Sparse Bayesian Learning for Structural Health Monitoring

Abstract

Recently-developed techniques for statistical pattern recognition have been investigated for their applicability to Structural Health Monitoring (SHM). One of the state-of-the-art pattern recognition techniques is the Support Vector Machine (SVM) which determines decision boundaries from the data corresponding to different damage features; it does this by simultaneously maximizing the margin between data from different damage states in the transformed feature space and minimizing the misclassification error. However, the errors caused by modeling and measurement result in inevitable misclassification and so a probabilistic treatment of learning from data and making damage predictions becomes important. In this paper, a recently-developed technique called the Relevance Vector Machine (RVM), which can be viewed as a probabilistic version of the SVM, is described and a comparison is presented between the results of the RVM and SVM methods. RVM uses Bayesian updating between different model classes to determine the most probable model class that defines the decision boundary based on the available dynamic data. This most probable model class is used to perform robust probabilistic predictions for new dynamic data from a structure with unknown damage. RVM has several advantages over SVM, such as more sparsity in terms of the number of model parameters that are automatically selected from the data and automatic determination of the trade-off between the fit to the data and model complexity; however, it is more computationally intensive than SVM. Finally, some illustrative examples are presented of performing SHM using RVM on various simulated structures, including buildings and bridges, which suggest that the RVM approach is a promising SHM technique that is deserving of further study, especially using real data.

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