Etienne Lehembre
email: etienne.lehembre@unicaen.fr

Bruno Cremilleux
email: bruno.cremilleux@unicaen.fr

Jean-Luc Lamotte
email: jean-luc.lamotte@unicaen.fr

Abdelkader Ouali
email: abdelkader.ouali@unicaen.fr

Albrecht Zimmermann
email: albrecht.zimmermann@unicaen.fr

Keywords: Pattern selection, Structured pattern mining, Local deviation

The purpose of pattern mining is to help experts understand their data. Following the assumption that an analyst expects neighbouring patterns to show similar behavior, we investigate the interestingness of a pattern given its neighborhood. We define a new way of selecting outstanding patterns, based on an order relation between patterns and a quality score. An outstanding pattern shows only small syntactic variations compared to its neighbors but deviates strongly in quality. Using several supervised quality measures, we show experimentally that only very few patterns turn out to be outstanding. We also illustrate our approach with patterns mined from molecular data.

Introduction

The purpose of data mining is to help experts to analyze their data by providing valuable results. When those results come in the form of patterns, whether conjunctions of attributes or items, sequences, trees, or graphs, a recurring problem is that there are simply too many of them for a human to work through. Once this problem was recognized, research first focused on reducing the output through the notion of condensed representations [START_REF] Pasquier | Discovering frequent closed itemsets for association rules[END_REF], a plethora of quality measures [START_REF] Tan | Selecting the right objective measure for association analysis[END_REF], and pattern set mining techniques [START_REF] De Raedt | Constraint-based pattern set mining[END_REF] were designed, all of which fall short, however. Even when creating condensed representations, there are typically still hundreds or even thousands of patterns left, as is the case no matter which quality measure one uses. In addition, the latter lead to the question which measure to use for a given task. Pattern set mining, finally, works well enough when the goal is to create a set of non-redundant patterns to be used as descriptors in downstream tasks such as classification or clustering, but less so when it comes to offering an expert an interpretable result set.

Here, we start from the assumption that an analyst expects that patterns which are neighbors in the pattern space show similar behavior. Hence, a pattern showing different behavior from what one expects given similar patterns deserves a second look. To find these patterns, which we will call outstanding going forward, we use a Hasse Diagram (HD), a directed acyclic graph (DAG), as a representation of the pattern space. This DAG encodes a partial order between patterns whose interestingness is quantified by a quality measure. Patterns that are scored very differently than the average of neighboring patterns are considered outstanding.

The main contribution of the paper is a new way of selecting outstanding patterns, given an order relation between patterns, and a quality measure on patterns. We formulate our idea in general terms since it can be applied for any pattern language (e.g., items, sequences, graphs). With items, we illustrate our approach by using the lattice of formal concepts derived from data as the encoding HD. We define the notion of a selector, a function that outputs the set of outstanding patterns given a HD and a quality measure. Outstanding patterns will then be those that show only small syntactic variations compared to their neighbors but deviate strongly in quality. Notably, this deviation is not necessarily positive: a pattern might be outstanding because it correlates much more weakly with a class label, for instance, than its neighbors. Using several supervised quality measures, we show experimentally that only very few patterns turn out to be outstanding and that the number varies depending on the measure. Our contribution is an outgrowth of the concept of activity cliffs [START_REF] Stumpfe | Evolving concept of activity cliffs[END_REF] on molecular data, which define a noticeable modification of the biological activity for a small modification of the chemical structure. We therefore also illustrate our method on using patterns mined from molecular data, which are the main focus of our application interest.

The paper is organized as follows. In the next section, we discuss the literature related to our problem setting and proposal. In Section 3, we introduce necessary background knowledge. In Section 4, we present the selector. In Section 5, we report experimental results on transactional data derived from UCI data sets and on molecular data and discuss them. We conclude in Section 6.

Related work

Since the introduction of constraint-based pattern mining, an on-going theme has been how to help the experts identify the most valuable patterns from result sets containing thousands or even millions of them. A well established solution is to find a condensed representation of the patterns such as closed [START_REF] Pasquier | Discovering frequent closed itemsets for association rules[END_REF][START_REF] Yan | Closegraph: mining closed frequent graph patterns[END_REF] or free patterns [START_REF] Boulicaut | Free-sets: a condensed representation of boolean data for the approximation of frequency queries[END_REF], i.e., maximal or minimal patterns from the support-based equivalence classes. Since real data are often noisy, [START_REF] Boulicaut | Free-sets: a condensed representation of boolean data for the approximation of frequency queries[END_REF] proposed error-tolerant variants.

Another direction is to focus on the best patterns according to quality measures [START_REF] Tan | Selecting the right objective measure for association analysis[END_REF]. The survey [START_REF] Vreeken | Interesting patterns[END_REF] divides measures in two categories: absolute measures and advanced ones. Advanced measures are based on statistical models (independence model, partition models, MaxEnt models) having different complexities. However, there are numerous measures and it remains difficult to clearly identify the advantages and limitations of each one. The quality of a selected pattern can be assessed via syntactically linked patterns during computation [START_REF] Crémilleux | How your supporters and opponents define your interestingness[END_REF], somewhat similar to our proposal.

Recent research has highlighted the benefits of the unexpectedness of a pattern when contrasted with given information depending either on the data or on prior knowledge of the analyst [START_REF] Bie | Maximum entropy models and subjective interestingness: an application to tiles in binary databases[END_REF]. For instance, by sampling patterns fulfilling data-independent constraints under assumptions about the symbol distribution (i.e. null models), the authors of [START_REF] Besson | Parameter tuning for differential mining of string patterns[END_REF] derive a model of background noise, and identify thresholds expected to lead to interesting results, i.e. results that diverge from the expected support derived from super-and sub-patterns. Another approach combines sampling and isotonic regression in order to arrive at pattern frequency spectrum for frequent itemset mining [START_REF] Van Leeuwen | Fast estimation of the pattern frequency spectrum[END_REF]. By comparing those thresholds to ones derived from data where all items are independent, one can identify thresholds or which the result set is expected to contain interesting patterns. Self-sufficient itemsets, finally, are itemsets the support of which cannot be predicted from their sub-sets or super-sets [START_REF] Webb | Self-sufficient itemsets: An approach to screening potentially interesting associations between items[END_REF]. However, these approach are limited to itemset data. Our method differs in that we do not make assumptions about syntactic relationships between patterns. In addition, we do not make an independence assumption w.r.t. pattern elements.

Also closely related to our work, in the context of web queries modeled according to the setting of the Formal Concept Analysis, [START_REF] Dau | Concept similarity and related categories in searchsleuth[END_REF] uses the siblings of a node to define the interestingness of a new query. However, the method does not take into account the whole set of siblings and it is linked to frequencies observed in the extents and intents of the concepts whereas our approach can use any quality measure defined on patterns.

Background

As usual in the pattern mining paradigm, let us consider D a dataset, L a pattern language and a partial order relation on the patterns in L. The support of a pattern p, Supp(p), is the number of transactions containing p. The pattern space can be modelled by its Hasse diagram, a DAG whose set of vertices maps the set of patterns and whose edges depict the order relation: there is an edge (p, q) from a pattern p to a pattern q if p q and if there is no other pattern r between p and q ( p r and r q). From an edge (p, q), we say that p is a parent of q, that q is a child of p. The siblings of a pattern is the set of patterns that share a common parent with it. Figure 1 depicts an example of these relationships: the siblings of the pattern S (in red) are S i (in purple), the parents of S are P i (in blue).

In the itemset setting, D is a set of transactions, each transaction containing one or more distinct literals called items I. A pattern X is an element of 2 I . The order relation on the patterns is the usual inclusion relation ⊆ . In the itemset setting and considering closed itemsets [START_REF] Pasquier | Discovering frequent closed itemsets for association rules[END_REF], the Hasse diagram is then a Galois lattice [START_REF] Davey | Introduction to Lattices and Order, Second Edition[END_REF].

Many quality measures have been described in the literature [START_REF] Tan | Selecting the right objective measure for association analysis[END_REF][START_REF] Vreeken | Interesting patterns[END_REF] and the interestingness of a pattern will be quantified by a measure f :

L × D → R. P1 P2 S S1 S2 S3 S4
Fig. 1. Retrieving siblings (purple / Si and red / S) from a source vertex (red) and its parents (blue / Pi).

Outstanding Pattern Selector: how to exploit siblings

To select outstanding patterns, the method is based on the principle that an analyst expects patterns that are neighbors in the pattern space to show similar behavior. Therefore a pattern showing different behavior from its neighbors according to a quality measure f deserves attention. The sibling patterns being structurally close, their quality should be similar. If a pattern is scored differently from its siblings, it is highly interesting as a outstanding sibling. Thus, we seek for local variations of interestingness. This phenomenon is not captured when f is applied to each pattern individually, as is usual in the frequent or association pattern setting. Concretely, we say that a pattern X is outstanding when its quality deviates from the mean quality of its siblings S(X). The sibling mean µ(S(X), D) is:

µ(S(X), D) = s∈S(X) f (s, D) |S(X)|
Then µ(S(X), D) is compared to the standard deviation of the siblings:

σ(S(X), D) = s∈S(X) (f (s, D) -µ(S(X), D)) 2 |S(X)|
The selector is defined as:

OP S(L, f, D, δ) = {X ∈ L : |f (X, D) -µ(S(X), D)| ≥ δ * σ(S(X), D)}
Thus, X is outstanding if its quality deviates at least δ standard deviations from the mean of the qualities of its siblings, δ being a user-supplied parameter. We consider the quality measure as a random variable, which distribution varies locally, while staying normally distributed around a local mean. Moreover, the behavior of the quality measure will impact the selection. A homogeneous quality measure will lead the selector to select a few chosen ones while an heterogeneous quality measure will produce more outliers.

One of the appeals of using the standard deviation instead of a classic threshold is that the selector adjusts to its environment: if the siblings of a pattern are all relatively close to a particular support value, a small increase over this value can be interesting. Similarly, take the example of the growth rate [START_REF] Dong | Efficient mining of emerging patterns: Discovering trends and differences[END_REF] as the quality measure f . Let us assume furthermore that D is partitioned into two classes, and most of the siblings are Jumping Emerging Pattern (JEP) [START_REF] Dong | Efficient mining of emerging patterns: Discovering trends and differences[END_REF][START_REF] Kane | Minimal Jumping Emerging Patterns: Computation and Practical Assessment[END_REF], i.e. patterns that have a support of zero in the negative class. JEPs have a tendency to overfit; our selector, on the other hand, keeps a JEP only if it indicates a local deviation. Moreover, it can select interesting patterns that are not JEP.

In practice, as shown in the next section, the number of outstanding patterns is small, allowing a human domain expert to manually inspect them.

Experiments

In this section, we show experimental results illustrating the reduction in patterns, as well as the behavior of four quality measures. In the next section, we provide results on itemset data, and in Section 5.3 on graph data representing molecules. We use our experiments to answer several questions:

-Does selecting outstanding patterns reduce the size of the result set significantly? -Does changing the quality measure change how many patterns are outstanding? -Can outstanding patterns be easily characterized in terms of the score they receive from an interestingness measure? -Do outstanding patterns from self-sufficient itemsets, another type of pattern that takes itemsets' neighborhoods into account, albeit syntactic ones?

Itemset data

The data we used are itemset data derived from UCI data sets, which we downloaded from the CP4IM repository4 . The data have been binarized by the maintainers of the repository, the majority class named positive class, and minority classes merged into a single negative class. We performed closed frequent set mining with minimum support thresholds (denoted by θ) of 10%, 15%, and 20%. In the resulting graph G(V, E) each vertex is labeled with a closed itemset. We tested four quality measures: χ 2 , confidence, normalized Growth Rate (NGR) 5 :

N GR(X, D) = 1.0 if GR(X, D) = ∞ N GR(X, D) = GR(X,D) 1+GR(X,D)
otherwise and Weighted Relative Accuracy (WRAcc). For the latter three, we chose the positive class as target. For the OPS threshold, we chose δ = 2 since 95% of all values of a normal distribution fall into the interval [µ -

2 • σ, µ + 2 • σ].
As Figure 2 shows, only very few itemsets are outstanding compared to their siblings, with at most 3.052% selected by confidence and NGR on the splice data set for the 10% minimum support threshold. Notably, this is in addition to the reduction achieved by mining closed itemsets. We take this as evidence that selecting outstanding patterns results in small enough result sets that domain experts could inspect them (and their neighborhoods) manually to gain deeper insight into the underlying phenomena. We can also compare the behavior under different support thresholds, i.e. the results for a single data set and a single measure, and for different quality measures, i.e. the results in a single line.

While increasing the support threshold mostly reduces the number of outstanding patterns as well, this is not always the case, as can be seen for the zoo-1 data set, for instance. Using confidence or GR as a quality measure leads to fewer outstanding patterns than using χ 2 and WRAcc does, with the exception of the splice-1 (10%) and vote (10%, 15%) data sets. A particularly remarkable data set is the tic-tac-toe one where not a single pattern stands out.

Notably, using different quality measures lead to different sets of outstanding patterns to be selected. Figure 3 shows a heatmap representation of the Jaccard similarity between result sets for three example data sets. For the primary-tumor data set (middle), there is little similarity between the different results, for the soybean data set (right-most figure), confidence and GR give very similar results. The full set of figures can be found in the supplementary material.

As we mentioned in the introduction, outstanding patterns are not necessarily among the best patterns in terms of class correlation, for instance. This is shown by Fig. 4 on the primary tumor data set with the confidence measure: for all minimum support thresholds, also itemsets with low confidence are selected. Figures for other data sets and quality measures can be found in the supplementary material available at https://github.com/Etienne-Lehembre/Outstanding-Pattern-Selector.git.

Comparison to self-sufficient itemsets

A method that is close in spirit to our proposal are the self-sufficient itemsets proposed by Webb et al. [START_REF] Webb | Self-sufficient itemsets: An approach to screening potentially interesting associations between items[END_REF]. Self-sufficient itemsets, can be considered independently from each other, as can outstanding patterns, which is not the case for patterns selected by pattern mining techniques. The full definition of selfsufficiency is too involved to reproduce here6 but self-sufficiency includes the requirement that the probability of itemsets' occurrence cannot be inferred by the probability of subsets' and supersets' occurrences. This requirement translates into comparing itemsets to their predecessors and successors in a DAG where vertices are labeled with the full set of possible itemsets and edges indi- cating extension of itemsets with individual items. We therefore want to know how many of the outstanding itemsets we select are self-sufficient and vice versa.

We ran the OpusMiner implementation available at https://eda.mmci.unisaarland.de/prj/selfsufs/ on the UCI data sets mentioned above. The lower part of Table 1 reports the number of self-sufficient itemsets and a comparison to Figure 2 shows that there is no obvious relationship between the number of outstanding and self-sufficient itemsets. Not all self-sufficient itemsets are frequent under the minimum support thresholds we use, and the bottom-most row of Table 1 shows their number for the three different support thresholds.

Self-sufficient itemsets also cannot expected to be closed itemsets. We therefore identified for each self-sufficient itemset the corresponding closed frequent itemset, and compared this set to the set of outstanding itemsets selected. Table 2 shows for each support and each quality measure which proportion of outstanding itemsets are also self-sufficient (left-hand column per quality measure) and which proportion of self-sufficient itemsets are also outstanding (right-hand column). Missing lines correspond to settings where all values are 0.0, which includes in particular the tic-tac-toe data set.

Table 2. Self-sufficient and outstanding itemsets for different minimum supports θ and different quality measures. For each measure, left-hand column shows the proportion of outstanding itemsets that are self-sufficient, right-hand column displays the proportion of self-sufficient that are outstanding.

Data set θ χ 2

Confidence NGR WRAcc mushroom 10 0.16 0.48 0.25 0.14 0.25 0.14 0.29 0.48 mushroom 15 0.13 0.15 0.33 0.13 0.33 0.13 0.14 0.13 primary-tumor 10 0.02 0.08 0.00 0.00 0.00 0.00 0.00 0.00 primary-tumor 15 0.02 0.09 0.00 0.00 0.00 0.00 0.00 0.00 primary-tumor 20 0.03 0.12 0.00 0.00 0.00 0.00 0.00 0.00 soybean 10 0.03 0.02 0.00 0.00 0.04 0.02 0.12 0.02 soybean 15 0.12 0.06 0.00 0.00 0.17 0.03 0.00 0.00 soybean 20 0.18 0.07 0.00 0.00 0.20 0.03 0.00 0.00 splice-1 10 0.13 0.10 0.06 0.10 0.06 0.10 0.12 0.10 vote 10 0.18 0.10 0.00 0.00 0.00 0.00 0.00 0.00 vote 15 0.12 0.05 0.00 0.00 0.00 0.00 0.00 0.00 vote 20 0.10 0.03 0.00 0.00 0.00 0.00 0.00 0.00 zoo-1 10 0.10 0.02 0.33 0.05 0.33 0.05 0.00 0.00 zoo-1 15 0.10 0.02 0.50 0.05 0.50 0.05 0.00 0.00 zoo-1 20 0.12 0.02 0.33 0.06 0.33 0.06 0.00 0.00

Generally speaking, we can remark that outstanding itemsets stand not to be self-sufficient and vice versa. W.r.t. individual data sets, we can observe some interesting phenomena. For mushroom at θ = 10% and χ 2 /WRAcc, only one of the four outstanding itemsets is self-sufficient but ten of the self-sufficient itemsets are represented by it, i.e. they are subsets that cover the same transactions. Once we increase the minimum support to 20%, there is no itemset left that is both self-sufficient and outstanding. For the vote data set, there is a certain correspondence between outstanding and self-sufficient itemsets for χ 2 but none whatsoever for the other quality measures.

Structured pattern selection

This section gives an experimental illustration of our method on graph-structured data. This experiment is motivated by the study of chemical and biological data BCR-ABL from ChEMBL237 . In the data, every molecule is labeled as active or inactive; their structure represented as graphs. Negative data is denoted by D -in the following. From the 1485 graphs of the data set, we extract closed frequent sub-graphs with at most 7 nodes, and θ = 10.

As in the case of the closed itemsets we considered above, edges in the resulting DAG connect two vertices u and v if u is labeled with a maximal predecessor of the closed graph labeling v. As before, we assess the behavior of different quality measures: χ 2 , confidence, NGR, WRAcc. As we can see in Table 3, we select at most 1.7% of mined patterns. We also notice different behaviors for different quality measures: whereas NGR and confidence select small sets, WRAcc and χ 2 select more than six times as many, a number of patterns that could be hard to process by a human domain expert. The left-most column shows the distribution of pattern scores, the center column the mean score for neighborhoods, and the right-most one the relative relevance, i.e. deviation of patterns from the mean of their neighborhood, normalized by the standard deviation. Blue histograms are for outstanding patterns, red for non-outstanding ones. As before, we see that outstanding patterns are not necessarily strongly correlated with the active class but might also be those that are unexpectedly weakly correlated (or even negatively correlated). We also see that while the majority of outstanding patterns are two standard deviations off their neighborhood's mean score, there are patterns that deviate even more strongly.

Expert analysis upon an outstanding pattern and its family

The NGR used in the preceding section tends to discount jumping emerging patterns, which are however rather interesting in the context of activity analysis. In the following section we will therefore use another quality measure called GR max , which avoids the ∞ problem but gives JEPs its due:

GR max (X, D) = |D -| if GR(X, D) = ∞ GR max (X, D) = GR(X, D) otherwise
We applied GR max to the data-set BCR-ABL extracted from ChEMBL. In Table 4, order indicates the number of nodes in the smallest free/generator sub-graph corresponding to closed graphs, allowing us to structure the graph into several layers. A closed graph together with its generator patterns induces an equivalence class of graph patterns covering the same data graphs. Each column correspond to a layer, numbered with its order. Rows Total indicates the number of equivalence classes in a layer, Selected the number of selected equivalence classes, and Percentage the percentage of selected equivalence classes. We observe that most of the outstanding patterns are found in the third and fourth layer. This is why the following analysis will be conducted on equivalence classes extracted from the third and fourth layers. Starting from the outstanding pattern, an expert can expect to gain insight into structure-activity relationships (SAR) [START_REF] Métivier | The pharmacophore network: A computational method for exploring structure-activity relationships from a large chemical data set[END_REF]. As an illustration, consider the center node of Figure 6. It shows an outstanding pattern appearing in 61 molecules, as well as its parents labelled as 676 and 373, colored according to their GR max value with lighter colors corresponding to higher values. Larger nodes have a higher relative relevance. One of the parents, which differs only by one element syntactically, has significantly higher support values than the others. On both labelled parents, we see a large amount of children that include both patterns that do not correlate with the target class at all, and others that correlate very strongly. Furthermore we see that this family has several selected siblings (labelled nodes which are neither 676, nor 373). It implies that several subsets of molecules are outstanding regarding of each individual families for each pattern. It implies that the molecules' super-sets of our entry point contain cliffs [START_REF] Stumpfe | Evolving concept of activity cliffs[END_REF] regarding the molecular activity. The outstanding pattern is therefore an entry point to visual analysis by the expert. Therefore, the outstanding pattern is an entry point for a visual analysis by the expert.

Conclusion

We have proposed a new way of selecting outstanding patterns by comparing them to neighboring patterns: a pattern is outstanding if it deviates clearly from the average of neighboring patterns w.r.t. the value of a quality measure. Our proposal is independent of the pattern language or the quality measure used. As experimentally shown, our selection patterns method leads to a strong reduction in the size of the result set, making the manual exploration by domain experts possible. Results differ significantly between different quality measures, i.e. the choice of quality measure becomes meaningful.

Finally, our selector puts an emphasis on the outstanding pattern's context. The selected pattern is interesting, but its parents, as well as its siblings, are also objects of interest. It can lead us to siblings linked to more than one outstanding pattern. Parents of such siblings become very interesting because outstanding pattern can have either positive or negative qualities, depending on the underlying data. Therefore, our selector offers a new way to study cleaving points inside the pattern language, and thus, the data, putting human in the loop.

Fig. 2 .

 2 Fig. 2. Selection statistics (#outstanding patterns/#patterns/%) on UCI data-sets.

Fig. 3 .

 3 Fig. 3. Heatmap representation of Jaccard similarity for sets of outstanding patterns selected for different quality measures for mushroom (θ = 10%), primary-tumor (θ = 15%), soybean (θ = 15%).

Fig. 4 .

 4 Fig. 4. Distribution of confidence values for the primary tumor data set, outstanding patterns in the bottom row, non-outstanding patterns on top. Results for minimum support 10% in the left-most column, 15% center, 20% right-most.

Fig. 5 .

 5 Fig. 5. Selection histograms for NGR (top) and WRAcc (bottom).

Figure 5 ,

 5 Figure 5, shows histograms of the scores for GR (top), and WRAcc (bottom).The left-most column shows the distribution of pattern scores, the center column the mean score for neighborhoods, and the right-most one the relative relevance, i.e. deviation of patterns from the mean of their neighborhood, normalized by the standard deviation. Blue histograms are for outstanding patterns, red for non-outstanding ones. As before, we see that outstanding patterns are not necessarily strongly correlated with the active class but might also be those that are unexpectedly weakly correlated (or even negatively correlated). We also see that

Fig. 6 .

 6 Fig. 6. Selected outstanding pattern (centered) along with its parents, and children of the parents. Labeled nodes are selected by OPS or important parent (373 and 676).

Table 1 .

 1 Characteristics for selected UCI datasets and their number of self-sufficient itemsets.

	Data set	Mushroom Primary-tumor Soybean Splice-1
	Transactions	8124	336	630	3190
	Items	119	31	50	287
	Density	18%	48%	32%	21%
	Self-sufficient itemsets	69	16	55	38
	for θ = 10%/15%/20% 69/68/53	13/11/8	49/33/30 30/9/3
	Data set	Tic-tac-toe	Vote	Zoo-1
	Transactions	958	435	101
	Items	27	48	36
	Density	33%	33%	44%
	Self-sufficient itemsets	24	39	64
	for θ = 10%/15%/20% 24/24/0	39/39/39	62/60/48

Table 3 .

 3 Selection statistics on graph data.

	Quality measure χ 2 Confidence NGR WRAcc
	Selected	247	30	32	257
	Percentage	1.589% 0.193% 0.205% 1.653%
	Total # patterns		15,544

Table 4 .

 4 Results on BCR-ABL using GRmax

		Order 1 Order 2 Order 3 Order 4 Order 5 Order 6 Total
	Total	6	307	5 388	8 269	1 534	40	15 544
	Selected	0	6	203	175	12	0	396
	Percentage 0.00% 1.95% 3.77% 2.12% 0.78% 0.00% 2.55%

https://dtai.cs.kuleuven.be/CP4IM/datasets/

We normalize the growth rate because the unnormalized growth rate can have ∞ as a value, which prevents the calculation of mean and standard deviation.

We direct the interested reader to the original publication.

https://www.ebi.ac.uk/chembl/

Acknowledgements. This work was partially funded by the ANR project InvolvD (ANR-20-CE23-0023).


Camille Dumat

teaching and research institutions in France or abroad, or from public or private research centers.

Conclusion de l'exposition Sustainable Urban Agricultures (UA) : Vector for Ecological Transition !

Open Archive TOULOUSE Archive Ouverte (OATAO)

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Any correspondence concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr • Actually, UAs are opportunities for citizens to be consulted and fully involved in the development of their environment. The public space directly concerned by the UA is mobilized on issues such as health, well-being, sustainable food and biodiversity: many associations propose UA projects that create social links at various scales. • You can also access to a wide range of UA resources on the "Réseau-Agriville" to share your knowledge and knowhow (free inscription).

• UA projects promote inclusive education, transdisciplinarity, agile and reflective pedagogy and competency-based approach.

Let's build Ecological Transition in our Universities! Thanks to all the researchers for participation

C E R T O P

•

  Sustainable urban agriculture (UA) and ecological transition are questioning, echoing, interacting, developing together in the various territories! • Perceived a few years ago as an ephemeral phenomenon, UAs are now anchored in cities on a global scale and widely institutionalized.

  Infographiste UT2J PR Dumat C. INP-ENSAT, CERTOP Axe Transition Ecologique, Réseau-Agriville Dr Pierart A. Post-doctorant à l'UCLM, Réseau-Agriville Razous A. Chargée de communication du CERTOP Saucian M. & Suchon S. M1 à l'INPT et UT2J • The present UA&ET-17 exhibition is open access available on OATAO, "Réseau-Agriville" (http://reseau-agriville.com/). • Moreover, the proceedings of the UA&ET-17 symposium coordinated by the CERTOP and LISST laboratories (PR Dumat C., Dr Sochacki L., Dr Bories O.) are also available on OATAO (Archives Ouvertes).

18346 To cite this version : Dumat, Camille Conclusion de l'exposition Sustainable Urban Agricultures (UA) : Vector for Ecological Transition ! (2017) In: Sustainable Urban Agricultures (UA) : Vector for Ecological Transition, 6 June 2017 -9 June 2017 (Toulouse,

  This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID :

	France). (Unpublished)


Camille Dumat. Introduction de l'exposition Sustainable Urban Agricultures (UA) : Vector for Ecological Transition !. Sustainable Urban Agricultures (UA) : Vector for Ecological Transition, Jun 2017, Toulouse, France. pp. 1-1. hal-03658552 Open Archive TOULOUSE Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 18345 To cite this version : Dumat, Camille Introduction de l'exposition Sustainable Urban Agricultures (UA) : Vector for Ecological Transition ! (2017) In: Sustainable Urban Agricultures (UA) : Vector for Ecological Transition, 6 June 2017 -9 June 2017 (Toulouse, France). (Unpublished) Any correspondence concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr EXHIBITION OF THE INTERNATIONAL RESEARCH SYMPOSIUM, Sustainable Urban Agricultures (UA) : Vector for Ecological Transition ! UA Specificities : Biological agriculture permits to decrease sanitary risks and to re-use urban organic wastes Generally little available urban surfaces: Conflicts of use Crucial to check, manage and improve environmental quality with sustainable practices The information and collective construction of the UA projects are crucial steps UA projects are multidisciplinary and carry several different ecological services Open access supplementary information on UA are available on Reseau-Agriville : http://reseau-agriville.com/ g i c a l T r a n s it io n


Thibaut Billard

Cédric Abadie

Keywords: Partial Discharges measurement, Pulse width modulation, Aircraft, Motors, Pressure effects, Wavelet transforms I Fourier Transform IGBT: Insulated-Gate Bipolar Transistor MSE: Mean Squared Error PD: Partial Discharge PDEV: Partial Discharge Extinction Voltage PDIV: Partial Discharge Inception Voltage PWM: Pulse Width Modulation SiC: Silicon Carbide SNR: Signal to Noise Ratio WT: Wavelet Transform VIII. BIOGRAPHIES

At the dawn of this new millennium, transportations facing a much greener approach, the main aircrafts manufacturers have to change their paradigms: to replace the combination of hydraulic, pneumatic, electrical and mechanical power by a « More » (and "All" in the future) Electrical Aircraft approach consisting in drastically increasing the power density of electrical power systems without compromising on reliability. The increasing demand for more on board electrical power has led to increase the voltage and/or to change its shape. Such an increase may lead, depending on many parameters related to the electrical characteristics of the power chain (power converter, voltage waveform (dV/dt, frequency, …), the cables length, the type of machine driven) or to the environment (pressure, temperature, relative humidity) to the Partial Discharges Ignition in systems which were not supposed (and have not been designed) to endure them.

Partial Discharges are voltage-dependent electrical discharges in insulation, which:

-do not lead to a direct breakdown of the system, -lead to a gradual deterioration of the insulating material and to its premature failure -is often defined as "the silent enemy Recent advances made in the related different topics i.e on line PD detection under PWM voltage, influence of the pressure, influence of the components types…will be presented and discussed regarding their consequences.

II. INTRODUCTION

In aeronautics, the concept of the "more electrical aircraft" was able to grow thanks to the evolution of power electronics in recent years, the increase of power density, accompanied T. Lebey is with LAPLACE, Université de Toulouse, 118 route de Narbonne, 31062 Toulouse, France (thierry.lebey@laplace.univ-tlse.fr) T. Billard and C. Abadie are with IRT Saint Exupéry, 118 route de Narbonne, 31432 Toulouse, France (thibaut.billard@irt-saintexupery.com, cedric.abadie@irt-saintexupery.com) by a decrease in cost, which had considerably spread the use of power converters for Adjustable Speed Drive (ASD) applications [START_REF] Roboam | New trends and challenges of electrical networks embedded in more electrical aircraft[END_REF]. Until recently, one could find various energy sources used in aircraft: pneumatic, hydraulic, and electric energy. The concept of the "more electric aircraft" involves replacing pneumatic and/or hydraulic energy by the electric one. These two axes of evolution are respectively called "Bleedless" and "Hydraulicless" architectures. The interest in removing one of these energy vectors is to increase the reliability and safety of onboard equipment while reducing weight and maintenance costs. However, due to the power demand, developing the electrical network resulted in an increase of the voltage magnitude.

There are two main families of motors: first, low-voltage motors with winding formed of cylindrical conductors wound randomly, and second, high-voltage motors with winding formed of rectangular conductors, are classified respectively as Type I and Type II [START_REF]Rotating electrical machines -Part 18-41: Partial discharge free electrical insulation systems (Type I) used in rotating electrical machines fed from voltage converters -Qualification and quality control tests[END_REF].

Like any equipment, electric motors undergo more or less severe aging over time, influenced by various phenomena. These degradations can come from thermal, mechanical, or electrical phenomena. For electric motors, the weakest part is usually the electrical insulation system [START_REF] Stone | Stator insulation problems associated with low voltage and medium voltage PWM drives[END_REF]. The failure of this system generally results in complete motor failure. The use of long cables connecting the inverter to the motor may cause significant overvoltage at the motor terminals [START_REF] Kaufhold | Failure mechanism of the interturn insulation of low voltage electric machines fed by pulse controlled inverters[END_REF]. In addition, the shape of applied voltage using "Pulse Width Modulation" (PWM) is comprised of pulse trains. Because of these pulses, voltage is no longer distributed homogeneously along the coil [START_REF] Fenger | The impact of humidity on PD inception voltage as a function of rise-time in random wound motors of different designs[END_REF]. In that case, large differences in voltage between turns are present [START_REF] Bidan | Development of a new off-line test procedure for low voltage rotating machines fed by adjustable speed drives (ASD)[END_REF], [START_REF] Bidan | Transient voltage distribution in inverter fed motor windings: Experimental study and modeling[END_REF]. Moreover, associated with the low-pressure conditions present in depressurized areas of the aircraft, these important voltage differences may cause partial discharge (PD) ignition. PDs are electrical discharges that partially short-circuit the insulation. These discharges induce a phenomenon of erosion, due to the bombardment of charged particles, chemical deterioration, and local thermal stresses on the insulation system. Partial discharges are the sign of the next insulation system failure.

It is necessary to detect the partial discharges ignition voltage to assess the quality of electrical system insulation in the equipment and to qualify the system. For systems operating under AC or DC, there are many well-known detection methods. However, this detection is much more complex under PWM in low-voltage motors and more particularly in Type 1 machines that are used in more electric aircraft. The main problem with PWM power supply is that partial discharge signals are embedded in the electromagnetic noise generated by the switching.

In order to determine the PD appearance in a motor, it is

Recent advances in on-line PDs'detection in power conversion chains used in aeronautics Thibaut Billard, Cédric Abadie and Thierry Lebey important to carry out these tests under real operating constraints (electrical, environmental, mechanical ...): on-line measurement is mandatory. However, despite the representativeness of the test, if the detection system modifies the constraints present on the system under test, the results will be biased. It is therefore necessary to use a system which does not affect the reliability and the test configuration of the system under test. A non-intrusive measurement makes it possible to satisfy these conditions.

III. PDS DETECTION IN LOW-VOLTAGE MOTORS

In the recent works related to the detection of PD in machines fed by a PWM inverter, the more promising track has been the pioneering work done in [START_REF] Fabiani | A UHF Technique for Advanced PD Measurements on Inverter-Fed Motors[END_REF] when conventional technique for measuring technique could not be used anymore due to noise generated by the inverter. Still, the use of a high pass filter has proven to be successful to detect PDs in a small machine (0.3 kW) fed by a commercially available bipolar square voltage generator. Based on this work, an experimental set-up has been developed to go one step further in the field of EV electric motor and detect partial discharges on-line in electric motor. It consists in 4 key parts: non-intrusive sensor, high-pass filtering, controllable high voltage PWM power supply and high speed acquisition.

A. Sensor

Using non-intrusive sensors is mandatory for equipment reliability. A simple sensor was developed for this purpose. Initially, the sensor was developed to offer a less expensive (regarding cost) alternative to inductive sensors. This sensor was made using a 1.5 m coaxial cable, then stripped on its cut extremity to expose the metallic inner core over a length of 1 cm. The coaxial cable is stripped further, but only to expose the inner insulator for 1 cm without any ground shield. This was done to prevent any undesired contact between the metallic inner core and the shortened ground shield. This sensor is not an antenna. It is sensitive to distance and must be placed as close to the discharge area as possible. In the case of stator tests, it is placed on the power cable close to the stator terminals.

B. PWM like power supply

The power supply is a PWM like inverter. This PWM inverter has been entirely conceived, designed, and built at the Laplace Laboratory. This PWM inverter can simultaneously supply two phases with bipolar controllable voltage waveforms. The high voltage source generates voltages up to 1.7 kV DC on the converter input and supports peak currents up to 50A. The IGBTs are designed to support up to 1.5 kV, which allows testing low voltage motors and searching for the partial discharge inception voltage (PDIV). The inverter provides modular bipolar voltage. The pulse duration, the time between pulses, and the switching frequency are adjustable, making it possible to create PWM voltage.

This system enables to perform various tests, for example along one phase, or between two phases, or between phase to ground allowing to perform off-line testing relatively close to the actual stress that the test equipment can withstand. Voltage measurement is performed using a differential voltage probe.

C. Filtering

The use of filters is essential in partial discharge detection, and more particularly in the case of PWM power supply [START_REF] Tozzi | Off-line and on-line pd measurements on induction motors fed by power electronic impulses[END_REF]. The difficulty of detecting PD during steep voltage edges is to increase the signal-to-noise (SNR) to measure low amplitude signals with high-frequency components among large amplitude signals with lowfrequency components. The bandwidth of the filter and its cutoff frequency are the most important parameters in this filter's design. The frequency spectrum of a discharge extends up to at least 1 GHz, as the noise generated by the PWM supply seems to not exceed a few hundred MHz (for the power supply used at the Laplace laboratory). The filter cutoff frequency should be greater than the frequency for noise suppression of commutations and must be adapted to the voltage rise time.

D. Acquisition

The acquisition tool used is an oscilloscope (Tektronix MSO 5204 Digital Oscilloscope) with a digital bandwidth of 2 GHz and a sampling frequency of 5GS/s. The frequency spectrum of a discharge extends up to at least 1 GHz, and with the cutoff frequency of the filters used being a few hundred MHz, it is possible to detect partial discharges.

E. Off-Line experiments

An example of the experimental set-up used to perform the off-line tests is summarized in Fig. 1. The interest of the filter is shown in figures 2 &3. Due to the noise induced by switching, it is impossible to observe anything (Fig. 2) whereas the effect of adding a high-pass filter allows to detect the partial discharge signal as witnessed by the observation of the figure 4 showing a "glow" or "pseudo-glow" discharge [START_REF] Billard | Partial discharge in electric motor fed by a PWM inverter: off-line and on-line detection[END_REF]. It is important to note that, up to now, on-line testing had never been reported. It is the aim of the work reported here to present these characterizations in the aeronautical environment for voltage close to the PDIV.

IV. IMPROVEMENT OF THE DETECTION METHOD

A. Sensor study

One of the issues with home-made sensors is the inherent lack of repeatability in their elaboration. Clearly, slight variations can occur and may lead to changes in their responses. Furthermore, sensor properties can evolve over time with handling. The solution we found was to use a Jack-SMA connector, connected to the end of a coaxial cable (Fig. 5). This sensor is robust, inexpensive, and standardized. It also has about the same geometry and size as the home-made coaxial cable sensor. Another problem is the positioning of the sensor. Due to its geometry, achieving good contact and adequate holding on the power cable can be complex particularly due to vibrations during on-line testings. For this reason, we developed special 3D-printed pliers to ensure good contact regardless of the cable gauge. The sensor is based on a capacitive coupling. Sensor sensitivity can therefore be increased simply by improving the coupling capacitance value. This is achieved by increasing the contact surface by putting copper tape on the surface of the power cable to control the interacting area and thus the value of the induced capacity (Fig. 6).

B. Development of a digital processing method to remove noise

In literature, different techniques for extracting PD signals from raw data are proposed. The article [START_REF] Sriram | Signal denoising techniques for partial discharge measurements[END_REF] performed a comparison of some of these noise suppression methods based on several parameters. All these methods are compared according to the Mean Squared Error (MSE) between the raw signal and the noise-suppressed signal as well as the execution time of filtering. Based on these criteria, Wavelet Denoising and Low-pass Filtering methods have proven to be the most effective. In our case, since the electromagnetic noise induced by switching has low-frequency components, the low-pass filtering is not possible. The best technique for extracting PD signals is therefore the Wavelet Denoising method.

The wavelet transform (WT), just as the Fourier transform (FT) is a mathematical signal processing tool that decomposes a signal into different basic functions. The basic functions of the FT being the sine and cosine, the result of applying this method provides information only on the frequency content of the signal of interest. The disadvantage lies in not knowing the moment at which each frequency component appears.

Besides that, the basic functions of the WTs called "wavelets" allow two-dimensional resolution in the frequency and time domains. Moreover, in comparison, the FT shows extreme efficiency for analyzing periodic phenomena, time-invariant and stationary techniques, while WT screens all components produced by transients, of variable time and non-stationary [START_REF] Vigneshwaran | An improved threshold estimation technique for partial discharge signal denoising using Wavelet Transform[END_REF].

Therefore, with the PD signal being of a non-periodic nature and exhibiting very fast transient characteristics, the WT approach seems more suitable in this context. More details on the denoising method may be found in [START_REF] Abadie | Numerical signal processing methods for partial discharge detection in more electrical aircraft[END_REF].

1) Noise source

The aim of our work being to perform on-line measurements on real industrial test benches, the presence of noise in the signal of interest cannot be avoided. To be considered as a PD, the signal should therefore appear with sufficient recurrence and be large enough to be considered other than just random noise.

The main sources of noise may be divided into different categories, classified by the interference produced [START_REF] Vigneshwaran | An improved threshold estimation technique for partial discharge signal denoising using Wavelet Transform[END_REF], [START_REF] Satish | Wavelet-based denoising of partial discharge signals buried in excessive noise and interference[END_REF]:

• Periodic pulse interference caused by power electronics or other periodic operations.

• Discrete spectral interferences (DSI) embody a continuous sinusoidal signal caused, for example, by AM/FM radio emission or power line communication systems.

• Stochastic pulse interference amplitude and moments of random occurrence caused by operations of occasional workers, power electronics, lightning strikes... Fig. 7 shows that it is impossible to measure PD signal, the amplitude of the noise induced by switching being too large compared to the PD amplitude. 2) Method validation For validation of the proposed WT, PD measurements were achieved on twisted pair of enameled wires (nominal diameter Ø = 1.31 mm) fed by a PWM like power supply at atmospheric pressure. Twisted pair samples were made according to usual norms and recommendations [START_REF]IEC 60851:2008 Winding wires -Test methods[END_REF]. This type of samples is representative of the winding that can be found in randomly wound motors. The signals denoised by wavelet transform are compared to analogic filtered signals.

Fig. 8 shows the reconstruction signal similar to the filtered analogical signal. The only difference between the two signals being the amplitude. Reconstruction with the automated choice enables retrieving a PD signal having an amplitude four times larger than the one filtered analogically. The digital denoising method based on continuous wavelet transform is functional and it sets all the wavelet transform configuration parameters automatically. This method has real interest compared to high-pass filtering since human expertise is no longer required to remove noise in signals.

On the other hand, it is important to note the limitations of this technique. First, to be functional, it is necessary for the signal to be discretized with a large sampling frequency in order to represent fast signals. Then, it is worth to be noted that the amplitude of the signal reconstructed by the method may present a significant error due to the frequency band overlap corresponding to each level of decomposition. But, another type of error is also induced when using a high-pass filter since all frequency components below the cutoff frequency are removed. The pros and cons of each method must therefore be considered prior to any choice.

C. Influence of pressure

Some of the electrical equipment devoted to aircraft applications may be located in depressurized areas, and while operating, the temperature can vary widely. Pressure and temperature parameters have an influence on the discharge inception voltage and may also modify their nature. Therefore, for such operating conditions, it is important to pay particular attention to the detection system characteristics in order to achieve the best SNR while filtering the noise induced by the voltage switching.

The works described in the following is focused on the pressure since it is the most impacting factor on PDs' ignition.

1) Experimental set-up

To perform tests close to aeronautical conditions, a vacuum chamber was used with a sufficiently large volume to be able to perform tests on samples ranging from twisted pairs to stators. Pressure could vary from atmospheric pressure up to a few tens of millibars. In order to study the influence of pressure on the ability of the method to detect PDs, tests were performed at different pressures under AC voltage and under PWM like voltage for sake of comparison. The main idea is to compare the impact of this parameter on the discharge characteristics while enabling a comparison between the different sensors.

This involves two hypotheses:

• The partial discharge ignition voltage is the same, whatever the voltage waveform

• The nature of the discharge remains the same, whatever the voltage waveform Experiments were performed on twisted pair samples of enameled wires. Last, non-intrusive current transformer sensor (Rogowski type sensor) was also tested in such an environment. This sensor essentially behaves like a transformer. The primary winding is actually the circuit in which partial discharge must be detected, with one cable going through a tore ferrite loop representing the magnetic circuit. The output secondary winding thus provides an image of the current going through the primary winding. The bandwidth at -3dB is between 0.5 and 80MHz.

2) Influence of pressure under AC a) Influence of the sensor on detection PDIV and PDEV are first checked at different pressures and AC voltage. A decrease in PDIV is clearly observed in Fig. 9 with decreasing pressure. This phenomenon corresponds to expected behavior and is in good agreement with Paschen's law. The PDIV values measured for each sensor is compared. Jack-SMA sensor with an additional capacitive effect is the most sensitive one.

b) Influence of the cut-off frequency of the filter on detection

The main idea is to study the impact of pressure on detection, with respect to the change in the nature of the discharge. Since the frequency content may be modified in that case, adapting the cut-off frequency to detect PDs must be envisaged. As the filter is suspected of inducing errors on PDIV, its impact under AC voltage at different pressure values is studied. These tests were performed at different pressure values with high-pass filters presenting cut-off frequencies of 50, 90, and 200 MHz and the Jack-SMA sensor with an additional capacitive effect.

The measured PDIV is artificially increased using highpass filters (Fig. 10) and it is all the more so true that the higher the cut-off frequency, the larger the PDIV at 100 and 400 mbar. It is therefore assumed that the high-frequency components of the spectrum are too small under such conditions. It is therefore necessary to increase the voltage to detect partial discharge (which already appeared at 444 Vpeak). As an example, with the 200 MHz filter, the PDIV is about three times larger than the one measured with the sensor without filtering. This same phenomenon was not observed at atmospheric pressure and 700 mbar: the filter cut-off frequency had no impact on the PD. This is a proof that modifying the pressure leads to a modification of the discharge spectrum.

c) Spectral analysis

A study on the discharge frequency spectra for the different pressures under study is performed. For each pressure level, 30 acquisitions of PD were recorded using the Jack-SMA sensor. The spectrum of each of them is determined and their average value is plotted (Fig. 11).

Since PDIV is a function of the pressure, it can therefore be assumed that the amplitude of these discharges will vary as a function of the pressure and the results are normalized in order to compare the shape of the PDs frequency spectra. For each pressure, the frequency spectrum has been normalized with respect to its maximum value. This normalization prevents the comparison of the amplitudes of these spectra as a function of the pressure. Nevertheless, it makes it possible to highlight the evolution of the most energetic frequency ranges as a function of the pressure.

It is obvious that the amplitude of the high-frequency components (40MHz -100MHz) decreases with a decrease of the pressure while the amplitude of the low-frequency components (9MHz -40MHz) increase. Moreover, at 100 mbar, for frequencies above 30 MHz, the signal amplitude is almost null despite some rays around 50 MHz that may contain a small portion of the discharge energy. Some rays around 100 MHz can be observed at 100 mbar, though these rays do not match PD signals, but rather to noise induced by external systems during tests.

3) Influence of pressure under PWM a) Influence of the sensor on detection

In the case of detection under PWM, it is not possible to detect the PDs without filtering the electromagnetic noise associated with the dV/dt. The response of the sensors without filtering and with high-pass filtering at 290 MHz is compared. This cut-off frequency allows a complete denoising for the three sensors, nevertheless in the case of the Rogowski sensor the PDs signals also appear to be filtered. This is due to the fact that the bandwidth of this sensor is not sufficient when using high-pass filters. Indeed, the bandwidth (at -3dB) of the sensor does not exceed 80 MHz and since the filter cut-off frequency is higher, all the signals are filtered. Subsequently, only the optimized Jack-SMA and Jack-SMA sensors will be presented.

PDIV and PDEV were measured for different pressure values. Discharges were detected using a Jack-SMA sensor filtered analogically using different cut-off frequencies (185,290 and 390 MHz). The PD signals were observed for the three different cut-off frequencies simultaneously. For the conditions under study, only the filter cut-off frequencies above 290 MHz provides full electromagnetic dV/dt noise removal. Not surprisingly, the PDIV value decreases with pressure and whatever the filter for each pressure (from 100 mbar to 1013 mbar), PDIV remains the same (Fig. 12).

b) Influence of the cut-off frequency of the filter on detection

As previously mentioned, the cut-off frequencies do not influence the measured PDIV, but it is interesting to observe their influences on the amplitude of the PDs measured. Not surprisingly, it can be seen that an increase in the cut-off frequency of the filters induces a decrease in the amplitude of the measured PD signals. However, under PWM, the cut-off frequency does not lead to errors on the PDIV. It is therefore important to study the spectrum of the PDs under PWM to understand this difference with the AC case.

c) Spectral analysis

In order to confirm the influence of pressure on the amplitude of high-frequency components, the same study as the one performed under AC was undertaken for PWM-like voltage. Nevertheless, it is more complex in this case to analyze the frequency content since it is necessary to remove all the noise induced during the switching while maintaining the "entire" PD signal. Hence, a special procedure is proposed to carry out this study:

• Measure of PDIV (using the appropriate filter)

• Acquire the signal without any filtering, for a voltage value of 90% of PDIV (signal without PD)

• Acquire the signal without any filtering at PDIV (signal with PD) • Calculate the difference between the signal with PD and the signal without PD • Calculate the frequency spectrum of the difference This procedure has, nevertheless, some limits:

• If the filter is not adapted, there may be an error on the PDIV

• Generally, for a voltage value of 90% of PDIV, the PDEV is reached but in some cases this may not be the case • This procedure is only valid if the noise is repeatable, if the noise varies too much from one acquisition to another the analysis will be totally false In this case, it can be seen that the amplitudes of the frequency components are in the same range for all the pressure values. It has therefore been decided to normalize all the frequency spectra with respect to the amplitude of an identical frequency component for the four pressure values. This makes it possible to observe the variation in the shape of the frequency spectrum as well as the modification of the amplitude of the frequency components as a function of the pressure.

First of all, it is important to note that the spectrum of the PD signals under such conditions extends over a wider frequency range than that observed under AC voltage. The question is to know if this is due to a change in the discharges nature.

The magnitude of high-frequency components (80 -400MHz) decreases with pressure while the amplitude of the low-frequency components (8MHz -80MHz) increase. Such behavior may be detrimental to the accuracy of the PDIV measurements. For a pressure of 100 mbar, the magnitude of the components above 300 MHz for the PD spectrum is very small. Pressure has a significant influence on the detection of partial discharges, and specifically on their characteristics. A decrease in pressure causes a change in their frequency spectrum. High-frequency components of the discharge signals tend to decrease or even disappear at very low pressure. In addition, the sensors used are sensitive to rapid current variations. If the frequency components are shifted to lower frequencies, the bandwidth of the sensors may not be sufficient to detect them. An error in determining the PDIV can be made in this case. As detection in PWM voltage requires the use of high-pass filters to remove the noise induced by switching, there may be a complete suppression of the frequency components associated with the PDs. However, we observed that the discharge frequency spectrum covers a much larger frequency range than with AC. Therefore, the method is functional regardless of the pressure and voltage form tested.

V. VALIDATION ON ENGINE TEST BENCHES

The purpose of investigating industrial test benches is to check the validity of the detection method, particularly the sensor used. As a matter of fact, this sensor was tested in a laboratory environment but a few tests were also carried out on industrial test benches [START_REF] Billard | Off-line and on-line partial discharges detection in low voltage motors of electric vehicle fed by a PWM inverter using nonintrusive sensor[END_REF], [START_REF] Cella | On-line partial discharges detection in conversion systems used in aeronautics[END_REF].

A. "Simple" PD detection

For this test, it was possible to vary the speed and bus voltage over a wide range. First, a test with a DC bus voltage of 554V was conducted. This test was intended to adjust oscilloscope calibers and optimize selection of the filters. Fig. 15 shows the voltage at the machine terminals and the output signals from the different sensors. Overvoltages are observed on the phase to phase voltage measurement. These surges have a maximum amplitude of 770V peak. Since the sensors are saturated by switching, using high-pass filters to suppress electromagnetic noise is mandatory.

1) Study on the winding

In the case below, the filters were replaced by filters with a lower cutoff frequency (100 MHz). A signal similar to a PD signal can be seen in Fig. 16.

The temporal position of the signal was observed to compare it to the maximum voltage in order to confirm the assumption that these signals correspond to discharges. Fig16. shows that the sensor signal appears at the maximum value of the phase to phase voltage UW. Fig. 17 shows a comparison of the different sensors. They all detect the same signal but its magnitude is a function of the sensor type: the largest signal being obtained for the jack SMA+ additional capacitive effect. These tests detect signals similar to partial discharges on representative equipment operating under normal conditions. • Signals appearing from the same voltage as the PDIV measured under AC supply voltage The proposed detection system is functional. The increase in the sensor's coupling capacitance can increase the magnitude of the measured signals significantly. Ten times greater amplitude can be seen compared to the "single" sensor. Twice greater amplitude was observed relative to the inductive sensor.

2) Denoising by CWT method

The denoising method based on wavelet decomposition has only been validated on laboratory samples. It is therefore particularly interesting to apply under real constraints in an industrial environment.

The results of the denoising method applied to the previous case are given in Fig. 18. Our method allows suppressing the noise (blue curve) and leads to a good reconstruction of the PD signal. Moreover, the amplitude of the signal reconstructed thanks to the numerical method is five times greater than the signal filtered analogically. In the case under study presented before, there was few doubts regarding the presence of discharges, but in other cases, not shown here, the proposed method improves the denoising.

B. PD detection in machines fed by SiC inverter

With the concept of "more electric aircraft", higher voltage levels and changing electrical architectures (notably the increased use of converters) was observed. Future projects (related to hybrid propulsion for e.g.) are considering a further increase in voltage levels. In a relatively near future (20 years), voltage up to several kilovolts may be envisioned. In addition, silicon carbidebased (SiC) power components will probably replace the current silicon-based components in some high efficiencies and high power density applications. The use of high voltage will increase the risk of partial discharge occurrence, while the evolution of electronic components will result in an increase in switching speed and consequently an increase in the noise frequency spectrum.

In this context, it is important to determine whether our detection method will always be functional. Currently, some domains already use voltages on the order of kilovolts and are operating converters using SiC components. Some tests were carried out on an industrial test bench using on SiC converters on prototype motors with an important length of cabling, allowing a clear demonstration of the ability of the method to detect PDs.

a) PD detection

Tests were performed with a SiC converter supplied by a 750 V DC bus and the cable length between the inverter and the motor was about ten meters.

Under such conditions, the overvoltages amplitude is about 1100 V and the dV / dt have a value of 10 kV/ȝs. To eliminate the noise induced by these voltage fronts, it was necessary to use high pass filters having a cut-off frequency of 500 MHz. There are no characteristic signals that coincide temporally with all fronts, indicating that the filter is adequate for removing noise-induced switching.The observed signals in Fig. 19 and Fig. 20 have many of the characteristics necessary to determine the presence of discharges:

• Low recurrence • Signals seem to coincide temporally with peak voltages Another interesting result of this study concerns the ability of detecting PDs despite the use of filters having a high cut-off frequency. Generally, the amplitude of the frequency components of PDs, appearing under PWM for 3 kV / ȝs edges, is very low beyond 300 MHz. In the case of motors operating at higher voltages, the PDs not only appear during the front but also on the continuous part of the square waveform (Fig. 23). The appearance of PDs in this type of machines is much more studied [START_REF] Stone | Experience with on-line partial discharge measurement in high voltage inverter fed motors[END_REF], [START_REF] Fabiani | Relation between space charge accumulation and partial discharge activity in enameled wires under PWM-like voltage waveforms[END_REF]. Due to the similar behavior, it may be stated that the method is also efficient under such conditions.

VI. CONCLUSION

The proposed method proved its efficiency through tests on different motor test benches and enabled to highlight various phenomena that can lead to false positives to take into account when analyzing results. In industrial scenarios, partial discharge tests must be superimposed on other tests, which means that it is important not to disturb the existing set-up and testing. Our method fulfilled all these requirements.

From a general point of view, the detection system can be transposed to other areas than aeronautics. The method has already been tested in the field of railway and automobile for nearly equivalent voltage levels. Moreover, the current trend is an increase of voltage magnitude for future aircrafts. The method has demonstrated its ability to detect PDs in the case of motors operating at higher voltages and will therefore be transposable to future equipments that will operate with these new voltage levels.

Fig. 1 .

 1 Fig. 1. Scheme of the complete off-line detection system

Fig. 2 .Fig. 4 .

 24 Fig. 2. detection without filtering

Fig. 5 .

 5 Fig. 5. Jack-SMA sensor mounted on its holding system

Fig. 6 .

 6 Fig. 6. Simple optimization of the sensor sensitivity

Fig. 7 .

 7 Fig. 7. Noisy signal induced by switching (black)

Fig. 8 .

 8 Fig. 8. PWM like voltage shape (blue), sensor signal filtered at 200 MHz (black), PD signal reconstructed by WT with the automated choice of the mother wavelet ("coif1" in this case) (red)

Fig. 9 .

 9 Fig. 9. Influence of pressure on PDIV for three sensors under AC voltage

Fig. 10 .

 10 Fig. 10. Influence of filter cut-off frequencies on the PDIV at different pressure values under AC voltage

Fig. 11 .

 11 Fig. 11. Normalized changes of PD spectrum under AC voltage as a function of pressure

Fig. 12 .

 12 Fig. 12. Influence of pressure on PDIV for two sensors under PWM like voltage

Fig. 13 .

 13 Fig. 13. Influence of filter cut-off frequencies on the PDIV at different pressure values for two sensors

Fig. 14 .

 14 Fig. 14. Normalized changes of PD spectrum under PWM-like voltage as a function of pressure

Fig. 15 .

 15 Fig. 15. Phase to phase voltage UW (blue), sensor signal on U without filtering (red), sensor signal on W without filtering (green)

Fig. 16 .

 16 Fig. 16. Phase to phase voltage UV (black), phase to phase voltage UW (blue), phase to phase voltage VW (red), sensor signal on phase U filtered at 100 MHz (green), Zoom of the sensor signal and all the maximum voltage

Fig. 17 .

 17 Fig. 17. Phase to phase voltage UV (black), sensor (jack SMA) signal on phase U filtered at 100 MHz (blue), sensor (inductive) signal on phase U filtered at 100 MHz (red), sensor (jack SMA + additional capacitive effect) signal on phase U filtered at 100 MHz (green) These signals have all the features of partial discharges: • Low recurrence • PD signal temporally coinciding with peak voltages • Consecutive signals at different voltage polarities.• Signals appearing from the same voltage as the PDIV measured under AC supply voltage The proposed detection system is functional. The increase in the sensor's coupling capacitance can increase the magnitude of the measured signals significantly. Ten times greater amplitude can be seen compared to the "single" sensor. Twice greater amplitude was observed relative to the inductive sensor.

Fig. 18 .

 18 Fig. 18. Phase to phase voltage UW (black), sensor signal on phase U without filtering (blue), sensor signal on phase U filtered at 100 MHz (red), sensor signal reconstructed by CWT (green) (note the scale changes)

Fig. 19 .

 19 Fig. 19. PD research on a motor supplied by a SiC converter

Fig. 21 .

 21 Fig. 21. Temporal position of PDs on two periods

Fig. 22 .

 22 Fig. 22. Zoom and persistence on a voltage edge to observe temporal position of PDs

Fig. 23 .

 23 Fig.23. PD patterns at 1.8 kV (peak value) with bipolar and unipolar square waveforms[START_REF] Stone | Experience with on-line partial discharge measurement in high voltage inverter fed motors[END_REF]

His research works were performed in Laplace Laboratory. He is currently working for Liebherr Aerospace and is on temporary assignment atIRT St Exupery. got his MSc in Electrical Engineering in 2013 from University of Poitiers. He is currently pursuing the Ph.D.


V Laquerbe
email: vincent.laquerbe@isae.fr

R Pascaud

T Callegari

L Liard

O Pascal

-Saint-Malo Modélisation et caractérisation expérimentale d'un résonateur microruban reconfigurable en fréquence par décharge plasma

Dans ce papier, la reconfigurabilité en fréquence d'un résonateur microruban par décharge plasma est démontrée. Des simulations plasma (prenant en compte la dynamique des fluides, l'électrostatique, etc.) sont considérées afin d'intégrer un modèle de plasma réaliste dans les simulations électromagnétiques du résonateur. Les résultats de simulation sont cohérents avec la mesure et rendent prometteur cette technique d'intégration de plasma volumique dans des circuits microondes.

Introduction

La recherche de compacité et de simplicité dans les systèmes de communications favorise l'émergence de nouvelles solutions reconfigurables permettant un fonctionnement multibandes. D'un point de vue pratique, l'agilité en fréquence peut être réalisée à l'aide d'éléments localisés (diodes PIN, varactors, etc.) ou l'utilisation de matériaux reconfigurables (cristaux liquides, ferroélectriques, etc.) [START_REF] Petosa | An overview of tuning techniques for frequency-agile antennas[END_REF].

Parmi les nouvelles technologies étudiées, le plasma possède des caractéristiques intéressantes [START_REF] Sokoloff | Non-thermal plasma potentialities for microwave device reconfigurability[END_REF]. En effet, il s'agit d'un milieu dispersif dont la permittivité diélectrique relative peut prendre des valeurs inférieures à 1. Contrairement à ce qui est proposé dans [START_REF] Semnani | Plasma-enabled tuning of a resonant rf circuit[END_REF] où le plasma est considéré comme un élément localisé, nous suggérons d'implémenter un plasma volumique dans un résonateur microruban pour contrôler sa fréquence de résonance.

Dans ce papier, nous présentons en premier lieu une modélisation originale couplant des outils de simulation plasma et électromagnétique pour la simulation de ce problème multi-physiques [START_REF] Laquerbe | Modeling and experimental measurements of a tunable microstrip resonator using plasma discharges[END_REF]. Les résultats numériques sont ensuite confrontés à des mesures réalisées sur un prototype pour différentes pressions et gaz [START_REF]Frequency-agile microstrip resonator using dc plasma discharge[END_REF].

Principe théorique

Un plasma est un milieu neutre dans lequel interagissent des particules chargées (électrons et ions) et des particules neutres. Dans notre application, nous considérons des plasmas non-magnétisés froids et hors équilibre thermodynamique. La permittivité relative de ces plasmas est généralement représentée par le modèle de Drude [START_REF] Lieberman | Principles of Plasma Discharges and Materials Processing[END_REF] :

ε p (ω) = 1 - ω 2 p ω(ω + iν) , ω 2 p = e 2 n e m e ε 0 (1)
où ν, ω p , e, n e , m e et ε 0 sont respectivement la fréquence de collision (pertes), la fréquence angulaire du plasma, la charge électrique élémentaire, la densité électronique, la masse de l'électron et la permittivité du vide. Le contrôle de la densité électronique n e permet donc de modifier ε p et ainsi d'obtenir, par exemple, des constantes diélectriques comprises entre 0 et 1. L'idée proposée ici est de générer puis contrôler un plasma dans la cavité d'un résonateur microruban afin de modifier sa fréquence de résonance.

Description du dispositif

La Figure 1 présente le système complet composé de deux lignes microruban 50 Ω imprimées sur un substrat d'une épaisseur de 813 µm et de constante diélectrique 3.55. Les deux lignes sont montées en série avec un résonateur circulaire de rayon r = 10 mm. Afin d'optimiser l'allumage du plasma, la cavité plasma a été agrandie et une troisième électrode, qui fait office de cathode, a été ajoutée au circuit. La tension DC est appliquée entre le patch circulaire et la cathode de la partie inférieure. Une décharge est ainsi générée dans la cavité plasma (h cavité = 10 mm) puis diffuse à l'intérieur de la cavité microonde au travers du plan de masse par une grille de trous usinée à cet effet. Enfin, deux fentes ont été ajoutées au résonateur afin de réduire sa fréquence propre à vide, ce

Modélisation numérique

Étant donné que le plasma est un milieu fortement hétérogène, sa répartition spatiale au sein de la géométrie considérée a été étudiée avec le code numérique 2D GD-Sim (Glow Discharge SIMulation) [START_REF] Boeuf | Two-dimensional model of a capacitively coupled rf discharge and comparisons with experiments in the gaseous electronics conference reference reactor[END_REF]. Ce code permet de modéliser une décharge plasma DC à plusieurs électrodes afin d'obtenir des paramètres plasmas (densité électronique, courant d'ionisation, etc.) réalistes et cohérents avec la géométrie du dispositif, le gaz et la pression considérés pour la décharge. Ces simulations ont permis d'extraire des profils de densité électronique 2D au sein de la cavité, comme présentés sur la Figure 3.

Pour chaque paramètre d'excitation (tension et courant d'ionisation fixés), on modélise ensuite le milieu plasma par 5 contours géométriques dans lesquels la densité (et donc la constante diélectrique) est supposée constante. Ces profils sont ensuite extrapolés de manière à les adapter à la cavité 3D du résonateur réel et notamment à la géométrie complexe de la grille de diffusion. Cette extrapolation permet de prendre en compte les gaines qui sont générées entre le plasma et les autres interfaces : la grille de diffusion, le résonateur et le substrat. Cette nouvelle représentation 3D est enfin importée dans le logiciel Ansys HFSS afin de simuler les paramètres S du résonateur chargé par ce plasma non uniforme.

La Figure 4 présente les contours de densité électronique obtenus en simulation 2D pour une tension d'entrée donnée, ainsi que le modèle HFSS à 5 couches associé. La discrétisation 3D a été limitée à 5 couches afin de réduire les ressources informatiques nécessaires lors de la simulation électromagnétique.

Résultats numériques et expérimentaux

Une première série d'expériences a été réalisée en faisant varier le courant I DC dans la décharge en considérant de l'argon à 2 Torr (environ 2.67 mbar). A cette pression, la fréquence de collision est estimée à ν ≈ 3 GHz (valeur calculée avec BOLSIG+ [START_REF] Hagelaar | Solving the boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models[END_REF]). La Figure 5 présente les paramètres S simulés et mesurés du système pour deux courants I DC . On remarque un décalage entre la fréquence de résonance à vide (obtenue sans plasma) mesurée et simulée, principalement due aux tolérances de fabrication du prototype (alignement des cavités et valeur de la permittivité des substrats notamment).

On observe par ailleurs sur la Figure 5 que la présence du plasma dans la cavité permet d'augmenter la fréquence de résonance. Un décalage de 231 MHz, soit 5.5 %, a été observé pour un courant d'ionisation de 147 mA. Plus le courant augmente, plus la densité électronique dans la cavité augmente et donc plus le décalage en fréquence est important. Les variations du courant d'ionisation I DC permettent à priori un contrôle linéaire de la fréquence de résonance. Cette est représentée sur la Figure 6 où l'on a tracé l'agilité en fréquence du résonateur en fonction du courant I DC pour le prototype expérimental et pour le modèle simulé sous Ansys HFSS.

Malgré une tendance linéaire assez proche, on remarque que la simulation minimise l'agilité en fréquence du résonateur. L'extrapolation du profil 2D simulé n'étant pas immédiate à cause de la complexité de la grille de diffusion, les profils 3D considérées en simulation sousestiment vraisemblablement la densité électronique dans la dimension orthoradiale, ce qui conduit à cet écart entre la simulation et la mesure.

Etude de l'influence du gaz

Plusieurs décharges ont également été étudiées expérimentalement dans de l'argon et du néon, pour différentes pression. Les Figures 7 et 8 présentent l'agilité en fréquence et les pertes d'insertion relatives (c'est-à-dire normalisé au cas sans plasma) en fonction du courant dans la décharge.

L'agilité en fréquence varie linéairement avec le courant I DC ce qui permet une reconfigurabilité directe du résonateur. En fonction du gaz et de la pression considérés, l'agilité diffère néanmoins. De la même manière, les pertes d'insertion relatives augmentent de manière linéaire avec I DC .

Dans l'argon, augmenter la pression conduit en théorie à une augmentation de la densité électronique, et donc de l'agilité en fréquence, alors que la mesure produit l'effet inverse. Cela peut s'expliquer par le phénomène de diffusion à travers la grille qui n'est pas le même lorsque la pression change. En particulier, à P = 5 Torr, il a été observé expérimentalement que la décharge ne parvient pas à diffuser à travers tous les trous de la grille, ce qui explique au final une densité moyenne dans la cavité microonde plus faible, mais une pression plus élevée. Ce phénomène explique par ailleurs la similitude entre les différentes pertes d'insertion mesurées. Malgré un plus forte pression, la densité est moins importante et donc le plasma génère moins de pertes. Toutefois, à 5 Torr, le plasma à base de néon produit un meilleur décalage en fréquence du fait de la diffusion plus efficace de la décharge. La densité électronique dans la cavité est plus grande et l'agilité en fréquence aussi. De plus, comme le néon génère moins de perte que l'argon à ces pressions [START_REF] Lieberman | Principles of Plasma Discharges and Materials Processing[END_REF], les pertes d'insertion ne sont pas plus importantes que dans l'argon. Afin de mieux comparer les performances de chaque gaz, il est plus pratique de normaliser l'agilité en fréquence obtenue par les pertes qu'elle génère. On définit ainsi un facteur de mérite (FdM) propre à chaque configuration (pression et type de gaz).

Le Tableau 1 présente le facteur de mérite obtenu pour les mesures des Figures 7 et 8. L'argon à 1 Torr apparait être la meilleure solution. Lorsque la pression augmente, ses performances diminuent grandement et le néon a un facteur de mérite deux fois plus grand. Il serait intéressant de considérer le cas du néon à 1 Torr mais aucune décharge n'a été allumée à cette pression pour des tensions inférieures à 600 V, qui est la limite du té de polarisation utilisé dans le montage expérimental. Néanmoins, si n e augmente, alors l'agilité en fréquence devient plus large. Dans ce contexte, d'autres types de décharges plasma pourraient permettre d'obtenir des densités plus grandes. Les plasmas RF ou pulsés seraient dans cette optique une alternative intéressante pour générer des décharges à 1 Torr dans le néon, ce qui devrait permettre d'atteindre des valeurs de FdM plus importantes.

Agilité

Conclusion

Un concept innovant de résonateur microonde par cavité plasma reconfigurable a été proposé. L'intégration d'une décharge plasma dans cette cavité permet de modifier la constante diélectrique du gaz et autorise ainsi l'agilité en fréquence. Des études plasma 2D ont permis de modéliser l'hétérogénéité du plasma dans ces configurations (densité électronique non uniforme, présence de gaine aux parois, etc.). Les simulations électromagnétiques intégrant ces modélisations réalistes sont cohérentes avec la mesure et confirment la capacité de cette solution à modifier la fréquence de résonance de résonateurs microruban à plasma.

L'étude expérimentale de l'influence du gaz utilisé pour la décharge et de sa pression a mis en évidence des comportements spécifiques permettant de générer une agilité en fréquence de plusieurs %. L'estimation de la densité électronique moyenne dans la cavité microonde laisse supposer que cette technique peut être améliorée en utilisant des décharges plasma à plus fortes densités électroniques, qui est par exemple le cas pour des sources RF ou microondes.

Figure 1 .

 1 Figure 1. Vue éclatée du système complet constitué du circuit microonde et de la géométrie additionnelle permettant l'allumage du plasma.

Figure 2 .

 2 Figure 2. Vue de dessus du système complet placé sous vide lorsqu'un plasma d'argon est allumé dans la cavité plasma.

Figure 3 .

 3 Figure 3. Densité électronique 2D simulée dans la cavité plasma et microonde pour différentes tensions.

Figure 4 .

 4 Figure 4. Cartographie 2D de densité électronique pour U DC = 400 V et l'extrapolation 3D correspondante.

Figure 5 .

 5 Figure 5. Paramètres S mesurés et simulés lorsque I DC = 0 mA et I DC = 147 mA.

Figure 6 .

 6 Figure 6. Agilité en fréquence mesurée et simulée en fonction du courant.

Figure 7 .

 7 Figure 7. Agilités en fréquence mesurées pour différentes valeurs de courant I DC et de pression dans l'argon et le néon.

Figure 8 .

 8 Figure 8. Pertes d'insertion relatives mesurées pour différentes valeurs de courant I DC et de pression dans l'argon et le néon.

Figure 9 .

 9 Figure 9. Estimation du n e dans la cavité requis pour obtenir le même décalage en fréquence, d'après les simulations électromagnétiques.

  Enfin, des simulations numériques à l'aide du logiciel commercial Ansys HFSS ont permis d'estimer les densités moyennes n e à l'intérieur de la cavité microonde qu'il aurait été nécessaire d'avoir pour générer un décalage en fréquence donné. La Figure9représente les valeurs de n e obtenues pour les trois cas précédents. Les densités moyennes estimées sont cohérentes avec ce qui est normalement atteint avec des plasmas DC.

			IL relative	FdM
		(MHz/mA) (dB/mA) (MHz/dB)
	Ar 1 Torr	1.57	-0.015	106
	Ar 5 Torr	0.34	-0.011	30
	Ne 5 Torr	1.01	-0.017	61
	Tableau 1. Performances du résonateur à plasma pour
		différents gaz et pression.

Remerciements

Les auteurs souhaitent remercier la DGA pour son soutien financier ainsi que O. Pigaglio et son équipe pour la fabrication des circuits.