A Kernel Least Squares Based Approach for Nonlinear Quality-Related Fault Detection

In this paper, a nonlinear quality-related fault detection approach is proposed based on kernel least squares (KLS) model. The major novelty of the proposed method is that it utilizes KLS model to exploit the entire correlation between feature and output matrices. First, it uses a nonlinear projection function to map original process variables into feature space in which the correlation between feature and output matrices is realized by means of KLS. Then, the feature matrix is decomposed into two orthogonal parts by singular value decomposition and the statistics for each part are determined appropriately for the purpose of quality-related fault detection. Compared with existing kernel partial least squares (KPLS) based approaches, the proposed new method has the following obvious advantages. 1) It extracts the full correlation information of feature matrix, while KPLS-based approaches only use the partial correlation of several selected latent variables; therefore, it is more stable than the existing ones. 2) It omits the iterative computation of KPLS model and the determination of the number of latent variables; therefore, it is more efficient in engineering implementation. 3) It only uses two statistics to determine the type of fault, while most of the KPLS-based approaches need four; therefore, it has a more simple diagnosis logic. For simulation verification, a widely used literature example and an industrial benchmark are utilized to evaluate the performance of the proposed method.