Les fondements impurs de l'autonomie

Gisèle Sapiro Dans Peut-on dissocier l'oeuvre de l'auteur ?, j'ai analysé, dans le sillage de Foucault, en quoi l'identification entre « l'auteur1 » et son « oeuvre » est une construction sociale, qui fonde aussi bien la responsabilité pénale que la propriété littéraire et artistique. Elle fonde aussi l'autonomie des champs de production culturelle et intellectuelle.

Entre identification et désidendification

Cette identification n'est cependant jamais parfaite, et l'histoire de l'art et de la littérature peut être relue à travers les formes d'identification (autobiographie, autoportrait) ou de désidentification (fictionnalisation, déplacements dans le temps et dans l'espace, métaphorisation ou symbolisation). L'histoire des procès littéraires est jalonnée par des revendications de désidentification entre l'auteur et son oeuvre: l'avocat de Flaubert eut la plus grande peine à convaincre le tribunal que son client ne faisait pas l'apologie de l'adultère, parce que son impassible narrateur ne le condamnait pas et qu'il adoptait par endroits le point de vue de son personnage ; Baudelaire, lui, n'échappa pas à la sanction pour avoir peint le mal de façon « obscène » et « immorale »2 . Dès le XIXe siècle, les écrivaines poursuivies réclamaient à juste titre une distinction entre représentation et apologie. La notion de « distanciation » entrée dans la jurisprudence française en 2005 est un autre moyen de distinguer le point de vue de l'auteur et celui de ses personnages, ainsi que l'explique Anna Arzoumanov. Que des auteurs tel Houellebecq jouent de la fiction pour faire passer des discours prohibés (islamophobe en l'occurrence) dans l'espace public3 ne doit pas conduire à renoncer à cette distinction. En revanche, lorsque la fiction est un instrument de stigmatisation raciste et sexiste d'une personne, comme dans le cas du récit « Obono l'africaine », publié par Valeurs actuelles le 27 août 2020 (et portant sur Danièle Obono), elle ne peut protéger d'une sanction : c'est ce qu'a confirmé la cour d'appel en novembre 20224 .

La vision du monde de l'auteure

Cependant, par-delà les personnages, l'oeuvre véhicule toujours d'une façon ou d'une autre la vision du monde de l'auteure. Des critiques marxistes tel Lucien Goldmann l'avaient théorisé avant la critique féministe. György Lukács expliquait toutefois que l'oeuvre de Balzac véhiculait les contradictions sociales de son temps, à l'insu des positions réactionnaires de son auteur. Car le travail créateur ne peut se réduire aux intentions de l'auteure, iel charrie des représentations sociales de son époque, et une des questions de la critique pourrait être dans quelle mesure l'oeuvre reproduit ou subvertit ces représentations5 . Cela vaut pour la peinture et pour le cinéma. Mais les représentations ne suffisent pas à subsumer l'oeuvre. La forme n'a rien de neutre. Le choix d'épouser le point de vue d'Emma Bovary par le discours indirect libre faisait advenir ce point de vue dans l'espace public où il n'avait pas droit de cité, non parce qu'elle était une femme mais parce que c'était une petite bourgeoise auquel était réservé un traitement comique dans la tradition classique. Les procédés stylistiques, l'ironie, toutes les formes de valorisation et de dépréciation expriment la vision du monde et le système de valeurs sous-jacents à l'oeuvre. Des procédés équivalents se retrouvent dans les autres arts, y compris la musique comme l'attestent les études féministes citées par Catherine Deutsch, ou l'analyse par Jean-Jacques Nattiez de l'antisémitisme présent dans certaines oeuvres de Wagner6 .

C'est à la fois contre l'histoire littéraire qui appréhendait « l'homme et l'oeuvre » (jamais la « femme »), mais aussi contre la critique marxiste, qu'ont émergé le new criticism et le structuralisme (inspiré du formalisme russe). Ces deux courants déplaçaient les clés de l'interprétation de l'auteure aux critiques et recentraient l'analyse sur la forme. Ils revendiquaient l'autonomie de la critique littéraire par rapport à l'histoire, la sociologie, l'anthropologie, le droit. Si leur apport à l'analyse formelle des oeuvres est majeur, leur institutionnalisation a fait obstacle à la critique féministe émergente, comme à la critique marxiste. Néanmoins, la critique féministe s'est rapidement affirmée en histoire de l'art, du cinéma, de la photographie, notamment autour de la notion de « male gaze ». Elle est demeurée plus marginale en musicologie comme le souligne Catherine Deutsch. De même la critique postcoloniale a remis en cause les présupposés de l'autonomie de l'oeuvre dans toutes les disciplines.

Critiquer plutôt qu'effacer

Les contributions s'accordent toutes sur l'idée que le travail critique est préférable à l'effacement. Dans la conclusion du livre, j'écrivais que l'effacement des oeuvres du canon risque d'effacer les traces de la violence symbolique qui, quelles que soient les normes de l'époque, s'est bel et bien exercée sur les groupes minorés à travers les représentations qu'en donnaient les oeuvres. Il est donc nécessaire d'en faire l'anamnèse. Ce qui ne veut pas dire qu'il ne faille pas réévaluer leur place dans le canon en déconstruisant celui-ci, comme l'ont entrepris de longue date les critiques féministes. académies [START_REF]Seules six femmes ont eu le prix Nobel de littérature de 1901 à[END_REF] . Ces hiérarchisations ne reposaient pas sur des valeurs purement esthétiques ou scientifiques, mais sur des préjugés. Comme le souligne Anne-Marie Thiesse, « l'écrivain national » est un homme [START_REF] Thiesse | La Fabrique de l'écrivain national[END_REF] .

Appropriation, sacralisation et profits

Reine Prat et Geneviève Sellier rappellent que la figure de l'auteure tend à monopoliser le capital symbolique associé à l'oeuvre au détriment du travail collectif de production de l'oeuvre travail collectif que la sociologie a depuis longtemps mis en avant. Cependant, l'appropriation des oeuvres par leurs auteures n'allait pas de soi et fut, comme la conquête de l'autonomie face aux tribunaux, une lutte. La propriété littéraire, puis artistique, fut avant tout revendiquée par les intermédiaires culturels qui demandaient le monopole de l'exploitation des oeuvres et qui en demeurent les principaux bénéficiaires. Dans le droit étasunien, c'est le producteur qui est l'auteur d'un film [START_REF] Pacouret | Les droits des auteurs de cinéma[END_REF] . Et ce sont ces intermédiaires qui continuent à capitaliser sur les auteurs scandaleux.

La sacralisation de l'auteur, qui s'origine dans le romantisme (lequel incluait des figures féminines comme George Sand et Mary Shelley), a été institutionnalisée par le système d'enseignement et par les rituels de funérailles nationales, de panthéonisation et de commémoration, dans le cadre de la construction des identités nationales [START_REF] Thiesse | La Création des identités nationales : Europe, XVIII e -XX e siècle[END_REF] . Il en va de même pour les figures de grands penseurs ou savants, presque toutes masculines.

C'est pourquoi une véritable histoire sociale des champs de production culturelle et intellectuelle requiert d'analyser et de déconstruire ces mécanismes de consécration, qui va des prix et récompenses aux honneurs officiels. Comment expliquer qu'un Matzneff ait remporté le prix Renaudot pour un essai comprenant une apologie de la pédocriminalité ? Et, certes, ce n'est pas par affinité idéologique que Céline ou Maurras ont été inscrits au livre des commémorations nationales : mais que signifie de commémorer la date de naissance de ces auteurs ? La figure de l'auteur est une institution qui doit être déconstruite, sans remettre en cause le droit légitime des créateurices à tirer des profits symboliques et économique de leur travail et en déconstruisant aussi les formes d'exploitation et récupération de leurs oeuvres.

La notion abstraite d'auteur comme catégorie juridique et analytique sera orthographiée telle quelle, elle sera féminisée lorsqu'il s'agit de la personne de l'auteure. J'emploierai ici le féminin générique italisé (voir https://www.nouvelobs.com/bibliobs/20210308.OBS41110/inclusive-une-autre-ecriture-est-possible.html).

Voir mon livre La Responsabilité de l'écrivain. Littérature, droit et moral en France, XIX-XXIe siècle, Paris, Seuil, 2011.

Jérôme Meizoz, « Le roman et l'inacceptable », in L'Oeil sociologique et la littérature, Genève, Slatkine, p. 196.

Anna Arzoumanov, Amina Damerdji et Gisèle Sapiro, « Analyses littéraires et sociologiques de l'injure raciste : retour sur l'affaire Obono/ Valeurs actuelles », in Dominique Lagorgette et Denis Ramond (dir.), Lutter contre les stéréotypes, Paris, PUF, coll. « La vie des idées », 2023.

Voir la deuxième partie de mon livre Les Écrivains et la politique en France, de l'affaire Dreyfus à la guerre d'Algérie, Paris, Seuil, 2018.

Jean-Jacques Nattiez, Wagner antisémite, Paris, Bourgois, 2019


Deyae Badri

Cyril Toublanc
email: cyril.toublanc@oniris-nantes.fr

Michel Havet

Olivier Rouaud

Olivier Rouaud Thermal

numerical modelling and field experimental validation

Keywords: spiral-freezer, frost, numerical modelling, evaporator, food freezing

Thermal and hydraulic behaviors of a finned coil heat exchanger coupled with fixed-speed fans during frost

formation in an industrial food freezer:

INTRODUCTION

Freezing is regarded as one of the best methods for long-term food preservation as chemical reactions and microbial growth are reduced at low temperatures. Blast freezing is the process of pushing the air cooled by the evaporators (around -40 °C) at high velocity (>3 m/s), using fans, across a food product in order to freeze the product as fast as possible.

When the moisture in the air encounters a surface with a temperature below 0 °C, frost formation occurs. In industrial freezing where temperatures are very low, frost formation is therefore almost inevitable. When accumulated on the surface of the heat exchanger, it leads to a decrease of its thermal performance which, after a period of time and if no corrective action is taken, leads to non-conforming food products at the freezer outlet due to a too low degree of freezing. To overcome practically this problem, it is possible to extend the residence time of the products within the equipment but this solution can only be temporary and it is then imperative to defrost the finned coil heat exchanger. The solution would be to have a dimensioning and a controlling of the freezers adapted to the treated products and to the industrial practices. To do this, it is important to understand how, during a production session, the heat transfer resistance and the airflow resistance evolve.

Several studies have been carried out to investigate the frosting/defrosting process in different conditions and for different geometries. Many researchers have investigated the frosting phenomenon by focusing on the evaporator since it is the critical component. In addition, most of these researches have been performed under air-conditioning conditions [START_REF] Léoni | State-of-the-Art Review of Frost Deposition on Flat Surfaces[END_REF]. For deep freezing conditions (low temperature and high air relative humidity), the available literature is more limited [START_REF] Aljuwayhel | Experimental Investigation of the Performance of Industrial Evaporator Coils Operating under Frosting Conditions[END_REF]. This paper aims to bridge the gap of the literature by investigating with both numerical and experimental approaches the thermal and hydraulic behavior of a finned tube heat exchanger during frost formation.

EXPERIMENTAL AND NUMERICAL STUDY

The freezer, which is the main object of the present study, is a spiral air blast freezer operating with an ammonia overfeed finned tube evaporator and having a cooling capacity of about 126 kW. It is a real system of an agrifood French company that produces frozen pizzas and which regularly faces to non-conform food products due to frost accumulation on the evaporator.

The 2-pass spiral air-blast freezer, depicted in Figure 1, comprises a set of 24 spirals, resulting in a cumulative belt length of 370 meters. The evaporator employed in this system is a finned and tube heat exchanger, through which cold air is circulated by an axial fan, ensuring uniform airflow distribution across the entire width of the freezer. This installation should run during a full production day, i.e., at least more than 15 hours without any significant decrease of the refrigerating capacity. Indeed, a single defrosting sequence is daily launched outside production hours during the night. Unfortunately, it happens that after only few hours of production, the staff notices that the products are inadequately frozen upon existing the freezer. In this circumstance, they have to increase the residence time of products within the freezer by reducing the speed of the conveyor belt, which, in turn, decreased the production rate. Occasionally, this adjustment only served as a temporary solution, necessitating a complete halt in production to manually remove frost from the evaporator using a scrubbing brush. Such a situation was encountered during the test campaign. That day the manufacturer was producing large unpackaged rectangular pizzas. Each was measuring l: 510 × w: 310 x h: 10 mm and had a residence time of about 42 minutes. The frozen pizzas have around 1.6 kg as unitary mass. Table 1 summarizes all the system data and operating conditions. Thereafter, the experimental campaign will be described and the numerical model will be presented.

Material and Methods

An experimental investigation has been conducted by GEPEA laboratory, CETIAT industrial technical center and GEA Refrigeration company. The objective of this study was to determine the nominal operational conditions, which were subsequently used to initialize and configurate the numerical model. The second objective was to examine the freezing system behaviour during a typical production day in a frozen food manufacturing facility.

2.1.1. Air pressure and velocity measurements Pitot tubes were placed downstream and upstream of the evaporator and the fan in order to measure the static and total pressures. These measurements were carried out in nominal conditions first (freezing system being turned off), in order to determine the nominal heat exchanger pressure-drop, the frontal air velocity and the fan nominal pressure and airflow rate. Thereafter, the same measurements were made under frost conditions in order to dynamically monitor the influence of frost.

The static and total pressure were measured with a Pitot tube (KIMO 0 -1,000 Pa ±3 Pa). By considering the evaporator frontal area, the air velocity was deduced.

The Pitot tubes were placed downstream and upstream of the evaporator and the fan. The cold coil has been divided into several meshes where the pressure sensors have been placed. It has been observed that the air velocity was uneven over the entire coil. This was due to the non-uniform ventilation and air distribution. For this reason, the air velocity values in each cell were recorded, and then averaged over the entire coil surface.

Under dry conditions, the velocity was not homogeneous on the whole surface, it oscillated between 3.57 and 5.14 m/s. The calculated average velocity being 4.32 m/s, the resulting volume airflow rate was approximately 76,000 m 3 /h. The nominal fan static pressure was 231 Pa. According to the characteristic curve of the fan, this gives almost the same flow to that measured.

2.1.2.

Frost growth and cross section area restriction A recording camera was placed below the evaporator (at the inlet airside) (Figure 2) to monitor its front side. Also, it took pictures every 7 seconds. The camera, specifically a GO5000 model, is equipped with a sensor (2,560 × 2,048 pixels) associated with a RICOH FL-BC2518-9M lens with a focal length of 25 mm. The lens was positioned 60 cm from the ground, which means that the camera-object distance was 103 cm. Under these conditions, the observation area window was 0.22 m² (529 mm × 423 mm) which represented around 2.2 % of the total frontal section. The resolution of the image is 207 µm / pixel.

The camera was turned on during the cooling start-up period, just before food production. A recorded film was made at the rate of one image every 7 seconds. Several disturbances are visible in the film, slight movements of the camera, sudden change in brightness due to door opening or staff intervention, etc. From this film, 487 images were extracted with a time step of 112 s. As shown on Figure 3, the histograms of the images were normalized, using ImageJ software, to smooth out differences in illumination. In the CTAn software, the images were filtered in order to increase the local contrasts with a conditional mean filter (in 2D, round kernel of radius 3, threshold 50).

In ImageJ, the images have been aligned on the initial image (Stack Reg function) and a film has been made. An early image of the film was chosen to create the initial mask that offers a good contrast between the background and the coil. The mask was made from an overlay for the vertical tubes followed by thresholding. Then, this initial reference image was subtracted from all the following images, resulting in a film that exclusively captured the formation of frost during the recording. Finally, the mask was applied to these images, subjected to thresholding (gray level 44) to enhance the visibility of the formation in the free section of the coil. By employing this method, the area of the openings could be accurately calculated.

2.1.3.

Air-product heat exchange quality For the convective heat transfer coefficient of the food freezing process, a large number of convective heat transfer coefficient correlations have been obtained on the basis of experimental research, which can be directly used to calculate the convective heat transfer coefficient between food and air. However, these correlations are usually restricted to specific application conditions. For specific geometries and flow field in industrial process, it is often complex to adopt these heat transfer coefficient correlations. Thereby, a specific correlation was developed for the actual conditions. The air-product convective heat transfer coefficient was measured by a specific heat flux sensors (Figure 4) placed, at different moments during the production day over 15 hours, on the conveyor at the freezer inlet. The sensor spent, as the product, 42 minutes before being picked up. The results were used in order to bring out an average air-product convective heat transfer coefficient for each passage. Two thermocouples were integrated into the experimental setup. One thermocouple was used to measure the air temperature while the second one was placed within the heat flux cell to monitor its temperature throughout the 42 minutes residence time.

Image example (image 460)

Frost image (image-reference)

Frost with mask Thresholded image Figure 5 illustrates the first recording measurement of the convective heat transfer coefficient (freezer empty) as function of the position on the conveyor belt. The position is defined depending on the full conveyor belt length L0. It could be observed that the heat transfer coefficient oscillates depending on the horizontal distance from the fan. It is maximum when the products are on the fan side and minimum when they are on the opposite side. As consequence, for simplification reason, the convective heat transfer coefficient was averaged.

At each moment, the corresponding air velocity was defined by experimental results in order to perform the following empirical correlation:

𝜶 𝒑 = 𝟐𝟐. 𝟑 × 𝑽 𝒂 𝟎.𝟒 (Eq. 1)
This correlation is valid for an apparent air velocity ranging from 2.5 m/s and 4.5 m/s.

Product water losses during freezing

The frost deposited on the exchanger is influenced by the relative humidity inside the freezer, which in turn depends on the water released by the products during their freezing process. Successive weight measurements of many products throughout the production day were done. A sampling of three products every half-hour (around one sample every 30 minutes) was performed. The weight of the same products was measured successively at the inlet and the outlet of the tunnel. As depicted in Table 2 the rate of water loss during the freezing process for both pizza types represent almost 1.1% of the initial pizza weight. This value is in agreement with typical blast freezer application [START_REF] Rouaud | Heat and Mass Transfer Modelling during Freezing of Foodstuffs[END_REF].

Numerical study

The frost process and the overall system is modelled in Modelica, an equation-based, object-oriented modelling language [START_REF] Fritzson | Introduction to Object-Oriented Modeling and Simulation with Modelica Using OpenModelica[END_REF].

Evaporator and condenser models

The evaporator and condenser models were chosen from the heat exchangers package of TIL library. The models are generally composed using cells (finite volume elements) to represent the two fluid flows and the separating wall resulting in a sandwich structure. A record geometry is adapted in order to describe the actual geometric parameters and material types. Then, internal functions compute the external and internal surfaces as well as the external and internal cross-sectional areas. These outputs are transmitted to the air, wall and fluid elements in order to solve heat transfer, mass transfer, pressure drop, and fin efficiency correlations.

For the refrigerant side, a constant heat transfer coefficient of 2,000 W.m -2 .K -1 is assumed for the evaporator while the internal heat transfer coefficient is calculated using the correlation provided by Shah and London [START_REF] Shah | Laminar Flow Forced Convection in Ducts -1st Edition. 1st Edition[END_REF]. For airside, we have selected the heat transfer and pressure drop correlations based on the work of von Haaf [START_REF] Haaf | Wärmeübertragung in Luftkühlern[END_REF]) that were also used by Tegethoff [START_REF] Tegethoff | Eine Objektorientierte Simulationsplattform Für Kälte-, Klima-Und Wärmepumpensysteme[END_REF]) and Schmidt [START_REF] Schmidt | Eine Methode Zur Numerischen Untersuchung von Strömung Und Wärmeübertragung in Komplexen Geometrien[END_REF].

The variation of both cross section and heat transfer area due to frost accumulation is taken into consideration using the void ratio and the similarity theorem of triangles, as suggested by [START_REF] Westhäuser | Untersuchung Der Vereisung von Mikrokanal-Wärmeübertragern[END_REF].

Frost model

Since the present study focuses on an overall refrigeration system-level simulation, the aim was to develop a suitable frost model that takes as much as possible the physical phenomena but without any secondary details and computational complexity. The literature review showed that the only available empirical correlation able to predict frost properties under freezing conditions is not suitable to finned tube geometry [START_REF] Mao | Frost Characteristics and Heat Transfer on a Flat Plate under Freezer Operating Conditions: Part I, Experimentation and Correlations[END_REF]. Moreover, the CFD based models seemed to be inconvenient with this type of industrial application [START_REF] Kim | Frosting Model for Predicting Macroscopic and Local Frost Behaviors on a Cold Plate[END_REF]. Therefore, a quasi-steady state modeling of frost accumulation is adopted, considering the frost layer as a one-dimension porous medium subject to heat (Eq.2) and mass transfer (Eq.3).

𝑸 ̇𝒔 ′′ = 𝜶 𝒂 × (𝑻 𝒂,𝒊𝒏 -𝑻 𝜹 ) (Eq. 2)

Where 𝑇 𝛿 is the frost surface temperature, 𝛼 𝑎 is the convective heat transfer coefficient. 𝜌 𝑓𝑟 is the local density of the frost layer, 𝜌̅ 𝑓𝑟 and 𝛿 𝑓𝑟 are the average density and thickness of the frost layer, respectively.

𝜌̅ 𝑓𝑟

𝑑𝛿 𝑓𝑟 𝑑𝑡 = 𝑚̇𝛿 ′′ is the densification rate and 𝛿 𝑓𝑟 𝑑𝜌 ̅ 𝑓𝑟 𝑑𝑡 = 𝑚̇𝜌 ′′ is the thickening or the growth rate. The main goal of this physical model is to define each quantity of 𝑚̇𝛿 ′′ and 𝑚̇𝜌 ′′ . For this purpose, the balance equations are divided in several parts ranging from the frost-air interface and cascading down to the cold plate at x=0 [START_REF] Qiao | Transient Modeling of Two-Stage and Variable Refrigerant Flow Vapor Compression Systems with Frosting and Defrosting[END_REF].

Separator model

The separators models were chosen from the TIL library Accumulator package. Their dynamic model is described by [START_REF] Strupp | Investigation of Low Pressure Accumulators in CO2 Refrigeration Cycles[END_REF] and [START_REF] Bockholt | Transient Modelling of a Controllable Low Pressure Accumulator in CO2 Refrigeration Cycles[END_REF].

Expansion valve model

The expansion valves models were selected from Valves package. Orifice valve model based on expansion coefficient is adopted. The model calculates the mass flow rate in function of the pressure drop using Bernoulli's equation. The mass flow rate could be computed by the equation below:

𝒎 ̇𝒗 = 𝑨 𝒆𝒇𝒇 . √(𝒑 𝟏 -𝒑 𝟐 ). 𝟐𝝆 𝟏 (Eq. 4)
where Aeff is the effective flow area, 𝜌 1 is the inlet refrigerant density, 𝑝 1 and 𝑝 2 are the inlet and outlet pressures, respectively. The effective flow area of the high-pressure side expansion valve is fixed at 4×10 -6 m². For the low-pressure side, the effective flow area is variable in order to maintain a fixed pressure in the low-pressure tank.

Fan model

The fan model was selected from Fans package. A second order fan defined by quadratic characteristics and consideration of power losses is coupled to the evaporator. In our case, the fan used is the Woods® axial fan 48J ½, made with an 20° pitch angle, turning at a fixed 50 Hz frequency and has a maximal fin efficiency of 82%.

𝒎 ̇𝒗 ′′ = 𝝆 ̅ 𝒇𝒓 𝒅𝜹 𝒇𝒓 𝒅𝒕 + 𝜹 𝒇𝒓 𝒅𝝆 ̅ 𝒇𝒓 𝒅𝒕 (Eq. 3)

Medium

In the present model, gas, liquid, two-phase fluid and heat ports are used in order to transmit pressure, enthalpy, mass flow rate and heat flux.

Based on VDI heat atlas database (VDI Heat Atlas 2010) the moist air properties are calculated while the ammonia properties are based on Refprop 10.0 [START_REF] Lemmon | REFPROP Documentation Release 10[END_REF]. These two media are defined in a component called SIM (system information manager) that stores all information related to their properties and also computes numerical information like the total refrigerant mass and total inner volume which are important system parameters.

Cooling tower

A model of a cooling tower with a water pump, featuring an ideally controlled mass flow rate as input signal is selected from Building library. This cooling tower is based on Approach temperature defined as the difference between the cold water temperature leaving the tower and the ambient wet bulb temperatures. This model is chosen in order to simplify the freezing system model since the cooling tower is considered for second interest in the whole analysis.

2.2.8. Screw Compressor For this industrial ammonia systems, the compressor type used is a screw compressor with a fixed speed and variable capacity. The capacity is regulated using a slide valve. When the slide valve is opened, a portion of the gas inside the compressor is vented back to the suction port. This provides regulation down to 10% of full capacity. This type of regulation is easy but it affects the compressor efficiency. To model this type of compressor, a model inspired from Liu et al. [START_REF] Liu | A New Model of Screw Compressor for Refrigeration System Simulation[END_REF]) is developed. It consists of predicting the compressor volumetric efficiency as function of pressure ratio and other variables detailed in equation (Eq.5).

𝜼 𝒗 = 𝒂𝝉 𝟏 𝒌 𝝉 -𝟏 + (𝒃 + 𝒄𝝉 -𝟏 )𝝉 𝟏 𝟐𝒌 √𝟐𝒗 𝟏 (𝒑 𝟐 -𝒑 𝟏 ) (Eq.5)
where, 𝜏 is the ratio of the discharging pressure and the suction pressure, k is the polytropic index, and a b and c are coefficients obtained through constructor data regression.

Since the relation between the slide position and the swept volume is not linear, a correcting factor is used to predict the volumetric efficiency for part-load conditions. Therefore, the volumetric efficiency can be calculated with equation (Eq.6).

𝜼 𝒗 = 𝜼 𝒗 𝟏𝟎𝟎% 𝒇(𝑺 𝒗𝒑 ) (Eq.6)

where, 𝜂 𝑣 100% is the full load volumetric efficiency, 𝑓(𝑆 𝑣𝑝 ) is a correcting polynomial of degree 5 expressed as function of valve slide position. It is determined to fit with measured data. Doing this, the sucked vapor mass flow rate and the power transferred to the ammonia are deduced.

2.2.9.

Internal freezer space and product The interior freezer space including tunnel and products is modelled by an air volume with a heat flow source and a humidifier. The heat flow source represents the head load of the products to be frozen, thermal loads of air infiltrations, wall thermal losses, the conveyor belt heat load, and heat exchange between the tunnel and duct area. The humidifier modelled by a water vapor source represents water losses of the product during freezing. In addition, a hydraulic resistor is added to the air loop in order to take into consideration the pressure drop inside the freezer tunnel (Figure 7).

Control

All the system control is carried out by PID controllers. The latter are used to:

₋ Control the driver position of the compressors in order to maintain constant the pressures at the Vapor-Liquid separators (Low and medium pressures). The minimum driver position is limited to 40%; ₋ Control the valve section in order to maintain constant the filing level of the vapor liquid separator of medium pressure; ₋ Control the water flow rate of condenser pump in order to maintain constant the condensation pressure; ₋ Control the cooling tower fan speed in order to maintain constant the water exit temperature at the set point.

Results and discussions

As can be seen on Figure 8, the pressure drop across the evaporator continues to increase during the production cycle.

The initial value is approximately 220 Pa, which corresponds to the experimental measurement and manufacturer's documentation at the nominal operating conditions. Operating under frosting conditions, the pressure drop increases to reach approximately 400 Pa, that means an increase of 100% compared to the initial value. This increase is due to the accumulation of frost on the coil, which ultimately has the effect of reducing the airflow through the coil. Note that the pressure supplied by the fan is the reverse image of the pressure drop: the fan undergoes pressure changes. The residual static pressure, determined through experimental measurements, is represented by the grey curve and is assumed to represent the pressure drop across the tunnel. The formation and accumulation of frost on the heat exchanger surface leads to a smaller airflow passage area. This has a direct impact on airside conditions by increasing the pressure drop across the coil. The experimental data indicates that the pressure drop progressively increases from 220 Pa to around 450 Pa by the end of the experiment. The actual model exhibits a similar trend. Numerical values are within 5% far from the experimental results. By the end of production cycle, an intervention was made in order to scrape the front of the evaporator coil from frost. This operation proved to be effective, as evidenced by the slight reduction in pressure drop observed in the experimental curve. By the end, the pressure drop was around 380 Pa. This intervention could explain the discrepancy between numerical and experimental results by the end of the day. One can observe from Figure 9 that the air cross section area was reduced by almost 60% during the day.

The numerical model accurately predicts a similar trend during 15 hours. The difference between the numerical and experimental results could be attributed to multiple factors. The primary factor is the limited section captured by the camera which constitue only 2.2 % of the entire air passage section. considering that the frost is not distributed uniformly on the front face, this opening rate may not represent the average opening rate of the entire cold coil. Additionally, minor discrepancies could arise from measurement uncertainties.

Another phenomenon directly related to the blockage of the airflow passage section is the reduction of the Air-product heat transfer coefficient. According to Figure 10, the convective heat transfer coefficient decreases slowly at beginning of the freezing process then it increases slightly at the 12 th hour of the production day. This could be attributed to the change of product after a freezing stop of one hour. Since the freezer was empty for an hour, the performance was slightly improved and the convective heat transfer coefficient at the introduction of the second product reached approximately 38 W.m -2 .K -1 compared to the end of the first production where it was around 36 W.m -2 .K -1 . This operation could also explain the slight difference between numerical and experimental results. The interpretation of the whole situation could be that the reduction is directly attributed to the blockage of airflow passage due to the frost build-up. Taking into consideration the hydraulic coupling between the fan and the coil, the airflow reduces in fan-supplied evaporator which is one of the main causes of the heat exchange reduction. The cross-section area has been blocked by 80%, the pressure drops increases by 100%, and the heat transfer coefficient decreases by about 20%. It is to note that the standard deviation does not reflect the measurement uncertainty but rather the deviation of the convective coefficient values that varies as the heat flux device passes through the tunnel.

It is worth noting that this older type of installation may not fall within the realm of new blast freezer technologies, which are specifically designed for managing a specific high product moisture. Furthermore, it is used for freezing food products (Pizzas) directly from the oven, with a tomato sauce at a temperature of 40 °C. This could explain the significant degradation of performances, as observed both experimentally and numerically.

Indeed, resizing and designing the evaporator geometry to ensure the longest possible operating time before defrosting is a crucial step in addressing this phenomenon. However, it does not negate the fact that controlling product moisture loss is essential in industrial freezers. The difference in water vapor pressure between the food surface and the surrounding atmosphere (air freezer) drives dehydration, and this effect is more pronounced when the product is initially at a higher temperature (40 °C). Precooling the product before introducing it into the freezer can also be one of the recommended solutions ( [START_REF] Badri | Review on Frosting, Defrosting and Frost Management Techniques in Industrial Food Freezers[END_REF])).

CONCLUSIONS

A theoretical model of a whole and complete freezing system subjected to frost accumulation has been developed based on Modelica oriented object language. The model prediction agreed well with their experimental data in terms of air pressure drop, blockage ratio of the evaporator cross section area and the air-product convective heat transfer coefficient. As frost build-up, the free cross section area decreases resulting in an increase of pressure drops and a decrease of the air volume flow rate supplied by the fan. Moreover, the low thermal conductivity of the frost layer adds an additional thermal resistance between the air and the refrigerant. This degradation is clearly noticed in the heat exchange quality between air and the product. The comparisons between the simulation and experimental data show that the proposed model can be used to better understand the heat transfer and flow transient characteristics of the freezing system under real frosting conditions in order to optimize the design of the equipment. Further numerical results and analysis could be exploited to obtain possible data about the local aspect of frost on the evaporator as well as the effect of the frost accumulation on the energy performance and on the quality of the product during a typical industrial production day.

Figure 1 :

 1 Figure 1: Schematic of the studied spiral air blast freezer under frosting conditions.

Figure 2 :

 2 Figure 2: Location of the recording camera in front of the evaporator.

Figure 3 :

 3 Figure 3: Example of image processing.

Figure 4 :

 4 Figure 4: Airflow device for convective heat transfer coefficient measurement on conveyor (TPVOYAGER-CVT500).

Figure 5 :

 5 Figure 5: First air-product convective heat transfer coefficient measurements as function of the position on the conveyor belt.

  The model equations are directly implemented and solved in Dymola environment version 2020x. In this paper, the components' models are adapted from TIL (Richter and Braunschweig n.d.) and Building libraries (Wetter et al. 2014) coupled with self-developed models. The numerical model architecture is presented in the Figure 6.

Figure 6 :

 6 Figure 6: Freezing system modeling architecture.

Figure 7 :

 7 Figure 7: Air loop model on Dymola layout.

Figure 8 :

 8 Figure 8: Experimental and numerical results: Fan pressure, pressure drop through the evaporator coil and tunnel.

Figure 9 :

 9 Figure 9: Experimental and numerical results of the cross-section area opening ratio.

Figure 10 :

 10 Figure 10: Experimental and numerical results: air-product convective heat transfer coefficient.

Table 1 : Freezing system data and operating conditions.

 1

	Evaporator type	Finned tube
	Evaporator coil feeding type	Controlled pressure receiver liquid overfeeds
	Evaporator circuiting type	Parallel
	Evaporator fin pitch	Progressive fin pitch 24/12/8 mm
	Nominal capacity	126 kW
	Refrigerant	Ammonia
	Evaporation Temperature	-40 °C
	Evaporator air inlet temperature (nominal)	-35 °C
	Number of fans	1
	Nominal airflow rate	76,000 m 3 /h
	Nominal air velocity at the front area	4.32 m/s
	Vapor-Liquid separator capacity (Low pressure)	6 m 3
	Vapor-Liquid separator capacity (Medium pressure) 3 m 3
	Condenser water cooler system	Cooling tower

Table 2 : Experimental results of the amount of food water losses during freezing.

 2

	Pizza (1.6 kg each)	Water losses during freezing
	Average losses (g)	16.8
	Standard deviation (g)	2.2

ACKNOWLEDGEMENTS

This work was supported by the French Agency for Ecological Transition through the FOODEFREEZE project (Grant n°1881C0024). The authors thank the partners CETIAT and GEA who carried out the measurements of pressures and airflow. They also thank Luc Guihard and Sylvie Chevallier for their help in performing experiments and image analysis, respectively.

NOMENCLATURE

A area (m²) T temperature (K) ṁ mass flow rate (kg.s -1 ) V velocity (m/s) ṁ" mass flux (kg.s -1 .m -2 ) α convective heat transfer coefficient (W.m -2 .K -1 ) p pressure (kPa) η efficiency


Christophe Cérin
email: christophe.cerin@univ-paris13.fr

Mathilde Jay
email: mathilde.jay@inria.fr

Laurent Lefèvre
email: laurent.lefevre@inria.fr

Denis Trystram
email: denis.trystram@imag.fr

A Methodology and a Toolbox to Explore Dataset related to the Environmental Impact of HTTP Requests

Keywords: Computing for Sustainability, Using Big Data Analytics to improve sustainability, Measuring

EcoIndex has been proposed to evaluate the absolute environmental performance of a given URL using a score ranging from 0 to 100 (the higher, the better). In this article, we make a critical analysis of the initial approach and propose alternatives that no longer calculate a plain score but allow the query to be situated among other queries. The generalized critiques come with statistics and rely on extensive experiments (first contribution). Then, we move on to low-cost Machine Learning (ML) approaches (second contribution) and a transition before obtaining our final results (third contribution). Our research aims to extend the initial idea of analytical computation, i.e., a relation between three variables, in the direction of algorithmic ML computations. The fourth contribution corresponds to a discussion on our implementation, available on a GitHub repository. Along with the paper, we invite the reader to examine the question: What attributes make sense for our problem?, or equivalently, what is a relevant data policy for studying digital environmental impacts? Beyond computational questions, it is important for the scientific community to focus on this question in particular. We currently promote using wellestablished ML techniques because of their potential, which we discuss in the paper. However, we also question techniques for their frugality or otherwise. Our data science project is still at the data exploration stage. We also want to encourage synergy between technical expertise and business knowledge because this is fundamental for advancing the data project.

I. Introduction

To avoid dramatic consequences of climate change, all sectors of the global economy, including Information Communication Technology (ICT), must keep their greenhouse gas (GHG) emissions in line with the Paris Agreement [START_REF] Trystram | The Paris Agreement[END_REF]. The literature contains estimates of ICT's GHG emissions, which put ICT's share of global GHG emissions between 1.8% and 2.8% in 2022 1 . Authors in [START_REF] Freitag | The real climate and transformative impact of ict: A critique of estimates, trends, and regulations[END_REF] found pronounced differences and many debates concerning the underlying assumptions behind the documented studies, which could suggest that global emissions from ICT are as high as 2.1%-3.9%. Some scenarios expect a rate of 20% in 2050 [START_REF]Lean ICT: Towards Digital Sobriety[END_REF], which is considerable.

Can we quantify the environmental footprint when we click on a web page? To note the quality of an HTTP (HyperText Transfer Protocol) request, let's imagine that we have a tool like the Nutri-Score in France for food products that allows us to give it a grade between A and G. Let's also assume that these requests are archived in a public database like the HTTParchive 2 . By regularly exploring this database, we could track the evolution of the environmental footprint of Web requests. This article first presents the logic behind the EcoIndex environmental metric 3and discusses its limitations.

Our motivation comes from our belief that the initial EcoIndex model is unsatisfactory (we call it the historical EcoIndex) and thus, we propose a new scientific direction to bypass certain limitations, for instance, if the methods scale well with an increased number of attributes. Thus, we make proposals to extend the initial definition according to new attributes, all of which relate to energy consumption or production and location. The idea is to switch from a purely analytical view of the EcoIndex metric to a 'Data Science' problem because of the potential for more investigations in that domain, for instance, in considering dimensionality reduction techniques.

We use basic and effective ML techniques to gain more confidence in the research direction. So, the objective is also to investigate the step of data exploration of any Data Science project while simultaneously questioning the nature and type of data to be considered in building a model that is acceptable and understandable to all. It's in this case that we could leverage mechanisms to change habits and get the public to adhere to an eco-responsible digital approach.

Thus, the paper organization is as follows: Section II discusses related works, tools, and techniques related to 'power' monitoring, generally, or for the HTTP. Section III presents the calculation of the historical EcoIndex and its limits. We also make a statistical study to show if our assumptions about limits are a reality. Section IV describes our approaches and positions them with historical EcoIndex. Each new approach has an experimental part to highlight the conceptual differences to the historical calculation. Section V gives the lessons learned and general comments. Finally, Section VI summarizes our work and presents some exploratory directions.

At last, note that, section III and section IV follow their own "methodology and results" format. We do prefer this organization to bring closer ideas and concrete results rather than a unique experimental section.

II. Related works

A. Impact of ICT on the Environment New information technologies (ICT) are rapidly evolving and deployed to make our world smarter, safer, and more sustainable. Based on [START_REF] Berkhout | Impacts of information and communication technologies on environmental sustainability: Speculations and evidence[END_REF], the author distinguishes three levels of effects of ICT on the environment: 1st order effects (direct effects of ICT caused by their physical production, use, and disposal), 2nd order effects (impacts of ICT on other sectors), and 3rd order effects (structural ones), which include rebound effects [START_REF] Gossart | Rebound effects and ICT: A review of the literature[END_REF], among them, the direct, indirect, and economy-wide effects. In the case of the direct rebound effect, lower energy cost induces price reductions that trigger an increase in the demand for the cheaper good. In the case of the indirect rebound effect, when a resource is used more efficiently, and its price goes down, it induces the consumption of other commodities (e.g., consumers buy extra TVs with the money they saved due to an energy-efficient washing machine or dishwasher of grade A+++). The economy-wide rebound effect appears when declining energy prices reduce the prices of intermediate and final goods throughout the economy and cause structural changes in production patterns and consumption habits. For example, cheaper gasoline enables people to live further away from their workplace by making it less expensive to drive longer distances to work.

Thus, it is crucial to examine technologies based on their potentially harmful effects on a sustainable world. We started such a project in [START_REF] Cérin | The ecoindex metric, reviewed from the perspective of data science techniques[END_REF], a preliminary work on the environmental impact of HTTP requests according to the EcoIndex vision, and where we put forward and test ideas. Contrary to this previous work, this paper provides more solid investigations and assumptions verification. It also contains more experimental work, available on GitHub to replay all the scenarios we discuss.

B. Estimating and measuring the energy consumption of IT pieces of equipment

Different techniques estimate power from hardware characteristics or power measures outside the hardware. Hardware performance counters help deliver cache misses and many other low-level details. They are connected to an API (Application Programming Interface) to expose their values to software power models. Several software-based power meters [START_REF] Jay | An experimental comparison of software-based power meters: focus on CPU and GPU[END_REF] are available to estimate power consumption and energy usage, while hardware power meters are external devices that can also measure power consumption.

The HPC PowerStack community promotes tools, among them the Variorum4 , an extensible, vendorneutral library for exposing power and performance capabilities of low-level hardware events across diverse architectures in a user-friendly manner.

Regarding the measure of environmental indicators, people have also developed Python libraries such as CodeCarbon5 , CarbonTraker6 , and ImpactTracker [START_REF] Henderson | Towards the systematic reporting of the energy and carbon footprints of machine learning[END_REF]. CodeCarbon, which we use, in this paper, estimates and tracks carbon emissions from your compute engine and quantifies and analyzes their impact. Carbon-Tracker is a tool for tracking and predicting the energy consumption and carbon footprint of training deep learning models as described in [START_REF] Anthony | Carbontracker: Tracking and predicting the carbon footprint of training deep learning models[END_REF]. ImpactTracker creates a leaderboard for energy-efficient reinforcement learning algorithms to incentivize responsible research in this area as an example for other areas of ML.

III. Presentation of the calculation of the historical EcoIndex and critical analysis

A. Predicting energy consumption of IT resources

Estimating the carbon footprint of human activities can only be done indirectly. The method used, in general, relies on a targeted activity model. This is the case for EcoIndex 7 , which is only concerned with HTTP requests. This metric is based on the "3-tier" concept considering the three parameters client, server, and network, which in the model are weighted. In short, EcoIndex is a tool that, for a given URL, makes it possible to evaluate its absolute environmental performance using a score out of 100 (higher is better), its relative ecological performance using a score from A to G, the technical footprint of the page (weight, complexity, etc.), and the associated environmental footprint (greenhouse gases and water).

The "historical" version of EcoIndex is a plug-in to be installed on the browser that works as follows: One provides a URL to EcoIndex, which transfers it to the server side. The server responds and returns to the browser an HTML page containing the answers to the request. The plug-in measures the footprint of the application in terms of the number of elements in the web page (the number of HTML tags, noted DOM), the number of requests in the returned page (noted REQ), and finally, calculates the number of bytes of the returned HTML page (noted SIZE) that have passed through the network. Thus, EcoIndex implicitly takes into account the cost of sending data across the network. These values are fed into the EcoIndex algorithm to calculate the performance and environmental footprint.

B. How does EcoIndex work?

The term EcoIndex refers both to a set of best practices for building a website and to a software tool that evaluates several factors for a given URL:

• its absolute environmental efficiency using a score function on a scale of 0 to 100 (the higher the score, the better),

• its relative environmental performance using a score from A to G as known for household devices or food (Nutri-Score),

• the technical footprint of the page (weight, complexity, etc.),

• the associated environmental footprint (greenhouse gases generated, water resources consumed, etc.). EcoIndex aims to help as many people as possible become aware of the environmental impact of HTTP requests and propose concrete solutions to reduce it. Let us now zoom in on the four previous metrics (which do not consider the best practices component). They are simple to understand, even for non-specialists. However, this model has limitations that will be explored step by step in the following.

C. Limitations inherent to the 3-tier model

The complementary analysis of an expert is essential for a complete and reliable operational evaluation 7 https://github.com/cnumr/GreenIT-Analysis of environmental performance. Indeed, EcoIndex does not take into account, in the sense of a life cycle analysis, the environmental impact of the computer making the request nor of the complete user's browsing. Only a query isolated from usage is analyzed, such as the Nutri-score or the washing machines purchased at any supermarket store. Similarly, when the request is resolved on the server side in a data center (for example, at Google when the URL is http://www.google.com), EcoIndex does not take into account the environmental impact of these servers in the classical sense of life cycle assessments (LCA), nor of the different network equipment that is crossed between the user terminal and the data center 8 .

EcoIndex is not at the same level as an LCA, and it is a tool anchored in the 3-tier model, a highlevel approach with limitations to capture fine-grained phenomena. However, it allows for discussion of models and their attributes that would significantly characterize the environmental impact of the Web, reduced to the dimension of HTTP requests. The positive sides of EcoIndex are that the loading, creation, and display of the page in the browser are not simulated and that the three parameters DOM, REQ, and SIZE (see Equation 1), capture an architecture that governs the macroscopic operation of a request on the Web thus EcoIndex makes sense.

D. Limitations inherent to the calculation itself

In detail, the environmental performance is calculated based on normalized parameters representing each third of the client/server architecture (see Equation 1) by a weighted sum, where the weights are determined by macroscopic studies once and for all. They do not consider variations over time or the user's geographical location.

Moreover, when looking closer at the open source implementation of EcoIndex, it is not directly the parameters DOM, REQ, and SIZE that are considered but values corresponding to quantiles. In Equation 1, quantiles are hidden in the F functions. A few values have been determined by retrieving the three parameters from URLs in a reference URL database, the HTTParchive 9 . This database offers open data, and, in our case, we used the April 2022 extraction. Basically, each line of the extraction gives a URL, i.e., a request that occurred in April 2022 on the Internet.

One question that arises is the stability of these quantiles over time: are they the same in 2023 as in 2020, when they were determined for the historical EcoIndex? A priori, websites are regularly reviewed to adopt better eco-design practices over time; therefore, there is no reason for the quantiles to be fixed once

EcoIndex = 100 - 3 * F DOM (DOM ) + 2 * F REQ (REQ) + 1 * F SIZE (SIZE) 6 (1)
and for all. In the same vein, we can also make a minor remark on the fact that some sites, for example, those of the big media, are dynamic and that the value of EcoIndex is likely to evolve from day to day, but probably not too abruptly, for example from A to G. EcoIndex seems to us to be robust to this phenomenon. However, the A-G grades correspond to the EcoIndex ranges of 100-81 for A and 10-0 for G. How were these different limits determined? Do they compare to the quantiles for the HTTParchive EcoIndex measures? They are close but different.

E. Limitations inherent in the attributes that make sense

The historical model only lends itself, a priori, to introducing new attributes other than the 3-tiers in the model incompletely, as we have pointed out (not taking into account the environmental impact of the user's terminal and the server). We could consider, for example, introducing in the model notions of the energy mix and, in this case, propose a new EcoIndex+ indicator that would show grades turned to A for decarbonated energies used on the client and serverside and grades turned to G if the powers involved are carbonated. If the HTTP request goes through a 4/5G mobile, we could also aggregate the CO2 impact of the operator, which would lead to a richer view of the EcoIndex+.

To be more exhaustive in the attributes to be injected in EcoIndex+, we need, on the one hand, for the community to agree on these new attributes, and then we need to have associated computational methods able to process a large number of attributes using classical machine learning techniques that allow for processing models with several hundreds of characteristics at low cost!

F. Statistical analyses of our dataset

We first conducted some experiments for the historical EcoIndex to check if working with quantiles leads to issues or not. Experiments correspond to statistical treatments, and a dedicated Jupyter notebook is available on our GitHub repository 10 . We used a dataset of more than 100k URLs, all coming from the April 2022 dataset of the HTTParchive. We first observed the distribution of requests' number, DOM number, and transfer data size parameters. We noticed that the number of DOM nodes does not follow a Poisson distribution like the number of HTTP/HTTPS on the page or the number of kb transferred. However, we also considered the empirical distribution function (also called an empirical Cumulative Distribution Function, eCDF), which is the distribution function associated with the practical measure of a sample. Each value at any specified value of the measured variable (DOM, REQ, or SIZE) is the fraction of observations of the measured variable that are less than or equal to the specified value. In this case, we also noticed the Poisson distribution of the parameters, with a slight difference in the number of DOM nodes.

The ExoIndex has a uniform distribution on our dataset; see Figure 1 confirming that our dataset is diverse and big enough regarding the dataset initially used by GreenIT. There is nothing special to notice except that the numbers of values at the extreme part of the spectrum are few, which is expected and confirms that the definition of the EcoIndex is relevant.

Then we studied the impact of each parameter (DOM, REQ, SIZE) on the EcoIndex. The pair plot we used helps us understand the best features to explain a relationship between two variables or form separate clusters. The main diagonal subplots are the univariate histograms (distributions) for each attribute. Check with the notebook.

We noticed that the parameters are highly correlated visually. We also noticed that the parameters correlate highly with the EcoIndex, as was expected. While the number of DOM and the number of requests relate higher than 0.8, the data transfer size has a 0.63 correlation which indicates that it is less significant. If we include the outliers, the correlations drop between 0.3 and 0.6.

The original javascript code considers 10, 25, 40, 55, 70, and 80 as delimiters to give the grades (A-G). We decided to compute the quantiles for each parameter since we know their measured values for each HTTP request. Then, we noticed that the difference in values for the quantiles (the original and the computed ones) is relatively small. We observe in Figure 2 a larger difference for the request variable.

Then, we switched to the computation of the EcoIndex with new quantiles. The distribution of the new EcoIndex, as with the historical EcoIndex, follows that of the number of DOM nodes, and this is logical since it is the most impactful parameter. The two distributions obtained with new and historical quantiles are close. Intuitively, this point was unexpected, but it confirms a slight variation in the quantiles between 2020 (the ones used for the historical EcoIndex) and 2022 (the ones computed on our 2022 dataset).

In Figure 3, with 60 bins for the histogram, we observe that the difference in values for the two EcoIndex is at a maximum of 2500 on the y axis and that the difference may be positive or negative, ranging from -4 to +5.5 on the x. Thus, Figure 3 represents the distribution of the difference between calculations. Since the difference is slight, the two computed EcoIndex are similar. Finally, we found that the cosine similarity metric is close to 1, meaning that the computed EcoIndex (historical and new) are very similar. Thus, the new quantiles do not significantly impact the measurements. We conclude with a stability of the original quantiles over time, meaning that we can continue to use the quantiles from the historical EcoIndex.

IV. The novel approaches

A. Motivations and hypotheses

We showed in the previous section that the process does not require calculating each quantile again each time we change the dataset. However, we have not answered what happens if the weights change. In this case, it is, therefore, necessary to launch a benchmark, the HTTP archive, for example, at each new weighting. Remember that the choice for the weights is based on macro-studies of the ICT field, which is out of the scope of this paper. We now discuss approaches that do not require a systematic switch to a benchmark; thus, they are more generic than the previously known ones. We consider two types of approaches. The first ones continue to produce a score, whereas the second builds a map of the global situation.

In the first case, we design approaches without the notion of quantiles in mind. In the second case, we can position a given HTML request regarding similar requests. These methods have been proposed in [START_REF] Cérin | The ecoindex metric, reviewed from the perspective of data science techniques[END_REF]. In this paper, we provide arguments to compare them from a qualitative point of view. We aim to study how robust one proposal is, compared to another. We also aim to experiment with categorical data and for the second type of approach.

B. Techniques from the data sciences

We can turn to data science techniques to satisfy the requirements that have just been stated. The techniques of the first type allow us to project a point in an N-dimensional space onto the line while preserving the desirable property. If two points are close in the N-dimensional space, they will also be nearby on the line. Thus, the EcoIndex remains associated with one and only one value: the position on the line is the EcoIndex measure. This measure is easy to implement and does not need to go through quantiles. The triplet (DOM, REQ, SIZE) is projected directly on the line. The potential bias of quantiles is avoided.

1) Techniques that reduced to a single value: We now give a brief overview of the techniques. Remind that implementations, we mean the full details, are available on our GitHub repository or in reading our preliminary work [START_REF] Cérin | The ecoindex metric, reviewed from the perspective of data science techniques[END_REF].

The first technique we use, according to this vision, to compute the EcoIndex is based on Random Projection [START_REF] Bingham | Random projection in dimensionality reduction: Applications to image and text data[END_REF], [START_REF] Achlioptas | Database-friendly random projections[END_REF], [START_REF] Siddharth | Randpro-a practical implementation of random projection-based feature extraction for high dimensional multivariate data analysis in r[END_REF] This well-known technique is a widely popular technique used in approximate similarity searches. Approximate search allows highdimension exploration search. Thus, the technique allows dimensionality reduction, which is one new goal of this paper, aiming to prepare the future of EcoIndexes. Note that, if we try several random matrices for projections, all do not lead to the same ordering on the line. The important fact here is to keep the same random matrix for all the experiments. The second technique uses the Locality Sensitive Hashing (LSH) concept. LSH [START_REF] Indyk | Approximate nearest neighbors: Towards removing the curse of dimensionality[END_REF], [START_REF] Gionis | Similarity search in high dimensions via hashing[END_REF] is again a widely popular technique used in approximate similarity searches, i.e., for nearest neighbor searches in high-dimensional spaces.

The general idea is to consider the neighbors of a given (DOM, REQ, SIZE) triplet, then to summarize all of them through a single value (centroid) given a certain (DOM ′ , REQ ′ , SIZE ′ ), and then approximate the EcoIndex as the sum DOM ′ + REQ ′ + SIZE ′ . According to our formulation, two distinct queries may have the same neighbors because they are close in the initial 3-D space. Thus, they may both have the same EcoIndex. This effect is intended because we want to focus on the similarities between queries.

The third technique is to search for collinearities as follows. In geometry, two or more points are said to be collinear if they lie on the same line. Hence, the collinear points are the set of points that lie on a single straight line.

Intuitively, we compute 'the most collinear' vectors to a given vector (DOM, REQU EST, SIZE), and then we summarize all of them through a single value (centroid) given a particular (DOM ′ , REQ ′ , SIZE ′ ). Finally, we approximate the EcoIndex as the sum

DOM ′ + REQ ′ + SIZE ′ .
The root-mean-square error (RMSE) is a frequently used measure of the differences between values predicted by a model or an estimator and observed values. Tables I, II and III make pairwise comparisons of the techniques, according to the RMSE quality metric, and over more than 100k URLs from our dataset (url_4ecoindex_dataset.csv). Remind that we compare EcoIndex values ranging from 0 to 100.

As a local conclusion of this study, the new approaches seem significantly different since the RMSEs are sparse. We are in the presence of three different techniques that reduce the computation to a single Another possibility we explore further in the paper is to consider that the "ground truth" is given by the method with the less energetic consumption or the less CO2 production method. We also conducted experiments to compare the RMSE of the historical EcoIndex with the three other methods, and the conclusion is similar to the previous one. Regarding the metric, the historical EcoIndex is different from all other methods.

However, a comparison between techniques can be made by considering, first, the execution time of one execution and, second, the carbon footprint to solve an HTTP request. CodeCarbon, as we mentioned earlier, is a Python software package that seamlessly integrates into your Python codebase. It estimates the amount of carbon dioxide (CO2) produced by personal computing resources to execute the code.

Table IV shows the measurements we have taken for the energy consumption and CO2 emission of the four methods, including the historical EcoIndex, referenced as EcoIndex in the table. Given 100k (DOM, REQ, SIZE) triplets, we measured the environmental costs of the execution for computing the EcoIndex. The Energy and CO2 metrics are those given by the Codecarbon tool. The notebook was an 11th Gen Intel(R) Core(TM) i7-1185G7 @ 3.00GHz with 32GB of RAM.

It is worth noting that, as expected, because we use a KNN search with the LSH implementation, which demands a lot of resources, the LSH method is the most critical, having an order of magnitude even less good than the collinearity method, hence an X in the column. We also observe that the collinearity method is too energy inefficient because of the implementation that requires too many intermediary data structures. Finally, the best method is the random projection method, as expected, due to its algorithmic simplicity. This is the method of choice because it scales up (with respect to the number of parameters it can process) compared to the calculation of the historical EcoIndex.

Notice that our implementation of the historical EcoIndex is sensitive to the location where we Note also that the measures in Table V correspond to a measurement of the full cycle (determination of the three parameters, then the computation of the EcoIndex, given the parameters). In contrast, values in Table IV correspond to the computation of the EcoIndex only, given the parameters.

From the experiments and results shown in Table V, we conclude that it makes sense to consider the location (in some way to be determined) in the computation of an environmental impact of HTTP requests.

C. Building a map

Instead of reducing the problem to a single value, we propose to use the Self Organizing Map (SOM) representation. SOM is usually present in the exploration phase of a data science project, and it clusters data for finding representative data in large datasets. It is an unsupervised machine learning technique used to produce a low-dimensional (typically two-dimensional) representation of a higher-dimensional data set while preserving the topological structure of the data. SOM forms a semantic map where similar samples are mapped close together and dissimilar ones apart.

In practice, SOM usage is for clustering, data visualization, anomaly detection, etc. More concretely, we can use SOMs to build a recommender system or to identify trends and patterns. Another example, we can also draw a U-Matrix, representing a self-organizing map (SOM) where the Euclidean distance between the codebook vectors of neighboring neurons is depicted in a grayscale image. This image is used to visualize the data in a high-dimensional space using a 2D image.

In this subsection, we engage our study in the direction of dealing with much more than three attributes. The general question is, for instance, "How to introduce new attributes into the model to capture specific insights related to the environmental impact of ICT" as the energy mix. We would also like to consider if the HTTP request goes through a 4/5G network or fiber. We want to aggregate in the model the CO2 impact of the TELCO operator. In short, we are convinced that we have to deal with a potential of 10, 20, or more attributes, all related to "energy."

We, therefore, propose to focus on the following attributes found in public datasets at Enedis11 (France's national electricity supplier) and Arcom12 (France's telecom regulatory agency), in addition to the (DOM, REQ, SIZE) attributes.

From Enedis, we have access, city by city, to the annual consumption and production of electricity, which can be low-carbon or not. The Arcom performs throughput tests (4G/5G or fiber) based on HTTP requests. It also gives the GPS position of the location from which the HTTP request originated. So we can know the city and link it with Enedis data.

The intuitive idea is to introduce a new model based on the location and the type of electricity used. We do not believe that "a universal" grade, independent of the territory, makes sense. We also believe that making HTTP requests from a device powered by green energy should lead to a better overall score than a device powered by a non-green source.

Topological maps (SOM) help us in this respect. They group together in similar situations. So, by zooming in on the points on the map around a query, we'll be able to find the cities that look like this query and the queries that look like me.

In this way, we no longer produce a grade but a fairly general view of the state of the System, having executed all the HTTP requests of the topological map. We retain the possibility of making comparisons for one or more attributes between two requests of our choice.

We have implemented this model according to Scikit-learn [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF], and Susi [START_REF] Riese | Supervised and Semi-Supervised Self-Organizing Maps for Regression and Classification Focusing on Hyperspectral Data[END_REF] packages. Hyperparameters 13 for Susi are also documented, and we used the defaults. All the technical details (name and meaning of attributes) are available on our GitHub repository. Finally, based on the som_dataset.csv dataset available on our repository, we get the topological map depicted in Figure 5. The (DOM, REQ, SIZE) attributes are given by the EcoIndex method.

The attributes we consider in these experiments, namely those extracted by som.py and som_test1.py, are given in Figure 4. The corresponding CSV files are som_dataset.csv and som1.csv.

The view we get in Figure 5 Thus, now, we can query the classification to analyze the "points" with the same color and, maybe, to find patterns in our dataset of EcoIndex values. Here, for our toy example, namely the som_dataset.csv dataset, we found that the most impacting factor for the clustering is the request parameter.

The view we get in Figure 6, based on som1.csv, som.py, dealing with categorical data (operator, city, and URL), shows the U-matrix (unified distance matrix) where light colors depict closely spaced node codebook vectors and darker colors indicate more widely separated node codebook vectors. Thus, groups of light colors can be considered clusters, and the dark parts are the boundaries between the clusters. In this case, we observed that the data forms three clusters, which is more informative than the plot in Figure 7. With 7 it is more difficult to isolate the clusters in the top left and bottom right and the oblique one in the middle of the plot.

V. Lessons learned and general comments

In this paper, we turned to data science techniques to satisfy the requirements stated and discussed in Section III. This scientific field has developed strategies to manage many attributes, such as random projection or Linear Sensitive Hashing (LSH) techniques. They are simple to understand, and this is positive to stay in the spirit of the simplicity of the original definition of the EcoIndex.

The first technique allows us to project a point in an N-dimensional space onto the line while preserving the desirable property. If two points are close in the Ndimensional space, they will also be close to the line. Thus, the EcoIndex remains associated with one and only one value. This measure is easy to implement and does not require quantiles like the historical EcoIndex. The potential bias of quantiles is avoided.

With our second technique, Data science also allows us to no longer define the EcoIndex metric as a reduction to one value but to consider a twodimensional map obtained from a transformation of the N-dimensional space, where the points of this map are grouped by affinity. We can thus situate a particular triplet (DOM, REQ, SIZE) to neighbors. The technique's name is Self-Organizing Map (SOM), and we developed an example with about 15 attributes. Again, this technique bypasses the bias for quantiles and opens new directions for exploring datasets of the considered new domain. Our implementations and experiments aimed to validate that several alternative definitions to the historical definition lead to nonaberrant, acceptable, and differentiating EcoIndex values.

The competitive advantage of our methods is related to the fact that the chosen procedures, all of which come from data science, allow a scaling on the number of attributes we may consider now or in the future. Indeed, we exemplify that we should include in the definition of EcoIndex attributes of location (country, region, department, city, neighborhood) or even attributes of the type of electricity production (nuclear, gas, coal, solar, wind). The reason is twofold. First, we do not believe in a global grade. Second, we believe that local information is the more important for deriving a model. Third, the type of electricity powered by our computers should be introduced in the models that are supposed to capture the environmental impacts of ICT.

Technically speaking, in our implementations we encode attributes that are strings, such as city name, according to a hash, given an integer value.

Our methods would allow, by design, the number of attributes to increase while maintaining a fast computation time, thus saving energy. Thus, we are convinced that Data science is the right direction to go further. We also believe that we are on the right track for proposing recommendations in the long term. For instance, by examining the topological map (SOM) A t t r i b u t e s s e l e c t e d i n som_dataset by som . py : 'dom ' , ' s i z e ' , ' r e q u e s t s ' , ' EcoIndex ' , ' GreenHouseGaz ' , ' water ' , ' PageChargeeMoins10s ' , ' temps_en_secondes ' , ' Conso t o t a l e (MWh) ' , ' Conso moyenne (MWh) ' , ' P h o t o v o l t a i q u e ' A t t r i b u t e s s e l e c t e d i n som_dataset by som_test1 . py : o p e r a t e u r ; l a t i t u d e ; l o n g i t u d e ;CP; v i l l e ; u r l ; dom ; r e q ; s i z e ; EcoIndex ; GreenHouseGaz ; water ; PageChargeeMoins5s ; temps_en_secondes ; Conso_totale_ (MWh) ; Conso_moyenne_ (MWh) ; P h o t o v o l t a i q u e at a particular point, the recommendation could be to avoid visiting this or that website because it consumes or produces much more CO2 than another site. SOM provides richer information compared to a score. So now we come to the question of how to use the SOM, and for this, we need to turn to civil society and environmental impact experts.

VI. Conclusion and research directions

This paper discussed the EcoIndex, an environmental score for an HTTP request, and some of its limitations. It also compared qualitatively alternative approaches. We balance between interpretability and explainability with an insight into interpretability. Interpretability focuses on understanding the inner workings of the models, while explainability focuses on explaining the decisions made. On the explainability plan, we call on the entire IT community and the citizens to mobilize on the issues raised in this article. Crossing, in particular, competencies in Architecture, Systems, Networks, and Learning is necessary.

EcoIndex, from the point of view of environmental impact metrics and good practices in website ecodesign, is a simple approach that contributes to a better understanding of the phenomena and issues related to the role of digital technology in global warming. The indicator is exciting in the logic of improving successive versions of websites.

We discussed several contributions: a detailed analysis of the weaknesses of the current calculation, consumption measurements for the new methods, the demonstration that location makes sense and that it should constitute one or more new attributes in the model, an implementation perspective of the most promising methods for a future and new measurement of the environmental impact of HTTP requests.

Much work remains to be done to deepen our knowledge and better understand the relationships between the different high-level models of the 3-tier architecture type and the field analyses of the life cycle of a digital product or equipment (LCA). On the other hand, it would be necessary to qualify and learn about data sets related to the studied domain (modeling phase) to use the model(s) in practice. Finally, there is the issue of standardization, particularly at the international level. Standards accompany the development and trade of products and services that meet objectives such as social concerns (consumer protection, safety, and security of services).

Thanks to the ideas presented in the article, the initial toolbox available on our GitHub repository for calculating the environmental cost is enriched with new methods from machine learning. In supplement to the dataset exploration steps, we propose now to investigate the question of utilizing the representations we exposed. As exposed above, we believe that a recommendation system for the citizens may help to encourage them to take a more environmentally friendly approach to ICT.

The work presented in this article is ultimately placed in an even more general context. First, can we observe, year after year, an evolution of the environmental impact of IT? Being optimistic, Web developers are concerned about good environmental practices and modify, over time, the HTTP pages they maintain having a bad EcoIndex. The Web, as a whole, has a chance to control its environmental impact for a long time from the moment we equip ourselves with a "weather forecasting system."

Figure 1 .

 1 Figure 1. Distribution of EcoIndexes

Figure 2 .

 2 Figure 2. Quantile's similitude for the request parameter

Figure 3 .

 3 Figure 3. Histogram of the difference between quantiles

  , based on som_dataset.csv, som.py, shows the distribution of the EcoIndex in one class (top of the Figure) and the distribution of the values into three classes (bottom of the Figure) according to the SOM clustering algorithm.

Figure 4 .Figure 5 .

 45 Figure 4. Attributes under consideration with SOM experiments

Figure 7 .

 7 Figure 7. Clustering with public data from Enedis, Arcom issued from som1.csv

Table V

 V Sensitivity analysis regarding the location

	Location	URL	GRADE	CO2
	JAPAN	https://www.nii.ac.jp/en/faculty/digital_content/andres_frederic/	C	3.317e-05 kg
	JAPAN	https://research.nii.ac.jp/~andres/official/content_e.html	A	3.154e-06 kg
	FRANCE https://www.nii.ac.jp/en/faculty/digital_content/andres_frederic/	C	1.220e-05 kg
	FRANCE	https://research.nii.ac.jp/~andres/official/content_e.html	A	1.280e-06 kg

https://www.youtube.com/watch?v=UM3EW01_PUY&t= 143s&ab_channel=Jean-MarcJancovici

https://httparchive.org/

https://www.ecoindex.fr/a-propos/

https://variorum.readthedocs.io/en/latest/

https://github.com/mlco2/codecarbon

https://github.com/lfwa/carbontracker

https://github.com/christophe-cerin/Ecoindex-Revisited

https://www.enedis.fr

https://www.arcom.fr/

https://susi.readthedocs.io/en/latest/hyperparameters. html

Acknowledgments

This work is partially supported by the Multidisciplinary Institute on Artificial Intelligence (MIAI) at Grenoble Alpes (ANR-19-P3IA-0003). This work is also conducted during the Délégation with Centre National de la Recherche Scientifique (CNRS) of Mr. Cérin. Thanks to the institutional support of the CNRS, the universities of Grenoble Alpes, and Sorbonne Paris Nord.

//ecoinfo.cnrs.fr/category