Abstract
In this paper we propose a visual approach for the analysis of nonlinear multivariable systems whose dynamic behaviour can be defined in terms of locally linear MIMO (Multiple Input, Multiple Output) behaviours that change depending on a given set of variables (such as e.g. the working point). The proposed approach is carried out in two steps: 1) building a smooth 2-D map of such set of variables using Self-Organizing Maps (SOM) and 2) obtaining a local MIMO ARX (Auto-Regressive with eXogenous input) model for each SOM unit. The resulting structure allows to estimate the process data with an accuracy comparable to other state-of-the-art nonlinear estimation techniques but, in addition, it allows to visualize the MIMO dynamics information stored in the SOM using component planes as done in the SOM literature, bringing the power of visualization to acquire insight useful for process understanding and for control system design. The proposed approach is applied to an industrial-scale version of the well known 4-tank plant, showing a comparison in terms of estimation accuracy with a global linear estimator and with a NARX (Nonlinear Auto-Regressive with eXogenous input) estimator based on a Multi-Layer Perceptron (MLP), as well as, visualizations of MIMO dynamic features such as directionality, RGA (Relative Gain Array), and singular frequency gains for the aforementioned plant.
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References
Sjoberg, J., Zhang, Q., Ljung, L., Benveniste, A., Delyon, B., Glorennec, P., Hjalmarsson, H., Juditsky, A.: Nonlinear black-box modeling in system identification: a unified overview. Automatica 31(12), 1691–1724 (1995)
Chen, S., Billings, S., Grant, P.: Non-linear system identification using neural networks. International Journal of Control 51(6), 1191–1214 (1990)
Giannakis, G., Serpedin, E.: A bibliography on nonlinear system identification. Signal Processing 81(3), 533–580 (2001)
Dayal, B., MacGregor, J.: Multi-output process identification. Journal of Process Control 7, 269–282 (1997)
Peng, H., Wu, J., Inoussa, G., Deng, Q., Nakano, K.: Nonlinear system modeling and predictive control using the RBF nets-based quasi-linear ARX model. Control Engineering Practice (2008)
Yu, D., Gomm, J., Williams, D.: Neural model input selection for a MIMO chemical process. Engineering Applications of Artificial Intelligence 13(1), 15–23 (2000)
Principe, J.C., Wang, L., Motter, M.A.: Local dynamic modeling with self-organizing maps and applications to nonlinear system identification and control. Proceedings of the IEEE 86(11), 2240–2258 (1998)
Cho, J., Principe, J.C., Erdogmus, D., Motter, M.A.: Modeling and inverse controller design for an unmanned aerial vehicle based on the self-organizing map. IEEE Transactions on Neural Networks 17(2), 445–460 (2006)
Johansson, K.: The quadruple tank process: A multivariable laboratory process with an adjustable zero. IEEE Transactions on Control Systems Technology 8(3), 456–465 (2000)
Díaz Blanco, I., Cuadrado Vega, A.A., Diez González, A.B., Fuertes Martínez, J.J., Domínguez González, M., Reguera, P.: Visualization of dynamics using local dynamic modelling with self organizing maps. In: de Sá, J.M., Alexandre, L.A., Duch, W., Mandic, D.P. (eds.) ICANN 2007. LNCS, vol. 4668, pp. 609–617. Springer, Heidelberg (2007)
Díaz Blanco, I., Domínguez González, M., Cuadrado, A.A., Fuertes Martínez, J.J.: A new approach to exploratory analysis of system dynamics using som. applications to industrial processes. Expert Systems With Applications 34(4), 2953–2965 (2008)
Kohonen, T., Oja, E., Simula, O., Visa, A., Kangas, J.: Engineering applications of the self-organizing map. Proceedings of the IEEE 84(10), 1358–1384 (1996)
Kohonen, T.: Self-Organizing Maps. Springer, Heidelberg (1995)
Domínguez González, M., Reguera, P., Fuertes, J.: Laboratorio Remoto para la Enseñanza de la Automática en la Universidad de León (España). Revista Iberoamericana de Automática e Informática Industrial (RIAI) 2(2), 36–45 (2005)
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Díaz, I., Cuadrado, A.A., Diez, A.B., Fuertes, J.J., Domínguez, M., Prada, M.A. (2009). Visualization of MIMO Process Dynamics Using Local Dynamic Modelling with Self Organizing Maps. In: Palmer-Brown, D., Draganova, C., Pimenidis, E., Mouratidis, H. (eds) Engineering Applications of Neural Networks. EANN 2009. Communications in Computer and Information Science, vol 43. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03969-0_12
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DOI: https://doi.org/10.1007/978-3-642-03969-0_12
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