A density‐based collaboration preserving projection for fault detection

The development of effective dimensionality reduction methods for fault detection in industrial processes is essential for ensuring safety. The performance of dimensionality reduction methods depends heavily on the extraction of effective and comprehensive features. To achieve a more accurate representation of data characteristics and enhance fault detection performance, we propose a novel data dimensionality reduction method for fault detection, called density‐based collaboration preserving projection (DCPP). First, an adaptive neighbour selection strategy is proposed to dynamically select the neighbours for each sample, enabling the adjacency graph constructed using each sample and its neighbours to accurately reflect the local structure of the data. Second, DCPP effectively preserves the topological structure of the data in the spatial dimension and captures dynamic features in the temporal dimension. Third, a data cleaning method is proposed to label samples that deviate from the dominant structure, and targeted weight coefficients are constructed for these samples to enhance the reliability of DCPP in extracting features in the spatial dimension. All distance measures employ geodesic distance instead of traditional Euclidean distance, allowing for a more accurate assessment of the actual distance between two points within the manifold structure. Finally, the effectiveness of the proposed method is validated through simulation experiments.