Fault Detection Based on Diffusion Maps and <i>k</i> Nearest Neighbor Diffusion Distance of Feature Space

Abstract

Dimensionality reduction is a fundamental task of high-dimensional data analysis in order to reduce redundant information of the collected data. In this paper, we apply diffusion maps framework to address this problem, and then propose a novel fault detection technique based on the k nearest neighbor diffusion distance method of feature space. First, normal high-dimensional data sets are mapped into a low-dimensional feature space by analyzing the insightful relationship between data points, and feature space can represent major information of raw data. Subsequently, like the traditional kNN method, the sum of k nearest neighbor diffusion distance is computed and the kernel density estimation method is used to set a threshold of a normal process. Comparing these two methods, modeling using k nearest neighbor diffusion distance method of feature space can economize storage space and increase the speed of fault detection. In addition, this method can solve nonlinear equation of industrial process data, and the non-Gaussian characteristics of modeling data can be solved by using kernel density estimation method. Finally, the effectiveness of diffusion maps algorithm in the aspect of data classification is verified by the numerical examples and the superiority of the proposed method is illustrated by the monitoring of TE process.