This paper introduces a novel extension of the multi-system optimisation method, known as the 3C concept, tailored for optimising budget allocation for bridge interventions at the network level. This extended methodology accounts for the interdependencies among bridges due to their spatial proximity within the network. It incorporates direct and user costs, bridge performance indicators, and a bridge deterioration model. A real-world case study involving a portfolio of 555 bridges demonstrates the practicality of the methodology, efficiently determining the optimal intervention sequence. Over an 18-year analysis period, the proposed methodology achieved a 23% reduction in total costs by combining repairs for bridges with high to severe damage and maintenance for the others. This represents a significant improvement compared to the traditional approach, used by bridge management agencies, which relies exclusively on maintenance. The optimised procedure outperforms human intuition in managing complex bridge networks, particularly over extended periods. This methodology can assist transportation agencies in implementing and exploring various scenarios by adjusting the time between consecutive interventions and budget constraints, supporting comprehensive analysis and informed decision-making.

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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

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

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

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

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

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

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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Traffic counts collect information that is valuable, for example, in bridge and road design or maintenance processes. The average daily traffic volume is often the most collected measure of vehicular traffic, which is used in the design or assessment of major highways. Permanent control stations, situated in key locations of the highway network, gather data the entire year. However, one of the disadvantages of traffic count data is that most counters used, do not measure total vehicle weight and axle load data. Traffic counts display only the classification of vehicles, traffic volume, average daily traffic, and annual average daily traffic. Axle loads on the other hand are required, for example, as input in the design of pavement and new bridges, and the reliability assessment of existing ones. Weigh-in-motion (WIM) systems are usually used to collect vehicle load data. The State of Mexico (in central Mexico) has 115 permanent vehicle counting stations with 745 traffic counting points in its federally administered road network. However, due to the lack of WIM stations, it is not possible to obtain axle load data. In this paper, a Bayesian Network (BN) quantified with data from WIM stations in the Netherlands is used to describe the weight and length distribution of heavy vehicles registered in the permanent vehicle counting stations of the State of Mexico federal highways. The Dutch and Mexican vehicle types are matched according to similar characteristics. Later, synthetic WIM observations from the BN model are analysed through extreme value theory and vehicle loads with selected return periods are computed for all study counting points. The outcome is a mapping methodology with a linked database. The traffic volumes and extreme loads can then be easily found and compared with other highways in the network. This work shows that hazard maps can be implemented to provide importantly and summarized information to understand the risks of extreme traffic loads and to help in the reliability assessment and maintenance strategies of pavements and bridges.@en

In the bridge industry, current traffic trends have increased the likelihood of having the simultaneous presence of both extreme live loads and earthquake events. To date, their concurrent interaction has scarcely been systematically studied. Prevailing studies have investigated the isolated existence of either live loads or seismic actions. In an effort to fill this gap in the literature, a non-parametric Bayesian Network (BN) has been proposed. It is aimed at evaluating the conditional probability of failure for a reinforced concrete bridge column, subject simultaneously to the actions mentioned above. Based on actual data from a structure located in the State of Mexico, a Monte Carlo Simulation model was developed. This led to the construction of a BN with 17 variables. The set of variables included in the model can be categorized into three groups: acting loads, materials resistances and structure force-displacement behavior. Practitioners are then provided with a tool for unspecialized labor force to gather information in situ (e.g. Weight-In-Motion data and Schmidt hammer measurements), which can be included in the network, leading to an updated probability of failure. Moreover, this framework also serves as a quantitative tool for bridge column reliability assessments. Results from the theoretical model confirmed that the bridge column probability of failure was within the expected range reported in the literature. This reflects not only the appropriateness of its design but also the suitability of the proposed BN for reliability analysis.@en