Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

The Performance and Service Life Prediction of High Performance Concrete in Sulfate and Acidic Environments

Concrete substructures are often subjected to environmental deterioration, such as sulfate and acid attack, which leads to severe damage and causes structure degradation or even failure. In order to improve the durability of concrete, the High Performance Concrete (HPC) has become widely used by partially replacing cement with pozzolanic materials. However, HPC degradation mechanisms in sulfate and acidic environments are not completely understood. It is therefore important to evaluate the performance of the HPC in such conditions and predict concrete service life by establishing degradation models. This study began with a review of available environmental data in the State of Florida. A total of seven bridges have been inspected. Concrete cores were taken from these bridge piles and were subjected for microstructural analysis using Scanning Electron Microscope (SEM). Ettringite is found to be the products of sulfate attack in sulfate and acidic condition. In order to quantitatively analyze concrete deterioration level, an image processing program is designed using Matlab to obtain quantitative data. Crack percentage (Acrack/Asurface) is used to evaluate concrete deterioration. Thereafter, correlation analysis was performed to find the correlation between five related variables and concrete deterioration. Environmental sulfate concentration and bridge age were found to be positively correlated, while environmental pH level was found to be negatively correlated. Besides environmental conditions, concrete property factor was also included in the equation. It was derived from laboratory testing data. Experimental tests were carried out implementing accelerated expansion test under controlled environment. Specimens of eight different mix designs were prepared. The effect of pozzolanic replacement rate was taken into consideration in the empirical equation. And the empirical equation was validated with existing bridges. Results show that the proposed equations compared well with field test results with a maximum deviation of ± 20%. Two examples showing how to use the proposed equations are provided to guide the practical implementation. In conclusion, the proposed approach of relating microcracks to deterioration is a better method than existing diffusion and sorption models since sulfate attack cause cracking in concrete. Imaging technique provided in this study can also be used to quantitatively analyze concrete samples.