A Geodetic Network is a network of point interconnected by direction and/or distance measurements or by using Global Navigation Satellite System receivers. Such networks are essential for the most geodetic engineering projects, such as monitoring the position and deformation of man-made structures (bridges, dams, power plants, tunnels, ports, etc.), to monitor the crustal deformation of the Earth, to implement an urban and rural cadastre, and others. One of the most important criteria that a geodetic network must meet is reliability. In this context, the reliability concerns the network's ability to detect and identify outliers. Here, we apply the Monte Carlo Method (MMC) to investigate the reliability of a geodetic network. The key of the MMC is the random number generator. Results for simulated closed levelling network reveal that identifying an outlier is more difficult than detecting it. In general, considering the simulated network, the relationship between the outlier detection and identification depends on the level of significance of the outlier statistical test.
In the development of neural networks, many realizations are performed to decide which solution provides the smallest prediction error. Due to the inevitable random errors associated with the data and the randomness related to the network (e.g., initialization of the weight and initial conditions linked to the learning procedure), there is usually not an optimal solution. However, we can advantage of the idea of making several realizations based on resampling methods. Resampling methods are often used to replace theoretical assumptions by repeatedly resampling the original data and making inferences from the resampling. Resampling methods provide us the opportunity to do the interval prediction instead of only one point prediction. Following this idea, we introduce three resampling methods in neural networks, namely Delete-d Jackknife Trials, Delete-1 Jackknife Trials, and Hold-Out Trials. They are discussed and applied to a real coordinate transformation problem. Although the Delete-1 Jackknife Trials offer better results, the choice of resampling method will depend on the dimension of the problem at hand.
A mais recente versão da teoria da confiabilidade tem sido utilizada para descrever a capacidade de um sistema de medição em detectar, identificar e remover outliers a um certo nível de probabilidade. Entretanto, as aplicações desta teoria têm sido direcionadas para redes simuladas de nivelamento. Aqui, por outro lado, aplicamos a teoria no contexto de redes baseadas nos sistemas de posicionamento por satélites GNSS (Global Navigation Satellite System), a partir de dados reais coletados em campo. Testamos se as covariâncias entre as componentes da linha base têm efeito sobre a confiabilidade. Verificamos que as covariâncias entre as componentes da linha base aumentam a taxa de sucesso na identificação de outlier e, portanto, aumentam a confiabilidade da rede. O menor outlier identificável – ao nível de 80% de correta identificação – teve uma redução média de ~30% para as componentes ΔX e ΔY, e ~14% para ΔZ em comparação ao cenário com covariâncias nulas. O aumento do nível de significância melhora a confiabilidade em ambos os cenários (covariâncias nulas e não-nulas) na mesma proporção. Porém, para altos níveis de significância (α > 0,1) e sistemas com boa redundância (ri > 0,5), a confiabilidade para um modelo estocástico com covariâncias nulas se aproxima do caso em que as covariâncias não são nulas. Na ausência de um modelo estocástico mais realista (covariâncias não-nulas) e para sistemas com boa redundância local (ri > 0,5), deve-optar por regiões críticas maiores ( k < 2,8).
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