Efficient Iterative Dynamic Kernel Principal Component Analysis Monitoring Method for the Batch Process with Super-large-scale Data Sets.

Abstract

The Internet environment has provided massive data to the actual industrial production process. It not only has large amounts of data but also has a high data dimension, which brings challenges to the traditional statistical process monitoring. Aiming at the nonlinearity and dynamics of industrial large-scale high-dimensional data, an efficient iterative multiple dynamic kernel principal component analysis (IMDKPCA) method is proposed to monitor the complex industrial process with super-large-scale high-dimensional data. In KPCA, a new KKT matrix is first created by using kernel matrix K. According to the properties of the symmetric matrix, the newly constructed matrix has the same eigenvector as the original matrix K; hence, each column of the matrix K can be used as the input sample of the iteration algorithm. After iterative operation, the kernel principal component can be deduced fleetly without the eigen decomposition. Because the kernel matrix is not stored in the algorithm beforehand, it can effectively reduce the computation complexity of the kernel. Especially for a tremendous data scale, the traditional eigen decomposition technology is no longer appropriate, yet the presented method can be solved quickly. The autoregressive moving average (ARMA) time series model and kernel principal component analysis (KPCA) are combined to build the IDKPCA model for dealing with the dynamics and nonlinearity in the industrial process. Eventually, it is applied to monitor faults in the penicillin fermentation process and compared with MKPCA to certify the accuracy and applicability of the proposed method.