Optimal model-based state estimation in mechanical and structural systems

SUMMARY In many applications, such as control, monitoring, assessment, and failure detection in mechanical and structural systems, the state of the system is sought. However, in almost all cases, the full state vector is not directly measured, and it must be reconstructed from sparse measurements contaminated by noise. If in addition, the excitations are not (or cannot be) measured, such as the case with wind loads, wave loading, and others, the problem becomes more challenging and standard deterministic methods are not applicable. This paper presents a model-based state estimation algorithm for online reconstruction of the complete dynamic response of a partially instrumented structure subject to realizations of random loads. The proposed algorithm operates on noise-contaminated measurements of dynamic response, a finite element model of the system, and a spectral density description of the random excitation and noise. The main contribution of the paper is the development of a second-order estimator that can be directly implemented as a modified version of the finite element model of the system while minimizing the state error estimate covariance. The proposed observer results in a suboptimal Kalman filter that can be implemented as a modified version of the original finite element model of the system with added dampers and collocated forces that are linear combinations of the measurements. The proposed method is successfully illustrated and compared with the standard Kalman filter in a mass–spring–damper system under various ideal and nonideal conditions. Copyright © 2011 John Wiley & Sons, Ltd.

[1]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[2]  K. Judd.  Nonlinear state estimation, indistinguishable states, and the extended Kalman filter , 2003 .

[3]  Michael A. Demetriou,et al.  Natural second-order observers for second-order distributed parameter systems , 2004, Syst. Control. Lett..

[4]  Jiuchao Feng,et al.  Real-time nonlinear structural system identification via iterated unscented Kalman filter , 2012 .

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

[6]  B.N. Datta,et al.  Multi-input partial eigenvalue assignment for the symmetric quadratic pencil , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[7]  Biswa Nath Datta,et al.  Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems: A new optimization approach , 2010 .

[8]  D. Luenberger.  Observing the State of a Linear System , 1964, IEEE Transactions on Military Electronics.

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

[10]  Mark J. Balas.  Do All Linear Flexible Structures Have Convergent Second-Order Observers? , 1999 .

[11]  Rustem V. Shaikhutdinov,et al.  Bayesian State Estimation Method for Nonlinear Systems and Its Application to Recorded Seismic Response , 2006 .

[12]  Suresh M. Joshi,et al.  Design of Optimal Second-Order State Estimators , 1991 .

[13]  Dionisio Bernal,et al.  State Estimation in Structural Systems with Model Uncertainties , 2008 .

[14]  H. Waller,et al.  The application of state observers in structural dynamics , 1990 .

[15]  Maria Pina Limongelli,et al.  Optimal location of sensors for reconstruction of seismic responses through spline function interpolation , 2003 .

[16]  Daniel J. Inman,et al.  Square-root state estimation for second-order large space structuresmodels , 1989 .

[17]  S. T. Mau,et al.  Story-Drift, Shear, and OTM Estimation from Building Seismic Records , 1994 .

[18]  B. Datta,et al.  ORTHOGONALITY AND PARTIAL POLE ASSIGNMENT FOR THE SYMMETRIC DEFINITE QUADRATIC PENCIL , 1997 .

[19]  Alan J. Laub,et al.  Kalman filtering for second-order models , 1988 .