A sequential Bayesian inversion algorithm is proposed for the estimation of unknown parameters in computationally demanding physical models, a frequent challenge in industrial applications. The approach aims to accurately infer the posterior distribution of the parameters, ensuring that it is concentrated as possible around the true values while minimizing the number of direct model evaluations. To achieve this, a multi-fidelity meta-modeling strategy is employed within a reduced-order space, leveraging recursive Gaussian process regression to approximate the projection functions efficiently. The meta-model and the projection matrix are iteratively refined in a sequential way, by incorporating new training data selected based on the evolving posterior distribution, ensuring that only the most informative simulations are performed. This approach enables precise parameter estimation while controlling computational costs. Numerical and experimental case studies on the thermal modeling of a single-layer wall illustrates the method’s effectiveness in identifying thermal properties from four functional outputs. A comparative analysis with a fixed-cost identification strategy highlights the robustness of the proposed sequential method, demonstrating robust parameter estimates across iterations and a progressive reduction of uncertainty. By adaptively targeting the most valuable simulations, this algorithm efficiently balances computational cost and estimation accuracy, making it particularly well-suited for industrial applications involving expensive simulation codes.

The review explores coupled heat and moisture transfers in bio-based and geosourced materials from experimental and numerical viewpoint. It summarizes the underlying physical phenomena, the models developed over several decades, and the resulting simulation tools up to the building scale. The article deals with an analysis of results, limitations, recent advances, and key points requiring clarification. This work emphasizes the importance of simulation software in assessing energy efficiency, preventing moisture-related issues, and ensuring occupant comfort. Various strategies, including model simplifications, model order reduction, and the use of neural networks, are presented to mitigate computation time in addressing hygrothermal issues. Additionally, standardized experimental methods for determining model input parameters are discussed, acknowledging the associated uncertainty. The establishment of a database on experimentally measured thermal performance of earth construction is also attempted. The review highlights studies comparing experimental results and simulations at the wall scale, emphasizing influential factors in hygroscopic materials such as hysteresis. Classical models are deemed less than entirely satisfactory, especially concerning moisture profiles within hygroscopic materials, but recent improvements show promise in addressing this issue. Finally, the main subjects at the building scale dealing with the hygrothermal behavior, the indoor comfort and the building energy consumption are reviewed. It underscores the limited number of studies comparing hygrothermal simulations to sensors outputs in occupied building.

Meta-modelling and Bayesian inversion technique are proposed for fast and accurate in-situ estimation of the total thermal resistance (RTot) of walls using non-intrusive wall instrumentation. Various sources of uncertainties are taken into account to provide an enhanced credible interval for the thermal resistance estimate. In the considered protocol, a small zone of the internal surface of the wall is excited by a prototype to get faster in situ estimation and to limit the influence of external weather conditions. To be independent of the heat transfer coefficients and of the misknown layer thicknesses, which are difficult to estimate, we use herein the measurements of internal and external surface temperatures as boundary conditions in a thermal direct problem reformulated. A meta-model of the thermal model is created based on a statistical multi-fidelity approach with two levels of fidelity, Resistance-Capacitance (RC) and 1D models, to achieve the Bayesian estimation of the total thermal resistance in a reasonable computation time. The RTot estimation method is applied to realistic internal insulated walls (IIW), from poorly to highly insulated, under different weather conditions. Several numerical tests are carried out and credible intervals are provided to study the importance of the wall initial condition, the excitation time and the instrumentation. Finally, an experimental application is conducted using real measurements on an internal insulated wall (IIW) in Nancy (France). The obtained experimental results show that, in a short excitation time (10h) with a reduced instrumentation, the proposed method accurately estimates the minimum wall thermal resistance. For a standard wall of about 4 m2 K/W, a relevant estimate of RTot with a relative deviation less than 10% can be achieved by using a polynomial initial temperature profile proposed in this study, sufficient measurements and an excitation time of 3 days. This study thus offers prospects for improved energy assessment of buildings before and after renovation.

According to the World Health Organization, every year more than 4 million premature death worldwide are due to outdoor air pollution.Many sectors, e.g traffic, agriculture, industry, and housing, contribute to this.Herein, we focus on NO 2 pollution in urban areas caused by traffic.In fact, at Université Gustave Eiffel, on the one hand, experimental works are in progress to develop operational depolluting panels based on ZnO photocatalysis [1].On the other hand, to reduce air pollutant human exposure we propose a full numerical strategy from diagnosisvia the determination of critical highly polluted areas -to remediation via the smart placement of the depolluting panels in urban areas.Firstly, a city digital twin and computational fluid dynamics (CFD) are used to get detailed cartography of the NO 2 concentration at the district scale.From these numerical simulations, we retain high-concentration areas in the frequented zone as a quantity of interest.Then, a goal-oriented placement of depolluting panels is proposed to improve the selected quantities of interest using the adjoint framework.This work can be seen as an extension of previous works from the authors dealing with goal-oriented error estimation [2], goal-oriented model updating [3] and goal-oriented sensor placement [3,4].The proposed numerical strategy will be illustrated over a district in Paris.We consider two wind scenarios (directions and amplitudes), which are characteristic of the Paris region, and realistic NO 2 sources on each road provided by the regional air quality agency "Airparif".First practical recommendations for depolluting panels deployment will be presented.

A two-step numerical strategy based on a district digital twin is presented to efficiently deploy a limited number of depolluting panels in urban areas. In a diagnosis stage, a detailed pollutant concentration map is computed using CFD to identify critical highly polluted areas. Then, in a remediation stage, the optimal placement of depolluting panels as regards of urban airflow is determined to locally mitigate the air pollution in the exposed areas. For this purpose, a spatial sensitivity indicator calculated from an adjoint framework is proposed. The approach is applied to two real case studies: the full-scale laboratory district “Sense-City” under controlled conditions and a district area in Paris using realistic NOx traffic emission and wind conditions. In both case studies, it is shown that depolluting panels should be placed on a part of the sidewalks, the building facades and the roads adjacent to the sidewalks to reduce the high NOx concentration on some sidewalks and on first-floor building windows, thus preventing outdoor/indoor pollutant transfer. It is also proven that the proposed strategy is more efficient than a non-smart massive deployment of depolluting panels to improve the air quality in exposed areas. In addition to practical recommendations, this numerical strategy can provide a help-decision tool for city managers to design depolluting panels-based mitigation actions.

As majority of people spend 90% of their time in indoor environment, air quality has become an important scientific field in the last few decades. Indoor air quality is affected by many factors. One of the significant factors is outdoor air pollutions [1]. They enter the indoors through ventilation systems or natural ventilation and may stay indoors for a long time due to the airtightness of buildings. The present study especially focuses on nitrogen dioxide (NO2) concentration in a natural ventilating room that comes from outdoor pollutant sources such as vehicle emissions. In the present study, we have performed numerical simulations of a controlled environment in Sense-City urban area [2]. Sense-City is a unique full-scale equipment that can reproduce controlled conditions of temperature, humidity, airflow and pollution using an atypical climatic chamber. Reynolds Averaged Navier-Stokes (RANS) simulations have been carried out to calculate indoor and outdoor NO2 concentrations. RANS simulations are performed in two steps: district scale and building scale. Pressure values and pollutant concentrations are extracted from the district scale simulation and applied to the building scale simulation as boundary conditions. As expected, a sensitivity analysis study shows that the NO2 concentration in the building depends mainly on the pollutant concentration at the windows. Once opening windows, indoor pollutant concentration reached the almost same level of that of outdoor within a few minutes. Therefore, the interaction between indoor and outdoor air quality cannot be negligible for indoor air quality. This study can be useful for engineers and for local authorities to understand the importance of considering the interaction of the indoors and outdoors, the potential and limitation of RANS simulation in a natural ventilating. Considering the limitation of the number of sensors for air pollution in real applications, Computational Fluid Dynamics (CFD) is promising to obtain air pollutant distribution cartography. It can also be used as a decision-support tool for relevant urban planning such as the optimal placement of sensors and depolluting systems in urban areas.

According to WHO, outdoor air pollution causes about 4.2 millions deaths per year in the world. To tackle the problem of air pollution from traffic, depolluting panels based on ZnO photocatalysis [1] can be locally deployed in urban areas. Herein, we propose a virtual testing approach for the optimal placement of depolluting panels at the district scale. It is inspired by previous research works on the optimal placement of gas sensors [2]. Firstly, the district digital twin is used in computational fluid dynamics simulations to perform fine cartographies of the air flow and the concentration pollutants. These simulations allow the identification of critical areas where people can be exposed to high level of pollutant. Then, the pollutant concentration in the determined critical area is defined as a “quantity of interest” and the associated adjoint advection-diffusion-reaction problem is solved. Relevant positions of depolluting panels are obtained by post-processing the adjoint concentration field. In the presentation, the numerical strategy will be illustrated on a real small district in the equipment “Sense-City” [3]. First results show a good agreement between the measured and the simulated turbulent air flow [4]. In incoming works, gas dispersion tests are to be conducted in Sense-City to validate the prediction of the pollutant concentration map and to verify the efficiency of the depolluting panels whose position was determined from the proposed virtual testing approach

Computational Fluid Dynamics (CFD) is increasingly used to describe the airflow in urban environments. In this study, we aim to simulate and to validate the airflow in a full-scale urban area submitted to controlled climatic conditions through an impressive climatic chamber. This non-standard equipment named “Sense-City” is made up of a 400 m2 realistic district with buildings and street layout. The Sense-City urban area is highly instrumented, which allows notably the validation of physical models and simulations and the test of innovative urban solutions. Using a URANS model, with the k-omega SST model as the closure model, a CFD analysis is made on the turbulent airflow in Sense-City at a reasonable computational cost. The simulated velocities and turbulent kinetic energy are compared with measurements collected at a pedestrian level using a 3D ultrasonic anemometer. We show that the numerical simulations correctly predict the flow direction and flow characteristics such as regions of near-zero velocity. Geometry simplifications, uncertainties on the boundary conditions and the use of a coarse mesh and time discretization to fulfill operational purposes have led to a Root Mean Square Error (RMSE) score of 0.26 m/s on the velocity magnitude.

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.

In this work we investigate a variational data assimilation method to rapidly estimate urban pollutant concentration around an area of interest using measurement data and CFD based models in a non-intrusive and computationally efficient manner. In case studies presented here, we used a sample of solutions from a dispersion model with varying meteorological conditions and pollution emissions to build a Reduced Basis approximation space and combine it with concentration observations. The method allows to correct for unmodeled physics, while significantly reducing online computational time.

According to the latest assessments made by the world health organization (WHO 2016), the atmospheric pollution (air), has become one of the main causes of morbidity and mortality in the world, with a steep growth of respiratory diseases, increase in lung cancer, ocular complications, and dermis diseases [1,2,3]. Currently, there are governments which still underestimate investments in environmental care, turning their countries into only consumers and predators of the ecosystem [1,2,3]. Worldwide, several cities have been implementing different regional strategies to decrease environmental pollution, however, these actions have not been effective enough and significant indices of contamination and emergency declarations persist [1,2,3]. Medellin is one of the cities most affected by polluting gases in Latin America due to the high growth of construction sector, high vehicular flow, increase in commerce, besides a little assertive planting trees system, among other reasons [1,2,3]. With the purpose of providing new researching elements which benefit the improvement of air quality in the cities of the world, it is pretended to mathematically model and computationally implement the behavior of the flow of air, e.g., in zones in the city of Medellin to determine the extent of pollution by tightness, impact of current architectural designs, vehicular transport, high commerce flow, and confinement in the public transport system. The simulations allowed to identify spotlights of particulate tightness caused by architectural designs of the city which do not benefit air flow. Also, recirculating gases were observed in different zones of the city. This research can offer greater knowledge around the incidence of pollution generated by structures and architecture. Likewise, these studies can contribute to a better urban, structural and ecological reordering in cities, the implementation of an assertive arborization system, and the possibility to orientate effective strategies over cleaning (purification) and contaminant extracting systems.

The challenges of understanding the impacts of air pollution require detailed information on the state of air quality. While many modeling approaches attempt to treat this problem, physically-based deterministic methods are often overlooked due to their costly computational requirements and complicated implementation. In this work we extend a non-intrusive Reduced Basis Data Assimilation method (known as PBDW state estimation) to large pollutant dispersion case studies relying on equations involved in chemical transport models for air quality modeling. This, with the goal of rendering methods based on parameterized partial differential equations (PDE) feasible in air quality modeling applications requiring quasi-real-time approximation and correction of model error in imperfect models. Reduced basis methods (RBM) aim to compute a cheap and accurate approximation of a physical state using approximation spaces made of a suitable sample of solutions to the model. One of the keys of these techniques is the decomposition of the computational work into an expensive one-time offline stage and a low-cost parameter-dependent online stage. Traditional RBMs require modifying the assembly routines of the computational code, an intrusive procedure which may be impossible in cases of operational model codes. We propose a less intrusive reduced order method using data assimilation for measured pollution concentrations, adapted for consideration of the scale and specific application to exterior pollutant dispersion as can be found in urban air quality studies. Common statistical techniques of data assimilation in use in these applications require large historical data sets, or time-consuming iterative methods. The method proposed here avoids both disadvantages. In the case studies presented in this work, the method allows to correct for unmodeled physics and treat cases of unknown parameter values, all while significantly reducing online computational time. (C) 2019 Elsevier Inc. All rights reserved.

Computation Fluid Dynamics (CFD) simulation has become a routine design tool for i) predicting accurately the thermal performances of electronics set ups and devices such as cooling system and ii) optimizing configurations. Although CFD simulations using discretization methods such as finite volume or finite element can be performed at different scales, from component/board levels to larger system, these classical discretization techniques can prove to be too costly and time consuming, especially in the case of optimization purposes where similar systems, with different design parameters have to be solved sequentially. The design parameters can be of geometric nature or related to the boundary conditions. This motivates our interest on model reduction and particularly on reduced basis methods. As is well documented in the literature, the offline/online implementation of the standard RB method (a Galerkin approach within the reduced basis space) requires to modify the original CFD calculation code, which for a commercial one may be problematic even impossible. For this reason, we have proposed in a previous paper, with an application to a simple scalar convection diffusion problem, an alternative non-intrusive reduced basis approach (NIRB) based on a two-grid finite element discretization. Here also the process is two stages: offline, the construction of the reduced basis is performed on a fine mesh; online a new configuration is simulated using a coarse mesh. While such a coarse solution, can be computed quickly enough to be used in a rapid decision process, it is generally not accurate enough for practical use. In order to retrieve accuracy, we first project every such coarse solution into the reduced space, and then further improve them via a rectification technique. The purpose of this paper is to generalize the approach to a CFD configuration.

This work aims at investigating the use of reduced basis (RB) methods to diminish the cost of numerical simulation of elastoplasticity problems arising from geotechnics modeling, and involving parameter-dependent partial differential equations (PDEs). Computation times for large three-dimensional analysis commonly take tens of hours, making optimization procedures or sensitivity analysis, relying on repeated simulations, hardly feasible. In many cases the geotechnical analysis requires very specific features such as highly non-linear constitutive laws, making the necessary modification of the FE calculation code for a standard RB method impossible. An approach making it possible to use the reduced basis framework without having to modify the code gives the so-called non-intrusive reduced basis method a versatility of great practical interest. Our approach involves the computation of less expensive (but less accurate) FE approximation during the online stage and improvement of those solutions using a RB-based rectification method.

As the population increases, cities must constantly reassess their urban planning. However, this must be done in such a way to preserve the quality of life of its inhabitants. Energy saving, sustainable water and air quality are some of the important challenges associated with growing cities. In this context, the monitoring of the different urban flows (pollution, heat) is very important. For instance data assimilation approach can be used in monitoring. These methods incorporate available measurement data and mathematical model to provide improved approximations of the physical state. The effectiveness of modeling and simulation tools is essential. Advanced physically based models could provide spatially rich small-scale solution, however the use of such models is challenging due to explosive computational times in real-world applications. Beyond computational costs, physical models are often constrained by available knowledge on the physical system. To overcome these difficulties, we resort the Parameterized-Background Data-Weak (PBDW) method introduced in [1]. The PBDW formulation combines a set of solutions (a reduced basis [2]) from the physically based model, and the experimental observations, in order to provide a real-time and in-situ state estimate. The reduced basis is used to diminish the cost of using a high-resolution model by exploiting the parametric structure of the governing equations. In addition, variational data-assimilation techniques are used to correct the model error. In this work we extend the PBDW method to the monitoring of urban flows as an important use case but also as an example of the very generic approach that proves well suited to Online monitoring over large scales. In case studies presented here, the method allows to correct for unmodeled physics and treat cases of unknown parameter values, all while significantly reducing online computational time. REFERENCES [1] Y. Maday, A.T Patera, J.D. Penn and M. Yano, “A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics”, Int. J. Numer. Meth. Engng (2014).

The aim of this paper is to develop some techniques for automation of the mappings (between working and reference domains) required by reduced basis methods: the development of geometry mappings is indeed often a substantial impediment to the implementation of reduced basis techniques, especially in the context of the reduced basis element method (RBEM) and the reduced basis component method (RBCM). In the RBCM context, the geometry mappings are applied at the level of components. The methods have been tested on various cases to understand the limits of the approach and try to foresee and overcome the possible failures.

In this article, we introduce and analyse some two-grid methods for nonlinear elliptic eigenvalue problems of the form -div(D del u) + Vu + f (u(2))u = lambda u, parallel to u parallel to(L2) = 1. We provide a priori error estimates for the ground state energy, the eigenvalue lambda and the eigenfunction u, in various Sobolev norms. We focus in particular on the Fourier spectral approximation (for periodic boundary conditions), and on the P-1 and P-2 finite element discretizations (for homogeneous Dirichlet boundary conditions), taking numerical integration errors into account. Finally, we provide numerical examples illustrating our analysis.

In thermal building applications, simplified physical models are commonly used by engineers. In multizone models, a building is decomposed into zones and envelopes. As the temperature is assumed homogeneous in the zones, the time evolution of the zone temperature is described by an ordinary differential equation. Concerning the envelopes, a one-dimensional partial differential equation is considered. This simplifed physical model allows to simulate at a reasonable computation cost the thermal behavior of the building. It is particularly useful to evaluate the energy effciency of the building and to propose an optimal control of the building systems such as the heating and the ventilation.