Data Reconstruction And Application Based On Independent Component Analysis

There are many reasons why measurements may be missing from a data set. Missing measurements occur periodically when sensors fail or are taken off-line for routine maintenance. In other situations, measurements are removed from a data set because gross measurement errors occur or samples are simply not collected at the required time. In these cases, the measurements are missed at random times. In other situations, missing measurements occur on a very regular basis. A common example occurs when sensors have different sampling periods.But the traditional method of dealing missing data does not apply to the industrial system of many variables now. Therefore, this article uses independent component analysis as the main mathematical tools. The basic principles of independent component analysis is through the multi-dimensional analysis of data related to the high-end statistics, independent of each other to find hidden information elements, between the high-end components to complete the removal of redundant and independent source of the signal extraction. The main content of this dissertation is as follows:1. Introduced basic concepts of the missing data and data reconstruction of, and a brief introduction to multiple statistical methods in the application of data reconstruction.Gave a briefing on the main element analysis methods of basic concepts, and their statistics SPE method of calculation. At the same time, the success of the PCA method of data was lost Reconstruction and TEP process to achieve the simulation test.2. Based on the principal component of the lack of leads based on the statistical properties of high-end independent element analysis methods and data in the reconstruction of the method in addition to process data must be subordinate to the Gaussian distribution or independent distribution of restraint, and to extract the process As far as possible independent of each other signal source, significantly decreased the reconstruction of the original data and data errors. This paper has tried to introduce the ICA two different ways: FastICA and the ICA based on Parzen nuclear estimates, and are using statistics SPE and successful completion of the reconstruction of the data and use simulation examples prove the superiority.3. In some real industrial processes, the relations of variables are supposed linear. Sometimes the assumption can lead to some incorrect results. Therefore, a process monitoring method based on nonlinear ICA is applied in the Data reconstruction. Some positive results are also given.4. Finally, some beneficial explorations in the field of process monitoring are made, and some future research areas are highlighted.