Deformation Analysis

Abstract

More than one century has elapsed since Gauss and Legendre developed the least squares method. Since that time many improvements have been introduced to the original work of these two great scientists. The method rapidly proves to be a very powerful tool in many fields of science and technology. For surveying engineering, the method is still used for adjustment of geodetic networks, photogrametry and other survey branches.

One of the most important applications is the deformation analysis. Although this branch is partially similar to other adjustment problems, it takes the method to its extreme ends. This is because deformation depends entirely in the optimality of the mathematical model of the network considered. Therefore topics like outlier detection, variance components estimation and reliability are applied extensively in deformation analysis studies.

In the last decade Sudan has witnessed a revolutionary development in its infrastructure. This can be realized in the huge dams, oil exploitation and mining projects. This high cost projects requires a very careful design to protect people's lives and properties from hazards. Deformation analysis can play a very important role in monitoring the behavior of these huge structures, the development of new design techniques and in protecting people from the hazards caused by the damage of such big structures.

Traditionally, deformations are usually detected by the well known global congruency test. However, this method gives an idea of the overall deformation in specific areas. Moreover, complicated mathematical methods for the decomposition of the quadratic form, gives rise to the location of deformations at specific points. In this research a simple new statistical technique is developed to detect deformations at specific points directly. The test statistic of this method is based on the ratio of the height displacement to its standard deviation. This Baarda like test statistic is assumed to have standard normal distribution. Test results show that this test is very effective since it can locate a deformation of 0.05cm at the very high confidence level 99%. Further studies are required to test the new strategy performance in other reference frames.