Some Studies On Statistical Process Monitoring Based On PCA

In face of the drastic market competition, corporations improve the demand for process control and management. Therefore, the traditional methods entirely based on manpower are outdated and can not satisfy the complicated desire of quality control. Having no use for complex mechanism model, statistical process monitoring method based on principal component analysis (PCA) can monitor process through extracting important information from raw data using statistical method and then transforming them into several significative indices. The method not only takes sufficient use of the existing information and is well realizable, but also greatly reduces the procedure of process monitoring, which make it attractive both in industry and academia. The method has been widely used in industrial processes, and has great significance in decreasing cost and improving product quality.Traditional PCA algorithm is a linear way, the preconditions of its application are that process variables are normally distributed and no auto-correlation among them. However, most of industrial processes are complicated and always violate the preconditions, so the PCA-based method behaves unsatisfactorily. Besides, the traditional method suffers the following demerits: monitoring indices use different measuring units; the algorithm for the confidence limit of monitoring indices is localized on the assumption that process variables meet norm distribution; the method is applicable only when process variables have no missing data, while the real industrial processes always have some missing data and most of the existing reconstruction methods are linear by making the index SPE minimum.Aiming at the disadvantages of the PCA-based method, the main contributions and innovations are as follows:1) The extension of PCA. Both PCA and probabilistic PCA (PPCA) are special cases of factor analysis (FA), their applications are inferior to FA in universality. For this reason, a monitoring method based on FA is proposed.2) Improve the monitoring indices and present a non-parametric algorithm for confidence bounds. An improved SPE index is introduced based on Mahalanobis distance. It is consistent with the T2 index in measuring unit and enhances the monitoring performance. Furthermore, to reduce the monitoring workload, an overall index is developed by combining the improved index and T2 index. Owing to the well classified characteristic in high-dimensional space, a kernel PCA (KPCA)-based method is proposed to calculate the confidence limit of monitoring indices, the method monitors the mapped values of indices in high-dimensional space based on PCA, which indirectly achieves the calculation of confidence limit and need not more calculations.3) Extend the methods of data reconstruction. An improved SPE-based method is presented to evaluate missing data and improves reconstruction performance. In order to realize reconstruction of nonlinear data, a novel neural network named partly input-training neural network is proposed, of which the missing variables to reconstruct are selected as the inputs. Different from the conventional network, the weights and biases of the novel network have already been obtained by the other networks. By back-propagation algorithm, the reconstruction is achieved just through adjusting the network inputs. Otherwise, the FA-based method is discussed for data estimation and applied into"soft sensor".4) Overcome the problems on non-Gaussian process monitoring. Mixture PPCA (MPPCA) is improved by building models in two steps: the first step is to set up mixture Gaussian models and the following is to develop principal component (PC) models using PPCA, which considers the difference of PCs'explanation to process variables. Monitoring based on PPCA is introduced into local models to assure the consistency of monitoring indices and lessen the load of monitoring. Further, all monitoring charts in MPPCA models are integrated into only one chart via probability and process monitoring can be achieved just by the chart. To monitor the processes with both nonlinear and non-Gaussian feature, a kernel ICA (KICA)-based method is brought forward and analyzed.5) On the monitoring of nonlinear process. The dissertation proposes a hierarchical inputs-training neural network and further proposes a nonlinear PCA based on the network, which can orderly find nonlinear PCs and quantitatively determine the number of PCs according to the predicting error. In order to overcome the shortcoming of KPCA, two feasible methods are presented, one is using neural network to build nonlinear PC model and the other is reducing the number of model data by sparse KPCA. Kernel PPCA is introduced into industrial process to build probability model and monitor the mapped value based on PPCA.Finally, some significative considerations or some problems waiting for answers are given.