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TECHNICAL PAPERS

Unified Probabilistic Approach for Model Updating and Damage Detection

[+] Author and Article Information
Ka-Veng Yuen

Department of Civil and Environmental Engineering, University of Macau, Macau, Chinakvyuen@umac.mo

James L. Beck

Division of Engineering and Applied Science, California Institute of Technology, Mail Code 104-44, Pasadena, CA 91125jimbeck@caltech.edu

Lambros S. Katafygiotis

Department of Civil Engineering, Hong Kong University of Science and Technology, Clearwater Bay, Kowloon, Hong Kong

J. Appl. Mech 73(4), 555-564 (Sep 29, 2005) (10 pages) doi:10.1115/1.2150235 History: Received July 11, 2004; Revised September 29, 2005

A probabilistic approach for model updating and damage detection of structural systems is presented using noisy incomplete input and incomplete response measurements. The situation of incomplete input measurements may be encountered, for example, during low-level ambient vibrations when a structure is instrumented with accelerometers that measure the input ground motion and the structural response at a few instrumented locations but where other excitations, e.g., due to wind, are not measured. The method is an extension of a Bayesian system identification approach developed by the authors. A substructuring approach is used for the parameterization of the mass, damping and stiffness distributions. Damage in a substructure is defined as stiffness reduction established through the observation of a reduction in the values of the various substructure stiffness parameters compared with their initial values corresponding to the undamaged structure. By using the proposed probabilistic methodology, the probability of various damage levels in each substructure can be calculated based on the available dynamic data. Examples using a single-degree-of-freedom oscillator and a 15-story building are considered to demonstrate the proposed approach.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Single-degree-of-freedom oscillator model (Example 1)

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Figure 2

Contours of the updated PDF projected onto the (k,c) plane of the undamaged oscillator (Example 1)

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Figure 3

Gaussian approximation for the conditional PDFs of the stiffness and damping coefficient of the undamaged oscillator (Example 1)

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Figure 4

Probability of damage for the stiffness (Example 1)

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Figure 5

Fifteen-story building model (Example 2)

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Figure 6

Contours of the updated PDF projected onto the (θ1,θ2) plane of the undamaged structure (Example 2)

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Figure 7

Gaussian approximation for the conditional PDFs of the stiffness parameters θ1 and θ2 of the undamaged structure (Example 2)

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Figure 8

Response time history (top) and its contribution from the earthquake only (bottom) at the first floor of the damaged structure (Example 2)

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Figure 9

Probability of damage for the stiffness parameters θj, j=1,…,15 (Example 2)

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