Variance-Reduced Particle Filters for Structural System Identification Problems
Publication: Journal of Engineering Mechanics
Volume 139, Issue 2
Abstract
A few variance reduction schemes are proposed within the broad framework of a particle filter as applied to the problem of structural system identification. Whereas the first scheme uses a directional descent step, possibly of the Newton or quasi-Newton type, within the prediction stage of the filter, the second relies on replacing the more conventional Monte Carlo simulation involving pseudorandom sequence with one using quasi-random sequences along with a Brownian bridge discretization while representing the process noise terms. As evidenced through the derivations and subsequent numerical work on the identification of a shear frame, the combined effect of the proposed approaches in yielding variance-reduced estimates of the model parameters appears to be quite noticeable.
Get full access to this article
View all available purchase options and get full access to this article.
References
Arulampalam, S., Maskell, N., Gordon, N., and Clapp, T. (2002). “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking.” IRSJ Intl. Conf. on Intelligent Trans. Signal Process., 50(2), 174–188.
Banerjee, B., Roy, D., and Vasu, R. M. (2011). “A pseudo-dynamical systems approach to a class of inverse problems in engineering.” Proc., R. Soc. Lond. A, 465(2105), 1561–1579.
Caflisch, R. E. (1998). “Monte Carlo and quasi-Monte Carlo methods.” Acta Numer., 7, 1–49, Cambridge University Press, Cambridge, U.K.
Chatzi, E., and Smyth, A. W. (2009). “The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing.” Structural control and health monitoring, 16(1), 99–123.
Ching, J., Beck, J. L., Porter, K. A., and Shaikhutdinov, R. (2006). “Bayesian state estimation method for nonlinear systems and its application to recorded seismic response.” J. Eng. Mech., 132(4), 396–410.
Doucet, A. (1998). “On sequential simulation-based methods for Bayesian filtering.” Technical Rep. CUED/F-INFENG/TR.310(1998), Dept. of Electrical Engineering, Univ. of Cambridge, Cambridge, U.K.
Doucet, A., Godsill, S., and Andrieu, C. (2000). “On sequential Monte Carlo sampling methods for Bayesian filtering.” Stat. Comput., 10(3), 197–208.
Evensen, G. (2003). “The Ensemble Kalman Filter: Theoretical formulation and practical implementation.” Ocean Dyn., 53(4), 343–367.
Faure, H. (1982). “Discrepance de suites associees a un systeme de numeration (en dimension s).” Acta Arithmetica, 41(4), 337–351.
Gordon, N. J., Salmond, D. J., and Smith, A. F. M. (1993). “Novel approach to nonlinear/non-Gaussian Bayesian state estimation.” IEEE Proc. F. Radar Signal Process., 140(2), 107–113.
Halton, J. (1960). “On the efficiency of certain quasirandom sequences of points in evaluating multidimensional integrals.” Numer. Mathematik, 2(1), 84–90.
Jazwinski, A. H. (1970). Stochastic processes and filtering theory, Academic Press, New York.
Jeroen, D. H., Thomas, B. S., and Gustafsson, F. (2006). “On resampling algorithms for particle filters.” IEEE Nonlinear Statistical Signal Processing Workshop, IEEE, New York, 79–82.
Julier, S. J., and Uhlmann, J. K. (1997). “A new extension of the Kalman filter to nonlinear systems.” Proc. SPIE., 3068, 182–193.
Kuipers, L., and Niederreiter, H. (1974). Uniform distribution of sequences, Wiley, New York.
Kwok, N., Fang, G., and Zhou, W. (2005). “Evolutionary particle filter: Re-sampling from the genetic algorithm perspective.” Int.: Proc., IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems, Edmonton, AB, Canada, 1053–1058.
Lieven, N. A., and Ewins, D. J. (2001). “Experimental modal analysis (theme issue).” Philos. Trans. R. Soc. Lond. A, 359(1778), 1–219.
Ljung, L. (1997). System identification: theory for the user, Prentice Hall, Englewood Cliffs, NJ.
Moro, B., (1995). “The full Monte.” Risk, 8(2), 57–58.
Morokoff, W. J., (1998). “Generating quasi-random paths for stochastic processes.” SIAM Review, 40(4), 765–788.
Niederreiter, H. (1978). “Quasi-Monte Carlo methods and pseudo-random numbers.” Bull. Am. Math. Soc., 84, 957–1041.
Peeters, B., and Roeck, G. D. (2001). “Stochastic system identification for operational modal analysis.” J. Dyn. Syst. Measure. Control, 123(4), 659–667.
Pintelon, R., and Schoukens, J. (2001). System identification: A frequency domain approach, IEEE Press, New York.
Ristic, B., Arulampalam, S., and Gordon, N. (2004). Beyond the Kalman filter: Particle filters for tracking applications, Artech House, Boston.
Saha, N., and Roy, D. (2009). “A Girsanov particle filter in nonlinear engineering dynamics.” Phys. Lett. A, 373(6), 627–635.
Sajeeb, R., Manohar, C. S., and Roy, D. (2009). “Rao-Blackwellization with substructuring for state and parameter estimations of a class of nonlinear dynamical systems.” Int. J. Eng. Uncertainty Haz. Assess. Mitigation, 1(1–2), 81–99.
Sajeeb, R., Manohar, C. S., and Roy, D. (2010). “A semi-analytical particle filter for identification of nonlinear oscillators.” Probab. Eng. Mech., 25(1), 35–48.
Schlenkrich, S., and Walther, A. (2009). “Global convergence of quasi-Newton methods based on adjoint Broyden updates.” Appl. Numer. Math., 59(5), 1120–1136.
Sobol', I. Y. M. (1967). “On the distribution of points in a cube and the approximate evaluation of integrals.” Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 7(4), 784–802.
Tanizaki, H. (1996). Nonlinear filters: Estimation and applications, Springer, Berlin.
Tanizaki, H., Mariano, R. S. (1998). “Nonlinear and non-Gaussian state-space modeling with Monte Carlo simulations.” J. Econom., 83(12), 263–290.
Zhu, G., Liang, D., Liu, Y., Huang, Q., and Gao, W. (2005), “Improving particle filter with support vector regression for efficient visual tracking.” Proc., Int. Conf. Image Processing, Vol. 2, Genoa, Italy, 422–425.
Information & Authors
Information
Published In
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jan 22, 2012
Accepted: May 24, 2012
Published online: May 28, 2012
Published in print: Feb 1, 2013
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.