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2019 | OriginalPaper | Buchkapitel

Model Order Reduction Using Fuzzy C-Means Clustering and Particle Swarm Optimization

verfasst von : Nitin Singh, Niraj K. Choudhary, Rudar K. Gautam, Shailesh Tiwari

Erschienen in: Smart Innovations in Communication and Computational Sciences

Verlag: Springer Singapore

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Abstract

The hybrid method which combines the evolutionary programming technique, i.e., based on the swarm optimization algorithm and fuzzy c-means clustering method is used for reducing the model order of high-order linear time-invariant systems in the presented work. The process of clustering is used for finding the group of objects with similar nature that can be differentiated from the other dissimilar objects. The reduction of the numerator of original high-order model is done using the particle swarm optimization algorithm, and fuzzy c-means clustering technique is used for reducing the denominator of the higher-order model. The stability of the model is also verified using the pole zero stability analysis, and it was found that the obtained reduced-order model is stable. Further, the transient and steady state response of the obtained lower-order model as compared to the other existing techniques are better. The output of the obtained lower-order model is also compared with the other existing techniques in the literature in terms of ISE, ITSE, IAE, and ITAE.

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Literatur
1.
Zurück zum Zitat B. Bandyopadhyay and S. Lamba, “Time-domain Pade approximation and modal-Pade method for multivariable systems,” IEEE Transactions on Circuits and Systems, vol. 34, no. 1, pp. 91–94, Jan. 1987. B. Bandyopadhyay and S. Lamba, “Time-domain Pade approximation and modal-Pade method for multivariable systems,” IEEE Transactions on Circuits and Systems, vol. 34, no. 1, pp. 91–94, Jan. 1987.
2.
Zurück zum Zitat W. Enright and M. Kamel, “On selecting a low-order model using the dominant mode concept,” IEEE Transactions on Automatic Control, vol. 25, no. 5, pp. 976–978, Oct. 1980. W. Enright and M. Kamel, “On selecting a low-order model using the dominant mode concept,” IEEE Transactions on Automatic Control, vol. 25, no. 5, pp. 976–978, Oct. 1980.
3.
Zurück zum Zitat M. Hutton and B. Friedland, “Routh approximations for reducing order of linear, time-invariant systems,” IEEE Transactions on Automatic Control, vol. 20, no. 3, pp. 329–337, Jun. 1975. M. Hutton and B. Friedland, “Routh approximations for reducing order of linear, time-invariant systems,” IEEE Transactions on Automatic Control, vol. 20, no. 3, pp. 329–337, Jun. 1975.
4.
Zurück zum Zitat V. Krishnamurthy and V. Seshadri, “Model reduction using the Routh stability criterion,” IEEE Transactions on Automatic Control, vol. 23, no. 4, pp. 729–731, Aug. 1978. V. Krishnamurthy and V. Seshadri, “Model reduction using the Routh stability criterion,” IEEE Transactions on Automatic Control, vol. 23, no. 4, pp. 729–731, Aug. 1978.
5.
Zurück zum Zitat T. N. Lucas, “Some further observations on the differentiation method of modal reduction,” IEEE Transactions on Automatic Control, vol. 37, no. 9, pp. 1389–1391, Sep. 1992. T. N. Lucas, “Some further observations on the differentiation method of modal reduction,” IEEE Transactions on Automatic Control, vol. 37, no. 9, pp. 1389–1391, Sep. 1992.
6.
Zurück zum Zitat V. Singh, D. Chandra, and H. Kar, “Improved Routh–PadÉ Approximants: A Computer-Aided Approach,” IEEE Transactions on Automatic Control, vol. 49, no. 2, pp. 292–296, Feb. 2004. V. Singh, D. Chandra, and H. Kar, “Improved Routh–PadÉ Approximants: A Computer-Aided Approach,” IEEE Transactions on Automatic Control, vol. 49, no. 2, pp. 292–296, Feb. 2004.
7.
Zurück zum Zitat T. N. Lucas, “Scaled impulse energy approximation for model reduction,” IEEE Transactions on Automatic Control, vol. 33, no. 8, pp. 791–793, Aug. 1988. T. N. Lucas, “Scaled impulse energy approximation for model reduction,” IEEE Transactions on Automatic Control, vol. 33, no. 8, pp. 791–793, Aug. 1988.
8.
Zurück zum Zitat N. Saxena, A. Tripathi, K. K. Mishra, and A. K. Misra, “Dynamic-PSO: An improved particle swarm optimizer,” 2015, pp. 212–219. N. Saxena, A. Tripathi, K. K. Mishra, and A. K. Misra, “Dynamic-PSO: An improved particle swarm optimizer,” 2015, pp. 212–219.
9.
Zurück zum Zitat S. Mukherjee, Satakshi, and R. C. Mittal, “Model order reduction using response-matching technique,” Journal of the Franklin Institute, vol. 342, no. 5, pp. 503–519, Aug. 2005. S. Mukherjee, Satakshi, and R. C. Mittal, “Model order reduction using response-matching technique,” Journal of the Franklin Institute, vol. 342, no. 5, pp. 503–519, Aug. 2005.
10.
Zurück zum Zitat K. Hammouda and F. Karray, “A comparative study of data clustering techniques,” University of Waterloo, Ontario, Canada, 2000. K. Hammouda and F. Karray, “A comparative study of data clustering techniques,” University of Waterloo, Ontario, Canada, 2000.
11.
Zurück zum Zitat D. Napoleon and S. Pavalakodi, “A new method for dimensionality reduction using K-means clustering algorithm for high dimensional data set,” International Journal of Computer Applications, vol. 13, no. 7, pp. 41–46, 2011. D. Napoleon and S. Pavalakodi, “A new method for dimensionality reduction using K-means clustering algorithm for high dimensional data set,” International Journal of Computer Applications, vol. 13, no. 7, pp. 41–46, 2011.
12.
Zurück zum Zitat J. Kennedy, J. F. Kennedy, R. C. Eberhart, and Y. Shi, Swarm intelligence. Morgan Kaufmann, 2001. J. Kennedy, J. F. Kennedy, R. C. Eberhart, and Y. Shi, Swarm intelligence. Morgan Kaufmann, 2001.
13.
Zurück zum Zitat T. Zeugmann et al., “Particle Swarm Optimization,” in Encyclopedia of Machine Learning, C. Sammut and G. I. Webb, Eds. Boston, MA: Springer US, 2011, pp. 760–766. T. Zeugmann et al., “Particle Swarm Optimization,” in Encyclopedia of Machine Learning, C. Sammut and G. I. Webb, Eds. Boston, MA: Springer US, 2011, pp. 760–766.
14.
Zurück zum Zitat Y. Shi and R. Eberhart, “A modified particle swarm optimizer,” 1998, pp. 69–73. Y. Shi and R. Eberhart, “A modified particle swarm optimizer,” 1998, pp. 69–73.
15.
Zurück zum Zitat B. Alatas, E. Akin, and A. B. Ozer, “Chaos embedded particle swarm optimization algorithms,” Chaos, Solitons & Fractals, vol. 40, no. 4, pp. 1715–1734, May 2009. B. Alatas, E. Akin, and A. B. Ozer, “Chaos embedded particle swarm optimization algorithms,” Chaos, Solitons & Fractals, vol. 40, no. 4, pp. 1715–1734, May 2009.
16.
Zurück zum Zitat C. B. Vishwakarma and R. Prasad, “System reduction using modified pole clustering and Pade approximation,” in XXXII National systems conference, NSC, 2008, pp. 592–596. C. B. Vishwakarma and R. Prasad, “System reduction using modified pole clustering and Pade approximation,” in XXXII National systems conference, NSC, 2008, pp. 592–596.
17.
Zurück zum Zitat M. G. Safonov and R. Y. Chiang, “Model reduction for robust control: A schur relative error method,” International Journal of Adaptive Control and Signal Processing, vol. 2, no. 4, pp. 259–272, Dec. 1988. M. G. Safonov and R. Y. Chiang, “Model reduction for robust control: A schur relative error method,” International Journal of Adaptive Control and Signal Processing, vol. 2, no. 4, pp. 259–272, Dec. 1988.
18.
Zurück zum Zitat J. Pal, “Stable reduced-order Padé approximants using the Routh-Hurwitz array,” Electronics Letters, vol. 15, no. 8, p. 225, 1979. J. Pal, “Stable reduced-order Padé approximants using the Routh-Hurwitz array,” Electronics Letters, vol. 15, no. 8, p. 225, 1979.
19.
Zurück zum Zitat R. Prasad and J. Pal, “Stable reduction of linear systems by continued fractions,” Journal-Institution of Engineers India Part El Electrical Engineering Division, vol. 72, pp. 113–113, 1991. R. Prasad and J. Pal, “Stable reduction of linear systems by continued fractions,” Journal-Institution of Engineers India Part El Electrical Engineering Division, vol. 72, pp. 113–113, 1991.
20.
Zurück zum Zitat P. Gutman, C. Mannerfelt, and P. Molander, “Contributions to the model reduction problem,” IEEE Transactions on Automatic Control, vol. 27, no. 2, pp. 454–455, Apr. 1982. P. Gutman, C. Mannerfelt, and P. Molander, “Contributions to the model reduction problem,” IEEE Transactions on Automatic Control, vol. 27, no. 2, pp. 454–455, Apr. 1982.
Metadaten
Titel
Model Order Reduction Using Fuzzy C-Means Clustering and Particle Swarm Optimization
verfasst von
Nitin Singh
Niraj K. Choudhary
Rudar K. Gautam
Shailesh Tiwari
Copyright-Jahr
2019
Verlag
Springer Singapore
DOI
https://doi.org/10.1007/978-981-10-8971-8_8