Fault detection via local and nonlocal embedding

A novel algorithm named local and nonlocal embedding (LNLE) is proposed for fault detection of industrial processes in this paper. LNLE is a linear dimensionality reduction technique for preserving both local and global information in the training data. Aligned with the objective function of neighborhood preserving projections (NPE) which means to preserve the local data structure, a new objective function is developed to preserve the relationship between a sample and others which lie in its nonlocal area. Then, a unified optimization is constructed by minimizing the distances among neighborhood samples and maximizing the distances among nonlocal samples with an orthogonal constraint of the mapping matrix for extracting a compact representation of the original data space. Finally, the utility and feasibility of the proposed algorithm are demonstrated through a numerical example and TE benchmark process.