A double window state observer for detection and isolation of abrupt changes in parameters

Byrski, J. ; Byrski, W.

International Journal of Applied Mathematics and Computer Science, Tome 26 (2016) no. 3, pp. 585-602.

Résumé

The paper presents a new method for diagnosis of a process fault which takes the form of an abrupt change in some real parameter of a time-continuous linear system. The abrupt fault in the process real parameter is reflected in step changes in many parameters of the input/output model as well as in step changes in canonical state variables of the system. Detection of these state changes will enable localization of the faulty parameter in the system. For detecting state changes, a special type of exact state observer will be used. The canonical state will be represented by the derivatives of the measured output signal. Hence the exact state observer will play the role of virtual sensors for reconstruction of the derivatives of the output signal. For designing the exact state observer, the model parameters before and after the moment of fault occurrence must be known. To this end, a special identification method with modulating functions will be used. A novel concept presented in this paper concerns the structure of the observer. It will take the form of a double moving window observer which consists of two signal processing windows, each of width T . These windows are coupled to each other with a common edge. The right-hand side edge of the left-side moving window in the interval [t − 2T, t − T ] is connected to the left-hand side edge of the right-side window which operates in the interval [t − T, t]. The double observer uses different measurements of input/output signals in both the windows, and for each current time t simultaneously reconstructs two values of the state—the final value of the state in the left-side window z_T (t − T ) and the initial value of the state z₀(t − T ) in the right-side window. If the process parameters are constant, the values of both the states on the common joint edge are the same. If an abrupt change (fault) in some parameter at the moment t_A = t − T occurs in the system, then step changes in some variables of the canonical state vector will also occur and the difference between the states will be detected. This will enable localization of the faulty parameter in the system.

Détail

Keywords: fault detection, fault isolation, exact state observer, parameter abrupt changes, derivative reconstruction, linear continuous system
Mots-clés : detekcja uszkodzeń, lokalizacja uszkodzeń, dokładny obserwator stanu, układ ciągły liniowy

Bibliographie

[1] Basseville, M. and Nikiforov, I.V. (1993). Detection of Abrupt Changes. Theory and Application, Prentice Hall, Englewood Cliffs, NJ.

[2] Blanke, M., Kinnaert, M., Lunze, J. and Staroswiecki, M. (2003). Diagnosis and Fault-Tolerant Control, Springer, Berlin.

[3] Byrski, J. (2014). Finite Memory Algorithms for Signal Processing in the Diagnosis of Processes, Ph.D., thesis, AGH University of Science and Technology, Kraków.

[4] Byrski, J. and Byrski, W. (2012a). Design and implementation of a new algorithm for fast diagnosis of step changes in parameters of continuous systems, 8th IFAC Symposium on Fault Detection Supervision and Safety for Technical Processes, SAFEPROCESS’12, Mexico City, Mexico, pp. 695–700.

[5] Byrski, W. (1995). Theory and application of the optimal integral state observers, 3rd European Control Conference, ECC’95, Rome, Italy, pp. 52–66.

[6] Byrski, W. (2003). The survey for the exact and optimal state observers in Hilbert spaces, 7th European Control Conference, ECC03, Cambridge, UK.

[7] Byrski, W. and Byrski, J. (2012b). The role of parameter constraints in EE and OE methods for optimal identification of continuous LTI models, International Journal of Applied Mathematics and Computer Science 22(2): 379–388, DOI: 10.2478/v10006-012-0028-3.

[8] Byrski, W. and Fuksa, S. (1996). Linear adaptive controller for continuous system with convolution filter, Proceedings of the IFAC 13th Triennial World Congress, San Francisco, CA, USA, pp. 379–384.

[9] Carlsson, B., Ahlen, A. and Sternad, M. (1991). Optimal differentiation based on stochastic signal models, IEEE Transactions on Signal Processing 39(2): 341–353.

[10] Chen, J. and Patton, R. (1999). Robust Model-Based Fault Diagnosis for Dynamic Systems, Kluwer Academic, Boston, MA.

[11] Chen, J. and Zhang, H. (1991). Robust detection of faulty actuators via input observers, International Journal of System Science 22(10): 1829–1839.

[12] Chiang, L., Russell, E. and Braatz, R. (2001). Fault Detection and Diagnosis in Industrial Systems, Springer, London.

[13] Costa, O.L., Fragoso, M.D. and Marques, R.P. (2005). Discrete-Time Markov Jump Linear Systems, Springer, Berlin.

[14] Costa, O.L., Fragoso, M.G. and Todorov, M.G. (2013). Continuous-Time Markov Jump Linear Systems, Springer, Berlin.

[15] Ding, X. (2013). Model-Based Fault Diagnosis Techniques, Springer, London.

[16] Ding, X. and Guo, L. (1996). Observer-based fault detection, 13th IFAC World Congress, San Francisco, CA, USA, pp. 157–162.

[17] Frank, P.M. (1990). Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy—a survey and some new results, Automatica 26(3): 459–474.

[18] Fuksa, S. and Byrski, W. (1984). General approach to linear optimal estimator of finite number of parameters, IEEE Transactions on Automatic Control 29(5): 470–472.

[19] Ibir, S. (2004). Linear time-derivative trackers, Automatica 40(3): 397–405.

[20] Isermann, R. (2006). Fault-Diagnosis Systems, Springer, Berlin.

[21] Jouffroy, J. and Reger, J. (2015). Finite-time simultaneous parameter and state estimation using modulating functions, IEEE Conference on Control Applications (CCA), Sydney, Australia, pp. 394–399.

[22] Korbicz, J., Kościelny, J.M., Kowalczuk, Z. and Cholewa, Z. (Eds.) (2004). Fault Diagnosis. Models, Artificial Intelligence, Application, Springer, Berlin.

[23] Lai, T.L. and Shan, J.Z. (1999). Efficient recursive algorithms for detection of abrupt changes in signals and control systems, IEEE Transactions on Automatic Control 44(5): 952–966.

[24] Lincon, S.A., Sivakumar, D. and Prakash, J. (2007). State and fault parameter estimation applied to three-tank bench mark relying on augmented state Kalman filter, ICGST Journal of Automatic Control and System Engineering 7(1): 33–41.

[25] Medvedev, A. (1996). Fault detection and isolation by functional continuous deadbeat observers, International Journal of Control 64(3): 425–439.

[26] Niedzwiecki, M. (1994). Identification of time-varying systems with abrupt parameter changes, Automatica 30(3): 447–459.

[27] Nuninger, W., Kratz, F. and Ragot, J. (1998). Finite memory generalised state observer for failure detection in dynamic systems, IEEE Conference on Decision Control, Tampa, FL, USA, pp. 581–585.

[28] Orani, N., Pisano, A. and Usai, E. (2010). Fault diagnosis for the vertical three-tank system via high-order sliding-mode observation, Journal of the Franklin Institute 347(6): 923–939.

[29] Patton, E., Frank, P. and Clark, R. (2000). Issues of Fault Diagnosis for Dynamic Systems, Springer, Berlin.

[30] Preisig, H.A. and Rippin, D.W.T. (1993). Theory and application of the modulating function method, Computers and Chemical Engineering 17(1): 1–16.

[31] Qu, R. (1996). A new approach to numerical differentiation and integration, Mathematical and Computer Modelling 24(10): 55–68.

[32] Reger, J. and Jouffroy, J. (2009). On algebraic time-derivative estimation and deadbeat state reconstruction, IEEE Conference on Decision and Control, Shanghai, China, pp. 1740–1745.

[33] Rolink, M., Boukhobza, T. and Sauter, D. (2006). High order sliding mode observer for fault actuator estimation and its application to the three tanks benchmark, German-French Institute for Automation and Robotics, http://hal.archives-ouvertes.fr/hal-00121029/en/.

[34] Sainz, M., Armengol, J. and Vehi, J. (2002). Fault detection and isolation of the three-tank system using the modal interval analysis, Journal of Process Control 12(2): 325–338.

[35] Simani, S., Fantuzzi, C. and Patton, R. (2003). Model Based Fault Diagnosis in Dynamic Systems Using Identification Techniques, Springer, London.

[36] Smith, M.S., Moes, T.R. and Morelli, E.A. (2003). Real-time stability and control derivative extraction from F-15 flight data, AIAA Atmospheric Flight Mechanics Conference and Exhibit, Austin, TX, USA, p. 5701.

[37] Theilliol, D., Noura, H. and Ponsart, J.C. (2002). Fault diagnosis and accommodation of a three-tank system based on analytical redundancy, ISA Transactions 41(3): 365–382.

[38] Ukil, A. and Zivanovic, R. (2007). Application of abrupt change detection in power systems disturbance analysis and relay performance monitoring, IEEE Transactions on Power Delivery 22(1): 365–382.

[39] Unbehauen, H. and Rao, G.P. (1987). Identification of Continuous Systems, North Holland, Amsterdam.

[40] Vainio, O., Renfors, M. and Saramaki, T. (1997). Recursive implementation of FIR differentiators with optimum noise attenuation, IEEE Transactions on Instrumentation and Measurement 46(5): 1202–1207.

[41] Wang, W., Bo, Y., Zhou, K. and Ren, Z. (2008). Fault detection and isolation for nonlinear systems with full state information, 17th IFAC World Congress, Seoul, Korea, pp. 901–909.

[42] Wei, T., Hon, Y.C. and Wang, Y.B. (2005). Reconstruction of numerical derivatives from scattered noisy data, Inverse Problems 21(2): 657–672.

[43] Young, P. (1981). Parameter estimation for continuous-time models—a survey, Automatica 17(1): 23–39.