Nonlocality-constrained Locality Sparse Preserving Projections and Its Application to Fault Detection

Locality preserving projections, which preserve the neighborhood relationship of data, has been successfully applied in process monitoring. However, these methods neglect non-locality structure information and cannot guarantee the relationship of samples faraway. Locality preserving sparse modeling proposed recently use sparse coding to get a set of overcomplete basis, and well-represented inherent structural features from the raw data. Owing to sparse coding for learning local sparse structure features and representing raw data appropriately, we propose non-locality-constrained locality sparse preserving projections. First, we extract the sparse code and represent the global structure information by using sparse coding; second, we preserve the locality structure characteristics with non-locality relationship constraint, and estimate the probability densities of different sparse codes, which are set up with different weighting values to evaluate their contribution to faults; then, we build a combined statistical index for fault detection based on process status; Finally, we validate the proposed method using a numerical study and the Tennessee Eastman benchmark process, and compare it with several models. The monitoring results indicate its superior performance.