Constructing Bayesian networks (BN) for practical applications presents significant challenges, especially in domains with limited empirical data available. In such situations, field experts are often consulted to estimate the model’s parameters, for instance, rank correlations in Gaussian copula-based Bayesian networks (GCBN). Because there is no consensus on a ‘best’ approach for eliciting these correlations, this paper proposes a framework that uses probabilities of concordance for assessing dependence, and the dependence calibration score to aggregate experts’ judgments. To demonstrate the relevance of our approach, the latter is implemented to populate a GCBN intended to estimate the condition of air handling units’ components—a key challenge in building asset management. While the elicitation of concordance probabilities was well received by the questionnaire respondents, the analysis of the results reveals notable disparities in the experts’ ability to quantify uncertainty. Moreover, the application of the dependence calibration aggregation method was hindered by the absence of relevant seed variables, thus failing to evaluate the participants’ field expertise. All in all, while the authors do not recommend to use the current model in practice, this study suggests that concordance probabilities should be further explored as an alternative approach for the elicitation of dependence.@en

Immersed tunnels are positive buoyant structures during installation and negative buoyant after installation. A tunnel is composed of sequential immersed elements that are coupled to each other in joints. Tunnel elements consist of segments which are compressed to each other by longitudinal post-tensioning. After immersion the tunnel is supported by the seabed and the longitudinal post-tension is cut at the joints between segments. Therefore, the structure is a segmented lining which is sensitive for settlements due to non uniform circumstances over the length of the tunnel. An uneven response of the bedding underneath the tunnel introduce shear forces in joints of an immersed tunnel. Because immersed tunnels need to be buoyant during installation, they have limitations on weight and geometry, the size and therefore the capacity of these shear keys is limited because the height of the tunnel, as shear keys are applied in the walls of the tunnel. The foundation response is influenced by many factors related to subsoil but also to construction and dredging tolerances. The shear forces were derived as a function of different covariance lengths for subsoil stiffness and dredging tolerances for different tunnel layouts. In reliability analyses, using two different probabilistic methods, exceedance probabilities of maximum shear forces are derived for one lay out using Non Parametric Bayesian Networks and Vine Copulas. The analyses give more insight in to the magnitude of the shear forces in joints both in conditioned and unconditioned situations and this can be used for the design of immersed tunnels.

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The Netherlands has traditionally focused on managing flood risk. However, the frequent occurrence of droughts in recent years has brought attention to managing both extremes. Transitions between these opposite extremes pose additional challenges to water management, requiring a trade-off between water storage during dry periods and flood control during wet periods. In this study, we develop a framework to define wet and dry meteorological events and study their transitions using timeseries of meteorological data namely, precipitation, temperature and potential evapotranspiration. The magnitudes of event characteristics are retained, which presents a different approach to the normalized climate indices (like the Standardized Precipitation Index) commonly used in literature. We apply this framework to the Dutch part of the Meuse River basin in northwestern Europe using climate observations between 1951 and 2022. Our analysis shows a statistically significant increase in the amount of water lost from potential evapotranspiration compared to water gained from precipitation between April and September of the water year and an increase in the length of this drying period over the past decades. Such trends in the drying period are related to variability in potential evapotranspiration caused by rising temperatures in the region, indicating the potential for increased water shortage in Spring and Summer due to future temperature increases. We also identify abrupt transitions between opposite extreme events where there is a lack of water at the end of the second event as meteorological situations that challenge water management due to overlapping impacts like flash flooding, less time for water storage, and reduced water availability. We see such conditions occur in 6% of the wet-dry transitions and 20% of the dry-wet transitions, highlighting meteorological scenarios to which the hydrological response of the catchment can be simulated to increase our understanding of the combined risk of floods and droughts.@en

Accurate estimation of extreme discharges in rivers, such as the Meuse, is crucial for effective flood risk assessment. However, hydrological models that estimate such discharges often lack transparency regarding the uncertainty in their predictions. This was evidenced by the devastating flood that occurred in July 2021, which was not captured by the existing model for estimating design discharges. This article proposes an approach to obtain uncertainty estimates for extremes with structured expert judgment using the classical model (CM). A simple statistical model was developed for the river basin, consisting of correlated generalized extreme value (GEV) distributions for discharges from upstream tributaries. The model was fitted to seven experts' estimates and historical measurements using Bayesian inference. Results were fitted only to the measurements were solely informative for more frequent events, while fitting only to the expert estimates reduced uncertainty solely for extremes. Combining both historical observations and estimates of extremes provided the most plausible results. The classical model reduced the uncertainty by appointing the most weight to the two most accurate experts, based on their estimates of less extreme discharges. The study demonstrates that with the presented Bayesian approach that combines historical data and expert-informed priors, a group of hydrological experts can provide plausible estimates for discharges and potentially also other (hydrological) extremes with relatively manageable effort.@en

The authors regret the acknowledgments in the published article are incomplete. The complete acknowledgments are as follows: “This research was supported by the Mexican National Council for Science and Technology (CONACYT) under project number 2019-000021-01EXTF-00564 CVU 784544. The authors would like to thank Dr. Andrés Antonio Torres Acosta, Research Professor at the Department of Sustainable and Civil Technologies, School of Engineering and Sciences, Tecnológico de Monterrey for his contributions to this research.” The authors would like to apologise for any inconvenience caused. ____________________________.

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Around the world, an increasing amount of bridge infrastructure is ageing. The resources involved in the reassessment of existing assets often exceed available resources and many bridges lack a minimum structural assessment. Therefore, there is a need for comprehensive and quantitative approaches to assess all the assets in the bridge network to reduce the risk of collapsing, damage to infrastructure, and economic losses. This paper proposes a methodology to quantify the structural criticality of bridges at a network level. To accomplish this, long-run site-specific simulations are conducted using Bayesian Networks and bivariate copulas, utilizing recorded traffic data obtained from permanent counting stations. To enhance the dataset, information from Weigh-in-Motion systems from different regions was integrated through a matching process. Subsequently, the structural response resulting from the simulated traffic is assessed, and the extreme values of the traffic load effects are obtained for selected return periods. Site-specific bridge criticality as a performance indicator for traffic load effects is derived by comparing the extreme load effects with the design load effects. The outcomes are mapped to facilitate visualization employing an open-source geographic information system application. To illustrate the application of the methodology, a total of 576 bridges within a national highway network are investigated, and a comparison with a popular simplified method is shown. The methodology herein presented can be used to assist in assessing the condition of a bridge network and prioritizing maintenance and repair activities by identifying potential bridges subjected to major load stress.@en

Healthcare decision making, including regulatory and reimbursement decisions, is based on uncertain assessments of clinical and economic value. This arises from the evidence supporting those assessments being uncertain, incomplete, or even absent. Qualitative, structured expert elicitation (SEE) is a valuable tool for extracting expert knowledge about an uncertain quantity and formulating that knowledge as a probability distribution. This creates a useful input to decision modeling and support, particularly in areas with limited evidence, such as advanced therapy products, precision medicine, rare diagnoses, and other areas with high uncertainty.

Structured SEE protocols are used to improve the transparency, accuracy, and consistency of quantitative judgments from experts, limiting the effect of heuristics and biases. This task force report introduces 5 commonly used protocols for SEE (Sheffield elicitation framework; modified Delphi method; Cooke’s classical method; investigate, discuss, estimate, aggregate protocol; and the Medical Research Council reference protocol). It describes the common elements of SEE, discusses how these protocols differ in their implementation of those elements and illustrates the use of the protocols.

The report then reviews the relevant constraints on implementing SEE within the context of healthcare decision making and considers the strengths and weaknesses of these protocols in light of those considerations. Because this is an introductory report on an emerging topic, specific recommendations on practice are not made. However, there are broad recommendations based on the suitability of the different protocols in various decision contexts. The report concludes with recommendations for further research to better guide future practice.@en

Aquaculture at sea is gaining increasing importance, not only as a (local) food source but also due to its potential of being combined with other offshore activities such as wind parks. Nevertheless, experience of offshore aquaculture is limited. This study aims to provide a framework to evaluate offshore aquaculture suitability accounting for the probabilistic dependence between relevant variables. This framework is applied to obtain suitability maps of aquaculture for the North Sea for the blue mussel Mytilus edulis and the sugar kelp Saccharina latissima. For each of these species, three ecological variables are selected and the optimal growth and critical survival limits are defined. Here, suitability is defined as the probability of meeting these conditions. Data on the selected variables is extracted from a large-scale 3D hydrodynamic and ecological model of the northwest European Shelf, of which daily extremes are sampled. The probabilistic model is developed using bivariate copula models, which are fitted to each variable pair to describe their joint distribution function at each studied location. Empirical distribution functions are used to describe the univariate distribution function of each variable and location. Using Monte-Carlo simulations, the probability of meeting the optimal and critical limits is estimated and suitability maps accounting for the probabilistic dependence between the variables are generated. In addition, suitability maps disregarding the dependence are generated and compared to those accounting for the probabilistic dependence. It was found that considering the dependence between variables significantly improves the accuracy of the results for optimal and critical growth conditions for both species. The presented method allows to identify potential areas where blue mussel and sugar kelp cultivation is the most suitable. For instance, in this study, a north-south elongated area west of the German and Danish coast appears to be most suitable for blue mussels, while estuaries and rivers are found the most suitable for the sugar kelp.

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In this paper we discuss PyBanshee, which is a Python-based open-source implementation of the MATLAB toolbox BANSHEE. PyBanshee constitutes the first fully open-source package to quantify, visualize and validate Non-Parametric Bayesian Networks (NPBNs). The architecture of PyBanshee is heavily based on its MATLAB predecessor. It presents the full implementation of existing tools and introduces new modules. Specifically, PyBanshee allows for: (i) choosing fully parametric one-dimensional margins, (ii) choosing different sample sizes for the model-validation tests based on the Hellinger distance, (iii) drawing user-defined sample sizes of the NPBN, (iv) sample-based conditioning sampling (similarly to the closed-source proprietary package UNINET by LightTwist Software) and (v) visualizing the comparison between the histograms of the unconditional and conditional marginal distributions. New detailed examples demonstrating new features are provided.@en

This contribution presents an assessment at a regional (island) scale of the beach erosion due to storm events under Climate Change. The approach adopted to assess beach erosion at the island scale consisted of three modules. First, the location, dimensions and other attributes of the Cypriot beaches were recorded on the basis of widely-available satellite imagery. Secondly, sea levels and waves were modeled along the coast under different climatic scenarios and dates in the 21st century. Finally, using these projections beach retreat due to the relative mean sea level rise (RSLR) and extreme sea levels (ESLs) was estimated using ensembles of analytical and numerical cross-shore morphodynamic models, respectively. Extreme sea levels (ESLs) were projected to (a) increase by up to 60% in 2100 from their baseline (2000) levels, and (b) vary along the coast, with the highest ESLs (and corresponding waves) projected for the southern and western coasts. The mostly narrow Cypriot beaches (91% recorded maximum widths of < 50 m) showed increased exposure to erosion. In 2100, about 47% and 72% (based on the median model estimates) of the 241 unprotected Cypriot beaches will be permanently eroded, due to mean sea level rise (SLR), to 50% of their present maximum width, depending on the scenario. In addition to the long-term erosion due to SLR, severe storm erosion is projected by 2050 even under the RCP4.5 scenario; the 100-year extreme sea level event (ESL100) may overwhelm (at least temporarily) 49% of the currently unprotected Cypriot beaches without effective adaptation responses, with the most exposed beaches located along the northern coast. As the beach carrying capacity and hedonic value will be severely compromised, effective adaptation policies and technical measures will be urgently required.

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Aquaculture is gaining importance in the current context of continuous growth population as a source of (local) food resources and its potential of being combined with other uses at sea (e.g.: offshore energy production or tourism). Consequently, within the European Horizon 2020 project UNITED, the combination of mussel and seaweed cultivation together with wind energy production in the German North Sea is investigated. Here, the feasibility of the mussel Mytilus edulis and seaweed Saccharina latissima based on their ecological needs is analysed. Ecological data from a three-dimensional hydrodynamic and ecological model covering the northwest European continental shelf is used. For each of the two species, three variables are selected as relevant, including in both of them the water temperature. In addition, chlorophyll-a and dissolved oxygen are considered for mussels, and dissolved inorganic nitrogen and phosphorus are selected for seaweed. Temperature is selected as dominant variable so its daily maxima for the growing months are selected together with the concomitants of the other variables. Gaussian Mixture distributions (see McLachlan and Peel (2000)) and truncated Gaussian kernel distributions (see Bowman and Azzalini (1997)) are used to model the marginal distributions of the random variables. Bivariate copulas are fitted for each pair of variables to describe their dependence structure. Finally, probabilities of being within the optimal ranges of the relevant variables are calculated. Chlorophyll-a concentration and temperature are the most limiting variables for mussels and seaweed, respectively. Relatively low probabilities are obtained, since ranges for optimal growth are considered. Generally, it is feasible to cultivate mussels and seaweed at this location based on the selected ecological variables, as the probability of variables reaching values outside growth limits for the species is low. @en

Finite Element (FE) modeling often requires unavoidable simplifications or assumptions due to a lack of experimental data, modeling complexity, or non-affordable computational cost. One such simplification is modeling corrosion phenomena or material properties, which are usually assumed to be uniform throughout the structure. However, e.g., corrosion has a local nature and severe consequences on the behavior of steel structures that should not be overlooked. To improve the current numerical modeling techniques in aging steel bridges, this paper proposes a Gaussian Copula-based Bayesian Network (GCBN) approach to model the spatial variability of structural element properties. Accordingly, a study of the automatic Bayesian network generation process is first conducted. Subsequently, the methodology is applied to a severely damaged riveted steel bridge built in 1897. The results show that the methodology has excellent flexibility for generating properties variability in FE models at a low computational cost, thus ensuring its practical feasibility and robustness for accurate numerical modeling.

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An accurate estimation of wind and wave variables is key for coastal and offshore applications. Recently, copulas have gained popularity for modelling wind and waves multivariate dependence, since accounting for the hydrodynamic relationships between them is needed to ensure reliable estimations of the required design values. In this study, copula-based Bayesian networks (BNs) are explored as a tool to model extreme values of significant wave height (Hs), wave period, wave direction, wind speed and wind direction. The model is applied to a case study located in the Alboran sea, close to the Spanish coast, using ERA5 database. Extreme values of Hs are sampled using Yearly Maxima and concomitant values of the missing variables are used. K-means clustering algorithm is applied to separate the different wave components and a BN is built for each of them. The assumption of modelling the dependence between the variables using Gaussian copulas and the structure of BNs are supported with the d-calibratioson score. Fitted marginal distributions are introduced in the nodes of the BNs and their performance is assessed using in-sample data and the coefficient of determination. The BN models proposed present high performance with a low computational cost proving to be powerful tools for modelling the variables under investigation. Future research will include different locations and databases. @en

Vine copulas have become the standard tool for modelling complex probabilistic dependence. It has been shown that the number of regular vines grows extremely quickly with the number of nodes. Chimera is the first attempt to map the vast space of regular vines. Software for operating with regular vines is available for R, matlab and Python. However, no dataset containing all regular vines is available. Our atlas of regular vines, Chimera, comprises all 24 4 × 4 matrices representing regular vines on 4 nodes, 480 5 × 5 matrices representing regular vines on 5 nodes, 23,040 6 × 6 matrices representing regular vines on 6 nodes, 2,580,480 7 × 7 matrices representing regular vines on 7 nodes and 660,602,880 8 × 8 matrices representing regular vines on 8 nodes. Regular vines in Chimera are classified according to their tree-equivalence class. We fit all regular vines to synthetic data to demonstrate the potential of Chimera. Chimera provides thus a tool for researchers to navigate this vast space in an orderly fashion.

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Investigating the reliability of ancient hydraulic structures constructed without modern probabilistic criteria allows an understanding of why and how the structure fails. In this paper, we present an extended method, firstly introduced by Torres-Alves and Morales-Nápoles (2020), to perform the reliability analysis of the Nezahualcoyotl's dike that was designed (most likely) without probabilistic criteria. The dike was built around 1450 by the Aztec empire dividing Lake Texcoco from north to south (present-day Mexico City). We estimate the probability of failure due to overflow. By using a discrete time-state Markov chain and bi-variate copulas to generate large synthetic observations of the environmental variables precipitation and evaporation. In addition to the previous methodology, two sources of uncertainty were taken into account (i) the characterization of the environmental conditions during the dry season to estimate initial water levels on the lake and (ii) the influence of surface runoff and subsurface seepage losses on the water levels. The extended method allows for better characterization of the lacustrine system. Therefore an improved extent of the hydrology of the system and a more reliable estimation of the probability of failure of Nezahualcoyotl's dike are presented. @en

Investigating the reliability of ancient hydraulic structures constructed without modern probabilistic criteria allows an understanding of why and how the structure fails. In this paper, we present an extended method, firstly introduced by Torres-Alves and Morales-N´apoles (2020), to perform the reliability analysis of the Nezahualcoyotl’s dike that was designed (most likely) without probabilistic criteria. The dike was built around 1450 by the Aztec empire dividing Lake Texcoco from north to south (present-day Mexico City). We estimate the probability of failure due to overflow. By using a discrete time-state Markov chain and bi-variate copulas to generate large synthetic observations of the environmental variables precipitation and evaporation. In addition to the previous methodology, two sources of uncertainty were taken into account (i) the characterization of the environmental conditions during the dry season to estimate initial water levels on the lake and (ii) the influence of surface runoff and subsurface seepage losses on the water levels. The extended method allows for better characterization of the lacustrine system. Therefore an improved extent of the hydrology of the system and a more reliable estimation of the probability of failure of Nezahualcoyotl’s dike are presented. @en

Before the year 1519, the Valley of Mexico was a closed basin and at the bottom of the valley, an extensive system of shallow lakes was formed. Within this lacustrine system, the capital of the Aztec empire, Tenochtitlan, was built. The Aztecs were known for their impressive constructions and complex hydraulic structures, of which the most impressive structure was the Nezahualcoyotl dike. This structure was constructed across Lake Texcoco. Its principal function was to protect the city of Tenochtitlan from high water levels at the lake. However, there is not enough information about the reliability of this dike. Mainly due to two reasons, today there are no remains left of the dike and most of the lacustrine system is drained. In this paper, we present a method to study the reliability of the Nezahualcoyotl dike under two failure modes, overturning and sliding. This is done by following up on the work presented by Torres-Alves & Morales-Nápoles (2020) where they developed a hydrological characterization of the lacustrine system and studied the dike under one failure mode, overflow. The proposed analysis aims to provide a more realistic assessment of the reliability of the dike as a flood defense mechanism. @en

The Wettelijk Beoordelingsinstrumentarium (WBI) is the legal set of instruments for flood risk analysis in the Netherlands. Often, engineers have the impression that some failure probabilities of flood defenses resulting from these instruments are overestimated. In an effort to better estimate the failure probabilities of dikes along the Dutch river Rhine, this study sets out to assess them with experts and compare them to model results. We used Cooke's method for combining experts’ estimates in a structured way and follow two approaches to estimate a system failure probability. In the first approach, experts estimate discharges that lead to at least one dike failure. This gives plausible results; failure probabilities between 1/30 and 1/17.000 in a year. The second approach is based on adjusting existing model-based assessment results, by estimating the model-bias and incorporating additional dependencies. This mostly leads to large, implausible, failure probabilities: Experts tend to give more conservative answers as they are asked for detailed estimates without clear reference values. This results in large uncertainty and consequently (too) high failure probabilities. Our research shows that when applied in a clear frame of reference, structured expert judgments can be successfully used for estimating the reliability of Dutch flood defenses.

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Weigh-in-motion (WIM) systems help to collect data such as vehicular loads, individual axle loads, vehicle type, and number of axles. This is relevant in engineering because traffic load performs an essential function in the design of new bridges and in the reliability assessment of existing ones, in traffic analysis and other areas of engineering. Therefore, when WIM data is not available, computing synthetic WIM observations that adequately approximate the statistical dependence between variables is important. In this paper, WIM measurements from the Netherlands and Brazil were analysed, and a set of non-parametric Bayesian Networks (NPBNs) is presented. This paper significantly improves on previous results by allowing observations of inter-axial distance to be generated, by allowing several sources of data to be used in the modelling and by making software available to researchers and practitioners interested for generating synthetic observations based on the distribution of vehicle type. In particular, statistical models to describe the weight and length of different vehicle types are derived. Three NPBNs were quantified using data from: (i) six WIM locations of the motorway network of the Netherlands, (ii) one WIM location in one city route of Rotterdam, The Netherlands, and (iii) one WIM location of one highway in Araranguá city located in the south of Brazil. Additionally, a Graphical User Interface (GUI) for the six Dutch WIM motorways locations was developed. To illustrate a possible use of the model when WIM data is not available. The GUI was used to compute synthetic WIM observations using data collected through traffic counters gathered in Toluca city in central Mexico, as input. This paper shows that the methodology here presented is widely applicable and depends only on the assessment of vehicle type configuration.

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Non-parametric Bayesian networks (NPBNs) are graphical tools for statistical inference widely used for reliability analysis and risk assessment and present several advantages, such as the embedded uncertainty quantification and limited computational time for the inference process. However, their implementation in hydrological studies is still scarce. Hence, to increase our understanding of their applicability and extend their use in hydrology, we explore the potential of NPBNs to reproduce catchment-scale hydrological dynamics. Long-term data from 240 river catchments with contrasting climates across the United States from the Catchment Attributes and Meteorology for Large-sample Studies (CAMELS) data set will be used as actual means to test the utility of NPBNs as descriptive models and to evaluate them as predictive models for maximum daily river discharge in any given month. We analyse the performance of three networks, one unsaturated (hereafter UN-1), one saturated (hereafter SN-1), both defined only by hydro-meteorological variables and their bivariate correlations, and one saturated network (hereafter SN-C), consisting of the SN-1 network and including physical catchments' attributes. The results indicate that the UN-1 network is suitable for catchments with a positive dependence between precipitation and discharge, while the SN-1 network can also reproduce discharge in catchments with negative dependence. The latter can reproduce statistical characteristics of discharge (tested via the Kolmogorov–Smirnov statistic) and have a Nash–Sutcliffe efficiency (NSE) ≥0.5 in ∼40 % of the catchments analysed, receiving precipitation mainly in winter and located in energy-limited regions at low to moderate elevation. Further, the SN-C network, based on similarity of the catchments, can reproduce discharge statistics in ∼10 % of the catchments analysed. We show that once a NPBN is defined, it is straightforward to infer discharge and to extend the network itself with additional variables, i.e. going from the SN-1 network to the SN-C network. However, the results also suggest considerable challenges in defining a suitable NPBN, particularly for predictions in ungauged basins. These are mainly due to the discrepancies in the timescale of the different physical processes generating discharge, the presence of a “memory” in the system, and the Gaussian-copula assumption used for modelling multivariate dependence.@en