Clément Bellanger

Jane Hung

Nyoman Juniarta

Vincent Leroux

Bernard Maigret

Amedeo Napoli
email: amedeo.napoli@loria.fr

Chemoinformatics approaches to help antibacterial discovery

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Bacterial and parasitic diseases are the second leading cause of death worldwide, according to reports on antibiotic research released recently [START_REF] Braine | Race against time to develop new antibiotics[END_REF][START_REF] Mckenna | The coming cost of superbugs: 10 million deaths per year[END_REF][START_REF] Matthew J Renwick | A Critical Assessment of Incentive Strategies for Development of Novel Antibiotics[END_REF]. Currently, a pressing public health concern originates from bacterial resistance to the available arsenal of antibiotics. This natural phenomenon is occurring more and more frequently, probably due to evolutionary pressure fueled by mis-use/over-use of current drugs. The emergence of "superbugs" resistant to entire antibiotic classes may render traditional antibiotics obsolete in the coming years, with potentially dramatic consequences [START_REF] Mckenna | The coming cost of superbugs: 10 million deaths per year[END_REF]. Consequently, new antibiotics are desperately needed, preferably featuring novel mechanisms of action in order to successfully fight multidrug-resistant strains [START_REF] Ezekiel | How to Develop New Antibiotics[END_REF][START_REF] Fernandes | The global challenge of new classes of antibacterial agents: an industry perspective[END_REF][START_REF] Nathan | Antibiotic resistance-problems, progress, and prospects[END_REF].

Unfortunately, the amount of money being spent in antibiotics R&D is woefully inadequate as major pharmaceutical companies mostly focus on different pathologies according to their pipelines. Drugs against chronic diseases highly common in modern developed countries (e.g cardiovascular deficiencies, diabetes, obesity) certainly promise higher and faster returns to the shareholders, yet there are certainly a lot of profits to be potentially made with antibiotics. For instance, once the death toll for hospital-acquired infections of multidrug-resistant strains of the likes of Staphylococcus aureus become unacceptable (and that will happen too soon if no progress is made), a new efficient antibiotic class could eventually turn out to be the only option to save lives.

In this context, in order to make progress in this field, resorting to more modern techniques, even if those have not demonstrated similar success rates so far in classical drug discovery programs, looks like a rational choice. Computer-aided techniques have already proven their usefulness to save time and money in the drug discovery process [START_REF] Spellberg | The future of antibiotics[END_REF]. In particular, ligand-based drug design calculations (i.e. QSAR) are now well-recognized as fast and efficient approaches in the hit-to-lead early drug discovery phase. Knowledge discovery approaches (e.g machine learning, data mining, neural networks) are less mature in the context of drug design but their success in other applied computing fields make them increasingly promising. They are also especially popular in academia since provided they are combined with very strong interdisciplinary expertise; they may allow overcoming the lack of experimental data useful for medicinal chemistry projects compared to what is existing in the industry. Furthermore, one hope is that progress in the chemoinformatics field [START_REF] Bajorath | Chemoinformatics for Drug Discovery[END_REF] could eventually allow finding possible "hidden gems" amongst the millions of available chemicals from providers, companies or laboratory collections, and even established drugs.

Here, we present an in silico strategy targeting antibacterial molecules identification in a virtual screening context. Our final goal is to be able to highlight molecules within existing chemical collections with a high probability of being potential antibacterials and that could not be found using most of the existing similar approaches.

Considering the huge variety of molecular descriptors that can be used [START_REF] Todeschini | Molecular Descriptors for Chemoinformatics[END_REF] in order to describe molecular properties, the problem is how to achieve an optimal selection of molecular attribute sets in order to analyze, with highest accuracy, chemical diversity/similarity among large (>1M objects) chemical libraries. Such "optimally-selected descriptors" should provide the most efficient rules which can be used next to describe molecules with a common behavior, in this case antibacterial potency. Dimensionality reduction in the descriptors space has already been considered as an important issue in QSAR methods [START_REF] Howe | Data reduction and representation in drug discovery[END_REF][START_REF] Heureux | Locally Linear Embedding for dimensionality reduction in QSAR[END_REF][START_REF] Liu | A comparative study on feature selection methods for drug discovery[END_REF][START_REF] Reutlinger | Nonlinear dimensionality reduction and mapping of compound libraries for drug discovery[END_REF][START_REF] Sirois | Selection of molecular descriptors with artificial intelligence for the understanding of HIV-1 protease peptidomimetic inhibitors-activity[END_REF]. The knowledge discovery phase would then next allow to extract, among large chemical datasets, compounds presenting all the same required action.

It is demonstrated that the resulting filters are efficient, and those will serve as references to evaluate future new knowledge extraction methods we are currently investigating.

Methods

2.1.1 Molecular data sets. In order to train feature selection techniques for discriminating antibacterials and non-antibacterials, we built several molecular training sets of both antibacterial and nonantibacterial molecules from different sources.

• Set P1 (positive) is constituted by 150 antibacterials that are part of the current standards of care in France [START_REF] Vidal | Dictionnaire Vidal 2016 (French PDR -Physician's Desk Reference[END_REF]. • Set P2 is the antibacterials subset of the MDDR 2016 database [START_REF]BIOVIA Databases | Bioactivity Databases: MDDR[END_REF]. It comprises 2854 molecules annotated as possessing antibacterial potency and not already referenced in the P1 set. • Set P3 is the Life Chemicals [START_REF]Life Chemicals[END_REF] supplier's antibacterial library.

As retrieved for this study, it contains 38907 small-molecule, drug-like compounds available for purchase, that have been selected from the full supplier catalog using proprietary classifiers. • Sets N1 (negative), N2, N3 and N4 are built from MDDR molecules that are not tagged as antibacterials but having completely different known activities. N1 has 1519 analgesic compounds, N2 has 3654 compounds targeted at cardiovascular diseases, N3 comprises 17796 compounds marked as "antagonist" and N4 34210 marked as "inhibitor". • Set N5 is an ensemble of Life Chemicals molecules available for purchase not found in P2 nor in N1-N4. It comprises 52604 molecules from the cancer-, central nervous systemand analgesic-focused libraries.

To focus our study on small molecules, all molecules in our data sets were imposed to have molecular weight less than 600 Daltons.

A single 3D conformation of all these compounds was obtained from Corina [START_REF] Sadowski | Comparison of automatic three-dimensional model builders using 639 X-ray structures[END_REF].

Attribute sets.

For each molecule, a set of 4885 attributes were calculated from the Dragon software [START_REF] Howe | Data reduction and representation in drug discovery[END_REF] describing constitutional, topological and geometrical properties. While molecular descriptors calculations are available in several QSAR platforms [START_REF]Molecular Descriptors[END_REF], Dragon combines a particularly large choice and diversity with a clear and detailed technical documentation. Attributes where values were missing were removed. Some of the attributes were found perfectly correlated; in such cases we removed all but one attribute from each group. This resulted in a baseline number of 4532 attributes. Models were run on data sets with 5 different attribute sets that will be referred to as F0, F1, F2, F3 and F4 next. F0 contains the baseline 4532 attributes while F1-F4 have filters applied in order to limit the number of attributes; such restrictions may positively impact the final classifier performance. All filters are based on thresholds about computed values. F1 eliminates attributes that result in a data distribution with standard deviation σ < 0.01 and with pair correlation ρ ≥ 0.4. F2 excludes σ < 0.01 and ρ ≥ 8. F3 excludes σ < 0.001 and ρ ≥ 8. F4 excludes σ < 0.1 and ρ ≥ 8.

Classification algorithms.

We applied the following popular classification techniques: support vector machines (SVM) [START_REF] Cortes | Support-vector networks[END_REF] with linear kernel, random forest (RF) [START_REF] Breiman | Random forests[END_REF], logistic regression (LR) [START_REF] Barbara G Tabachnick | Using Multivariate Statistics[END_REF], gradient boosted trees (GBT) [START_REF] Jerome H Friedman | Greedy function approximation: a gradient boosting machine[END_REF], naive Bayes (NB) [START_REF] Tom | Machine Learning[END_REF], and decision trees (DT) [START_REF] Tom | Machine Learning[END_REF]. Besides predicting classes, most of these methods output a measure for feature importance that can be used to infer relationships between specific molecular properties and activity (here: identification as antibacterial). All classifications were implemented in Python language using Scikit-learn [START_REF] Buitinck | ECML PKDD Workshop: Languages for Data Mining and Machine Learning[END_REF][START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF]. SVM was implemented using the LIBSVM package [START_REF] Chang | LIBSVM: A library for support vector machines[END_REF] with a linear kernel. For SVM and LR, the testing data was normalized based on the training data, regularization parameter C was varied by factors of 10 from 10 -6 to 10. Regularization is a process of introducing extra terms to reduce overfitting by discouraging complexity. For RF and GBT, 1000 estimators were used because there was no significant improvement using more. Tuning the C parameter was found to improve performance (as measured by precision) so by averaging the results of the first step for each value of C. The best performing C was chosen for each data set.

2.1.4

Training process methological details. Different scoring methods like precision (probability of a positively classified element being positive), recall (probability of a positive element being positively classified), accuracy (probability of a correct classification), f 1 scor e (harmonic mean of precision and recall) and AUC (area under the ROC curve) were calculated. The most relevant score for our purposes and our main metric is precision because we want a high probability of our predicted antibacterial molecules being true antibacterial molecules. For screens involving a large number of molecules, of which only a few are to be chosen for closer study, it is important to choose compounds with the maximum likelihood of being antibacterial. However, recall must be high enough to obtain enough molecules to test. When looking for new potential antibacterial molecules, it is very important that after classification we obtain a list of molecules that is reliable rather than a more ambiguous list containing both more antibacterials and non-antibacterials. ANOVA and Tukey's Honest Significant Difference (HSD) were used to identify which means were significantly different (with significance for p < 0.05).

At each phase of the validation/optimization process, different independent runs are done. A discriminating parameter α was therefore introduced to derive the molecule final classification, which may not be consistent. The α is defined as follows: a molecule is being considered antibacterial if it was classified as such in at least α% of the runs.

Results and discussion

2.2.1 Summary of starting datasets. As explained in Section 2.1.1, the molecules were collected from market, MDDR, and Life Chemicals. This set of molecules is illustrated in Figure 1.

From those molecules, five data sets are constructed. Each of them has the same set of molecules, but different attributes, according to standard deviation and pair correlation explained in Section 2.1.2. The resulting number of attributes on each data set is detailed in Table 1.

2.2.2

Training and testing strategy. Three distinct training/testing stages were implemented:

(1) Our first step was to evaluate all classifiers performance. For that, we trained all methods (SVM, LR, RF, GBT, DT, NB) against the on-market antibacterials set P1 as the positive set and Life Chemicals non-antibacterials N5 as the negative set. Because the non-antibacterial class is over-represented, we randomly undersampled this class to do cross validation. Therefore, a random set of 150 N5 molecules was generated.

Next, 100 random P1 and N5 molecules were used for training and the remaining 100 (50 in each set) formed a test set. This process was repeated 50 times. The aim of this first stage is to allow the identification of the most appropriate attribute set and filter out the least interesting classifiers. (2) Next, the three top-performing classifiers from the first stage are retained and applied to an independent set of data. The F0 descriptor set (4532 unfiltered attributes) is trained against P1 and a set of 150 random N5 molecules, then the resulting classifier tested on an ensemble composed of P2, N1, N2, N3 and N4 (all from the MDDR database) assuming all P2 molecules are actual antibacterials and that there is no antibacterial in N1, N2, N3 and N4. This training process is repeated 10 times and the number of times each molecule was classified as non-antibacterial and antibacterial was recorded. Then we calculated the total combined precision and recall with the antibacterial being the positive class. Because there were 10 runs, we decided on molecules' "final" classification by using the α parameter defined before. (3) For our third step, we applied the models from the second step to the P1 and N4 MDDR set. We trained the classifier on the 2854 P2 MDDR antibacterials and 2854 randomly chosen MDDR N1, N2, N3. The training was repeated 10 times and the number of times each molecule was classified as non-antibacterial and antibacterial was recorded.

Attribute set comparison and initial classifier evaluation.

In the first step described above, we have tested all classifiers against all attribute sets. The results are summarized in Table 7.

All classifiers perform better than chance regarding our main metric precision. SVM, LR, RF, and GBT have better precision than NB and DT across the 5 different attribute sets. SVM appears to be the best performer with respect to our main metric precision for all data sets, though it is not significantly different from RF for attribute set F1 and from LR for F2 and F3. Over 99% precision is reached with SVM for all sets except F1, but it suffers from lower accuracy and recall, meaning it only correctly classifies a small percentage of antibacterials but those that are classified as antibacterial are correct. This can be seen most clearly in the F0 case, where accuracy and f 1 scor e are 67.7% and 52.1%, respectively, compared to > 90% for LR, RF, and GBT; the relatively low accuracy and f 1 scor e , as well as low training accuracy (68.2%) and f 1 scor e (53.2%), are indications of under-fitting by this model.

The precision results with F2, F3, and F4 are comparable to F0. In particular, the SVM precision with F0, F2, F3, and F4 is not significantly different, but the accuracy, f 1 scor e , and AUC are worse with F0. The improved performance of some of the classifiers with reduced attribute sets may be due to some sensitivity to highlycorrelated attributes or over-fitting to irrelevant attributes. F1 still results in > 90% precision for SVM, LR, RF, GBT, but the results are significantly worse than with F0, F2, F3, and F4, probably because important attributes were eliminated by the low correlation threshold. Definitions for F2, F3, and F4 do not result in such a problem, since metric scores are similar for all classifiers.

Final classifier selection.

In our final step, we took the best performing models-SVM, LR, and RF-trained on the P1 and N5 sets to test the MDDR data. Separately testing on the MDDR P2 antibacterials and non-antibacterials (i.e. N1 analgesic, N2 cardiovascular, N3 antagonist, N4 inhibitor), we calculated the proportion of molecules correctly classified where molecules classified as antibacterial in at least α percent of runs were classified as antibacterial; for each classifier, we also combined the MDDR data and calculated the precision and recall with respect to antibacterial where a molecule was classified as antibacterial if it was (Table 8). A low value of α (less than 50%) can be used if we want a permissive definition of antibacterial, but generally we are most interested in values above 50%.

Similar to previous results, SVM shows higher precision but lower recall. The MDDR non-antibacterials (N1-N4) have high percentage of correct classifications for all α values while less than 20% of MDDR antibacterials are classified correctly. Despite this, because the proportion of non-antibacterials compared to antibacterials is 20:1, precision ranges from 8% to 100% while recall stays below 20%. SVM with moderate α may be used as a model that outputs a small list of molecules that are very likely to be antibacterials; however, this list could also be too small for efficient experimental testing.

LR shows very erratic results with varying α. For low α values, most antibacterials in the test set are retrieved, while for high α (less stringent screening), most non-antibacterials are correctly found. Around α = 80%, the non-antibacterials show a steep rise in proportion of correct classifications and precision jumps from 6% to 23%, achieving a maximum of 48%. Most non-antibacterials were classified as antibacterial between 1 and 7 times out of 10 runs. This inconsistency makes LR an untrustworthy model for our purposes.

As expected from an ensemble model, RF shows more consistent results. Precision stays around 10-12%, which is far smaller than the highest precisions achieved by SVM and LR. Although RF classifies most non-antibacterials as such, a large number of them are false positives compared to the number of true positives. RF's recall is much better than SVM, so RF could be used as an alternative in case it is worth sacrificing the precision of SVM for higher recall. To maximize precision, we choose SVM for the last training stage.

KNOWLEDGE DISCOVERY WITH DECOMPOSABLE MODELS

In Section 2, we inspected a number of chemical molecules to know which features could characterize antibacterials. To do that, we used the properties of each molecule, summing up to thousands of molecular attributes providing a significant amount of data to be analyzed for knowledge discovery.

In order to minimize the required time and space, before we mine the data, we should reduce the dimension of the data set, as a transformation step according to the basic steps of KDD [START_REF] Fayyad | From data mining to knowledge discovery in databases[END_REF]. It is performed by combining some attributes into one, or by completely eliminating some of them.

Within the thousands attributes for each molecule, we can identify some redundancies and therefore, we can ignore an attribute if it can be merged or replaced with another attribute. The selected attributes should be able to define the molecules without significant loss of information. Beside the redundancies, we should also ignore the attributes which are not informative.

Log-linear analysis

Log-linear analysis (LLA) can find any associations among attributes, allowing feature selection according to those associations.

Suppose that we have a data set W AR of certain molecules with three variables: molecular weight (W ), number of atoms (A) and ring perimeter (R). Relationship between two variables can be studied with two-way χ 2 test of association. However, if we have more than two variables, we need to do a multiway frequency analysis to study the two-and three-way associations. LLA is an extension of multiway frequency analysis, and tries to discover any statistical relationships between three or more non-continuous variables. It will create a model (like the one in Eq. 1) to find the log of expected frequencies.

For the W AR, LLA tries to answer some relationship questions. Is a molecule's weight related to its number of atoms? Is a molecule's number of atoms related to its ring perimeter? Is there a three-way relationship among molecular weight, number of atoms, and ring perimeter? By knowing ring perimeter of a molecule, can we predict its weight?

To do a multiway frequency analysis with LLA, we develop a linear model of the logarithm of expected cell frequencies. An example of such model is shown in Eq. 1, with each term representing an association. As the number of variables increases, the number of associations also increases. With three variables in data set W AR, we have seven possible associations: one three-way associations, three two-way associations, and three one-way associations. The model in Eq. 1 contains all possible associations. To keep the simplicity of a model, LLA tries to find which association will be kept or removed.

To do that, we should determine the significance of an association by examining the goodness-of-fit of the model containing it.

Eventually, with thousands of variables, the number of possible associations will be so large that it would be impractical to test each association. This limitation can be solved by Chordalysis.

3.1.1 Log-linear model. Log-linear model is represented as an equation to find a logarithm of E (expected frequency of a combination of variables' values). From data set WAR, we can generate a model that contains all possible associations. This is the saturated model, which can be written as:

ln E war = θ + λ W (w) + λ A (a) + λ R (r ) + λ W A (wa) + λ W R (wr ) + λ AR (ar ) + λ W AR (war ) (1)
where θ is a constant, and λ term represents an effect. Each λ has values as many as the number of levels, and these values sum to zero. For example, since we define three levels of molecular weight: light, medium, and heavy, λ W (w) has three possible non-zero values: for light (λ W (lig)), medium (λ W (med)), and heavy (λ W (hvy)), with λ W (lig) + λ W (med) + λ W (hvy) = 0.

A log-linear model can be hierarchical or non-hierarchical. A hierarchical model can be represented by its highest-order association in square brackets. For example, a model [W A][R] contains λ W A (wa) and λ R (r ), as well as λ W (w) and λ A (a).

Furthermore, if a model is a sub-model of another, their G 2 difference is itself a G 2 . Therefore,

[W A][R] is a sub-model of [W A][W R],
i.e. we can find all λ terms of

[W A][R] in [W A][W R].
By comparing their G 2 to χ 2 table, we can obtain their significance. If both models are significant, we can choose the less complex one ([W A][R]) if their G 2 difference is not significant.

Chordalysis

There are two ways to select which associations to include in a log-linear model, backward elimination and forward selection. Backward elimination starts from a saturated model and eliminates non-significant associations one by one. On the other hand, forward selection starts from an empty model and iteratively adds an association until the difference is not significant. The existing LLA considers all possible associations to determine which one to be added or removed. This becomes infeasible when the number of attributes increases, since the number of associations is exponential w.r.t. it.

Chordalysis tries to guide the existing LLA in selecting which associations are significant enough to be included in the model [START_REF] Petitjean | A statistically efficient and scalable method for log-linear analysis of high-dimensional data[END_REF][START_REF] Petitjean | Scaling loglinear analysis to high-dimensional data[END_REF]. This method is focusing on decomposable log-linear models, whose G 2 can be calculated by inspecting the maximal cliques and minimal separators of the corresponding graph.

As a forward approach, Chordalysis starts with an empty graph as initial model. It has neither vertex nor edges. Then at the first step of each iteration, the candidate models are generated. Each candidate M c differs from the current best model M * by a single edge only. Therefore, we try to add an edge at each iteration. This edge addition must keep the graph chordal, hence the name Chordalysis.

Based on the fact that the graph is chordal and differs by an edge between iterations, the G 2 computation is scalable to thousand variables [START_REF] Petitjean | Scaling log-linear analysis to datasets with thousands of variables[END_REF].

After the score calculations, Chordalysis selects the best M c . Its score is then compared to the significance threshold. If it is lower, then we replace M * with M c and continue to the next iteration. If not, then the current M * is the final model because the G 2 difference by adding an association is not significant.

The significance threshold α is updated at each iteration so it does not accept a candidate too often. This update rule follows the layered critical values [START_REF] Webb | Layered critical values: a powerful direct-adjustment approach to discovering significant patterns[END_REF]. At iteration i, where the current best model M * has L edges, the significance threshold α i is:

α i = α 2 L • S i (2)
where S i is the search space, i.e. the number of chordal graphs that can be formed by adding a single edge to M * , and α is a p-value threshold (usually set to 0.05).

Having a graph representing associations among attributes, we then perform feature selection based on this graph. The attributes which are independent (have no association) are kept, because they can't be represented by another attribute. Then, basically we remove the attributes that have only one association. For example, if we encounter a connected component shown in Fig. 2b we keep only attribute d. This means that d can represent c, e, and f . But there is an exception for some of those one-association attributes. If a connected component has only 2 vertices, like the one in Fig. 2a, we randomly choose one attribute and discard the other.

Classification of antibacterials and non-antibacterials

The attributes that are selected using Chordalysis will be used in three machine learning method to classify dataset of antibacterials and non-antibacterials. The first method is Support Vector Machine (SVM) [START_REF] Cortes | Support-vector networks[END_REF]. Given a dataset of labelled points, SVM builds a hyperplane that best separates the two labels. To deal with non-linearly separable dataset, SVM use a kernel to map points to higher dimension.

The second method is random forest [START_REF] Breiman | Random forests[END_REF]. It constructs a family of decision trees which have different training set between each other. To classify data, each tree gives a classification (or "vote"), and random forest takes the majority vote.

The third method is naive Bayes [START_REF] Tom | Machine Learning[END_REF] that is based on Bayes' theorem. When classifying a data d, naive Bayes calculates the posterior probability of each class given d. The classifier then chooses the class that has higher posterior probability.

Result

To measure the goodness of each classifier, we use five metrics: accuracy, precision, recall, AUC, and f 1 scor e .

Here we focus on 3025 antibacterial molecules, which is composed by 152 molecules from market and 2873 molecules from MDDR antibacterials. From those molecules, we defined 4885 attributes. Besides removing missing-valued attributes and perfectly correlated attributes (like the previous work in Section 2), we also removed attributes that have the same value for all molecules. This resulted in 3769 attributes.

Some of the attributes are continuous. Because LLA and Chordalysis work on discrete variables, these numerical attributes are preprocessed so that all of them become discrete. This preprocessing step is applied to attributes which have more than 10 distinct values. Equal-width discretization method is used, with 10 bins as desired output.

Attribute selection.

Chordalysis was tested on 3769 attributes, using α = 0.05 as p-value threshold, and it found 1024 associations. The selection procedure explained in Section 3.2 results in 3171 selected attributes.

From each filter of the work in Section 2, we have four sets of selected attributes. As seen in Table 1, filters 2, 3, and 4 gave us around 500 attributes each; those will be next referred to as S2, S3, and S4 respectively. In order to compare Chordalysis-based feature selection, we let Chordalysis find more associations without being limited by p-value threshold. After some experiments, we found that after 3613 associations were found, the selection procedure applied on the graph resulted in a set of 595 selected attributes. We call this set SC. Since S2, S3 and S4 are very similar, all three sets are referred to as S2-4.

All attributes are uniquely categorized within the Dragon software into 29 attribute families. Fig. 3 and4 show how those families are distributed within the different sets, with weights in percentages for S2-4 being defined as the average value between S2, S3 and S4. Table 3 summarizes the results of Chordalysis-based selection, and also highlights the overlap between SC and S2-4.

2D atom pairs are by far the most prevalent family in all cases, accounting to 33, 63 and 20% of the total attributes population in the original, SC and S2-4 sets respectively. It is very clear that Chordalysis privileged this family, now twice as present in SC compared to the original set, while on the contrary, it is significantly less important in S2-4.

The atom-centred fragments, CATS 2D and functional group counts families were not prevalent in the original set (2, 3, and 3% respectively), and become over-selected in all reduced sets, with CATS 2D being more prevalent in S2-4 compared to SC. These 3 sets account for 23% of SC, so with the addition of 2D atom pairs only 15% is remaining.

The relative diversity of the different sets can be compared by focusing on the number of families accounting for more than 5% of the total number of attributes and on their total weight (see Figure 8). Only the 4 aforementioned families obey these criteria in SC, totaling 85% of the set. There are 7 families with more in S2-4 (73%); 4 in the original set (56%). Therefore, three attribute families are seen significantly more prevalent in S2-4 compared to the original set (26% / 15%), but are almost completely filtered out by Chordalysis: 2D autocorrelations, 3D-MoRSE and GETAWAY descriptors. Apart from these families, there is a consensus between S2-4 and SC regarding the removal of some attribute families from the original set, with SC appearing more stringent than S2-4. Indeed, the 2D matrix-based descriptors, edge adjacency indices and RDF descriptors account together for 22, <1 and 5% in the original, SC and S2-4 sets respectively. This suggests that those descriptors are not of much value for modeling the probability that a given chemical compound would possess antibacterial properties.

Eventually, it should be noticed that while SC size compared to the original set is 12%, only a single attribute family has been filtered less than 50%: drug-like indices. This is specific to SC (5 attributes are retained by S2, S3 and S4). There were only 27 residues of this kind in the original set, which is not significant enough to determine that there could be a correlation between drug-likeness and antibacterial potency that would be most efficiently selected by Chordalysis. Table 2 lists the number of overlapping selected attributes from S2, S3 and S4 with SC. Table 3 summarizes SC-related data for most-relevant attribute families identified above, and highlights the number of consensus attributes i.e. attributes found in all sets.

3.4.2

Training/testing strategy. Using attributes in SC, we trained SVM, random forest, and naive Bayes on data from market antibacterials, MDDR antibacterials, Life Chemicals non-antibacterials, and MDDR non-antibacterials. After the training process, the three classifiers are tested on Life Chemicals list of predicted antibacterials. The results are summarized in Table 4. By tuning the parameter C for SVM, we get the best result for C = 0.01.

Based on the values of all metrics used to evaluate classifier performance, it appears that SVM and RF perform significantly better than naive Bayes. The two best performing model -SVM and random forest-were then trained on the market antibacterials and Life Chemical antibacterials to test the MDDR data. We regarded a molecule as an antibacterial if it is classified as such in at least α percent of runs. The precision and recall of the two models are shown in Table 5-6. SVM has better recall on the majority of alphas, and it has higher precision for α ≥ 20.

CONCLUDING REMARKS

We evaluated several popular classification methods, including SVM, LR, and RF, for classifying molecules as antibacterial or nonantibacterial. Such machine learning approaches were already successfully used for drug/non-drug classification [START_REF] Byvatov | Comparison of support vector machine and artificial neural network systems for drug/nondrug classification[END_REF][START_REF] Givehchi | Impact of descriptor vector scaling on the classification of drugs and nondrugs with artificial neural networks[END_REF][START_REF] Korkmaz | Drug/nondrug classification using support vector machines with various feature selection strategies[END_REF][START_REF] Ayca C Pehlivanli | Drug/nondrug classification with consensual Self-Organising Map and Self-Organising Global Ranking algorithms[END_REF], but [START_REF] Janecek | Efficient feature reduction and classification methods[END_REF][START_REF] Lian | Discovery of Influenza A virus neuraminidase inhibitors using support vector machine and Naïve Bayesian models[END_REF][START_REF] Rathod | Classification of Human Pregnane X Receptor (hPXR) Activators and Non-Activators by Machine Learning Techniques: A Multifaceted Approach[END_REF][START_REF] Shahid | SVM based descriptor selection and classification of neurodegenerative disease drugs for pharmacological modeling[END_REF][START_REF] Vyas | A study of applications of machine learning based classification methods for virtual screening of lead molecules[END_REF] are in good general agreement with our own observations. In future work, we should favor the use of SVM and RF over the other classifiers evaluated here in order to perform virtual screening of chemical databases for finding most probable antibacterials.

One important finding of this work is that for such a task, the choice of the classifier appears to have much more impact than the selection of molecular descriptors. We have chosen to evaluate all available descriptors from the Dragon software, without any consideration of the relative relevance of each of those. This "blind" approach has the advantage of being totally unbiased, but puts more stress on the classifiers.

Furthermore, in Section 3, we describe the application of the Chordalysis technique for molecular attribute set reduction. We show that it leads to improved performance when a machine learning technique is used next to discriminate between antibacterials and compounds with no antibacterial activity. It is suggested that a two-step strategy, with a Chordalysis-refined attribute set being fed to a SVM classifier could be highly efficient for antibacterials identification. An alternate techniques for selecting an optimal attribute set [START_REF] Tang | Feature selection for classification: A review[END_REF], such as recursive feature elimination [START_REF] Guyon | Gene selection for cancer classification using support vector machines[END_REF][START_REF] Xue | Effect of molecular descriptor feature selection in support vector machine classification of pharmacokinetic and toxicological properties of chemical agents[END_REF], RF variable importance [START_REF] Cano | Automatic selection of molecular descriptors using random forest: Application to drug discovery[END_REF], SVM variable selection [START_REF] Chang | LIBSVM: A library for support vector machines[END_REF], tabu search [START_REF] Tahir | Simultaneous feature selection and feature weighting using Hybrid Tabu Search/K-nearest neighbor classifier[END_REF][START_REF] Zhang | Feature selection using tabu search method[END_REF], and evolutionary algorithms [START_REF] Freitas | Advances in Evolutionary Computing[END_REF] should be further studied. In the process, precise clues on implementing new attributes that could be more efficient for our purpose (antibacterials selection) than the broad generic reference set of molecular attributes that is available in the Dragon software could be obtained. When we reach a state where no clear methodological improvement could be reached, we will apply the optimized methodology to mine chemical space for possible new antibacterials. A limited number of hits from this virtual screening process will be tested experimentally. Only interesting results backed up by the resulting experimental data will validate the ongoing chemoinformatics approach.

Figure 1 :

 1 Figure 1: Diagram showing the intersections between molecules from market, MDDR, and Life Chemicals.

Figure 2 :

 2 Figure 2: Examples of connected components with 2 vertices (a) and more than 2 vertices (b).

Figure 3 :

 3 Figure 3: The distribution of families in 4885 original attributes, 595 attributes of SC, and around 500 attributes of S2-4.

  S2-4 set: 26 families, 563 attributes on average

Figure 4 :

 4 Figure 4: Distribution of major attribute families in (a) the original set, (b) set SC, and (c) average of S2, S3, and S4. All values in percentages. Only sets weighting >5% are represented. Categories in green are the 4 most-represented in SC. Those in orange with description in italic are mostly filtered out of both SC and S2-4. Grey ones summarize remaining families (1-5% and <1%).

Table 1 :

 1

Rules and number of attributes of each filter Filter Stddev Pair correlation Selected attributes 1 ≥ 0.010 < 0.4 87 2 ≥ 0.010 < 0.8 576 3 ≥ 0.001 < 0.8 588 4 ≥ 0.100 < 0.8 524

Table 3 :

 3 Population of most relevant attribute families. Last column is the number of attributes present in all sets (SC, S2, S3 and S4). Percentages correspond to the number of retained attributes from the original set.

	Attribute family	Original set	SC	Overlap
	2D atom pairs	1596	373 (23%)	80
	2D matrix-based	550	2	1
	Edge adjacency ind.	324	2	1
	GATEWAY	273	7	1
	Functional group cnt.	154	66 (43%)	24
	CATS 2D	150	31 (21%)	19
	Atom-centered frag.	115	38 (33%)	10
	Drug-like indices	27	15 (56%)	1
	TOTAL	4885	595 (12%) 144 (3%)

Table 4 :

 4 Means and standard deviations of classifiers' metrics on the test set. All data in percentages.

	Metric	SVM (C = 0.01) Random Forest Naive Bayes
	Accuracy	97.0 ± 2.5	96.6 ± 1.5	55.7 ± 1.4
	Recall	98.9 ± 2.0	95.6 ± 1.5	21.2 ± 0.6
	Precision	95.9 ± 3.5	98.3 ± 2.2	93.7 ± 9.1
	AUC	99.3 ± 1.1	99.5 ± 0.4	65.3 ± 4.5
	f 1 scor e	97.3 ± 2.2	96.9 ± 1.3	34.5 ± 1.0

Table 5 :

 5 Precision and recall of random forest classifier on the test set. All values in percentages.

	α	4532 attributes	SC
		Precision Recall Precision Recall
	10	10.0	71.2	11.6	65.4
	20	10.7	68.4	11.8	64.5
	30	11.8	65.4	12.2	63.5
	40	11.8	65.4	12.2	63.5
	50	12.3	64.3	12.3	63.0
	60	13.3	61.5	12.6	62.4
	70	14.1	60.1	12.8	61.8
	80	14.1	60.1	12.8	61.8
	90	15.1	59.1	13.0	61.2
	100	16.6	56.3	13.3	60.1

Table 6 :

 6 Precision and recall of SVM classifier on the test set. All values in percentages. variance and correlation. Using those was not found to improve performance. When looking at precision as our main metric, our results show that the SVM classifier with a tuned C parameter ranks first but has much lower accuracy and f 1 scor e . For a dataset of potential antibacterial molecules, SVM could be used to find a reliable list of antibacterial molecules. Another method like RF with lower precision but better accuracy and f 1 scor e may be used if a greater number of classified antibacterials is desired.Previous investigations of the merit and drawbacks of several learning methods

	α	4532 attributes	SC
		Precision Recall Precision Recall
	10	21.3	16.4	11.1	82.7
	20	24.0	15.2	13.3	78.1
	30	25.9	12.8	17.0	71.9
	40	25.9	12.8	17.0	71.9
	50	26.6	12.5	19.0	69.9
	60	27.4	11.8	23.8	65.1
	70	27.9	11.4	27.2	62.4
	80	27.9	11.4	27.2	62.4
	90	27.7	10.0	31.8	58.7
	100	32.4	9.2	39.9	53.4
	none were applied to antibacterials. Along with our initial 4532 at-
	tribute data set (F0), we tested 4 reduced sets (F1-F4), filtered on the
	basis of data

Table 7 :

 7 Means and standard deviations of precision metrics of all classifiers. All values are in percentages. Attribute set F0 (full Dragon set) SVM (C = 10 -5 ) LR (C = 10 -2 ) ± 4.1 92.1 ± 3.4 79.1 ± 4.3 92.5 ± 5.0 Accuracy 88.2 ± 2.5 88.7 ± 2.5 91.9 ± 3.0 90.4 ± 3.0 78.9 ± 3.8 77.5 ± 4.2 f 1 scor e 87.2 ± 3.0 88.1 ± 2.9 91.7 ± 3.1 90.2 ± 3.1 78.8 ± 4.2 72.5 ± 6.2 AUC 94.8 ± 2.0 94.5 ± 1.9 97.3 ± 1.3 96.4 ± 1.9 78.9 ± 3.8 90.0 ± 3.6 F2 SVM (C = 10 -4 ) LR (C = 10 -6 ) ± 2.7 96.5 ± 2.5 89.2 ± 4.8 85.5 ± 4.7 Accuracy 86.9 ± 3.2 89.3 ± 3.9 95.1 ± 2.5 95.3 ± 1.9 88.7 ± 4.0 88.5 ± 3.7 f 1 scor e 84.8 ± 4.2 88.0 ± 4.1 95.0 ± 2.6 95.3 ± 1.9 88.6 ± 4.2 89.0 ± 3.5 AUC 96.0 ± 1.8 95.7 ± 2.2 98.9 ± 0.9 98.8 ± 0.9 88.7 ± 4.0 89.7 ± 3.9 F3 SVM (C = 10 -4 ) LR (C = 10 -6 ) ± 2.3 96.2 ± 2.4 88.6 ± 5.0 86.6 ± 4.8 Accuracy 87.3 ± 2.7 88.9 ± 3.1 94.8 ± 2.3 95.2 ± 1.8 88.6 ± 3.8 89.0 ± 3.3 f 1 scor e 85.4 ± 3.4 87.6 ± 3.8 94.7 ± 1.8 95.1 ± 1.9 88.7 ± 3.8 89.4 ± 3.2 AUC 96.4 ± 1.5 95.6 ± 1.9 98.6 ± 0.9 98.8 ± 0.8 88.6 ± 3.9 91.0 ± 3.3

	RF	GBT	DT	NB

Table 8 :

 8 The proportion, precision, and recall of MDDR molecules correctly classified 1 using SVM, LR, and RF. All values are in percentages.

					SVM
	α	P2 2 N1 2 N2 2 N3 2 N4 2 Precision Recall
	10	16.2 98	88.9 94.4 90.4 8.7	16.2
	20	15.1 98.6 96.4 98.7 98.1 29.4	15.1
	30	13.5 100 100 100 100 100	13.5
	40	13.5 100 100 100 100 100	13.5
	50	13.2 100 100 100 100 100	13.2
	60	11.4 100 100 100 100 100	11.4
	70	17	100 100 100 100 100	17
	80	17	100 100 100 100 100	17
	90	10.2 100 100 100 100 100	10.2
	100 9.5	100 100 100 100 100	9.5
				Logistic Regression
	α	P2	N1	N2	N3	N4	Precision Recall
	10	70	0	0	0	0	3.4	70
	20	66.6 0	0	0	0	3.2	66.6
	30	63.2 0	0	0	0	3.1	63.2
	40	63.2 0	0	0	0	3.1	63.2
	50	61.7 0	0	0	0	3.0	61.7
	60	59.1 0	0	0	0.2	3.0	59.1
	70	57.4 0	0	0	93.5 6.1	57.4
	80	57.4 0.2	0.1	0.1	100 6.7	57.4
	90	55.1 69.1 68.6 80	100 23.3	55.1
	100 51.2 91.3 88.2 94.5 100 48.7	51.2
				Random Forest
	α	P2	N1	N2	N3	N4	Precision Recall
	10	71.5 77.2 70.5 76.2 67.4 18	71.5
	20	68.9 79.9 67.7 73.3 67.4 10.2	68.9
	30	65.6 84.3 74.4 79.6 77	11.2	65.6
	40	65.6 84.3 74.4 79.6 77	11.2	65.6
	50	64.4 85.4 76	87	73	11.8	64.4
	60	61.7 87.6 80.6 84.3 74.9 12.5	61.7
	70	60.4 88.6 80.6 84.3 74.9 12.3	60.4
	80	60.4 88.6 79.1 83.1 74.9 12.3	60.4
	90	58.5 90	84.2 87.6 76.6 13.2	58.5
	100 54.9 91.1 82.2 85.7 76.6 12.1	54.9

A molecule is regarded as an antibacterial if it is classified as such in at least α% of runs.

P2, N1, N2, N3, and N4 refer to the antibacterial, analgesic, cardio, antagonist, and inhibitor MDDR subsets respectively.


C.-H Bonnard

A Blavette
email: anne.blavette@ens-rennes.fr

S Bourguet
email: salvy.bourguet@univ-nantes.fr

F Rongère

T Kovaltchouk
email: thibaut.kovaltchouk@ac-reims.fr

T Soulard
email: thomas.soulard@ec-nantes

Towards the optimal use of an existing MRE electrical network from an electrothermal perspective

Marine renewable energy (MRE) is an interesting sustainable source of power. However, planning the cost-effective integration of MRE, and in particular of wave energy, in the energy mix remains a challenge as its levelized cost of energy (LCOE) is still greater than these of more conventional energy sources. This paper describes a preliminary study about the energy production management of a simulated point absorberbased WEC farm that could be installed in the vicinity of the SEM-REV site, i.e. the French multi-technology open sea test site. The proposed approach is based on the temporal analysis of the electrothermal behavior of the export cable of the SEM-REV. The models developed under Matlab-Simulink ® , are generic and can be easily extended to other WEC types and more sophisticated models and control strategies, as well as to other energy sources (e.g. offshore wind). It is demonstrated in this work that there is room to maximize the utilization of the export cable, which allows to increase wave electricity production during a predetermined sea-state sequence with limited to no curtailment.

I. INTRODUCTION

Marine renewable energy (MRE) is an interesting and sustainable source of power. However, planning the integration of MRE, and in particular of wave energy, in the energy mix remains a challenge as its levelized cost of energy (LCOE) is still greater than these of more conventional energy sources [START_REF] Astariz | Evaluation and comparison of the levelized cost of tidal, wave, and offshore wind energy[END_REF], [START_REF] Astariz | The economics of wave energy: A review[END_REF], [START_REF] Uihlein | Wave and tidal current energy-a review of the current state of research beyond technology[END_REF]. Many studies have addressed the design optimization of the MRE farms electrical infrastructure. More precisely, they have mainly focused on cable length and rated current [START_REF] Bull | Electrical cable utilization for wave energy converters[END_REF], [START_REF] Wijethunga | Collector cable design based on dynamic line rating for wind energy applications[END_REF], [START_REF] Olsen | Dynamic temperature estimation and real time emergency rating of transmission cables[END_REF], [START_REF] Dahmani | Modélisation, optimisation et analyse de fiabilité de topologies électriques ac de parcs éoliens offshore[END_REF], [START_REF] Sharkey | Dynamic electrical ratings and the economics of capacity factor for wave energy converter arrays[END_REF], and WECs spatial layout [START_REF] Bailey | Variability and stochastic simulation of power from wave energy converter arrays[END_REF], [START_REF] Carballo | Wave farm impact based on realistic wavewec interaction[END_REF]. One of the next steps consists in addressing the future challenges regarding the use of the electric infrastructures, such as the existing test sites (e.g. SEM-REV, bimep). In particular, this paper discusses the potential for increasing the number of WECs in a wave farm without grid reinforcement by taking into account less conservative, and more realistic, operational constraints. This approach stems from the observation that highly conservative, and relatively irrelevant, design constraints are generally applied to wave farms. More precisely, the design of a wave farm export cable is based on the maximum value of the electric current profile flowing through the cable, regardless of the duration during which it is applied to the latter. In other words, this method considers implicitly that a fictive, constant current profile, whose magnitude is equal to the actual maximum current value, is applied to the cable at any time [START_REF]Calculation of the Cyclic and Emergency Current Rating of Cables. Part 2: Cyclic Rating of Cables Greater Than 18/30 (36[END_REF], [START_REF]Electric cables Calculation of the current rating Part 1-1: Current rating equations (100 % load factor)[END_REF], [START_REF]Electric cables Calculation of the current rating Part 2-1: Thermal resistance Calculation of thermal resistance[END_REF]. Based on this observation, and on the potentially highly fluctuating power output of a wave farm, one of our previous studies showed that a submarine power cable can carry, on a temporary basis, significantly more current than its rated value, the latter being evaluated under fictive, constant current conditions [START_REF] Matine | Optimal sizing of submarine cables from an electro-thermal perspective[END_REF]. Hence, it was proposed to consider thermal limits rather than current limits, as the latter may be quite irrelevant in the case of a highly fluctuating current output. This approach is similar to the concept of dynamic line rating (DLR) used for transmission lines in that it proposes to consider dynamic thermal limits rather than to rely entirely on a fixed current limit established under worst or nearworst case conditions [START_REF] Michiorri | Forecasting for dynamic line rating[END_REF]. However, these two approaches differ as in DLR, several current limits are defined based on varying external meteorological conditions (e.g. wind speed, air temperature). On the contrary, in our approach, the external conditions, such as soil temperature and moisture for instance, are constant but the potential for electric current increase is made possible by 1) the soil large heat capacity, 2) the variable nature of the wave energy resource. This is illustrated in Fig. 1 where a current profile and the corresponding temperature profile are shown: despite large current fluctuations, the environment (soil and sea) acts as a damper with a certain thermal inertia, thus leading to temperature fluctuations of smaller magnitude. In this work, we are going one step further and we present a preliminary study about the optimal energy production management of a wave farm inspired from the SEM-REV test site, i.e. the French multi-technology open sea testing site managed by Ecole Centrale de Nantes [START_REF]The SEM-REV website[END_REF]. As shown in Fig. 2, it is located near Le Croisic (France). Thanks to the thermal inertia of the overall system, composed of the cable and of its environment (soil and sea), and the fluctuating current generated by a wave farm, a submarine export cable can temporarily carry more current than its rated value, which is defined under static, (near-)worst case conditions, as mentioned earlier. This paper describes three case studies based on a direct-drive, point absorber-based WEC farm with negligible energy storage, thus presenting a highly variable power output. The point absorbers are controlled passively with a damping factor depending on the sea-state considered. Our approach is two-fold. First, as electric currents greater than the rated value can be safely tolerated in the system on a temporary basis, we analysed whether the wave electricity production during highly energetic sea-states could be increased with limited to no curtailment, thus leading to an increased wave farm capacity factor. Second, a simple farm power production strategy has been applied by (de)activating the WECs with respect to marine weather conditions (i.e. sea-state parameters) in order to maximize the overall energy production while still not exceeding the thermal constraints. The proposed approach, implemented under Matlab-Simulink ® , is generic and can be extended to other WEC types and to more sophisticated models and strategies. The rest of the paper is divided into four sections. Section II describes the electrothermal modeling of the cable that transmits the energy to the onshore network. Then, Section III describes the numerical simulations. Finally, Section IV details the results, followed by the conclusion of the paper. Fig. 3. Cross section picture of the export cable considered for our case studies. This 3 × 95 mm 2 copper cores cable (that was designed to carry a constant electric current of 290 A) is currently installed in the SEM-REV test site located off Le Croisic (see Fig. 2), France and is managed by École Centrale de Nantes [START_REF]The SEM-REV website[END_REF].

II. CABLE ELECTROTHERMAL MODELING

The model used in this study is intended to reproduce the electrothermal behaviour of the 24 km export cable installed in the SEM-REV test site (see Fig. 2). We considered that this 3-phase, 20 kV, XLPE insulation cable is buried at a 1.5 m depth in soil, where thermal properties are deemed to be homogeneous and constant, and where thermal resistivity

ρ th = 0.7 m•K•W -1 and heat capacity C th = 2 MJ•m -3 •K -1 .
Also, based on a previous work [START_REF] Cea | Maintenance corrective et prdictive des cbles de fermes nergtiques offshore[END_REF], it was considered necessary that the cable materials consider the temperature dependence of the specific heat C p (T ) in J/(kg.K), of the thermal conductivity κ(T ) in W/(m.K), and of the electrical resistivity ρ e (T ) in Ω.m. One can find the materials data we used in [START_REF] Mark | Physical properties of polymers handbook Second edition[END_REF], [START_REF] Eichhorn | A critical comparison of xlpe-and epr for use as electrical insulation on underground power cables[END_REF], [START_REF] Qi | Thermal and mechanical properties of epr and xlpe cable compounds[END_REF], [START_REF]Electric cables Calculation of the current rating Part 2-1: Thermal resistance Calculation of thermal resistance[END_REF]. However, compared to our previous models based on the finite element method [START_REF] Matine | Optimal sizing of submarine cables from an electro-thermal perspective[END_REF], and which required an important computing time, in this paper a simplified model based on the well-known analogy between electrical and thermal physics [START_REF] Robertson | An electrical-analog method for transient heat-flow analysis[END_REF], [START_REF]Electric cables Calculation of the current rating Part 2-1: Thermal resistance Calculation of thermal resistance[END_REF], and implemented under the Matlab-Simulink ® software [22], was used for the sake of computing speed.

III. NUMERICAL SIMULATIONS

A. Introduction

All the case studies presented in this paper used the same sea-state sequence shown in Fig. 4. Regarding the initial conditions, we used a predefined sea-state with wave height H s = 1 m and wave period T p = 12 s. It was assumed that at initial time t=0 s, the system was in a dynamic steadystate where the cable temperature fluctuates around a constant value which is assumed to be the initial temperature for the simulations considered here. We have also computed the cable current carrying capacity I cc ≈ 330 A which corresponds to the maximum constant RMS value of the current that can be transmitted in the cable without exceeding the maximum allowed temperature of the cable cores, i.e. T max = 90 °C for a XLPE-insulated cable, as it is the case here. The difference between the rated value of 290 A and the calculated current carrying value, i.e I cc ≈ 330 A, may be explained by the fact that we do not consider potential hot spots, which could be the case at landfall or at each junction box. Also, a I). Note that it is a completely fictitious sequence but based on plausible durations and transitions between each sea-states based on Fig. E2 and E3 of [START_REF] Ruggiero | Sediment transport study: Baseline observations and modeling for the reedsport wave energy site[END_REF]. security margin, unknown to the authors of this paper, may have been taken into account in the initial design studies, thus decreasing the value of the rated current. Without more information on these specific points, we deliberately chose to use the highest value, i.e. I cc ≈ 330 A, as a reference. This constitutes a worst-case scenario leading to a minimal margin for current increase. However, it is important to note that the goal of this paper is to assess the potential for current increase on a submerged, continuous section of an export cable, independently of the influence of other cable elements and parts for which specific actions, such as replacement, may be undertaken.

B. Current profile generated by a WEC farm

In order to model the wave farm, we used a wave-to-wire model implemented under Matlab-Simulink ® , as described in [START_REF] Blavette | Influence of the wave dispersion phenomenon on the flicker generated by a wave farm[END_REF]. The farm was composed of up to 36 identical 1 MVA heaving buoys controlled passively, as modelled in [START_REF] Kovaltchouk | Influence of control strategy on the global efficiency of a direct wave energy converter with electric power take-off[END_REF]. Note that a single peak period T p = 12 s is considered, i.e. the value of the damping factor B pto is constant and equal to B pto = 680 × 10 3 Nms. Due to the random nature of wave power, the power generated by a WEC farm, especially when it is based on direct-drive point absorbers with little to no storage, can be extremely fluctuating. This is reflected in the current that flows in the export cable as shown in [START_REF] Babarit | Numerical benchmarking study of a selection of wave energy converters[END_REF], [START_REF] Matine | Optimal sizing of submarine cables from an electro-thermal perspective[END_REF] and as illustrated in Fig. 1.

C. Case studies description

The main objective of this paper is to determine the number of additional WECs which could be installed in the farm without exceeding the cable cores temperature constraints. To do so, three different scenarios are considered:

• Case 1 : The number of WEC is kept constant with N W EC = N i W EC . N i W EC corresponds to the maximum number of WECs which can be connected to the wave farm without exceeding I cc , i.e.

max (I f arm (t)) | N W EC ≤ I cc (1)
• Case 2 : N W EC is also kept constant with N W EC = N + W EC . N + W EC corresponds to the maximum number of WECs which can be connected to the wave farm without exceeding the cable cores temperature constraints, i.e.

max (T core (t)) | N W EC ≤ T max (2)
• Case 3 : The number of WECs N W EC = N v W EC is allowed to vary. This can be achieved by (de)activating WECs between different sea-states. However, the cable cores temperature constraints must still be satisfied, i.e.

max (T core (t)) | N W EC (t) ≤ T max (3)
Case 1 can be seen as corresponding to an initial and existing WEC farm where the conservative approach considering only maximum current constraints. Case 2 can be envisaged as improvement over Case 1 where temperature constraints are considered instead of current constraints. In this case, N W EC is constant throughout the sea-state sequence. Finally, Case 3 is deemed to represent a further enhancement compared to Case 2, as N W EC is allowed to vary. It is important to note that in this preliminary study, economical considerations were not taken into account. In other words, the number of additional WECs (either N + W EC or N v W EC ) was not limited due to economical reasons, but only due to technical constraints. This was meant to assess, at a first stage, the theoretical potential for farm expansion. This paper can therefore be considered as presenting a proof-of-concept study. Once this step is validated, further work will include additional constraints, including economical ones.

IV. RESULTS

A. Case 1

As we can see in Fig 5, the temperature of the cable cores is far below the limit of 90 °C that is suggested in IEC standards and is used by many power cables manufacturers. Such results confirm, as shown in a previous study [START_REF] Matine | Optimal sizing of submarine cables from an electro-thermal perspective[END_REF], [START_REF] Cea | Maintenance corrective et prdictive des cbles de fermes nergtiques offshore[END_REF], that eq. ( 1) was not suitable for sizing power cables in the case of a WEC farm generating highly fluctuating currents. A number of 11 WECs has been found (N i W EC = 11). This number corresponds to the number defined based on the most conservative approach taking into account maximum current constraints only. It will be used as the baseline to compare the results for the two other case studies.

B. Case 2

The results of Case 2 are presented in Fig. 6. In this case, 2 more WECs could be installed in the farm permanently, i.e. (N + W EC =N i W EC + 2). This represents an increase of 18.2%, both in terms of WEC number and in terms of harnessed energy compared to Case 1 (see Table II). It is also worth mentioning that the temperature of the cable external sheath, which is in direct contact with the soil, is close to the maximum limit that is generally recommended to prevent the soil from drying out. A maximum value of 60°C may be allowed, considering that the soil is sufficiently humid [START_REF] Dorison | Modélisation et dimensionnement des liaisons souterraines[END_REF], which is supposed to be the case in a sea water environment. a Considering the sequence of sea-states given in Fig. 4 and neglecting the Region 0 that is irrelevant in Case 3. b Considered as the reference case. c See Table III for more details.

C. Case 3

The results of Case 3, where N v W EC was varying between 13 to 15, are presented in Fig. 7. Note that we neglect the Region 0, which represents the first step for the computation of the temperature, where initial conditions and short duration of the period lead to an irrelevant number of WECs. One can see that the temperature calculated in Case 3 is closer to T max = 90 °C over the total duration of the simulation, which means that the cable utilization is approaching its maximum. However, considering that the calculated temperature remains below 90 °C over the entire sea-state sequence, there is still room for improvement in terms of energy production with finer tuning and more comprehensive control of the WECs. Excluding Region 0, the expected energy production of Case 3 is between 12.7% and 33.5% more than this of Case 1 and is up to 12.8% more than this of Case 2 (see Table III). If we consider the entire duration of the simulation, Case 3 generates 27.0% more energy than this of Case 1, which is significant (see Table II). In Case 3, the external sheath temperature reaches and finally exceeds slightly the value of 60°C, and may thus require to lower the number of WECs. It is worth mentioning that, in this sense, the temperature of the external sheath can be a bottleneck and may require further studies as we discussed in Section IV-B (Case 2) . V. CONCLUSION

The study described in this paper, that can be seen as a proof-of-concept analysis, deals with the optimal use of an existing MRE farm and is focused on the thermal response of the export cable to the fluctuating current of a wave farm in a sea-state sequence that considers different wave heights. It is shown that the combination of a wave farm fluctuating current and the thermal inertia of the cable and of its direct environment, composed of the soil and of the sea, may allow an increase of the number of WECs in the existing farm, which could lead to an increase of the energy production of up to 27%. This is an interesting option that could be considered to maximize the utilization of the MRE farms electrical infrastructure. The study also highlights some potential bottlenecks such a slightly excessive external sheath temperature, which could lead the soil to dry out. Future work will consider nearly a year of real sea-state data from the SEM-REV test site, which will allows us to perform a more comprehensive study with the use of a realistic and longer sea-state sequence.

ACKNOWLEDGMENT

The research work presented in this paper was conducted in the frame of the BlueGrid project, funded by the Brittany Regional Council and the ENS-Rennes, which are gratefully acknowledged. It is worth mentioning that this work would not have been possible without the help of École Centrale de Nantes that manages the SEM-REV test site.

Fig. 1 .

 1 Fig. 1. Example of a RMS current profile generated by a WEC farm composed of 20 WECs considering a Hs = 6 m and Tp = 9 s sea-state. The current profile is very fluctuating and ranges between 70 A and 700 A while in the same time the temperature varies only from 76°C to 81°C.

Fig. 2 .

 2 Fig. 2. The SEM-REV open sea test site is located in western France, near Le Croisic. The physical installation of the 24 km export cable studied in this paper follows the dotted path. It connects the SEM-REV offshore hub to an onshore substation and finally to the local network belonging to French DSO Enedis (red and dark green paths). Figure modified, courtesy of École Centrale de Nantes [16].

  Fig. 2. The SEM-REV open sea test site is located in western France, near Le Croisic. The physical installation of the 24 km export cable studied in this paper follows the dotted path. It connects the SEM-REV offshore hub to an onshore substation and finally to the local network belonging to French DSO Enedis (red and dark green paths). Figure modified, courtesy of École Centrale de Nantes [16].

Fig. 4 .

 4 Fig.[START_REF] Bull | Electrical cable utilization for wave energy converters[END_REF]. Sequence of sea-states that has been used for all simulation cases (see TableI). Note that it is a completely fictitious sequence but based on plausible durations and transitions between each sea-states based on Fig.E2and E3 of[START_REF] Ruggiero | Sediment transport study: Baseline observations and modeling for the reedsport wave energy site[END_REF].

b

  Increase or decrease by step of ∆Hs = 0.2 m distributed uniformly over the region duration. c Increase or decrease by step of ∆Hs = 0.25 m distributed uniformly over the region duration.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Temperature calculated in different locations of the cable for Case 1, i.e. with a wave farm composed of 11 WECs. As we can see, the cable cores temperature are far fromTmax = 90 °C, as allowed by the manufacturer and suggested in IEC standards.

Fig. 7 .

 7 Fig. 7. Temperature calculated different locations of the cable for Case 3, i.e. with a wave farm composed of 12 to 15 WECs. As we can see, the cable cores temperature is very close to Tmax = 90 °C.

TABLE I DESCRIPTION

 I OF THE SEA-STATE SEQUENCE + .

	Region	Wave height Hs (m)	Duration (h)
	0	1	1
	1	1 to 3	12 a
	2	3	24
	3	3 to 6	12 b
	4	6	24
	5	6 to 3	12 b
	6	3	12
	7	3 to 1	12 a
	8	1	12

+ The sea-states sequence is based on a single peak period Tp = 12 s, for all wave heights Hs.

TABLE III DETAILED

 III RESULTS AND ENERGY PRODUCTION GAIN FOR CASE 3. First step of the simulation. Due to the initial temperatures and the short duration of Region 0, the number of WECs is irrelevant.

	Region	N v W EC	Gain 1 a	Gain 2 b
	0 c	25	+224.2%	+189.2%
	1	15	+33.5%	+12.8%
	2	14	+25.9%	+6.7%
	3	13	+24.3%	+0%
	4	13	+28.7%	+0%
	5	13	+24.3%	+0%
	6	14	+25.8%	+6.6%
	7	14	+26%	+6.6%
	8	14	+12.7%	+4.8 %

a Compared to Case 1. b Compared to Case 2. c