Spatio-Temporal Fractal Manifold Learning on Structure Health Monitoring

Abstract

Structure Health Monitoring (SHM) usually involves a large amount of spatio-temporal data, for which feature engineering is used to recognize the damage patterns. 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 increased 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. A new technique called Spatio-Temporal Fractal Manifold (STFM) learning to detect abnormal behaviors of spatio-temporal data. 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 (FD). Next, topological manifold learning performs spatial dimension reduction, where high dimensional data can be projected in 2D/3D spaces for better classification and visualization. Both intra-series and inter-series correlation will be represented in the low dimensional embeddings. The proposed methodology is demonstrated and validated with two datasets.