“Parameter and State Estimation of Large-Scale Complex Systems Using Python Tools”
Authors: M. Anushka S. Perera, Tor A. Hauge and Carlos F. Pfeiffer,Affiliation: Telemark University College and Glencore Nikkelverk (Kristiansand)
Reference: 2015, Vol 36, No 3, pp. 189-198.
Keywords: Kalman filter, Modelica, Observability, Python, state and parameter estimation
Abstract: This paper discusses the topics related to automating parameter, disturbance and state estimation analysis of large-scale complex nonlinear dynamic systems using free programming tools. For large-scale complex systems, before implementing any state estimator, the system should be analyzed for structural observability and the structural observability analysis can be automated using Modelica and Python. As a result of structural observability analysis, the system may be decomposed into subsystems where some of them may be observable --- with respect to parameter, disturbances, and states --- while some may not. The state estimation process is carried out for those observable subsystems and the optimum number of additional measurements are prescribed for unobservable subsystems to make them observable. In this paper, an industrial case study is considered: the copper production process at Glencore Nikkelverk, Kristiansand, Norway. The copper production process is a large-scale complex system. It is shown how to implement various state estimators, in Python, to estimate parameters and disturbances, in addition to states, based on available measurements.
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DOI: 10.4173/mic.2015.3.6DOI forward links to this article:
| [1] Sungho Kim, Jaejung Urm, Dae Shik Kim, Kihong Lee and Jong Min Lee (2018), doi:10.1007/s11814-018-0134-5 |
[1] Bona, B. and Smay, R.J. (1966). Optimum reset of ship's inertial navigation system, Aerospace and Electronic Systems, IEEE Transactions on. (4):409--414. doi:10.1109/TAES.1966.4501790
[2] Cox, H. (1964). On the estimation of state variables and parameters for noisy dynamic systems, Automatic Control, IEEE Transactions on. 9(1):5--12. doi:10.1109/TAC.1964.1105635
[3] Doucet, A., Godsill, S., and Andrieu, C. (2000). On sequential Monte Carlo sampling methods for Bayesian filtering, Statistics and computing. 10(3):197--208. doi:10.1023/A:1008935410038
[4] Fitzgerald, R.J. (1971). Divergence of the Kalman filter, Automatic Control, IEEE Transactions on. 16(6):736--747. doi:10.1109/TAC.1971.1099836
[5] Gelb, A. (2001). Applied optimal estimation, The M.I.T. press.
[6] Hermann, R. and Krener, A.J. (1977). Nonlinear controllability and observability, IEEE Transactions on automatic control. 22(5):728--740. doi:10.1109/TAC.1977.1101601
[7] Isidori, A. (1995). Nonlinear control systems, Springer Science & Business Media.
[8] Jazwinski, A.H. (2007). Stochastic processes and filtering theory, Courier Corporation.
[9] Julier, S.J., Uhlmann, J.K., and Durrant-Whyte, H.F. (1995). A new approach for filtering nonlinear systems, In American Control Conference, Proceedings of the 1995, volume3. IEEE, pages 1628--1632. doi:10.1109/ACC.1995.529783
[10] Kloeden, P.E., Platen, E., and Schurz, H. (2012). Numerical solution of SDE through computer experiments, Springer Science & Business Media.
[11] Lie, B. and Hauge, T.A. (2008). Modeling of an industrial copper leaching and electrowinning process, with validation against experimental data, In Proceedings SIMS. pages 7--8.
[12] Lin, C.T. (1974). Structural controllability, Automatic Control, IEEE Transactions on. 19(3):201--208. doi:10.1109/TAC.1974.1100557
[13] Liu, Y.-Y., Slotine, J.-J., and Barabasi, A.-L. (2013). Observability of complex systems, Proceedings of the National Academy of Sciences. 110(7):2460--2465. doi:10.1073/pnas.1215508110
[14] Ljung, L. (1979). Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems, Automatic Control, IEEE Transactions on. 24(1):36--50. doi:10.1109/TAC.1979.1101943
[15] Margaria, G., Riccomagno, E., and White, L.J. (2004). Structural identifiability analysis of some highly structured families of statespace models using differential algebra, Journal of mathematical biology. 49(5):433--454. doi:10.1007/s00285-003-0261-3
[16] Moraal, P. and Grizzle, J. (1995). Observer design for nonlinear systems with discrete-time measurements, Automatic Control, IEEE Transactions on. 40(3):395--404. doi:10.1109/9.376051
[17] Perera, M. A.S., Lie, B., and Pfeiffer, C.F. (2015). Structural Observability Analysis of Large Scale Systems Using Modelica and Python, Modeling, Identification and Control. 36(1):53--65. doi:10.4173/mic.2015.1.4
[18] Potter, J.E. (1965). A matrix equation arising in statistical filter theory, volume 270, National Aeronautics and Space Administration.
[19] Reinschke, K.J. (1988). Multivariable control: a graph theoretic approach, 1988.
[20] Simon, D. (2006). Optimal State Estimation: Kalman, H-Infinity, and Nonlinear Approaches, Wiley-Interscience.
[21] Slotine, J.-J.E., Li, W., etal. (1991). Applied nonlinear control, volume 199, Prentice-hall Englewood Cliffs, NJ.
[22] Song, Y. and Grizzle, J.W. (1992). The extended Kalman filter as a local asymptotic observer for nonlinear discrete-time systems, In American Control Conference, 1992. IEEE, pages 3365--3369, 1992.
[23] Strang, G. and Borre, K. (1997). Linear algebra, geodesy, and GPS, Sia.
BibTeX:
@article{MIC-2015-3-6,
title={{Parameter and State Estimation of Large-Scale Complex Systems Using Python Tools}},
author={Perera, M. Anushka S. and Hauge, Tor A. and Pfeiffer, Carlos F.},
journal={Modeling, Identification and Control},
volume={36},
number={3},
pages={189--198},
year={2015},
doi={10.4173/mic.2015.3.6},
publisher={Norwegian Society of Automatic Control}
};