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Actuator and Sensor Fault Detection and Failure Prediction for Systems with Multi-dimensional Nonlinear Partial Differential Equations

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  • Control Theory and Applications
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Abstract

This paper presents a new model-based fault detection and failure prediction framework for a class of multi-input and multi-output (MIMO) nonlinear distributed parameter systems (DPS) described by partial differential equations (PDE) with actuator and sensor faults. The fault functions cover both abrupt and incipient faults. A Luenberger type observer is used to monitor the health of the DPS as a detection observer on the basis of the nonlinear PDE representation of the system and by utilizing only the measured output vector. By taking the difference between measured and estimated outputs, a residual signal is generated for fault detection. If the detection residual exceeds a predefined threshold, a fault is claimed to be active. Once an actuator or a sensor fault is detected, an appropriate fault parameter update law is developed to learn the fault dynamics online with the help of an additional measurement. Later, an explicit formula is introduced to estimate the time-to-failure in the presence of an actuator/sensor fault by utilizing the limiting values of the output vector along with the estimated fault parameter vector. Eventually, the effectiveness of the proposed detection and prediction framework is demonstrated on a nonlinear process.

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References

  1. D. Miljković, “Fault detection methods: A literature survey,” Proc. of the 34th International Convention MIPRO, pp. 750–755, 2011.

  2. R. Isermann, “Model-based fault-detection and diagnosis-status and applications,” Annual Reviews in Control, vol. 29, no. 1, pp. 71–85, 2015.

    Article  Google Scholar 

  3. J. J. Gertler, “Survey of model-based failure detection and isolation in complex plants,” IEEE Control Systems Magazine, vol. 8, no. 6, pp. 3–11, 1988.

    Article  Google Scholar 

  4. J. Chen and R. J. Patton, Robust Model-based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, MA, USA, 1999.

    Book  Google Scholar 

  5. J. Yang, F. Zhu, X. Wang, and X. Bu, “Robust sliding-mode observer-based sensor fault estimation, actuator fault detection and isolation for uncertain nonlinear systems,” International Journal of Control, Automation, and Systems, vol. 13, no. 5, pp. 1037–1046, 2015.

    Article  Google Scholar 

  6. C. P. Tan, F. Crusca, and M. Aldeen, “Extended results on robust state estimation and fault detection,” Automatica, vol. 44, no. 8, pp. 2027–2033, 2008.

    Article  MathSciNet  Google Scholar 

  7. X. G. Yan and C. Edwards, “Adaptive sliding-mode-observer-based fault reconstruction for nonlinear systems with parametric uncertainties,” IEEE Transactions on Industrial Electronics, vol. 55, no. 11, pp. 4029–4036, 2008.

    Article  Google Scholar 

  8. M. Shabanian and M. Montazeri, “A neuro-fuzzy online fault detection and diagnosis algorithm for nonlinear and dynamic systems,” International Journal of Control, Automation, and Systems, vol. 9, no. 4, pp. 665, 2011.

    Article  Google Scholar 

  9. Y. Wu and J. Dong, “Fault detection for T-S fuzzy systems with partly unmeasurable premise variables,” Fuzzy Sets and Systems, vol. 338, pp. 136–156, 2018.

    Article  MathSciNet  Google Scholar 

  10. J. Dong, Y. Wu, and G. Yang, “A new sensor fault isolation method for T-S fuzzy systems,” IEEE Transactions on Cybernetics, vol. 47, no. 9, pp. 2437–2447, 2017.

    Article  Google Scholar 

  11. K. Zhang, B. Jiang, and P. Shi, “Adjustable parameter-based distributed fault estimation observer design for multiagent systems with directed graphs,” IEEE Transactions on Cybernetics, vol. 47, no. 2, pp. 306–314, 2017.

    Google Scholar 

  12. S. Ghantasala and N. H. El-Farra, “Robust actuator fault isolation and management in constrained uncertain parabolic PDE systems,” Automatica, vol. 45, no. 10, pp. 2368–2373, 2009.

    Article  MathSciNet  Google Scholar 

  13. A. Alonso and B. E. Ydstie, “Stabilization of distributed systems using irreversible thermodynamics,” Automatica, vol. 37, pp. 1739–1755, 2001.

    Article  MathSciNet  Google Scholar 

  14. M. Demetriou and N. Kazantzis, “A new actuator activation policy for performance enhancement of controlled diffusion processes,” Automatica, vol. 40, pp. 415–421, 2004.

    Article  MathSciNet  Google Scholar 

  15. Q. Fu, W. G. Gu, P. P. Gu, and J. R. Wu, “Iterative learning control for a class of mixed hyperbolic-parabolic distributed parameter systems,” International Journal of Control, Automation, and Systems, vol. 14, no. 6, pp. 1455–1463, 2016.

    Article  Google Scholar 

  16. H. L. Xing, D. H. Li, and W. S. Cui, “Robust control guaranteeing uniform ultimate boundedness for a class of mismatched uncertain parabolic distributed parameter systems,” International Journal of Control, Automation, and Systems, vol. 11, no. 4, pp. 728–733, 2013.

    Article  Google Scholar 

  17. A. Armaou and M. Demetriou, “Robust detection and accommodation of incipient component and actuator faults in nonlinear distributed processes,” AIChE Journal, vol. 54, pp. 2651–2662, 2008.

    Article  Google Scholar 

  18. M. Demetriou, A. S. Ackleh, and S. Reich, “Detection and accommodation of second order distributed parameter systems with abrupt changes in the input term: Existence and approximation,” Kybernetika, vol. 36, no. 1, pp. 117–132, 2000.

    MathSciNet  MATH  Google Scholar 

  19. W. Mu, J. Wang, and W. Feng, “Fault detection and fault-tolerant control of actuators and sensors in distributed parameter systems,” Journal of the Franklin Institute, vol. 354, no. 8, pp. 3341–3363, 2017.

    Article  MathSciNet  Google Scholar 

  20. A. Friedman, Partial Differential Equations of Parabolic Type, Courier Corporation, 2013.

  21. J. Cai, H. Ferdowsi, and S. Jagannathan, “Model-based fault detection, estimation, and prediction for a class of linear distributed parameter systems,” Automatica, vol. 66, pp.122–131, 2016.

    Article  MathSciNet  Google Scholar 

  22. J. Cai, H. Ferdowsi, and S. Jagannathan, “Model-based actuator fault accommodation for distributed parameter systems represented by coupled linear PDEs,” Proc. of IEEE Conference on Control Applications (CCA), pp. 978–983, 2015.

  23. H. Ferdowsi and S. Jagannathan, “Fault diagnosis of distributed parameter systems modeled by linear parabolic partial differential equations with state faults,” ASME Journal of Dynamic Systems, Measurement, and Control, vol. 140, no. 1, pp. 011010–011010–6, 2018.

    Article  Google Scholar 

  24. J. Deutscher, “Fault detection for linear distributed-parameter systems using finite-dimensional functional observers,” International Journal of Control, vol. 89, no. 3, pp. 550–563, 2016.

    Article  MathSciNet  Google Scholar 

  25. F. Fischer and J. Deutscher, “Flatness-based algebraic fault diagnosis for distributed-parameter systems,” Automatica, vol. 117, p. 108987, 2020.

    Article  MathSciNet  Google Scholar 

  26. T. Meurer, “On the extended Luenberger-type observer for semilinear distributed-parameter systems,” IEEE Transactions on Automatic Control, vol. 58, no. 7, pp. 1732–1743, 2013.

    Article  MathSciNet  Google Scholar 

  27. A. Baccoli, Y. Orlov, and A. Pisano, “On the boundary control of coupled reaction-diffusion equations having the same diffusivity parameters,” Proc. of IEEE Conference on Decision and Control (CDC), pp. 5222–5228, 2014.

  28. Z. Yao and N. H. El-Farra, “Robust fault detection and reconfiguration in sampled-data uncertain distributed processes,” Proc. of IEEE Conference on Decision and Control (CDC), pp. 4925–4930, 2011.

  29. A. Baniamerian and K. Khorasani, “Fault detection and isolation of dissipative parabolic PDEs: Finite-dimensional geometric approach,” Proc. of the American Control Conference, pp. 5894–5899, 2012.

  30. J. Sarangapani, Neural Network Control of Nonlinear Discrete-time Systems, vol. 21, CRC Press, 2006.

  31. M. Krstic and A. Smyshlyaev, Boundary Control of PDEs: A Course on Backstepping Designs, vol. 16, Siam, 2008.

  32. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, 1952.

  33. A. Smyshlyaev and M. Krstic, Adaptive Control of Parabolic PDEs, Princeton University Press, 2010.

  34. H. Ferdowsi and S. Jagannathan, “A unified model-based fault diagnosis scheme for non-linear discrete-time systems with additive and multiplicative faults,” Transactions of the Institute of Measurement and Control, vol. 35, no. 6, pp. 742–752, 2013.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Northern Illinois University, 590 Garden Rd, DeKalb, IL, 60115, USA

    Hasan Ferdowsi

  2. Electrical and Computer Engineering Department, Missouri University of Science and Technology, 301 W. 16th St., Rolla, MO, 65409, USA

    Jia Cai & Sarangapani Jagannathan

Authors
  1. Hasan Ferdowsi
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  2. Jia Cai
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  3. Sarangapani Jagannathan
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Corresponding author

Correspondence to Hasan Ferdowsi.

Additional information

Hasan Ferdowsi received his Ph.D. degree in electrical engineering at Missouri University of Science and Technology in December 2013. He is currently an Assistant Professor of Electrical Engineering at Northern Illinois University (NIU), where he has been a faculty since 2017. He is the director of Autonomous Robotics and Controls (ARC) lab at NIU and research interests include fault diagnosis and fault-tolerant control, adaptive control and estimation, distributed systems, autonomous vehicles, and robotics.

Jia Cai received her Ph.D. degree in electrical engineering at Missouri University of Science and Technology in 2016. She worked as an Electrical Engineer at Predictronics Corp. between 2017 and 2019, and has been a Software Engineer at Microsoft since 2019. Her research interests include adaptive control, fault diagnosis and prognosis as well as mathematical optimization.

Sarangapani Jagannathan is a Rutledge-Emerson Distinguished Professor of the Electrical and Computer Engineering at the Missouri University of Science and Technology. He was a Site Director for the NSF Industry/University Cooperative Research Center on Intelligent Maintenance Systems for 13 years. His research interests include learning and adaptation, neural network control, secure human-cyber-physical systems, prognostics, and autonomous systems/robotics.

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Ferdowsi, H., Cai, J. & Jagannathan, S. Actuator and Sensor Fault Detection and Failure Prediction for Systems with Multi-dimensional Nonlinear Partial Differential Equations. Int. J. Control Autom. Syst. 20, 789–802 (2022). https://doi.org/10.1007/s12555-019-0622-3

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  • DOI: https://doi.org/10.1007/s12555-019-0622-3

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