Recursive identification of noisy autoregressive models via a noise-compensated overdetermined instrumental variable method

• Autorzy: Barbieri Matteo , Diversi Roberto

Identyfikatory

DOI

10.61822/amcs-2024-0005

• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to develop a new recursive identification algorithm for autoregressive (AR) models corrupted by additive white noise. The proposed approach relies on a set of both low-order and high-order Yule-Walker equations and on a modified version of the overdetermined recursive instrumental variable method, leading to the estimation of both the AR coefficients and the additive noise variance. The main motivation behind our proposition is introducing model identification procedures suitable for implementation on edge-computing platforms and programmable logic controllers (PLCs), which are known to have limited capabilities and resources when dealing with complex mathematical computations (i.e., matrix inversion). Indeed, our development is focused on condition monitoring systems, with particular attention paid to their integration onboard industrial machinery. The performance of the recursive approach is tested using both numerical simulations and a laboratory case study. The obtained results are very promising.

Słowa kluczowe

EN

system identification; noisy autoregressive model; recursive estimation; Yule-Walker equation; condition monitoring system

PL

identyfikacja systemu; model autoregresyjny; system monitorowania

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2024
• Tom: Vol. 34, no. 1
• Strony: 65--79
• Opis fizyczny: Bibliogr. 53 poz., rys., tab., wykr.

Twórcy

autor

Barbieri Matteo

• Department of Electrical, Electronic and Information Engineering “Guglielmo Marconi” (DEI), University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy

autor

Diversi Roberto

• Department of Electrical, Electronic and Information Engineering “Guglielmo Marconi” (DEI), University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy

Bibliografia

• [1] Abramovich, Y.I., Spencer, N.K. and Turley, M.D. (2007). Time-varying autoregressive (TVAR) models for multiple radar observations, IEEE Transactions on Signal Processing 55(4): 1298-1311.
• [2] Baillie, D.C. and Mathew, J. (1996). A comparison of autoregressive modeling techniques for fault diagnosis of rolling element bearings, Mechanical Systems and Signal Processing 10(1): 1-17.
• [3] Barbieri, M., Bosso, A., Conficoni, C., Diversi, R., Sartini, M. and Tilli, A. (2018). An onboard model-of-signals approach for condition monitoring in automatic machines, in M. Zelm et al. (Eds), Enterprise Interoperability: Smart Services and Business Impact of Enterprise Interoperability, Wiley Online Library, London, pp. 263-269.
• [4] Barbieri, M., Diversi, R. and Tilli, A. (2019). Condition monitoring of ball bearings using estimated AR models as logistic regression features, Proceedings of the 18th European Control Conference (ECC 2019), Naples, Italy, pp. 3904-3909.
• [5] Barbieri, M., Nguyen, K.T., Diversi, R., Medjaher, K. and Tilli, A. (2021). RUL prediction for automatic machines: A mixed edge-cloud solution based on model-of-signals and particle filtering techniques, Journal of Intelligent Manufacturing 32(5): 1421-1440.
• [6] Basseville, M. (1988). Detecting changes in signals and systems - A survey, Automatica 24(3): 309-326.
• [7] Bobillet, W., Diversi, R., Grivel, E., Guidorzi, R., Najim, M. and Soverini, U. (2007). Speech enhancement combining optimal smoothing and errors-in-variables identification of noisy AR processes, IEEE Transactions on Signal Processing 55(12): 5564-5578.
• [8] Box, G.E., Jenkins, G.M., Reinsel, G.C. and Ljung, G.M. (2015). Time Series Analysis: Forecasting and Control, John Wiley & Sons, Hoboken.
• [9] Cadzow, J. (1982). Spectral estimation: An overdetermined rational model equation approach, Proceedings of the IEEE 70(9): 907-939.
• [10] Chan, Y. and Langford, R. (1982). Spectral estimation via the high-order Yule-Walker equations, IEEE Transactions on Acoustics, Speech, and Signal Processing 30(5): 689-698.
• [11] Davila, C.E. (1998). A subspace approach to estimation of autoregressive parameters from noisy measurements, IEEE Transactions on Signal Processing 46(2): 531-534.
• [12] Davila, C.E. (2001). On the noise-compensated Yule-Walker equations, IEEE Transactions on Signal Processing 49(6): 1119-1121.
• [13] Diversi, R. (2018). Identification of multichannel AR models with additive noise: A Frisch scheme approach, Proceedings of the 26th European Signal Processing Conference (EUSIPCO 2018), Rome, Italy, pp. 1252-1256.
• [14] Diversi, R., Guidorzi, R. and Soverini, U. (2008). Identification of autoregressive models in the presence of additive noise, International Journal of Adaptive Control and Signal Processing 22(5): 465-481.
• [15] Diversi, R., Soverini, U. and Guidorzi, R. (2005). A new estimation approach for AR models in presence of noise, IFAC Proceedings Volumes 38(1): 160-165.
• [16] Esfandiari, M., Vorobyov, S.A. and Karimi, M. (2020). New estimation methods for autoregressive process in the presence of white observation noise, Signal Processing 171(6): 107480.
• [17] Friedlander, B. (1984). The overdetermined recursive instrumental variable method, IEEE Transactions on Automatic Control 29(4): 353-356.
• [18] Grivel, E., Gabrea, M. and Najim, M. (2002). Speech enhancement as a realisation issue, Signal Processing 44(12): 1963-1978.
• [19] Guidorzi, R., Diversi, R., Vincenzi, L., Mazzotti, C. and Simioli, V. (2014). Structural monitoring of a tower by means of MEMS-based sensing and enhanced autoregressive models, European Journal of Control 20(1): 4-13.
• [20] Güler, I., Kiymik, M.K., Akin, M. and Alkan, A. (2001). AR spectral analysis of EEG signals by using maximum likelihood estimation, Computers in Biology and Medicine 31(6): 441-450.
• [21] Haykin, S.S. and Steinhardt, A.O. (1992). Adaptive Radar Detection and Estimation, Wiley-Interscience, New York.
• [22] Hilgert, N. and Vila, J.-P. (1999). D-step ahead Kalman predictor for controlled autoregressive processes with random coefficients, International Journal of Applied Mathematics and Computer Science 9(1): 207-217.
• [23] Jia, L.J., Kanae, S., Yang, Z.J. and Wada, K. (2003). On bias compensation estimation for noisy AR process, Proceedings of the 42nd IEEE Conference on Decision and Control (CDC 2003), Maui, USA, pp. 405-410.
• [24] Kay, S. (1979). The effects of noise on the autoregressive spectral estimator, IEEE Transactions on Acoustics, Speech, and Signal Processing 27(5): 478-485.
• [25] Kay, S. (1980). Noise compensation for autoregressive spectral estimates, IEEE Transactions on Acoustics, Speech, and Signal Processing 28(3): 292-303.
• [26] Kay, S.M. (1988). Modern Spectral Estimation, Prentice-Hall, Englewood Cliffs.
• [27] Kovacevic, B.D., Milosavljevic, M.M. and Veinovic, M.D. (1995). Robust recursive AR speech analysis, Signal Processing 44(6): 125-138.
• [28] Labarre, D., Grivel, E., Berthoumieu, Y., Todini, E. and Najim, M. (2006). Consistent estimation of autoregressive parameters from noisy observations based on two interacting Kalman filters, Signal Processing 86(10): 2863-2876.
• [29] Lim, J. and Oppenheim, A. (1978). All-pole modeling of degraded speech, IEEE Transactions on Acoustics, Speech, and Signal Processing 26(3): 197-210.
• [30] Lipiec, B., Mrugalski, M., Witczak, M. and Stetter, R. (2022). Towards a health-aware fault tolerant control of complex systems: A vehicle fleet case, International Journal of Applied Mathematics and Computer Science 32(4): 619-634, DOI: 10.34768/amcs-2022-0043.
• [31] Ljung, L. (1999). System Identification - Theory for the User, Prentice-Hall, Upper Saddle River.
• [32] Mahmoudi, A. and Karimi, M. (2010). Parameter estimation of autoregressive signals from observations corrupted with colored noise, Signal Processing 90(1): 157-164.
• [33] Mahmoudi, A. and Karimi, M. (2011). Inverse filtering based method for estimation of noisy autoregressive signals, Signal Processing 91(7): 1659-1664.
• [34] Paliwal, K. (1988). A noise-compensated long correlation matching method for AR spectral estimation of noisy signals, Signal Processing 15(4): 437-440.
• [35] Pardey, J., Roberts, S.K. and Tarassenko, L. (1996). A review of parametric modelling techniques for EEG analysis, Medical Engineering & Physics 18(1): 2-11.
• [36] Petitjean, J., Diversi, R., Grivel, E., Guidorzi, R. and Roussilhe, P. (2009). Recursive errors-in-variables approach for AR parameter estimation from noisy observations. Application to radar sea clutter rejection, Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2009), Taipei, Taiwan, pp. 3401-3404.
• [37] Petitjean, J., Grivel, E., Bobillet, W. and Roussilhe, P. (2010). Multichannel AR parameter estimation from noisy observations as an errors-in-variables issue, Signal, Image and Video Processing 4: 209-220.
• [38] Rouffet, T., Grivel, E., Vallet, P., Enderli, C. and Kemkemian, S. (2015). Combining two phase codes to extend the radar unambiguous range and get a trade-off in terms of performance for any clutter, Proceedings of the 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2015), Brisbane, Australia, pp. 1822-1826.
• [39] Sakai, H. and Arase, M. (1979). Recursive parameter estimation of an autoregressive process disturbed by white noise, International Journal of Control 30(6): 949-966.
• [40] Sikora, M. and Sikora, B. (2012). Improving prediction models applied in systems monitoring natural hazards and machinery, International Journal of Applied Mathematics and Computer Science 22(2): 477-491, DOI: 10.2478/v10006-012-0036-3.
• [41] Söderström, T. and Stoica, P. (1989). System Identification, Prentice-Hall, Inc., Hemel Hempstead.
• [42] Stoica, P. and Moses, R. (2005). Spectral Analysis of Signals, Pearson Prentice Hall, Upper Saddle River.
• [43] Treichler, J.R. (1979). Transient and convergent behaviour of the adaptive line enhancer, IEEE Transactions on Acoustics, Speech and Signal Processing 27(2): 53-62.
• [44] Wang, W. and Wong, A.K. (2002). Autoregressive model-based gear fault diagnosis, Journal of Vibration and Acoustics 124(3): 172-179.
• [45] Wang, X. and Makis, V. (2009). Autoregressive model-based gear shaft fault diagnosis using the Kolmogorov-Smirnov test, Journal of Sound and Vibration 327(3): 413-423.
• [46] Wu, W.R. and Chen, P.C. (1997). Adaptive AR modelling in white Gaussian noise, IEEE Transactions on Signal Processing 45(5): 1184-1191.
• [47] Xia, Y. and Zheng, W.X. (2015). Novel parameter estimation of autoregressive signals in the presence of noise, Automatica 62(12): 98-105.
• [48] Zhang, Y., Liu, B., Ji, X. and Huang, D. (2017). Classification of EEG signals based on autoregressive model and wavelet packet decomposition, Neural Processing Letters 45: 365-378.
• [49] Zhang, Y., Wen, C. and Chai Soh, Y. (2000). Unbiased LMS filtering in the presence of white measurement noise with unknown power, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 47(9): 968-972.
• [50] Zheng, W.X. (1997). Estimation of autoregressive signals from noisy measurements, IEE Proceedings - Vision, Image and Signal Processing 144(1): 39-45.
• [51] Zheng, W.X. (1999). A least-squares based method for autoregressive signals in the presence of noise, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 46(1): 81-85.
• [52] Zheng, W.X. (2000). Autoregressive parameter estimation from noisy data, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 47(1): 71-75.
• [53] Zheng, W.X. (2006). On estimation of autoregressive signals in the presence of noise, IEEE Transactions on Circuits and Systems II: Express Briefs 53(12): 1471-1475.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).