Ali Tidjani
email: alitidjani680@gmail.com

Maxime Redondin
email: maxime.redondin@vedecom.fr

Laurent Bouillaut
email: laurent.bouillaut@ifsttar.fr

Dimitri Daucher
email: dimitri.daucher@ifsttar.fr

Impact of road infrastructure characteristics on road markings

Keywords: Road markings, FAMD, AHC, road infrastructure, surface signing, degradation

Road markings channel traffic flows and guide road users visually, especially at night. Their quality and reliability are, therefore, important issues which must be closely followed to ensure the safety of road users and especially their perceptibility for the future autonomous cars. Thus, previous study has shown that it is possible to segment markings of the center line into maintenance strategic areas. However, this study didn't take into account all the characteristics of road infrastructures that could have an impact on the degradation of markings. Indeed, depending on the structure and complexity of all road infrastructures, these road markings could present a different degradation process over the time and in specific areas. So, the identification of these areas can help road managers to develop localized maintenance strategies. In this study, a Factor Analysis of Mixed Data (FAMD) combined with an Agglomerative Hierarchical Clustering (AHC) is proposed as the method to identify these areas or clusters in the case of the French National Road 4 (NR4).

Introduction

The surface signing regroups, all the marks on roads used to materialize the rules of use of the ways open to the public traffic. It is an important aid to driving, channeling traffic flows, specifying rules of roads, materializing parkings and guiding the user visually, especially at night. Recent papers from VEDECOM Institute (Revilloud, Gruyer et Rahal, A lane marker estimation method for improving lane detection 2016) (Revilloud, Gruyer and Rahal, A new multi-agent approach for lane detection and tracking 2016) show that a clear and visible horizontal signage is more important than a roadway in good condition for an autonomous vehicle.

The road markings are made perceptible at night thanks to their retroreflection luminance. Indeed, markings return the light emitted by the headlights of a vehicle towards its driver. In other words, retroreflection allows the visibility of road markings in night time.

The retroreflection luminance is quantified by devices called retroreflectometers. Figure 1 presents the case of the Ecodyn from MLPC [START_REF] Nextroad | ECODYN mlpc® -Signing visibility[END_REF]. The device is designed to be fixed on a vehicle and measured dynamically the retroreflection of road markings (Fig. 1(a)). The measuring process is to attach the unit on the right or left side of the inspection vehicle. A white light source illuminates the marking at 6 m at the front of the camera and the amount of retro-reflected light is However, road markings are subjected to a phenomenon of degradation. The figure 2 present it. A new marking is a white object and admits a strong retroreflection luminance (600 𝑚𝑐𝑑 𝑚² 𝑙𝑥 ⁄ ⁄

). Over time, the marking undergoes a decrease in their level of retroreflection luminance. In the best case, it will become a grey object and admit a low retroreflection luminance (50 𝑚𝑐𝑑 𝑚² 𝑙𝑥 ⁄ ⁄

). . As this degradation of markings is an important issue, it is necessary for road network managers to take care of the [START_REF] Nextroad | ECODYN mlpc® -Signing visibility[END_REF] markings to avoid any unfortunate consequences. Also, it must be added that the development of a system maintenance strategy requires a first analysis study which can allow identifying maintenance areas of road markings. In addition, the literature of the last thirty years presents mainly models of degradation based on regression methods. For example, [START_REF] Lu | Performance of traffic markings in cold regions[END_REF] proposed an exponential model as a function of age of markings, [START_REF] Abboud | Cost and longetivity based scheduling of paint and thermoplastic striping[END_REF],developed different exponential models as a function of the Annual Average Daily Traffic (AADT) and the age of markings, [START_REF] Sitzabee | Pavement marking degradation modeling and analysis[END_REF] proposed a multilinear model as a function of time, the initial retroreflection, the AADT, the lateral locations of markings and marking color However, this approach remains relatively difficult to apply to the reality of the field.

The thesis report of Maxime Redondin (M. [START_REF] Redondin | Approches de classifications à partir de données fortement censurées pour l'analyse de fiabilité et la définition de stratégies de maintenance -Application aux marquages routiers dans un contexte de véhicules autonomes[END_REF] presents different maintenance strategies for road markings according to their retroreflection luminance. This thesis shows that it is possible to segment, at the scale of a road, the markings of the center line in strategic areas of maintenance (M. [START_REF] Redondin | Temporal clustering of retroreflective marking[END_REF]) and analyzed the life cycles of the markings of the center line through a Weibull analysis (M. Redondin, L. Bouillaut, et al. 2018). However, this thesis didn't consider the different characteristics of a road infrastructure that could have an impact on the degradation of markings.

The ambition of this study is to segment the road infrastructure according to different characteristics such the degradation of the pavement, the road surface signing or traffic lanes configuration. This approach produces an identification of strategic areas of maintenance based on the road infrastructure. The general objective of this study is the evaluation of the impact of the characteristics of road infrastructure on the quality of road markings. In other words, the central question that will be dealt with throughout this study is to know to what level road infrastructure can impact the strategic areas of road markings maintenance.

In this study, a Factor Analysis of Mixed Data (FAMD) [START_REF] Escofier | Analyses factorielles simples et multiples (Objectifs, méthodes et interpretation)[END_REF] [START_REF] Pagès | Analyse Factorielle de Données Mixtes[END_REF]) combined with an Agglomerative Hierarchical Clustering (AHC) [START_REF] Tufféry | Data Mining and Statistics for Decision Making[END_REF]) is proposed as the method to identify strategic areas of road markings maintenance.

Then, three markings lines are identified: the center line, the emergency one and the edge one. The annual inspections of these three marking lines are provided by CEREMA and a monitoring of the bitumen is provided by DIR EST. Also, some data bases that describe the major characteristics of road infrastructures such as the types of roadways were collected on the Ministère de l'Ecologie et de la Transition Energétique (the French Ministry of ecological and solidarity transition) website. A fusional algorithm has been elaborated to gather all these data bases into a big one before applying the FAMD and AHC.

As an illustration of this approach, a 100km section of the French National Road 4 (NR4) is considered.

After the introduction of the classification algorithm, this paper will focus on the fact that the surface signing is more segmented according to both characteristics and parameters of the considered road infrastructure. Another interesting point is that the areas which weren't classified in the previous study (M. [START_REF] Redondin | Temporal clustering of retroreflective marking[END_REF]) have been classified in new clusters in this case.

Finally, this study is a first step to introduce the modeling and optimization of road infrastructure maintenance for the autonomous car.

Collection of the used data

This section presents the three data sources. To simply, each variable is defined by a key word. The study is based on different inspections realized between 2007 and 2015.

The first data source is provided by CEREMA EST. The surface signing is annually inspected each September since 2007. The chosen retroreflectometer is an Ecodyn. Three lines are identified: the broken center line, the emergency one and the median strip one. However, the FAMD considers only the center and the emergency line because those of the median strip line is not available all over the NR4. To simply: C20XY, E20XY, M20XY represent respectively the retroreflection luminance evaluated during the 20XY campaign of the Center, Emergency and Median strip line.

The second data source is provided by DIR EST. The pavement is yearly inspected. The different types of bitumen identified are: Pure Thin Bitumen (PTB), Modified Thin Bitumen (MTB), Very Thin Bitumen (VTB), Very Thin Bitumen Modified (VTBM), Semi Granular Bitumen (SGB), Semi Granular Modified Bitumen (SGMB) and High Module Coated (HMC). There was no replacement of bitumen between 2007 and 2015. The age (Age) of pavement is also provided.

The final data source is provided by the French Ministry of ecological and solidarity transition. The ministry launched an open data initiative in 2017 as part of the Open Data in a goal of transparency in the light of several sectors (Ministère de l'Ecologie et de la Transition Energétique 2018). The objectives of the government in making the data available to the public are to inform decision makers and citizens in a transparent way about the state of the heritage and the use of public funds, to provide data to the digital sector companies who develop user services and strengthen the role of the state as a service provider in certain areas. The Ministry feeds and publishes a dozen sub-bases.

Each Point of Reference (PR) is localised in Lambert coordinates 93. The distance in meter of each consecutive PR is deduced.

The traffic lane between two PRs are descripted (see figure 3):

• single lane: 2 ways superior to 7m (2(> 7)), • single lane: 2 ways inferior to 7m (2(< 7)), • single lane: 3 ways superior to 10m (3(> 10)), • single lane: 3 ways inferior to 10m (3(< 10)), • single lane: 4 ways (4),

• separate lane 2 × 2 ways (2 × 2),

• separate lane 2 × 1 way (2 × 1). Crossings on a given PR: interchange with a highway (Interchange), crossing with another road (Crossing) and split. In other case, there is no specific observation (No).

The general degradation level of the roadway: Excellent (Exc), Acceptable (Acc), Bad, Poor.

Other information between two PRs: the Annual Average Daily Traffic (AADT) and the width of roads (Width). The databases are updated year after year and allow a follow-up in time. After the collection of these databases, a fusional algorithm has been elaborated to gather them into a big one that will serve as the support to the methodological framework. This final database defined each PR by a specific road infrastructure, a degradation level of pavement and a monitoring of the surface signing. This description is done by qualitative and quantitative variables. The FAMD proposes a data management and identifies different correlation between variables. The final clustering identified different PR which admit both a similar description and a similar monitoring of markings.

Methodological framework of the study

Factorial Analysis of Mixed Data

The Factorial Analysis of Mixed Data (FAMD) is dedicated to the analysis of data containing both qualitative and quantitative variables. In practice, the FAMD behaves globally as a Principal Component Analysis (PCA), transforming the qualitative data into a Complete Disjunctive Table (CDT). In fact, a CDT makes it possible to transform qualitative data into a new table indicating whether individuals possess the property of the qualitative variable in question. The CDT's weight is fixed by [START_REF] Pagès | Analyse Factorielle de Données Mixtes[END_REF].

PCA is an exploratory technique that summarizes the information contained in a set of data into several synthetic variables which are linear combinations of the original variables based on data discrimination.

To produce a summary of information in the sense of the PCA is to establish a similarity between individuals, to search for groups of homogeneous individuals, to highlight a typology of individuals. As for the variables, it is to highlight the links between them, by means of synthetic variables and to highlight a typology of variables. The PCA seeks in a general way to establish links between these two typologies.

One of the main objectives of this method is to reduce the size of the set of original variables or, in other words, the representation of the maximum amount of information contained in the starting variables using a reduced number of new variables, correlated between them. Indeed, a small set of non-correlated variables is easier to understand and use in different analyses than a larger one.

Thus, the first steps of the FAMD under the formalism of the PCA correspond to upstream data processing. As a first step, the data table is split in two: the quantitative data on the one hand and the qualitative data on the other. In accordance with this formalism, the first table is normalized. The qualitative part is transformed into a CDT, each column of which is weighted by the inverse of the square root of the standard deviation. Finally, it is just about merging the two tables. The resulting table is interpretable by the PCA.

After these steps, the following ones correspond to two different but complementary points of view: the matrix of individuals and the matrix of correlations. The first describes each individual according to the descriptive variables and the second describes the descriptive variables according to the individuals. On each matrix, the eigenvalues are calculated and the eigenvectors are deduced. Then successive Hilbert projections to a twodimensional Cartesian plane are made to represent the map of individuals and the circle of correlations. The map usually has point clouds. Here, each cloud represents individuals who tend to share the same descriptive variables. The circle presents the main discriminating variables: the closer the variable is to the circle boundary, the more discriminating it is. Moreover, the more variables are distant, the more they are opposed. In the opposite, the closer two variables are, the more they are associated.

Each eigenvector contributes to the total variance of the ACP model. The principal components are the vectors that contribute the most.

Agglomerative Hierarchical Clustering

The Agglomerative Hierarchical Clustering (AHC) is an iterative classification method whose principle consists in producing sequences of nested partitions of increasing heterogeneity (between the partition in N classes where each object is isolated, and the partition in 1 class which groups all the objects) [START_REF] Tufféry | Data Mining and Statistics for Decision Making[END_REF].

The AHC is usable as soon as there is a notion of distance: in a space of individuals or in a space of variables. It is necessary to have defined the distance of two objects, which is generally natural, and the distance of two classes, which leaves more possibilities. It is precisely this distance that constitutes the criterion.

The algorithm of the AHC is established according to the following scheme:

1. The initial classes are the objects; 2. The distances between classes are calculated; 3. The two closest classes are merged and replaced by one; 4. Resume from 2. until you have only one class, which contains all the objects.

It should be emphasized at this level that the dissimilarity criterion used in the studies here is Ward's distance. This choice is justified by the fact that Ward's distance minimizes the loss of information because of data aggregation. This distance is defined by Eq.1 as:

𝑑 𝑊 (𝑋, 𝑌) = 𝑑(𝑥, 𝑦)² 1 𝑛 𝑋 + 1 𝑛 𝑌 (1)
4. Application to the French National Road 4

The French National Road 4

The National Road 4 (NR4), located in the department of Marne, is French National Road that connects Paris and Strasbourg. It is the basic example that will serve as a support in this study. The previous study (M. [START_REF] Redondin | Temporal clustering of retroreflective marking[END_REF]) identified five strategic areas on this road as shown in Figure 4 below. This figure also shows that the streets of Vitry le François are inaccessible.

The five clusters of the figure 4 are such as:

• The cluster 1 corresponds to open country roads. • The cluster 2 corresponds mainly to the region of Vitry-le-François. • The cluster 3 corresponds to the bypass of Sézanne. • The cluster 4 corresponds to the bypass of Fère-Champenoise. • The cluster 5 corresponds to a local highway near of Sommesous. However, these clusters of the last study are obtained without considering the road infrastructure characteristics (M. [START_REF] Redondin | Approches de classifications à partir de données fortement censurées pour l'analyse de fiabilité et la définition de stratégies de maintenance -Application aux marquages routiers dans un contexte de véhicules autonomes[END_REF].

Factorial Analysis of Mixed Data on NR4

After applying the PCA to the reconstructed quantitative data and qualitative data transformed into a CDT (through an algorithm of the FAMD developed on the software R), the proportions of the total variance explained by the first eleven main components are as presented by the Figure 5. It shows that the first component alone accounts for 14.7% of the total variance and the three first combined explain 33.2% of the variance. There are several criteria for choosing the number of components in a given study. The most common criterion is the Kaiser one. It is such that: an eigenvalue greater than 1 indicates that the principal component (PC) concerned, represents more variance compared to a single original variable, when the data are standardized. This is usually used as the threshold from which the main components are kept. Note that this is only applied when the data is normalized. In the present study, this criterion leads to the selection of 8 axes, explaining 59.9% of the total information contained in the data.

Another method for determining the number of principal components is the Karlis-Saporta-Spinakis criterion (KSS). The KSS is defined by the equation (2). Indeed, this criterion is one of the most reliable for determining the number of main axes because it takes into account a ratio between the number of variables and the number of individuals. This selection principle consists in retaining the components whose eigenvalues are greater than KSS with: 𝑝 the number of variables and 𝑛 the one of the individuals. This is, indeed, a robust variant of Kaiser's principle [START_REF] Karlis | A simple rule for the selection of Principal Components[END_REF].

𝐾𝑆𝑆 = 1 + 2√ 𝑛 -1 𝑝 -1 (2)
The application of the Karlis-Saporta-Spinakis principle selects the first nine main components with which, results a space having a large proportion of the total variance.

The interpretation of the factorial axes is done sequentially, for each axis and each point cloud, by looking at the contributions to the formation of the axes. The variables contributing most to the formation of a given axis are those whose coordinates on this axis are close to 1 in absolute value.

The first Component opposes single floor 2 ways with acceptable condition, without crossing, and thin coated, modified bitumen to separate floor 2 × 2 ways that are in excellent condition.

The second component opposes single floor 2 ways with an acceptable condition, without crossing, and lined with pure thin asphalt with separate floor 2 × 2 ways that are in poor condition and crossing a portion with a difference in level.

The third one opposes single floor 2 ways with poor condition, crossing a portion with a difference in level and semi-grained bitumen pavement to separate floor 2 × 2 ways that are in poor condition and without crossing.

The remaining components can be described in a lighter way. Component 4 opposes markings whose pavement condition is acceptable to sections admitting emergency stop strip. Component 5 opposes single floor 4 ways in state mediocre with separate floor 2 × 2 ways crossing an elevation gain. Component 6 opposes single floor 4 ways in poor condition and made of pure paved bitumen very thin bitumen modified. Component 7 opposes separate floor 2 × 1 way in poor condition made of pure semi-grained bitumen to the rest. Component 8 is between pavements in an acceptable condition having an exchanger and made of very thin bitumen pure with separate floor 2 × 1 way in bad state and without crossing. The last component selected opposes the single floor 3 ways without any particular intersection with single floor 4 ways in acceptable condition with interchange or crossing and made of pure semi-grained bitumen.

Correlation between different characteristic of the NR4

After the main component's selection procedure, the variables of the study can be projected on the two first main components.

The Figure 6 is the circle of correlation of the variables. It shows the relationships between all variables in this study. It can be interpreted as follows:

• Positively correlated variables are grouped together;

• Negatively correlated variables are positioned on opposite sides of the chart origin (opposite quadrants);

• The distance between the variables and the origin measures the quality of representation of the variables. Variables that are far from origin are well represented by the PCA. In this circle of correlations, the variables 2(< 7), HMC, Crossing and 3(< 10), for example, are positively correlated. This means that markings that are situated in the same areas have the same properties. However, markings that are correlated with the variable 2 × 2 and those which are correlated with the variable 2(> 7) have opposite properties. The markings of center line C2009, C2007 and C20013 are positively correlated with the markings of emergency line E2011, E2012, E2010 and E2009 while they are negatively correlated to E2014, E2015, E2013 and E2008.

Map of individuals and clustering

To segment the markings lines after the PCA, the next step is about to choose the number of clusters through the Agglomerative Hierarchical Clustering.

One solution would be to represent the jumps of inertia of the dendrogram which will make it possible to retain the optimal number of classes.

Indeed, depending on the height of the dendrogram section, the number of classes differs. In the first place, an analysis of the form of the dendrogram may give an indication of the number of classes to be retained. It is the jumps of inertia that allow this analysis.

Thus, after analyzing the inertial jumps obtained from the inertia graph, the dendrogram can be split into 2, 4, 7, 9 or 14 classes. To choose the optimal number among the five candidates, it is necessary to conduct a case-by-case study and choose the best one.

The selection criterion adapted for this study is the one of the qualities of the representation of individuals and variables according to the number of clusters selected. According to this criterion, individuals who tend to group together consider that they belong to the same cluster. And so, the best representation is that which allows a good distinction of different classes.

After confronting the five cases, it is the 9class score that stands out with the best quality representation. This partition in 9 classes is represented by the dendrogram of the figure 7 below. On the other hand, the projection of the individuals, and their 9 selected clusters, on the first factorial plane is also presented in figure 8. This figure makes it possible to better visualize the different groups of markings. It also allows them to associate the different characteristics given by the variables of the road infrastructure. Indeed, its reading of the map of markings is done by referring to the circle of correlations of the variables (figure 6). This Chart of Figure 8 is known as the map of individuals (here markings). Its reading is facilitated by the circle of correlations (see figure 6) translating as a compass. According to the four quadrants, each marking, can be described by the corresponding variables in the same quadrant.

The chart (figure 8) particularly shows that the cluster 1 in red color is particularly split in two. And another observation can be made on the cluster 9 in pink. This cluster is the one of areas of the NR4: it is isolated.

Cluster projected on the NR4

In this classification in nine clusters, the cluster 1 (see figure 9) in red color is particularly split in two. This is due to the fact that the markings of this cluster are laid mainly on two types of roads: separate floor 2 × 2 ways and single floor 2 ways.

It appears that the markings of the cluster 1 are posed on separate floor 2 × 2 ways and single floor 2 ways in excellent condition. On these roads, the presence of a little elevation, exchanger and plan is noted and more than half (58%) are coated with pure thin bitumen. The markings on the center line deteriorated considerably in 2010, two years after being laid.

In cluster 2, 55% of markings have acceptable pavement condition and 45% are in excellent condition. The roadways are almost totally (99%) paved with very thin modified bitumen and are separate floor 2 × 2 ways. In this cluster, there is the presence of plan and markings have evolved rather stable over time.

Cluster 3 includes only the markings whose pavements are in bad condition and it is essentially separate floor 2 × 2 ways coated with very thin modified bitumen. The presence of altitude difference is quite important (10%).

A significant number of Cluster 4 markings have poor road conditions (69%). These include markings on single floor 4 ways coated with very thin modified bitumen. The crossing with a Plan is quite remarkable (13%). A rather peculiar evolution of the level of retro-reflection of the edge line, which had a significant increase between 2007 and 2008 then a considerable decline before stabilizing, is also noticed.

Cluster 5 markings have an acceptable pavement condition and are essentially laid on single floor 2 ways. This is the only cluster that contains a single floor 3 ways portion which size is little than 10.5 m.

Cluster 6, on the other hand, is the one of separate floor 2 × 2 ways paved with very thin modified bitumen and in acceptable condition. There is a significant difference in altitude (75%) and heat exchanger (25%). In this cluster, the retro-reflection luminance level of the center line shows a remarkable peak in 2011 and for the emergency one it is in 2008 that a peak appears.

Cluster 7 groups together mainly single floor 2 ways coated with pure thin bitumen and in acceptable condition. It is the only cluster in which there is no crossing and its bitumen is the oldest of all and has the lowest daily traffic rate.

The group in which all the portions of roads are in excellent condition is the cluster 8. It contains a separate floor 2 × 2 ways. Apart from the presence of elevation and plan in this cluster, a fairly large percentage of exchanger is noticed.

Finally, cluster 9 displays a significant percentage of elevation gain (92%). Single floor 2 ways and separate floor 2 × 2 ways covered with modified semi-grained bitumen and in acceptable condition are encountered. The three types of markings in this cluster show a similar evolution.

In addition, a monitoring of the different lines of markings can be carried out according to the different years of the study.

Markings lines monitoring

From now, the median strip line is segmented according to the proposed clustering. As shown in the following figure 10, the follow-up of markings is deepened by observing each line of markings within the various clusters obtained. The evolution of road markings is remarkable in some clusters. For example, in the cluster 1, the markings of the center line deteriorated considerably in 2010, two years after being laid. In cluster 4, a rather peculiar evolution of the level of retro-reflection of the edge line markings, which had a significant increase between 2007 and 2008 then a considerable decline before stabilizing, is also noticed. In cluster 6, the retroreflection level of the center line markings has a remarkable peak in 2011 and for the emergency line markings it is in 2008 that a peak appears. In the cluster 9, the three types of markings lines show a similar evolution.

Comparison with previous study

To obtain strategic zones for the maintenance of road markings, Redondin (M. Redondin, Approches de classifications à partir de données fortement censurées pour l'analyse de fiabilité et la définition de stratégies de maintenance -Application aux marquages routiers dans un contexte de véhicules autonomes 2018) obtained 5 clusters through an AHC applied to the markings of the center line.

Obtaining groups of markings makes it possible to develop localized maintenance strategies by analyzing in particular the properties of the markings of these different groups. However, the AHC applied to center line markings, without considering certain infrastructure characteristics, does not give results covering the entire study portion of the RN4. In fact, the black area around Vitry le François (see figure 4), for example, is part of the unclassified zones. Also, it must be added that the previous study (M. [START_REF] Redondin | Temporal clustering of retroreflective marking[END_REF]) is limited to the center line of markings in its AHC.

The first noticeable difference between the two figures (figure 4 and figure 9) concerns the unclassified areas in the case of center line markings only. On the other hand, taking into account all the characteristics of the road infrastructure has made it possible to classify these unclassified areas. Also, it must be added that when the center line markings are analyzed alone, the groups obtained have a high degree of overlap in certain areas. This is not the case in the study of all road infrastructures where the different clusters are relatively well distinguished.

These differences in the number of clusters and areas of overlap between clusters bear witness to the impact of road infrastructure characteristics in the classification of horizontal road markings. This is a strong point of what has been accomplished in this study and is also more relevant than the case of the study of the center line only.

Conclusion

Road markings play an important role in the guidance of vehicles in general and future autonomous vehicles. This is especially true if we are interested to all road infrastructures that must be maintained to guarantee maximum safety for vehicular traffic.

The first results of this study show that considering all the characteristics of infrastructures makes it possible to segment road markings more effectively for strategic areas of maintenance. Indeed, the nine areas obtained in this study are better distinguishable (with less overlap) than those obtained without taking into account all the properties of road infrastructures. Another highlight of this work is that there are no more unclassified zones than what happens when we only consider horizontal road markings.

Moreover, this study made it possible to highlight a classification of all the road infrastructures contained in the data collected through the FAMD combined with an AHC methodology. This classification, compared to that of the center line markings, made it possible to detect the impact of road infrastructure properties on horizontal signage. Therefore, it would be interesting to analyze the life cycles of the markings of the center line, the emergency one and the edge one through a Weibull analysis.

In the end, it would be interesting to extend the present study by a panel type econometrics modeling to evaluate the level of impact of road infrastructure features on horizontal signaling.

Fig. 2 .

 2 Fig. 2. Road markings degradation over the time Available inspection devices stipulate that the retroreflection luminance of markings is the only measure used for evaluating marking degradation. The NF EN 1436 rules (AFNOR 2009 ) indicates that a new marking must admit a minimum of 150 𝑚𝑐𝑑 𝑚² 𝑙𝑥 ⁄ ⁄. As this degradation of markings is an important issue, it is necessary for road network managers to take care of the

Fig. 1 .

 1 Fig. 1. (a) The retroreflectometer Ecodyn, (b) Measurement process[START_REF] Nextroad | ECODYN mlpc® -Signing visibility[END_REF]

Fig. 3 .

 3 Fig. 3. (a) Single floor 2 ways, (b) single floor 3 ways, (c) single floor 4 ways, (d) separate floor 2 × 2 ways, (e) separate floor 2 × 1 way.

Fig. 4 .

 4 Fig. 4. The NR4 broken center line segmented into 5 replacement areas Then, geometrical interpretations of the matrices of the individuals and correlations are carried out: the geometric axes are formed by the eigenvectors, the hyperplane of the individuals and the hypersphere of the correlations are represented. Descriptive variables are always enclosed in the hypersphere which radius is 1 (Pagès 2004).Then successive Hilbert projections to a twodimensional Cartesian plane are made to represent the map of individuals and the circle of correlations. The map usually has point clouds. Here, each cloud represents individuals who tend to share the same descriptive variables. The circle presents the main discriminating variables: the closer the variable is to the circle boundary, the more discriminating it is. Moreover, the more variables are distant, the more they are opposed. In the opposite, the closer two variables are, the more they are associated.Each eigenvector contributes to the total variance of the ACP model. The principal components are the vectors that contribute the most.

Fig. 5 .

 5 Fig. 5. Proportions of the variance explained by the factorial axes.

Fig. 6 .

 6 Fig. 6. Circle of correlations associated to the NR4

Fig. 7 .

 7 Fig. 7. Dendrogram associated to the segmented map of individuals

Fig. 8 .

 8 Fig. 8. Map of individuals associated to the NR4

Fig. 9 .

 9 Fig. 9. The location of clusters on the RN4

Fig. 10 .

 10 Fig. 10. Markings lines monitoring

Acknowledgement

VEDECOM and IFSTTAR thank the DIR Est and the CEREMA for inspection data on the National Road 4.


Hélène Serré

Marion Dohen

Susanne Fuchs

Silvain Gerber

Amélie Rochet-Capellan

Speech and breathing in different conditions of limb movements and over time

come   L'archive ouverte pluridisciplinaire

INTRODUCTION

Speech relies on specific adaptation of breathing control in close link with cognitive activity [START_REF] Henderson | Temporal patterns of cognitive activity and breath control in speech[END_REF][START_REF] Grosjean | Breathing, pausing and reading[END_REF]. For instance, it is well known that during speech production, inhalation phases are shorter and exhalation phases longer than during quiet breathing [START_REF] Conrad | Speech and respiration[END_REF]. The cognitive and physiological demands of the speech task affect the breathing profile [START_REF] Wang | Breath group analysis for reading and spontaneous speech in healthy adults[END_REF][START_REF] Rochet-Capellan | Changes in breathing while listening to read speech: the effect of reader and speech mode[END_REF]. At the same time, the respiratory constraint may shape speech planning [START_REF] Włodarczak | Respiratory constraints in verbal and non-verbal communication[END_REF][START_REF] Włodarczak | Communicative needs and respiratory constraints[END_REF]. But adaptation of breathing control is also involved in limb movements. For example, breathing frequency increases with physical effort [START_REF] Hoffmann | Dynamics of the locomotor-respiratory coupling at different frequencies[END_REF]. It also seems that breathingspeech vs. breathing-limb coordination could be changed with training: theater actors [START_REF] Monteagudo | The effects of actors vocal exercises for relaxation on fluency: A preliminary study[END_REF] and athletes [START_REF] Mcdermott | Running training and adaptive strategies of locomotor-respiratory coordination[END_REF] might show different speech / breathing coordinative profiles. Previous works suggest that limb movement as well as learning could be relevant paradigms to further question the speech-breathing link. In line with this idea, we analyzed this link over time in different conditions of limb movements.

METHOD

Eleven native speakers of German participated in this study. Their task was to watch short videos while sitting on a chair. They were then invited to retell the stories in different conditions: hands free (HF), hands blocked (HBl), hands biking on a mini-bike (HBi) vs. legs biking (LB) on the same mini-bike (Figure 1, left). Participants were recorded twice in the same conditions, on two different days. They also came back ten days later to retell the story in the HF condition only.

Speech and breathing were recorded synchronously using a microphone and the Inductance Plethysmograph system Respitrace®. Limb motion was also recorded using an Optitrack system but is not analyzed in the current paper. Interpausal units of speech (IPU) and breathing cycles were labeled automatically in Matlab and then checked and corrected when needed using Praat (Figure 2). The following measurements were considered to characterize the breathing cycles and the speech breath groups (in line with our previous work, cf. [START_REF] Rochet-Capellan | Take a breath and take the turn: how breathing meets turns in spontaneous dialogue[END_REF]):

-DurCycle: The duration of the breathing cycle (from the onset of the inhalation phase to the offset of the exhalation phase); -SymCycle: The symmetry of the breathing cycle (duration of the inhalation phase divided by the total duration of the cycle); -DurSpeech: The duration of the breath group (from the onset of the first interpausal unit to the offset of the last one produced on a same cycle); We considered how these parameters changed according to the experimental condition and the day of recording.

RESULTS

The following linear mixed model (log(DurSpeech)~condition*day+(1|participant)) for DurSpeech measurements shows a significant effect of the day (z-value=2.271 p-value= 0.0232) but no effect of the condition. The amplitude of the effect was about +0.40 seconds from day 1 to day 2 in both cases. Neither the day, nor the condition significantly affected the asymmetry of the breathing cycle (Figure 3, middle).

DISCUSSION

The increase in breathing cycle and breath group durations in these preliminary analyses might be related to a decrease of the cognitive load on day 2 as compared with day 1. Indeed, despite a non-significant effect of the condition, changes between day 1 and day 2 seem clearer for the unusual conditions of speech production (here, hands still and hands biking). These two conditions may induce a greater cognitive load than more usual conditions such as h ands free or biking with the legs. This could be evaluated by supplementary analyses of the linguistic content and the disfluencies. Further analyses of the correlation between the duration and amplitude of inhalation and the number of syllables per breath group should also help to understand to which extent these changes are related to changes in speech planning. Finally, analyses of the regularity of limb motion in the hand and leg biking conditions should help quantify the degree of familiarity to the task (e.g. in this case, smaller variability should be observed on day 2 with a different biking rate).

Figure 2 :

 2 Figure 2: Identification of the breath group and the breathing cycle on the acoustic signal (top) and thorax trajectory (bottom) Figure 1: Experimental conditions, from left to right: Hands Free (HF), Hands Blocked (HBl), Legs Biking (LB), Hands Biking (HBi).

Figure 3 :

 3 Figure 3: Measurements as a function of day (1 and 2) and experimental condition (HF, HBl, LB, HBi). Top: mean of the duration of the breathing cycles; Middle: mean of the symmetry of the breathing cycles (inhalation duration/cycle duration); Bottom: mean of the duration of the breath groups

Table 1 :

 1 Means and standard deviations of DurCycle and DurSpeech as a function of day

	Mean (± std)	Cycle duration	Breath group
		(sec)	duration (sec)
	day 1	5.75 (±1.10)	4.86 (±1.12)
	day 2	6.13 (±1.12)	5.25 (±1.12)
	Total	5.94 (±1.23)	5.05 (±1.13)

ACKNOWLEDGMENTS

This research is jointly supported by the French National Research Agency (ANR-17-FRAL-0005-01) and the German Research Foundation (DFG) as part of the SALAMMBO project (Spoken Language in Motions: Learning and Adaptation of Speech Communication in the context of Body Motions)


A Khiter

B Balannec

Anthony Szymczyk

Omar Arous

N F Nasrallah

P Loulergue

Behavior of volatile compounds in membrane distillation: the case of carboxylic acids

Keywords: Membrane Distillation, volatile molecules, carboxylic acids, selective separation

published or not. The documents may come

Behavior of volatile compounds in membrane distillation: The case of carboxylic acids

Introduction:

Membrane distillation (MD) is a thermal-based membrane operation allowing to separate molecules according to their volatilities. During the last decade, MD has gained considerable interest mainly because of its low electricity requirement as the separation apparent driving force (a temperature difference between the feed and permeate side of the membrane module) can be created using lowgrade energy sources including renewable energy [START_REF] Ali | Membrane technology in renewable-energydriven desalination[END_REF][START_REF] Gopi | Perspective of renewable desalination by using membrane distillation[END_REF] or waste heat [START_REF] Byrne | A review on the coupling of cooling, desalination and solar photovoltaic systems[END_REF][START_REF] Diaby | Design study of the coupling of an air gap membrane distillation unit to an air conditioner[END_REF][START_REF] Thomas | Membrane distillation research & implementation: Lessons from the past five decades[END_REF].

Because of its relatively low sensitivity to polarization concentration compared to high pressure-driven membrane processes, MD has been particularly applied for seawater desalination as well as brine concentration including for full-scale application. Beside, niches applications have also been considered including, for example, wastewater treatment [START_REF] Cath | Membrane contactor processes for wastewater reclamation in space: II. Combined direct osmosis, osmotic distillation, and membrane distillation for treatment of metabolic wastewater[END_REF][START_REF] Criscuoli | Treatment of dye solutions by vacuum membrane distillation[END_REF][START_REF] Loulergue | Chapter 9 -Membrane processes for wastewater remediation[END_REF], fruit juice concentration [START_REF] Nene | Membrane distillation for the concentration of raw cane-sugar syrup and membrane clarified sugarcane juice[END_REF][START_REF] Alves | Orange juice concentration by osmotic evaporation and membrane distillation: A comparative study[END_REF][START_REF] Gunko | Concentration of apple juice using direct contact membrane distillation[END_REF], biomolecule extraction from fermentation broths [START_REF] Lewandowicz | Application of membrane distillation for ethanol recovery during fuel ethanol production[END_REF][START_REF] Tomaszewska | Production of ethanol from lactose in a bioreactor integrated with membrane distillation[END_REF][START_REF] Loulergue | Air-gap membrane distillation for the separation of bioethanol from algal-based fermentation broth[END_REF] or nutrient recovery [START_REF] Xie | Ammonia removal by sweep gas membrane distillation[END_REF][START_REF] Quist-Jensen | Membrane crystallization for phosphorus recovery and ammonia stripping from reject water from sludge dewatering process[END_REF].

From the separation point of view, considering the application of MD for desalination or for these niches applications, the issues strongly differ. Thus, desalination by MD is a relatively "simple" separation as the objective is to separate water (a volatile compound) from salts (nonvolatile compounds). For this application, the main challenges associated to the use of MD are thus the process stability (scaling, fouling and wetting issues) and the optimization of the overall energy consumption and process efficiency. Regarding the niches applications above-mentioned, the separation objectives A c c e p t e d m a n u s c r i p t might be different. Thus, if the feed fluid contains a mixture of different more or less volatile molecules, these challenges remain-but the question of the selectivity of the separation arises additionally. For example, in the case of the extraction of a biomolecule from a fermentation broth, one may want to extract solely the targeted molecule without any fermentation by-products. In the same way, during the treatment of petroleum wastewater, the unwanted transportation of volatile organic compounds through the membrane might impair the treated water quality. Thus, the existence of a mixture of volatile solutes into the MD feed solutions make the separation more complex than in the simple case of a feed containing only nonvolatile compounds in water. In this case, the solute concentration in the permeate can be increased or decreased compared to that of the feed solution [START_REF] Loulergue | Air-gap membrane distillation for the separation of bioethanol from algal-based fermentation broth[END_REF][START_REF] Salls | Evaluation of semi-volatile contaminant transport in a novel, gas-tight direct contact membrane distillation system[END_REF][START_REF] Yao | Volatile fatty acids and biogas recovery using thermophilic anaerobic membrane distillation bioreactor for wastewater reclamation[END_REF].

Achieving selective separations thus require a better understanding of volatile molecules behavior during MD. In previous studies, MD separation efficiency has been related to different physicochemical parameters of the solutes. MD being a liquid-vapor equilibrium based separation process, it is not surprising that the Henry's constant has been demonstrated to be a key parameter controlling the solute transport through the membrane [START_REF] Salls | Evaluation of semi-volatile contaminant transport in a novel, gas-tight direct contact membrane distillation system[END_REF][START_REF] Wijekoon | Rejection and fate of trace organic compounds (TrOCs) during membrane distillation[END_REF][START_REF] Winglee | Modeling the Concentration of Volatile and Semivolatile Contaminants in Direct Contact Membrane Distillation (DCMD) Product Water[END_REF][START_REF] Yao | Effects of volatile organic compounds on water recovery from produced water via vacuum membrane distillation[END_REF]. However, other parameters such as molecular weight [START_REF] Winglee | Modeling the Concentration of Volatile and Semivolatile Contaminants in Direct Contact Membrane Distillation (DCMD) Product Water[END_REF] or solute hydrophobicity [START_REF] Wijekoon | Rejection and fate of trace organic compounds (TrOCs) during membrane distillation[END_REF][START_REF] Yao | Effects of volatile organic compounds on water recovery from produced water via vacuum membrane distillation[END_REF] are also known to influence the separation efficiency.

Accordingly, the most transferred compound is not always the most volatile one [START_REF] Yao | Effects of volatile organic compounds on water recovery from produced water via vacuum membrane distillation[END_REF]. Besides the intrinsic properties of the molecules, other parameters related to the feed solution composition can also affect the separation efficiency such as the solute concentration [START_REF] Loulergue | Air-gap membrane distillation for the separation of bioethanol from algal-based fermentation broth[END_REF][START_REF] Garcı ́a-Payo | Air gap membrane distillation of aqueous alcohol solutions[END_REF][START_REF] Kujawska | Removal of volatile organic compounds from aqueous solutions applying thermally driven membrane processes. 2. Air gap membrane distillation[END_REF], the presence of ionic species (salting-out effect) [START_REF] Loulergue | Air-gap membrane distillation for the separation of bioethanol from algal-based fermentation broth[END_REF][START_REF] Banat | Membrane distillation for dilute ethanol: Separation from aqueous streams[END_REF] or the pH [START_REF] Winglee | Modeling the Concentration of Volatile and Semivolatile Contaminants in Direct Contact Membrane Distillation (DCMD) Product Water[END_REF][START_REF] Won | Treatment Performance of Direct Contact Membrane Distillation for Volatile[END_REF] and its local variation due to concentration polarization [START_REF] Yang | Sustainable waste water deammonification by vacuum membrane distillation without pH adjustment: Role of water chemistry[END_REF]. Finally, operating parameters such as feed temperature, feed flow-rates and MD cell configuration for example are also known to play a role in the separation efficiency [START_REF] Alkhudhiri | Membrane distillation: A comprehensive review[END_REF].

For solutions containing a mixture of volatile solutes, the complex interplay of these different parameters thus makes it challenging the prediction of the separation efficiency by MD. There is thus a need for a better understanding of the behavior of volatile compounds in MD as well as the influence of their physicochemical environment.

A c c e p t e d m a n u s c r i p t

In this context, this study aimed at investigating the behavior of different solutes of the same type according to the feed solution composition and the operating conditions. A set of three carboxylic acids (formic acid, acetic acid and succinic acid) was considered as they can be produced individually, or in mixture, by fermentation [START_REF] Song | Production of succinic acid by bacterial fermentation[END_REF][START_REF] Wang | Novel membrane-based biotechnological alternative process for succinic acid production and chemical synthesis of bio-based poly (butylene succinate)[END_REF][START_REF] Álvarez | Challenges in the Greener Production of Formates/Formic Acid, Methanol, and DME by Heterogeneously Catalyzed CO2 Hydrogenation Processes[END_REF][START_REF] Zeng | New bioproduction systems for chemicals and fuels: Needs and new development[END_REF] and because acetic acid is present in mining wells and thus can be found in produced water [START_REF] Yao | Effects of volatile organic compounds on water recovery from produced water via vacuum membrane distillation[END_REF] but as well in other types of wastewaters [START_REF] Yao | Volatile fatty acids and biogas recovery using thermophilic anaerobic membrane distillation bioreactor for wastewater reclamation[END_REF]. In this study, air-gap membrane distillation (AGMD) was considered because this configuration is the most widely used when dealing with (semi)industrial scale facilities [START_REF] Thomas | Membrane distillation research & implementation: Lessons from the past five decades[END_REF]. The individual effects of the carboxylic acid structure, the concentration, pH and feed temperature on separation performances were studied.

Finally, it was demonstrated how it can be taken advantage of the understanding of the behavior of acetic acid in MD to successfully achieve selective separation of ethanol from an acetic acid/ethanol aqueous mixture (typical separation in bioethanol production).

Material and methods

Feed solutions

Formic acid (purity > 98 %, Sigma-Aldrich, Germany), glacial acetic acid (VWR chemicals, France), succinic acid (> 99 %, Sigma-Aldrich, Germany), ethanol (96 % v/v, VWR chemicals, France) and deionized water (resistivity: 18 MΩ cm) were used to prepare the feed solutions.

Different carboxylic acid-water binary mixtures with acid concentrations in the range of 5 -30 g.L -1 were considered as well as a water -ethanol (10 g.L -1 ) -acetic acid (2 g.L -1 ) solution.

The main features of the molecules used in this study are gathered in table 1.

A c c e p t e d m a n u s c r i p t PTFE membranes with a pore size of 0.2 µm and a polypropylene backing (Gore, USA) were used.

According to manufacturer's data, these membranes had a thickness of 280 µm, a porosity of 80 % while the liquid entry pressure was 238 kPa. The contact angle of the pristine membrane was 131 ± 3° (determined by the sessile drop method and using a GBX-DS apparatus equipped with a video acquisition system and the Windrop++ software). The air-gap thickness was set to 2 mm using polypropylene spacers. All experiments were performed using the same membrane cassette as no membrane fouling was observed. Pure water flux measurements were performed between experiments to check the membrane integrity and cleanliness.

AGMD experiments were performed by adjusting the feed temperature in the range 37-60°C while the coolant fluid temperature was kept constant at 15 ± 1°C. Feed and coolant flowrates were adjusted to 4 L.min -1 . A total recycling of the concentrate and permeate towards the feed tank was performed in order to ensure a constant composition of the feed solution (volume reduction ratio VRR = 1).

A c c e p t e d m a n u s c r i p t

Separation performance evaluation

AGMD separation performance was evaluated in terms of total permeate flux (J), acid rejection (R) and separation factor (SF).

The permeate flux (Jp) can be defined as follows:

𝐽 𝑝 = ∆𝑚 ∆𝑡 * 𝑆 (1)
With:

-Δm the permeate mass collected (kg) -Δt the sampling time (h) -S the effective membrane surface (m 2 )

The permeate was sampled periodically and all measurements were performed in duplicate to calculate an average value. The precision on the permeate flux calculation was better than 5%.

The rejection of carboxylic acids (Ri) was calculated using equation 2. Retentate and permeate concentrations were determined by ion chromatography.

𝑅 𝑖 = 1 - 𝐶𝑝 𝑖 𝐶 𝑓𝑖 (2)
With:

-Cpi the concentration of compound i in the permeate (g.L -1 ) -Cfi the concentration of compound i in the feed (g.L -1 ) Finally, the separation factor (eq. 3) was used to quantify the efficiency of the selective separation of two compounds i and j.

𝑆𝐹 𝑖/𝑗 = 𝐶 𝑝,𝑖 /𝐶 𝑓,𝑖 𝐶 𝑝,𝑗 /𝐶 𝑓,𝑗 = 1-𝑅 𝑖 1-𝑅 𝑗 (3) With:
A c c e p t e d m a n u s c r i p t -SF the separation factor -Cp,i and Cf,i the concentration of compound i (g.L -1 ) in the permeate and in the feed respectively -Cp,j and Cf,j the concentration of compound j (g.L -1 ) in the permeate and in the feed respectively

Determination of apparent energy activation

In MD, for sufficiently high temperature difference between the two side of the membranes, the variation of the permeate fluxes with feed temperature might be modeled according to an Arrheniustype equation, basing on the feed temperature, enabling to determine the apparent energy of activation for molecule transfer through the membrane (Eapp) [START_REF] Peng | Desalination by membrane distillation adopting a hydrophilic membrane[END_REF][START_REF] Mengual | Heat and mass transfer in vacuum membrane distillation[END_REF][START_REF] Kujawa | Driving force and activation energy in air-gap membrane distillation process[END_REF][START_REF] Al-Gharabli | Biomimetic hybrid membranes with covalently anchored chitosan -Material design, transport and separation[END_REF].

𝐽 𝑖 = 𝐽 0,𝑖 exp (- 𝐸 𝑎𝑝𝑝,𝑖 𝑅𝑇 𝑓 ) (4)
With:

-Ji the molar flux of compound i across the membrane (mol.h -1 .m -2 ) -J0,i is a pre-exponential factor for compound i (Ji flux at infinite temperature) (mol.h -1 .m -2 ) -Eapp,i is the apparent energy of activation of compound i (J.mol -1 ) -R is the universal gas constant (8.314 J.mol -1 .K -1 ) -Tf is the absolute feed temperature (K) Equation ( 4) can be linearized allowing the determination of the apparent energy of activation (Eapp) from the slope of equation [START_REF] Thomas | Membrane distillation research & implementation: Lessons from the past five decades[END_REF].

𝐿𝑛(𝐽

𝑖 ) = 𝐿𝑛(𝐽 0,𝑖 ) - 𝐸 𝑎𝑝𝑝,𝑖 𝑅𝑇 𝑓 (5)

Feed and permeate analysis

Carboxylic acid quantification in the feed and permeate solutions was performed by ion chromatography. A Dionex DX120 system equipped with a Dionex AS11-HS (4×250 mm) column coupled to a conductivity detector was used. The injection volume was set at 250 μL and the separation A c c e p t e d m a n u s c r i p t was performed using a mixture of potassium hydroxide (KOH) and water as eluent. The operating conditions were as follow: 0-10 min (isocratic 10 mM); 10-25 min (gradient from 10 to 45 mM); 25-35 min (isocratic 45 mM). The eluent flow rate was adjusted to 1 mL min -1 .

HPLC was used to quantify the ethanol concentration in feed solution and permeate samples. A HPX-87H (300 × 7.8 mm, BIO-RAD, Hercules, CA, USA) column was used. It was maintained at 45 °C using an oven (Cro-Cir TM, Cluzeau Info-Labo, ste Foy La Grande, France) and fed using an isocratic pump (WATERS 510, Milford, MA, USA) with sulfuric acid (0.01 N) as eluent at a flow rate of 0.7 mL⋅min -1 .

Detection was performed by means of a refractometer (ERC 7512, Shimadzu).

Results and discussion

Carboxylic acid rejection in AGMD

Influence of the carboxylic acid structure

The influence of the carboxylic acid structure on AGMD performance was studied using binary carboxylic acid-water (10 g.L -1 , natural pH) mixtures as the feed solutions. , Jacid in the range 0-0.07 mol h -1 .m -2 ). The lower acid fluxes compared to the water ones, even for the formic acid having vapor pressure greater than water, can be explained by the low concentration of carboxylic acid in the feed solution (10 g.L -1 , i.e. 0.22 mol.L -1 , 0.17 mol.L -1 and 0.09 mol.L -1 for the formic, acetic and succinic acids respectively). Thus, this low amount of solutes in the feed solution limits the potential acid fluxes. Accordingly, in the present conditions, the permeate was mostly composed of water causing the total permeate flux to be insensitive to the acid structure.

On the other hand, acid rejection was highly dependent on the acid structure. Thus, formic and acetic acids were partially rejected by the membrane while full-rejection was observed for succinic acid.

Furthermore, formic acid was less rejected by the membrane than acetic acid. These results were in good accordance with the respective volatility of the different acids as formic acid was the most volatile molecule while succinic acid was the less volatile one (Table 1). In addition, it is interesting to note that formic and succinic acids had different transfer behaviors despite having close values of logP (but different vapor pressure and boiling points). This revealed that, in the tested conditions, acid volatilities seemed to play a greater role on molecule transfer trough the membrane compared to their hydrophilic/hydrophobic features.

A c c e p t e d m a n u s c r i p t

Influence of the feed temperature

The influence of the feed temperature (37-60°C) on separation performance was studied using binary acid-water solutions (10 g.L -1 , natural pH). Figure 2 shows the evolution of both the permeate flux and the acid retention for the three carboxylic acids. Figure 2a shows the variation of the permeate flux according to the feed temperature. The well-known increase of the permeate flux with the feed temperature was observed. It was explained by the vapor pressure difference (which is the separation driving force) increase with the feed temperature according to Antoine's law [START_REF] Alkhudhiri | Membrane distillation: A comprehensive review[END_REF]. Thus, for a constant temperature of coolant fluid, the separation driving force increases with the feed temperature thus leading to an increased permeate flux.

Furthermore, as observed previously, the acid nature had no influence on the permeate flux, whatever the feed temperature. As explained before, this was be due the low amount of acid in both the feed and permeate fluids [START_REF] Loulergue | Air-gap membrane distillation for the separation of bioethanol from algal-based fermentation broth[END_REF][START_REF] Garcı ́a-Payo | Air gap membrane distillation of aqueous alcohol solutions[END_REF]. Whatever the acid nature, the minimum permeate flux value was 1.0 kg.h - 1 .m -2 at 37°C while a maximum permeate flux of roughly 4.0 kg.h -1 .m -2 was reached at a feed temperature of 60°C. When looking at the acid rejection (Figure 2b), the impact of the feed temperature depended on the acid structure. Thus, a constant and full rejection was observed for the succinic acid. However, formic and acetic acids rejections were found to be dependent on the feed temperature. In the present conditions, acetic acid rejection decreased from 0.78 to 0.61 while formic acid rejection varied from 0.68 to 0.54 when the feed temperature increased from 37°C to 60°C. Finally, it was observed that the acetic acid rejection was higher than that of formic acid rejection whatever the feed temperature, in good accordance with the molecule volatilities.

In order to get more insights into the variation of the acids rejection with the feed temperature, the natural logarithm of the molar fluxes of water and carboxylic acids through the membrane was plotted against the reciprocal temperature (Figure 3). It was thus possible to calculate, for each compound, the apparent energy barrier of transport through the membrane using the linearized Arrhenius equation (Eq. 5). Note that, for the sake of clarity, only one curve is displayed for the water flux as it was found to be similar for the three experiments with the three different carboxylic acids. Succinic acid was also excluded as full rejection was observed whatever the feed temperature.

From figure 3, it can be observed that the variation of the natural logarithm of the water flux with the reciprocal temperature was linear for the whole range of feed temperature considered. This indicated that, in the tested conditions, the water transport through the membrane followed an Arrhenius-type law and thus was a temperature-activated process. Kujawa and Kujawski have previously found that the water transport in AGMD could be described by an Arrhenius-type model basing on the feed temperature only for sufficiently high temperature difference between the feed and permeate sides of the membrane, i.e. more than 35°C in their study [START_REF] Kujawa | Driving force and activation energy in air-gap membrane distillation process[END_REF]. In our case, the Arrhenius-type model was found to be valid for the whole range of feed temperature considered from 37 to 60°C, i.e. for temperature difference ranging from 22 to 45°C (Tcoolant = 15°C). This difference could be explained by the difference in the properties of the membrane used in the two studies. Thus, membrane structure A c c e p t e d m a n u s c r i p t (thickness, roughness, pore size, porosity, tortuosity) and surface properties (chemistry of the material, hydrophobicity) are known to highly impact the transport properties in MD [START_REF] Kujawa | Driving force and activation energy in air-gap membrane distillation process[END_REF][START_REF] Al-Gharabli | Biomimetic hybrid membranes with covalently anchored chitosan -Material design, transport and separation[END_REF][START_REF] Kujawa | Highly Efficient Hydrophobic Titania Ceramic Membranes for Water Desalination[END_REF].

The variation of the natural logarithm of the acid flux with the reciprocal temperature was linear for the formic and acetic acids. Apparent energies of activation could be calculated, for each compound, from the slope of the curves (Eq. 5). Water had the lowest value of 52.7 kJ.mol -1 . This value was found to be of the same order of magnitude compared to others calculated in previous studies dedicated to AGMD [START_REF] Kujawa | Driving force and activation energy in air-gap membrane distillation process[END_REF]. Apparent energies of activation was 62.6 and 67.2 kJ.mol -1 for the formic and acetic acids respectively. A higher apparent energy activation indicates a higher sensitivity to temperature (Eq. 4).

In other words, for a given increase of feed temperature, the transmembrane flux increase was greater for the carboxylic acids than for water flux. Accordingly, when the temperature was increased, an increased acid concentration in the permeate occurred causing an acid rejection drop (Figure 2b).

Influence of the acid concentration

The influence of the acid concentration (5-30 g.L -1 , natural pH) on the permeate flux, at different feed temperatures, is shown in figure 4a for binary carboxylic acid-water mixtures. Succinic acid was not considered as full retention was observed for all previous tested operating conditions. Again, it was found that the permeate flux increased with temperature while it was insensitive to the feed solution composition (i.e. acid concentration). Furthermore, whatever the acid concentration, the rejection decreased when the feed temperature increased (as shown for 10 g/L in the previous section). On the other hand, whatever the feed temperature, acid rejection was shown to increase with the acid concentration (Figure 4b and4c). Carboxylic acids form dimers in the gas phase and in aqueous solutions as a result of both hydrogen bonding (C=O---H-O) and hydrophobic interactions between their alkyl chains [START_REF] Chen | Revisiting the Carboxylic Acid Dimers in Aqueous Solution: Interplay of Hydrogen Bonding, Hydrophobic Interactions, and Entropy[END_REF]. Considering the dimerization equilibrium (molecule 1 + molecule 2 ↔ dimer) and the reported experimental values of pKD (= -logKD, with KD the dimerization thermodynamic constant) in the range 0.73 -1.45 for acetic acid at 25°C [START_REF] Schrier | The Influence of Hydrogen and Hydrophobic Bonds on the Stability of the Carboxylic Acid Dimers in Aqueous Solution[END_REF], it comes that the concentration of acetic acid dimers is roughly proportional to the square of the acetic acid concentration introduced in the system (the same is true for formic acid dimers for which pKD was reported in the range 1.24 -2.08 at 25°C [START_REF] Schrier | The Influence of Hydrogen and Hydrophobic Bonds on the Stability of the Carboxylic Acid Dimers in Aqueous Solution[END_REF]). It is therefore hypothesized that the increase in the rejection of both formic and acetic acids with concentration results from the more significant formation of dimers as the concentration increases.

This point is interesting as it is contrary to what is classically observed for pressure-driven processes (which are alternative membrane techniques that can be used for carboxylic acid separation from water [START_REF] Han | Nanofiltration of model acetate solutions[END_REF][START_REF] Kang | Removal of organic acid salts from simulated fermentation broth containing succinate by nanofiltration[END_REF]) for which solute rejection tends to decrease with increasing solute concentration due to concentration polarization (and surface charge screening effects in the case of charged solutes). It is also worth noting that the absence of rejection decrease with increasing feed concentrations has previously been reported in MD for water-ethanol mixtures [START_REF] Loulergue | Air-gap membrane distillation for the separation of bioethanol from algal-based fermentation broth[END_REF].

The present results thus suggested that AGMD might be a suitable alternative to pressure-driven processes for the concentration/separation of carboxylic acids.

Influence of the pH of the feed solution

In order to evaluate the influence of the acid dissociation rates on their rejection, the influence of the pH of the feed solution was studied both for the formic and acetic acids (5 g.L -1 ). For each acid, a set of experiments were performed for which the adjustment of the pH of the feed solution allowed to reach different dissociation rates.

A c c e p t e d m a n u s c r i p t

Figure 5a shows the relative distribution of both the acetic acid and acetate ion according to the pH of the solution. The pKa of acetic acid varies from 4.76 to 4.81 with temperature increasing from 25°C to 60°C [START_REF] Harned | The Dissociation Constant of Acetic Acid from 0 to 60° Centigrade1[END_REF] and thus can be considered constant in the temperature range investigated in this study.

Accordingly, three different solutions at pH equal to 2.8 (≈ 100 % R-COOH), 4.8 (50/50 % R-COOH/R-COO -) and 7.0 (≈ 100 % R-COO -) were considered. The rejection rates (Tfeed = 60°C) obtained for the different feed solutions are shown on figure 5b. The rejection rate was found to vary with the pH of the feed solution. The lowest rejection rate was observed at pH 2.8 (< 0.6) while the maximum rejection rate (99.8) was observed at pH 7. These results thus revealed the increase of the rejection rate with the acetic acid dissociation rate: the higher the relative amount of acetate ions, the higher the rejection rate. From a thermodynamic point of view, this result can be explained by the fact that ions can not be vaporized in the present conditions.

The pKa of formic acid varies from 3.75 to 3.81 with temperature increasing from 25°C to 60°C [START_REF] Harned | The Ionization Constant of Formic Acid from 0 to 60°1[END_REF] .

Considering formic acid-water binary mixtures of pH 2.2, 3.7 and 7.3 the same behavior as for acetic acid was observed (Figures 5c and5d).

Implications for selective separation of ethanol-acetic acid aqueous mixtures

The production of bioethanol by yeast fermentation usually leads to complex aqueous mixtures containing ethanol and acetic acid, a by-product of the bioreaction [START_REF] Gryta | Separation of volatile compounds from fermentation broth by membrane distillation[END_REF][START_REF] Gryta | The study of membrane distillation used for separation of fermenting glycerol solutions[END_REF][START_REF] Fan | Inhibition effect of secondary metabolites accumulated in a pervaporation membrane bioreactor on ethanol fermentation of Saccharomyces cerevisiae[END_REF][START_REF] Sayed | Enhancement of ethanol production from synthetic medium model of hydrolysate of macroalgae[END_REF]. MD has previously been demonstrated to be a suitable technique to extract ethanol the fermentation broths. The permeate obtained is thus an aqueous mixture with enriched ethanol content compared to the feed solution.

However, acetic acid might also be found in the permeate thus requiring extra purification steps [START_REF] Gryta | Separation of volatile compounds from fermentation broth by membrane distillation[END_REF][START_REF] Gryta | The study of membrane distillation used for separation of fermenting glycerol solutions[END_REF][START_REF] Gryta | The fermentation process integrated with membrane distillation[END_REF]. Taking part of the knowledge obtained from the parametric study presented above, the Two different water/ethanol (8 g.L -1 )/acetic acid (2 g.L -1 ) mixtures having a pH of 3.0 and 7.0 respectively were prepared and treated using AGMD. Figure 6 displays the concentration of ethanol and acetic acid in both the feed and permeate solutions for the two different feed fluids. At pH 3 and 7, an increase of the ethanol concentration in the permeate was observed compared to the feed meaning that the ethanol was successfully extracted from the feed solution. On the other hand, at pH 3 a partial transmission of acetic acid through the membrane was observed leading to a rejection rate of 56 %. Interestingly, at pH 7, the almost full rejection of the acetic acid was observed (99.6 %) and a negligible concentration of acetic acid was detected in the permeate solution (< 0.01 g.L -

1

). The results obtained here indicated that the feed solution properties play a key role towards the selectivity of the separation. In addition, it was underlined that a simple adjustment of the feed chemistry is a possible technique to favor the selective separation of the ethanol from acetic acid by MD. Thus, by adjusting the pH of the solution to 7, it was possible to increase the ethanol/acetic acid separation factor by 2 orders of magnitude (from 8 to 842) compared to that of pH 3.

It was here demonstrated that the physicochemistry of the feed solution plays a key role on AGMD separation performance. The results obtained thus underlined that, when MD is used as a downstream unit operation following a (bio)reactor, it is necessary to take into consideration the separation technique specifications when designing the (bio)production step. Thus, depending on the operating conditions during the (bio)reaction, the physicochemical properties of the obtained mixture might vary a lot and thus drastically impact the separation efficiency. It is thus desirable to perform the joint optimization of the coupled (bio)production/separation steps instead of the individual optimization of each steps.

Conclusion

The behavior of volatile compounds in MD is poorly understood. In this context, This study aimed at investigate the rejection efficiency of MD towards carboxylic acids (formic, acetic and succinic acids) under different operating conditions.

In the tested conditions, it was demonstrated that the permeate flux increased with the feed temperature but was insensitive to the other studied parameters (acid type, acid concentration, pH of the feed solution). On the other hand, acid rejection was found to be highly dependent of the carboxylic acid structure (the more volatile acid being the less retained by the membrane). It was also found that the acid rejection increased with the acid dissociation rate as well as with its concentration in the feed solution. This MD feature is interesting as the opposite phenomenon is usually observed for pressure-driven membrane processes due to polarization concentration (and possible surface charge screening).

Figure 1 :

 1 Figure 1: Influence of carboxylic acid structure on permeate flux and rejection (a) and molar transmembrane fluxes of water and carboxylic acids (b) for each carboxylic acid aqueous mixture (10 g.L -1 , natural pH, Tfeed = 50°C, Tcoolant = 15°C, feed and coolant flowrates 4 L.min -1 )

Figure 2 :

 2 Figure 2: Influence of the feed temperature on the permeate flux (a) and acid rejection (b) (binary acid-water solution at 10 g.L -1 , natural pH, Tcoolant = 15°C, feed and coolant flowrates 4 L.min -1 )

Figure 3 :

 3 Figure 3: Variation of molar fluxes of the different compounds through the membrane against the reciprocal feed temperature (binary acid-water solution at 10 g.L -1 , natural pH, Tcoolant = 15°C, feed and coolant flowrates 4 L.min -1 )

Figure 4 :

 4 Figure 4: Influence of the acid concentration on (a) the permeate flux, (b) the acetic acid rejection

A c c e p t e d m a n u s c r i p tFigure 5 :

 5 Figure 5: Dissociation rate of acetic acid according to pH (a), influence of the feed solution pH on the

  s c r i p t aim of this part of the study was to demonstrate the ability of AGMD to perform the selective ethanolacetic acid separation.

Figure 6 :

 6 Figure 6: Acetic acid and ethanol concentrations in the feed and permeate solutions during the AGMD of water -ethanol (8 g.L -1 ) -acetic acid mixtures (2 g.L -1 ) at pH 3 (a) and 7 (b) (Tfeed=60°C, Tcoolant = 15°C, feed and coolant flowrates 4 L.min -1 )

A c c e p t e d m a n u s c r i p t

  Finally, it was demonstrated how it can be taken advantage of the understanding of the behavior of acetic acid in MD to successfully achieve selective separation of ethanol from an acetic acid/ethanol aqueous mixture by a simple feed solution pH adjustment in the typical case of the extraction of bioethanol from a fermentation broth.

A c c e p t e d m a n u s c r i p t A c c e p t e d m a n u s c r i p t

Table 1 :

 1 characteristics of the molecule used in this study

		Chemical	Molecular	LogP	Vapor	Boiling	pKa at
		formula	weight		pressure at	temperature	25°C
			(g.mol -1 )		25°C (kPa)	(°C)
	Formic acid a	CH2O2	46.0	-0.54	5.7	101	3.75
	Acetic acid a	C2H4O2	60.1	-0.17	2.1	118	4.75
	Succinic acid a	C4H6O4	118.1	-0.59	0.1 b	235	4.21 and
						(decomposes)	5.64
	Ethanol	C2H6O	46.1	-0.31	7.8	78	15.9
	Water (as	H2O	18.0	-	3.1	100	-
	reference) a
	a Data obtained from [32-36] except the vapor pressure calculated by Antoine's law
	b At 55°C (no data available at 25°C)
	2.2 AGMD set-up
	A commercial laboratory scale AGMD facility (XZero AB, Sweden) was used. It was equipped with a
	membrane cassette containing two flat-sheet membranes (total effective membrane area 0.195 m²).

Acknowledgements:

Dr. Hayet Djelal is acknowledged for the ethanol concentration determination by HPLC analyses performed at Unilasalle-EME. A. Khiter acknowledges the « Ministère de l'enseignement supérieure et de la recherche scientifique Algérienne, direction de la coopération et des échanges interuniversitaires » for funding (Grant 378/PNE/FRANCE/2016/2017).