Simplicial Complex-Enhanced Manifold Embedding of Spatiotemporal Data for Structural Health Monitoring

Structural Health Monitoring requires the continuous assessment of a structure's operational conditions, which involves the collection and analysis of a large amount of data in both spatial and temporal domains. Conventionally, both data-driven and physics-based models for structural damage detection have relied on handcrafted features, which are susceptible to the practitioner's expertise and experience in feature selection. The limitations of handcrafted features stem from the potential for information loss during the extraction of high-dimensional spatiotemporal data collected from the sensing system. To address this challenge, this paper proposes a novel, automated structural damage detection technique called Simplicial Complex Enhanced Manifold Embedding (SCEME). The key innovation of SCEME is the reduction of dimensions in both the temporal and spatial domains for efficient and information-preserving feature extraction. This is achieved by constructing a simplicial complex for each signal and using the resulting topological invariants as key features in the temporal domain. Subsequently, curvature-enhanced topological manifold embedding is performed for spatial dimension reduction. The proposed methodology effectively represents both intra-series and inter-series correlations in the low-dimensional embeddings, making it useful for classification and visualization. Numerical simulations and two benchmark experimental datasets validate the high accuracy of the proposed method in classifying different damage scenarios and preserving useful information for structural identification. It is especially beneficial for structural damage detection using complex data with high spatial and temporal dimensions and large uncertainties in reality.