Online Noise Identification for Joint State and Parameter Estimation of Nonlinear Systems

AbstractThe quality of structural parameter identification in nonlinear systems using Bayesian estimators, such as the unscented Kalman filter (UKF), depends heavily on the assumptions about the state and observation noise processes. In most practical situations though, the noise statistics are not known a priori. While the literature is rich in the area of offline approaches to noise estimation (often as part of model updating in general; the focus is not necessarily on noise parameters), there seems to be shortage of online implementations, which would be useful in structural health monitoring. Assuming that both noises (in the state and observation equations) are additive Gaussian processes, this study investigates how their statistics could be adaptively estimated online during the identification. By introducing certain distributional assumptions for the unknown noise parameters which exploit conjugacy, noise updating is simplified and is suitable for online applications. The proposed method is valida...

[1]  Thomas B. Schön,et al.  System identification of nonlinear state-space models , 2011, Autom..

[2]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[3]  Rudolph van der Merwe,et al.  The unscented Kalman filter for nonlinear estimation , 2000, Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373).

[4]  R. Mehra.  Approaches to adaptive filtering , 1972 .

[5]  Zoubin Ghahramani,et al.  Learning Nonlinear Dynamical Systems Using an EM Algorithm , 1998, NIPS.

[6]  Sami F. Masri,et al.  Development of data-based model-free representation of non-conservative dissipative systems , 2007 .

[7]  J. Beck.  Bayesian system identification based on probability logic , 2010 .

[8]  Andrew W. Smyth,et al.  Application of the unscented Kalman filter for real‐time nonlinear structural system identification , 2007 .

[9]  Rudolph van der Merwe,et al.  The Unscented Kalman Filter , 2002 .

[10]  Eleni Chatzi,et al.  The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non‐collocated heterogeneous sensing , 2009 .

[11]  Geoffrey E. Hinton,et al.  Parameter estimation for linear dynamical systems , 1996 .

[12]  C. Papadimitriou,et al.  The effect of prediction error correlation on optimal sensor placement in structural dynamics , 2012 .

[13]  Costas Papadimitriou,et al.  Updating robust reliability using structural test data , 2001 .

[14]  Vinay A. Bavdekar,et al.  Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman filter , 2011 .

[15]  Costas Papadimitriou,et al.  On prediction error correlation in Bayesian model updating , 2013 .

[16]  F. Javier Cara,et al.  An approach to operational modal analysis using the expectation maximization algorithm , 2012 .

[17]  Arno Solin,et al.  Expectation maximization based parameter estimation by sigma-point and particle smoothing , 2014, 17th International Conference on Information Fusion (FUSION).

[18]  D. Simon.  Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches , 2006 .

[19]  Eleni Chatzi,et al.  Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty , 2010 .

[20]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[21]  J. Beck,et al.  Updating Models and Their Uncertainties. I: Bayesian Statistical Framework , 1998 .