Continuous Stirred Tank Reactor Fault Detection Using Higher Degree Cubature Kalman Filter
Keywords:continuous stirred tank reactor, cubature kalman filter, estimator, fault detection, nonlinear system
AbstractContinuous Stirred Tank Reactor (CSTR) plays a major role in chemical industries, it ensures the process of mixing reactants according to the attended specification to produce a specific output. It is a complex process that usually represent with nonlinear model for benchmarking. Any abnormality, disturbance and unusual condition can easily interrupt the operations, especially fault. And this problem need to detect and rectify as soon as possible.Â A good knowledge based fault detection using available model require a good error residual between the measurement and the estimated state. Kalman filter is an example of a good estimator, and has been exploited in many researches to detect fault. In this paper, Higher degree Cubature Kalman Filter (HDCKF) is proposed as a method for fault detection by estimation the current state. Cubature Kalman filter (CKF) is an extension of the Kalman filter with the main purpose is to estimate process and measurement state with high nonlinearities. It is based on spherical radial integration to estimate current state by generating cubature points with specific value. Conventional CKF use 3rd degree spherical and 3rd degree radial, here we implement Higher Degree CKF (HDCKF) to have better accuracy as compared to conventional CKF. High accuracy is required to ensure no false alarm is detected and furthermore good computational cost will improve its detection. Finally, a numerical example of CSTR fault detection using HDCKF is presented. Implementation of HDCKF for fault detection is compared with other filter to show effective results.
F.Pierri, G.Paviglianiti, F.Caccavale, M.Mattei. â€œObserver-based sensor fault detection and isolation for chemical batch reactorsâ€. Engineering Applications of Artificial Intelligence, vol. 21, no. 8, pp 1204â€“1216, 2008.
B.Khajali, J.Poshtan. â€œ Fault Detection of a CSTR Using and Observer-Based Method and Particle Filters.â€ Journal of Control and System Engineering, vol 1, pp 30-36, 2013.
Y.Chetouani. â€œDesign of A Multi-Model Observer-Based Estimator for Fault Detection and Isolation (FDI) Strategy: Application to A Chemical Reactor.â€ Brazilian Journal of Chemical Engineering, vol. 25, no. 4, pp 777-788, 2008.
M. Du, J. Scott, P. Mhaskar. â€œActuator and sensor fault isolation of nonlinear process systems.â€ Chemical Engineering Science 104. 2013. 294-303
Y.Zhang, X.R.Li. â€œDetection and Diagnosis of Sensor and Actuator Failures Using IMM Estimator.â€ IEEE Transactions on Aerospace and Electronic System, vol. 34, no. 4, 1998.
S.Bahmanpour, M.Bashooki, and M.H.Refan. â€œState estimation and fault diagnosis of industrial process by using of particle filters.â€ Proceeding 6th WSEAS International Conference on Signal Processing, Greece, pp 208-213, 2007.
I. Arasaratnam, S. Haykin, and R.J. Elliott. â€œDiscrete-time nonlinear filtering algorithms using Gauss-Hermite quadrature.â€ Proc. IEEE., vol. 95, no. 5, pp. 953-977, 2007.
S. J. Julier and J. K. Uhlmann. â€œUnscented filtering and nonlinear estimation.â€ Proc. IEEE, vol. 92, no. 3, pp. 401â€“422, Mar. 2004.
K.Xiong, C.Chan, H.Zhang. â€œDetection of Satellite Attitude Sensor Faults Using The UKF.â€ IEEE Transactions on Aerospace and Electronic Systems, Vol. 43, no. 2, pp. 480â€“491, 2007.
I. Arasaratnam and S. Haykin. 2009. â€œCubature Kalman filters.â€ IEEE Trans. Autom. Control, vol. 54, no. 6, 2009. 1254â€“1269.
S.Y. Wang, J.C. Feng, and C.K. Tse. â€œSpherical simplex-radial cubature Kalman filter.â€ IEEE Signal Process. Lett., vol. 21, no. 1, pp. 43-46, 2014
B. Shovan and Swati. â€œSquare-root Cubature-Quadrature Kalman Filter.â€ Asian Journal of Control, vol. 16, no. 2, pp. 617â€“622, 2014.
X. Tang, J. Wei, K. Chen. â€œSquare-Root adaptive Cubature Kalman Filter with application to spacecraft attitude estimation.â€ 15th International Conference on Information Fusion (FUSION), (012.1406-1412.
J. Zarei, E. Shokri, and H.R. Karimi. â€œConvergence analysis of Cubature Kalman filter.â€ in European on Control Conference (ECC), 2014, pp. 1367-1372.
W.Li, Y.Jia. 2012. â€œLocation of mobile station with maneuvers using an IMM-based Cubature Kalman Filter.â€ IEEE Transactions on Industry Electronics 59 11. 2012. 4338-4348
B. Shovan and Swati. â€œCubature Quadrature Kalman Filter.â€ IET Signal Processing, vol. 7, no. 7, pp. 533â€“541, 2013
B. Jia, M. Xin, and Y. Cheng. 2013. â€œHigh-degree Cubature Kalman Filter.â€ Automatica, vol. 49, no. 2, 2013. 510-518.
S.Zhang, M.Baric. â€œA Bayesian Approach to Hybrid Fault Detection and Isolation.â€ IEEE 54th Annual Conference on Decision and Control (CDC), 2015
W.Wang, X.Chen. â€œApplication of Improved 5th Cubature Kalman Filter in Initial Strapdown Inertial Navigation System Alignment for Large Misalignment Angles.â€ Sensors 2018. 18. 659
Z.Li, W.Yang, D.Ding, Y.Liao, â€œA Novel Fifth Degree Cubature Kalman Filter for Real Time Orbit Determination by Radar.â€ Mathematical Problems In Engineering 2017. 9
J.Zarei, E.Shokri. â€œRobust sensor fault detection based on nonlinear unknown input observer.â€ Measurement, vol. 48, pp 355-367,.2014.
J. Zarei, J. Poshtan. â€œDesign of nonlinear unknown input observer for process fault detection.â€ Industrial & Engineering Chemistry Research 49 22. 2010. 11443â€“11452
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