Progressive damage identification using dual extended Kalman filter

AbstractExisting Kalman filter-based parameter identification algorithms estimate the system parameters as either sole states or a subset of augmented states. While the former approach requires the measurement to be sufficiently clean, the latter is reported to have numerical stability issues. Since the parameters are estimated in both these approaches in an optimal sense, in the presence of a significant variation in parameters (due to damage), the estimates may often diverge. In this article, we propose an online health monitoring scheme powered by dual extended Kalman filtering technique to simultaneously estimate the system parameters along with the response states of a reduced-order system. To capacitate damage localization beyond sensor resolution, the proposed method employs location-based structural properties as system parameter. This reduces the dimensionality of the formulation from $${4n^2}$$4n2 elements in the state matrix to only a few physical parameters. Unnecessary estimation of a large number of unmeasured response states has been avoided by employing the system reduction technique and thus by describing the system using only measured DOFs. This in turn enables estimating a poorly observed system as a fully observed one. Two numerical experiments are performed on two degrading structures: an Euler–Bernoulli beam and a bridge truss to demonstrate the competency of the algorithm with reduced-order models.

[1]  S. Haykin.  Kalman Filtering and Neural Networks , 2001 .

[2]  Ardeshir Bahreininejad,et al.  Damage detection of truss bridge joints using Artificial Neural Networks , 2008, Expert Syst. Appl..

[3]  James L. Beck,et al.  Preface to the Special Issue on Phase I of the IASC-ASCE Structural Health Monitoring Benchmark , 2004 .

[4]  Hooshang Jazayeri-Rad,et al.  Applying a dual extended Kalman filter for the nonlinear state and parameter estimations of a continuous stirred tank reactor , 2011, Comput. Chem. Eng..

[5]  Achintya Haldar,et al.  Novel Unscented Kalman Filter for Health Assessment of Structural Systems with Unknown Input , 2015 .

[6]  Ka-Veng Yuen,et al.  Online estimation of noise parameters for Kalman filter , 2013 .

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

[8]  R. Ghanem,et al.  Structural-System Identification. I: Theory , 1995 .

[9]  A Corigliano,et al.  4637 - IDENTIFICATION OF LAMINATE MECHANICAL PROPERTIES VIA EXTENDED KALMAN FILTER , 2013 .

[10]  Sigurd Ivar Aanonsen,et al.  Reservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter , 2005 .

[11]  Eleni Chatzi,et al.  Particle filter scheme with mutation for the estimation of time‐invariant parameters in structural health monitoring applications , 2013 .

[12]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[13]  Roger Ghanem,et al.  Structural System Identification. II: Experimental Verification , 1995 .

[14]  Ali Kaveh,et al.  Online detection of the breathing crack using an adaptive tracking technique , 2007 .

[15]  Achintya Haldar,et al.  Unscented Kalman filter with unknown input and weighted global iteration for health assessment of large structural systems , 2016 .

[16]  Charles R. Farrar,et al.  A summary review of vibration-based damage identification methods , 1998 .

[17]  C. Papadimitriou,et al.  A dual Kalman filter approach for state estimation via output-only acceleration measurements , 2015 .

[18]  David A. Nix,et al.  Vibration–based structural damage identification , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[19]  Yu Lei,et al.  Hilbert-Huang Based Approach for Structural Damage Detection , 2004 .

[20]  Saeed Eftekhar Azam,et al.  Dual estimation of partially observed nonlinear structural systems: A particle filter approach , 2012 .

[21]  Erik A. Johnson,et al.  Phase I IASC-ASCE Structural Health Monitoring Benchmark Problem Using Simulated Data , 2004 .

[22]  T. Westerlund,et al.  Remarks on "Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems" , 1980 .

[23]  Charles R. Farrar,et al.  Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review , 1996 .

[24]  Saeed Eftekhar Azam,et al.  Online Damage Detection in Plates via Vibration Measurements , 2015 .

[25]  Ajoy Kumar Das,et al.  Health Assessment of Large Two Dimensional Structures Using Limited Information: Recent Advances , 2012 .

[26]  J. L. Roux.  An Introduction to the Kalman Filter , 2003 .

[27]  David Cebon,et al.  Parameter and state estimation for articulated heavy vehicles , 2011 .

[28]  M. Hoshiya,et al.  Structural Identification by Extended Kalman Filter , 1984 .

[29]  Rune Brincker,et al.  Vibration Based Inspection of Civil Engineering Structures , 1993 .

[30]  Eric A. Wan,et al.  Dual Extended Kalman Filter Methods , 2002 .

[31]  Gregory L. Plett,et al.  Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 3. State and parameter estimation , 2004 .

[32]  Alberto Corigliano,et al.  Impact induced composite delamination: state and parameter identification via joint and dual extended Kalman filters , 2005 .

[33]  P. Kumar,et al.  Theory and practice of recursive identification , 1985, IEEE Transactions on Automatic Control.

[34]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[35]  Stefano Mariani,et al.  Unscented Kalman filtering for nonlinear structural dynamics , 2007 .

[36]  Saeed Eftekhar Azam.  Dual Estimation and Reduced Order Modeling of Damaging Structures , 2014 .

[37]  Elias B. Kosmatopoulos,et al.  Development of adaptive modeling techniques for non-linear hysteretic systems , 2002 .

[38]  Andrew W. Smyth,et al.  On-Line Parametric Identification of MDOF Nonlinear Hysteretic Systems , 1999 .

[39]  E. Stear,et al.  The simultaneous on-line estimation of parameters and states in linear systems , 1976 .

[40]  A. Corigliano,et al.  Parameter identification in explicit structural dynamics: performance of the extended Kalman filter , 2004 .

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