Publications

Interferometric Synthetic Aperture Radar (InSAR) has proved its efficiency for displacementmonitoring in urban areas. However, the large volume of data generated by this technology turnsthe retrieval of information useful for structure monitoring into a big data problem. In this study, anew tool (SARClust) to analyze InSAR displacement time series is proposed. The tool performs theclustering of persistent scatterers (PSs) based on dissimilarities between their displacement time seriesevaluated through dynamic time warping. This strategy leads to the formation of clusters containingPSs with similar displacements, which can be analyzed together, reducing data dimensionality, andfacilitating the identification of displacement patterns potentially related to structural damage. Aproof of concept was performed for downtown Lisbon, Portugal, where ten distinct displacementpatterns were identified. A relationship between clusters presenting centimeter-level displacementsand buildings located on steep slopes was observed. The results were validated through visualinspections and comparison with another tool for time series analysis. Agreement was found inboth cases. The innovation in this study is the attention brought to SARClust

The hydrostatic-season-time (HST) model is a widely used method in the safety assessment of dams and for the estimation of reversible and irreversible deformations due to different load scenarios. After implementing an optimal HST-model to observational data, the residual time series can still expose some underlying periodicities. In our contribution, the underlying periodicities and their contribution to residual minimisation are further analysed by the Lomb–Scargle normalised periodogram frequency method. The extended HST-model, obtained by adding additional sinusoidal terms for the statistically most significant frequencies, presents a slight statistical improvement on the optimal HST-model. Statistically significant frequencies may not be justified or correlated to some physical process of the dam, but they make it possible to identify a pattern in the analysed period. The analyses are performed for the radial direction of long-term displacement time series measured at the topmost reading station of an inverted pendulum system in the central cantilever of the Alqueva concrete arch dam

The three authors of this paper work at the Applied Geodetic Division of the National Laboratory for Civil Engineering (LNEC), in Lisbon, Portugal. LNEC is a state owned research and development institution founded in 1946. It works in the various domains of civil engineering (structures, hydraulic, geotechnics, environment, materials, among others), giving it a unique multidisciplinary perspective in this field. The main goals of the LNEC are to carry out innovative research and development and to contribute to the best practices in civil engineering. The Applied Geodetic Division nowadays develops works in two domains: the geodetic surveying of large dams and other engineering structures for monitoring purposes, and the processing of digital images with applications in several domains, which includes the study of the evolution of pathologies in engineering works. Originally the processing of digital images made use mostly of the chromatic information included in the images (from satellite images to close range photographs). But recently it has evolved to extract information of the geometry of the objects by the generation of point clouds. This use of close range photographs (from distances of decimetres to a few meters), which started in the summer of 2014, looks very promising and we, the authors, are identifying possible areas where the use of point clouds and orthomosaics that can be of interest to our colleagues of LNEC, civil engineers mostly. This paper presents the first examples where point clouds and orthomosaics, generated from close range photographs, can help civil engineers on their studies. The photogrammetic products were all generated using the free open-source software Micmac (Multi-Image Correspondances, Méthodes Automatiques de Corrélation) from IGN (Institut National de l’Information Géographique et Forestière, France).

Les ports et autres infrastructures construits sur des côtes exposées à de fortes houles ont besoin d’être protégés. Une telle protection peut être obtenue par des digues ou brise-lames. Les digues à talus ont en général une meilleure résilience pendant les événements les plus agressifs. Un endommagement des digues affaiblit la structure et peut entraîner la perte de la capacité de protection, ce qui peut avoir des conséquences environnementales et économiques très graves. Pour cette raison, les brise-lames doivent être soumis à une surveillance régulière pour la détection des anomalies. Cet article présente quelques exemples de l'utilisation de drones dans la surveillance de la sécurité de ces structures, et décrit en particulier deux vols menés avec des drones et quelques possibilités d'extraction de données pour obtenir des informations d'intérêt pour les responsables de la sécurité.

This work presents several approaches in the validation of the hydrodynamic model Tuflow on the simulation of flood extents and water levels, based on satellite SAR imagery. A methodology that uses a simplified bathymetry in the river main course is employed, which proves to be reliable and accurate for high-flow events. This was made possible as the digital terrain model was acquired in a dry period, accounting for large dry areas in the river bed, avoiding in this way the need of expensive river bathymetry surveys. Also, two methods are applied to the SAR imagery to extract the flood boundaries: visual interpretation followed by manual delimitation and an object-based algorithm approach. The hydraulic model is tested on a reach of the Tagus River, Portugal, where the largest flood inundation areas occur, using a historical flood event to verify its robustness and reliability. The accuracy of model prediction is done through comparisons of water levels at a hydrometric station and the determination of commission and omission errors of flood extent, between the reference SAR image and the predicted inundation. It was concluded that the methodology followed in this work is well suited for the hydraulic model validation.

This article describes the implementation of a monitoring system on the breakwater at the Funchal Port (Madeira Island, Portugal) for the purpose of understanding its dynamic behavior and the temporal evolution of structural health. The monitoring system focuses on the breakwater superstructure and aims to identify the evolution of damage on the breakwater and analyze the impact of cruise ships docking and undocking. The system includes the measurement of displacements through geodetic techniques using global navigation satellite systems and the measurement of vibrations using accelerometers. Ten observation campaigns were performed over almost 3 years. As the measured displacements during this period were less than 7.5 mm it can be concluded that, despite some visible cracks, the breakwater superstructure did not suffer significant structural changes. It was shown from the measured acceleration records that some of the main modal parameters could be identified, namely the main natural frequencies of the superstructure. Through an analysis of the natural frequencies progression over time, it will be possible to identify deterioration effects on the foundation and/or the superstructure. The comparison of natural frequencies identified could be useful to evaluate the impact of these events on structural health.

A fusão de dados provenientes de diferentes tipos de instrumentos pode dar uma informação mais completa para a monitorização do comportamento de estruturas de engenharia civil, em particular nas pontes de grande vão. O objectivo da fusão de deslocamentos medidos com o GNSS e de acelerações, é tirar partido da precisão conseguida com o GNSS, em baixas frequências, e da grande sensibilidade dos acelerómetros, em altas frequências, e obter uma única série temporal de deslocamentos, longa e de grande resolução. Através dum filtro de Kalman será possível integrar deslocamentos medidos, com uma frequência de amostragem de, por exemplo, 1 Hz, e acelerações medidas, com uma frequência de amostragem de, por exemplo, 100 Hz, de modo a obter uma série temporal de deslocamentos de longa duração e com uma resolução de 100 Hz. Nesta comunicação apresentam-se os resultados preliminares dum ensaio realizado num modelo estrutural simples correspondente a um edifício de três pisos, instrumentado com antenas GNSS da Topcon e acelerómetros da Kinemetrics, modelo Episensor ES-U2, e da Nanometrics, modelo Titan SMA, tendo em vista a futura aplicação desta metodologia em pontes de grande vão.

There is an increasing trend to apply GNSS continuous observation of short baselines to the monitoring of engineering works, such as bridges and dams, for their structural analysis and safety control. In the case of large dams, one important application of the GNSS continuous observation is the establishment of early warning systems that demand accurate, frequently updated information and where the analysis of the baseline time series, in order to separate signal from noise is mandatory. The paper presents a study on the performance of linear filters of the asymmetric moving average (AMA) type to smooth baseline time series. The transfer function of the AMA is adopted as a smoothing criterion to define an adequate order for the AMA, in face of the spectral density function of the baseline time series. One series of measurements of a short test baseline (325 m), materialized in the campus of the National Laboratory for Civil Engineering, is used as an example of the proposed strategy.

Summary: A Bayesian estimator with informative prior distributions (a multi-normal and an inverted gamma distribution), adequate to displacement estimation at dam monitoring net-works, is presented. The hyper-parameters of the prior distributions are obtained by Bayesian empirical methods with non-informative priors. The performances of the Bayes estimator and the classical generalized lest squares estimator are compared using two measurements of the horizontal monitoring network of a concrete gravity dam: the Penha Garcia dam (Portugal). In order to test the robustness of the two estimators, gross errors are added to one of the measured horizontal directions: the Bayes estimator proves to be significantly more robust than the generalized least squares estimator.

Results from the application of Persistent Scatterers Interferometry in Lisbon Metropolitan Area revealed two previously unknown subsiding urban areas: one (Laranjeiras) is located in the center of Lisbon; another (Vialonga) is to be found toward the North, in an industrial region crossed by Lisbon's main highway and railway lines. The two subsiding sectors are bordered by sharp velocity gradients, and the subsidence pattern appears partially delimited by mapped geologic faults. Surface geology and urbanization alone are unable to explain the phenomena. In the Vialonga area, the historical record of water pore pressure shows a clear decline of the levels (up to 65 m in 27 years), providing evidence of over-exploitation of groundwater resources. Limited information from wells drilled inside and outside the subsidence area points to a spatial correlation between the subsidence and the water pressure levels, and suggests that faults could be acting as hydraulic barriers in the aquifer system. The surface subsidence detected is probably caused by compaction of a clay-rich Oligocene-aged aquitard, led by over-exploitation of adjacent aquifers. The same Oligocene aquitard layer is present in the Laranjeiras area, immediately bellow a multi-layered sand–clay–limestone Miocene aquifer, but further work is needed to diagnose the possibility of over-exploitation of groundwater here. In this work we were able to independently confirm the PSI results, by comparing autonomous PSI results processed for the same geographical areas, and by comparing PSI with leveling and continuous GPS derived subsidence velocities, whose close match provided further ground validation of the space-borne PSI technique.

Like in other surveying works, UAV flights require prior work that involves flight planning and equipment preparation and, often, many complementary tasks. These may involve bringing together technicians from different domains, booking a car and possibly accommodation, and some time-consuming complementary bureaucratic work. Teams operating UAVs know how much the flights are affected by weather conditions. The wind is the weather variable that, in proportion (number of occurrences per year), causes the major number of changes to a scheduled work. Obtaining reliable information about the intensity of the wind, a few days in advance, is an asset for those who have to carry out the various tasks mentioned previously. There are several websites from which one can access weather forecasts. Is any website better because it presents more reliable data? The data and the analysis presented in the paper will give some clues. The data includes wind speed, registered daily, at 12:00 (pm) for a year, by a meteorological station with online data, which belongs to a meteorological institute. Also on a daily basis, several websites with meteorological data were consulted, and wind speed forecasts for the same hour for up to four days in advance were collected. An analysis of the data can provide information about whether there is a website that stands out for the quality of the forecasts, and if there is a need to consult several websites to have better information.

A measurement system based on GNSS (Global Navigation Satellite System) was installed at Cabril dam in order to monitor displacements at the top of the central section. The GNSS system consists of two receivers (stations), one located on the crest of the dam, in central section, and the second located on the left bank, on the top of a medium voltage pole of a line deactivated and cut to be about 6 m high, to work as reference station. Unfortunately, this GNSS monument is exposed to solar radiation and wind effects. Consequently, it is expected that these environmental factors could cause sub-daily noise in the estimation of the dam displacements due to the thermal tilts of the monument. This paper is concerned with the assessment of the impact of this GNSS monument on the noise in the continuous GNSS time series. In GNSS time series analysis, frequency-domain signature is obtained by converting time-domain data into its unique frequency components using a Fast Fourier Transform (FFT). Through the analysis of frequency-domain signal signatures, the dam displacement seasonal can be detected and isolated from the noise eventually caused by the GNSS monument instability.

Geometria das formas de fundo (altura e comprimento) com recurso a levantamento aéreo utilizando um UAV na lagoa de Albufeira

OSOM - SYSTEMATIC MONITORING OF MARITIME WORKS - is a monitoring programme developed by the Portuguese National Laboratory for Civil Engineering (LNEC) to support the decision-making process relative to the maintenance schedule, or even repairing time, of maritime works. The main goal of this programme is the monitoring of the structure’s behaviour, through the analysis of the data collected during monitoring campaigns performed by LNEC. In recent years, the programme has been enhanced with new functionalities, being one of the most important contributions the integration of photogrammetric surveys, with drones, to improve visual inspections. The stage of testing this new source of information has already been completed and, for this reason, drones and photogrammetric methods are fully incorporated in the now-called OSOM+ programme. Nevertheless, there is still place for new studies that will help, in the near future, to make the drone surveys more efficient. This paper presents an ongoing study and some conclusions that are emerging

An infrastructure of three corner reflectors for Sentinel-1 was deployed at the National Laboratory for Civil Engineering campus, in Lisbon, Portugal, with the collaboration of the IDL, FCUL. The infrastructure is formed by two triangular trihedral reflectors (1 x 1 m) and by a third one following a model proposed by the team. The third reflector is formed by two rectangular trihedrals with the vertical axis in common, each of the individual reflectors is oriented towards the ascending and the descending passes of Sentinel-1. Additionally, a Global Navigation Satellite System (GNSS) antenna is permanently installed on the reflector’s axis. This study presents the first precision assessment for displacements measured at the infrastructure using Persistent Scatterer Interferometry (PSI). The PSI processing was performed with SARPROZ software using 19 Sentinel-1A images acquired between October 2017 and May 2018. The reflectors’ displacements are being monitored through levelling and GNSS. Levelling is performed for all reflectors every two weeks. Nearby persistent scatterers are included in the levelling line. A second permanent GNSS antenna is installed on a building roof in the campus to be used as a reference. PSI double-differences were compared to levelling and GNSS ones, projected onto the sensor line-of-sight. Precisions of 1.1 mm and 1.6 mm were achieved for the triangular trihedral reflectors, while 1.2 mm and 1.5 mm were obtained for the rectangular trihedral ones. However, during March 2018, strong winds have damaged the structure on which the rectangular trihedral reflectors are installed. If the evaluation is performed considering only the dates before the failure or only the dates after the damage was fixed, precisions of 0.7 mm and 0.8 mm are obtained. These results suggest submillimetre precision might be possible to achieve. Processing a larger time series of images acquired after the damage fix will be needed to confirm.

The “Project ELEVAR– Study of Vertical Structures with Robotized Aircrafts”, has as its main objective the development of an aircraft for the autonomous photogrammetric surveys of vertical surfaces, namely of dam walls, bridge, pillars, and facades of buildings and monuments. The photographs obtained will support the visual inspections carried out in the scope of monitoring and safety control of civil engineering works. The aircraft will navigate through stereoscopic cameras, sensors and dedicated algorithms that allow the autonomous positioning and three-dimensional reconstruction of the structures without the aid of GNSS systems in areas of poor signal coverage or where high precision is required. The photographic surveys will be carried out with a distinct, high-definition camera, aided by a system that allows to acquire images at the desired moment. The system is being developed by a consortium of three entities the company TEKEVER ASDS (leader), integrating the Institute of Systems and Robotics of Instituto Superior Técnico and the National Laboratory for Civil Engineering. This paper presents the project and the results achieved.

O projeto "ELEVAR – Estudo Localizado de Estruturas Verticais com Aeronaves Robotizadas", financiado pelo programa COMPETE, tem como objetivo principal o desenvolvimento de uma aeronave destinada à realização autónoma de levantamentos fotográficos de superfícies verticais, nomeadamente paramentos de barragens, pilares de pontes e fachadas de edifícios e de monumentos. As fotografias obtidas servirão de apoio às inspeções visuais realizadas no âmbito do acompanhamento e controlo de segurança das obras de engenharia civil. A navegação da aeronave será realizada através de câmaras estereoscópicas, sensores e algoritmos dedicados que permitem o posicionamento autónomo e reconstrução tridimensional das estruturas sem o auxílio de sistemas GNSS em zonas de fraca cobertura de sinal ou em que é necessária alta precisão. Os levantamentos fotográficos serão realizados com uma câmara distinta, de alta definição, auxiliada por um sistema que permite adquirir imagens no instante pretendido. O sistema está a ser desenvolvido por um consórcio liderado pela empresa TEKEVER ASDS, integrando o Instituto de Sistemas e Robótica do Instituto Superior Técnico e o Laboratório Nacional de Engenharia Civil. A presente comunicação destina-se a apresentar o projeto e os resultados alcançados nos primeiros 18 meses de atividade.

The team developed a bidirectional corner reflector (CR) with the goal of achieving displacements from Sentinel-1 ascending and descending passes for the same point. From those observations, vertical and horizontal displacements are being determined and their uncertainty is being assessed through comparison to levelling and GNSS measurements. The bidirectional CR is composed by two rectangular trihedrals with the vertical axis in common. A GNSS antenna is permanently installed on that axis and the base where the reflector is installed enables it to move along pre-defined directions. The reflector vertical displacements are also being monitored through levelling every two weeks. This CR is part of an infrastructure installed in LNEC, which also includes two individual triangular trihedral CRs. One of those is also installed on a movable base, in order to allow the comparison between CRs of different shapes. Two evaluations of the measurements’ uncertainty will be presented: one with all the CRs being static and another one with the CRs moving along the line-of-sight of the descending pass. Uncertainty assessment for displacements along other directions will be performed in the future.

During the design process of rubble mound breakwaters scale model, tests are required to study the hydraulic and structural behaviour of the proposed structure under predefined sea wave conditions. The main goal of such tests is to study the structure overtopping and infer on damage progression by quantifying displacements of the armour layer units. To detect and measure these displacements different methodologies were tested: photogrammetry and 3D scan. All the methods were used to produce point clouds. Some points on the model of the breakwater and its surroundings were coordinated by surveying methods and used to access the accuracy. This paper describes the methodologies used and the results achieved.

Odelouca is the second largest earth dam in Portugal and holds an important water reservoir. A displacement map for the slopes around the reservoir during the initial phase of the first filling was built using a multitemporal interferometric synthetic aperture radar (MTI) technique. A method based on cluster and time series analysis is proposed in order to find patterns on the obtained scatterers. The points are aggregated through a measure of the similarity between their displacement time series and form clusters, whose properties can then be evaluated. The analysis can be complemented by additional information for a better understanding of the influence on the ground of the storage of such a large amount of water. Three different patterns were identified on the data: stable scatterers, scatterers moving away from the sensor and scatterers moving towards it. A set of outliers was also detected. One of the clusters may contain points susceptible to landslide occurrence.

O calendário Gregoriano não é mais do que uma reforma do calendário Juliano, devido a Júlio César, que adaptou os formalismos romanos a uma antiga estrutura solar de origem egípcia. Este ensaio descreve a história do calendário Gregoriano e dos calendários da bacia do Mediterrâneo e do Oriente Próximo, com ele mais ou menos aparentados.

Interferometric synthetic aperture RADAR is an applied geodesy technique, which enables displacement measurement through satellite images. A literature review of the technique principles and of previous studies regarding its application to structural health monitoring allowed the identification of a few bottlenecks to the operational usage of this cost-effective technology for monitoring purposes.Three research lines were defined. First, a data mining strategy was developed to extract structural behaviour information from displacement time series from thousands of points on the region of interest, with tens of observation epochs each. Second, displacements from this technique were integrated into a previously existing monitoring system and were used to expand it to a larger number of points on the structure and to its surroundings. Third, an experimental infrastructure was deployed in order to perform several tests for displacement validation and uncertainty assessment. The infrastructure included a new model of artificial reflector to the satellite signals, purposefully developed in the scope of this study.The developed methods enabled the successful monitoring of different types of civil and geotechnical structures. Slope behaviour around water reservoirs was assessed during both the reservoir first impoundment and regular operation. Differential displacements were detected on building-blocks at a cultural heritage urban area and concrete arch dam responses to temperature loads were identified. The experimental work showed the achieved displacements agreed with those of other geodetic techniques and uncertainties around 2 mm were obtained for the measurements.In conclusion, interferometric synthetic aperture RADAR is a promising technique, able to provide useful information for structure monitoring, such as aiding in the planning of in situ monitoring activities and in identifying space-time patterns in structural behaviour. Thanks to its spatial coverage, observation period of a few days and achieved displacement uncertainty, it is advantageous to complement existing monitoring systems with data from this technique.

O Simulador de Cenários Sísmicos, LNECloss, é uma ferramenta computacional que permite avaliar perdas em consequência de um cenário sísmico especificado [LESSLOSS, 2007]. Esta ferramenta automática compreende vários módulos, como sejam, a modelação da acção sísmica no substrato rochoso e à superfície, a avaliação dos danos no edificado e a avaliação das perdas económicas e humanas. O Simulador foi integrado como aplicação externa num Sistema de Informação Geográfica (SIG) [Sousa, 2006]. Foram identificadas algumas necessidades de desenvolvimento no Simulador, que compreendem, por um lado, o alargamento do seu domínio geográfico para além do território de Portugal Continental, nomeadamente para o Arquipélago dos Açores, que possui uma taxa de ocorrência de sismos muito elevada e, por outro, a sua disponibilização através da Web, com um carácter autónomo, ou seja, que não necessite de alguma plataforma de informação geográfica tendo no entanto as suas capacidades no que respeita ao mapeamento e à síntese gráfica e tabular dos efeitos de um cenário sísmico. De entre as características deste simulador WebSIG, saliente-se uma interface gráfica de fácil operação, permitindo a sua utilização por agentes da protecção civil, no que respeita ao planeamento e à gestão da emergência na eventualidade de ocorrência de um sismo.

Neste relatório apresenta-se, de forma sucinta, a atividade de investigação realizada no âmbito do projeto ImEngine no período 2014-2023. Os resultados da atividade são analisados e avaliados, em face dos objetivos inicialmente previstos.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto INFRASAR no período 2014-2023. Os resultados da atividade são analisados e avaliados, em face dos objetivos inicialmente previstos.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto MEGA no período 2015-2023. Os resultados da atividade são analisados e avaliados, em face dos objetivos inicialmente previstos.

Este relatório apresenta os procedimentos do levantamento fotogramétrico, realizado com um drone, assim como as ações complementares, destinados a obter informação de carácter geométrico da praia da Cova Gala em 2020. Este documento inclui ainda uma análise da qualidade dos produtos gerados e uma comparação com o levantamento realizado em 2019, cerca de um ano antes.

Este relatório apresenta os resultados da campanha de nivelamento geométrico das bocas de furos de captação de água na proximidade da Base das Lajes, realizada pelo Núcleo de Geodesia Aplicada do Departamento de Barragens de Betão do LNEC, em outubro de 2020. Os resultados são as cotas, num referencial local, das bocas dos furos de captação de água.

Este relatório apresenta os procedimentos dos levantamentos fotogramétricos, realizados com um drone, assim como as ações complementares, efetuadas em 2019, destinados a obter informação de carácter geométrico das praias de Cova - Gala, Vieira e São Pedro de Moel.

Neste relatório apresenta-se, de forma sucinta, a atividade de investigação realizada no âmbito do projeto ImEngine no período 2014-2017. Os resultados da atividade são analisados e avaliados, em face dos objetivos inicialmente previstos, sendo proposta uma extensão do projeto, e respetiva revisão do plano de atividades, para os próximos dois anos.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto INFRASAR no período 2014-2017. Os resultados da atividade são analisados e avaliados, em face dos objetivos inicialmente previstos, sendo proposta uma extensão do projeto e revisão do plano de atividades para os próximos dois anos.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto MEGA no triénio 2015-2017. Os resultados da atividade são analisados e avaliados, em face dos objetivos inicialmente previstos, sendo proposta uma revisão do plano de atividades para os próximos dois anos.

O relatório apresenta uma proposta de plano de estudos para a tese de doutoramento da bolseira Dora Roque, a realizar no Núcleo de Geodesia Aplicada do Departamento de Barragens de Betão do Laboratório Nacional de Engenharia Civil. O objetivo principal do estudo é contribuir para a operacionalização da geodesia InSAR na determinação de deslocamentos para o controlo de segurança de estruturas.

O trabalho aborda simultaneamente a distribuição do desvio padrão da amostra aleatória normal e a distribuição do desvio padrão do modelo de Gauss-Markov, designados genericamente por desvio padrão empírico. Após mostrar que o desvio padrão empírico é um estimador excêntrico que subestima o desvio padrão da amostra ou do modelo, conforme o caso, são apresentadas correções de excentricidade. É também tratada a estimação do desvio padrão da amostra e do modelo em cenário Bayesiano, com diferentes distribuições anteriores. O trabalho é rematado por casos de estudo baseados na simulação de amostras normais e por um exemplo concreto relacionado com o controlo da precisão de um distanciómetro eletromagnético.

O presente trabalho apresenta uma metodologia genérica para a regularização de problemas inversos lineares mal colocados e a sua aplicação às redes altimétricas e planimétricas usadas na monitorização de deslocamentos de pontos notáveis de grandes barragens por métodos da Geodesia Aplicada. A metodologia é ilustrada por intermédio de três casos de estudo.

This paper deals with the beta-binomial model, which is an important stochastic model within the scope of the Bayesian statistical inference. After a short review of the binomial and beta distributions, the paper presents the closed formulae for the posterior probability density function of the binomial trial parameter and for the prior predictive and for the posterior predictive probabilities of the successes in binomial experiments. A description of the Bayesian methodology to test different hyper-parameters for the conjugate prior probability density functions of the beta family is also presented. Finally, the beta-binomial model is illustrated with a study case related to the quality control of the geodetic observation of large dams.

O presente trabalho, além de uma revisão sintética da abordagem frequencista, trata da abordagem Bayesiana da análise de regressão linear multivariada. É apresentada uma compilação de procedimentos e fórmulas para a estimação dos coeficientes da regressão, sob três cenários de informação anterior. Finalmente, o trabalho ocupa-se dos problemas da predição de respostas e da comparação de modelos de regressão.

The work presents the theoretical definitions of the gamma, multi-gamma, digamma and trigamma functions as well as operational approximations to compute their values. A more precise alternative, due to Robert Windschitl, to the traditional approximation of the gamma function by the Stirling’s series, is reported. The work is completed with a study case, related to the geodetic monitoring of large dams, that illustrates the previous concepts and definitions.

O trabalho descreve os princípios da análise Bayesiana, usando como caso de estudo a amostra aleatória normal identicamente distribuída. Após um curto preâmbulo histórico, são resumidos, na Secção 2, os conceitos mais importantes da análise frequencista. Nas secções seguintes, são abordados os temas Bayesianos mais importantes, tais como a estimação, pontual e regional (Secção 5), e o teste de hipóteses sobre os parâmetros da distribuição da amostra (Secção 6). As distribuições anteriores de Laplace, Jeffreys e conjugada normal-gama invertida são apresentadas na Secção 4. O problema da eliciação paramétrica das distribuições anteriores conjugadas é tratado na Secção 7. Palavras Chave: distribuições anteriores e posteriores, divergência de Kullback-Leibler, eliciação paramétrica, factor de Bayes, fórmula de Bayes, verosimilhança.

Este trabalho define uma estratégia, apoiada o mais possível nas disponibilidades do LNEC, para a calibragem dos distanciómetros electromagnéticos (DEM) usados pelo Núcleo de Geodesia Aplicada na observação geodésica de barragens.

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