Research Of Multiscale PCA With Application To Multivariate Statistical Processs Monitoring

Development of Wavelet technique has brought ever-growing Progress of the research and application of Multivariate Statistical Process Monitoring. Based on the theory of Wavelet Analysis and Principal Component Analysis , Multiscale PCA is introduced which combines the ability of PCA to decorrelate the variables by extracting a linear relationship, with that of wavelet analysis to extract deterministic features and approximately decorrelate autocorrelated measurements. The superior performance of MSPCA for process monitoring is illustrated by several examples. Main research work and contributions of this dissertation are as following:Pre-processing (Filtering)the measurements from industryWith basic theory about Wavelet Analysis, the primary algorithm was completed including Wavelet Transform and Inverse Wavelet Transform using Matlab. After a brief description of the fundamental theory of wavelet analysis from the view of multiresolution estimating, A method of de-noising via wavelet thresholding was introduced including the selection of wavelet functions and the calculation of threshold. Then an improved method, namely translation invariant de-noising was proposed. Experiment shows the result is practicable. Online multiscale filtering was introduced and applied to the emulationalsignal from Matlab and process measurements form industry. Multiscale PCA with Application to Multivariate Statistical Process MonitoringFirstly, the principle of PCA for Multivariate Statistical Process Monitoring is mastered and the NIPALS algorithm is completed , then principal component modeling, (Squared Prediction Error) statistics and statistics are calculated. Secondly, for improving the performance of PCA that modeling by it is done at a single scale, wavelet analysis and PCA are combined for a new kind of Multivariate Statistical Process Monitoring tools: Multiscale PCA. The basic algorithm of MSPCA are completed in Matlab. Finally, MSPCA is applied to three different kind of measurements or process: uncorrelated Gaussian measurements, process of the No.1 lines of the atmospheric and vacuum towers and reversed-flow catalytic combustion process in which temperature measurements change periodically. Compared with PCA, the performance of MSPCA for Process Monitoring is superior.Recursive PCA for statistical process monitoring For resolving the problem that fixed-model of PCA is hard to adapt the slow and normal process changing, we studied the basic Principle and algorithm and derived the formulas of Recursive covariance matrix, Recursive Scores and loadings, Recursive determination of the number of Principal Components and alarm thresholds. The result shows that MSPCA is more effective than PCA for uncorrelated Gaussian measurements .