Nonlinear stochastic modeling to improve state estimation in process monitoring and control

AIChE Journal

Volumn 57, Issue 4, 2011, Pages 996-1007

  Lima, Fernando V ^a   Rawlings, James B ^a  

^a Wisconsin Electric Machines and Power Electronics Consortium   (United States)

Author keywords

Covariance estimation; Nonlinear modeling; Process control; State estimation; Stochastic modeling

Indexed keywords

ADVANCED MONITORING; AUTOCOVARIANCES; CHEMICAL PROCESS; COVARIANCE ESTIMATION; DESIGN METHOD; HIGH QUALITY; IN-PROCESS MONITORING; LEAST-SQUARES TECHNIQUES; LINEAR TIME VARYING; MODEL ERRORS; NOISE COVARIANCE; NON-LINEAR DYNAMICS; NONLINEAR MODELING; NONLINEAR PROCESS MODELS; NONLINEAR STATE ESTIMATION; OPERATING DATA; PLANT MEASUREMENT; POLYMERIZATION PROCESS; PROCESS DISTURBANCES; SENSOR NOISE; STATE ESTIMATORS; STOCHASTIC DISTURBANCE MODEL; STOCHASTIC DISTURBANCES; STOCHASTIC MODELING;

CHEMICAL REACTORS; ESTIMATION; LEAST SQUARES APPROXIMATIONS; NONLINEAR ANALYSIS; NONLINEAR SYSTEMS; PROCESS MONITORING; STATE ESTIMATION; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

PROCESS CONTROL;

EID: 79952596020     PISSN: 00011541     EISSN: 15475905     Source Type: Journal    
DOI: 10.1002/aic.12308     Document Type: Article

References (55)

1. Odelson BJ, Rajamani MR, Rawlings JB. A new autocovariance least-squares method for estimating noise covariances. Automatica. 2006; 42: 303-308.
2. Odelson BJ, Lutz A, Rawlings JB. The autocovariance least-squares method for estimating covariances: application to model-based control of chemical reactors. IEEE Control Syst Technol. 2006; 14: 532-541.
3. Rajamani MR, Rawlings JB. Estimation of the Disturbance Structure from Data Using Semidefinite Programming and Optimal Weighting. Technical Report 2007-02, TWMCC, Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, WI, 2007. Available at:
4. Rajamani MR, Rawlings JB. Estimation of the disturbance structure from data using semidefinite programming and optimal weighting. Automatica. 2009; 45: 142-148.
5. Rajamani MR, Rawlings JB, Soderstrom TA. Application of a New Data-Based Covariance Estimation Technique to a Nonlinear Industrial Blending Drum. Technical Report 2007-03, TWMCC, Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, WI, 2007. Available at:
6. Mehra RK. On the identification of variances and adaptive Kalman filtering. IEEE Trans Automat Contr. 1970; 15: 175-184.
7. Mehra RK. Approaches to adaptive filtering. IEEE Trans Automat Contr. 1972; 17: 903-908.
8. Carew B, Bélanger PR. Identification of optimum filter steady-state gain for systems with unknown noise covariances. IEEE Trans Automat Contr. 1973; 18: 582-587.
9. Bélanger PR. Estimation of noise covariance matrices for a linear time-varying stochastic process. Automatica. 1974; 10: 267-275.
10. Neethling C, Young P. Comments on Identification of optimum filter steady-state gain for systems with unknown noise covariances. IEEE Trans Automat Contr. 1974; 19: 623-625.
11. Noriega G, Pasupathy S. Adaptive estimation of noise covariance matrices in real-time preprocessing of geophysical data. IEEE Trans Geosci Remote Sens. 1997; 35: 1146-1159.
12. Åkesson BM, Jørgensen JB, Poulsen NK, Jørgensen SB. A generalized autocovariance least-squares method for Kalman filter tuning. J Process Control. 2008; 18: 769-779.
13. Kristensen NR, Madsen H, Jørgensen SB. Parameter estimation in stochastic grey-box models. Automatica. 2004; 40: 225-237.
14. Kristensen NR, Madsen H, Jørgensen SB. A method for systematic improvement of stochastic grey-box models. Comput Chem Eng. 2004; 28: 1431-1449.
15. Grancharova A, Kocijan J, Johansen TA. Explicit stochastic predictive control of combustion plants based on Gaussian process models. Automatica. 2008; 44: 1621-1631.
16. Kocijan J, Murray-Smith R. Nonlinear predictive control with a Gaussian process model. In: Murray-Smith R, Shorten R, editors. Switching and Learning in Feedback Systems, Volume 3355 of Lecture Notes in Computer Science. Heidelberg, Germany: Springer-Verlag, 2005: 185-200.
17. Kocijan J, Likar B. Gas-liquid separator modelling and simulation with Gaussian process models. Simulat Model Pract Theor. 2008; 16: 910-922.
18. Rajamani MR. Data-Based Techniques to Improve State Estimation in Model Predictive Control. PhD Thesis, University of Wisconsin-Madison, Madison, WI, 2007.
19. Valappil J, Georgakis C. Systematic estimation of state noise statistics for extended Kalman filters. AIChE J. 2000; 46: 292-308.
20. Jazwinski AH. Stochastic Processes and Filtering Theory. New York: Academic Press, 1970.
21. Julier SJ, Uhlmann JK. Unscented filtering and nonlinear estimation. Proc IEEE. 2004; 92: 401-422.
22. Vachhani P, Narasimhan S, Rengaswamy R. Robust and reliable estimation via unscented recursive nonlinear dynamic data reconciliation. J Process Control. 2006; 16: 1075-1086.
23. Qu CC, Hahn J. Computation of arrival cost for moving horizon estimation via unscent Kalman filtering. J Process Contr. 2009; 19: 358-363.
24. Kandepu R, Imsland L, Foss BA. Constrained state estimation using the unscented kalman filter. In: Procedings of the 16th Mediterranean Conference on Control and Automation, Ajaccio, France, June, 2008: 1453-1458.
25. Teixeira BOS, Tôrres LAB, Aguirre LA, Bernstein DS. Unscented filtering for interval-constrained nonlinear systems. In: Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, December 9-11, 2008: 5116-5121.
26. Handschin JE, Mayne DQ. Monte Carlo techniques to estimate the conditional expectation in multistage nonlinear filtering. Int J Control. 1969; 9: 547-559.
27. Gordon NJ, Salmond DJ, Smith AFM. Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proc F-Radar Signal Process. 1993; 140: 107-113.
28. Doucet A, Godsill S, Andrieu C. On sequential Monte Carlo sampling methods for Bayesian filtering. Stat Comput. 2000; 10: 197-208.
29. Arulampalam MS, Maskell S, Gordon NJ, Clapp T. A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans Signal Process. 2002; 50: 174-188.
30. Chen WS, Bakshi BR, Goel PK, Ungarala S. Bayesian estimation of unconstrained nonlinear dynamic systems via sequential Monte Carlo sampling. Ind Eng Chem Res. 2004; 43: 4012-4025.
31. Lang L, Chen WS, Bakshi BR, Goel PK, Ungarala S. Bayesian estimation via sequential Monte Carlo sampling-constrained dynamic systems. Automatica. 2007; 43: 1615-1622.
32. Ungarala S, Li K, Chen Z. Constrained Bayesian state estimation using a cell filter. Ind Eng Chem Res. 2008; 47: 7312-7322.
33. Ungarala S, Li K. The use of a cell filter for state estimation in closed-loop NMPC of low dimensional systems. J Process Control. 2009; 19: 550-556.
34. Rao CV, Rawlings JB. Constrained process monitoring: moving- horizon approach. AIChE J. 2002; 48: 97-109.
35. Robertson DG, Lee JH, Rawlings JB. A moving horizon-based approach for least-squares state estimation. AIChE J. 1996; 42: 2209-2224.
36. Robertson DG, Lee JH. On the use of constraints in least squares estimation and control. Automatica. 2002; 38: 1113-1124.
37. Rao CV, Rawlings JB, Mayne DQ. Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations. IEEE Trans Automat Contr. 2003; 48: 246-258.
38. Alessandri A, Baglietto M, Battistelli G. Moving-horizon state estimation for nonlinear discrete-time systems: new stability results and approximation schemes. Automatica. 2008; 44: 1753-1765.
39. Rawlings JB, Bakshi BR. Particle filtering and moving horizon estimation. Comput Chem Eng. 2006; 30: 1529-1541.
40. Rajamani MR, Rawlings JB. Improved state estimation using a combination of moving horizon estimator and particle filters. In: Proceedings of the American Control Conference, New York, USA, July 11-13, 2007.
41. Zavala VM, Laird CD, Biegler LT. A fast computational framework for large-scale moving horizon estimation. In:DYCOPS, Vol. 3, Cancun, Mexico, June, 2007: 21-30.
42. Zavala VM, Laird CD, Biegler LT. A fast moving horizon estimation algorithm based on nonlinear programming sensitivity. J Process Contr. 2008; 18: 876-884.
43. Kraus T, Kühl P, Wirsching L, Bock HG, Diehl M. A moving horizon state estimation algorithm applied to the Tennessee Eastman benchmark process. In: IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, Heidelberg, Germany, 2006: 377-382.
44. Diehl M, Ferreau HJ, Haverbeke N. Efficient numerical methods for nonlinear MPC and moving horizon estimation. In: Proceedings of the International Workshop on Assessment and Future Directions of NMPC, Pavia, Italy, September, 2008.
45. Haseltine EL, Rawlings JB. Critical evaluation of extended Kalman filtering and moving horizon estimation. Ind Eng Chem Res. 2005; 44: 2451-2460.
46. McAuley KB, MacGregor AE, Hamielec AE. A kinetic model for industrial gas-phase ethylene copolymerization. AIChE J. 1990; 36: 837-850.
47. Dadebo SA, Bell ML, McLellan PJ, McAuley KB. Temperature control of industrial gas phase polyethylene reactors. J Process Contr. 1997; 7: 83-95.
48. Gani A, Mhaskar P, Christofides PD. Fault-tolerant control of a polyethylene reactor. J Process Control. 2007; 17: 439-451.
49. Kloeden PE, Platen E. Numerical Solution of Stochastic Differential Equations. Berlin: Springer Verlag, 1992.
50. Jenkins GM, Watts DG. Spectral Analysis and Its Applications. 500 Sansome Street, San Fransisco, California: Holden-Day, 1968.
51. Sontag ED. Mathematical Control Theory, 2nd ed. New York: Springer-Verlag, 1998.
52. Schmidt SF. Application of state-space methods to navigation problems. In: Leondes CT editor. Advances in Control Systems, Vol. 3. New York: Academic Press, 1966: 293-340.
53. Brown RG, Hwang PYC. Introduction to Random Signals and Applied Kalman Filtering. New York, Wiley, 1997.
54. Farrell JA, Barth M. The Global Positioning System and Inertial Navigation. McGraw-Hill, 1998.
55. Farrell JA. Aided Navigation: GPS with High Rate Sensors. McGraw-Hill, 2008.