Stable Robust Extended Kalman Filter
Publication: Journal of Aerospace Engineering
Volume 30, Issue 2
Abstract
In this paper, a stable and robust filter is proposed for structural identification. This filter resolves the instability problems of the traditional extended Kalman filter (EKF). Instead of ad hoc assignment of the noise covariance matrices in the EKF, the proposed stable robust extended Kalman filter (SREKF) provides real-time updating of the noise parameters. This resolves the well-known instability problem of the EKF due to improper assignment of the noise covariance matrices. Furthermore, the proposed SREKF is capable of removing abnormal data points in a real-time manner. As a result, the parametric identification results will be more reliable and have fewer fluctuations. The proposed approach will be applied to structural damage detection of degrading linear and nonlinear structures in comparison with the plain EKF, utilizing highly contaminated response measurements. It turns out that the estimation error of the state vector and the structural parameters is lower than the EKF by one and two orders of magnitude, respectively.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (51508201), the State Key Laboratory of Subtropical Building Science, South China University of Technology (2016ZB26), and the Science and Technology Development Fund of the Macau SAR government under Research Grant FDCT/012/2013/A1. These generous supports are gratefully acknowledged.
References
Bao, Y., et al. (2014). “Compressive sensing-based lost data recovery of fast-moving wireless sensing for structural health monitoring.” Struct. Control Health., 22(3), 433–448.
Beck, J. L. (2010). “Bayesian system identification based on probability logic.” Struct. Control Health, 17(7), 825–847.
Beck, J. L., and Katafygiotis, L. S. (1998). “Updating models and their uncertainties. I: Bayesian statistical framework.” J. Eng. Mech., 455–461.
Beck, J. L., and Yuen, K. V. (2004). “Model selection using response measurements: Bayesian probabilistic approach.” J. Eng. Mech., 192–203.
Bhalla, S., and Soh, C. K. (2004). “Structural health monitoring by piezo-impedance transducers. I: Modeling.” J. Aerosp. Eng., 154–165.
Chang, P. C., Flatau, A., and Liu, S. C. (2003). “Review paper: Health monitoring of civil infrastructure.” Struct. Health Monit., 2(3), 257–267.
Durovic, Z. M., and Kovacevic, B. D. (1999). “Robust estimation with unknown noise statistics.” IEEE Trans. Autom. Control, 44(6), 1292–1296.
Fan, W., and Qiao, P. (2011). “Vibration-based damage identification methods: A review and comparative study.” Struct. Health Monit., 10(1), 83–111.
Fitzgerald, R. (1971). “Divergence of the Kalman filter.” IEEE Trans. Autom. Control, 16(6), 736–747.
He, W. Y., and Zhu, S. (2015). “Moving load-induced response of damaged beam and its application in damage localization.” J. Vib. Control, in press.
Hou, Z., Noori, M., and Amand, R. S. (2000). “Wavelet-based approach for structural damage detection.” J. Eng. Mech., 677–683.
Huang, Y., Beck, J. L., Wu, S., and Li, H. (2014). “Robust Bayesian compressive sensing for signals in structural health monitoring.” Comput. Aided Civ. Inf., 29(3), 160–179.
Jazwinski, A. H. (1970). Stochastic processes and filtering theory, Academic Press, New York.
Kalman, R. E., and Bucy, R. S. (1961). “New results in linear filtering and prediction theory.” J. Basic Eng., 83(1), 95–108.
Kerschen, G., Worden, K., Vakakis, A. F., and Golinval, J. C. (2006). “Past, present and future of nonlinear system identification in structural dynamics.” Mech. Syst. Sig. Process, 20(3), 505–592.
Koh, C. G., and See, L. M. (1994). “Identification and uncertainty estimation of structural parameters.” J. Eng. Mech., 1219–1236.
Kuok, S. C., Ng, I. T., and Yuen, K. V. (2015). “Study of the attenuation relationship for the Wenchuan Ms 8.0 earthquake.” Earthquake Eng. Eng. Vib., 14(1), 1–11.
Kuok, S. C., and Yuen, K. V. (2012). “Structural health monitoring of Canton Tower using Bayesian framework.” Smart Struct. Syst., 10(4-5), 375–391.
Lei, Y., Chen, F., and Zhou, H. (2015). “An algorithm based on two-step Kalman filter for intelligent structural damage detection.” Struct. Control Health Monit., 22(4), 694–706.
Li, H. N., Li, D. S., and Song, G. B. (2004). “Recent applications of fiber optic sensors to health monitoring in civil engineering.” Eng. Struct., 26(11), 1647–1657.
Ljung, L., and Gunnarsson, S. (1990). “Adaptation and tracking in system identification—A survey.” Automatica, 26(1), 7–21.
Lynch, J. P., Partridge, A., Law, K. H., Kenny, T. W., Kiremidjian, A. S., and Carryer, E. (2003). “Design of piezoresistive MEMS-based accelerometer for integration with wireless sensing unit for structural monitoring.” J. Aerosp. Eng., 108–114.
Mehra, R. K. (1970). “On the identification of variance and adaptive Kalman filtering.” IEEE Trans. Autom. Control, 15(2), 175–184.
Meinhold, R. J., and Singpurwalla, N. D. (1989). “Robustification of Kalman filter models.” J. Am. Stat. Assoc., 84(406), 479–486.
Mohamed, A. H., and Schwarz, K. P. (1999). “Adaptive Kalman filtering for INS/GPS.” J. Geodesy, 73(4), 193–203.
Moncayo, H., Marulanda, J., and Thomson, P. (2009). “Identification and monitoring of modal parameters in aircraft structures using the natural excitation technique (NExT) combined with the eigensystem realization algorithm (ERA).” J. Aerosp. Eng., 99–104.
Mu, H. Q., Xu, R. R., and Yuen, K. V. (2014). “Seismic attenuation relationship with homogeneous and heterogeneous prediction-error variance models.” Earthquake Eng. Eng. Vib., 13(1), 1–11.
Mu, H. Q., and Yuen, K. V. (2015). “Novel outlier-resistant extended Kalman filter for robust online structural identification.” J. Eng. Mech., 04014100.
Odelson, B. J., Rajamani, M. R., and Rawlings, J. B. (2006). “A new autocovariance least-squares method for estimating noise covariances.” Automatica, 42(2), 303–308.
Papadimitriou, C., Fritzen, C. P., Kraemer, P., and Ntotsios, E. (2011). “Fatigue predictions in entire body of metallic structures from a limited number of vibration sensors using Kalman filtering.” Struct. Control Health, 18(5), 554–573.
Sethi, V., Song, G., and Qiao, P. (2006). “System identification and active vibration control of a composite I-beam using smart materials.” Struct. Control Health, 13(4), 868–884.
Simoen, E., Papadimitriou, C., and Lombaert, G. (2013). “On prediction error correlation in Bayesian model updating.” J. Sound Vib., 332(18), 4136–4152.
Sohn, H., Farrar, C. R., Hemez, F., and Czarnecki, J. (2004). “A review of structural health monitoring literature from 1996–2001.” Los Alamos National Laboratory, Los Alamos.
Vestroni, F., and Noori, M. (2002). “Hysteresis in mechanical systems—Modeling and dynamic response.” Int. J. Nonlinear Mech., 37(8), 1261–1262.
Wang, J., and Qiao, P. (2007). “Improved damage detection for beam-type structures using a uniform load surface.” Struct. Health Monit., 6(2), 99–110.
Worden, K., Farrar, C. R., Manson, G., and Park, G. (2007). “The fundamental axioms of structural health monitoring.” Proc. R. Soc. A Math. Phys. Eng. Sci., 463(2082), 1639–1664.
Yan, W. M., Yuen, K. V., and Yoon, G. L. (2009). “Bayesian probabilistic approach for the correlations of compressibility index for marine clays.” J. Geotech. Geoenviron., 1932–1940.
Yi, T. H., Li, H. N., and Gu, M. (2013a). “Experimental assessment of high-rate GPS receivers for deformation monitoring of bridge.” Measurement, 46(1), 420–432.
Yi, T. H., Li, H. N., and Gu, M. (2013b). “Recent research and applications of GPS-based monitoring technology for high-rise structures.” Struct. Control Health, 20(5), 649–670.
Yi, T. H., Li, H. N., and Zhang, X. D. (2015). “Health monitoring sensor placement optimization for Canton Tower using immune monkey algorithm.” Struct. Control Health, 22(1), 123–138.
Yuen, K. V. (2010). Bayesian methods for structural dynamics and civil engineering, Wiley, New York.
Yuen, K. V., Beck, J. L., and Katafygiotis, L. S. (2006). “Unified probabilistic approach for model updating and damage detection.” J. Appl. Mech., 73(4), 555–564.
Yuen, K. V., Hoi, K. I., and Mok, K. M. (2007). “Selection of noise parameters for Kalman filter.” Earthquake Eng. Eng. Vib., 6(1), 49–56.
Yuen, K. V., and Katafygiotis, L. S. (2005). “Model updating using noisy response measurements without knowledge of the input spectrum.” Earthquake Eng. Struct., 34(2), 167–187.
Yuen, K. V., and Katafygiotis, L. S. (2014). “Modal decomposition using multi-channel response measurements.” Probab. Eng. Mech., 37, 60–73.
Yuen, K. V., and Kuok, S. C. (2011). “Bayesian methods for updating dynamic models.” Appl. Mech. Rev., 64(1), 010802.
Yuen, K. V., and Kuok, S. C. (2015). “Efficient Bayesian sensor placement algorithm for structural identification: A general approach for multi-type sensory systems.” Earthquake Eng. Struct., 44(5), 757–774.
Yuen, K. V., Liang, P. F., and Kuok, S. C. (2013). “Online estimation of noise parameters for Kalman filter.” Struct. Eng. Mech., 47(3), 361–381.
Yuen, K. V., and Mu, H. Q. (2011). “Peak ground acceleration estimation by linear and nonlinear models with reduced order Monte Carlo simulation.” Comput. Aided Civ. Infrastruct. Eng., 26(1), 30–47.
Yuen, K. V., and Mu, H. Q. (2012). “A novel probabilistic method for robust parametric identification and outlier detection.” Probab. Eng. Mech., 30, 48–59.
Yuen, K. V., and Mu, H. Q. (2015). “Real-time system identification: An algorithm for simultaneous model class selection and parametric identification.” Comput. Aided Civ. Inf., 30(10), 785–801.
Zhu, S., Chen, Z., Cai, Q., Lei, Y., and Chen, B. (2014). “Locate damage in long-span bridges based on stress influence lines and information fusion technique.” Adv. Struct. Eng., 17(8), 1089–1102.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 30 • Issue 2 • March 2017
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Feb 23, 2015
Accepted: May 4, 2016
Published online: Jul 21, 2016
Discussion open until: Dec 21, 2016
Published in print: Mar 1, 2017
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.