Aplicação do teste sequencial de razão de verossimilhança para identificação de pontos instáveis em uma rede de trilateração

Abstract

Structure monitoring consists of determining, at a certain level of probability, whether points strategically located on the monitored structure moved or keeped stable, between two epochs. This issue is a pressing concern in engineering works, given that unexpected movements of a magnitude above normal can lead to major disasters. Given the importance of the topic, a class of researchers has dedicated themselves to developing and improving monitoring strategies. Typically, variations in the coordinates of points are considered, which are the unknown parameters in most mathematical problems analyzing geodetic deformations. However, this approach requires the linearization of the model, which leads to a reduction in the capacity of statistical tests. Therefore, researchers have been working on solutions that present an essentially linear mathematical model, based on the differences between observations (and no longer on the differences between parameters). In many cases, however, statistical tests confront the null hypothesis – that there were no displacements – to a single alternative hypothesis – that, possibly, points moved. As a result, control of the occurrence of false detections (Type I Error) is not adequately carried out. Considering the limitations of approaches previously presented in the literature, this research presents the application of a new methodology, based on sequential likelihood ratio tests to identify unstable points, which compares the null hypothesis to multiple alternative hypotheses, adequately controlling the Type I Error Furthermore, the methodology, applied in this work on real data from a trilateration network with 6 points located on the Monte Carmelo campus of the Federal University of Uberlândia, is rigorous, in the sense that it allows the correct identification of displaced points regardless of injunctions of control points. The results obtained point to a correct identification rate of around 74% in the case of the absence of control point injunction, with 100% correct detection in the identified cases, at a significance level of α = 0.1. When considering the setting of 3 control points, the correct identification rate rises to around 96%. The results obtained show the potential of the developed technique, bringing the possibility of new validations in future scenarios, using new networks, new geometries and case studies, for example.