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Published 2015 | public
Journal Article

Hierarchical Sparse Bayesian Learning for Structural Health Monitoring with Incomplete Modal Data

Abstract

For civil structures, structural damage due to severe loading events such as earthquakes, or due to long-term environmental degradation, usually occurs in localized areas of a structure. A new sparse Bayesian probabilistic framework for computing the probability of localized stiffness reductions induced by damage is presented that uses noisy incomplete modal data from before and after possible damage. This new approach employs system modal parameters of the structure as extra variables for Bayesian model updating with incomplete modal data. A specific hierarchical Bayesian model is constructed that promotes spatial sparseness in the inferred stiffness reductions in a way that is consistent with the Bayesian Ockham razor. To obtain the most plausible model of sparse stiffness reductions together with its uncertainty within a specified class of models, the method employs an optimization scheme that iterates among all uncertain parameters, including the hierarchical hyper-parameters. The approach has four important benefits: (1) it infers spatially sparse stiffness changes based on the identified modal parameters; (2) the uncertainty in the inferred stiffness reductions is quantified; (3) no matching of model and experimental modes is needed, and (4) solving the nonlinear eigenvalue problem of a structural model is not required. The proposed method is applied to two previously studied examples using simulated data: a ten-story shear-building and the three-dimensional braced-frame model from the Phase II Simulated Benchmark problem sponsored by the IASC-ASCE Task Group on Structural Health Monitoring. The results show that the occurrence of false-positive and false-negative damage detection is clearly reduced in the presence of modeling error (differences between the real structural behavior and the model of it). Furthermore, the identified most probable stiffness loss ratios are close to their actual values.

Additional Information

© 2015 by Begell House, Inc. Original Manuscript Submitted: 09/30/2013; Final Draft Received: 12/08/2014. This work was supported by the U.S. National Science Foundation under award number EAR-0941374 to the California Institute of Technology. This support is gratefully acknowledged by both authors. This research is also supported by grant from the National Natural Science Foundation of China (NSFC grant no. 51308161), which partially supported the first author and this support is gratefully acknowledged.

Additional details

Created:
August 20, 2023
Modified:
October 24, 2023