Efficient model updating and health monitoring methodology using incomplete modal data without mode matching

A methodology is presented for Bayesian structural model updating using noisy incomplete modal data corresponding to natural frequencies and partial mode shapes of some of the modes of a structural system. The procedure can be used to find the most probable model within a specified class of structural models, based on the incomplete modal data, as well as the most probable values of the system natural frequencies and the full system mode shapes. The method does not require matching measured modes with corresponding modes from the structural model, which is in contrast to many existing methods. To find the most probable values of the structural model parameters and system modal parameters, the method uses an iterative scheme involving a series of coupled linear optimization problems. Furthermore, it does not require solving the eigenvalue problem of any structural model; instead, the eigenvalue equations appear in the prior probability distribution to provide soft constraints. The method appears to be computationally efficient and robust, judging from its successful application to noisy simulated data for a ten-storey building model and for a three-dimensional braced-frame model. This latter example is also used to demonstrate an application to structural health monitoring.

[1]  Lambros S. Katafygiotis,et al.  Bayesian modal updating using complete input and incomplete response noisy measurements , 2002 .

[2]  J. Ko,et al.  Localization of damaged structural connections based on experimental modal and sensitivity analysis , 1998 .

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

[4]  James L. Beck,et al.  Monitoring Structural Health Using a Probabilistic Measure , 2001 .

[5]  Keith D. Hjelmstad,et al.  Damage detection and assessment of structures from static response , 1997 .

[6]  C. Papadimitriou,et al.  A probabilistic approach to structural model updating , 1998 .

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

[8]  James L. Beck,et al.  New Bayesian Model Updating Algorithm Applied to a Structural Health Monitoring Benchmark , 2004 .

[9]  D. Bernal.  Load Vectors for Damage Localization , 2002 .

[10]  Lambros S. Katafygiotis,et al.  Bayesian time–domain approach for modal updating using ambient data , 2001 .

[11]  Masoud Sanayei,et al.  PARAMETER ESTIMATION INCORPORATING MODAL DATA AND BOUNDARY CONDITIONS , 1999 .

[12]  N Stubbs,et al.  NONDESTRUCTIVE DAMAGE EVALUATION IN COMPLEX STRUCTURES FROM A MINIMUM OF MODAL PARAMETERS , 1995 .

[13]  Lambros S. Katafygiotis,et al.  Probabilistic approach for modal identification using non‐stationary noisy response measurements only , 2002 .

[14]  J. Beck,et al.  Asymptotic Expansions for Reliability and Moments of Uncertain Systems , 1997 .

[15]  A. K. Pandey,et al.  Experimental verification of flexibility difference method for locating damage in structures , 1995 .

[16]  James L. Beck,et al.  A Bayesian probabilistic approach to structural health monitoring , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[17]  Lambros S. Katafygiotis,et al.  Bayesian spectral density approach for modal updating using ambient data , 2001 .

[18]  James T. P. Yao,et al.  Structural safety evaluation based on system identification approaches : proceedings of the Workshop at Lambrecht/Pfalz , 1988 .

[19]  S. F. Masri,et al.  Proceedings of the International Workshop on Nondestructive Evaluation for Performance of Civil Structures , 1988 .