This study addresses the critical challenge of modeling and mapping urban air quality to ascertain pollutant concentrations in unmonitored locations. The advent of low-cost sensors, particularly those deployed in vehicular networks, presents novel datasets that hold the potential to enhance air quality modeling. This research conducts a comprehensive review of ten statistical models drawn from existing literature, using both fixed and mobile low-cost sensor data, alongside ancillary variables, within the urban confines of Nantes, France. Employing a methodology that includes cross-validation of data from low-cost sensors and validation on fixed air quality monitoring stations, this paper evaluates the models' performance in scenarios of temporal interpolation and prediction. Our findings reveal a pronounced bias in the model outputs when reliant on low-cost sensor data compared to the verification data obtained from fixed stations. Furthermore, machine learning models demonstrated superior performance in predictive scenarios, suggesting their enhanced suitability for forecasting tasks. The study conclusively indicates that reliance solely on data from low-cost mobile sensors compromises the reliability of air quality models, due to significant accuracy deficiencies. Consequently, we advocate for a directed focus towards the integration and calibration of low-cost sensor data with information from fixed monitoring stations. This approach, rather than an exclusive emphasis on the complexity of statistical modeling techniques, is pivotal for achieving the precision required for effective air quality management and policy-making.

This paper explores Vecchia likelihood approximation for modeling physical phenomena sensed by mobile and fixed low-cost sensors in urban environments. A three-level hierarchical model is proposed to simultaneously accounts for the physical process of interest and measurement errors inherent in low-cost sensors. Several innovative configurations of Vecchia's approximation are investigated, including variations in ordering strategies, distance definitions, and sensor-specific conditioning. These configurations are evaluated for approximating the likelihood of a spatio-temporal Gaussian process, using simulated data based on real mobile sensor trajectories across Nantes, France. Our findings highlight the effectiveness of the min-max distance algorithm for ordering, reaffirming existing literature. Additionally, we demonstrate the utility of a random ordering approach that doesn't require prior definition of a spatio-temporal distance. These two ordering configurations achieved, on average, 102% better results in log Kullback-Leibler divergence compared with four other ordering schemes studied. Results are supplemented with Asymptotic Relative Efficiency analysis, offering practical recommendations for optimizing parameter estimation. The proposed model and preferred Vecchia configuration are applied to real-world air quality data collected using mobile and fixed low-cost sensors. This application underscores the model's practical value for pollution mapping and prediction in environmental monitoring. This study advances the use of Vecchia's approximation for addressing computational challenges of Gaussian models in large-scale spatio-temporal datasets from environmental monitoring with low-cost sensor networks.

A better understanding of urban climate is needed to adapt cities so they become more resilient to heat waves. This understanding will allow to manage cities in such a way that they do not accentuate the phenomenon of urban heat island. The paper presents a new model called EtiC based on 2-D micro-meteorological models for the rural and urban boundary layer modeling. The EtiC model simulates the thermal behavior of buildings by taking into account the thermal inertia of walls, floors, and roofs, as well as ventilation, heating, and air conditioning. It also considers visible and infrared radiation. The EtiC model was tested on three experimental cases in Basel, Toulouse, and two areas of Paris, for which RMSE values of 1.06, 0.77, 0.8, and 0.84 were obtained, respectively. EtiC is available for download under the GPL~3.0 license on GitLab at https://gitlab.univ-eiffel.fr/patrice.chatellier/eptic.

Wastewater from urban areas contains a large amount of thermal energy. It constantly exchanges this energy with its surrounding. This study analyzes the thermal exchanges between wastewater and its immediate environment. A mathematical model is constructed that allows to predict the level and velocity of the water in the sewer as a function of time. From this information, the model calculates the heat transfer between the wastewater and the surrounding soil. The results show that the soil temperature can be modified over a maximum thickness of 5 to 10 m. Close to the sewer, soil temperature is constantly influenced by the wastewater, while the soil beyond 10 m does not participate to the exchange. Regarding the heat exchange between wastewater and its environment, the results show that at least 90% of the heat exchange takes place with soil through the part of the pipe in contact with the wastewater while only 10% of the exchange takes place through the air contained in the pipe. The simulations also show the interest of carrying out charge/discharge of thermal energy with the ground surrounding a sewer. For a sewer of 1800 m length and a wastewater flow of 65m3/h during the day and 35m3/h during the night, one can expect to transfer up to 76 kW during the day and discharge 40 kW during the night. In addition, the flow rate plays an important role in the heat transfer process, especially with a partially filled sewer pipe. A higher flow rate means a larger wet area in the pipe and thus an increase in heat exchange. This preliminary analysis shows that the sewer network can be used as an underground thermal storage system to cope with the variations in heating and cooling demand with the goal of improving urban energy efficiency.

Due to global urbanization, urban areas are encountering many environmental, social, and economic challenges. Different solutions have been proposed and implemented, such as nature-based solutions and green and blue infrastructure. Taking into consideration exogenous factors that are associated with these solutions is a crucial question to assess their possible effects. This study examines the possible explanatory factors and their evolution until the year 2054 of several solutions in the Île-de-France region: wastewater heat-recovery, surface geothermal energy, and heat-mitigation capacities of zones. This investigation is performed by a series of statistical models, namely the ordinary least squares (OLS) and the geographically weighted regressions (GWR), integrated within a geographic information system. The main driving factors were identified as land use/land cover and population distribution. The results show that GWR models capture a large part of spatial autocorrelation. Apropos of prediction results, areas with low, medium, and high potential for implementing specific solutions are determined. Furthermore, the implementation capacities of solutions are compared with the demand depicted as the need for slowing down the effects of surface urban heat islands and the dependence on fossil energy. Moreover, the heat mitigation capacities are not at all times distinctively linked to human activities. Further investigations are needed to discover the remaining possible reasons, particularly air quality, water, vegetation, and climate change.

With the advancement of technology and the arrival of miniaturized environmental sensors that offer greater performance, the idea of building mobile network sensing for air quality has quickly emerged to increase our knowledge of air pollution in urban environments. However, with these new techniques, the difficulty of building mathematical models capable of aggregating all these data sources in order to provide precise mapping of air quality arises. In this context, we explore the spatio-temporal geostatistics methods as a solution for such a problem and evaluate three different methods: Simple Kriging (SK) in residuals, Ordinary Kriging (OK), and Kriging with External Drift (KED). On average, geostatistical models showed 26.57% improvement in the Root Mean Squared Error (RMSE) compared to the standard Inverse Distance Weighting (IDW) technique in interpolating scenarios (27.94% for KED, 26.05% for OK, and 25.71% for SK). The results showed less significant scores in extrapolating scenarios (a 12.22% decrease in the RMSE for geostatisical models compared to IDW). We conclude that univariable geostatistics is suitable for interpolating this type of data but is less appropriate for an extrapolation of non-sampled places since it does not create any information.

We present an original goal-oriented inverse method for model parameter identification. Initially developed in [1], it is based on dual analysis and consists in a modified version of the concept of Constitutive Relation Error. It stands out from standard deterministic inverse methods by its formulation, as it focuses on the accurate prediction of a specific quantity of interest, and aims at automatically identifying and updating the model parameters involved in its computation alone. To further reduce the CPU time of the multi-query inversion process, that also involves coupled time forward/backward systems to solve, the goal-oriented inverse method is beneficially complemented with model order reduction, using the Proper Generalized Decomposition (PGD) technique [2]. Eventually, the goal-oriented method is also employed for optimal sensor placement (experimental design), in order to drastically reduce the number of sensors which need to be deployed for the objective of the simulation. The proposed method is here applied and illustrated with transient heat transfer models encountered in building thermal problems. Inverse analysis with such models is a compulsory but costly task for the reliable evaluation of building thermal properties, accurate prediction of energy consumption, and therefore optimal driving of renovation strategy of power control. It usually involves a large number of parameters but a restricted number of available sensing data. In this framework, the goal-oriented method is first integrated in a software chain containing CAD and thermal dynamic simulation tools. Performance is then numerically evaluated on several test cases with real experiments. In particular, a two-story building of the Sense-City equipment with controlled climate scenarios and in-situ sensors is considered, with various quantities of interest [3]. It is shown that for all these and using the goal-oriented strategy, very few model parameters actually need to be updated, and little sensing information is necessary, without sacrificing accuracy. It is then a tool of choice for such applications.

In many cases, numerical simulations cannot accurately predict the settlements induced by the construction of shallow tunnels: the settlements troughs obtained numerically tend to be wider than the observed ones. This can lead to underestimating the differential settlements and thus the potential damages to buildings above ground. This article proposes an elastoplastic model aiming to improve the results of finite element simulations and more precisely the width of the settlement trough. The key feature is the introduction of transverse isotropy in the elastic part of the model. The model makes it possible to clearly identify the influence of each parameter on the mechanical behavior. In particular, one of the parameters controls the shape of the settlement trough. The model was implemented in the finite element code CESAR-LCPC and used to model the settlements observed during the construction of a tramway line in the outskirts of Paris. The results show the effectiveness of the proposed approach.

In this work, we present a non-intrusive method using the Reduced Basis framework in order to diminish the cost of numerical simulation arising from the computation of parameters-dependent Partial Differential Equations (PDE). This method involves the computation of less expensive (but less accurate) solutions of the PDE during the online stage, and a RB-based rectification step. It represents a good substitute for standard Reduced Basis methods when it is applied to urban flows modelling. This approach speeds up the CFD simulation while remaining non-intrusive in relation to the high fidelity model, which can allow to avoid practical problems (e.g. non-affine parametric dependence) associated to model reduction for complex air flows involved in many sophisticated methods of urban air quality modeling. Our focus here is on the validation of the non-intrusive method applied to the backward-facing step 2D benchmark.

This article introduces a new inverse method for thermal model parameter identification that stands out from standard inverse methods by its formulation. While these latter methods aim at identifying all the model parameters in order to fit the experimental data at best, the proposed goal-oriented inverse method focuses on the prediction of a specific quantity of interest, automatically identifying and updating the model parameters involved in its computation alone. To further reduce the computational time, the goal-oriented inverse method is associated with a model order reduction method referred to as Proper Generalized Decomposition (PGD). The objective of this original approach is to robustly predict the sought quantity of interest in a reduced computational time while using a limited measurement data set. The goal-oriented inverse method is developed and illustrated on transient heat transfer models encountered in building thermal problems. The first application deals with a simplified 1D heat transfer problem through a building wall with synthetic data, and the second one is dedicated to a real building with measured data. The performance of the approach is numerically assessed by comparing the results with those obtained using the classical least squares method (with Tikhonov's regularization). It is shown that the goal-oriented inverse method allows to robustly predict the sought quantities of interest, with an error of less than 5% by updating only the model parameters that affect it the most and thus leads to save computation time compared to standard inversion methods.

The article describes thermal datasets collected in a two-story concrete building of the Sense-City equipment during various controlled climatic scenarios. Using the Sense-City climatic chamber, we reproduced stationary thermal conditions, a typical winter climate of the south of France and Paris 2003 heat wave. Each of the three scenarios has a duration of about one week. The datasets contain temperature, heat flux and energy consumption sensor outputs. In [1], the stationary conditions data were exploited for an experimental identification of thermal characteristics of the building whereas the winter and the heat wave data were used in a goal-oriented model updating technique. The datasets can also be useful to validate modeling and simulation.

A goal-oriented inverse technique is proposed for the accurate computation of quantities of interest in thermal building problems. In contrast to the standard inverse methods, only the model parameters sensitive to the chosen quantity of interest are updated. The technique is applied to a real building in the Sense-City equipment. A two-zone thermal model described by 15 parameters is used. To study the robustness of the inverse method, two controlled climate scenarios conducted in Sense-City, i.e. the Carpentras (south of France) winter and the Paris 2003 heatwave, and five different quantities of interest are considered. For all the the chosen quantities of interest, it is shown that very few model parameters need to be updated by the inverse technique leading to a better estimation of the quantity of interest. The obtained results are experimentally validated using the sensor outputs and a controlled stationary climate test in the Sense-City equipment. The goal-oriented framework is also used for optimal sensor placement. A first application shows that the number of temperature sensors can be drastically reduced to compute a quantity of interest. Last, for operational use, the proposed method is integrated in a software chain containing computer-aided design and thermal dynamic simulation tools. All sensor outputs are provided in the companion paper [25].

Le present travail introduit une methode inverse d'identification de parametres vis-a-vis d'une quantite d'interet en thermique du bâtiment. Cette methode peut presenter un interet pour l'identification de caracteristiques thermiques d'enveloppes de bâtiments existants en vue de realiser des diagnostics de performances energetiques representatifs de leur comportement reel. Contrairement aux methodes standard de resolution de problemes inverses telles que la methode de regularisation de Tikhonov, qui ont pour objectif de recaler l'ensemble des parametres du modele afin de reproduire, le plus fidelement possible, les donnees mesurees, la methode d'identification de parametres vis-a-vis d'une quantite d'interet est formulee pour la prediction robuste de quantites physiques predefinies. Cette methode n'identifie que les parametres du modele auxquels la quantite d'interet recherchee est sensible. Elle permet ainsi de minimiser l'instrumentation et de reduire le temps de calcul. Une premiere application a l'echelle de l'enveloppe a permis de constater que la methode d'identification de parametres de modeles vis-a-vis d'une quantite d'interet presente une plus faible sensibilite au bruit de mesure par rapport aux methodes usuelles. Afin de reduire les temps de calcul, la methode inverse est couplee a une methode de reduction de modeles de type PGD (Proper Generalized Decomposition). La strategie developpee a ete appliquee a un modele R6C2 sur un chalet de l'equipement d'excellence « Sense-City » et les resultats obtenus ont ete compares a ceux de la methode de Tikhonov. On constate que la methode proposee permet l'identification robuste des quantites d'interet recherchees en quelques iterations, avec une erreur inferieure a 5% et en ne recalant que les parametres auxquels elles sont sensibles. Pour valider ces resultats sur un modele representatif de bâtiments reels, comprenant plusieurs zones thermiques et un plus grand nombre de parametres, une application sur le bâtiment R+1 de la mini-ville « Sense-City » est actuellement en cours d'etude.

•The review shows building energy consumption modeling and forecasting techniques.•Eight specific data-driven forecasting methods are described.•A focus is given on the data pre-processing methods and forecasting algorithms.•The supervised, unsupervised, reinforcement and machine learning tasks is discussed.

Le present travail introduit une methode inverse d'identification de parametres de modeles thermiques vis-a-vis d'une quantite d'interet. Cette methode a pour objectif de ne recaler que les parametres du modele ayant une influence sur une quantite d'interet donnee. Elle peut etre utilisee pour repondre au besoin en methodes numeriques pertinentes pour la realisation de diagnostics de performance energetique representatifs du comportement reel des bâtiments existants.

A significant proportion of the Paris metro tunnels comprise a masonry vault built out of stone blocks and mortar joints, and sidewalls and slabs made of unreinforced concrete. In order to provide the necessary data for future structural evaluation, an extensive laboratory testing programme has been conducted to characterize the materials of the tunnel separately, i.e., mortar, stone, and concrete. The tests, carried out on specimens taken from cores extracted from a 1930s tunnel, enabled to determine the mechanical properties, including direct tensile, shear strength, and mode I fracture energy, as well as the properties of the stone-mortar interface. Results show that the masonry mortar joints could reach 10 cm in width, and that blocks of stone varied in composition and porosity, thus producing a wide range of mechanical properties. The concrete was composed of large-sized aggregates and showed low stiffness and strength. Based on these experimental results, ratios between mechanical characteristics are hereby proposed. Perspectives on the use of this experimental data in a finite element model are then discussed.

The present paper introduces a goal-oriented approach for parameter calibration of thermal building models. In a context of reducing the global energy consumption and greenhouse gas emissions, the goal-oriented method may be used for a robust prediction of a quantity of interest. Contrary to standard inverse methods, we do not aim at identifying all the model parameters in view of simulating the global thermal behavior of the building. Only the model parameters involved in the computation of the quantity of interest are updated. The proposed inverse strategy can lead to low computational time and reduced instrumentation. To validate the method, a first application on a steady state heat transfer problem is presented.