Lise Kim
email: lise.kim*@ensam.eu

Esma Yahia
email: esma.yahia@ensam.eu

Frédéric Segonds
email: frederic.segonds@ensam.eu

Philippe Véron
email: philippe.veron@ensam.eu

Antoine Mallet
email: antoine.mallet@capgemini.com

i-DATAQUEST : a Proposal for a Manufacturing Data Query System Based on a Graph

Keywords: Graph Database, Query System, Information Retrieval, Manufacturing Data, Manufacturing Industry

During the manufacturing product life cycle, an increasing volume of data is generated and stored in distributed resources. These data are heterogeneous, explicitly and implicitly linked and they could be structured and unstructured. The rapid, exhaustive and relevant acquisition of information from this data is a major manufacturing industry issue. The key challenges, in this context, are to transform heterogeneous data into a common searchable data model, to allow semantic search, to detect implicit links between data and to rank results by relevance. To address this issue, the authors propose a query system based on a graph database. This graph is defined based on all the transformed manufacturing data. Besides, the graph is enriched by explicitly and implicitly data links. Finally, the enriched graph is queried thanks to an extended queries system defined by a knowledge graph. The authors depict a proof of concept to validate the proposal. After a partial implementation of this proof of concept, the authors obtain an acceptable result and a needed effort to improve the system response time. Finally, the authors open the topic on the subjects of right management, user profile/customization and data update.

1

Manufacturing Data Query

Leveraging the data product generated during its life cycle is a main issue for manufacturing industry. Manufacturing can be qualified as either discretei.e., the production of discrete items (e.g., cars, aircraft and appliances)or continuous process, i.e., the production process that lends itself to an endless flow of non-discrete product (e.g., pharmaceutical, food and beverage, chemicals and cosmetics) [START_REF]:2004 Industrial Automation Systems and Integration -Industrial Manufacturing Management Data -Part 1: General Overview[END_REF][START_REF] Pinquié | An illustrated glossary of ambiguous PLM terms used in discrete manufacturing[END_REF]. In this paper, our proposal is mainly dedicated to discrete manufacturing but could be enlarged to other domains. It requires collecting and managing data that are heterogeneous (including structured and unstructured data), explicitly and implicitly linked. Data are stored in distributed resources. One part is stored in information systems (PLM, ERP, MES etc.) databases which are supported by different data models and the other part are mainly unstructured and semi-structured data such as target tracking in spreadsheets, note taking in a text editor, reporting written in e-mail, etc. All this data are generated by different actors, using different languages, codifications and vocabulary. The rapid, exhaustive and relevant acquisition of information in this complex context is difficult. There is no unique point of access to get the requested information and this information is often difficult to access. The time spent searching for information represents a non-negligible part of the employee's working time estimated to 19% [START_REF] Chui | The social economy: Unlocking value and productivity through social technologies[END_REF].

When considering the relational nature of manufacturing data, the authors directed the work towards a graph-database query system. This choice allows the exploitation of all data relationships when searching. Besides, the authors have chosen to prioritize the search in all the textual content of the data (which can come from metadata, text files, but also images and tables). Indeed, the authors consider that textual content is of all other types (3D, schematic, etc.) the one that contains the most useful information for different people. The use of geometric content, images, diagrams, videos or any other type of non-textual content is therefore excluded from this paper to limit the study.

The authors present the main issues to be solved and deduce their main function required for a solution in section 2. A detailed state of the art by function is presented in section 3. The authors detail in section 4 the proposal and its partial validation and conclude with a discussion in section 5.

Key Challenges and Associated Functions

A retrieval information system is defined by three main functions which are : data preprocessing, query pre-processing and relevance evaluation of the data according to the query. Beyond the main requirements of a retrieval information system, which are fast time response, completeness and relevance of results, retrieving information in a manufacturing company context involves many other challenges. To answer these challenges, the authors proposed to enrich the three main functions of any query system with four supplementary functions derived respectively from each identified challenge, which are:

1. Data exploitation despite its syntactic heterogeneity: Data can be recorded in databases or in documents as text files. In order to optimize search capabilities, the system must be able to exploit the specifications of each type of data and return, as required, either a file list, a record list from a database, data linked to another through a relational database, a metadata value, a table cell value or a specific sentence in a text content. To answer this challenge, the authors define a function that integrates each searchable element in the graph data model. This concerns the metadata of the records in the databases, the metadata of semi and unstructured files, explicit relationship between database tables, the textual content of the text files, image files and tables. This function is called: "Function A -Process syntax specifics of data".

2.

Data exploitation despite vocabularies and languages heterogeneity: Data contains textual content defined by a wide variety of actors, especially in an extended enterprise. In order to optimize the query results displayed to the user, it is necessary to return all the relevant results, even if the language or the vocabulary used in the data content differs from the language or vocabulary used in the query. A new function is then needed to extend the search for query keywords to all its semantically related terms. For example, if the term battery is used in the query, results must contain those with the battery translation as batterie in French and the battery synonyms as accumulator. This function is called: "Function B -Search by Semantic Proximity".

3.Exploitation of implicit links between data: One impact of the distributed nature of data is the lack of links between data. For example, if the user searches for the price of a part using its functional reference but the price is associated with the supplier reference in another database, the search system must be able to detect the link between the two references in order to obtain the expected result. To answer this challenge, a function is then needed to detect implicit links between data. This function is called: "Function C -Detect implicit links between data".

Displaying results by relevance:

The ranking of results by relevance is essential to any query system that provides a significant number of results. It is therefore necessary to present the result according to a degree of relevance. The authors propose to define a system function called: "Function D -Rank the results in relevance order".

Related Works

The authors conduct a general state of the art considering several works that proposing query or analysis systems based on graph databases to deal with distributed and heterogeneous data source issues. In Table 1, the authors identify some works where each function consideration is evaluated. The treatment of syntactic heterogeneity is achieved by using a meta-model to be instantiated at each new information source in the work of [START_REF] Gröger | The Deep Data Warehouse: Link-Based Integration and Enrichment of Warehouse Data and Unstructured Content[END_REF] and by integrating as many plug-ins as necessary transformations in the work of [START_REF] Martínez-Bazan | DEX: High-performance exploration on large graphs for information retrieval[END_REF]. The works described in [START_REF] Gröger | The Deep Data Warehouse: Link-Based Integration and Enrichment of Warehouse Data and Unstructured Content[END_REF] and [START_REF] Henkel | Combining computational models, semantic annotations and simulation experiments in a graph database[END_REF] deal with the automatic detection of non-existent links mentioning the use of various analytics such as text mining and the use of Levenshtein distance. The work describes in [START_REF] Touré | STON: Exploring biological pathways using the SBGN standard and graph databases[END_REF] integrates the detection of links between data to be unified by rules involving the relationships and common properties between the data. Finally, the authors of [START_REF] Henkel | Combining computational models, semantic annotations and simulation experiments in a graph database[END_REF] integrate the notion of semantic search thanks to semantic annotation via bio-ontologies and result classification according to a model specific to biology. The authors of [START_REF] Lysenko | Representing and querying disease networks using graph databases[END_REF][START_REF] Yoon | Use of Graph Database for the Integration of Heterogeneous Biological Data[END_REF][START_REF] Bonnici | Comprehensive reconstruction and visualization of non-coding regulatory networks in human[END_REF][START_REF] Messina | BioGraph: a web application and a graph database for querying and analyzing bioinformatics resources[END_REF][START_REF] Noel | Big-data architecture for cyber attack graphs representing security relationships in nosql graph databases[END_REF][START_REF] Schabus | Spatially-Linked Manufacturing Data to Support Data Analysis[END_REF] don't integrate any of the functions mentioned, notably because the sources of the data involved are known and limited in number, which makes processing ad hoc.

As none of these works encompasses all the manufacturing industry challenges, the authors define a specific state of the art by function. It allows deeply defining the possible orientations transcribed in the scientific literature for each specific function. This study is described in the bullet list below.

 Function A -The treatment process of data syntactic specificity. The transformation of relational database schema into a graph database schema is a well-proven field. For some graph database, the transformation is conducted by ETL (Extraction Transformation and Load) tools plug-in 1 . This transformation allows the relationships retrieval between tables (with foreign keys) to generate graph links. Whereas, text extraction from document is possible with parser tools. Supported by natural language processing algorithms [START_REF] Chowdhury | Natural Language Processing[END_REF], the specific sentence detection according to language specificities such as grammatical rules can be done. Besides, property extraction from documents is possible with standard computer operation. Finally, spreadsheet syntax exploitation has already been done in papers like [START_REF] Zhu | A novel approach based on Neo4j for multi-constrained flexible job shop scheduling problem[END_REF] but the transformation is limited by adaptability of the different array formats.

 Function B -Search by enabling semantic proximity. Since the Latent Semantic Indexing proposed by the Information Retrieval field [START_REF] Dumais | Latent semantic indexing (LSI) and TREC-2[END_REF], the tendency is rather to exploit knowledge resources of semantic relation between terms supported by ontologies [START_REF] Kyriakakis | Enabling Ontology-based Search: A Case study in the Bioinformatics Domain[END_REF] or knowledge graph [START_REF] Xiong | Explicit Semantic Ranking for Academic Search via Knowledge Graph Embedding[END_REF]. Two orientations are then taken, query expansion or enrichment of indexed descriptors.

 Function C -Detect implicit links between data. Record Linkage is the task of finding two records referring to the same entity through different sources. Two objects can be associated if they have a common key. The typographical variations problems in this key are to be considered and can be solved by the comparison of common character strings (Levenshtein distance for example [START_REF] Navarro | A Guided Tour to Approximate String Matching[END_REF] ). The link can be accentuated according to the number of common labels, and according to the labels involved, which can be weighted based on a revelation criterion [START_REF] Fellegi | A theory for Record Linkage[END_REF]. On the other hand, it is also possible to use a knowledge graph and the user browsing history to detect link between data [START_REF] Hakkani-Tür | Using a knowledge graph and query click logs for unsupervised learning of relation detection[END_REF]. Besides, link prediction is an important research area in social network analysis where the existing link analysis allows to the new links prediction [START_REF] Cukierski | Graph-based Features for Supervised Link Prediction[END_REF].

 Function D -Rank the results in relevance order. The results ranking is carried out using several criteria. In the Information Retrieval field, the vector model used the number of terms occurrences. Other methods used by web search engines in the field of Search Engine Optimization should be considered [START_REF] Xing | Weighted PageRank algorithm[END_REF]. These methods use for example the popularity of the sites (are they often browsed or searched?), the page freshness (are they regularly updated?) and the pages authority (do other sites refer to them?) etc.

I-DATAQUEST, a Proposal for a Manufacturing Data Query System

Proposal Description

The authors define the proposal for a manufacturing data query system based on a graph in Fig. 1. The main object of the proposal is to offer to any manufacturing stakeholder the possibility to query all the company data. The back end of the proposed system contains three areas presenting the system main functions: data pre-processing, query pre-processing and relevance evaluation of the data according to the query. Each of these parts was then enriched by sub-blocks allowing to respond to the specific functions listed in section 2 and thus to the key challenges related to the study context. The details of the proposal implementation are briefly presented below. guage adapted to the graph database and it is adapted according to the values of 𝑄 𝑤 and 𝑄 𝑎 . For example, if 𝑄 𝑤 𝑖𝑠 𝑛𝑜𝑡 𝑛𝑢𝑙𝑙, 𝑄′ will integrate the query of all named or approximately named 𝑄 𝑤 and return the values as results. In addition, 𝑄′ will query all textual content and return specific sentences based on the terms of 𝑄 and using natural language processing algorithms. For example, in a requirement search query, it is then possible to search for all sentences expressing a requirement because they contain specific verbs and modals as 'require', 'must' etc. The query is also divided into several sub-queries to evaluate the ranking of the results. For example, the subquery querying only the labels named 'title' will return results of high relevance.

6. Query expansion. The terms used in query are extended to the relevant terms. The relevant terms defined with a knowledge graph 𝐺 𝑘 and according to a relevance score. This relevance score is calculated based on the frequency of the term use in previous queries. For in a car manufacturer context, if the user uses the term 'batterie' in French, which means both the musical instrument and the energy storage element, the English translation 'battery' and not 'drums' will by preferred because it is more often used. 7. Knowledge graph 𝐺 𝑘 creation. Merging both ontology and knowledge graph concepts, 𝐺 𝑘 is built using external resources such as [START_REF] Speer | ConceptNet 5.5: An Open Multilingual Graph of General Knowledge[END_REF] to obtain synonymous, related and translating terms used in 𝐺 𝑑 . 8. Knowledge graph 𝐺 𝑘 enrichment. When the user submits a query, the relevance score 𝑆 𝑟 between the query terms 𝑡 𝑞 and the terms selected in reformulation contained in 𝐺 𝑘 is increased. Conversely, when terms are deselected, the relevance score 𝑆 𝑟 is decreased. 9. Query reformulation. A cross-reference of the terms used in 𝑄 and all terms in relationship in 𝐺 𝑘 are proposed to the user as shown in Fig. 1. The user can select or deselect the terms to be included and thus reformulate the query. 10. Graph database querying. The query 𝑄′ is applied to the graph database 𝐺 𝑑 . 11. Results displaying. The results of the query of 𝐺 𝑑 according to 𝑄′ are displayed to the user in an order of relevance established by steps 2 and 9.

Proposal Validation

The authors checked that necessary functions defined in section 2 are taken into account in the proposal. The authors have transcribed the result in Table 2.

Table 2. Functions consideration in the proposal.

Step Query preprocessing Data preprocessing Relevance evaluation

Function A Function B Function C Function D 1,2, 4 X 7,8,9 X 5 X 7 X 3,10,11 X 8 X 6 X
A validation concerning the main requirements of a query system such as the fast response time, completeness and relevance of results must be conducted. This validation has been so far partially achieved. Indeed, only the first four functions in Table 2 has been developed for the moment (including step 1,2,5,6,7) and by excluding the automation of data transformation step.

The proof of concept developed by the authors uses different tools among the Python language, Apache Tika2 to extract the textual content of documents, Tesseract3 for the characters recognition in images documents and Neo4J4 as graph databases. Py2neo5 was selected to conduct the to Neo4j with Python language and DashByPloty6 generates a web interface suitable for data analysis. Fig. 3 shows the different tools used for each layer of the proposition.

Fig. 3. Proof of concepts tools

The dataset used to validate the author's approach, comes from a digital model of a drone project and enriched. It contains 686 elements, 47% of which are unstructured data, 22% tree structure data and 17% from a relational database. The authors identified 19 queries to meet the requirements of innovative uses in the manufacturing company and from its various departments. The expected answers per query were evaluated manually by browsing through each object in the dataset. For time measurement, the aim is to achieve less than one second between the submission of the query by the user and the display of the result according to [START_REF] Arapakis | Impact of Response Latency on User Behavior in Web Search[END_REF].

The measures used to evaluate Information Retrieval system are the recall (number of relevant documents found according to the number of relevant documents in the database) and the precision (number of relevant documents found according to the total number of documents display in result). A system returning all relevant results without displaying irrelevant results will have these two measurements equal to 1.

The results obtained are in Table 3. The results are compared to a first step where only node and labels without processing of texts and tables content, have been integrated in the graph database. Evaluation of the results shows a degraded query time. An important waste of time is due to the search for sentences in the textual content. There are ways to improve time such as the search for sentences on demand only but also by the integration of text content descriptors rather than the entire content, the reduced selection of labels to be used in a search, and the table content extracts on demand. It will therefore be necessary to evaluate each option according to the degradation of the other requirement values. However, the recall measurement improves and precision decreases with the increase in the number of results.

Perspectives

In order to address the issue of information retrieval in the context of manufacturing industry, the authors have highlighted the key challenges related to the manufacturing context and specifies the functions to be developed. These challenges have been defined according to the nature of the manufacturing data. These characteristics may be common to other domains, so it will be interesting to study the applicability of the solution to other domains in the future. A graph-based query system proposal was presented in this paper with three main functions and four specific functions. A proof of concept has been conducted for 4 of the 7 functions. This proposal responds to key challenges by first transforming the syntactic specificities of the data into a graphical data model, by extending the query terms to semantically close terms, by detecting and transforming the implicit links between the data into explicit links, and finally by classifying the results according to their relevance. It is therefore necessary to develop the integration of the remaining functions in order to complete the evaluation of the proposal. In addition to this work, some topics can be discussed. The user rights management is an important security issue. Indeed, unifying multiple data sources, the system integrates a variety of heterogeneous rights matrices, particularly in the extended enterprise context. The main orientation is then the creation of a specific rights management to the query system. This right management required the same complexity as the existing one, which is a greatest remaining challenge.

Beyond the management of user rights, the user profile information (who, what profession, with what history of use) is an important asset to improve the results relevance. One of the questions is whether knowledge graphs by profile or user is needed. If so, its feasibility will have to be assessed while still meeting the requirements.

Updating source data is also a feature to be considered in this proposal. This paper does not present the automation of data extraction from their sources but one orientation was taken in the creation and the update by batch. So the features to be considered are the creation, modification and deletion of nodes and relationships.

Finally, the authors wish to consolidate the detection of implicit links between data. This allows a better follow-up in change management as presented in [START_REF] Mordinyi | Evaluation of NoSQL graph databases for querying and versioning of engineering data in multi-disciplinary engineering environments[END_REF] with graphs and ontology.

Fig. 1 . 1 .

 11 Fig. 1. I-DATAQUEST -Architecture proposal for a manufacturing data query system 1. Heterogeneous data transformation. As in the ETL transformation rules and the spreadsheet-specific transformation rules set out in Part 3, heterogeneous data are transformed to the unified graph data model of 𝐺 𝑑 as shown in Fig. 2. (a) The node represents a document, a relational database record or a table row. (b) The nodes have relationships between them carried by the foreign keys of relational databases. (c) The nodes carry labels with a name and value that represent properties of documents, metadata of relational databases or columns value of a table content. (d) The label 'contents' integrating the textual content of the documents is added to each node concerned. (e) The 'relevance' label including a relevance score is added to each node.

Fig. 2 . 2 .

 22 Fig. 2. Transformation of heterogeneous data to the graph data model 2. Data enrichment. Implicit links between nodes are added to 𝐺 𝑑 . In line with the record linkage domain, these relationships are detected if a main label value (e.g. title, reference, name etc.) of a node is mentioned in a label of a node B. The weighting of this relationship is added according to the presence of versioning label values (e.g. version, revision, maturity etc.) of node A in the labels of node B. 3. Relevance return. As in popularity ranking methods for websites, when the user selects a query result, the value of the label 'relevance score' of the associated node in 𝐺 𝑑 is increased. 4. Query 𝑄 integration. The query 𝑄 integration is carried out by a graphical user interface represented in Fig. 1. The user expresses his need for information in two parts: 𝑄 = 𝑄 𝑤 • 𝑄 𝑎 with 𝑄 𝑤 terms representing the information type sought ('what') and 𝑄 𝑎 terms contained in the information sought ('about what'). In addition to the 'about what' field, the use of the 'what' field allows searching for the value of a specific node label (for example the search for the 'price' label of a node whose title is 'battery' is thus allowed when 𝑄 𝑤 = ′𝑝𝑟𝑖𝑐𝑒′ and 𝑄 𝑎 = ′𝑏𝑎𝑡𝑡𝑒𝑟𝑦′). 5. Transformation of the query 𝑄 to 𝑄′. The 𝑄 query is translated into the query lan-guage adapted to the graph database and it is adapted according to the values of 𝑄 𝑤 and 𝑄 𝑎 . For example, if 𝑄 𝑤 𝑖𝑠 𝑛𝑜𝑡 𝑛𝑢𝑙𝑙, 𝑄′ will integrate the query of all named or approximately named 𝑄 𝑤 and return the values as results. In addition, 𝑄′ will query all textual content and return specific sentences based on the terms of 𝑄 and using natural language processing algorithms. For example, in a requirement search query, it is then possible to search for all sentences expressing a requirement because they contain specific verbs and modals as 'require', 'must' etc. The query is also divided into several sub-queries to evaluate the ranking of the results. For example, the subquery querying only the labels named 'title' will return results of high relevance.

Table 1 .

 1 Related work evaluation according to the expected functions.

	References	Function A	Function B	Function C	Function D Rank
		Process syntax spe-	Search by Se-	Detect implicit	the results in rel-
		cifics of data	mantic Proximity	links between data	evance order
	[4]

Table 3 .

 3 Partial evaluation of the proposal

	Stage	Response time (s)	Precision	Recall
	First step : Only metadata	25	1	0.01
	Second step : With function A	79	0.60	0.45

https://neo4j.com/developer/neo4j-etl/

https://tika.apache.org

https://opensource.google/projects/tesseract

https://neo4j.com

https://py2neo.org/v4

https://plot.ly/dash/


Lise Kim
email: lise.kim@ensam.eu

Esma Yahia

Frédéric Segonds

Philippe Veron

Victor Fau

Essential issues to consider for a manufacturing data query system based on graph

Keywords:

Manufacturing industry data are distributed, heterogeneous and numerous, resulting in different challenges including the fast, exhaustive and relevant querying of data. In order to provide an innovative answer to this challenge, the authors consider an information retrieval system based on a graph database. In this paper, the authors focus on determining the essential functions to consider in this context. The authors define a three-step methodology using root causes analysis and resolution. This methodology is then applied to a data set and queries representative of an industrial use case. As a result, the authors list four major issues to consider and discuss their potential resolutions.

Introduction

The volume of data generated by the manufacturing industry is large and increasing; it represents 3.6 EB in 2018 and will increase by 30% for 2025 [START_REF] Reinsel | The Digitization of the World From Edge to Core[END_REF]. The organization of companies in silos (justified by the need for specialization of the different business) generates data that is both distributed and heterogeneous. A part of data is managed by different information system (PDM, ERP, MES…) and generate structured data, while the other data are unstructured data (text, image, 3D …). In addition, the data can be explicitly linked to each other (like in the parent-child relations of a digital mock-up) or implicitly linked (like between the 3D of a component and its user manual).

To perform their work, employees have to query the data in order to retrieve the needed information. This task becomes complicated and time consuming due to the increasing volume of data, which are heterogeneous and are saved in distributed resources. To solve these issues, it is necessary to define a data querying system that deliver exhaustive and relevant data as fast as possible.

To address this challenge, the authors worked to draw up the list of bare minimum issues to consider when defining the optimal framework. This paper is organized as follows: section 2 defines the main orientations chosen based on a stateof-the-art analysis. Section 3 describes the methodology used to draw up the list of issues. Section 4 describes the experimental conditions and presents the results. Section 5 concludes with discussion.

Graph database consideration

Querying information can be achieved through Information Retrieval Systems that need to access to data in order to provide the most relevant one. This objective is reached by managing the data in NoSQL databases rather than traditional relational databases, as the former is faster, more efficient and flexible [START_REF] Poriya | Type of NOSQL Databases and its Comparison with Relational Databases[END_REF]. The main categories of NoSQL like column database, key-value store and documentoriented database includes indexing and quick access to the information but lack expressing of the relationships between data in their schema. The graph databases answer to this issue and consequently are the more suitable in our context.

To emphasize the benefit of the graph database, different researches have shown the importance of analyzing data with strong relational nature as in [START_REF] Miller | Graph database applications and concepts with Neo4j[END_REF], applied in different manufacturing use cases as in [START_REF] Schalbus | Spatially-linked manufacturing data to support data analysis[END_REF]. Other works define a framework to allow data querying by transforming structured data [5] and unstructured data [6] into a graph, with enrichment by data linkage [6] with possible using ontologies for example in [START_REF] Mordinyi | Evaluation of NoSQL graph databases for querying and versioning of engineering data in multi-disciplinary engineering environments[END_REF]. In this article, the authors aim to define the prerequisites for a manufacturing query-data system by answering this question : "What are the minimum issues to be taken into account for a querying manufacturing data system based on the graph database?"

Methodology

In order to define only the bare minimum issues to consider when defining the query system, an iterative method has been implemented. This method is detailed below:

(1) Integration of data into a graph database. The data includes the minimum of information at initialisation (only metadata without text content). Metadata means all the properties carried by unstructured data and all metadata carried by structured data. Thus, each data is transformed into a node and each metadata integrates the properties of this node. On the other hand, the explicit relationships of relational databases are translated into relations between nodes (see Figure 1.).

(2) Application of queries to the graph database, here refers to the translation of the user query adapted to the graph. Query transformation includes, in particular, the path of relations between data (e.g. : query = employees related to 'additive manufacturing' become finds the nodes mentioning 'additive manufacturing' and linked to nodes carrying employee information and return the employee information) and the search for either a list of data (e.g.: query = battery) or a specific element within a data (e.g.: query = price of battery).

The notion of an element is translated by the search for the associated property (value of the property 'price') and the sentences identifying the element ("the price of battery is […]"). Natural Language Processing (NLP) [START_REF] Chowdhury | Natural language processing[END_REF] tools will be used here to find the sentences. (3) The evaluation of the proposal is conducted based on three requirements that are the response time (between the submission of the query and the result display), the completeness and the relevance of result (using precision 1 and recall 2 measures). The latter are calculated based on the expected results that are manually defined. When the results are below the accepted limits, the analysis of each error is then made (excess or missing data and too long execution data) in order to detect the root causes based on the Ishikawa diagram method 3 [9]). A score is then established by root cause according to its impact on the results (calculated with the number of errors associated with this root 1 The precision is the number of relevant documents found compared to the total number of documents proposed in the result for a given request. [START_REF] Poriya | Type of NOSQL Databases and its Comparison with Relational Databases[END_REF] The recall is defined by the number of relevant documents found with regard to the number of relevant documents in the database.

3 Method of analysis used to research and to represent the different possible causes of a problem.

Figure 1 -Data set transformation into the graph at initialization

cause over the total number of errors). Once, this list of root causes is identified, it allows to define the main issues to be treated.

Experimentation conditions and results

The study was based on a dataset composed of 686 elements, representing data from a drone manufacturing company, and distributed as following: 47% unstructured data including spreadsheets, videos, photos and textual documents; 22% tree structure data; 17% of data from relational databases and 15% of geometrical data. All these elements represent the data necessary for the development of a mechanical system (from design to prototyping through logistics, purchasing and project management). 19 queries have been written in response to innovative use cases characterized by Capgemini 4 (e.g.: a designer is looking to identify the product requirements or the justification for a product, a manager looking for identify an available team with the right skills, a salesperson looking for a customer's usage parameters, etc.). The expected performance thresholds are less than 1 second for time; this was fixed according to study conclusions on the impact of response latency in web search [START_REF] Arapakis | Impact of Response Latency on User Behavior in Web Search[END_REF]. The tools used are Neo4J 5 for storage and querying in a graph database and Standford CoreNLP 6 for the exploitation of natural language.

These tools are open source and relatively well documented.

After the first cycle of the methodology, the results are insufficient (see Table1). Analysis of the results of this first cycle has shown that more than half of the anomalies are caused by the lack of textual content of the data in the graph database. For example, the search for the battery reference does not give any result because the information is carried by the content of an excel named "Bill of Materials". In order to treat this issue, a second cycle was therefore launched to integrate the text content of unstructured data. The text content is extracted using Apache Tika 7 as a parsing tool (to extract text from a document) and Tesseract 8 as an Optical Character Recognition Tool (to extract text from an image). Then the extracted text is integrated into the graph by adding a property named 'content' to each node.

The results of this second cycle are visible in Table 1 and the list of root causes is listed in Table 2. It is possible to remove the cause (6), only cause of which at least one element of the initial architecture is supposed to be resolved (an optimization of OCR is necessary). The remaining root causes therefore provide the list of the bare minimum issues to be resolved.

Table 2 -Second cycle root causes

Root causes

Anomalies distribution

(1) No highlighting performed on the most relevant result 26%

(2) The information carried by the table format is not used 24%

(3) Information is carried by a term close to the keyword 19%

(4) The property carrying the information is close to the keyword 13%

(5) Searching through the implicit relationships is impossible 9% [START_REF] Groger | The Deep Data Warehouse: Link-based Integration and Enrichment of Warehouse Data and Unstructured Content[END_REF] The OCR algorithm didn't extract the correct characters 7% [START_REF] Mordinyi | Evaluation of NoSQL graph databases for querying and versioning of engineering data in multi-disciplinary engineering environments[END_REF] Extracting bulleted lists extraction is not correct 2%

Discussion

At the end of the second experimental cycle, 7 root causes remain present. The authors propose to classify them into 4 large families. Each one has a potential action plan in order to enhance the response time, recall and precision. The authors propose to prioritise, at first, the actions affecting both precision and recall: (a) Extracting text without format is not enough. The cause [START_REF] Reinsel | The Digitization of the World From Edge to Core[END_REF] indicates that it is necessary to translate the information carried by the table format (rows and column) in order to use it in query. For example, to detect a reference contained in a specific cell of a bill of materials. Cause [START_REF] Mordinyi | Evaluation of NoSQL graph databases for querying and versioning of engineering data in multi-disciplinary engineering environments[END_REF] indicates that bulleted lists processing is necessary for the performance of the chosen NLP tools. The table format and bulleted lists must be transformed to be used. (b) Searching for exact keyword or exact property is not enough. Causes [START_REF] Poriya | Type of NOSQL Databases and its Comparison with Relational Databases[END_REF] and ( 4) indicate that reconciliation between different terms is necessary. For example, if the term 'reference' is used in the query, the term 'Part Number' must also to be searched. The use of a semantic network as an ontology could resolve part of the errors [11]. (c) There is no order by relevance in the results. Cause (3) indicates that unexpected results (but potentially relevant) are displayed in the same way as expected results. For example, searching for the battery reference provides many results with the terms "reference" and "battery" in the content, but these results are far from the information being searched for. pre-labelling of data or additional filtering can be a solution. (d) The implicit links between data must be exploitable. In some cases, related elements such as an element's functional reference and its supplier reference are disjoined in the different enterprise systems. In order to resolve the cause (5), the integration of the implicit relationships between data must be integrated into a graph. The defined actions have a direct impact on increasing the precision and recall requirement and probably have a negative impact on the response time.

In conclusion, the above action list allows considering the essential functions for a query system construction, based on data graph and adapted to manufacturing data. This list was obtained according to the methodology described in section 3, with a heterogeneous, distributed and relational data set and by applying queries in response to expected uses in the manufacturing industry.

4

  Company of digital services in the manufacturing industry.

	5 https://neo4j.com
	6 https://standfordnlp.github.io/CoreNLP/
	7 https://tika.apache.org/
	8 https://opensource.google/projects/tesseract

Table 1 -

 1 First and second cycles results


Kenza Amzil
email: kenza.amzil@ensam.eu

Esma Yahia

Nathalie Klement

Lionel Roucoules

Causality learning approach for

Keywords: Industry 4.0, monitoring and supervision, key performance indicators, causality, artificial intelligence, machine learning, decision support

Introduction

Over the last decades, the industrial world has known a wide emergence of Information Technologies that have led to a convergence towards a new industrial revolution commonly called Industry 4.0. This latter aims at exploiting the growing technologies as a backbone to integrate objects, humans, machines, and processes [START_REF] Schumacher | A Maturity Model for Assessing Industry 4.0 Readiness and Maturity of Manufacturing Enterprises[END_REF], in order to better overtop customers' requirements increasingly stringent about costs, quality and deadlines. All of this requires making right decisions at the right moment. Thus, the three following features should be considered [START_REF] Wang | Implementing Smart Factory of Industrie 4.0: An Outlook[END_REF]: (i) horizontal integration, which aims to optimize the value chain by connecting it beyond the company's perimeter; (ii) vertical integration of systems and subsystems, with production management tools through hierarchical levels, (iii) end-to-end integration of engineering across the value chain. The main enablers of vertical integration are real time monitoring and supervision [START_REF] Silva | IDARTS -Towards intelligent data analysis and real-time supervision for industry 4.0[END_REF]. Monitoring is achieved by collecting data to inform about the systems' current state, and does not have any direct action on decision making, while supervision must provide functions that may affect the conduct of the monitored system, such as parameterization, re-planning, or optimization, based on the current state [START_REF] Combacau | Supervision and monitoring of production systems[END_REF]. Supervision must also be able to recognize and report abnormal situations, so that stakeholders can take well-founded decisions. Also, deviations should be detected preferably before they happen, so that actions can be taken on the factors that have caused it. In this context, KPIs serve as a strong monitoring mean [START_REF] Yin | Improved PLS Focused on Key-Performance-Indicator-Related Fault Diagnosis[END_REF] that quantifies processes and engaged action effectiveness [START_REF] Neely | Performance measurement system design: A literature review and research agenda[END_REF].

The purpose of this paper is to provide an approach to conduct prediction and diagnosis in order to detect abnormal situations and identify their causes. For this, the focus will be on analyzing KPIs' values, by exhaustively identifying and prioritizing the root factors that affect them. Significant researches [START_REF] Moeuf | The industrial management of SMEs in the era of Industry 4.0[END_REF][START_REF] Pérez-Álvarez | Tactical business-processdecision support based on KPIs monitoring and validation[END_REF][START_REF] Georgakopoulos | Internet of Things and edge cloud computing roadmap for manufacturing[END_REF][START_REF] Nudurupati | Performance measurement in the construction industry: an action case investigating manufacturing methodologies[END_REF] confirm that the analysis of KPIs' values, and the identification of their influencing factors, often performed by experts in an empirical and descriptive way, do not allow exhaustive and exact identification of all direct and indirect causes of each KPI deviation. These empirical analyses conducted by following some specific problem solving approaches, may omit many factors that affect the investigated KPI, and mutual influence between the identified factors may not be noticed. Hence, this kind of analysis remains subjective and only represents the known part of reality, often leaving a hidden part we totally ignore [START_REF] Belis | Causalité, propension, probabilité[END_REF]. Besides, KPIs may change over time and have new influencing factors. These reflections have led us to make our hypothesis, which is to take in consideration all available data, since experts may omit certain factors, mistakenly judging them as being uninvolved in the evolution of the KPIs' values. Thus, we propose to build a causal learning approach in order to identify and prioritize influencing factors. This approach is based on the strong assumption of collecting data from as many sources as possible, including physical world and information systems, by instrumenting as much as we can the systems to be monitored, as well as their environments, so that our analysis can exhaustively highlight all the leading causes among this data. The proposed approach can be applied in the production context as well as in other engineering contexts.

The rest of this article is organized as follows. In section 2, we describe the global approach of the proposal, focusing on data analysis. Section 3 summarizes a use case and discuss the first results. Conclusion and future work are given in section 4.

Methodology of the proposal

The goal of the methodology is to be able to identify all the affecting factors of a given KPI, and to prioritize them in order to provide decision support by identifying actions which are more relevant to engage for improving the KPI value. These actions will have a more pronounced added value if they are taken before deviation occurs, hence the interest in predicting the KPI's values. The diagram shown in Fig. 1 describes the bricks that make up data analysis that will lead us to our goal.

(i) Causal analysis based on Bayesian Networks (BN), which aims at identifying the factors affecting the addressed KPI. The BN form a class of multivariate statistical models that has become popular as an analytical framework in causal studies, where causal relations are encoded by the structure of the network [START_REF] Beinlich | The ALARM Monitoring System: A Case Study With Two Probabilistics Inference Techniques for Belief Networks[END_REF][START_REF] Pearl | Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference[END_REF][START_REF] Ellis | Learning causal Bayesian network structures from experimental data[END_REF]. However, the construction of the BN's structure is itself based on the experts' a priori knowledge. To cope with this, several algorithms exist to learn the structure [START_REF] Niculescu | Bayesian network learning with parameter constraints[END_REF] (constraint based algorithms, and score based algorithms), and to compute the structure's associated conditional probabilities. (ii) Prediction: in order to anticipate actions to be taken on the factors identified by the causal analysis, the KPI value should be predicted and, if any deviation is detected, actions are engaged at the right time. In our case, this prediction is made possible by means of Artificial Neural Networks (ANN). ANN are used to solve complex problems and enable learning and modeling nonlinear and complex relationships between inputs and outputs. (iii) ANN parameters' definition: in order to predict one given KPI, the optimal structure of the ANN must be defined and must meet a reasonable computing time with good prediction results. For our case, a multilayer perceptron ANN is used, and for having a good compromise computing time/prediction accuracy, the authors followed, for one single KPI, an experimental approach to adjust the ANN's parameters (e.g. number of layers, learning rate, etc.). Since many KPIs need to be predicted, an optimal ANN structure needs to be defined for each KPI, thus, we need to provide greater genericity to our proposal in order to avoid following the same long experimental approach for each single KPI prediction ANN structure. For this, the authors suggest, in this brick, to adjust the ANN parameters using an optimization algorithm, so that optimal ANN for any KPI prediction can easily be generated. (iv) Prioritization of the impacting factors: causal analysis provides us with the existing causality links between the factors and the addressed KPI, and mutual influences between the factors themselves so that we can go through the causality links until the root cause. In case of deviation, it would be wise to prioritize the impacting factors identified in (i). For this issue, weights of the used ANN are employed, since the weights represent the strength of connections between units of the ANN, and highlight the degrees of importance of the values of inputs [START_REF] Han | Learning both weights and connections for efficient neural networks[END_REF]. (v) Decision support: given the outputs of precedent steps, a decision support can be provided in case of deviation to adjust the implicated factors by priority order.

Use case and results

To implement the proposed methodology of data analysis, the authors have constructed a representative summary dataset to validate that the experiments are correct. This dataset respects, in a very flexible way, a certain amount of causality rules that have been previously defined to be compared with the resulting causality links.

The use case addresses one KPI: the production cycle time. The rest of the dataset is made of variables that may affect, or not, the addressed KPI: the day of the week, the time slot, the month, the indoor temperature, the operator's heart rate, his stress level, the defaults number, and the training level. The goal is to identify, among this dataset, variables that affect the production cycle time, and to prioritize them. To build a realistic and more relevant use case, the authors have made sure that the dataset does not follow these rules in an exclusive way. Basically, this KPI is calculated using two information: the remaining time for production, and the number of produced units. Given this, if deviation is detected, both information do not give answers neither to understand how did this happen nor to trace back to root causes. The above-presented approach was applied to this use case. (i) Causality analysis: we used a constraint based algorithm (Peter and Clarck (PC) algorithm) to define the structure of the BN that will allow identifying the causal links. PC algorithm is a constrained based algorithm that begins with a complete undirected graph, and removes the edges between pairs which are not statistically significantly related by performing conditional independence (CI) tests, then it looks for the V-structures and directs the edges using two other rules (see [START_REF] Tsagris | M Bayesian Network Learning with the PC Algorithm: An Improved and Correct Variation[END_REF] for more information). This algorithm was modified by adding one more constraint, in order to avoid having meaningless causality links (e.g. defaults that may cause day change is a meaningless link). The steps of this constraint verification are: (1) identify and define variables that can not be changed (e.g. the current hour or day), and (2), remove the edges which go to the nodes representing these variables. The final resulting graph corresponds to the starting assumptions (Fig 2 .a), but does not show a causality link between temperature and cycle time, even if the data was constructed assuming that. (ii) Prediction and (iii) ANN parameters' definition: the KPI prediction was implemented using a multilayer perceptron ANN, with a K-fold cross validation. The predicted value is either 1 or 0 according to whether or not the cycle time will deviate or not, the prediction is 92% accurate (Fig 2 .b). The ANN that gave us these predictions is made up of 5 hidden layers. This ANN's parameters were found using an experimental approach, since the parameters' optimization algorithm is still being under development. Concerning (iv) the impacting factors prioritization, ANN's weights used for the prediction were employed to give a ranking of all available factors, and the ranking corresponds to the starting assumptions. Fig. 2.c shows that we obtain the same prioritization even if the prediction models' structures are different (conditioned on the fact that they have a predictive power upper than 85% in our case). The figure shows three lists, all with the same nodes ranking (4-0-3-1-2-5-6). To prove that this ranking is consistent, we have created a new dataset with the same rules and assumptions as the first one. First, we have used this dataset to test our prediction model; the resulting prediction accuracy was 89%. Then, we have replicated the same dataset five times, and each time, we changed the values of one influencing variable individually (day (1), temperature (3), stress [START_REF] Combacau | Supervision and monitoring of production systems[END_REF], training [START_REF] Moeuf | The industrial management of SMEs in the era of Industry 4.0[END_REF], or defaults (6)), to evaluate the impact of each of these influencing variables. Each time, we replaced one variable (e.g. stress) by random values in the same range of variation as the initial values, letting the other variables as they were. Then, we predicted our KPI with the new dataset, using the same model that we have previously built, then we evaluated the prediction. We predicted 0: time slot 1: day 2: month 3: temperature 4: stress 5: heart rate 6: defaults 7: training five times, in addition to the first prediction, in order to see the impact of each of the five influencing variables. Finally, we compared the performances of each of the five predictions that have been run, by superimposing their receiver operating characteristic (ROC) curves, and we evaluated the performance of each prediction by calculating the area under the curve (Fig. 3.a). We can see that the curves reflect the ranking, and that the ranking of the areas under the curves corresponds to the ranking of the variables in the obtained list. Fig. 3.b shows the results obtained by repeating the same operation, but this time, instead of replacing the concerned variable values by random values in their range of variation, the concerned variable was treated as if its values were missing, and replaced the initial values with their mean, then we predicted the KPI. We have repeated the same operation for the five variables. ROC curves are obviously different from the ones in Fig3.a, but the ranking is the same. To better see the gaps between the curves, we only represented the four curves that do not intersect in Fig. 3.b, from where we can easily see the gaps between the prediction qualities even without calculating the areas under the curves.

Conclusion and future work

In this paper, we presented a causality learning approach for KPI supervision. The main idea was to collect as much data as possible in order to conduct an exhaustive data analysis. This analysis is based on BN structure learning, KPI prediction using ANN, and influencing factors prioritization. The proposal is actually in its early phases of development and many aspects need to be addressed, like the test and benchmarking of other algorithms and tools of learning BN structure. Moreover, we should enrich our causality learning with results of decisions taken by considering the impacting factors and their ranking proposed by the supervision system, to see if the KPI is evolving in the right sense, and hence to validate the analysis robustness. Also, a complete use case should be implemented using real industrial data to validate the proposed methodology performance beyond the constructed use case.

Fig. 1 .

 1 Fig. 1. SADT diagram representing the functions of the data analysis.

Fig. 2 .

 2 Fig. 2. Results: (a) causal graph, (b) prediction results, (c) factors prioritization.

Fig. 3 .

 3 Fig. 3. Results: (a) ROC curves by replacing each time one variable by random values in its variation range, (b) ROC curves by replacing each time one variable by its values' mean.


Paolo Cattaneo
email: paolo.cattaneo@cea.fr

Frederic Damian

Jean-Charles Le Pallec

Elsa Merle

Didier Schneider

000254 Development of a multiphysics Best-Estimate approach for LWR reference calculation

Keywords: LWR Multiphysics, Best-estimate, APOLLO3®, CORPUS, FLICA4

The aim of the work presented here is to produce a best-estimate multiphysics calculation scheme to predict the power distribution at a fine scale for steady-state conditions. By best-estimate, it is meant that several modelling options are explored in order to find the best trade-off between quality of the results and computing time. In respect of the multiphysics, the simulation should simultaneously take into consideration neutronics, thermal-hydraulics and thermal-mechanics. The test case selected for the analysis is a 3D cluster of 5x5 PWR fuel assemblies, all of 4% enriched UO2, but at different burnups. Two reflector isotopic compositions are considered, 50% water, 50% stainless steel on one side, and 5% water, 95% stainless steel on the others. Neutronics simulations are done at the pin cell level, following the classical two-steps approach (fuel assembly calculation in fundamental mode and fuel 3D core calculation using Diffusion, SPN or SN resolution). Discrete Ordinates of order 8 (S8) at 30 energy groups is used as reference neutronics method. Its results are compared with S8 at 20 energy groups, Simplified Spherical Harmonics of order 3 (SP3) at 8 energy groups and 2 groups diffusion calculations. Thermal-hydraulics is simulated with a 3D four equations model at the quarter of assembly level. 1D heat conduction is solved for an average fuel rod per quarter of assembly. For both analyses (isothermal and coupled calculations), the SP3 with 8 groups predicts the power distribution within a relative error within a root mean square of 0.45% over the entire core, lasting 1.65% of the computing time. This performance makes it the best-estimate calculation scheme, within the considered study context. Moreover, the analysis shows that the composition of the reflector, which strongly affects the power distribution, has no impact on the results produced by the SP3 solver compared to the reference solution.

Introduction

The objective of the work presented in this paper is to develop a multiphysics calculation scheme able to predict a set of local parameters (including power distribution, fuel temperature and critical heat flux) of a PWR reactor during start-up and operation (steady state) with a high level of accuracy. The calculation scheme will follow the best-estimate approach, as targeted by the authors. In other words, the scheme should optimize the time factor while guarantying the quality of the estimation of targeted variables. In the development process of such calculation scheme, a dedicated part is devoted to the development of a reference calculation scheme that will be used to evaluate the modelling assumptions adopted in the best-estimate approach.

It is here reported the first step toward the objective of this work: the implementation of a steady-state calculation scheme capable of calculating a set of local parameters of a mini-core (including power distribution). The considered application is composed of 5x5 PWR assemblies surrounded by a reflector layer, top and bottom reflectors being included as well. The assembly's dimensions are representative of a PWR. Two different isotopic compositions are considered for the radial reflector in order to evaluate the impact of the leakage on calculation scheme adopted: 95% of stainless steel, 5% (heavy reflector) water and 50% stainless steel, 50% water (standard reflector). The fuel assemblies are loaded with 4% enriched uranium, but the burnup map follows a chessboard-like configuration with values 0 or 15 MWd/kg (the corners are at 15 MWd/kg, see Fig. 1). The central assembly is at 30 MWd/kg. The choice of the problem's size results from the trade-off between representativeness and computation time, considering that a systematic study will be carried out. Moreover, the small dimension of the core entails a power distribution more peaked than in standard PWR. At constant average linear power, a higher power form factor corresponds to a higher maximum linear power and a stronger multiphysics coupling, in the sense that variables are more linked to each other. Since several years, the fine multiphysics modelling is a growing priority for many nuclear research teams. Some examples of the state of the art are available in [START_REF] Turner | The virtual environment for reactor applications (VERA): design and architecture[END_REF][START_REF] Jung | Practical numerical reactor employing direct whole core neutron transport and subchannel thermal/hydraulic solvers[END_REF]. In this context, CEA develops the multiphysics tool CORPUS [START_REF] Le Pallec | Neutronics/Fuel Thermomecanics coupling in the Framework of a REA (Rod Ejection Accident) Transient Scenario Calculation[END_REF] based on the SALOME platform [4]. The main CORPUS ambition is to develop and maintain a set of best-estimate calculation schemes for different operating/accidental situations in the framework of complete scenarios analysis. CORPUS gathers several independent codes and provides tools to help data exchanges among them. The neutronics code used for the calculation scheme is APOLLO3® [START_REF] Schneider | APOLLO3®: CEA/DEN deterministic multi-purpose code for reactor physics analysis[END_REF], the deterministic multi-purpose code, able to perform both lattice and core calculations. It also includes a 1D, four equations thermal-hydraulics model, which is also capable of solving for the heat conduction in the fuel [START_REF] Patricot | THEDI: a multi-1D two-phase flow solver for neutronic codes[END_REF]. With respect to the thermal-hydraulics, the dedicated tool in CORPUS is FLICA4 [START_REF] Toumi | FLICA4: a three dimensional two-phase flow computer code with advanced numerical methods for nuclear applications[END_REF], which offers a 3D, four equations model. This work starts with a comparison among several neutronics models, at constant fuel temperature, moderator density and boron concentration. It follows the analysis of the impact of the two reflector compositions on the power distribution. Then, the obtained coupling scheme is described and its impact on reactivity and power distribution is assessed. The neutronics solvers are compared again, being coupled to a given thermal-hydraulics model in order to find the best-estimate scheme in terms of quality of local power prediction. Finally, the sensitivity of the coupling scheme results to the reflectors composition is assessed with comparisons to the reference multiphysics scheme.

Comparison of various neutronics models using fixed thermodynamic parameters

By fixed thermodynamic parameters, it is meant that the core conditions are known a priori, hence they might not be coherent with the actual power distribution. Instead of having iterations among solvers exchanging field of variables until convergence, fixed parameters are imposed and only neutronics is considered, as it is represented in Fig. 2. Even if APOLLO3® offers the possibility to perform direct 3D calculations (single-step) [START_REF] Santandrea | Accelerated polynomial axial expansions for full 3D neutron transport MOC in the APOLLO3® code system as applied to the ASTRID fast breeder reactor[END_REF], in order to ensure the scalability to bigger domains and the possibility to implement advanced multiphysics iteration schemes, the widely used two steps approach is preferred here. The first step, lattice calculations, deals with a very accurate resolution of a subdomain of the problem (the 2D section of a fuel assembly with simplified boundary conditions) under a set of possible core conditions. The results are synthetized in homogenized and collapsed cross-sections stored in a multi-parametrized library. In this way, the problem dimension is significantly reduced. During the second step, i.e. core calculations, these equivalent cross-sections are used to solve the entire problem (combination of the subdomains) on the 3D configuration. The equivalent cross-sections are produced so that they preserve the reaction rates between the high and the low dimension problems as calculated by the lattice solver. With the super-homogenization equivalence procedure (SPH) [START_REF] Kavenoky | The SPH homogenization method[END_REF], it is possible to store cross-sections reproducing the reference results when used by a specific core solver. Since the neutron energy spectrum in the reflector strongly depends on the surrounding assemblies, for its cross-sections a different approach is used, the 1D traverses technique [START_REF] Sandrin | An analysis of reflector homogenization techniques for full core diffusion calculations[END_REF]. Equivalent reflector cross-sections for a specific solver are obtained preserving the reference albedos at the core-reflector interface.

For the following analysis, cross-section libraries were produced by homogenizing the fuel assembly at the pin cell level and collapsing the number of groups to 2, 8, 20 and 30. For the lattice calculations, the method of characteristics (MOC) [START_REF] Santandrea | A neutron transport characteristics method for 3D axially extruded geometries coupled with a fine group self-shielding environment[END_REF] with 281 energy groups is used in fundamental mode (critical buckling research with the B1 Homogeneous leakage model). These cross-sections are used by several neutronics models from diffusion to SPN and SN. The MINOS solver [START_REF] Baudron | MINOS : A simplified Pn solver for core calculation[END_REF] is used for the first two and the SN is part of the MINARET solver [START_REF] Moller | Minaret, a deterministic neutron transport solver for nuclear core calculations[END_REF]. For every set of cross-sections, the SPH equivalence calculation is performed. The neutronics models are 2 groups diffusion (Diff.-2g), 8 groups Simplified Spherical Harmonics of order 3 (SP3-8g), 20 and 30 groups Discrete Ordinates of order 8 (S8-20g and S8-30g). In addition to these, two groups cross-sections homogenized over the quarter of assembly have been produced for the diffusion solver. The S8 is used with the Discontinuous Galerkin method of order two both radially and axially, while for the SP3 and for the diffusion it is adopted the mixed dual finite element method with Raviart-Thomas basis functions of order two, both radially and axially. The calculation radial mesh is equal to the one used for the homogenization. The calculation axial mesh is constant in the core and it is equal to 0.14224 m, in the top reflector it is 0.13 m and in the bottom one it is 0.09 m. The cross-sections are produced for a set of fuel effective temperatures, moderator densities, boron concentrations and burnups. The reflector is modelled as homogeneous, hence only an energy condensation of the cross-sections is done. Only the 2 groups cross-sections are produced with reference albedos equivalence technique, because this method is shown not to perform well for eight or more energy groups, for the others cross-sections no equivalence is applied. For simplicity and due to their weaker dependence, reflector cross-sections are produced only for nominal conditions.

For the following comparison, the fuel effective temperature, the moderator density and the boron concentration are constant in the core; their values respectively are 655.8 °C, 0.701012 g/cm 3 and 600 ppm. The burnup map is the one described in the introduction (see Fig. 1). The boron concentration could also be considered as a multiphysics parameter, in the sense that the thermal-hydraulics solver might be used also to predict boron transport in the core. In this work, this effect is not taken into account. The compared variables are the reactivity, the 3D power distribution (fuel pin level) and the computation time. The S8-30g is used as reference for the other calculations. The results obtained for the heavy reflector are summarised in Table 1. The SP3-8g predicts the integrated power at the pin cell scale within a root mean square (RMS) of the relative error that is rather satisfying, especially taking into account the much shorter computing time.

S8-30g S8-20g SP3-8g Diff.-2g Diff.-2g (quart) keff [-] 1.
The errors of the Diff.-2g on cell are evaluated on both the pin cell discretization and the quarter of assembly one. For the coarser mesh comparison, an interpolation is done for both the diffusion and the reference results. The discrepancies on the finer mesh are considered too high. Attention should be given to the fact that Diff.-2g with quarter of assembly discretization is compared to the reference only on the coarser mesh, as it is possible to notice on Fig. 3. Even if the diffusion approximation is based on hypotheses that are more valid for coarser meshes, the diffusion on cell produces better results than the one on quarter of assembly. This might be the consequence of the adjustment of cross sections with the SPH equivalence technique. Similar results are obtained for the standard reflector; in that case, the discrepancies are of the same order of magnitude, but slightly higher.

The plots of the power distribution comparison with SP3-8g and 2 groups diffusion on the quarter of assembly are available in Fig. 3. These methods represent the potential best-estimate and the standard approaches. In every comparison, the highest errors are close to the top and bottom reflector. This was rather predictable because no equivalence process has been performed for the reflector cross-sections, except for both 2 groups diffusion cross-sections. Furthermore, the neutron flux gradient is the highest close to the reflector, hence a refinement of the calculation axial mesh might be tested. In both comparisons, in terms of solver precision, the SP3-8g is very close to the reference. The results are excellent in the central part of the core and in terms of maximum power prediction. However, since the purpose of this scheme is more general, a better reflector modelling has to be used to improve the results also in its proximity. The overall performance of the SP3-8g makes of it a good candidate for the best-estimate model.

Neutronics calculation sensitivity on the reflector composition

In this section, the S8-30g is used to assess the modelling sensitivity of the two considered radial reflectors. The comparison in terms of reactivity and power distribution parameters are shown in Table 2, for the core parameters specified in the previous section. The difference in multiplication factor is significant, at least for the current configuration. The discrepancies relative to the power distributions are shown in the radial section of the hot spot plane of the core available in Fig. 4. The elevations of the hot-spot for the two reactor configurations coincide.

The radial power profile is considerably flattened in the case of the heavy reflector. The heavy reflector allows to shift the power distribution from the centre to the corners, reducing the maximum power from 462 to 431 W/cm. The only exception is the outermost layer of pin cells at the interface for which the power is higher with the standard reflector (neutrons thermalisation higher due to the different water percentages).

Description of the current coupling scheme

This coupling scheme architecture is developed with the objective of enabling physical modelling (neutronics, thermal-hydraulics and thermal-mechanics) at the appropriate scale. More in details, this scheme focuses on an efficient local power distribution calculation while the coolant properties (densities and temperature) might be estimated at various scale, from sub-channel to coarser scales. As far as the thermal calculation is concerned, local fuel pin temperature is needed to evaluate the heat flux on the cladding. This is a crucial parameter for the safety analysis, because it affects the possibility of having a boiling crisis. Empirical correlations provide a critical heat flux beyond which Departure from Nucleate Boiling (DNB) may occur.

From the numerical point of view, the coupled problem is modelled as a system of non-linear equations.

The thermal-hydraulic and the thermal-mechanic equations are not linear. In the coupling scheme, also the neutronics becomes not linear. Because, the cross-sections depend on the fuel temperature and moderator density, which are affected by the heat source, hence by the neutron flux. The approach used in this work is fixed-point iterations with under-relaxation, a rather standard solution. It consists in successively solving the equations using the most updated variables. The computational cost is sufficiently low for this type of study and the scheme has proven to be stable, therefore the improvement of the numerical scheme is not addressed in the present work.

In Fig. 5, it is schematized how variables are exchanged among the solvers in the considered coupling scheme. FLICA4 is solving both the thermal-mechanics (reduced to heat conduction) and the thermal-hydraulics. In steady state conditions, if the thermal-mechanics model is 1D, a further simplification might be applied. The heat is not accumulating anywhere, so the wall heat flux is automatically defined by the heat source and the geometry. Therefore, the heat conduction can be solved as a post-processing of the thermal-hydraulics. All the results presented in this section are produced using this coupling scheme. With respect to the thermal-hydraulics, the 3D porous modelfour equations of FLICA4 is used. Each fuel assembly is represented using four meshes. The top and the bottom reflectors are modelled. The radial one is not, because its influence on the adjacent assemblies is low and the radial reflector cross-sections are not parametrized in moderator density. A representation of the three different scales adopted for neutronic, thermal-hydraulic and heat conduction calculations is given in Fig. 6. Eight mixing grids are also considered. Closed surfaces are used only at core boundaries, no heat nor mass transfer out of the core are considered. Inlet enthalpy and water mass flux are representative of a standard PWR. One equivalent fuel rod is modelled per each thermal-hydraulic region. Heat conduction is solved with a 1D model, considering the gap heat transfer coefficient to be constant and the fuel conductivity only depending on the temperature. The adopted scale for neutronics allows to calculate the power distribution at the pin cell level with the thermodynamic quantities averaged on the quarter of assembly. The data exchanges and the iteration scheme are managed in the CORPUS SALOME environment. The latter allows prompting the codes, and to get and set fields and variables. SALOME offers a standardized way of storing and recovering meshes and fields, the MED format. Such a tool offers the possibility to persistently store data on a format based on Hierarchical Data Format (HDF) [14], but also to exchange data among solvers directly in memory. Many interpolation tools are available in SALOME. During every iteration, APOLLO3® and FLICA4 need to exchange fields of variables. Apart from the diffusion model, which is on the quarter of assembly discretization, the neutronics is at the pin cell scale, hence interpolation is needed every time a field is exchanged. Effective fuel temperature and density are exchanged as an intensive field, their volume integral over the domain is conserved. The integral power is transferred as an extensive field, the summation over the regions is preserved.

In following sections, this scheme is used to assess the impact of adding the thermal-hydraulic and thermal-mechanic feedback, to find its best-estimate version and evaluating the impact of the reflector composition.

Impact of multiphysics modelling

In this section, the results from the coupling scheme are compared to the ones obtained in the first part using constant parameters. In Fig. 7, it is reported the comparison of the power distributions obtained with the two approaches. In both cases, the neutronics model is the S8-30g. As expected, the coupled scheme finds a power shape whose maximum is shifted from the centre to the bottom of the core due to the higher moderator density. The axial profile is radically changed, especially in the core periphery, where the moderator density and the fuel temperature differ the most from their average values. In terms of radial variation, the coupled solution is quite flatter, as it is also possible to see comparing the radial peaking factors (Pxy) in Tables 4 and1. The total power peaking factor increases from 2.45 to 2.78, causing the maximum linear power increase from 392 to 445 W/cm (the average linear power is 160 W/cm). As it is possible to see in Table 3, in terms of reactivity, all the models agree on a variation around 470 pcm. The temperature and density distribution are compared to the constant values imposed in the previous sections, 655.8 °C, 0.701012 g/cm 3 . The results show that the different coupling schemes agree quite well on the estimation of the impact of multiphysics calculation.

Neutronics solver comparison in the coupling scheme

In this section, analogously to the second one, the neutronics solvers performances are studied, in this case, within the coupling scheme with quarter of assembly thermal-hydraulics model and one average pin per quarter of assembly for the heat conduction. The stand-alone thermal-hydraulics and heat conduction calculations need approximately the same time as the one required by the 2 groups diffusion simulation at the fuel cell scale. Such a proportion is not exactly kept in the coupled calculation, because the two models may converge at different paces.

Table 4 contains the performance analysis of the neutronics solver in the multiphysics calculations. The SP3-8g confirms its excellent performance also in the coupling scheme, the maximum absolute discrepancy with the reference power distribution is equal to 2.34%. As it is possible to see in Fig. 8, the highest errors are still in the proximity of the reflectors were the power is the lowest. In terms of maximum linear power, the SP3-8g is in good agreement with the reference. The shape and the global magnitude of the error on power distribution are comparable to the ones obtained at constant parameters. The overall performance of the SP3-8g makes of it the best-estimate model for this study context.

Calculation scheme sensitivity on reflector composition

The impact of the reflector composition is here assessed with the reference coupling scheme (the one with S8-30g as neutronics model). In Table 5, the results in terms of reactivity and power distribution are shown. The discrepancy on the power distribution is illustrated in Fig. 9, for which the radial section of the core at the hot point is reported. In this case, the maximum discrepancies are not in the plane of the hot point; they are in the top and the bottom regions of the core. However, a significant reduction of the power peak is seen in the hot spot radial section. The hot-spot plane is not exactly at the same elevation for the two core configurations, the one with the standard reflector is around 10 cm lower than the one with the heavy reflector. The global results on the impact of reflector composition are similar to the ones obtained with the isothermal model. The reactivity difference has increased up to 931 pcm. Both the radial power peaking factors have decreased in the coupled calculations. Moreover, the heavy reflector does offer a flatter radial profile and a more reactive core. In terms of maximum linear power, the higher form factor entails 487 W/cm of peak power, so 10% higher than the one corresponding to the heavy reflector.

Conclusion

The objective of this work is to develop a best-estimate multiphysics scheme to predict the local power in steady state conditions. The domain of application is a 3D 5x5 PWR mini-core, with a layer of radial reflector and top and bottom reflectors. Two isotopic compositions are considered for the radial reflector, the water-stainless steel mixture is either 50% and 50% (standard reflector) or 5% and 95% (heavy reflector).

In a preliminary comparison of neutronics solvers at isothermal conditions, the SP3 with 8 energy groups has emerged as the best compromise between precision and calculation time. The standard deviation of the relative error on the power profile, in comparison to the S8 with 30 energy groups, is of 0.63% over the fuel pin cell. The computing time is only 3.7% of the reference one. The radial reflector isotopic composition has proven to significantly change the radial power shape, yielding a flatter power distribution: the standard reflector power radial peaking factor is 2.12593, as compared to the heavy one of 1.98359. Moreover, the heavy reflector core is 756 pcm more reactive. However, the discrepancies identified using SP3-8g modelling are not amplified when changing the type of reflector.

In the second part, a multiphysics coupling scheme is built; several neutronics solvers, modelling the reactor at the fuel pin cell scale, are coupled with a thermal-hydraulics 3D four-equation model with a quarter of assembly discretization. The 1D heat conduction is solved for one average pin per quarter of assembly. The local power is predicted using thermodynamic variables averaged on the quarter of fuel assembly. The comparison between the constant parameters model and the coupled calculation point out the importance of coupled calculations. The different schemes show good agreement on the assessment of the impact of the other physics on neutronics.

In the coupled scheme, the comparison among the neutronics solvers underlines again the excellent performance of the SP3 with 8 energy groups. Using again the S8-30g model as reference, the root mean square of the relative error of the power distribution of the SP3-8g solver is found to be 0.45% over the fuel pin cell and the relative error on the maximum linear power is 0.07%. The computing time is only the 1.65% of the reference. The multiphysics assessment of the reflector composition impact leads to results coherent with the neutronics modelling. The radial power peaking factor for the heavy and the standard reflectors are respectively 1.87782 and 1.98945. The reactivity difference has increased up to 931 pcm. The maximum linear power with standard reflector is 10% higher, 487 W/cm.

After examining the performance of the SP3-8 g in the coupling scheme, it is considered to be bestestimate model, at least for this context of study.

In order to achieve higher performance and to be able to model bigger domains it is planned to test more advanced numerical algorithm. In addition, it is expected to explore coupling schemes with thermal-hydraulics and thermal-mechanics on finer scales.

Figure 1 :

 1 Figure 1: Burnup map at beginning of cycle. Values for the burnup of the fuel assembly in MWd/kg.

Figure 2 :

 2 Figure 2: Schematization of a generic reactor physics coupling scheme (left), in contrast to the neutronics at constant parameters (right).

ICAPP 2019 -

 2019 International Congress on Advances in Nuclear Power Plants France, Juan-les-pins -2019, May 12 │15

Figure 3 :

 3 Figure 3: Relative difference of the power distributions on the reactor core (reflector excluded). On the left SP3-8g vs S8-30g, on the right 2 groups diffusion (with quarter of assembly discretization) vs S8-30g.

ICAPP 2019 - 97 Table 2 :

 2019972 International Congress on Advances in Nuclear Power Plants France, Juan-les-pins -2019, May 12 abs((PHEAVY-PSTD)/PSTD))]core [%] 34.72 [RMS(ΔP/P))]core [%] 8.Neutronics parameters showing the sensitivity to the reflector composition: multiplication factor, reactivity difference, radial power peaking factor and distribution parameters of the relative power discrepancy.

Figure 4 :

 4 Figure 4: Relative difference of the power distributions in the core (reflector excluded), between the two reflector compositions. Northeast quarter of the radial section of the hot-spot plane of the core.

Figure 5 :

 5 Figure 5: Map of data exchange in the coupling scheme. As a first step, FLICA4 is solving both the thermal-hydraulics and the thermal-mechanics.

Figure 6 :

 6 Figure 6: Refinement level of each physics. For the thermal-mechanics one average fuel pin per quarter of assembly is represented.

Figure 7 :

 7 Figure 7: Axial cuts of the power distributions, on the left at constant parameters, in the centre as converged in the coupling scheme (reflector included). On the right, the 3D relative difference between the two cases (reflector excluded).

Table 4 :

 4 Performance assessment of neutronics solvers in the coupling scheme: multiplication factor, reactivity difference, maximum absolute value and root mean square of the relative errors on the power, radial power peaking factor, computing times ratio. Values in parentheses result from a comparison on the quarter of assembly. S8 calculations are performed with twenty processors, the others with only one.

Figure 8 :

 8 Figure 8: Relative difference between the power distributions on the reactor core (reflector excluded), as predicted by the coupled calculations. On the left SP3-8g vs S8-30g, on the right 2 groups diffusion with quarter of assembly discretization vs S8-30g.

Figure 9 :

 9 Figure 9: Relative difference of the power distributions in the core (reflector excluded), between the two reflector compositions. Northeast quart of the radial section of the hot-spot plane of the core.

Table 1 :

 1

		19746	1.19668	1.19670	1.19445	1.19415
	Δρ [pcm]	-	-54	-53	-210	-231
	[max(abs(ΔP/P))]core [%]	-	0.93	2.76	8.17 (3.54)	(4.19)
	[RMS(ΔP/P))]core [%]	-	0.16	0.63	1.26 (1.07)	(1.18)
	Fxy [-]	1.98359	1.98571	1.98380	1.96356 (1.61758)	(1.62164)
	q'MAX [W/cm]	431.06	431.53	432.34	427.72 (391.28)	(390.53)
	ti/tref [%]	100	63	3.7	0.1	0.001

Performance assessment of neutronics solvers: multiplication factor, reactivity difference, maximum absolute value and root mean square (RMS) of the relative errors on the power, radial power peaking factor, computing times ratio. The values in parentheses result from a comparison on the quarter of assembly. S8 calculations are performed with twenty processors, the others with only one.

Table 3 : Comparison of global parameters between the constant parameters and the coupled simulations: reactivity difference, distribution parameters of fuel temperature and moderator density discrepancies.

 3

ICAPP 2019 -International Congress on Advances in Nuclear Power Plants

  France, Juan-les-pins -2019, May 12 │15

		Heavy Reflector	Standard Reflector
	keff [-]	1.19073	1.17768
	ρHEAVY-ρSTD [pcm]		931
	Fxy [-]	1.87782	1.98945
	q'MAX [W/cm]	445.39	487.36
	[max(abs((PHEAVY-PSTD)/PSTD))]core [%]		41.99
	[RMS(ΔP/P))]core [%]		9.99

Table 5 : Neutronics parameters showing the impact of the reflector composition.

 5

Acknowledgment

Thanks to Roland Lenain and Cyril Patricot for their valuable help.