Aurélie Foucquier
email: aure-lie.foucquier@gmail.com

Sylvain Robert

Frédéric Suard

Louis Stephan

Arnaud Jay

Louis Stéphan

State of the art in building modelling and energy performances prediction: A review

Keywords: building modelling, energy consumption, energy performance, building thermal models, machine learning, building prediction model

Introduction

The building sector in the European Union is considered as the largest consumer of energy with using up to 40% of the final energy consumption [START_REF] Epbd | On the energy performance of buildings[END_REF]. More specifically, residential uses represent about 60% of total energy consumption of the building sector [START_REF] Poel | Energy performance assessment of existing dwellings[END_REF][START_REF] Balaras | European residential buildings and empirical assessment of the hellenic building stock, energy consumption, emissions and potential energy savings[END_REF]. To evaluate the energy performance of both residential and tertiary buildings, many parameters are required: thermal characteristics of the building, ventilation, passive solar system, indoor/outdoor climatic conditions and energy end-uses [START_REF] Poel | Energy performance assessment of existing dwellings[END_REF]. Considering these influencing factors, the average energy consumption in European Union raises to about 200 kWh/m 2 /year, distributed as shown in Fig ( 1) [START_REF] Balaras | European residential buildings and empirical assessment of the hellenic building stock, energy consumption, emissions and potential energy savings[END_REF][START_REF] Gaglia | Empirical assessment of the hellenic nonresidential building stock, energy consumption, emissions and potential energy savings[END_REF].

Thereby, it seems obvious to make significant efforts in terms of energy savings in building sector. For instance, the European Union established specific actions by introducing the EPBD (Energy Performance of Building Directive) dedicated to the building environmental issue [START_REF] Epbd | On the energy performance of buildings[END_REF]. This directive suggests to each EU states to target their own objectives. As a consequence, different projects of passive building emerged in Germany with PassivHaus, in Switzerland with Minergie and in France with Effinergie [START_REF]Low energy building in europe: current state of play, definitions and best practice[END_REF][START_REF] Bertez | The PASSIVE stake. Strategic overview on a global, structured and sustainable way for "efficient building[END_REF]. From a practical and scientific point of view, various solutions have been proposed both to increase the energy efficiency and to reduce greenhouse effects:

• An awareness campaign with the occupants on the environmental issue is necessary to reduce end-use energy consumption [START_REF] Barlow | Occupant comfort in UK offices -how adaptive comfort theories might influence future low energy office refurbishment strategies[END_REF]. Simple actions could decrease significantly the energy consumption as changing the space heating behaviour, unplugging the computer or mobile charger and unused devices, configuring the computer to hibernate after a given time of inactivity, avoiding waste of hot water and many other actions [START_REF] Carroll | Residential energy use behavior change pilot, CMFS Project Code B21383[END_REF].

• A second solution consists in the design of new dwellings or the refurbishment of existing dwellings with bringing energy-efficient improvements in agreement with the regulations given above. For instance, one way is to favour the exterior insulation and to replace simple glazing win-dows by double or triple glazing depending on the exposure of the room. However, the choice of energy-efficiency improvements is not obvious and the risk is to produce opposite effects.

• A third solution is to optimize the use of energetic systems as heating or cooling load. Indeed, new technologies give the possibility to improve significantly the energy efficiency. The integration of renewable energies in these systems is also quite efficient. For instance, Badescu and Sicre [START_REF] Badescu | Renewable energy for passive house heating part I. Building description[END_REF][START_REF] Badescu | Renewable energy for passive house heating II. Model[END_REF] evaluated the performance of the solar energy on a passive house in Germany and showed the possibility to reduce the heating demand to 5-6 kWh/m 2 /year.

• In addition to the two last proposals, a fourth solution is to use control and monitoring systems allowing controlled blackouts during specific moment of the day. Many authors have already showed the efficiency of such systems on the energy performance of the building [START_REF] Bohm | Monitoring the energy consumption in a district heated apartment building in Copenhagen, with specic interest in the thermodynamic performance[END_REF][START_REF] Paris | Heating control schemes for energy management in buildings[END_REF][START_REF] Petersen | Method for simulating predictive control of building systems operation in the early stages of building design[END_REF]. For example, very recently, Aswani et al. [START_REF] Aswani | Reducing transient and steady state electricity consumption in hvac using learningbased model-predictive control[END_REF] have published a work dealing with a model-predictive control of the HVAC systems able to control the indoor temperature of a room of a computer laboratory in the University of Berkeley. Previously, Mossolly et al. [START_REF] Mossolly | Optimal control strategy for a multi-zone air conditioning system using a genetic algorithm[END_REF] proposed a study comparing several control strategies in order to increase the energy performance in an academic building in Beirut, Lebanon. By determining the optimal control strategy, they recorded energy savings up to 30% during the summer. Moreover, these examples showed the ability to treat very large scale systems.

The design of building integrating all these efficiency measurements are usually "tested" and validated via software taking into account these specific aspects. The aim is to predict the improvements that could be made considering different designed management. So, scientists and engineers frequently resort to various and numerous simulation techniques. Depending on the use cases, several approaches are available: some of them based on the thermal knowledges and physical equations of the building and others based on the data collected inside the building.

We propose to give an overview of these existing methods. In Section 2, we will introduce the physical techniques called "white box" approaches used to model the thermal behaviour of a building. This kind of approach is used for several applications at different scales. For example, the white box scheme allows to evaluate the indoor temperature in a building for different time (year, month, day or hour) and spatial (the entire building, a room, a cell of a room) scales. Then, in Section 3, we will present the statistical or machine learning formulations called "black box" approaches mainly used in the aim to deduce a prediction model from a relevant data basis (for example, to forecast energy consumption or heating/cooling load in a given building). Finally, in Section 4, we will introduce solutions to couple the white and black box techniques to implement hybrid approaches also called "grey box" approaches.

Physical models: Building thermal behaviour modelling

Physical models are used to model the thermal behaviour in different varieties of buildings with their own specific needs: dwelling, office, hospital, school, firms... Some of them include models of space heating [START_REF] Liao | A simplied physical model for estimating the average air temperature in multi-zone heating systems[END_REF][START_REF] Badescu | Simple and accurate model for the ground heat exchanger of a passive house[END_REF], natural ventilation [START_REF] Li | Prediction of natural ventilation in buildings with large openings[END_REF][START_REF] Stephan | Optimizing opening dimensions for naturally ventilated buildings[END_REF], air conditioning system [START_REF] Wang | Dynamic simulation evaluation of building vav airconditioning system and of emcs on-line control strategies[END_REF], passive solar [START_REF] Ihm | Estimation of lighting energy savings from daylighting[END_REF], photovoltaic panel [START_REF] Clarke | The simulation od photovoltaic-integrated building facades[END_REF][START_REF] Chow | Building-integrated photovoltaic and thermal applications in a subtropical hotel building[END_REF], hygrothermal effects [START_REF] Ordenes | Estimation of thermophysical properties using natural signal analysis with heat and moisture transfer model[END_REF][START_REF] Qin | Simulation of whole building coupled hygrothermal airflow transfer in different climates[END_REF], financial issue [START_REF] Entrop | Evaluation of energy performance indicators and financial aspects of energy saving techniques in residential real estate[END_REF], occupants behaviour [START_REF] Aydinalp | Modeling of the appliance, lighting, and space-cooling energy consumptions in the residential sector using neural networks[END_REF][START_REF] Aydinalp | Modeling of the space and domestic hot-water heating energy-consumption in the residential sector using neural networks[END_REF][START_REF] Aydinalp-Koksal | Comparison of neural network, conditional demand analysis, and engineering approaches for modeling enduse energy consumption in the residential sector[END_REF], climate environment [START_REF] Gugliermetti | Climate models for the assessment of office buildings energy performance[END_REF], etc. The physical techniques are based on the solving of equations describing the physical behaviour of the heat transfer.

These equations can be written via the energy conservation law as Eq (1).

Φ int + Φ source = Φ out + Φ stock (1)
Φ int is the heat flux entering the system, Φ source the heat flux of an eventual heat source, Φ out the heat flux leaving the system and Φ stock the heat flux stored. The principal in and out-coming fluxes taking place in the heat transfer are the conduction through walls, the convection (both sensible and latent heat), the radiation and the ventilation.

To solve such physical problems, a large number of numerical software is available. Many authors proposed benchmarks to compare these software [START_REF] Wall | Distribution of solar radiation in glazed spaces and adjacent buildings. a comparison of simulation programs[END_REF][START_REF] Mcdowell | Integration of airflow and energy simulation using CONTAM and TRNSYS[END_REF][START_REF] Crawley | Contrasting the capabilities of building energy performance simulation programs[END_REF][START_REF] Woloszyn | Tools for performance simulation of heat, air and moisture conditions of whole buildings[END_REF][START_REF] Brun | Behavioural comparison of some predictive tools used in a low-energy building[END_REF]. For this reason, we will not develop here a software comparison. Theoretically, each building software is able to include each of mechanisms given above. They give the choice to users to select the mechanisms and the associated equations occurring in the system. But, Woloszyn [START_REF] Woloszyn | Tools for performance simulation of heat, air and moisture conditions of whole buildings[END_REF] and Crawley [START_REF] Crawley | Contrasting the capabilities of building energy performance simulation programs[END_REF] showed that many software are badly adapted to take into account the consequences of the humidity and that, generally, the effects of the latent heat are neglected.

Three main thermal building models are currently used: the multizone, zonal and CFD (Computing Fluid Dynamic) methods. We cannot say that one of these physical formulations is particularly better than another. Each of them has its own application and that is why the choice of the physical method depends essentially on the problem. In the following, we will detail and give some examples for each of these methods.

Each sections are built in the same way with a first part describing the principle of the approach, a second part with the advantages and the application field, a third part with the limitations of the method and a last part with some examples.

The CFD approach

Principle of the CFD approach

The most complete approach in the thermal building simulation is the CFD (Computational Fluid Dynamics) method. This is a microscopic approach of the thermal transfer modelling allowing to detail the flow field. It is based on the decomposition of each building zone in a large number of control volumes with an uniform or not global mesh. Thus, the CFD technique is recognized as a three dimensional approach.

Software using the CFD model are essentially based on the resolution of the Navier-Stokes equation. A huge number of CFD software are available such as FLUENT [4], COMSOL Multiphysics [1], MIT-CFD, PHOENICS-CFD [START_REF] Cham | Phoenics user manual for program version 3[END_REF]... Their application fields are very large and not always specific to building simulation. Indeed, they can be apply to every systems considering detailed flow description.

Advantages and application field of the CFD

The CFD method is mainly employed for its ability to produce a detailed description of the different flows inside buildings (airflow, pollutant flow,...). Consequently, the CFD is very well-adapted to the study of the particle transport as pollutant particles. Moreover, as we mentioned before, the volume is divided into several discrete control volumes with a uniform or non-uniform mesh. Thus, it allows to study very complex geometries of the building by minimizing locally the mesh of some specific parts.

Limitations of the CFD method

The main disadvantage of the CFD approach resides in its huge computation time [START_REF] Tan | Application of integrating multi-zone model with CFD simulation to natural ventilation prediction[END_REF], due to the fact that a complete detailed 3D-description of the building with a very fine mesh is absolutely required. Consequently, the smaller the mesh, the larger the computation time. However, given that the air velocity in at least 75% of the building is less than 0,5 m/s, it is not always necessary to apply the CFD technique in the entire building but just to specific constituents of the building as HVAC (Heating, Ventilation and Air Conditioning) equipment or appliances. Thus, it allows to reduce considerably the computation time. For this reason, the CFD is frequently coupled with less time-consuming thermal building simulation techniques as those that will be introduced in the following subsections or else statistical techniques as those that will be presented in the second part of this article. For example, Tan et al. [START_REF] Tan | Application of integrating multi-zone model with CFD simulation to natural ventilation prediction[END_REF] compared the full CFD simulation and the coupling between the CFD and another building simulation method for modelling the natural ventilation across large openings or atrium. They showed that the full CFD simulation would take more than ten hours, whereas the coupled method needs less than one hour. In the same way, Qin et al. [START_REF] Rong Qin | Research on a dynamic simulation method of atrium thermal environment based on neural network[END_REF] coupled a machine learning technique with a method coupling the CFD and a building energy model to predict the thermal dynamic behaviour in a large volume room as an atrium.

Moreover, the CFD method is quite limited by the complexity of the model implementation. Indeed, it is quite difficult to use it without previous knowledges on fluid dynamics and software. Furthermore, the CFD is also largely limited when it comes to model of the turbulence.

Examples

Zhai et al. [START_REF] Zhai | On approaches to couple energy simulation and computational fluid dynamics programs[END_REF] coupled a building simulation software called EnergyPlus [START_REF] Energyplus | eere.energy[END_REF] and the CFD software MIT-CFD to predict the cooling or heating demand both in an office and in an auto racing complex. The authors used EnergyPlus to determine the cooling or heating demand and MIT-CFD to find the airflow and temperature distribution in the zone volume. At each time step, EnergyPlus passed the informations to the CFD program that used them as boundary conditions. Then, the CFD program deduced the distribution of the air temperature in the thermal boundary layer and the convective heat transfer coefficients into the office. Finally, these outputs are injected in En-ergyPlus as inputs to improve the accuracy of the heating load prediction.

Other authors chose the same strategy. For example, Wang and Wong [START_REF] Wang | Coupled simulations for naturally ventilated residential buildings[END_REF] used a building simulation software ESP-r [START_REF] Clarke | Esp-a building and plant energy simulation system[END_REF] and FLUENT (a flow software using the finite volume method) [4] to simulate the natural ventilation in residential buildings. The ESP-r simulation contained the geometrical information, the construction thermal properties and the airflow network for the whole building. The place studied is a double zone building. To reduce the computation time, the authors chose to apply the CFD simulation only in one zone and to pilot the system by imposing pressure as opening boundary conditions. The ESPr simulation results provided boundary conditions to the CFD simulation.

Moreover, Srebric et al. [START_REF] Srebric | On-site experimental validation of a coupled multizone and CFD model for building contaminant transport simulations[END_REF] coupled a multizone tool called a ventilation simulating software CONTAM [START_REF] Dols | CONTAMW2.0 user manual[END_REF] with a CFD tool called PHOENICS-CFD [START_REF] Cham | Phoenics user manual for program version 3[END_REF] to evaluate the contaminant distribution in a building. First, they determined the airflow rates and the contaminant transport between zones. Then, they applied the CFD simulation only in the contaminant sources to deduce the airflow profile and the concentration distributions. These results are injected as fluxes in a new CONTAM simulation excluding the CFD domains. Finally, they evaluated the contaminant distribution. The authors showed that the coupled method is efficient in the zones very near the contaminant sources. However, in the other zones, the multizone approach remains the more appropriate method.

Finally, the CFD is particularly adapted to describe flow fields in buildings. However, the large computation time makes difficult the generalization to all building applications. Indeed, in some cases, it is not necessary to give a very fine description and a way to overcome the difficulties enforced by the CFD is to model the building behaviour in a simpler manner by giving a less detailed description of the interested zone [START_REF] Abadie | Improving the prediction of zonal modeling for forced convection airflows in rooms[END_REF]. The first degree of CFD's simplification is the zonal technique. It is a way to obtain this simpler modelling while maintaining the complexity in a 2D map.

The zonal approach

Principle of the zonal approach

The zonal method is the first degree of simplification of the CFD technique. It has been introduced by Bouia and Dalicieux [START_REF] Bouia | Simplified modelling of air movements inside dwelling room[END_REF] and Wurtz [START_REF] Wurtz | Three-Dimensional Modeling of Thermal and Airflow Transfers in Building Using an Object-Oriented Simulation Environment[END_REF] at the beginning of 1990's. This approach is a fast way to detail the indoor environment and to estimate a zone thermal comfort. Practically, it consists in dividing each building zone into several cells. One cell corresponds to a small part of a room. Thus, the zonal method can be assumed to a two dimensional approach. Fig ( 2) represents a scheme in case of zonal methods.

Advantages and application field of the zonal approach

The zonal formulation can treat a large volume space and the coupling between the system and its environment. The physical equations are solved for each cell of the zonal system. Consequently, it allows to determine the local variables in a 2D-map. Thus, it is possible to evaluate the spatial distribution of different fields like temperature, pressure, concentration or air velocity remaining at a quite reasonable computation time. Wurtz et al. [START_REF] Wurtz | An equation-based simulation environment to investigate fast building simulation[END_REF] showed that the zonal simulation is a suitable method for an accurate estimation of the temperature field in a room and of the indoor thermal comfort. Moreover, it allows also the visualization of building system airflows.

Several zonal building modelling software are available. One of them frequently employed to describe and to visualize indoor airflows is the so-called SimSPARK software [START_REF] Mora | Prédiction des performances thermo-aérauliques des bâtiments par association de modèles de différents niveaux de nesse au sein dun environnement orienté objet[END_REF]. Equations are solved by the object-oriented environment called SPARK [START_REF]SPARK 2.0 reference manual[END_REF]. Moreover, some researchers implemented their own zonal software as Haghighat with POMA [START_REF] Haghighat | Development and validation of a zonal model POMA[END_REF].

Limitations of the zonal approach

As we mentioned above, the zonal approach is a minimization of the complexity of the CFD method. Thereby, it is obvious that some studies normally well implemented via the CFD are not anymore feasible via the zonal method [START_REF] Inard | Contribution à létude du couplage thermique entre un émetteur de chauffage et un local[END_REF][START_REF] Wurtz | Two-and three-dimensional natural and mixed convection simulation using modular zonal models in buildings[END_REF][START_REF] Mora | Comparing zonal and cfd model predictions of isothermal indoor airflows to experimental data[END_REF]. Notably, some limitations reside in the following aspects:

• this technique requires previous knowledges on the flow profiles.

• it is not able to provide accurate results on the detailed description of the flow field.

• the study of the pollutant transport remains limited.

Examples

Inard et al. [START_REF] Inard | Prediction of air temperature distribution in buildings with a zonal model[END_REF] predicted the distribution of the air temperature inside a room with the zonal method. Especially, they proposed an original technique to model the mass air flow between two zones. Musy et al. [START_REF] Musy | Automatically generated zonal models for building air ow simulation: principles and applications[END_REF] studied the indoor thermal comfort in a room through the zonal software SPARK [START_REF]SPARK 2.0 reference manual[END_REF]. Particularly, the aim was to determine the vertical profile of temperature and the pollutant concentration repartition inside the room. Tittelein et al. [START_REF] Tittelein | Simspark platform evolution for lowenergy building simulation[END_REF] focused their works on the passive house and the methods to reduce the energy consumption of a building located in the region of Chambery, France. They compared the effects of a counter-flow ventilation and a single-flow ventilation on the energy efficiency.

Haghighat et al. [START_REF] Haghighat | Development and validation of a zonal model POMA[END_REF] implemented a software using the zonal approach called POMA (Pressurized zOnal Model with Airdiffuser). This software allows to predict the airflow pattern and the temperature distribution in a room which is naturally or mechanically ventilated.

Jiru and Haghighat [START_REF] Jiru | Modeling ventilated double skin facadea zonal approach[END_REF] computed the airflow and the temperature distribution in a ventilated double skin facade, using the zonal method. Specifically, they compared the time evolution of the temperature in three positions inside the facade. Parametric studies have been accomplished in order to test the influence of the cavity height, the flow rate and the presence of venetian blinds on the inlet-outlet temperature difference.

Brun et al. [START_REF] Brun | Experimental and numerical comparison of heat transfer in a naturally ventilated roof cavity[END_REF] proposed both experimental and numerical studies for modelling heat transfers in a naturally ventilated roof cavity in timber-frame buildings in Grenoble, France. They used as numerical software the zonal software SPARK [START_REF]SPARK 2.0 reference manual[END_REF] to estimate the resulted heat gain considering the naturally ventilated cavity use.

Stephan et al. [START_REF] Stephan | Optimizing opening dimensions for naturally ventilated buildings[END_REF] were interested in inverse methods for improving the performance of the natural ventilation in a room. By coupling SimSPARK [START_REF] Mora | Prédiction des performances thermo-aérauliques des bâtiments par association de modèles de différents niveaux de nesse au sein dun environnement orienté objet[END_REF] with an optimization software called GenOpt [START_REF] Michael | Genopt generic optimisation program[END_REF], they deduced the optimal size of the openings needed to maximize the performance of the natural ventilation.

Abadie et al. [START_REF] Abadie | Improving the prediction of zonal modeling for forced convection airflows in rooms[END_REF] implemented an in-house zonal model in order to improve airflow modelling of forced convection in building zones. Especially, they were interested in developing an accurate model of the jet mass flow. This model was validated on a one-zone building.

The zonal technique showed his efficiency in the description of flow profiles in building. However, such a detailed behaviour description is once again not always required and although it has been hugely enhanced with the zonal approach, the computation time can again be reduced by decreasing the complexity of the model. Thus, one more degree of simplification is proposed considering no more a multi-dimensional description of the building behaviour but a simple mono-dimensional visualization of the phenomenon occurring in the system.

The multizone or nodal approach 2.3.1. Principle of the nodal approach

This last approach, which is probably the simplest one is called the multizone technique (also called nodal method). It considers the following assumption : each building zone is an homogeneous volume characterised by uniform state variables. Thus, one zone is approximated to a node that is described by a unique temperature, pressure, concentration... Generally, a node represents a room, a wall or else the exterior of the building but it can be more specific like loads (internal occupancy or equipment gains, heating/cooling system). The thermal transfer equations are solved for each node of the system. In this term, the nodal method can be considered as a one-dimensional approach. Fig ( 3) is a scheme of the nodal modelling. TrnSys [START_REF] Klein | A transient simulation and program[END_REF], EnergyPlus [START_REF] Energyplus | eere.energy[END_REF], IDA-ICE [3], ESP-r [START_REF] Clarke | Esp-a building and plant energy simulation system[END_REF], Clim2000 [START_REF] Bonneau | Clim2000: modular software for energy simulation in buildings[END_REF][START_REF] Woloszyn | Whole building simulation tools: Clim[END_REF], BSim [START_REF] Rode | Whole building hygrothermal simulation model[END_REF][START_REF] Rode | Integrated calculation of hygrothermal conditions of buildings[END_REF] and BUILDOPT-VIE [25] are softwares using the nodal approach employed for building simulations.

In the literature, we can find two main methods used with the nodal approach: a first one consisting in solving transfer functions and a second one based on the finite difference method. Most software are designed from the first technique described by the transfer functions. The finite difference method is particularly employed for nodal approaches based on electrical analogies of walls introduced by Rumaniovski [START_REF] Rumaniovski | An adapted model for simulation of the interaction between a wall and the building heating system, Proceedings of the thermal performance of the exterior envelopes of buildings IV conference Orlando[END_REF]. It is very useful since it simplifies drastically the physical problem through a linearization of the equations and thus, reduces the computation time. The principle of the electrical analogy is to associate a thermal resistance R and a thermal capacity C to a wall. The analogy gives the following equivalence with the Ohm's law:

U 1 -U 2 = RI ⇔ θ 1 -θ 2 = e λ.S Φ L (2)
The temperature θ is equivalent to voltage U, the heat flux Φ L to current I and the thermal resistance e/λ.S to electrical resistance R. Several articles using this analogy have been published [START_REF] Mara | Empirical validation of the thermal model of a passive solar cell test[END_REF][START_REF] Fraisse | Development of a simplified and accurate building model based on electrical analogy[END_REF][START_REF] Gouda | Building thermal model reduction using nonlinear constrained optimization[END_REF][START_REF] Cron | Numerical analysis of hybrid ventilation performance depending on climate characteristics[END_REF][START_REF] Xu | Optimal simplified thermal models of building envelope based on frequency domain regression using genetic algorithm[END_REF][START_REF] Deng | Building thermal model reduction via aggregation of states[END_REF][START_REF] Bueno | A resistance-capacitance network model for the analysis of the interactions between the energy performance of buildings and the urban climate[END_REF][START_REF] Hazyuk | Optimal temperature control of intermittently heated buildings using Model Predictive Control: Part Ibuilding modeling[END_REF].

Advantages and application field of the nodal approach

The huge advantage of this technique resides in its ability to describe the behaviour of a multiple zone building on a large time scale with a small computation time. It is a particularly well-adapted tool for the estimation of the energy consumption and the time evolution of the space-averaged temperature into a room. Moreover, it can be used to predict the building air exchange rates and the airflow distribution between different rooms of a building. Some other applications as the ventilation efficiency or the pollutant transport for entire buildings can also be studied by this formulation [START_REF] Axley | Multizone Airflow Modeling in Buildings: History and Theory[END_REF][START_REF] Chen | Ventilation performance prediction for buildings: A method overview and recent applications[END_REF].

Concerning the electrical analogy, the main additional advantage is the simplicity to implement the transfer equations [START_REF] Bueno | A resistance-capacitance network model for the analysis of the interactions between the energy performance of buildings and the urban climate[END_REF].

Limitations of the nodal approach

Due to the simplification enclosed in the multizone approach, it has obviously some limitations to investigate some specific cases [START_REF] Mora | Comparing zonal and cfd model predictions of isothermal indoor airflows to experimental data[END_REF][START_REF] Abadie | Improving the prediction of zonal modeling for forced convection airflows in rooms[END_REF], better supported by the very complete CFD method.

• The study of the thermal comfort and the air quality inside a zone is quite difficult.

• The impact of loads on their close environment is not addressed (for example, a radiator with a plume).

• Despite the fact that it is a well-adapted method to study a multiple zone building, it is quite difficult to apply the nodal form to a room with a large volume.

• Although it is a good way to visualize the distribution of pollutant between some building zones, it does not allow to consider the local effects of a heat or pollutant source.

We propose in the following to give some examples of these methods and explain why the author chooses one method over another.

Examples

Kalogirou [START_REF] Kalogirou | Use of TRNSYS for modelling and simulation of a hybrid pvthermal solar system for cyprus[END_REF] used a multizone software TrnSys (Transient Simulation Program) [START_REF] Klein | A transient simulation and program[END_REF] to determine the energy consumption in a building in Nicosia, Cyprus. More specifically, the aim was to see how the energy demand behaves with a hybrid photovoltaic-thermal solar system (coupling of a normal PV panel and a heat exchanger) rather than a standard photovoltaic panel.

Ibanez et al. [START_REF] Ibanez | An approach to the simulation of PCMs in building applications using TRNSYS[END_REF] used the TrnSys software to study the efficiency of the phase change materials (PCM) in Lleida, Spain. To perform that, they considered a uniform indoor temperature in the room and determined its time evolution. By using the TrnSys software, they evaluated the influence of the PCM on different part of the envelope of the room (wall, ceiling and floor).

Zhai et al. [START_REF] Zhai | Assessment of natural and hybrid ventilation models in whole-building energy simulations[END_REF] studied the effects of the ventilation in summer on simulated data of indoor temperature with the multizone software EnergyPlus [START_REF] Energyplus | eere.energy[END_REF]. To achieve that, they compared experimental and simulated measures of indoor temperature in three distinct building offices: a single-story building with an automatically controlled air ventilation in Belgium, a three-story building with a manually controlled air ventilation in Denmark and another three-story building with an automatically controlled air ventilation in United Kingdom.

Cron et al. [START_REF] Cron | Numerical analysis of hybrid ventilation performance depending on climate characteristics[END_REF] used the electrical analogy to estimate the performance of hybrid ventilation. The system was composed of a fan assisted natural ventilation incorporating a control demand strategy based on indoor air temperature and CO 2 concentration.

More recently, Bueno et al. [START_REF] Bueno | A resistance-capacitance network model for the analysis of the interactions between the energy performance of buildings and the urban climate[END_REF] have developed an in-house resistance-capacitance model coupling the urban canopy with a building energy system. After a validation phase, they studied the effect of the urbanization on the energy consumption. And especially, they showed a 5% increase of cooling systems in summer totally compensated by a 5% decrease of the heating during winter in residential buildings. Moreover, they were interested in the influence of the indoor environment on the outdoor air temperatures.

Goyal and Barooah [START_REF] Goyal | A method for model-reduction of non-linear thermal dynamics of multi-zone buildings[END_REF] used the electrical analogy to implement a lumped thermal simulation model. It is able to predict the temperature and the humidity in multizone buildings from outside temperature and humidity, heat gains from occupants and solar radiation, supply air flow rates and supply air temperatures. Their objective was to decrease the order of this model by testing several reduction methods. Such scientific fields are really useful considering some applications such as HVAC control or monitoring.

Hazyuk et al. [START_REF] Hazyuk | Optimal temperature control of intermittently heated buildings using Model Predictive Control: Part Ibuilding modeling[END_REF] developed an in-house multizone model from the electrical analogy. They proposed a description of the walls and the floor by two identical resistances and one capacity. The thermal mass is characterized by a single capacity and windows by single resistances. Having this kind of simplified model allows to consider monitoring and control applications in more reasonable perspectives.

Discussion on the physical models

The previous paragraphs described several physical methods employed in the building modelling. We saw through the principles of each techniques and the previous examples that each physical method has its own application field. The most complete and detailed approach is the CFD. It allows to describe very finely each mechanism occurring in the building system. Especially, it is particularly adapted for modelling the convective phenomenon taking place in a large zone volume. For instance, we saw through the examples of Zhai et al. [START_REF] Zhai | On approaches to couple energy simulation and computational fluid dynamics programs[END_REF], Wang and Wong [START_REF] Wang | Coupled simulations for naturally ventilated residential buildings[END_REF] or Srebric et al. [START_REF] Srebric | On-site experimental validation of a coupled multizone and CFD model for building contaminant transport simulations[END_REF] the real necessity of using the CFD. Actually, in their study they treated very large volumes (office and auto racing complex) where the convective mechanisms are really complex. We mentioned above that the nodal approach assumes that the convection depends on the constant parameter h. So, it does not allow to treat large zones with a high accuracy. Thus, in these specific cases, the use of the CFD was necessary. However, it is difficult to simulate all phenomenon by using the CFD because of the huge computation time. This is the reason why it is usually coupled with nodal software as EnergyPlus or TRNSYS. The nodal approach is really well adapted to treat global resolution as the determination of uniform field. Contrary to the CFD, phenomenon are described less finely. The aim is to simplify as far as possible the resolution system by linearizing the major part of the equations (when it is physically possible). Thus, the technical complexity is significantly reduced and both the computation time. For instance, Kalogirou [START_REF] Kalogirou | Use of TRNSYS for modelling and simulation of a hybrid pvthermal solar system for cyprus[END_REF] chose the nodal method because on the one hand, its studied system was constituted of several interconnected zones and on the other hand, he was interested in a specific macroscopic variable (energy consumption) and not in the distribution field. In the same way, Goyal and Barooah [START_REF] Goyal | A method for model-reduction of non-linear thermal dynamics of multi-zone buildings[END_REF] and Hazyuk et al. [START_REF] Hazyuk | Optimal temperature control of intermittently heated buildings using Model Predictive Control: Part Ibuilding modeling[END_REF] showed the necessity of the multizone method via the electrical analogy in control and monitoring perspectives. The zonal method is an intermediate technique between nodal and CFD approaches. It is less accurate than the CFD but retains more informations compared to the nodal technique. As examples, Musy et al. [START_REF] Musy | Automatically generated zonal models for building air ow simulation: principles and applications[END_REF], Tittelein et al. [START_REF] Tittelein | Simspark platform evolution for lowenergy building simulation[END_REF] or Haghighat [START_REF] Haghighat | Development and validation of a zonal model POMA[END_REF] justified their choice of the zonal approach by the necessity to reduce the computation time compared with a CFD and the inability of the nodal method to provide detailed temperature and flow distribution and, in the same way, to predict the thermal comfort.

Moreover, all these techniques need some input parameters as meteorological data, geometrical data, thermo-physical variables or else occupancy and equipment scenario... However, these parameters are always expressed under a certain part of uncertainties. Furthermore, in addition to these parameter uncertainties, there are also the uncertainties induced by the assumptions. Actually, several assumptions with consequences on the model performance have to be made in order to reduce the complexity of the thermal mechanisms occurring in buildings. Thus, all these uncertainties lead to a real difficulty to evaluate the accuracy degree of the models. Consequently, it seems very hard to gather all heat building transfers in a general overview without accumulating too much uncertainties [START_REF] Macdonald | Quantifying the Effects of Uncertainty in Building Simulation[END_REF].

We propose to gather in Table (1) the specificity of each method.

Generally, an important default of the physical formulation is the fact that it suggests a detailed description of the physical behaviour. So, it implies expensive knowledge on the physical system, especially on the mechanisms occurring inside and outside the building geometry. Unfortunately, as we mentioned above, it is far from being always the case. In contrast, the statistical tools have the great faculty to product a model only from measures. So we propose now to detail some statistical techniques frequently used in the building simulation and energy performances for prediction.

Statistical methods using machine learning

The particularity of statistical models compared with physical methods is the fact that they do not require any physical Several statistical tools are able to build prediction model using learning methods. The great power of these techniques is the fact that they do not need to have much knowledge on the building geometry or the detailed physical phenomena to deduce an accurate prediction model. In contrast, they are totally based on measures and in such cases where it is difficult to collect data, it can become a real issue. Some of these methods have already been referenced by Zhao and Magoulès [START_REF] Zhao | A review on the prediction of building energy consumption[END_REF] .

We propose in the following part of this paper to describe the statistical techniques mainly employed in the field of the building energy forecasting: the linear multiple regression, the artificial neural network, the genetic algorithm and the support vector machine. These techniques belong to the branch of the artificial intelligence.

Each sections are designed in the following manner: a first part describes succinctly the principle of the method, a second part shows the advantages and drawbacks of the method, a third part presents the application field and a last part gives some examples using the method.

Multiple linear regression or conditional demand analysis (CDA)

The conditional demand analysis (CDA) is a linear multivariate regression technique applied to the building forecasting. The linear regression was introduced by Galton in 1886. In 1980, Parti and Parti were the first to propose a new method using the linear regression for the prediction of energy consumption in buildings : the conditional demand analysis [START_REF] Parti | The total and appliance-specific conditional demand for electricty in teh houshold sector[END_REF]. The idea was to deduce the energy demand from the sum of several end-use consumption added to a noise term. In this way, they could infer the monthly and yearly residential end-use consumption from household invoices in San Diego.

Principle of the CDA

The principle of the linear multivariate regression is to predict Y as a linear combination of the input variables (X 1 , X 2 , ..., X p ) plus an error term i .

y i = α 0 + α 1 .x i1 + α 2 .x i2 + ... + α p .x ip + i , i ∈ [1, n] (3)
n is the number of sample data, p the number of variables and α 0 a bias. For example, if the predicted output is the internal temperature, there can be as inputs the external temperature, the humidity, the solar radiation and the lighting equipment.

Advantages and limitations of the CDA

The CDA technique can be used both for prediction or forecasting and for data mining. This method has a main advantage which is the simplicity of use by beginners since no parameter has to be tuned. Indeed, no specific expertise of the method is required to manage such type of prediction method.

However, the multiple linear regression presents a major limitation due to its inability to treat non linear problems. It leads to a lack of flexibility in forecasting but also a real difficulty to manage the multicollinearity inside the prediction results (that is the correlation between several variables). A possible solution to overcome these difficulties is to use a preliminary feature selection formulation.

Application field in CDA

In the building sector, the multivariable regression is often used for forecasting energy consumption or comparing the evolution of energy demand between two different periods. However, it is also employed for the prediction indoor air conditions, the control of HVAC equipment, reliability aspects and systems management [START_REF] Lam | Regression analysis of high-rise fully air-conditioned office buildings[END_REF][START_REF] Freire | Development of regression equations for predicting energy and hygrothermal performance of buildings[END_REF]. The constraint is mostly present on data. Indeed, a large amount of data is required for a proper prediction and moreover the non collinearity between variables is necessary [START_REF] Aydinalp-Koksal | Comparison of neural network, conditional demand analysis, and engineering approaches for modeling enduse energy consumption in the residential sector[END_REF].

In the following, we will present some examples using the CDA for a building application.

Examples

Lafrance and Perron [START_REF] Lafrance | Evolution of residential electricity demand by end-use in quebec 1979-1989: A conditional demand analysis[END_REF] studied the evolution of the residential electricity demand at the regional level of Quebec in Canada. More specifically, they used the CDA as a signal processing tool and compared three years of data: 1979, 1984 and 1989.

Tiedermann [START_REF] Tiedermann | Using conditional demand analysis to estimate residential energy use and energy savings[END_REF] analysed the annual end-use consumption and the energy savings in the region of British Columbia in Canada. They studied also the energy consumption month by month and found two sudden increases: the first peak corresponds to November, December, January and February and is probably due to the use of the electric space heating and heating water. The second peak concerns the months of June, July and August and is related to the use of the air conditioning (central or portable).

Aydinalp-Koksal and Ugursal [START_REF] Aydinalp-Koksal | Comparison of neural network, conditional demand analysis, and engineering approaches for modeling enduse energy consumption in the residential sector[END_REF] used the CDA to model the residential end-use energy consumption in Canada at the national level. They kept their interest on several end-uses : appliances, lighting, space cooling, space heating and domestic hot water. Different energy sources have been studied: electricity, natural gas and oil. Each end-uses for each kind of energy were described by a linear regression.

More recently, Aranda et al. [START_REF] Aranda | Multiple regression models to predict the annual energy consumption in the spanish banking sector[END_REF] has implemented a multiple linear regression model which allows to predict the energy consumption in the banking sector in Spain and to suggest energy saving strategies to increase the energy efficiency. The authors chose a model able to combine the simplicity of the evaluation method and the accuracy in the result without needing a huge amount of input data.

For other applications, Givoni and Vecchia [START_REF] Givoni | Predicting thermal performance of occupied houses[END_REF] proposed to use multivariate linear regression to describe the daily indoor average, minimal and maximal temperatures from outdoor measurements in occupied houses in Descalvado, Brazil. They found that all these temperatures can be predicted only from outdoor average, minimal and maximal temperatures. However, they showed that it is possible to improve the prediction of the indoor maximal temperature by adding the contribution of the solar radiation. Likewise, they improved the prediction of the minimal temperature by incorporating the dependence of the daily diurnal swings.

Few years later, Krüger and Givoni [START_REF] Krüger | Predicting thermal performance in occupied dwellings[END_REF] showed that it is possible to reproduce from linear regression equations the indoor temperature behaviour in occupied low-cost houses in Curitiba, Brazil. More specifically, they linked linearly the average, minimal and maximal indoor temperatures to the average, minimal and maximal outdoor temperatures.

Nevertheless, due to the non flexibility of the method, it is very difficult to apply the linear regression techniques for the data analysis. The following method is able to predict both linear and non linear problem. It is called genetic algorithm.

Genetic algorithm (GA)

The genetic algorithm (GA) is a stochastic optimization technique deduced from an analogy with the evolution theory of Darwin. This artificial intelligence method has been introduced in 1975 by Holland [START_REF] Holland | Adaptation in natural and artificial systems[END_REF] but its use as an optimization tool for the building simulation started in the 1990's.

Principle of the GA

The principle of the genetic algorithm is based on the faculty of a given species to adapt itself to a natural environment and to survive extreme conditions. The genetic information is given by the gene sequences contained in the chromosome of an individual. In the GA process, all input variables are contained into one chromosome. This information can be coded in different way : binary, character string and tree. We will describe now the different step of the GA.

(1) Production of the original population.

(2) Evaluation of each chromosome based on the fitness value.

(3) Selection, crossover and mutation. The selection is responsible for selecting (at least) two chromosomes. After the selection step, the crossover phase can intervene, dealing with the exchange of a part of the information between the parents chromosomes. Then, the mutation operation can occur, consisting in in the substitution of a part of a chromosome by another.

(4) Insertion of the new chromosomes in the population. At the end of the above processes (selection, crossover and mutation), some new chromosomes are added to the old population for creating the new one.

(5) Process reiteration. Once we have reach this step, the process restarts with the second step on the new population until the user specified generation number is completed.

Fig ( 4) shows a scheme of the general operations in the genetic algorithm.

In the building simulation, GA is used to find a prediction model. The goal is to find a simple equation able to fit the problem. The form of the equation imposed by the user can have the following forms:

• linear Y = w 1 .X 1 + ... + w n .X n • quadratic Y = w 1 .X 1 +...+w n .X n +w l .X 1 .X 2 +...+w m .X 1 .X n + w p .X 2 .X 3 + w k .X n .X n-1 + w q .X 2 1 + ... + w r .X 2 n + w s • exponential Y = w 1 + w 2 .X w 3 1 + w 4 .X w 5 2 + ... + w l .X w l+1
n Y is the output (for example the energy demand), X i are the input variables (for example the outdoor temperature, the humidity, the solar radiation and the exposure) and w i are the weighting of each input variables. The GA is used to optimize the weighting w i of each variables.

Advantages and limitations of the GA

An important advantage of genetic algorithm is the fact it deals with a powerful optimization method able to resolve every problems provided the convexity of the describing function [START_REF] Caldas | Genetic algorithms for optimization of building envelopes and the design and control of hvac systems[END_REF]. Another essential advantage of the genetic algorithm is its ability to give several final solutions to a complex problem with a large number of input parameters. It allows the user to choose with his own judgement the most probable one. Obviously, this is also a drawback by the fact that the user can never be sure to have chosen the best solution, especially as the GA will not necessary generate the optimal solution. Another disadvantage of the GA is the large computation time. Some authors try to reduce this computation time by coupling the genetic algorithm with other statistical methods. Especially, Magnier and Haghigat [START_REF] Magnier | Multiobjective optimization of building design using TRNSYS simulations, genetic algorithm, and artificial neural network[END_REF] associated an artificial neural network to a genetic algorithm for estimating energy consumption and thermal comfort in a building. Another difficulty of the GA is the adjustment of the algorithm. Indeed, no rules are able to determine the number of individuals in the population, the number of generation or crossover and mutation probability. So, the only way to adjust the model is to test different combination. Another important limitation of the GAs is their capacity to generate local optimum leading to study the system locally instead of globally. Finally, the performance of the GA is really limited when the individuals present a similar evaluation value. In this case, the genetic algorithm can no longer evolve. Moreover, in this specific case, an important drawback is the fact that it is absolutely essential to postulate the form of the describing function.

Application field of the GA

In the building simulation, the genetic algorithm is mainly used for the determination of simple prediction models of the energy consumption and for the optimization of the equipment/load demand. The data basis can be both simulated or real and can contain instantaneous samples on several time scale (hourly, monthly or yearly) or samples averaged in time and/or space. As the CDA, a large amount of data is required.

We propose now to give some examples of works using the genetic algorithm.

Examples

Ooka and Komamura [START_REF] Ooka | Optimal design method for building energy systems using genetic algorithms[END_REF] were interested in the energyefficiency in building during a day. With two genetic algorithms, they provided the optimized combination of equipment capacity and optimized operational planning for cooling system during a period of 24 h with an electric turbo refrigerator and a heat pump and water heating system with two distinct heat pumps for hot water. For the equipment capacity, the authors used an algorithm with a population size of 10 individuals (2 sub-populations with a size of 5 individuals), a number of generation of 30, a crossover probability of 1, a mutation probability of 0.01 and a migration probability of 0.5. For the operation planning, the GA presented a population size of 24 individuals (3 sub-populations with a size of 8 individuals), a number of generation of 750, a crossover probability of 1, a mutation probability of 0.01 and a migration probability of 0.5. This work was applied to an hospital of Tokyo in Japan on a period of 24 hours.

Sadeghi et al. [START_REF] Sadeghi | Estimation of electricity demand in residential sector using genetic algorithm approach[END_REF] used the GAs to implement optimized prediction models of the annual electricity consumption per inhabitant in residential sector in Iran. Three forms of simple equations are tested: linear, quadratic and exponential. Their variables are the annual gross domestic product, the annual real price of electricity and the annual real price of natural gas. The population size is 60 individuals, the number generation raises to 400, the probability crossover is equal to 0.5 and the probability mutation 0.02. The fitness was evaluated by the reverse of the sum squared error. Thus, the criterion was to maximize the fitness value. The selection process was the roulette-wheel method.

In the same manner, previous works of Ozturk et al. [START_REF] Ozturk | Electricity estimation using genetic algorithm approach: a case study of Turkey[END_REF] studied the annual electricity consumption estimation in Turkey evaluated in the industrial sector and in the total electricity demand. The authors implemented two prediction models of the annual electricity consumption for both industrial and total turkish demand, allowing to predict the annual electrical demand from 2002 to 2025.

Nevertheless, it remains the problem due to the postulate of the kind of function. The following technique overcomes that by running as a black-box system. It is called the artificial neural network. Moreover, Datta et al. [START_REF] Datta | Application of neural networks for the prediction of the energy consumption in a supermarket[END_REF] compared the linear regression with the artificial neural network. They showed that this non linear technique performs quite better than the linear one. In the next part, we propose to introduce this technique and to give some examples from the literature.

Artificial neural network (ANN)

The artificial neural network (ANN) is a non-linear statistical technique principally used for the prediction. This artificial intelligence method was inspired by the central nervous system with their neurons, dendrites, axons and synapses. It has been introduced in its mathematical form by McCulloch and Pitts in 1943. They published with Lettvin and Maturana the first works on the neural network in 1959 [START_REF] Lettvin | What the frog's eye tells the frog's brain[END_REF].

Principle of the ANN

The basic mono-layer ANN containing just two layers (input and output neurons) is described as the following steps:

(1) Choice of the inputs x i considering the output(s). An initialisation step associates each input to a weight w i randomly chosen. The inputs are the neurons of the first layer.

(2) Application of the activation function f on the aggregation function. Most of the time, the aggregation function is a linear combination as:

I = f        n i=0 w i .x i        (4)
n is the number of input neurons and the product for i = 0 is the bias. The activation function is responsible for converting the weighted input into an output activation. It returns a number between 0 and 1, allowing to maintain the convergence (for example, sigmoid, Heaviside step or hyperbolic function). Fig [START_REF] Abadie | Improving the prediction of zonal modeling for forced convection airflows in rooms[END_REF] shows a scheme of one neuron layer.

Advantages and limitations of the ANN

An advantage of the ANN is that it does not need to detect the potential collinearity. Moreover, given their training faculty, another advantage of the ANN is its ability to deduce from data the relationship between different variables without any assumptions or any postulate of a model. Furthermore, it overcomes the discretization problem and is able to manage the data unreliability. Finally, the ANN suggests a large variability of the predicted variable form (yes/no, binary 0 or 1, continuous value...) and an efficient simulation time [START_REF] Kalogirou | Artificial neural networks for the prediction of the energy consumption of a passive solar building[END_REF].

However, the ANNs are significantly limited by the fact that this implies to have a relevant data basis. Indeed, it is really important to train an ANN with an exhaustive learning basis with representative and complete samples (for example, samples in different seasons or in different moments of the day or during week-end/holidays... and samples with each the same amount of informations). Another disadvantage of the ANN is its large number of undetermined parameters (with no rules to determine them).

Application field of the ANN

In the building simulation, the artificial neural network are usually used for the prediction of the energy consumption or the forecasting of energy use as the cooling or heating demand without knowing the geometry or the thermal properties of the building. Different kind of data basis can be considered depending on the time scale as the hour, the month or the year and the nature of the data (real or simulated and instantaneous or time/space-averaged data). One main condition is absolutely essential for applying the artificial neural network technique : the completeness of the learning data. Kalogirou has published many works on the building applications using the ANN [START_REF] Kalogirou | Building heating load estimation using artificial neural networks[END_REF][START_REF] Kalogirou | Artificial neural networks for the prediction of the energy consumption of a passive solar building[END_REF][START_REF] Kalogirou | Applications of artificial neural-networks for energy systems[END_REF][START_REF] Kalogirou | Use of TRNSYS for modelling and simulation of a hybrid pvthermal solar system for cyprus[END_REF]. Particularly, in 2000, he presented a bibliographic review summing up the applications of the ANN in the field of energy-engineering systems [START_REF] Kalogirou | Applications of artificial neural-networks for energy systems[END_REF].

To illustrate that, we propose now to give some examples using the ANN for building applications.

Examples

Kalogirou and Bojic [START_REF] Kalogirou | Artificial neural networks for the prediction of the energy consumption of a passive solar building[END_REF] published a paper dealing with the prediction of the energy consumption of a passive solar holiday home in Cyprus during a day in summer and in winter. The inputs are the season, characteristics of the insulation, the masonry thickness, characteristics of the heat transfer coefficient and time of the day. The output is the energy consumption in kWh with a time-step of 10 minutes. The authors used a recurrent neural network containing four layers with 23 neurons on the hidden layers.

Aydinalp et al. studied the canadian annual electricity consumption in residential sector of appliances, lighting and cooling in a first paper (ALC) [START_REF] Aydinalp | Modeling of the appliance, lighting, and space-cooling energy consumptions in the residential sector using neural networks[END_REF], and of space heating (SH) and domestic hot water (DHW) in a second paper [START_REF] Aydinalp | Modeling of the space and domestic hot-water heating energy-consumption in the residential sector using neural networks[END_REF]. In the first one, many inputs were used as appliances, weather, lighting, total heated area, socio-economic factors, etc... These informations were propagated along a feed-forward network containing one input layer with 55 neurons, three hidden layers each of them including 9 neurons, and one output layer with one neuron representing the average of the annual electricity consumption due to the ALC.

Neto and Fiorelli [START_REF] Neto | Comparison between detailed model simulation and artificial neural network for forecasting building energy consumption[END_REF] compared both an ANN model and a building software EnergyPlus for the forecasting of the energy demand in an administration building in Sao Paulo, Brazil. Two ANN model were tested: the first is a feed-forward neural network containing three layers : one input layer with 5 neurons (external temperature, humidity, two solar radiation parameters and day-type), one hidden layer with 21 neurons and one output layer with 1 neuron (daily total consumption). The second is a simpler ANN with only the external and internal temperature as inputs. The results for both simple ANN and complex ANN appeared to be very near, indicating that the humidity and the solar radiation were certainly less significant than the external temperature for the forecasting of energy demand in this specific building study.

Recently, Kwok and Lee [START_REF] Kwok | A study of the importance of occupancy to building cooling load in prediction by intelligent approach[END_REF] studied the influence of the occupancy on the cooling load in Hong-Kong, China. They compared three different neural networks called probabilistic entropy-based neural network (PENN) to predict the total building cooling load : a first ANN containing 6 neurons on the external layer each of them characterizing a weather parameter, a second ANN with one more neuron (so 7 external neurons in total) for the hourly total occupancy area and a third ANN with another one more neuron (so 8 external neurons in total) corresponding to the occupancy rate (modification induced by the human presence). They found the best fitting between real data and the prediction for the last model (with 8 external neurons). It shows the huge influence of the occupancy on the building cooling load.

Moreover, Escriva-Escriva et al. [START_REF] Escriva-Escriva | New articial neural network prediction method for electrical consumption forecasting based on building end-uses[END_REF] predicted the energy consumption based on building end-uses in University of Valencia,, Spain. They used an ANN with multi-layer perceptron architecture consisting on three layers. The input layer contains four neurons (maximum temperature, minimum temperature, average temperature on just one day period and the average temperature on the day before), the hidden layer contains 3 neurons and the output layer consists in one neuron characterizing the energy consumption.

Recently, Leung et al. [START_REF] Leung | The use of occupancy space electrical power demand in building cooling load prediction[END_REF] used the artificial neural network to predict the cooling load in a university building in Hong-Kong. They took care of the occupancy by introducing a power demand. Thus, the inputs parameters are climatic data, hour and day type and pretreated air unit operation schedule. The output is the electrical power demand of the building cooling system. They used a feed-forward network with three layers. They found promising results when the cooling load is higher than the occupancy power demand.

However, the ANN is hugely limited by its lack of interpretability and the fact that it requires a large amount of learning data and mainly a relevant and completeness data basis (that is no missing data in the data basis and same amount of information for each variables). The following technique overcomes these difficulties given that it supports heterogeneous data basis and introduces a describing function. This method is called the support vector machine.

Support vector machine (SVM)

The support vector machine (SVM) has been introduced in 1995 by Vapnik and Cortes [START_REF] Cortes | Support-vector networks[END_REF]. This artificial intelligence technique is usually used to solve classification and regression problems. We will focus our interest only on regression.

Principle of the SVM for regression

The principle of the SVM for regression is to find the optimal generalization of the model, in order to promote sparsity. Let us consider a given training data [(x 1 , y 1 ), ..., (x n , y n )], x i being in the input space and y i in the output space. In a non linear problem, the basic idea is to overcome the non-linearity by transforming the non linear relation between x and y in a linear map. The way to do that is to send the non linear problem in a high dimensional space called the feature space. As all regression techniques, the aim is to determine the function f (x) that fits best the behaviour of the problem. The particularity of the SVM is the fact that it authorizes an error or an uncertainty around the regression function. The function f has the following form:

f (x) =< ω, Φ(x) > +b (5)
Φ represents a variable in the high dimensional feature space and <, > a scalar product. ω and b are estimated by the following optimization problem called the primal objective function.

It corresponds to a minimization of the norm min

ω,b,ξ i ,ξ * i 1 2 || ω || 2 +C n i=1 ξ i + ξ * i (6) subject to            y i -< ω, Φ(x i ) > -b ≤ + ξ i < ω, Φ(x i ) > +b -y i ≤ + ξ * i ξ i , ξ * i ≥ 0
C is a regularization parameter (a trade-off between the flatness of f and the maximal tolerated deviation larger than ) imposed by users, ξ i and ξ * i are two slack variables allowing a flexibility of the constraints. Moreover, by introducing a kernel function defined as a dot product in the feature space k(x, x ) =< Φ(x), Φ(x ) >, it allows to substitute a complex non linear map to a linear problem without having to evaluate Φ(x).

Advantages and limitations of the SVM

The main difficulty in the SVM is to select the best kernel function corresponding to a dot product in the feature space and the parameters of this kernel function. Some examples of kernel function mainly used in regression by SVM are given below:

• the linear kernel k(x i , x) = x i .x • the polynomial kernel k(x i , x) = (x i .x + c) d • the radial basis function (RBF) kernel k(x i , x) = e ||x i -x|| 2 2σ 2
In addition to the kernel function parameters, two others constants have to be adjusted by users: the regularization constant C and the deviation .

The main advantage of the SVM is the fact that the optimization problem is based on the structural risk minimization principle (SRM). It deals with the minimization of an upper bound of the generalization error consisting of the sum of the training error. This principle is usually confronted to the empirical risk minimization (ERM) which only minimizes the training error. Another advantage is the fewer free parameters of optimization. Indeed, using the SVM technique required the adjustment of the regularization constant C and the margin . In contrast, the ANN method requires to know the topology of the inter-connections between neurons, the aggregation function, the number of hidden layers, the number of neurons on each hidden layers, the activation function, the learning algorithm (with the error calculation) and the learning value. In the same way, to implement a GA, we need to adjust the population size, the number of generation, the crossover probability and the mutation probability.

Application field of the SVM for regression

In building field, the SVM is mainly used for the forecasting of energy consumption or temperature. The system can be trained from different kind of data with various time scale (year, month, hour) and various nature (instantaneous or space/time averaged). There is usually no restriction on the data basis except the fact that vector data are required. And a huge advantage is the fact that it supports a heterogeneous data basis that a data basis where all variables do not have the same amount of information or where we can find missing data.

We will now focus our interest on the use of SVM in building prediction. We propose in the following part to introduce some examples.

Examples

The use of support vector machine in the forecasting of energy consumption in buildings is quite recent. In 2005, Dong et al. [START_REF] Dong | Applying support vector machines to predict building energy consumption in tropical region[END_REF] were the first to use SVM for the prediction of the building energy consumption. The aim was to predict the monthly energy consumption in four offices in Singapour. The input variables are the mean outdoor dry-bulb temperature, the relative humidity and the global solar radiation. The kernel function used is the radial basis function kernel.

Lai et al. [START_REF] Lai | Vapniks learning theory applied to energy consumption forecasts in residential buildings[END_REF] employed the SVM as a data mining tool for the prediction of the electrical consumption in residential sector in the region of Tohoku, Japan. Authors took as input parameters climate data as outdoor and indoor temperatures and humidities. They used the KXEN software [2] which consists in the implementation of the SVM method.

Li et al. [START_REF] Li | Predicting hourly cooling load in the building: A comparison of support vector machine and different artificial neural networks[END_REF][START_REF] Li | Applying support vec-tor machine to predict hourly cooling load in the building[END_REF] used the SVM in regression for the prediction of hourly cooling demand in Guangzhou, China. The aim was to predict the cooling demand hour by hour during summer in an office building. The input parameters are the outdoor dry-bulb temperature, the relative humidity and the global solar radiation. The SVM used as the kernel function a radial basis function.

Kavaklioglu [START_REF] Kavaklioglu | Modeling and prediction of turkeys electricity consumption using support vector regression[END_REF] used the support vector regression method to predict the electricity consumption in Turkey until 2026. The kernel function is the radial basis function. The input variables are socio-economic parameters as population, Gross National Product, imports and exports.

Paniagua-Tineo et al. [START_REF] Paniagua-Tineo | Prediction of daily maximum temperature using a support vector regression algorithm[END_REF] employed support vector regression method to model and predict the daily air outdoor temperature in several European countries. The model depends on many prediction variables as the maximum and minimum temperature, the precipitation, the relative humidity, the air pressure, the global radiation, the specific synoptic situation of the day and the so called monthly cycle. The kernel function is a Gaussian function.

Che et al. [START_REF] Che | An adaptive fuzzy combination model based on self-organizing map and support vector regression for electric load forecasting[END_REF] proposed to develop an adaptive fuzzy rule based prediction system combining the SVM in regression and a fuzzy inference method with the aim to forecast the electrical load in New South Wales. The authors used the radial basis function as kernel function.

Chen et al. [START_REF] Chen | Estimation of monthly solar radiation from measured temperatures using support vector machines e a case study[END_REF] estimated the monthly mean daily solar radiation in Chongqing, China via the support vector machine method. More particularly, the aim was to improve the state of data collected in the station. The authors chose to test three different kernel function: linear, polynomial and radial basis function. Also, they proposed to experiment seven combinations of input variables only based on the maximum temperature and the minimum temperature. Finally, they implemented 21 different SVM system.

Discussion on the statistical tools

Contrary to the physical techniques which are each associated with a specific application, we realize that no statistical tool has a better use for a problem than another. However, it is possible to classify them by complexity. Indeed, the linear multiple regression is probably the easier statistical method. It is able to give good prediction and does not need a real expertise to be implemented. But it is hugely limited by the fact that it assumes a linear description of phenomenon. The genetic algorithm is a bit less limited because it is able to treat both linear and non linear problems. But it suggests that the function describing the system behaviour is well-known. However, it is rarely the case. The artificial neural network overcomes this problem given that it does not need to give specific description. Nevertheless, it runs as a black-box system which makes the interpretability very difficult. Moreover, an important drawback of the ANN is the fact that it requires a large amount and a completeness of learning data. In contrast, the support vector machine has the huge advantage to do not need an exhaustive data basis. And due to the known kernel function, the problem remains interpretable. However, contrary to the artificial neural network, it requires to assume the form of the kernel function. Finally, we see that each of these statistical techniques has his own advantages and drawbacks and the choice of the method depends mainly on the user and on what he expects at the end of the study. So, the technique can be chosen according to the targeted outcome. We propose to sum up the specificity of each statistical technique in Table (2).

Hybrid models

The previous parts of this article showed the capacity of both detailed physical and statistical method in the building simulation. But they showed also the limitations of each techniques. Especially, the white box methods assume that all building characteristics, both thermal and geometric one, are well-known. This is usually the case for building design but it is more difficult to collect so many informations on existing buildings. However, to establish monitoring strategies, they are absolutely required. Moreover, these approaches suggest that we are able to describe all physical mechanisms with a high accuracy. Nevertheless, although most of the thermal phenomenon are wellknown, some of them are based on assumptions and remain difficult to model accurately as the natural ventilation often described by empirical equations. The black box methods are mainly limited by the fact that they absolutely required data and mostly in large amount. Moreover, it is usually difficult to interpret results obtained by statistical approaches in physical term. Otherwise, data mining techniques are specific to a building. Thus, the treatment of another building leads to a new modelling. In contrast, due to the general heat transfer equations, white box methods are usually applied generally.

It is possible to overcome the limitations of each techniques by coupling them. Indeed, the advantages of a method remove the drawbacks of the other one. For example, by retaining a part of physical meaning, one keeps always the interpretability of the problem. Moreover, building characteristics can be determine by optimization techniques as genetic algorithms. Thus, all physical and geometrical input parameters are not any more required. These hybrid methods combining physics and statistics are called "grey box" methods.

Principle of the hybrid approach

Generally speaking, the principle of the hybrid method are based on the coupling of statistical methods and physical models. In this way, several strategies are available.

A first strategy consists in using machine learning as physical parameters estimator. We will see in the following examples that most of the time, scientists couple a nodal model with genetic algorithms.

A second strategy is to use statistics in order to implement a learning model describing the building behaviour. This learning model is designed from a learning basis built from a physical approach. In the following, we will present some examples employing this technique.

A third strategy consists in using statistical method in fields where physical models are not effective and accurate enough. For example, end-uses are known to be really difficult to take into account in physical models. In contrast, statistical techniques allow to well-consider these end-uses. So, a solution would be to associate both physical and statistical methods in order to implement the complete system. Another application would be to determine the heat behaviour in a multiple zones building where the thermal properties of some rooms would be unknown. Thus, some zones could be physically studied while others would need to be described statistically via measurements collected in these zones. This strategy is currently not referenced in the building simulation literature. However, it has already been proven in other fields as the prediction of the battery behaviour [START_REF] Saha | An integrated approach to battery health monitoring using bayesian regression and state estimation[END_REF].

Advantages and limitations of the hybrid methods

The main advantage of the hybrid method is that it allows to consider only a limited number of data. Furthermore, the input parameters do not need to be fixed at the initial time of the simulation. Only bounds on physical parameters are required. Thus, a rough description of the building geometry and thermal parameters is sufficient. Also, the hybrid methods allow to retain a physical interpretation.

However, some drawbacks proper to each technique remain in hybrid method as the free parameters for statistical tool or the computation time needing for both physical or statistical codes.

A last drawback that is also an advantage is the fact that the grey box method couples two distinct scientific domains. Although it brings some difficulties for users to understand, it should be of a great scientific interest.

Application field of the hybrid method

This approach has been introduced at the beginning of the 1990's for a specific application which was the automatic control system. For example, Teeter and Chow [START_REF] Teeter | Application of functional link neural network to HVAC thermal dynamic system identification[END_REF] combined an artificial neural network with a single-zone thermal model to improve the efficiency of the HVAC control by performing the HVAC parameters identification. Other more recent examples are the works of Paris et al. [START_REF] Paris | Heating control schemes for energy management in buildings[END_REF][START_REF] Paris | Hybrid pid-fuzzy control scheme for managing energy resources in buildings[END_REF] who combined the fuzzy logic, a PID controller and a dynamic model describing the thermal behaviour of the building for implementing several heating control schemes. Furthermore, Nassif et al. [START_REF] Nassif | Optimization of hvac control system strategy using two-objective genetic algorithm[END_REF] applied an optimization process to HVAC system for monitoring issues. It consisted in identifying the zone air temperatures, the supply air temperature, the supply duct static pressure, the zone supply air temperature or reheat required, the minimum outdoor ventilation flow rate, and the chilled water supply temperature. In the same applications, we can also point out the work of Caldas and Norford [START_REF] Caldas | Genetic algorithms for optimization of building envelopes and the design and control of hvac systems[END_REF] on the control of HVAC systems.

As we mentioned above, another application of the hybrid model is the parameters identification. In this approach, the aim is to compute the set of input values corresponding to a given set of outputs. For instance, the objective may be to calculate the optimal thermal properties of the walls (conductivity, capacity, etc) given a target consumption/comfort level. The technique is to combine physical models -used to simulate the thermal behaviour of the building -and statistical technique to retrieve the set of optimal inputs corresponding to the desired outputs.

Concerning the amount of data required, it is quite reasonable by the fact that it includes a part of physical interpretation inside the program.

In the literature related to the subject, some papers focus on the coupling between nodal techniques for the thermal and geometrical representation and genetic algorithms for the parameters identification. We propose to detail some examples using the hybrid method in this specific way.

Examples

Lauret et al. [START_REF] Lauret | A genetic algorithm applied to the validation of building thermal models[END_REF] implemented a model resolving the state equations in a building with a very simple geometry in the Island of the Reunion in order to follow the evolution of the indoor dry air temperature. To do that, they combined a physical resolution by the finite difference method via the multizone software CODYRUN [START_REF] Boyer | A multimodel approach to building thermal simulation for design and research purposes[END_REF] with a genetic algorithm. The study is based on experimental data. The authors have shown in previous studies that the physical model alone was not allowed to return a good agreement with the real data [START_REF] Mara | Empirical validation of the thermal model of a passive solar cell test[END_REF][START_REF] Miranville | On the thermal behavior of roof-mounted radiant barriers under tropical and humid climatic conditions: modelling and empirical validation[END_REF]. In this study, they used the genetic algorithm to isolate the defective node measurement by forcing the value of some temperatures in specific place of the building. The aim is to optimize the value of the indoor dry air temperature.

Znouda et al. [START_REF] Znouda | Optimization of mediterranean building design using genetic algorithms[END_REF] studied energy consumption in a Mediterranean building in Tunisia. More specifically, they found the solutions to improve both the energy efficiency and the economic point of view by optimizing architectural parameters. To perform that, they coupled a simplified tool for building thermal evaluation specific to the Mediterranean countries called CHEOPS [START_REF] Ghrab-Morcos | CHEOPS: a simplified tool for thermal assessment of Mediterranean residential buildings in hot and cold seasons[END_REF] to a genetic algorithm for the architectural parameters identification. They studied the energetic and economic problem independently. The authors studied a solution adapted both in summer and in winter. They showed that it is difficult to solve this kind of multi-objective issue composed of two independent problems (energetic and economic) because the optimal solutions are different considering either saving energy or saving money.

Wang and Xu [START_REF] Wang | Simplified building model for transient thermal performance estimation using GA-based parameter identification[END_REF][START_REF] Wang | Parameter estimation of internal thermal mass of building dynamic models using genetic algorithm[END_REF] studied the building thermal transfer in summer in Hong-Kong. The building consists of three different buildings one of them containing offices, another a shopping center and the last one a restaurant. The study was based on data collected during a survey conducted in order to deduce the profile of occupancy and use of the lighting and equipment. They used the electrical analogy to predict the heating/cooling load by substituting the building envelope (the roof and the external wall) by two different 3R2C systems and by introducing an internal mass by a 2R2C system. The internal mass corresponds to all others heat storage materials as furnitures, carpet, partitions, equipment,... Combining the equations resolution with the genetic algorithm for the parameter identification, the authors optimized the values of the resistances and capacitances of the internal mass.

Tuhus-Dubrow and Krarti [START_REF] Tuhus-Dubrow | Genetic-algorithm based approach to optimize building envelope design for residential buildings[END_REF] implemented an hybrid model by combining the nodal software DOE-2 [START_REF] Winkelmann | doe-2 supplement, version 2.1e[END_REF] with genetic algorithms in order to determine the most efficient building shape considering different parameter sets and output's criterion. Among rectangle, U-shape, H-shape, T-shape, L-shape, cross-shape and trapezoidal buildings, the rectangle and trapezoidal one were the most efficient shapes both in term of en-ergy consumption and life-cycle cost. Nevertheless, variations between all studied shapes were quite small allowing to give a large flexibility to architects.

Siddarth et al. [START_REF] Siddharth | Automatic generation of energy conservation measures in buildings using genetic algorithms[END_REF] have coupled genetic algorithm and DOE-2 [START_REF] Winkelmann | doe-2 supplement, version 2.1e[END_REF] in order to establish a data basis allowing them to implement regression functions describing the annual energy consumption. Indeed, they used genetic algorithm to generate several set of parameters. Each set of parameters has been tested in DOE-2 [START_REF] Winkelmann | doe-2 supplement, version 2.1e[END_REF] which returned the annual energy consumption. Part of these set of parameters are then selected under an annual energy consumption criterion and injected inside a data basis, which will be used for the implementation of a regression function. Under this annual energy consumption model , they are, thus, allowed to suggest energy saving strategies.

Sahu et al. [START_REF] Sahu | Thermal design of airconditioned building for tropical climate using admittance method and genetic algorithm[END_REF] proposed a strategy consisting to couple electrical analogy model with a genetic algorithm for improving design building parameters to reduce plant load. More specifically, they identified the orientation, the shape, the roof and walls materials and window properties. They validated their results by comparing the model response with the commercial software TrnSys [START_REF] Klein | A transient simulation and program[END_REF].

Yang et al. [START_REF] Yang | An efficient evolutionary approach to parameter identification in a building thermal model[END_REF] tested several evolutionary algorithms to identify building parameters for energy savings. More specifically, they coupled the software HAMbase [START_REF] Dewit | HAMBase: Heat, Air and Moisture Model for Building and Systems Evaluation[END_REF] with these algorithms to optimize external and internal wall properties as the thermal resistances and capacities, and also long-wave and short-wave radiation coefficients as the emissivity or the absorptivity. Their objective was to minimize the fitness value defined as the mean absolute error.

Discussion on the hybrid methods

Through the previous examples, it appears that the hybrid method is mainly used for optimization applications. Contrary to statistical or physical approaches that we described above, the aim is not any more just to predict the thermal behaviour of a specific building but mainly to return different strategies able to improve energy efficiency. That is why, it is particularly adapted for the monitoring issues. Indeed, the hybrid technique selects the advantages of both physical and statistical methods and uses them to implement efficient models for monitoring and control applications. Thus, it allows to keep a part of physical interpretation while not requiring a really accurate description of all phenomena occurring in the heat building transfer.

The hybrid method is also a remarkable scientific challenge by the fact that it implies several scientific domains as physics and statistics. Indeed, it promotes the collaboration between these two disciplines. Thus, in the future, thanks to both statistician and physician experts and especially their ability to work together, the grey method could be extended to other new combinations models than the nodal approach coupled with genetic algorithms. Actually, it is quite limited by the computation time that can in certain cases becomes huge (in some cases, several days are needed for one parameters identification phase). For this reason, lots of improvements in the hybrid method must still be done. Other combination methods could probably be more efficient in term of computation time.

Following this idea, some works has been published. The technique proposed in those articles were introduced in the 1990's by Lam et al. [START_REF] Lam | Sensitivity analysis of energy performance of office buildings[END_REF][START_REF] Lam | Regression analysis of high-rise fully air-conditioned office buildings[END_REF]. They proposed a new strategy consisting in generating a data basis from a thermal dynamic simulation software. Those data are then used as input parameters in a regression tool. Several techniques can be used as regression techniques as multivariate regression, artificial neural network, support vector machine... The advantage is that it is possible to predict outputs from the regression equations without needing to resort to the simulation building software. Thus, this technique allows to reduce significantly the computation time.

In this specific case, Lam et al. [START_REF] Lam | Regression analysis of high-rise fully air-conditioned office buildings[END_REF] used the nodal software DOE-2 [START_REF] Winkelmann | doe-2 supplement, version 2.1e[END_REF] as data basis generator and implemented a prediction model from multivariate linear and non linear regression equations able to find the annual energy consumption function of 12 selected variables in air-conditioned office building in Hong-Kong.

Likewise, Freire et al. [START_REF] Freire | Development of regression equations for predicting energy and hygrothermal performance of buildings[END_REF] proposed a strategy consisting in generating a data basis from their in-house model called Pow-erDomus [START_REF] Mendes | Energy efficiency and thermal comfort analysis using the PowerDomus hygrothermal simulation tool[END_REF]. Those data are used as input parameters in a regression tool. The advantage is that it is then possible to predict outputs without needing to resort to simulation building software. This technique allows to reduce significantly the computation time. Particularly, they were interested in predicting the indoor temperature and the relative indoor humidity from the outdoor temperature, the relative outdoor humidity, the total solar radiation, the heating load and the HVAC power.

In the same way, Xu et al. [START_REF] Xu | The impact of place-based affiliation networks on energy conservation: An holistic model that integrates the influence of buildings, residents and the neighborhood context[END_REF] established a model coupling the nodal software EnergyPlus [START_REF] Energyplus | eere.energy[END_REF] with an artificial neural network for predicting the energy consumption. More specifically, they generated a data basis from the thermal model that they put as input parameters of the ANN. After training it, the ANN was able to deduce the prediction of the energy consumption.

More recently, Lee et al. [START_REF] Lee | Optimization of building window system in asian regions by analyzing solar heat gain and daylighting elements[END_REF] proposed to couple a regression analysis with a thermal simulation model to describe the influence of the size, thermal properties and orientation of windows in buildings considering 5 different climate zones in Asia. Their main goal was to deduced optimized parameter windows able to reduce the cooling or/and heating load.

Considering these promising perspectives, our team took recently part in this new scientific field by developing our own hybrid model. We propose to couple a simplified in-house thermal model based on the electrical analogy with a multivariate regression applied to several spatial subsets of an initial data basis designed from the thermal model. This method has already be tested for several applications [START_REF] Madu | Simulation in manufacturing: A regression metamodel approach[END_REF][START_REF] Jin | The use of metamodeling techniques for optimization under uncertainty[END_REF][START_REF] Villanueva | Optimisation multiagent par partitionnement adaptatif de lespace de conception, 20èmes Journes Francophones sur les Systmes Multi-Agents[END_REF]. Preliminary results are really promising concerning the feasibility of the method in building applications.

Most of these works present results validated on specific cases. An interesting outcome would be to find some generic regression equations. The main issue is that it probably requires a large amount of parameters. Larger the parameters quantity, larger the data basis and larger the resort to computation software and by this way the computation time. Thus, it is a really interesting issue since it is a great scientific challenge that could have a remarkable impact.

We propose to sum up in the Table (3) the properties of the hybrid techniques compared with those of physical and statistical tools.

Conclusion

In this paper, we have proposed a review of the main techniques and tools enabling building energy performances prediction. These techniques have been introduced along three categories, each of them associated to specific scientific paradigms and fields: First of all, approaches relying on physical models ("white box" methods) have been introduced. These may be divided into three sub-categories, which mainly correspond to a gradual rise of the level of details of building models: the multizone technique which considers the space as a homogeneous volume where all states variables are uniform, the zonal method which divides each room in several cells and the CFD method which describes each zones in several control volumes. Then, we have focused on methods based on machine learning (or "black box" methods), which rely on statistical treatments of building energy and comfort data. Four methods have been reviewed : conditional demand analysis, artificial neural networks, genetic algorithms and support vector machine. The last category of methods considered is the one of hybrid approaches which rely on both physical models in order to simulate building thermal behaviour and machine learning techniques in order to optimize input parameters. Finally, a critical synthesis has been performed in order to highlight for each method the most appropriate applications. The first kind of methods -those relying on physical models -are mostly applicable to contexts in which building design data are available, and especially in the scope of the design of a new building. Actually, those methods rely on quite detailed descriptions of buildings, notably entailing geometry, material properties, and energy systems features. While this information can be considered to be easily extractable from design data in the case of a new building, this is less than obvious for existing buildings (e.g. in the scope of a refurbishment). This is true for the most basic of these methods -the nodal one -but all the more true when we consider more advanced ones (zonal, CFD). When it comes to comparing those methods between them, the conclusion is quite straightforward: obviously, it is better to use more detailed models (CFD) for the sake of reliability and precision of simulation result, but models are more tedious to build and computation times are higher. Zonal methods can be considered as good trade-offs, but still, most simulation tools used today in "reallife" projects are based on nodal approaches. Nevertheless, a possible trend is a gradual shift to CFD methods with computers becoming more powerful. The second category of methods, which are based on machine learning techniques, are extremely useful in opposite situations, i.e. those in which one owns real energy and comfort data from the building but has little or no information about the design. But the reliability of these techniques is highly dependent on the quality and amount of available data, as were the physical approaches dependent on the complexity of the underlying model. It is however quite difficult to perform a qualitative and comparative assessment of the various techniques devised in this field, since -again -their performances will depend on the training data used as input. Compared to physical approaches, machine learning ones require less information about the building and may appear as easier to deploy. However, physical approaches are more handy in scopes where interpretation of physical phenomena is desired. At last, hybrid approaches appear as a very promising field for the near future [START_REF] Clarke | Simulation-assisted control in building energy management systems[END_REF]. They can be considered as a nice trade-off between physical and machine-learning based methods, and relax their drawbacks by combining them. Hybrid methods may be appreciated in situations were a building physical model is available, but is incomplete or does not offer enough details, and therefore has to be adapted and / or completed. When dealing with existing buildings, where it is usually difficult to rebuild detailed physical model, such approaches could be of great help.

Figure 1 :

 1 Figure1: Scheme of the energy uses distribution in buildings in residential and tertiary sector in 2001[START_REF] Balaras | European residential buildings and empirical assessment of the hellenic building stock, energy consumption, emissions and potential energy savings[END_REF][START_REF] Gaglia | Empirical assessment of the hellenic nonresidential building stock, energy consumption, emissions and potential energy savings[END_REF]

Figure 2 :

 2 Figure 2: Schematic representation of a problem solved with the zonal method (Courtesy of Maxime Trocmé) [125]

Figure 3 :

 3 Figure 3: Schematic representation of a problem solved with the multizone method (Courtesy of Maxime Trocmé)[125]

Figure 4 :

 4 Figure 4: Scheme of the general operation in the genetic algorithm

Figure 5 :

 5 Figure 5: Scheme of one neuron layer with the application of the activation function

Table 1 :

 1 Summary of the specificity of each physical technique

	Physical technique	Specificity of each technique	Application field	Advantages	Drawbacks
	CFD method	One cell=a control volume (3-D); Local state variables	Contaminant distribution; Indoor air quality; HVAC systems	Detailed description of the fluid flows occurring inside the building; Large volume zones	Huge computation time; Complexity of the model implementation
	Zonal method	One cell=a division of a room (2-D); Local state variables	Indoor thermal comfort; Artificial and natural ventilation	Spatial and time distribution of local state variables (temperature, concentration, pressure, airflow) in a large volume	Large computation time Requirement of a detailed description of the flow field and flow profiles
			Determination of the total
			energy consumption/ the
	Nodal method	One cell=a room (1-D); Uniform state variables	average of the indoor temperature/the cooling or heating load; Time evolution of the global energy consumption/ the	Multiple zone buildings; Reasonable computation time; Easier implementation	Difficulty to study large volume systems Unable to study local effects as heat or pollutant source
			space-averaged indoor
			temperature

information. No heat transfer equations, no thermal or geometrical parameters are preliminary needed. Indeed, statistical models are based on the implementation of a function deduced only from samples of training data describing the behaviour of a specific system. Thus, these methods are well adapted when the physical features of the considered building are not known.

Table 2 :

 2 Summary of the specificity of each statistical technique

	Statistical tool	Specificity of each technique	Application field	Advantages	Drawbacks
	Conditional Demand Analysis : Regression technique	Starting hypothesis: linear relation between variables and the output	Forecasting of the energy consumption; Evolution of the energy demand	Regression function describing the system	A large amount of training data / Non-collinearity between data
	Genetic Algorithm : Optimization technique	Starting hypothesis: equation form imposed by the user. Final result is not necessary the best solution	Prediction of the energy consumption; Optimization of the equipment or load demand	Function describing the system; Powerful optimization algorithm	A large amount of training data; Difficulties to adjust algorithm parameters Large computation time
	Artificial Neural Network : Regression technique	No starting hypothesis but huge "black box" which prevents from physical interpretations	Prediction of the energy consumption and energy uses	A huge training faculty	A large amount of exhaustive and representative data; No physical interpretation
	Support Vector Machine : Regression technique	Starting hypothesis: kernel function imposed by the user	Forecasting of the energy consumption or temperature	A reasonable amount of training data with mainly vector data; Minimization problem based on the SRM	Determination of the kernel function Difficulty to adjust parameters C and

Table 3 :

 3 Comparison between white, black and grey box techniques

	Methods	Building geometry	Training data	Physical interpretation
	Physical or "White box" method	A detailed description of the building geometry is required	No training data are required	Results can be interpreted in physical terms
	Statistical or "Black box" method	A detailed description of the geometry is not required	A large amount of training data collected over an exhaustive period of time is required	There are several difficulties to interpret results in physical terms
	Hybrid or "Grey box" method	A rough description of the building geometry is enough	A small amount of training data collected over a short period of time is required	Results can be interpreted in physical terms