Research Papers

Real-Time Identification of Time-Varying ARMAX Systems Based on Recursive Update of Its Parameters

[+] Author and Article Information
Saied Reza Seydnejad

Department of Electrical Engineering,
Shahid Bahonar University of Kerman,
22 Bahman Boulevard,
Kerman, Iran
e-mail: sseydnejad@uk.ac.ir

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 3, 2013; final manuscript received November 28, 2013; published online February 24, 2014. Assoc. Editor: Shankar Coimbatore Subramanian.

J. Dyn. Sys., Meas., Control 136(3), 031017 (Feb 24, 2014) (10 pages) Paper No: DS-13-1095; doi: 10.1115/1.4026341 History: Received March 03, 2013; Revised November 28, 2013

A new method for identification of time-varying ARMAX systems is introduced. This method is based on expansion of time-varying parameters of the ARMAX model onto a set of basis functions. A recursive formulation for updating the coefficients of the basis functions of the time-varying parameters of the system is proposed. Similar to non-real-time basis-function methods, the proposed real-time method has the capability of tracking fast changes in the parameters of a time-varying system much better than the standard Kalman and recursive least-squares (RLS) methods. A computationally efficient version of the algorithm is also presented with a small degradation in tracking properties of the original algorithm. Selection of different types of basis functions makes the new method very flexible for different applications.

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Mercere, G., Palsson, H., and Poinot, T., 2011, “Continuous-Time Linear Parameter-Varying Identification of a Cross Flow Heat Exchanger: A Local Approach,” IEEE Trans. Control Syst. Technol., 19, pp. 64–76. [CrossRef]
Deng, F., Remond, D., and Gaudiller, L., 2011, “Self-Adaptive Modal Control for Time-Varying Structures,” J. Sound Vib., 330(14), pp. 3301–3315. [CrossRef]
Sandberg, H., 2006, “A Case Study in Model Reduction of Linear Time-Varying Systems,” Automatica, 42, pp. 467–472. [CrossRef]
Giannakis, G., and Tepedelenlioglu, C., 1998, “Basis Expansion Models and Diversity Techniques for Blind Identification and Equalization of Time-Varying Channels,” IEEE Proc., 86(10), pp. 1969–1986. [CrossRef]
Tugnait, J. K., and Luo, W., 2004, “Blind Identification of Time-Varying Channels Using Multistep Linear Predictors,” IEEE Trans. Signal Process., 52(6), pp. 1739–1749. [CrossRef]
Zou, R., and Chon, K., 2004, “Robust Algorithm for Estimation of Time-Varying Transfer Functions,” IEEE Trans. Biomed. Eng., 51(2), pp. 219–228. [CrossRef] [PubMed]
Wang, H., Siu, K., Ju, K., Moore, L. C., and Chon, K. H., 2005, “Identification of Transient Renal Autoregulatory Mechanisms Using Time-Frequency Spectral Technique,” IEEE Trans. Biomed. Eng., 52(6), pp. 1033–1039. [CrossRef] [PubMed]
Ljung, L., and Soderstrom, T., 1987, Theory and Practice of Recursive Identification, Prentice-Hall, Upper Saddle River, NJ.
Soderstrom, T., and Stoica, P., 1989, System Identification, Prentice–Hall, Englewood Cliffs, NJ.
Niedzwiecki, M., 2000, Identification of Time-Varying Systems, John-Wiley & Sons, New York.
Toth, R., 2010, Modeling and Identification of Linear Parameter-Varying Systems, Springer, New York.
Tsatsanis, M. K., and Giannakis, G. B., 1993, “Time-Varying System Identification and Model Validation Using Wavelets,” IEEE Trans. Signal Process., 41(12), pp. 3512–3523. [CrossRef]
Niedzwiecki, M., and Kaczmarec, P., 2005, “Identification of Quasi-Periodically Varying Systems Using the Combined Nonparametric/Parametric Approach Systems,” IEEE Trans. Signal Process., 53(12), pp. 4599–4609. [CrossRef]
Niedzwiecki, M., and Klaput, T., 2003, “Fast Algorithms for Identification of Periodically Varying Systems,” IEEE Trans. Signal Process., 51(12), pp. 3270–3279. [CrossRef]
Bao, C., Hao, H., Lia, Z-X., and Zhu, X., 2009, “Time-Varying System Identification Using a Newly Improved HHT Algorithm,” Elsevier J. Comput. Struct., 87(23), pp. 1611–1623. [CrossRef]
Paleologu, C., and Benesty, J., 2008, “A Robust Variable Forgetting Factor Recursive Least-Squares Algorithm for System Identification,” IEEE Signal Process. Lett., 15, pp. 597–600. [CrossRef]
Cooper, J. E., and Worden, K., 2000, “On-Line Physical Parameter Estimation With Adaptive Forgetting Factors,” Elsevier J. Mech. Syst. Signal Process., 14(5), pp. 705–730. [CrossRef]
Xu, X., and You, Q., 2012, “Identification of Linear Time-Varying Systems Using a Wavelet-Based State-Space Method,” Elsevier J. Mech. Syst. Signal Process., 26, pp. 91–103. [CrossRef]
Lataire, J., Pintelon, R., and Louarroudi, E., 2012, “Non-Parametric Estimate of the System Function of a Time-Varying System,” Automatica, 48(4), pp. 666–672. [CrossRef]
Hsiao, T., 2008, “Identification of Time-Varying Autoregressive Systems Using Maximum a Posteriori Estimation,” IEEE Trans. Signal Process., 56(8), pp. 3497–3509. [CrossRef]


Grahic Jump Location
Fig. 1

Estimated parameters using RPEM method

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Fig. 2

Estimated parameters using PLR method

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Fig. 3

Estimated parameters using the TV-BFM of Eq. (11)

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Fig. 4

Estimated parameters using the STV-BFM of Eqs. (16)–(18)

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Fig. 5

Prediction error of different methods

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Fig. 6

Performance of STV-BFM with different values of λ

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Fig. 7

Performance of STV-BFM with different parameter update rates




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