Generalized orthogonal locality preserving projections for nonlinear fault detection and diagnosis

Following the intuition that process variable data usually distributes on or near a low-dimensional structure embedded in the input space due to the dependencies among numerous process variables, we propose a novel nonlinear dimensionality reduction method named Generalized Orthogonal Locality Preserving Projections (GOLPP) for nonlinear fault detection and diagnosis. GOLPP extends the recently proposed linear Orthogonal Locality Preserving Projections (OLPP) to nonlinear case using the kernel-trick. Specifically, GOLPP explicitly considers the low-dimensional structure in data and finds a nonlinear mapping from the input space to the reduced space that optimally preserves the structure and that simultaneously possesses the orthogonal property in a kernel feature space. By tailoring the definition of proximity between training samples, GOLPP can work in unsupervised or supervised setting: Unsupervised GOLPP preserves the geometry structure for compact data representation; Supervised GOLPP uses a new proximity definition to preserve the local discriminant structure as well as the geometry in each class for data discrimination. A fault detection method based on unsupervised GOLPP and a fault diagnosis method based on supervised GOLPP are developed. Simulation results on a simple nonlinear system and the benchmark Tennessee Eastman process show the superiority of the GOLPP-based fault detection and diagnosis methods over popular nonlinear methods.