The Method of Simulated Annealing for the Optimal Adjustment of the Nigerian Horizontal Geodetic Network
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Date
2010-10
Authors
Omogunloye, O.G.
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Abstract
The Horizontal Geodetic Network of Nigeria is made up of terrestrially arranged chains of triangles augmented by precise traverses. The work on the network began early 19th century but by 1930 the work was discarded and a re-observation of the network was carried out to the highest possible accuracy then, enhanced with high order geodimeter traverses which linked to other neighboring African networks.
The full network consists of 515 stations, with 2411 observations which comprise 2197 angular observations, 40 Laplace azimuths and 174 measured distances, part of which substituted for the sparse triangulation observations especially in the southern part of the country. The added observations contributed to strengthening of the network in the 1977 adjustment which however was not a holistic optimized adjustment, but rather, a phase adjustment. Based on the 1977 state of adjustment of the network, no meaningful distortion monitoring exercise can take place until the network is adjusted by an optimized simultaneous technique in order to ascertain the state and consistency of the network.
The use of the simulated annealing method, which has been successfully applied in other fields, is presented for the classical geodetic problem of simultaneous adjustment of the entire triangulation net using the least squares observation equation method. This method is an iterative heuristic technique (a method of solving problems by learning from past experience and investigating practical ways of finding a solution) in operations research. It uses a thermo dynamic analogy (Cooling theory) to adjust a network of unstable stations (changes to gaseous state) through fairly stable station coordinates (liquid state) to a stable station coordinates (solid state) so as to offer a solution that converges in a probabilistic sense (statistically based) to the global optimum. The simulated annealing method of optimization serves to help determine the position of all triangulation stations by means of minimizing the volume of the error hyper ellipsoid inherent in the solution to give an optimal configuration of the geodetic network. Computer programs were developed using Matlab Software and run on an adequately configured Pentium IV computer. Creation of an intelligent database was achieved through the interactive network of the data storage, processing, manipulation, analysis and retrieval of results of the adjustment.
The result of the new adjustment produced a generally consistent trend of changes in the distances and azimuths compared to the previous adjustments. Error analysis of all lines were carried out and the respective standard errors in distances and azimuths were determined. Relative and absolute error ellipses of all stations were determined and plotted. Statistical plots and analysis of the error ellipses of the network stations were also determined. The absolute and relative weakness/strength of the network stations coordinates after adjustment were shown and confirmed by the error plots to have the following geometry error distributions. That is, 90.5% of the 515 Network Stations fell within Network Standard deviation of 1- Sigma, 94.2% within 2-Sigma, while 98.3% fell within 3- Sigma
The distributions confirmed the high reliability of the Nigerian Horizontal Geodetic Network and its data quality. Re-strengthening exercise would be necessary using either the 1-Sigma or 2-Sigma region of network standard deviation
A data structure for the entire network was developed and necessary conclusions and recommendations are made for further action to update/upgrade the precision of the Nigerian horizontal geodetic network for future study.
Description
A Thesis Submitted to the School of Postgraduate Studies, University of Lagos
Keywords
Geodetic network , Optimum adjustment , Simulated annealing technique , Least squares technique , Research Subject Categories::TECHNOLOGY::Engineering mechanics
Citation
Omogunloye, O.G (2010). The Method of Simulated Annealing for the Optimal Adjustment of the Nigerian Horizontal Geodetic Network. A Thesis Submitted to University of Lagos School of Postgraduate Studies Phd Thesis and Dissertation, 143pp.