# Linear Switching System Identification Applied to Blast Furnace Data

### Amir H. Shirdel, Kaj-Mikael Björk, Markus Holopainen, Christer Carlsson, Hannu T. Toivonen

#### Abstract

Switching systems are dynamical systems which can switch between a number of modes characterized by different dynamical behaviors. Several approaches have recently been presented for experimental identification of switching system, whereas studies on real-world applications have been scarce. This paper is focused on applying switching system identification to a blast furnace process. Specifically, the possibility of replacing nonlinear complex system models with a number of simple linear models is investigated. Identification of switching systems consists of identifying both the individual dynamical behavior of model which describes the system in the various modes, as well as the time instants when the mode changes have occurred. In this contribution a switching system identification method based on sparse optimization is used to construct linear switching dynamic models to describe the nonlinear system. The results obtained for blast furnace data are compared with a nonlinear model using Artificial Neural Fuzzy Inference System (ANFIS).

#### References

- Bjork, K-M., Holopainen, M., Wikstrm, R., Saxen, H., Carlsson, C., Sihvonen, M.: Analysis of Blast Furnace Time Series Data with ANFIS. TUCS Technical Report 1094 ISBN 978-952-12-2986-2 (2013)
- Sontag, E. D.: Nonlinear regulation: The piecewise linear approach. IEEE Trans. Automatic Control, vol. 26, no. 2, pp. 346358, (1981)
- Lin, J. N., Unbehauen, R.: Canonical Piecewise-linear Approximations. IEEE Trans. Circuits Systems IFundamental Theory and Applications, vol. 39, no. 8, pp. 697699, (1992)
- Saad, A., Avineri, E., Dahal, K., Sarfraz, M.: Soft Computing in Industrial Applications, Springer (2007)
- Aliev, R. A., Fazlollahi, B, Aliev, R. R.: Soft Computing and Its Applications in Business and Economics, Springer, edition 5 (2004)
- Ohlsson, H.,Ljung, L., Boyd, S.: Segmentation of ARXmodels using sum-of-norms regularization. Automatica, vol. 46, pp. 1107-1111 (2010)
- Bako, L.: Identification of switched linear systems via sparse optimization. Automatica, vol. 47, pp. 668-677 (2011)
- Le, V. L., Lauer, F., Bako, L., Bloch. G.: Learning nonlinear hybrid systems: from sparse optimization to support vector regression. In: HSCC - 16th ACM International Conference on Hybrid systems: Computation and Control - 33-42 (2013)
- Lughofer, E. and Kindermann, S. (2010). SparseFIS: Datadriven learning of fuzzy systems with sparsity constraints. Fuzzy Systems, IEEE Transactions on, 18(2), 396-411.

#### Paper Citation

#### in Harvard Style

H. Shirdel A., Björk K., Holopainen M., Carlsson C. and T. Toivonen H. (2014). **Linear Switching System Identification Applied to Blast Furnace Data** . In *Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-758-039-0, pages 643-648. DOI: 10.5220/0005022806430648

#### in Bibtex Style

@conference{icinco14,

author={Amir H. Shirdel and Kaj-Mikael Björk and Markus Holopainen and Christer Carlsson and Hannu T. Toivonen},

title={Linear Switching System Identification Applied to Blast Furnace Data},

booktitle={Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2014},

pages={643-648},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005022806430648},

isbn={978-989-758-039-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - Linear Switching System Identification Applied to Blast Furnace Data

SN - 978-989-758-039-0

AU - H. Shirdel A.

AU - Björk K.

AU - Holopainen M.

AU - Carlsson C.

AU - T. Toivonen H.

PY - 2014

SP - 643

EP - 648

DO - 10.5220/0005022806430648