On Optimisation and Design of Geodetic Networks
Abstract: Optimisation of a geodetic network is performed to provide its pre-set quality requirements. Today, this procedure is almost run with the aid of developed analytical approaches, where the human intervention in the process cycle is limited to defining the criteria. The existing complication of optimisation problem was terminated by classifying it into several stages. By performing these steps, we aim to design a network with the best datum, configuration and the observation weights, which meets the precision, reliability and cost criteria.In this thesis, which is a compilation of four papers in scientific journals, we investigate the optimisation problem by developing some new methods in simulated and real applications.On the first attempt, the impact of different constraints in using a bi-objective optimisation model is investigated in a simulated network. It is particularly prevalent among surveyors to encounter inconsistencies between the controlling constraints, such as precision, reliability and cost. To overcome this issue in optimisation, one can develop bi-objective or multi-objective models, where more criteria are considered in the object function. We found out that despite restricting the bi-objective model with precision and reliability constraints in this study, there is no significant difference in results compared to the unconstrained model. Nevertheless, the constrained models have strict controls on the precision of net points and observation reliabilities.The importance of optimisation techniques in optimal design of displacement monitoring networks leads to the development of a new idea, where all the observations of two epochs are considered in the optimisation procedure. Traditionally, an observation plan is designed for a displacement network and repeated for the second epoch. In the alternative method, by using the Gauss-Helmert method, the variances of all observations are estimated instead of their weights to perform the optimisation. This method delivers two observation plans for the two epochs and provides the same displacement precision as the former approach, while it totally removes more observations from the plan.To optimise a displacement monitoring network by considering a sensitivity criterion as a main factor in defining the capacity of a network in detecting displacements, a real case study is chosen. A GPS displacement monitoring network is established in the Lilla Edet municipality in the southwest of Sweden to investigate possible landslides. We optimised the existing monitoring network by considering all quality criteria, i.e. precision, reliability and cost to enable the network for detecting 5 mm displacement at the net points. The different optimisation models are performed on the network by assuming single baseline observations in each measurement session. A decrease of 17% in the number of observed baselines is yielded by the multi-objective model. The observation plan with fewer baselines saves cost, time and effort on the project, while it provides the demanded quality requirements.The Lilla Edet monitoring network is also used to investigate the idea, where we assume more precise instruments in the second of two sequential epochs. In this study, we use a single-objective model of precision, and constrained it to reliability. The precision criterion is defined such that it provides the sensitivity of the network in detecting displacements and has a better variance-covariance matrix than at the first epoch. As the observations are GPS baselines, we assumed longer observation time in the second epoch to obtain higher precision. The results show that improving the observation precision in the second epoch yields an observation plan with less number of baselines in that epoch. In other words, separate observation plans with different configurations are designed for the monitoring network, considering better observation precision for the latter epoch.
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