(552a) Active Fault Diagnosis for Stochastic Nonlinear Systems

Detection of process malfunction and faults is becoming increasingly challenging for high-performance technical systems. The increased level of dynamical complexity in these systems makes them prone to abnormalities such as sensor faults, actuator faults and disturbances. Fault detection and isolation (FDI) has become a crucial component of advanced process monitoring and control applications to meet stringent requirements of complex systems. FDI is intended to first detect whether a fault has occurred and then identify which component has failed [1][2]. Active fault diagnosis (FD) involves designing the system input signals such that the outputs pertaining to various fault scenarios can be differentiated. Active FD is particularly useful when the outputs corresponding to the nominal behavior and different faulty scenarios overlap or when the control system masks the effect of faults [3]. Thus, active FD enables detection and isolation of faults that may not otherwise be possible under nominal operation.

Motivated by the above considerations, several studies have considered active FD for uncertain systems. An active FD approach for closed-loop uncertain systems is developed in [4] based on the so-called fault signature matrix. In [5], an active FD problem is formulated via explicitly characterizing the nonlinear way that faults affect the process evolution through supervisory feedback control. In [6], an optimization-based approach has been proposed to robustify the filter with respect to signatures of dynamic nonlinearities in the presence of given disturbance patterns with known statistical information. The active FD problem has also been formulated in a probabilistic framework to deal with time-invariant system uncertainties using generalized polynomial chaos (gPC) [7]. gPC replaces the implicit relations between the uncertain system parameters and dynamic state variables with a series of orthogonal polynomials, whose statistical moments can be readily computed from the expansion coefficients.

This work presents a model-based active FD approach for stochastic, nonlinear systems subject to time-invariant probabilistic uncertainties (e.g., uncertainties in initial conditions and parameters) and time-varying system disturbances. The gPC framework [8][9] is adapted for efficient propagation of stochastic disturbances. Chance constraints are included in the active FD problem to account for the practical considerations and system constraints in a stochastic setting. The proposed approach is demonstrated for continuous Acetone-Butanol-Ethanol (ABE) fermentation [10] under various sources of probabilistic uncertainties and multiple fault scenarios. The goal is to enhance fault diagnosability by isolating nominal process operation and multiple faulty scenarios. The case study involves four uncertainties related to initial conditions and enzyme production rates as well as additive process noise, where the process is subject to an actuator fault that affects the dilution rate and to a process fault characterized by butanol inhibition. The simulation results show the promise of the proposed approach for active fault diagnosis under stochastic uncertainty.

References

[1] Nikoukhah, R. and Campbell, S. L. (2004), Auxiliary Signal Design for Failure Detection. Princeton University Press.

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

[3] Zhang, X. J. (1989), Auxiliary Design in Fault Detection and Diagnosis. Springer, Berlin.

[4] Niemann, H. (2006), â??Active Fault Diagnosis in Closed-Loop Uncertain Systemsâ?. In Proceedings of the 6th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, pp. 587â??592, Beijing.

[5] Du, M. and Mhaskar, P. (2013), "Active Fault Isolation of Nonlinear Process Systems". AIChE Journal ,vol. 59, no. 7, pp. 2435-2453.

[6] Esfahani, P. M. and Lygeros, J. (2016), â??A Tractable Fault Detection and Isolation Approach for Nonlinear Systems With Probabilistic Performanceâ?. IEEE Transactions on Automatic Control, vol. 61, no. 3, pp. 633-647.

[7] Mesbah, A., Streif, S., Findeisen, R. and Braatz, R. D. (2014), "Active Fault Diagnosis for Nonlinear Systems with Probabilistic Uncertainties". In Proceedings of the IFAC World Congress. Cape Town, pp. 7079-7084.

[8] Xiu, D. and Karniadaki, G. E. (2003), "Modeling Uncertainty in Flow Simulations via Generalized Polynomial Chaos". Journal of Compurational Physics, vol. 187, pp. 137â??167.

[9] Bavdekar, V. A. and Mesbah A. (2016), â??Stochastic Nonlinear Model Predictive Control with Joint Chance Constraints.â? In Proceedings of the 10th IFAC Symposium on Nonlinear Control Systems, accepted, Monterey.

[10] Haus, S., Jabbari, S., Millat, T., Janssen, H., Fischer, R. J., Bahl, H., King, J. R., Wolkenhauer, O. (2011), â??A Systems Biology Approach to Investigate the Effect Of pH-induced Gene Regulation on Solvent Production by Clostridium Acetobutylicum in Continuous Cultureâ?. BMC Systems Biology, vol.5, pp. 1-13.