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Öğe Importance of probability levels for robustness analysis of geodetic networks(TAYLOR & FRANCIS LTD, 2014) Yetkin, M.; Berber, M.; Inal, C.Robustness Analysis is a natural merger of reliability and strain and defined as the ability to resist deformations caused by the maximum undetectable errors. Internal reliability criterion describes maximum undetectable errors in observations, which would not be detected by Baarda's statistical testing method (data snooping) based on the chosen Type I and II error probabilities. The non-centrality parameter is a function of probability levels and it plays an important role in Robustness Analysis. In this paper, it is aimed to show the impact of non-centrality parameter on the displacements and the relationship between the selected confidence level for confidence regions and threshold values in a geodetic network. For a geodetic network example, a GPS network is chosen and computations of displacements and threshold values (derived from confidence regions) have been carried out for both in-context and out-of context approaches. According to our results, the non-centrality parameter controls the magnitudes of displacements without affecting their relative behaviours. Statistically, lower probability levels are desired. However, if error probabilities are decreased, the non-centrality parameter increases. Since, the non-centrality parameter scales the displacements, a balance between both types of decision error is needed to obtain displacement values that are smaller than threshold values in order to reach a totally robust network at the required level of probability.Öğe L-1 NORM MINIMIZATION IN GPS NETWORKS(MANEY PUBLISHING, 2011) Yetkin, M.; Inal, C.The least squares method is a statistical tool for the estimation of unknown parameters. All the results which are derived from the method of least squares are deteriorated when outliers are present in the observation data. Therefore, outliers have to be detected and eliminated by using statistical tests or robust methods. For this purpose, L-1 norm minimization, which is a robust method, can be used in geodetic networks. In this paper, the formulation of L-1 norm minimization for correlated observations is presented. The method is applied to a simulated GPS network. The performances of the least squares method and L-1 norm minimization are compared in the cases of observations with or without outliers. Our example shows that L-1 norm minimization is a more successful method than the least squares method for outlier detection and the obtained coordinates are more reasonable and reliable than those from the least squares when some observations are burdened with blunders.Öğe Metaheuristic optimisation approach for designing reliable and robust geodetic networks(MANEY PUBLISHING, 2013) Yetkin, M.Robustness analysis is a combination of reliability and geometrical strength analysis using a strain technique. It refers to the ability of a network to resist deformations caused by the largest undetectable blunders. The displacement of each point in the network is computed in order to measure the robustness of the network. This paper tries to optimally design a geodetic network in the sense of high reliability and geometrical strength. For this purpose, a metaheuristic method called the shuffled frog leaping algorithm (SFLA) is used to solve the first order design problem in which the geometric configuration of the network is optimised. Such algorithms have been developed to determine high quality solutions to complex optimisation problems. The efficiency of the method is demonstrated using a synthetic network example. The results show that the displacements can be decreased by maximising the minimum redundancy number in the network. This procedure can yield both reliable and robust networks.Öğe THE OPTIMAL DESIGN OF BASELINE CONFIGURATION IN GPS NETWORKS BY USING THE PARTICLE SWARM OPTIMISATION ALGORITHM(TAYLOR & FRANCIS LTD, 2011) Yetkin, M.; Inal, C.; Yigit, C. O.The selection of the optimal GPS baselines can be performed by solving the geodetic second-order design (SOD) problem. In this paper, the particle swarm optimisation (PSO) algorithm, a stochastic global optimisation method, has been employed for the selection of the optimal GPS baselines to be measured in the field that will meet the postulated criterion matrix at a reasonable cost. PSO, which is an iterative-heuristic search algorithm in swarm intelligence, emulates collective behavior of bird flocking, fish schooling or bee swarming, to converge to the global optimum. The fundamentals of the algorithm are given. Then, the efficiency and the applicability of the algorithm are demonstrated with an example of GPS network. Our example shows that the PSO is practical because it does not produce negative or greater than maximum achievable weights of available instruments; it is effective because it yields networks that meet the optimisation criteria; and it is reliable because it converges to the global optimum of an objective function. It is also suitable for non-linear matrix functions that very often encountered in geodetic network optimisation.Öğe Optimal Design of Deformation Monitoring Networks Using the Global Optimization Methods(SPRINGER, 2015) Yetkin, M.; Inal, C.Geodetic networks are very important tools that can be used to monitor crustal movements or the deformation of structures. However, a geodetic network must be designed to sufficiently meet some network quality requirements such as accuracy, reliability, sensitivity and economy. This is the subject of geodetic network optimization. Traditional methods have been used for solving geodetic optimization problems. On the other hand, some evolutionary algorithms such as the particle swarm optimization algorithm have been started to be recently used. These methods are inspired by optimization and adaptation processes that are encountered in the nature. They are iterative procedures for quickly and efficiently solving complex optimization problems. They may provide global optimum solution or at least near-optimum solutions to problems. In this paper, the use of the shuffled frog-leaping algorithm for the optimal design of a deformation monitoring network is studied. The aim is to design and optimize a geodetic network in terms of high reliability.Öğe Robustness analysis using the measure of external reliability for multiple outliers(TAYLOR & FRANCIS LTD, 2013) Yetkin, M.; Berber, M.Robustness analysis is a natural merger of reliability and strain and defined as the ability to resist deformations induced by the maximum undetectable errors as determined from internal reliability analysis. Thus far, robustness analysis has been carried out using reliability theory based on the assumption of a single outlier. However, in practice, there might be multiple outliers in a data set. Therefore, measures of reliability for multiple outliers ought to be used. This paper extends robustness analysis so that it can determine the deformation induced by multiple undetected errors through the evaluation of a strain matrix using the proper external reliability measure. In this study, the question of whether a network is robust against deformations induced by two or more undetected outliers is investigated. The results indicate that in the case of multiple outliers, robustness of geodetic networks decreases.
