Principal Component Analysis And Its Application To Process Monitoring With Multi-rate Sampled Data

With the rapid development of modern industry and science and technology, modern process industry has higher requirement for production safety and product quality; a monitoring system is needed to be built to timely detect the change and fault and to prevent catastrophic accidents. Just for that purpose, the fault detection and diagnosis (FDD) is developed.Statistical monitoring method based on principal component analysis (PCA) is an important branch of fault diagnosis, which does not need complex mechanism model and through extracting important information from raw data using statistical method and then transforming them into several significant indices. As a result, the method has been widely used in industrial processes in industry and academia. When PCA is used, an assumption is often made that process variables are matched in time series, that is to say every variable has a sampling value at the same time. However, due to the consideration of economy, performance and other factors, multi-rate sampling is always applied. Therefore, certain variables may have no sampling values at some time, which limits the use of PCA.This thesis is based on the theory of PCA and multi-rate sampling system and systematically and deep studies PCA and its application to process monitoring with multi-rate sampled data.Through consulting references, provide complete summary on the development and current situation of PCA and its application to process monitoring with multi-rate sampled data. Based on this, a multi-variable sampling rate conversion algorithm (MRC) is proposed on the application of multi-sampling rate conversion technology. The algorithm achieves multi-variable sampling rate conversion by interpolation-filter-decimation, so that variables have the same sampling period. Then apply PCA to the data. The simulation results show that there is deviation between the data processed by MRC and the raw data, but the monitoring performance is good. Then, an improved nonlinear partial least squares algorithm (NIPALS) is proposed, which learns the method used by Salvador Garcia-Munoz etc., dividing the observation to two parts:the observable part and non-observable part. Firstly, use the observable part to impute the non-observable in certain form, the imputation is not accurate at first. Secondly, revise the imputation during the iteration until the imputation converges to a certain value. When the score matrix and loading matrix are calculated, impute the un-sampled data again. Finally, apply PCA modeling and monitoring, the un-sampled data during monitoring is imputed by the same method above. In order to test its effectiveness, the proposed method is compared with case deletion, mean imputation and EM(PCA) in the aspects of residual sum of squares, the number of principal components, the similarity degree of loading matrix and monitoring performance. The simulation results show that the proposed method effectively fills in missing data, maintains the structure of original data, and has a good monitoring performance.Finally, conclude with a summary and some further research areas in this thesis.