Damage Identification in a Truss Tower by Regularized Model Updating

This paper presents a sensitivity-based damage identification of a three-dimensional truss tower tested in the laboratory. A finite-element model is updated by modal parameters obtained from ambient vibration measurements. The paper focuses on details of modeling and model updating. To get a realistic model, it was necessary to include eccentric connections, bending stiffness in truss members, and foundation flexibility. For model updating, a number of mathematical techniques are combined in a consistent way, including regularization of the nonlinear updating problem and its linearization. Considering all these details correctly, damage in the truss has been successfully identified. However, it is also demonstrated how neglecting some of these algorithmic details can lead to incorrect results. It is also shown how static condensation can lead to a model that is valid for the undamaged case but cannot adequately represent the damaged case.

[1]  James L. Beck,et al.  Two-Stage Structural Health Monitoring Approach for Phase I Benchmark Studies , 2004 .

[2]  B. Weber,et al.  Structural damage detection using nonlinear parameter identification with Tikhonov regularization , 2007 .

[3]  Grace Wahba,et al.  A cross validated bayesian retrieval algorithm for nonlinear remote sensing experiments , 1985 .

[4]  Shirley J. Dyke,et al.  Experimental Phase II of the Structural Health Monitoring Benchmark Problem , 2003 .

[5]  R. Fox,et al.  Rates of change of eigenvalues and eigenvectors. , 1968 .

[6]  C. Vogel.  Computational Methods for Inverse Problems , 1987 .

[7]  Scott W. Doebling,et al.  Minimum-rank optimal update of elemental stiffness parameters for structural damage identification , 1996 .

[8]  Per Christian Hansen,et al.  Rank-Deficient and Discrete Ill-Posed Problems , 1996 .

[9]  Patrick Paultre,et al.  Consistent regularization of nonlinear model updating for damage identification , 2009 .

[10]  Curtis R. Vogel,et al.  An Overview of Numerical Methods for Nonlinear Ill-Posed Problems , 1987 .

[11]  D. Zimmerman,et al.  Structural damage detection using a minimum rank update theory , 1994 .

[12]  Gene H. Golub,et al.  Matrix computations , 1983 .

[13]  David C. Zimmerman,et al.  Eigenstructure assignment approach for structural damage detection , 1992 .

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

[15]  Erik A. Johnson,et al.  NATURAL EXCITATION TECHNIQUE AND EIGENSYSTEM REALIZATION ALGORITHM FOR PHASE I OF THE IASC-ASCE BENCHMARK PROBLEM: SIMULATED DATA , 2004 .

[16]  James L. Beck,et al.  Bayesian Analysis of the Phase II IASC–ASCE Structural Health Monitoring Experimental Benchmark Data , 2004 .

[17]  K. E. Chu,et al.  Derivatives of Eigenvalues and Eigenvectors of Matrix Functions , 1993, SIAM J. Matrix Anal. Appl..

[18]  J. L. Humar,et al.  Experimental verification of a vibration based damage detection technique , 2002 .

[19]  Lambros S. Katafygiotis,et al.  Application of a Statistical Model Updating Approach on Phase I of the IASC-ASCE Structural Health Monitoring Benchmark Study , 2004 .

[20]  Richard B. Nelson,et al.  Simplified calculation of eigenvector derivatives , 1976 .

[21]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[22]  Jun Yu,et al.  Investigation of a System Identification Methodology in the Context of the ASCE Benchmark Problem , 2004 .

[23]  P. Hansen.  Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion , 1987 .

[24]  Luciana R. Barroso,et al.  Damage Detection Utilizing the Damage Index Method to a Benchmark Structure , 2004 .

[25]  James M. Ricles,et al.  Damage detection in elastic structures using vibratory residual forces and weighted sensitivity , 1992 .

[26]  Dionisio Bernal,et al.  Flexibility-Based Approach for Damage Characterization: Benchmark Application , 2004 .

[27]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[28]  Tae W. Lim,et al.  Structural damage detection of space truss structures using best achievable eigenvectors , 1994 .