A Bayesian Probabilistic Approach to Damage Detection for Civil Structures
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This series includes technical reports prepared by faculty, students and staff who are associated with the John A. Blume Earthquake Engineering Center at Stanford University. While the primary focus of Blume Center is earthquake engineering, many of the reports in this series encompass broader topics in structural engineering and materials, computational mechanics, geomechanics, structural health monitoring, and engineering life-cycle risk assessment. Each report includes acknowledgments of the specific sponsors for the report and underlying research. In addition to providing research support, the Blume Center provides administrative support for maintaining and disseminating the technical reports. For more information about the Blume Center and its activities, see https://blume.stanford.edu.
There have been increased economic and societal demands to periodically monitor the safety of structures against long-term deterioration, and to ensure their safety and adequate performance during the life span of the structures. In this work, a Bayesian probabilistic framework for damage detection is proposed for the continuous monitoring of structures. The idea is to search for the most probable damage event by comparing the relative probabilities for different damage scenarios. The formulation of the relative posterior probability is based on an output error, which is defined as the difference between the estimated vibration parameters and the theoretical ones from the analytical model. The Bayesian approach is shown (1) to take into account the uncertainties in the measurement and the analytical modeling, (2) to perform damage diagnosis with a relatively small number of measurement points and a few modes, and (3) to systematically extract information from continuously obtained test data. A branch-and-bound search scheme is devised to expedite the search for the most likely damage event without exhaustively examining all possible damage cases. As an alternative to modal vectors, load-dependent Ritz vectors are incorporated into the Bayesian framework. The following advantages of Ritz vectors over modal vectors are shown: (1) in general, load-dependent Ritz vectors are more sensitive to damage than the corresponding modal vectors, and (2) by a careful selection of load patterns, substructures of interest can be made more observable. Furthermore, a procedure to extract Ritz vectors from vibration test is proposed, and the procedure is successfully demonstrated using experimental test data. Data from vibration tests of civil structures indicate that the environmental effects such as temperature, traffic loading, humidity can often mask subtle structural changes caused by damage. A linear adaptive filter is presented to discriminate the changes of modal parameters due to temperature changes from those caused by structural damage or other environmental effects. Results based on the field vibration test of a bridge indicate that the filter can reproduce the temporal variability of the frequencies so that the thermal effects on the vibration parameters can be differentiated from other environmental effects or potential structural damage.
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- Sohn, H and Law, KH. (1999). A Bayesian Probabilistic Approach to Damage Detection for Civil Structures. John A Blume Earthquake Engineering Center Technical Report 131. Stanford Digital Repository. Available at: http://purl.stanford.edu/bq540dj5997
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- John A. Blume Earthquake Engineering Center
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