Research On The Extraction Of Deformation Information With Principal Component Analysis

There might be some systematic drift and random fluctuation in the results of hydrostatic levelling instruments applied to high-speed railway’s real-time subsidence monitoring due to mechanical vibration, current train vibration, temperature and air pressure changes.Therefore, there is some difference between the results of hydrostatic levelling instruments and the results of precise leveling. Based on the PCA’s theory and mathematical model, the the grey system theory has been introduced to improve PCA to form the GPCA(Grey Principle Component Analysis), when the basis feature vectors has been improved in order to get a good effect on sequential deformation information extraction.This thesis is divided into five chapters:1. The first chapter mainly introduces the historical process and the domestic and foreign present research situation of the PCA method and deformation information extraction methods. Based on the above, the main line of this thesis is proposed: taking the PCA method as the theoretical foundation and the comprehensive analysis as the main line, focusing to make real and reasonable comprehensive evaluation of deformation monitoring objects.2. In the second chapter, by systematically studying the theoretical foundation and mathematical model of the PCA, the PCA’s congenital deficiencies were analyzed and summarized. Besides, by importing the grey system theory to improve the basic feature vectors we have gained the GPCA model for sequential deformation information extraction.3. The third chapter has studied in detail the theoretical basis of GPCA and deduced the mathematical model step by step, indicating that by intergrating the advantages of PCA and the grey system theory, the GPCA method is committed to research real law and and could compensate for the application of PCA on time series deformation information extraction.problems4. In fourth chapter, based on the sample data, we have developed the PCA/GPCA program using Microsoft VS2008 C# programming language which has been successfully applied to the experimental data processing. The results showed that: by introducing the grey theory, the calculation results of GPCA are more realistic, more accord with the objective regularity of time series data.5. The fifth chapter is the summary and prospect of this thesis, theoretical research and experimental results show that by introducing the grey system theory into the PCA to preprocess the raw time series data, the variation of the processed data with the dynamic characteristics is more close to the reality. Then, the comprehensive information extraction was been carried on with PCA method. In summary, the GPCA, as a comprehensive method, takes the advantages of PCA and the grey system, could make up for the lack of PCA on time series data processings.