This study extends the problem of fault detection (FD) for linear discrete-time systems with unknown input to non-linear systems. Moreover, based on physical consideration, the constraints of state are considered. A non-linear recursive filter is developed where the constrained state and the input are interconnected. Constraints which can improve the quality of estimation are imposed on individual updated sigma points as well as the updated state. The advantage of algorithm is that it is able to incorporate arbitrary constraints on the states during the estimation procedure. Unknown input which can be any signal is obtained by least-squares unbiased estimation and the state estimation problem is transformed into a standard unscented Kalman filter problem. By testing the mean of the innovation process, a real-time FD approach is proposed. Simulations are provided to demonstrate the effectiveness of the theoretical results.

References

1. 1)
  - 33. Sharma, R., Aldeen, M.: ‘Fault and disturbance reconstruction in non-linear systems using a network of interconnected sliding mode observers’, IET Control Theory Appl., 2011, 5, (6), pp. 751–763 (doi: 10.1049/iet-cta.2009.0592).
2. 2)
  - 21. Simon, D., Chia, T.L.: ‘Kalman filtering with state equality constraints’, IEEE Trans. Aerosp. Electron. Syst., 2002, 38, (1), pp. 128–136 (doi: 10.1109/7.993234).
3. 3)
  - 6. Hajiyev, C., Caliskan, F.: ‘Sensor and control surface/actuator failure detection and isolation applied to F-16 flight dynamic’, Aircraft Eng. Aerospace Technol., 2005, 77, (2), pp. 152–160 (doi: 10.1108/00022660510585992).
4. 4)
  - 25. Walker, D.M.: ‘Parameter estimation using Kalman filters with constraints’, Int. J. Bifurcation Chaos, 2006, 16, (4), pp. 1067–1078 (doi: 10.1142/S0218127406015325).
5. 5)
  - 10. Julier, S.J., Uhlmann, J.K.: ‘Unscented filtering and nonlinear estimation’, Proc. IEEE, 2004, 92, (3), pp. 401–422 (doi: 10.1109/JPROC.2003.823141).
6. 6)
  - 12. Li, P.H., Zhang, T.W., Ma, B.: ‘Unscented Kalman filter for visual curve tracking’, Image Vis. Comput., 2004, 22, (2), pp. 157–164 (doi: 10.1016/j.imavis.2003.07.004).
7. 7)
  - 15. Kitanidis, P.K.: ‘Unbiased minimum-variance linear state estimation’, Automatic, 1987, 23, (6), pp. 775–778 (doi: 10.1016/0005-1098(87)90037-9).
8. 8)
  - 26. Rao, C.V., Rawlings, J.B., Mayne, D.Q.: ‘Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations’, IEEE Trans. Autom. Control, 2003, 48, (2), pp. 246–258 (doi: 10.1109/TAC.2002.808470).
9. 9)
  - 22. Ko, S., Bitmead, R.R.: ‘State estimation for linear systems with state equality constraints’, Automatica, 2007, 43, (8), pp. 1363–1368 (doi: 10.1016/j.automatica.2007.01.017).
10. 10)
  - 9. Julier, S.J., LaViola, J.J.: ‘On Kalman filtering with nonlinear equality constraints’, IEEE Trans. Signal Process., 2007, 55, (6), pp. 2774–2784 (doi: 10.1109/TSP.2007.893949).
11. 11)
  - 4. Alessandri, A.: ‘Fault diagnosis for nonlinear systems using a bank of neural estimators’, Comput. Ind., 2003, 52, (3), pp. 271–289 (doi: 10.1016/S0166-3615(03)00131-3).
12. 12)
  - 16. Darouach, M., Zasadzinski, M.: ‘Unbiased minimum variance estimation for systems with unknown exogenous inputs’, Automatica, 1997, 33, (4), pp. 717–719 (doi: 10.1016/S0005-1098(96)00217-8).
13. 13)
  - 31. Soken, H.E., Hajiyev, C.: ‘Pico satellite attitude estimation via robust unscented Kalman filter in the presence of measurement faults’, ISA Trans., 2010, 49, (3), pp. 249–256 (doi: 10.1016/j.isatra.2010.04.001).
14. 14)
  - 5. Perhinschi, M.G., Lando, M., Massotti, L.et al.: ‘On-line parameter estimation issues for the Nasa Ifcsf-15 fault tolerant systems’, Proc. 20th Annual American Control Conf. (ACC), (2002).
15. 15)
  - 3. Rago, C., Prasanth, R., Mehra, R.K., Fortenbaugh, R., Ieee, : ‘Failure detection and identification and fault tolerant control using the Imm-Kf with applications to the Eagle-Eye Uav’, Proc. 37th IEEE Conf. on Decision and Control, (1998).
16. 16)
  - 11. Kandepu, R., Foss, B., Imsland, L.: ‘Applying the unscented Kalman filter for nonlinear state estimation’, J. Proces. Control, 2008, 18, (7–8), pp. 753–768 (doi: 10.1016/j.jprocont.2007.11.004).
17. 17)
  - 13. Dini, D.H., Mandic, D.P., Julier, S.J.: ‘A widely linear complex unscented Kalman filter’, IEEE Signal Process. Lett., 2011, 18, (11), pp. 623–626 (doi: 10.1109/LSP.2011.2166259).
18. 18)
  - 27. Rao, C.V., Rawlings, J.B., Lee, J.H.: ‘Constrained linear state estimation – a moving horizon approach’, Automatica, 2001, 37, (10), pp. 1619–1628 (doi: 10.1016/S0005-1098(01)00115-7).
19. 19)
  - 30. Kalman, R.E.: ‘A new approach to linear filtering and prediction problem’, IEEE Trans. Autom. Control, 1960, 82, (Series D), pp. 35–45.
20. 20)
  - 7. Xiong, K., Zhang, H.Y., Chan, C.W.: ‘Performance evaluation of Ukf-based nonlinear filtering’, Automatica, 2006, 42, (2), pp. 261–270 (doi: 10.1016/j.automatica.2005.10.004).
21. 21)
  - 29. Rotea, M., Lana, C.: ‘State estimation with probability constraints’, Int. J. Control, 2008, 81, (6), pp. 920–930 (doi: 10.1080/00207170701531149).
22. 22)
  - 17. Hsieh, C.S.: ‘Robust two-stage Kalman filters for systems with unknown inputs’, IEEE Trans. Autom. Control, 2000, 45, (12), pp. 2374–2378 (doi: 10.1109/9.895577).
23. 23)
  - 32. Hajiyev, C.M., Caliskan, F., Inst Electr, E.: ‘Fault detection in flight control systems via innovation sequence of Kalman filter’, UKACC Int. Conf. on Control'98, Vols I&Ii, 1998, pp. 1528–1533.
24. 24)
  - 18. Gillijns, S., De Moor, B.: ‘Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough’, Automatica, 2007, 43, (5), pp. 934–937 (doi: 10.1016/j.automatica.2006.11.016).
25. 25)
  - 8. Julier, S.J., Uhlmann, J.K.: ‘A new extension of the Kalman filter to nonlinear systems’, (1997).
26. 26)
  - 19. Gillijns, S., De Moor, B.: ‘Unbiased minimum-variance input and state estimation for linear discrete-time systems’, Automatica, 2007, 43, (1), pp. 111–116 (doi: 10.1016/j.automatica.2006.08.002).
27. 27)
  - 1. Zhang, Y.M., Li, X.R., Ieee, : ‘Detection and diagnosis of sensor and actuator failures using interacting multiple-model estimator’, Proc. 36th IEEE Conf. on Decision and Control, (1997).
28. 28)
  - 2. Maybeck, P.S.: ‘Multiple model adaptive algorithms for detecting and compensating sensor and actuator/surface failures in aircraft flight control systems’, Int. J. Robust Nonlinear Control, 1999, 9, (14), pp. 1051–1070 (doi: 10.1002/(SICI)1099-1239(19991215)9:14<1051::AID-RNC452>3.0.CO;2-0).
29. 29)
  - 28. Vachhani, P., Narasimhan, S., Rengaswamy, R.: ‘Robust and reliable estimation via unscented recursive nonlinear dynamic data reconciliation’, J. Process Control, 2006, 16, (10), pp. 1075–1086 (doi: 10.1016/j.jprocont.2006.07.002).
30. 30)
  - 23. Teixeira, B.O.S., Chandrasekar, J., Torres, L.A.B., Aguirre, L.A., Bernstein, D.S.: ‘State estimation for linear and non-linear equality-constrained systems’, Int. J. Control, 2009, 82, (5), pp. 918–936 (doi: 10.1080/00207170802370033).
31. 31)
  - 20. Kerwin, W.S., Prince, J.L.: ‘On the optimality of recursive unbiased state estimation with unknown inputs’, Automatica, 2000, 36, (9), pp. 1381–1383 (doi: 10.1016/S0005-1098(00)00046-7).
32. 32)
  - 24. Teixeira, B.O.S., Chandrasekar, J., Palanthandalam-Madapusi, H.J., Torres, L.A.B., Aguirre, L.A., Bernstein, D.S.: ‘Gain-Constrained Kalman Filtering for Linear and Nonlinear Systems’, IEEE Trans. Signal Process., 2008, 56, (9), pp. 4113–4123 (doi: 10.1109/TSP.2008.926101).
33. 33)
  - 14. Hsieh, C.S., Ieee, : ‘Optimal minimum-variance filtering for systems with unknown inputs’, WCICA 2006: Sixth World Congress on Intelligent Control and Automation, Vol 1–12, Conf. Proc., 2006, pp. 1870–1874.

Fault detection for non-linear system with unknown input and state constraints

References

Related content