Adaptive Identification of Autoregressive Processes
Publication: Journal of Engineering Mechanics
Volume 117, Issue 7
Abstract
Adaptive identification problems on coefficient matrices of an autoregressive model for multivariate and one‐dimensional nonstationary Gaussian random processes are investigated by applying the extended Kalman filter incorporated with a weighted global iteration. The major contributions of the present paper are the use of the extended Kalman filter for estimating time‐varying model parameters recursively, and the development of an effective method in terms of computer time. The results indicate that the coefficients of this recursive equation are identified simply, but extremely well, at the stage of their stable convergence to optimum. It is suggested that the method be applied for the analysis of multiple‐point array data of earthquake ground motion.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Anderson, B. D. O., and Moore, J. B. (1979). Optimal filtering. Prentice‐Hall, Englewood Cliffs, N.J.
2.
Cakmak, A. S., Sherif, R. I., and Ellis, G. (1985). “Modelling earthquake ground motions in California using parametric time series methods.” Soil Dyn. Earthquake Engrg., 4(3), 124–131.
3.
Cox, H. (1964). “On the estimation of state variables and parameters for noisy dynamic systems.” IEEE Trans. Automat. Control, AC‐9, 5–12.
4.
Deodatis, G., and Shinozuka, M. (1987). “An auto‐regressive model for non‐stationary stochastic processes.” Stochastic Mechanics, II, Columbia University, New York, N.Y., 227–258.
5.
Gersch, W., and Kitagawa, G. (1985). “A Time Varying AR coefficient model for modelling and simulating earthquake ground motion.” Earthquake Engrg. Struct. Dyn., 13, 243–254.
6.
Gersch, W., Taoka, G. T., and Liu, R. (1976). “Structural system parameter estimation by two‐stage least‐squares method.” J. Engrg. Mech., ASCE, 102(5), 883–899.
7.
Goodwin, G. C., and Sin, K. S. (1984). Adaptive filtering, prediction, and control. Prentice‐Hall, Englewood Cliffs, N.J.
8.
Griffiths, L. J., and Preito‐Diaz, R. (1977). “Spectral analysis of natural seismic events using autoregressive techniques.” IEEE Trans. Geosci. Electronics, GE‐15, 13–25.
9.
Hoshiya, M. (1988). “Application of the extended Kalman filter‐WGI method in dynamic system identification.” Stochastic structural dynamics—Progress in theory and applications, Elsevier Applied Science, 103–124.
10.
Hoshiya, M., Chiba, T., and Kusano, N. (1976). “Nonstationary characteristics of earthquake acceleration and its simulation.” J. Japan Soc. Civ. Engrg., 245(1), 51–58 (in Japanese).
11.
Hoshiya, M., Ishii, K., and Nagata, S. (1984). “Recursive covariance of structural responses.” J. Engrg. Mech., ASCE, 110(12), 1743–1755.
12.
Hoshiya, M., and Maruyama, O. (1987). “Identification of a running load and beam system.” J. Engrg. Mech., ASCE, 113(6), 813–824.
13.
Hoshiya, M., Maruyama, O., and Shinozuka, M. (1989). “Identification of bilinear severely systems.” Proc. ICOSSAR '89, 5th Int. Conf. on Structural Safety and Reliability, San Francisco, Calif., 1419–1425.
14.
Hoshiya, M., Naruyama, M., and Kurita, M. (1988). “Autoregressive model of spatially propagating earthquake ground motion.” Proc. Probabilistic Methods in Civil Engineering, ASCE, Blacksburg, Va., 257–260.
15.
Hoshiya, M., and Saito, E. (1984). “Structural identification by extended Kalman filter.” J. Engrg. Mech., ASCE, 110(12), 1757–1770.
16.
Hoshiya, M., and Shibusawa, S. (1986). “Response covariance to multiple excitations.” J. Engrg. Mech., ASCE, 112(4), 412–421.
17.
Jurkevics, A., and Ulrych, T. J. (1978). “Representing and simulating strong ground motion.” Bull. Seism. Soc. Am, 68(3), 781–801.
18.
Kopp, R. E., and Orford, R. J. (1963). “Linear regression applied to system identification for adaptive control systems.” AIAA J., 1(10), 2300–2306.
19.
Kozin, F. (1988). “Autoregressive moving average models of earthquake records.” J. Probabilistic Engrg. Mech., 3(2), 58–63.
20.
Liung, L. (1979). “Asymptotic behavior of the extended Kalman filter as parameter estimater for linear systems.” IEEE Trans. Automat. Control, AC‐24, 36–51.
21.
Liung, L., and Soderstrom, T. (1983). Theory and practice of recursive identification. MIT Press, Cambridge, Mass.
22.
Mendel, J. M. (1973). Discrete technique for parameter estimation. Marcel Dekker, New York, N.Y.
23.
Naganuma, T., Deodatis, G., and Shinozuka, M. (1987). “An ARMA model for two‐dimensional processes.” J. Engrg. Mech., ASCE, 113(2), 234–251.
24.
Nau, R. F., Oliver, R. M., and Pister, K. S. (1982). “Simulating and analyzing artificial nonstationary earthquake ground motions.” Bull. Seismol. Soc. Am., 72(2).
25.
Şafak, E. (1989a). “Adaptive modeling, identification, and control of dynamic structural systems, Part I: Theory, Part II: Applications.” J. Engrg. Mech., ASCE, 115(11).
26.
Şafak, E. (1989b). “Optimal‐adaptive filters for modeling spectral shape, site amplification, and source scaling.” Soil Dyn. Earthquake Engrg., 8‐2, 75–95.
27.
Samaras, E. P., Shinozuka, M., and Tsurui, A. (1985). “ARMA representation of random processes.” J. Engrg. Mech., ASCE, 111(3), 449–461.
28.
Takahashi, A., and Kawakami, H. (1988). “Estimation of wave propagation by AR model.” Proc. 43rd Annual Meeting, JSCE, 1002–1003 (in Japanese).
29.
Yong, P. C. (1984). Recursive estimation and time‐series. Springer‐Verlag, New York, N.Y.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 117 • Issue 7 • July 1991
Pages: 1442 - 1454
Copyright
Copyright © 1991 ASCE.
History
Published online: Jul 1, 1991
Published in print: Jul 1991
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.