D.; Alighanbari, H., Fault estimation of satellite reaction wheels using covariance based adaptive unscented Kalman filter, Acta Astronautica, 134, 159-169 (2017) · doi:10.1016/j.actaastro.2017.02.003 |
| [36] | Rajinikanth, V.; Latha, K., Identification and control of unstable biochemical reactor, International Journal of Chemical Engineering and Applications, 1, 1, 106-111 (2010) · doi:10.7763/IJCEA.2010.V1.18 |
| [37] | Reif, K.; Gunther, S.; Yaz, E.; Unbehauen, R., Stochastic stability of the discrete-time extended Kalman filter, IEEE Transactions on Automatic Control, 44, 4, 714-728 (1999) · Zbl 0967.93090 · doi:10.1109/9.754809 |
| [38] | Shahriari-kahkeshi, M.; Sheikholeslam, F.; Askari, J., Adaptive fault detection and estimation scheme for a class of uncertain nonlinear systems, Nonlinear Dynamics, 79, 4, 2623-2637 (2015) · doi:10.1007/s11071-014-1836-9 |
| [39] | Shaker, M. S.; Kraidi, A. A., Robust fault-tolerant control of wind turbine systems against actuator and sensor faults, Arabian Journal for Science and Engineering, 42, 7, 3055-3063 (2017) · Zbl 1390.93201 · doi:10.1007/s13369-017-2525-z |
| [40] | Simon, D., Optimal state estimation: Kalman, H infinity, and nonlinear approaches (2006), John Wiley & Sons |
| [41] | Steinberg, M., Historical overview of research in reconfigurable flight control. Proceedings of the Institution of Mechanical Engineers, part G, Journal of Aerospace Engineering, 219, 4, 263-275 (2005) · doi:10.1243/095441005X30379 |
| [42] | Talebi, H. A.; Khorasani, K.; Tafazoli, S., A recurrent neural-network-based sensor and actuator fault detection and isolation for nonlinear systems with application to the satellite’s attitude control subsystem, IEEE Transactions on Neural Networks, 20, 1, 45-60 (2008) · doi:10.1109/TNN.2008.2004373 |
| [43] | Tang, L.; Zhang, X.; DeCastro, J., Diagnosis of engine sensor, actuator and component faults using a bank of adaptive nonlinear estimators, 1-11 (2011) |
| [44] | Terejanu, G.; Singla, P.; Singh, T.; Scott, P. D., Adaptive Gaussian sum filter for nonlinear Bayesian estimation, IEEE Transactions on Automatic Control, 56, 9, 2151-2156 (2011) · Zbl 1368.93730 · doi:10.1109/TAC.2011.2141550 |
| [45] | Tudoroiu, N.; Zaheeruddin, M., Joint UKF estimator for fault detection and isolation in Heating Ventilation and Air Conditioning systems (2011) |
| [46] | Van Der Merwe, R.; Doucet, A.; De Freitas, N.; Wan, E. A., The unscented particle filter, Advances in Neural Information Processing Systems, 13, 584-590 (2001) |
| [47] | Van Eykeren, L.; Chu, P., Nonlinear model-based fault detection for a hydraulic actuator, 6678 (2011) |
| [48] | Venkatasubramanian, V.; Rengaswamy, R.; Kavuri, S. N.; Yin, K., A review of process fault detection and diagnosis: Part III: Process history based methods, Computers & Chemical Engineering, 27, 3, 327-346 (2003) · doi:10.1016/S0098-1354(02)00162-X |
| [49] | Wan, E. A.; Van Der Merwe, R., The unscented Kalman filter for nonlinear estimation, 153-158 (2000) |
| [50] | Wang, J.; Hu, L.; Chen, F.; Wen, C., Multiple-step fault estimation for interval type-II TS fuzzy system of hypersonic vehicle with time-varying elevator faults, International Journal of Advanced Robotic Systems, 14, 2 (2017) · doi:10.1177/1729881417699149 |
| [51] | Xiao, M.; Zhang, Y.; Fu, H., Three-stage unscented Kalman filter for state and fault estimation of nonlinear system with unknown input, Journal of the Franklin Institute, 354, 18, 8421-8443 (2017) · Zbl 1380.93262 · doi:10.1016/j.jfranklin.2017.09.031 |
| [52] | Xiong, K.; Zhang, H.; Chan, C., Performance evaluation of UKF-based nonlinear filtering, Automatica, 42, 2, 261-270 (2006) · Zbl 1103.93045 · doi:10.1016/j.automatica.2005.10.004 |
| [53] | Yan, Y.; Luh, P. B.; Sun, B., Fault detection of cooling coils based on unscented Kalman filters and statistical process control (2013) |
| [54] | Zarch, M. G.; Puig, V.; Poshtan, J.; Shoorehdeli, M. A., Fault detection and isolation using viability theory and interval observers, International Journal of Systems Science, 49, 7, 1445-1462 (2018) · Zbl 1482.93229 · doi:10.1080/00207721.2018.1454536 |
| [55] | Zeng, Y.; Xing, Y.-R.; Ma, H.-J.; Yang, G.-H., Adaptive fault diagnosis for robot manipulators with multiple actuator and sensor faults, 6569-6574 (2015) |
| [56] | Zhang, Y.; Jiang, J., Bibliographical review on reconfigurable fault-tolerant control systems, Annual Reviews in Control, 32, 2, 229-252 (2008) · doi:10.1016/j.arcontrol.2008.03.008 |
| [57] | Zhang, Y.; Qin, S. J., Adaptive actuator/component fault compensation for nonlinear systems, AIChE Journal, 54, 9, 2404-2412 (2008) · doi:10.1002/aic.11546 |
| [58] | Ziyabari, S. H. S.; Shoorehdeli, M. A., Robust fault diagnosis scheme in a class of nonlinear system based on UIO and fuzzy residual, International Journal of Control, Automation and Systems, 15, 3, 1145-1154 (2017) · doi:10.1007/s12555-016-0145-0 |
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