Spatiotemporal fractal manifold learning for vibration-based structural health monitoring

Structural health monitoring (SHM) usually involves a large amount of spatiotemporal data, for which feature engineering is used to extract health and damage indicators. For example, vibration-based structural damage detection methods have been widely used in SHM practices integrated with some machine learning techniques for clustering, classification, and prediction. Most existing machine learning techniques suffer from the curse of dimensionality, in which the performance of models decreases rapidly with an increase in the number of features. In addition, many classical machine learning techniques use hand-crafted features, and results are highly sensitive to the analyst's experiences in feature selection. This chapter proposes a new SHM technique called spatiotemporal fractal manifold learning to detect structural damage automatically. The key idea is to perform dimension reduction for the decomposed spatial and temporal dimensions. First, temporal dimension reduction by fractal analysis is performed, in which each signal will be represented by a single fractal dimension. Next, topological manifold learning performs spatial dimension reduction, where high-dimensional data can be projected in two-dimensional/three-dimensional spaces for better classification and visualization. Both intraseries and interseries correlation will be represented in the low-dimensional embeddings. The proposed methodology is demonstrated and validated with two benchmark datasets. The results showed high accuracy in classifying different damaged scenarios and are especially beneficial when high-dimensional data are involved in SHM from multiple sensory data at multiple locations.