Thierry Bouche
email: thierry.bouche@ujf-grenoble.fr

Claude Goutorbe
email: claude.goutorbe@ujf-grenoble.fr

Jean-Paul Jorda
email: jean-paul.jorda@edpsciences.org

Michael Jost

The EuDML metadata schema, version 1.0

Keywords: EuDML project, metadata schema, XML, interoperability

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

Introduction

The EuDML project

The EuDML project aims to design and build a collaborative digital library service that will collate the mathematical content brought by 11 of its partners and make it accessible from a single platform, tightly integrated with relevant infrastructures such as Zentralblatt MATH. As such, it is the first attempt toward a large-scale international implementation of a Digital Mathematics Library (DML), and is expected to pave the way towards a truly inclusive and global DML. In this direction, we will try to accommodate new associated partners and to interoperate with relevant infrastructures in the fields of scientific information. Interoperability needs published and documented standards, which is one of the tasks undertaken by EuDML's third work package.

Why a EuDML schema?

A public well-specified EuDML schema is needed:

1. Because content providers need to know which metadata they should expose to EuDML harvesters, which details and granularity is required (obligatory metadata), appreciated (fundamental metadata), and which further enhancements are expected to provide added value to their cooperation with the EuDML project (supplemental metadata). Thanks to the specification, they can see what information is wanted by EuDML. They can expose their holdings directly encoded in this way, or they can expose their "richest" format which contains all the relevant information to the extent possible. 2. Because the search engine has to know where to look for, e.g., an author when a user searches for an author. (Search for "Hilbert" as author must produce quite different results than searching for "Hilbert" as free text or within the whole record of a given item, think of "Hilbert space", "Hilbert transform", which can appear as key words, in titles, cited titles, etc.). The schema serves as a pivot norm for various provider formats and schemas. 3. Because the search engine has to know what to display when showing search result lists (Author, Title, bibliographic source, link to full text. . . ) as well as how to display complex structures (multilingual information, reference lists, mathematical formulae. . . ). It has thus to know how they are encoded in order to present them in the best shape for a given user in a given environment. 4. Because metadata enhancers toolsets have to work on a defined basis so that they know what they start from and where they store their results. Some examples: reference citation matching, duplicate detection and records merging or metadata enrichment from various sources. More specifically to our corpus: a metadata enhancer should be able to scan an existing metadata record to find, for instance, a reference to a formula, generate a new format for this formula (e.g., by OCR or translation to MathML from L A T E X code), and to store the resulting object in parallel to the pre-existing one(s). 5. Finally, EuDML must be able to export its content in a predictable, reusable way, for safety backups, interoperability, and to enable content providers to retrieve the EuDML-enhanced metadata for their collection of items, in order to improve their local collections to a higher level of quality. They need to know how this new information will be encoded so that they can use it. This cannot be done with their internal format, as many added-value elements will be beyond the scope of such format.

A metadata model for EuDML

This paper presents the first specification of the EuDML metadata schema, which is already used by the current prototype of the system. Its main goals are to:

-provide details on the structure, granularity, and encodings that should be supported by content partners (see § 2); -provide incentive to more content providers to contribute their best metadata to the EuDML central metadata repository using adequate schemas and interoperability devices (see § 2.5 and § 3.5); -present the NLM Journal Archiving and Interchange Tag Suite (JATS) as the general frame adopted to encode and exchange the EuDML metadata and list the changes needed in order to support all content types contributed to EuDML (see § 3); -introduce a set of best practices to ensure perfect understanding of tagging practice among EuDML partners (see § 4); -outline directions for improvements (see § 5).

Methodology & Definitions

This section describes the principles, methods and notions that are used to define the EuDML metadata schema in the next sections. As this document, and these specifications, will be revised during the EuDML project, we also describe how this further development might be carried out.

Scope of this work

Metadata is usually defined as "data about the data", so in order to target our work on metadata, it is important to make explicit what is the central data we expect to describe with our metadata.

EuDML being the digital metaphor of a mathematics oriented professional library, important concepts that will necessarily be handled in the system, and thus need some internal metadata schema, are: publication (publication containers such as journals or books, as well as individual contributions aka items), person (contributors, and users aka patrons), legal person (person's affiliations, publishers, etc.), user community, user annotation.

However, given the nature of the EuDML central repository, which will be assembled by aggregating content from a number of partner's catalogues, we are lead to single out the individual mathematical works in the library as our main relevant data, and hence to focus on a metadata schema designed to bear all relevant information that can be gathered, consolidated or generated for each integrated full text.

We thus consider publication containers, persons and their affiliations, and publishers, as peripheral information attached to some full text (yet supporting the ability to link to an authority list of such). We also discard all registered users information as well as their possible annotations in this iteration of our work, for these are considered private concepts to the EuDML system, thus inappropriate in a static, exportable representation of the library's content metadata.

The EuDML item

The central object in EuDML, used as the unit of delivery and thus as the pivot for the metadata schema, is an item.

EuDML defined relevant logical units that can be delivered in the context of EuDML in the following way:

"An item is a self-contained mathematical text which has been scientifically validated and formally published".

We warn readers from the library community that this definition is incompatible with that used in FRBR [START_REF]Functional requirements for bibliographic records[END_REF] terminology, where it would be rather called manifestation.

Loosely put, an item is the kind of mathematical content that would be reviewed in Zentralblatt MATH or Mathematical Reviews, so the relevance of this concept is quite consensual in the mathematical community. It is the object an unambiguous citation in a scientific article would point to, thus the importance of this concept for a reference library.

Two different editions of a book would be different items, but not a new print; two digitisations of the same article would be related to a single item, but the reprinting of that article in its author's collected works would yield a new item (hopefully related to the previous one). We must be very cautious with mathematical references that, although the same "ideal work" can be manifested through various channels such as a conference, an abstract, a full paper, or a monograph, it is not possible in subsequent works to refer uniquely to them collectively, as the actual details contained in each manifestation could differ enough to make the reference ambiguous. Even a solid abstract reference such as "the Hahn-Banach theorem" might be stated with quite varying hypothesis and conclusions depending on the context where it is manifested.

As the main focus of the EuDML project is to ease discovery, access, use and exchange of mathematical items, the EuDML item is thus the primary entity type described by the schema.

The identification of an item, as a formally published text, essentially requires bibliographic data which describes where and by whom it was published and depends on the type of publication (journal article, book, etc.).

For this version of the schema, we explicitly support the following publication types, which are logical subclasses of the generic "item" class:

-a multivolume work; -a book, namely

• a single volume from a multivolume work,

• a monograph (which might be a doctoral dissertation, a memoir. . . ),

• an edited book (a book that contains chapters or articles that have been written by different authors and collated by scientific editors, which might be a conference proceedings volume); -a part of a book such as a chapter, or a contribution in a proceedings volume; -a journal article.

Out of scope functionality

The following do not constitute requirements on EuDML services and are thus not in the scope of a EuDML metadata schema:

-Handle material that is not considered as having been persistently and formally published (e.g. preprints, personal web pages. . . ). -Special provisions for papers not generally accessible online (e.g. on paper only, in house access only, library catalogue. . . ). -Version control for documents, as EuDML only considers works in published final form.

-Complicated author/contributor structures for documents, as this is of no significance in math publishing. We won't try to record authors' contribution weights, ordered authors' list where either the first or the last name has more significance, etc. -Description of access embargo periods (moving wall) and other licensing, access barriers, digital rights management issues, since EuDML follows an eventual open access policy and leaves those issues under full control of the respective content (full text) providers.

Analysis of the EuDML metadata requirements

Metadata exists to support the functionalities expected from the system. In this section we describe the functional aspects of a Digital Mathematics Library (DML) that we intend to provide:

-Uniquely identify an item not only within EuDML, but across the whole mathematical literature.

-Discovery of published items by

• fielded search on various attributes such as author names, titles, publication year, subject, abstracts, journal title, key words, • browsing collections by selecting a starting point such as a given journal name, mathematical classification code, author name, • sorting and filtering search or browse results, • automated reference matching to help external resources turn their citations into links to EuDML items. -Retrieving a specific item through a known identifier such as a DOI, URI or other unique identifier. -Assert the relevance to the user of a given item through the display of attributes such as subject, abstract, language, and citations to and from that item. -Display and indexing of attributes in multiple languages or transliteration systems.

-Interlinking as a powerful access tool to mathematical resources. Examples of this consist of links to reviews in the major reviewing databases (Jahrbuch, Zentralblatt MATH, MathSciNet), and links to and from citations from subsequent works. -Linking to other material such as user provided annotations, author identification services. -Display of mathematical formulae in various formats based on the user's choice or capabilities (e.g. MathML, T E X, graphics, speech synthesis).

Besides the end user oriented functionalities, the schema should also serve as an exchange model.

Quality insurance on metadata

From the above requirements analysis, we derived the following functional definitions, which help identify more objectively whether a given item's metadata is eligible to support minimal digital library operation, standard full-featured operation, or advanced operation tweaked for EuDML math-specific content.

Obligatory metadata

We define obligatory metadata as the bare minimum of metadata information that is requested from EuDML data providers. This is not exactly a functional category but rather a policy requirement.

Obligatory metadata is the required minimum of metadata in order to unambiguously identify and handle a relevant mathematical publication in the scope of EuDML: Item type, authors, original title, bibliographic reference for this publication with enough structure so as to enable collection's browsing, unique identifier, URL of full text.

Fundamental metadata

Fundamental metadata is what satisfies the functional requirements for browsing, searching and reference matching over the collections at item level. It enables basic digital library interaction with the EuDML corpus.

The term fundamental was chosen so that it is clear which information is needed to provide the fundamental functionality expected by typical users. It is a qualitative superset of obligatory metadata.

If this information is relevant to the item described, then it must be present in the metadata. If it is absent from provider's original metadata, then our enhancing tool set must provide a solution in order to enable this publication in EuDML.

It contains obligatory metadata (see above) as well as standard optional information (abstract, key words, main language) that should be there, or generated by the project.

Supplemental metadata Beyond fundamental metadata, this is additional metadata that should be stored, generated, and exploited within EuDML.

Supplemental metadata is whatever goes beyond fundamental metadata (e.g. relations to subject ontologies, authority lists, MR/ZM IDs, multilingual, multiscript, bibliographies/references, interlinking, math handling. . . ), yet has relevance to the EuDML's corpus specificities and EuDML system functionalities.

The EuDML metadata schema

This section is about how EuDML metadata will be encoded and physically appear or be transported in certain given scenarios (such as during metadata harvest from EuDML data providers, or exposition of EuDML metadata to aggregators, e.g. Europeana, or for a "snapshot" or "dump" of EuDML contents).

As we do not want to reinvent the wheel, a quick survey of existing XML encodings was conducted, paying special attention to the following requirements:

-mathematical formulae should be supported in a variety of formats, including MathML; -rich text should be allowed where applicable, in other words the encoding used must account for a number of basic formatting elements such as typographical attributes; -the description of reference lists (bibliographies) should be taken into account, as they are an essential tool for researchers; -using a recognised and widely deployed standard would be a bonus. However, as we do not expect an existing XML document type definition or schema to be able to describe our data "out of the box", it should be easily customisable.

Review of evaluated metadata encodings

We evaluated the following schemas which all provide some partial solution to our query:

EULER Euler FP5 project metadata, which was developed for cataloguing (non-digital) resources existing in various European libraries [START_REF]The EULER application profile[END_REF]; SWAP Scholarly Works Application Profile in qualified Dublin Core, which essentially provides granularity to describe (with raw text metadata) any digital scholarly work (detailed bibliographic description, eprint versioning, validation status) [START_REF]Scholarly works Dublin Core application profile[END_REF] ; MODS Metadata Object Description Schema from the Library of Congress, which is pretty much an interchange format for multimedia library catalogues [START_REF]MODS schema[END_REF]; DML-DC Euclid/NUMDAM/GDZ recommendation on presenting DML metadata in simple Dublin Core, which was an attempt to qualify simple Dublin Core for making metadata interchange more useful between DMLs by URI-like prefixing repeated elements, as well as some best practices recommendations for mathematical expression encoding in titles and abstract [START_REF] Thierry Bouche | A recommended best practice for unqualified Dublin Core metadata records[END_REF]; MLAP Mathematical Literature Application Profile for Dublin Core by David Ruddy, which is a relatively strict yet very generic schema for interchanging precise bibliographic records of scholarly works [START_REF] Ruddy | Developing a metadata exchange format for mathematical literature[END_REF]. Besides the fact that mathematicians are eager to exchange this kind of information in order to build larger DMLs and further the interlinking of existing DMLs, this proposal has nothing specific to mathematical content; JATS NCBI/NLM Journal Archiving Tag Suite, which was created with the primary intent of providing a common format in which publishers and archives could exchange journal content [START_REF]NCBI) of the National Library of Medicine (NLM)[END_REF].

While Dublin Core metadata is nowadays a central device for wide interoperability, especially for enhancing visibility of heterogeneous collections, it was felt that DC based formats would be useful for exporting EuDML metadata but not for storing the consolidated master with all information and additions foreseen in the project's work plan. In fact, DC is so generic that, among its 15 elements, few are relevant to a digital library project such as EuDML, and a lot of structure has to be added to qualify and organise information we would expect from each of the principal elements. This is what application profiles such as EULER, SWAP, DML-DC and MLAP are aimed at, each of these developed with a specific aspect of literature interchange in mind. MODS is a more constrained framework that can be used, together with METS, in order to describe a precise bibliographic record of a catalogued object, as well as its physical description-no room exists, apart from using relations to external objects conforming to some other format, for encoding parts of an item's textual content like bibliographies. However, none of these provide support for mathematical knowledge encoded as such: the mathematically oriented standards just favour T E X notation as it can be embedded into any XML file as text modulo some escaping.

Inera Inc. provides some introduction to the NLM Journal Archiving Tag Suite (JATS in the following) [START_REF]NLM DTD Resources: Introduction[END_REF]:

The NLM Journal Archiving and Interchange DTD Suite, co-authored by Inera Inc., Mulberry Technologies, and NCBI, is the de facto standard full-text DTD for scholarly publishing.

Since the DTD was first released in April 2003, it has been (for the scholarly publishing world) rapidly adopted. Whereas ISO 12083 never achieved broad acceptance, the NLM DTD has already been adopted by hundreds of journals (probably north of 500) worldwide. Many small and medium-sized publishers have adopted the NLM DTD, and a number of larger publishers are preparing to deliver content according to the NLM DTD when asked. Most of the major journal publishing compositors and service suppliers are up to speed on the DTD and happy to deliver content tagged with it. The NLM DTD has also proven popular with aggregators. It is the "house" DTD of Atypon Systems and the recommended DTD for full-text content at Ingenta and Highwire Press. And, of course, NLM uses it for PubMed Central. The NLM DTD has been no less popular with libraries. In a joint press release, the British Library and the Library of Congress announced that they would support the NLM DTD as their archiving standard for electronic content. It has also been adopted by Portico (a major Mellon-funded archive effort).

Complemented by Mulberry Technologies, Inc. [8]:

The Journal Archiving and Interchange Tag Suite (also called the NLM DTD although it is available in DTD, XSD, and RNG forms) provides a common XML format for preserving the intellectual content of journal articles, independent of the form in which that content was originally delivered. The Tag Suite consists of Tag Sets for Archiving, Publishing, and Authoring journal article content and a Tag Set for Books and book material. The Tag Sets have been widely adopted by archives, libraries, and publishers and are supported by many data conversion vendors and XML tools. NISO (the National Information Standards Organization) is now working to make the JATS into a NISO standard.

As JATS was already used internally by one of our partners (EDP Sciences), and proved to have room to store faithfully all of the metadata encountered while reviewing the EuDML content to be integrated, and moreover provided standard structures for most of the new elements foreseen in the work plan (full text encoding, native support for MathML and alternative versions of formulae, notably), it was an easy task to select it as best candidate for our purpose. It is a trivial task to derive most DC based metadata from carefully organised JATS files (while the converse would require a JATS application profile in Dublin Core).

In summary, here are some decisive features that highlight NLM JATS as the best available framework to host EuDML metadata:

-It has been adopted as the internal format of one of our partners (EDP Sciences), and is already vastly deployed as an interchange format by many scientific publishers because of their interoperability with PubMed Central, JSTOR, or Portico. Its wide deployment and large user community makes it a good reference model for outer interoperability. -It is highly customisable and meant for customisation (nevertheless, we decided to keep minimal any deviation from the standard schemas in order to maximise wider interoperability). -It has room to store any kind of scholarly content up to the full text itself, and to store parallel versions of the same content encoded differently (which is crucial for our enhancing workflow).

-Last but not least, it is MathML-ready (yet allowing storage of alternative representation of the mathematical content).

JATS provides three DTDs that we will adapt for describing our three main content types:

-The Journal Archiving and Interchange Tag Set implements article3.dtd for journal articles (cf. http://dtd.nlm.nih.gov/archiving/) -The NCBI Book Tag Set implements book3.dtd for books and bookcollection3.dtd for collections of books (cf. http://dtd.nlm.nih.gov/book/)

Although JATS can be easily customised to fit any special need [START_REF] Beck | Proceedings of the Journal Article Tag Suite Conference 2010[END_REF], we will try to adhere to its readily published DTDs to the largest extent possible, specifying best practices recommendations in order to attain maximum compatibility among EuDML partners, and reliability of exchanged metadata with third parties.

The EuDML schema, initial version, based on JATS

To assess the suitability of JATS to our needs more objectively, the above analysis was completed by an attempt to transform large samples of available EuDML metadata as contributed by their providers to one of the JATS DTDs.

From this experience, we concluded that JATS needed more work to suit our needs, in two opposite directions:

1. The item types currently supported by JATS published DTDs are: journal article, book, and book collection (which is defined as "a series of books related in some manner"). While the EuDML "first class citizens" are more diversified, cf. the supported item types listed in § 2.2. We thus decided to organise all our content in three major containers: journal article, single book, and multiple volume books. The two first item types required very minor extensions to existing JATS schemas for article and book (such as allowing a conference description in a book metadata for conference proceedings that are not published in a journal). As the last one doesn't fit perfectly the JATS collection model, we created a new one, called mbook, which has the metadata of a book, but whose content is a list of separate books as in JATS collection. These slight deviations from the three standard JATS schemas form the initial version of our EuDML schema specification: see § 3.3. 2. A drawback of JATS versatility is that it doesn't impose strict constraints on metadata encoding, and often allows for different ways to encode the same information.

For efficiency of metadata interchange and exploitation in EuDML, we felt that we needed guidelines so as to have a common encoding practice and understanding among all EuDML partners and content providers. The initial version is outlined here, § 4, and available on our web site (see http://www.eudml.eu/eudml-metadata-specification). Further revisions will be released periodically based on feedback from other activities within the project.

EuDML metadata specification v. 1.0

The EuDML metadata schema version 1.0 as defined by deliverable D3.2 [START_REF] Jost | Delivrable D3.2: The EuDML metadata schema, initial version[END_REF] is implemented in three DTDs providing the 3 root elements holding XML metadata for three major types of items, namely journal articles, books, and multivolume works. A consequence of this choice is that some book parts (typically individual articles in a proceedings volumes), while being "first class citizens" in our abstract model, are described and exchanged within the whole book they belong to. This is a decision on the formal way used to store and transport our items' metadata, pragmatically rooted in the existing JATS DTDs, and in the fact that bibliographical data cannot be structured the same way for these different items. It is not intended to restrict in any way the items' records are exposed to or navigated by end users.

Journal articles are described with a minimal extension of the Journal Archiving and Interchange Tag Set version 3.0 with root element <article>:

-the @xml:lang attribute is allowed for the <issue-title> element. Books are described with a minor extension of the Book Tag Set version 3.0 with root element <book>:

-a child <conference> element (as in <article-meta>) is allowed in <book-meta>; this element is needed to describe conference proceedings volumes; -a child <book-part-id> with attribute @pub-id-type is allowed in <book-part-meta>; this element is used to preserve item-level identifiers, when parts of a book are EuDML items; -the @pub-id-type attribute to <book-id> and <book-part-id> can have values beyond a restricted list; it is used in particular to identify the authority who assigned the identifier. Multivolume works are described by a new root element <mbook>. Multivolume works' metadata is identical to <book> metadata, with the addition of references to individual constituents (volumes). The element <book-meta> is replaced by <mbook-meta> with same structure, except:

-a child <mbook-list> element is required in <mbook-meta>. It is a container for individual volumes, as in JATS collection DTD; -each component volume reference is captured by an <mbook-volume> element (child of <mbook-list>), with the following children:

• <title>: the title of the volume,

• any number of <book-id> and <ext-link> elements. While the EuDML internal machinery only needs <book-id>s in order to implement the multivolume work/individual book relationship, the <title> and <ext-link> elements should be useful to external applications for display and access purposes. Each individual volume in a multivolume work is encoded with the Book DTD.

Conversion summary

While developing this work, we converted large sample metadata sets from a number of partners to plain NLM DTD and inspected where conversion was difficult to achieve, when doubts or choices had to be made, when the target structure did not accommodate the source structure, etc. When we faced the necessity to choose between different structures offered by NLM DTD, we took note and started an open discussion within our working group which ended up in a number of best practices recommendations. When we found metadata that could not be faithfully stored in the existing NLM DTDs, we took note of this for further processing. Finally, we took the design decision to adhere as closely as possible to the existing NLM DTDs, implemented the small modifications that were required to faithfully store all encountered item types, and left aside some more modifications, waiting for more feedback from the actual implementation of the project to be realised in the forthcoming months.

The following table summarises the number of item types from various EuDML collections which were successfully converted in order to evaluate our results presented here.

this, we had to heuristically split some unstructured fields into tagged bibliographic references, e.g. We also tagged all L A T E X formulae encountered with NLM superstructure with MathML alternative encoding (see § 4.3). We thus have currently 206,775 tagged formulae in our metadata. They were mostly processed from T E X encoding embedded into a text field from the provider's metadata.

A note on interoperability

When acquiring metadata from different partners, it was observed that any reasonably structured format is rather easily converted to JATS format. The big drawback with many OAI-PMH servers is that they only serve the mandatory OAI-DC format in such a way that many different metadata elements are stored in the same, repeated Dublin Core element. As a consequence, only heuristics based on order of appearance, or pattern matching on an element's value allows disambiguating the metadata thus contributed. For instance, <identifier> can be used to transport an ISSN, a textual bibliographic reference, a URL, etc.

Qualified versions of Dublin Core that are modelled on the metadata schema with finest grain available to the content provider allow faithful interchange of metadata. Qualification can be embedded into the value of simple Dublin Core elements as in the DML-DC recommendation or similar qualification using URN-like prefixes, or it can use qualified elements and a documented application profile such as SWAP or MLAP.

As of writing this report, the best scenario for returning EuDML metadata to providers is to use the EuDML schema over OAI-PMH communication channels.

For interoperability and visibility beyond EuDML partners or associated partners, a simple transformation has been developed to represent a subset of EuDML metadata in OAI-DC (compliant with DML-DC) so that general harvesters can manage our metadata. A prototype implementation of this is available to the project partners in a dedicated OAI-PMH server. The recommendation itself is a work-in-progress, which is available to the project's partners in an internal wiki as a live HTML page they can edit. Its first version has been made accessible in an area of the www.eudml.eu website dedicated to developers' resources (http://www.eudml.eu/eudml-metadata-specification). Up-to-date documentation is in the process of being made available there for download as well: the specification, the DTDs and possible associated tools.

Special item types

Proceeding volumes were an interesting case, as they were handled in very different ways by different providers. As many EuDML partners were primarily journal digitisation projects, they had "journalised" proceedings, even when they were published as independent books: modelling a conference series as a journal, each proceedings volume as a journal issue, and each contribution as an article. However, the bibliographic metadata of a conference series publishing its yearly proceedings in a general lecture notes series, e.g., is quite different from that of a journal special issue. Our modifications of JATS standard DTDs is in this area are meant to have exactly the same details for each flavour of conference publishing. As soon as the volume holds conference proceedings, the conference details are placed in the metadata, either in <article-meta> for journal articles, or in <book-meta>. The <conference> element is the same in each case.

To set information about editors (e.g for a proceedings, when editors replace authors), <contrib> element is used together with @contrib-type attribute set to "editor".

Books, like articles, can have multiple translations of their title in JATS. For some reason, journal issue metadata is somewhat less detailed than for books. In EuDML you can have multiple <issue-title> elements, distinguished by their @xml:lang attributes. In the case of an article published in a special issue, its authors (or editors) should be distinguished from the issue editors: the <contrib> element is used together with @contrib-type attribute set to "issue-editor".

Identifiers and relations

The item-centric vision of the EuDML imposes to be very careful on identifiers and relations. Each EuDML item must have a unique persistent identifier. As it comes from elsewhere, it will also typically come with a number of different identifiers that we should register in order to enable further interoperability.

The item metadata record is something like a linking hub for the given item: it should hold links to various resources attached to the described item, as well as to other related items. Obviously, a relation needs some sort of identifier for the related object as well.

We identified three main classes of relations, for which we recommend to use three different JATS structures:

1. Primary identifiers identify an item or a container. They are assigned by the publisher (DOI, PII and specific internal identifier) or by the local DML. They are not necessarily associated with an URL. Such identifiers are stored in a dedicated element relative to the item's type (e.g. <article-id>). They must have a @pub-id-type attribute. 2. Document identifiers provide links to the different versions of the content pertaining to an item or a container on the provider's web site (the PDF version, the full HTML version, etc.). These identifiers come in the form of an activable link stored as @xlink:href attribute to the <self-uri> element. The combination of the mime-type and a controlled vocabulary for values allows to predict the nature of the resource the link points to.

3. External identifiers are primarily identifiers proceeding from other authorities, such as Zentralblatt MATH, Math. Reviews, CrossRef, which assign IDs to articles, authors, journals or books, or related resources. External identifiers must be set using <ext-link>, the value being the identifier itself.

An activable link should be stored as @xlink:href attribute when applicable while the @ext-link-type attribute should keep track of the identifying mechanism and authority. Links to related items (including other EuDML items) should use <ext-link> in a similar way.

Mathematics

Although the MSC reads "Mathematical subject classification", and although JATS provides a <subject> element, MSC should be encoded with the <kwd> element inside a <kwd-group> with attribute @kwd-group-type set to the actual scheme: "msc" followed by the year (e.g. "msc2000"). Inline and display mathematical formulae are expressed respectively with <inline-formula> and <disp-formula> elements. Both MathML and (La)T E X version of the same formula can be wrapped up using <alternatives> element. This mechanism will be extended so that other versions (accessible, aural) can be stored in a similar fashion.

It is recommended to attach a unique ID to each formula to ease further processing.

For T E X notation, it is recommended to put compilable code into the <tex-math> element. This means that the switch to math mode should be part of the element's value, and control sequences should be standard (standard meaning: macros defined in plain and L A T E X formats, possibly with AMS mathematical extensions). It is important because some environments such as multline change the internal grammar of their content while switching to math, and this would be lost. We currently recommend that the content of the <tex-math> element be literal T E X code with two characters (& and <) escaped using standard XML entities (& and <). Putting a full L A T E X source in a CDATA section (as exemplified in JATS documentation) is explicitly disapproved.

For instance A product of four (p, q)-sections (with p < q). should be encoded the following way.

A product of four <inline-formula id="d1e4"> <alternatives> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> <tex-math>$(p,q)$</tex-math> </alternatives> </inline-formula>-sections (with <inline-formula id="d1e20"> <alternatives> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo><</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> </mml:math> <tex-math>$p<q$</tex-math> </alternatives> </inline-formula>).

Conclusion & further work

We have exposed the rationale that leaded us to base the EuDML schema for descriptive metadata on NLM Journal Archiving and Interchange Tag Suite. We provided the current specification of the schema as a diff to three existing standard JATS DTDs. We also gave some examples of the recommendations we came up with so that design choices allowed by JATS are correctly understood by all partners. This work is assessed by the fact that we could convert all EuDML partner's metadata available to us into this framework. Now, EuDML is starting to exploit what we have generated so far. A number of tools are developed in order to improve the quantity as well as the quality of the metadata available to the project, they will evolve into various automated workflows. Using these tools, we should be able to get new metadata elements, that may superseed or just add to the items' descriptions. Duplicates, similar, and related items should also be detected. We will thus face the necessity to merge item records from a number of sources, some of them "trusted" (e.g. manual keywords or copy-edited translations), some of them much less so (computed similarity, guessed MSC, automatic translation, OCRed math formulae. . . ). We feel that the current schema is robust enough to store all this information faithfully side by side, while retaining its origin. Indeed, we think that managing this will boil down to adding a number of rules and attribute values to our Best practices. However, we are now expecting feedback from a number of project's activities to assess and refine the work reported here.

4 Best practices recommendation for mapping EuDML abstract metadata to the EuDML schema A

  best practices working group for representing EuDML metadata in JATS notation was formed. A set of recommendations has been developed, and has now been tested on all available EuDML items. Complete examples of EuDML XML files obeying these recommendations are available on our web site. We give some examples of the issues tackled below.

Acknowledgement This work is partly financed by the European Union through its Competitiveness and Innovation Programme (Information and Communications Technologies Policy Support Programme, "Open access to scientific information", Grant Agreement no. 250.503).

Collection

EuDML metadata (Schema) Notes In order to get the most out of the contributed metadata, all converted items meet the obligatory requirements, even when the original metadata didn't meet them. For

Gallica


Keywords: Condition Monitoring, Abnormal Condition Detection, Signal Grouping, Differential Evolution, Reactor Coolant Pump, Pressurized Water Reactor

INTRODUCTION

For monitoring the condition of a component, a (typically empirical) model estimating the values of measurable signals in normal conditions is built; during operation, the measured values are compared with those estimated ('reconstructed') by the model: a deviation between the observed and reconstructed values reveals the presence of an abnormal condition (Reifman, J. 1997). In practical industrial implementations, the performance of a single model estimating all the signals measured by the sensors, usually a very large number, may not be satisfactory. It has been shown that grouping the signals and then building a specialized model for each group allows to remarkably increase the condition monitoring performance [START_REF] Roverso | Solutions for plant-wide on-line calibration monitoring[END_REF][START_REF] Baraldi | Signal Grouping for Condition Monitoring of Nuclear Power Plant Components, Control and Human-Machine Interface Technologies NPIC&HMIT[END_REF]. In this work, a Wrapper approach has been employed to group the signals: a search algorithm is used as a "wrapper" around the condition monitoring model; during the optimization search, the performance of the condition monitoring model itself is directly used as evaluation function to compare the different groups selected by the search engine (Fig. 1). The algorithm considered in this work for reconstructing the equipment behavior in normal conditions is based on the Auto-Associative Kernel Regression method (AAKR) [START_REF] Hines | Development and Application of Fault Detectability Performance Metrics for Instrument Calibration Verification and Anomaly Detection[END_REF]. AAKR is an empirical modeling technique that uses historical observations of the signals taken during normal plant operation. We use the Differential Evolution (DE) algorithm as search engine for the identification of the optimal signal groups. The motivation of the choice is found in the DE ability of finding the optimal solution by efficiently scanning the search space in an acceptable computational time. Differential Evolution is a derivation of Genetic Algorithms [START_REF] Storn | Differential evolution -A simple and efficient adaptive scheme for global optimization over continuous spaces[END_REF]. DE applies evolution operations on the individuals' solutions of a population in order to perturb them by transmission of good properties, with the aim of finding an optimum. One difference with respect to GA is that DE is specifically built for optimization over continuous spaces and does so based on a floating-point representation. The specific evolutionary operations used in DE Differential Evolution for Optimal Grouping of Condition Monitoring Signals of Nuclear Components P. Baraldi, E. Zio, F. Di Maio & L. Pappaglione Politecnico di Milano, Milano, Italy, E-mail: piero.baraldi@polimi.it R. Chevalier and R. Seraoui

Electricité de France -R&D, France

ABSTRACT: We propose an approach for optimally grouping a large number of signals measured, for utilization in models for equipment condition monitoring. We use a Differential Evolution (DE) algorithm for the optimal identification of the groups; the decision variables of the optimization problem relate to the composition of the groups (i.e. which signals they contain) and the objective function (fitness) driving the search for the optimal grouping is constructed in terms of quantitative indicators of the performances of the condition monitoring models themselves: in this sense, the DE search engine functions as a wrapper around the condition monitoring models. A real case study is considered, concerning the condition monitoring of the Reactor Coolant Pump (RCP) of a nuclear Pressurized Water Reactor (PWR). The results of the grouping are evaluated with respect to the accuracy and robustness of the estimates of the monitored signals by the condition monitoring model developed on the optimal groups, and compared with those achieved with groups obtained using Genetic Algorithm wrapper approach.

are suited for such representation of the chromosomes, and drive the main improvements of DE with respect to GA. The DE-based wrapper approach is tested on a real case study concerning 46 signals selected among those used to monitor the reactor coolant pump of a Pressurized Water Reactor (PWR). The condition monitoring performance is evaluated with respect to metrics that measure i) the accuracy, i.e. the ability of the overall model to correctly and accurately reconstruct the signal values when the plant is in normal operation; ii) the robustness, i.e. the overall model ability to reconstruct the signal values in case of abnormal operation and consequent anomalous behavior of some monitored signals [START_REF] Efron | Estimating the error rate of a prediction rule: Improvement on cross-validation[END_REF]. The results are compared with those achieved by considering groups based on signal correlation and groups previously found in [START_REF] Baraldi | Generic algorithm-based wrapper approach for grouping condition monitoring signal of nuclear power plant components[END_REF]) by using a GA wrapper approach. values in one or more signals reveals the presence of faults [START_REF] Reifman | Survey of artificial intelligence methods for detection and identification of component faults in nuclear power plants[END_REF] , whereas, by observing the residuals x ˆ, given a current signal measurement vector, = obs x (x obs (1),…,x obs (n)), as a weighted sum of the historical observations. Appendix A provides the details of the method.

Search Algorithm

Successive generation

This is the original scheme proposed in [START_REF] Storn | Differential evolution -A simple and efficient heuristic for global optimization over continuous spaces[END_REF]: at the G th generation, for each vector x i,G in the population, called target vector, a noisy vector v i is generated randomly choosing three mutually different vector indices r 1 r 2 r 3 ∈ {1,2,…,NP} with 1∉{r 1 r 2 r 3 } ( )

1 2 3 , , , , i G r G r G r G v x F x x = + ⋅ - (1)
where the weighting (or scaling) factor F ∈ [0,2] is a user-defined parameter, kept constant during the optimization. This operation is termed mutation in DE.

Using the weighted difference, the entire process becomes self-organized because the step length for the perturbation is mainly affected by the progress state of the evolutionary process.

Through the evolution, the search space contracts or expands if the direction taken by the algorithm is correct or wrong, so the random step-length is self-adapted in every dimension accordingly with the dependence of the variable.

After mutation, the noisy vector is not directly compared with the target vector, but it is further modified by the crossover process, in which the noisy and target vectors are mixed according to some rule to create the trial vector u i , which inherits from them different pieces of chromosome. The crossover operator contributes to maintaining diversity inside the perturbed population, shuffling old and new information. This increases the probability of maintaining some good property from the target vector, and avoids drastic changes during the generation of new solutions. On the other hand, the role of crossover in DE has a secondary relevance compared to GA [START_REF] Storn | Differential evolution -A simple and efficient adaptive scheme for global optimization over continuous spaces[END_REF].

Due to the chromosome vectorial representation, as for real-coded GA, the crossover operator for DE is applied to each element of the array: each variable of the noisy vector and the target vector has the possibility to be part of the trial vector, entering the final fight for survival.

The most common crossover type adopted is the binomial approach: the trial vector is built by the following rule, gauged by a control parameter CR ∈ [0,1], which influences the probability that a noisy vector's variables are selected for the mutation process.

( ] ( ) ( ] ( ) , , , 0,1 0,1 ji G ji G ji G v if U CR or j irand NP u x if U CR and j irand NP  ≤ =  =  > ≠   (2) { } 1, 2, , j n ∀ ∈ …
where U(0,1) is a uniform continuous random value ∈[0,1], whereas irand(NP) is a uniform discrete random number in the set ∈{1,2,…,NP}. This ruling applied to the Bernoulli trials guarantees the inheriting of at least one element from the noisy vector in the trial vector even if the crossover rate CR is set to zero. The binomial crossover operator acts independently on every "gene", i.e. variable of the chromosome, as for classic GA multi-site crossover. A relevant difference with GA is that in the DE crossover procedure a chromosome of the current population and one just generated, the noisy vector, are mixed, rather than two solutions of the population. The resulting trial vector ( )

, 1 , 2 , , , , , i G i G i G ni G u u u u = …
(3) inherits portions from the noisy vector and from the target vector, as regulated by the parameter CR.

The trial vector obtained then enters the selection process where it is compared with the target vector x i,G , that is partially its parent according with the crossover rule. During the selection process, the population S is modified by substitution.

Referring to a Single Objective (SO) problem aiming at minimizing a single function f, if the trial vector's fitness is less than the target vector's fitness, the first will be a member of the next generation, replacing the target vector in the set S, and the trial vector is discarded:

     = + G i G i G i x u x , , 1 , ( ) ( ) otherwise x f u f if G i G i , , < (4)
{ } 1, 2 , , i N P ∀ ∈ …
The selection criterion in DE is greedy and quite different from the classical replacement criterion of GA: for sure the next generation will be better or at least equal to the previous generation.

The evolution of the DE algorithm follows these steps:

1. creation of an initial population of NP potential solutions and evaluation of their fitnesses; 2. for each solution of the population (target vector), selection of three solutions for reproduction; 3. for each target vector, creation of a noisy vector using the mutation process; 4. creation of a trial vector mixing target and noisy vectors; 5. comparison between each target vector and its related trial, and eventual replacement;

6. control of the stopping criteria: if some criterion is met, then stop, else return to step 2. The stopping criteria adoptable are the same as for GA. DE has been shown to have robustness, higher convergence speed than GA and even superior accuracy thanks to its greedy search preference.

APPLICATION

A real case study concerning 46 signals used to monitor the Reactor Coolant Pumps (RCPs) of a French PWR is considered. A dataset containing the signals values measured every hour for a period of 11 consecutive months has been considered to build the reconstruction model. To this purpose, the 46-dimensional available patterns (5798) have been divided into a set X S of 2798 patterns used to perform the DE optimization, i.e. to find the optimal grouping, and a validation set X V of 3000 patterns used to validate the condition monitoring performance of the grouping found. To this purpose a cross validation procedure has been performed on the patterns of X V order to accurately estimate the values of the performance metrics, in particular, a "4-fold" cross-validation error estimate is used. To this purpose, the original dataset is randomly partitioned into 4 blocks of equal size. One of these blocks is used as validation data subset for the evaluation of the performance metrics of interest, and the remaining three blocks are combined together to constitute the training data subset. The cross-validation process is then repeated 4 times, each time using a different block as validation set [START_REF] Efron | Improvements on crossvalidation: The .632+ bootstrap method[END_REF][START_REF] Kohavi | A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection[END_REF]. The objective of the search has been the minimization of a function which takes into account both the accuracy and the robustness of the grouping. The accuracy, i.e. the ability of the model to reconstruct correctly the signal values in normal plant behavior, has been measured by considering the metric auto ac A , which is the global accuracy obtained applying the disturbance to all the signals. An accurate condition monitoring model allows to reduce the number of false alarms, i.e. detections of faulty behaviors when no faulty conditions are actually occurring. The accuracy metric is typically defined as the mean square error (MSE) between the model reconstruction and the signal measured values. In this work, according to the (Zaharie, D. 2007), the metric auto ac A has been chosen, instead the MSE, because has been seen that using this metric as fitness function in the search engine allows to obtain a signal grouping which is able to achieve higher accuracy when applied to all data than with a little data set used to performing the search. This is due to the fact that the two metrics, MSE and auto ac A , differs only for the signal values which are disturbed in case of auto ac A , running a cross-validation procedure, while MSE is performed with all signals value in normal condition. The accuracy in the reconstruction of the disturbed signal i is defined as:

∑ = - - - = test N k nc test i ac test nc test auto i ac i k X i k X N i A 1 2 ) ( ) ( )) , ( ) , ( ( 1 ) (
(5) This metric measures the mismatch between signal reconstructions and signal values in normal plant operation. However, since it does not consider neither the difference between the reconstructions in the cases of disturbed and undisturbed signals, nor the magnitude of the signal deviation

)) , ( ) , ( (

) ( i k X i k X nc test i ac test - - -
it cannot be directly interpreted as a measure of model robustness. The robustness, i.e. the capacity to reconstruct properly the signals value when an anomaly occurs to the component has been measured by the metric auto ac S , which is the global robustness obtained applying the disturbance to all the signals. In abnormal plant conditions, a robust model reconstructs the value of a plant signal as if the plant were in normal operation: then, the differences between the measured and the reconstructed signal values can easily identify the abnormal condition. In this respect, real data measured by the sensors in abnormal plant conditions are usually not available because these latter are rare; then simulation is used to artificially inject abnormality by adding realistic deviations to the signals measured during normal plant operation. Let . Quantitative indicators of robustness can then be introduced as follows. The auto-sensitivity of the model to a disturbance applied on signal i is defined as [START_REF] Efron | Estimating the error rate of a prediction rule: Improvement on cross-validation[END_REF] , and finally taking, respectively, their mean values:

): ∑ = - - - - - - = test N k nc test i ac test nc test nc i ac test nc test auto i ac i k X i k X i k X i k X N i S 1 ) ( ) ( ) ( ) ,
q i A A q i auto i ac auto ac ∑ = = 1 ) ( ) ( (7)
q i S S q i auto i ac auto ac ∑ = = 1 ) ( ) ( (8)
For the grouping optimization problem, single objective (SO) function is obtained by aggregation of the two metrics as follows:

auto ac auto ac agg A S f ⋅ = (9)
In the next Section, the results obtained by the 'wrapper' scheme of Figure 2 with DE search engine are presented. As chromosomes, we simply take n-dimensional vectors of positive integers r∈{1,R}, where n is the number of monitored signals and R is the maximum number of groups reached by the DE: the integer value Rj of the j-th element of the vector indicates the group to which the j-th signal is assigned (Fig. 3). In our application, R has been taken equal to 5 as in [START_REF] Baraldi | Generic algorithm-based wrapper approach for grouping condition monitoring signal of nuclear power plant components[END_REF], in order to allow a fair comparison between the results achieved by the DE and the GA wrapper approaches. The crossover rate CR is set to 0.8 to adequately explore the search space, since it is very complex. The role of scaling factor is heavily significant in the convergence speed and success, with values under 0.15 success is not guaranteed and values over 0.5 the convergence speed slows down gradually. According to the recommendations reported in (Storn, R. & Price, K. 1997; Zaharie, D. 2007) the scaling factor F is set to 0.5. tends to monotonously decrease. This is due to the fact that the optimization is based on the minimization of a single fitness function which aggregates the two accuracy and robustness metrics (eq. 9), and thus a slight increasing of the robustness can be compensated by a decreasing of the accuracy. In this respect, optimization approaches in the framework of the Pareto analysis based on Multi-Objective Differential Evolution (MODE), could be explored to find a set of optimal solutions characterized by different compromises between accuracy and robustness. The groups obtained by the single-objective DE search are reported in Appendix B. Table 3 (columns 2) reports the performances obtained by the best solution found by the DE. These results are compared with those obtained by grouping the signals according to their correlation, i.e. by assigning to the same group the signals with an absolute value of the correlation coefficient larger than 0.8 [START_REF] Baraldi | Signal Grouping for Condition Monitoring of Nuclear Power Plant Components, Control and Human-Machine Interface Technologies NPIC&HMIT[END_REF]. Following this procedure, 4 groups have been identified, whereas the remaining 4 signals, characterized by a correlation coefficient with all other signals lower than 0.8, have been put together in a fifth group of uncorrelated signals (Appendix C). Although the two groupings are characterized by very similar values of fagg, they have different behaviors in terms of accuracy and robustness with the DE grouping being more robust but less accurate.

RESULTS

Simulation Pure DE

Simulation Hybrid DE

To improve auto ac A , we consider the opportunity of reducing the DE search space by decreasing the number of signals that must be reorganized in groups.

To this purpose, it has been observed that out of the 46 signals the correlation grouping builds a group formed by 30 highly correlated temperature signals that enables a very accurate and robust reconstruction of 24 of these 30 signals.

Than we have decided to adopt an hybrid approach which consists in keeping these 24 signals in a group (i.e. group 1) and using the DE search to optimize the group assignment of the remaining 22 signals. The correlating chromosome is formed by a vector of 22 elements (the signals which should be assigned to a group) which can take a value between 1 and 5 (the group to which the signal is assigned). We observe that one of the group to which the signals can be assigned is the group of the 24 signals identified by the correlation grouping itself. In this way, the dimension of the search space is reduced from the 5 46 (≈ 10 32

) possible combinations to 5 24 (≈ 10 17 ). Table 2 reports the DE parameters used within this hybrid approach. With the reduced dimension of the search space, the number of generations has been reduced to 250 leading to a reduction of the computational time. Appendix D reports the groups obtained by the hybrid approach. With respect to the correlation grouping one can notice that:

• groups 1 and 4 are identical in the two grouping approaches; • the other three groups differ only with respect to signals 10a and 10d, which are assigned to groups 2 and 5 by the hybrid approach and to group 3 by the correlation grouping.

≈50%.

The robustness of the solutions tends to remarkable decrease after generation 200 (Fig. 6). This behavior, which is found also in the pure DE search, is in this case more remarkable given that the robustness decreases of about 30%. Table 3 (column 4) reports the performances of the grouping found by the hybrid approach. The fitness results are lower than those obtained by the correlation grouping and pure DE approach. With respect to the correlation grouping, the DE allows finding a solution with about the same accuracy but more robust.

Comparison with a GA wrapper approach

In this Section, we compare the performance of the grouping obtained by DE with that obtained by GAs in [START_REF] Baraldi | Generic algorithm-based wrapper approach for grouping condition monitoring signal of nuclear power plant components[END_REF]. First of all, notice that GAs are not able to find a satisfactory solution in the case in which the search space is formed by all the possible combinations of the 46 signals, the fitness of the best grouping being equal to 0.0095. Using an hybrid correlation and GAs approach, where, analogously to what is done in the hybrid correlation and DE approach, the 24 highly correlated temperature signals are kept in a fixed group, we have obtained a grouping characterized by the performances reported in Table 3. The solution found by the hybrid DE and correlation approach is more performing than that found by the hybrid GAs and correlation approach with respect to robustness, for approximately the same accuracy. The groupings found by the two approaches (Appendixes D and E) differ only for the assignment of signals 10a and 10d which are two flow measurement signals characterized by a low correlation with all other 44 signals.

In order to compare the robustness of the groupings found by the two hybrid approaches, the reconstructions of signals 10d are compared in case of abnormal conditions. The abnormal conditions have been simulated by adding a linear drift to the signal values collected for 100 hours in normal conditions. Figure 7 shows the signal 10d behavior in case of normal conditions (top) and abnormal conditions (bottom). The signal values in abnormal conditions are then given in input to the AAKR reconstruction models. show the difference between the abnormal condition measurement and the reconstruction, which is used for the abnormal condition detection. Notice that after 60 hours the signal 10d reconstruction obtained by the hybrid DE and correlation grouping tends to be different from the abnormal condition measurement, allowing to identify the onset of an abnormal condition. On the contrary, the identification of the abnormal conditions results difficult using the hybrid correlation and GA grouping, given that the residuals between the signal measurement in abnormal conditions and the reconstruction do not remarkable deviate from zero.

CONCLUSION

In this paper, we have proposed an approach to optimal grouping for condition monitoring, based on a wrapper DE search approach. The approach has been applied to the condition monitoring of 46 RCP signals. The objective of the search has been to minimize a proper objective function which takes into account both the accuracy and robustness of the signal reconstructions. The obtained grouping has resulted more performing than that obtained by grouping the signals according to their correlation, or using a previously developed wrapper GA approach. We intend to continue our research work focusing on grouping approaches based on Multi-Objective Differential Evolution (MODE) optimization techniques in the framework of Pareto analysis. These approaches are expected to provide a set of optimal solutions characterized by different compromises between accuracy and robustness. Using these approaches, one can choose the solution with the most satisfactory tradeoff between the two objectives.

Figure 1 .

 1 Figure 1. Wrapper approach for optimal signals grouping.

  detect the component condition. In this respect, several methods of analysis of the residuals r for fault detection exist, e.g. the Sequential Probability Ratio Test (SPRT) (Hines, J.W. & Garvey D.R. 2006). The model considered in this work for reconstructing the component behavior in normal condition is based on the AAKR method (Hines, J.W. & Garvey D.R. 2006). The basic idea of the method is to reconstruct, using historical observations, the signal values in case of normal condition, nc

Figure 2 .

 2 Figure 2. Condition monitoring scheme.

Figure 3 .

 3 Figure 3. Chromosome structure.

Figures 4 -

 4 Figures 4-6 show the evolution of the fitness function fagg, the metrics auto ac A

Figure 4 .

 4 Figure 4. Evolution of the best (x) and mean (.) population fitness value at each generation.

Figure 5 .

 5 Figure 5. Evolution of the best (x) and mean (.) accuracy value at each generation.

Figure 6 .

 6 Figure 6. Evolution of the best (x) and mean (.) robustness value at each generation.

  Figure 8 (top) shows the reconstructions obtained by using the hybrid GA and correlation grouping and Figure 9 (top), the hybrid DE and correlation grouping. Finally, Figure 8 (bottom) and Figure 9 (bottom)

Figure 7 .

 7 Figure 7. Time evolution of signal 10d in normal condition during 100 consecutive hours (top); time evolution of signal 10d in abnormal condition, linearly drifted by 0.7% of the standard deviation.

Figure 8 .

 8 Figure 8. GA grouping. Reconstruction performed of signal 10d in abnormal condition, linearly drifted by 0.7% of

Figure 9 .

 9 Figure 9. DE grouping. Reconstruction performed of signal 10d in abnormal condition, linearly drifted by 0.7% of the standard deviation (top); difference with respect abnormal conditions (solid line) and normal conditions (crosses) (bottom).

  Table 1 reports the DE parameters used:

	Table 1. DE parameters. ______________________________________________ ____
	Population size	50
	Maximum number of generation		500
	Scaling factor (F)		0.5
	Crossover rate (CR)	0.8
	Number of patterns in the training set	500
	Number of patterns in the validation set	170
	Gene possible values
	[1,2,3,4,5] ______________________________________________ ____
	Notice that the optimization problem of identify-
	ing the best group for each one of the 46 sig-
	nals requires a search in a very large search space formed by 5 46 ≈ 10 32 possible solutions.
	For this reason, large number of generations
	(500) has been chosen for convergence of the
	DE to a satisfactory solution.
	After 300 generations, the whole population is
	basically converging : auto ac S	slightly increases af-
	ter generation 250, whereas auto

ac

A

Table 2 .

 2 Hybrid DE parameters.

	______________________________________________ ____
	Population size	50
	Maximum number of generation	250
	Scaling factor (F)	0.5
	Crossover rate (CR)	0.8
	Number of patterns in the training set	500
	Number of patterns in the validation set	250
	Gene possible values
	[1,2,3,4,5] ______________________________________________ ____

Table 3 .

 3 Performances of the different grouping methods.

	______________________________________________ ____
	Grouping	Correlation	Pure DE
	metrics ______________________________________________ ____
	A	0.00833 ± 0.00066	0.01173 ±
	0.00089
	S	0.29719 ± 0.00573	0.22515 ±
	0.00171
	fagg	0.00247 ± 0.00025	0.00264 ±
	0.00020 ______________________________________________ ____ ______________________________________________ ____
	Grouping	Hybrid DE	Hybrid GA
	metrics ______________________________________________ ____
	A	0.00867 ± 0.00062	0.00861 ±
	0.00075
	S	0.26781 ± 0.00282	0.28927 ±
	0.00227
	fagg	0.00229 ± 0.00017	0.00248 ±
	0.00023 ______________________________________________ ____

ACKNOWLEDGMENT

This research has been carried out under contract C935C50010 funded by EdF R&D.

APPENDIX A: AUTO-ASSOCIATIVE KERNEL REGRESSION METHOD

Let nc obs X -be a matrix of observed data whose generic element ( ) j k X nc obs , represents the k-th time observation, k=1,…,N, of the j-th measured signal, j=1,…,q, taken during normal plant condition. The basic idea of the method is to reconstruct the signal values in case of normal condition, nc

x ˆ, given a current signal measurement vector, = obs x (x obs (1),…,x obs (q)), as a weighted sum of the observations in nc obs X -. Thus, ) ( ˆj x nc , the reconstruction of ) ( j x obs , the j-th component of obs x , is given by:

The weights w(k) are similarity measures obtained by computing the Euclidean distance between the current sensor measurements obs x and the k-th observation of nc obs X -:

and inserting it in the Gaussian kernel:

where the signal h defines the Gaussian bandwidth. In order to provide in Eq. (A2) a common scale across the different signals measuring different quantities, it is necessary to normalize their values. In the present work, the signal values are normalized according to:

is a generic measurement of signal j and ) ( j µ and ) ( j σ are the mean and standard deviation of the j-th signal in nc obs X -.

APPENDIX B: PURE DE GROUPING

Group 1: 04a, 05a, 07a, 04b, 05b, 07b, 04c, 05c,07c,04d,05d,07d,17,20,31a,31b,31c,31d Group 2: 09a,12a,13a,14a,09b,12b,13b,14b,09c,12c,13c,14c,09d,12d,13d,14d,29a,29b,29c, 29d Group 3: 08a, 08b, 08c, 08d, 10a Group 4: 10b, 10c, 10d APPENDIX C: CORRELATION GROUPING Group 1: 04a, 05a, 07a, 09a,12a,13a,14a,04b,05b,07b,09b,12b,13b,14b,04c,05c,07c,09c,12c,13c,14c,04d,05d,07d,09d,12d,13d,14d,17,20 Group 2: 08a,08b,08c,08d Group 3: 10a,10b,10c,10d Group 4: 29a,29b,29c,29d Group 5: 31a,31b,31c,31d APPENDIX D: HYBRID DE Group 1: 04a, 05a, 07a, 09a,12a,13a,14a,04b,05b,07b,09b,12b,13b,14b,04c,05c,07c,09c,12c,13c,14c,04d,05d,07d,09d,12d,13d,14d,17,20 Group 2: 08a,08b,08c,08d,10a Group 3: 10b,10c Group 4: 29a,29b,29c,29d Group 5: 31a,31b,31c,31d,10d APPENDIX E: HYBRID GA Group 1: 04a, 05a, 07a, 09a,12a,13a,14a,04b,05b,07b,09b,12b,13b,14b,04c,05c,07c,09c,12c,13c,14c,04d,05d,07d,09d,12d,13d,14d,17,20 Group 2: 08a,08b,08c,08d Group 3: 10a,10b,10c Group 4: 29a,29b,29c,29d,10d Group 5: 31a,31b,31c,31d


INTRODUCTION

The aim of the present work is to propose a methodology to build a model in support of maintenance decision-making for a generic electrical component, in the case in which the only available information comes from an expert. This information is subjective, qualitative and very often in implicit form; for example, experts usually resort to linguistic variables like "high", "often" and "slow" and provide qualitative statements like "the environmental conditions are good". Thus, the information elicited from experts needs to be properly interpreted, represented and propagated through the model. To do this, the present work resorts to the theoretical framework of Fuzzy Logic (FL, Bojadziev & Bojadziev, 1996), due to its capability of dealing with imprecise variables and linguistic statements. In this respect, notice that if compared with Probability theory, the FL framework allows to treat uncertainty in a way more adherent to the expert"s way of reasoning.

The reminder of the paper is organized as follows: Section 2 illustrates in details the modeling solutions adopted to address the degradation process. Section 3 describes the model of the impact of the maintenance actions on the evolution of the degradation mechanism. Section 4 is dedicated to the description of the method proposed to estimate the maintenance policy performance indicators. A case study dealing with the optimization of a Condition-Based Maintenance (CBM) policy of a mediumvoltage circuit breaker is presented in Section 5. Results are given in Section 6 and conclusions are drawn in the last Section.

DEGRADATION MODEL

In all generality, the effectiveness and precision of degradation models increase when these are able to capture the specificity of the component, which derives from the particular environmental and operating conditions in which it works. In fact, in analogy to what happens with human beings, two similar components (i.e., of the same production lot) with the same calendar age will probably be in a different state if they have been operated differently, in different environmental conditions and/or under different stress levels. To model such situation, we resort to the concept of "effective age" of a component to describe the fact that age may evolve faster or slower than chronological time in adverse or favorable working conditions, respectively [START_REF] Martorell | Age-dependent reliability model considering effects of maintenance and working conditions[END_REF][START_REF] Kijima | Some results for repairable systems with general repair[END_REF][START_REF] Vesely | Risk evaluation of aging phenomena: The linear aging reliability model and its extensions[END_REF][START_REF] Samanta | Degradation modeling with application to aging maintenance effectiveness evaluations[END_REF]. Then, the effective age can be taken as indicator of the degradation state of the component; in other words, it can be considered like a physical variable that is representative of the health state of the component (e.g., in the same way as the crack length A new modeling framework of component degradation P. Baraldi ABSTRACT: Modeling the degradation process of a component is a fundamental issue for maintenance policy definition. In this work, a degradation model based on the concept of component "effective age" is proposed. The effective age of a component is treated like a physical variable, indicative of its degradation state, and allows to describe the fact that age may evolve faster or slower than chronological time in adverse or favorable working conditions, respectively. Under this concept, the objective of degradation modeling becomes the identification of the relations between the environmental and operating conditions of the component and its effective age. In particular, the proposed degradation modeling paradigm is thought to be applied to the situation, very common in practice, in which the only available information to build the model is that elicited from experts. The proposed modeling framework is applied to a real case study of a medium voltage test network. may be used to indicate the degradation state of a mechanical component, [START_REF] Baraldi | Modeling the effects of maintenance on the degradation of a water-feeding turbo-pump of nuclear power plant[END_REF]. Under this concept, the objective of degradation modeling becomes the identification of the relations between the environmental and operating conditions of the component and its "effective age".

The practical view undertaken in this work of building a degradation model based only on the expert"s information compels to properly address two issues:

1. The degradation process needs to be modeled as a discrete-state process, in recognition of the fact that experts are more familiar with this way of thinking of the degradation mechanisms [START_REF] Baraldi | Modeling the effects of maintenance on the degradation of a water-feeding turbo-pump of nuclear power plant[END_REF]. 2. There is no stochastic model available to describe the degradation behavior in normal operating conditions. These two features call for the development of a new degradation modeling paradigm; what we propose is discussed in the following.

Firstly, the concept of effective age (indicated by ) (t w ) is introduced as defined in the following Equation and sketched in Figure 1:

' ' ' ) ' ( ) ' ( )) ' ( ( ) ( t t t for t w t t t IF t w        (1) 0 ) 0 (  w where   ) ' ( ),..., ' ( 1 t IF t IF k 
is the "age speed", which depends on the values of the Influencing Factors (IFs, i.e., conditioning aspects of the component life such as environment, quality, etc.) at t=t'; its value is 1 in nominal working conditions. The variable ' t is the last time instant at which the occurrence of an event has changed the age speed of the component; finally, ' ' t is the next time instant at which the age speed will experience a further change (i.e., between ' t and ' ' t no event occurs that changes the age speed). Once the effective age has been defined, the possible degradation states of the system need to be identified. To this aim,

1  n thresholds, 1 1 ,...,  n w w
, are set on the effective age, which define the n degradation states D=1, 2,..., n (Figure 2). In this way, a relation between the effective age of the component and its discrete degradation states is established. The next step is to model the dependence of the age speed  on the component working conditions; these latter are characterized by means of a set of K IFs identified by the expert which define the func-

tion   K IF IF ,..., 1 
. In this regard, direct elicitation from the expert of the value of the age speed is not feasible, since this concept tends to remain intangible. Rather, what one can do is to ask the expert to assess, for a given combination of the IFs, the length of the time interval that the component takes to change its degradation state, and connect the age speed to this value. For example, if the expert knows that in certain conditions (characterized by a particular set of values  can be defined as:

* 3 2 1 2 *     t w w (2)
where 1

w and 2 w are the thresholds on the effective age which separate D=1 from D=2 and D=2 from D=3, respectively (Figure 2). However, since the information provided from the expert is expected to be of the form "If the environment is Mild, then the transition time is Small", a fuzzy approach (Bojadziev & [START_REF] Bojadziev | Fuzzy Sets, Fuzzy Logic, Applications[END_REF] is applied to deal with this type of qualitative information.

In practice, the Universe of Discourse (UoD, i.e., the set containing all the possible values) of each IF is firstly partitioned in a suitable number of fuzzy sets, e.g., "Good", "Medium" and "Heavy". The same is done for the transition time, which may be reasonably partitioned in "Small", "Medium" and "High", according to the expert"s view. Then, a set of fuzzy rules are elicited from the expert to relate each combination of the IFs to the transition time. For the sake of clarity, we recall that fuzzy rules are made up of two parts: antecedent or premise and consequence or conclusion; for example, the antecedents of the rule "If IF 1 is Good and …. and IF K is Heavy then the transition time is Small" are "If IF 1 is Good",…, If IF K is Heavy", whereas the consequent is "the transition time is Small'. A degree of truth is associated to each of the antecedents of every rule, which describes to what extent the values of the variables describing the current situation under analysis match the expert view (e.g., the degree of truth that the current value of IF 1 belongs to the set Good, from the expert"s point of view). Then, a degree of truth is assigned to each rule, inferred on the basis of the degrees of truth of its constituents. Finally, all the rules are logically aggregated to provide a fuzzy set that describes the implication on transition time; this set is finally defuzzified [START_REF] Bojadziev | Fuzzy Sets, Fuzzy Logic, Applications[END_REF] into a crisp value of the transition time, which is provided in input to Eq. ( 2) to find the age speed.

MAINTENANCE MODEL

A number of maintenance models in which the maintenance actions impact on the effective age have been proposed in the literature (e.g., [START_REF] Martorell | Age-dependent reliability model considering effects of maintenance and working conditions[END_REF][START_REF] Wang | A survey of Maintenance policies of deteriorating systems[END_REF][START_REF] Pham | Imperfect Maintenance[END_REF][START_REF] Doyent | Classes of imperfect repair models based on reduction of failure intensity or virtual age[END_REF][START_REF] Kumar | Propotional hazard model A review[END_REF]. However, these models do not fulfill the requisite of relying only on the knowledge of the expert, who usually does not think in terms of age reduction to judge the efficiency of a repair. To this aim, a set {O 1 , O 2 ,…, O n } containing all the possible outcomes of a repair action is introduced; each member of this set represents the degradation state in which the component is left after the maintenance action. Namely, O 0 refers to the As Bad As Old (ABAO) maintenance actions, whereas the generic outcome O i describes the event "after the repair, the degradation state of the component is left to the beginning of D=i". The expert is asked to assess the likelihood that the maintenance action will actually bring the component in D=i, for i=1, 2,…, n. In the spirit of this work, the likelihood of a future event is partitioned in 4 fuzzy sets, namely "Very low", "Low", "High" and "Very High", as shown in Figure 3.

For example, let us consider the particular situation in which only three degradation states are defined (i.e., D=1, 2, 3), and the CBM policy foresees that the component overtakes repair actions if it is found in degradation state D=2 at inspection; no maintenance action is performed in D=1, whereas the component is replaced if found in D=3. Then, the possible outcomes of a repair action are:

-O 0 : the degradation is left unchanged (ABAO) -O 1 : the degradation is lowered to the beginning of D=1 (As Good As New, AGAN)

-O 2 : the degradation is lowered to the beginning of D=2 -O 3 : the degradation is increased to the beginning of D=3 (bad maintenance)

Figure 3: Fuzzification of the likelihood of the events O i .

For the sake of simplicity, let us assume that the expert believes that only the outcomes O 0 and O 2 are possible. In this case, denoting by L 0 and L 2 the likelihood that the outcome of a repair will be O 0 and O 2 , respectively, the expert"s assessment may be expressed by the following sentences:

-

L 0 is Low -L 2 is High
On the other side, several factors may influence the likelihood of the outcome of a repair, such as the number of repairs already done, the starting degradation state, the skill of the operator, etc. In the present illustrative example, only the number of repairs overtaken in the past is considered. In particular, two fuzzy sets "Low" and "High" for the linguistic variable "number of repairs already done" are defined (Figure 4).

In this case, denoting by N the number of repairs performed on the component, the expert"s assessments may be expressed by the following rules: These rules can be implemented for any specific value of N; then, rules 1) and 3) are aggregated to give L 2 , and rules 2) and 4) to give L 0 . Two crisp values are finally obtained from the defuzzification of L 2 and L 0 , which are then normalized to represent the probabilities associated to the two possible results of the maintenance action.

1) If N is Low then L 2 is High. 2) If N is Low then L 0 is Low. 3) If N is High then L 2 is Low. 4) If N is High then L 0 is High.

INTEGRATION OF THE FUZZY MODEL AND MONTE CARLO SIMULATION

One relevant issue in the quantification of the model proposed is the integration of the FL model, which provides the failure rate associated to the degradation state, and the Monte Carlo (MC) module, which simulates the stochastic failure behavior of the component and the changes in the IFs caused by random external events. The output provided by the simulation module is the estimation of the component mean unavailability over the mission time, which is taken in this work to measure the performance of the maintenance policy to be assessed.

The solution proposed in [START_REF] Baraldi | Modeling the effects of maintenance on the degradation of a water-feeding turbo-pump of nuclear power plant[END_REF] to embed the fuzzy module in the MC scheme is adopted in this work. Briefly, a large number of trials or histories (i.e., random walks of the system from one configuration to another) are simulated and the portion of mission time in which the system is in a down state is collected in every trial; finally, these values are averaged to provide an estimation of the desired quantity, i.e., the average unavailability over the mission time.

CASE STUDY

The objective of the present case study is to optimize the maintenance of a Medium-Voltage Circuit-Breaker (MVCB), which protects a short circuit network for testing various devices such as breakers, isolators, disconnector switches, etc. (Figure 5). The breaker is placed just after the generator, and its main function is to interrupt the short circuit current when required. Every time the MVCB interrupts the current, an electric arc takes place between its contacts, which consequently, wear off. If the degradation state is Very Bad, then the breaker loses its interrupting capability; in this case, the arc is not readily extinguished and serious damages can occur before other emergency systems clear the fault. A CBM policy is performed to prevent the wear from reaching a critical value. This is based on periodic visual inspec-tions, in which the breaker is disassembled and the degradation state of the contacts controlled. In particular, three alternative scenarios are possible upon inspection:

-Contacts are as good as new: no action is taken and the breaker is put back together. -Contacts are worn but the interrupting capability is still good: in this case, manual polishing is performed to smooth the surface of the contacts and decrease their electrical resistance. -Contacts are heavily worn: the interrupting capability is at risk and they must be replaced with new ones. Since maintenance actions, as well as failures, have a cost, the best Inspection Interval (II) is a non trivial issue which can be effectively addressed by means of a MC simulation over a long time span, e.g., 15 years.

The results of the process to elicit from the expert the information to build the model are summarized in the following.

Degradation states

The contact resistance is a good indicator of the contacts degradation. This quantity has never been measured, but it is possible to conceive a practical procedure to get this information at every inspection. Three degradation states can be defined:

-D=1: contacts are as good as new.

-D=2: contact resistance is affected by arc wear, and maintenance (contact polishing) can effectively reduce it. -D=3: contacts must be replaced.

A failure event may also occur in every degradation state. It is assumed that the failure times are exponentially distributed, with failure rates that depend on the degradation states.

Influencing factors

The only variable that characterizes the environment is the interrupted current in each test: the higher the interrupted current, the heavier the wear by arc erosion. Most of the current settings range from 10 to 50 kA, so we introduce three fuzzy sets for the environment, namely "Low", "Medium" and "High". For the sake of simplicity, triangular membership functions are considered [START_REF] Bojadziev | Fuzzy Sets, Fuzzy Logic, Applications[END_REF]0 (Figure 6).

Effect of the influencing factors on the effective age

When the contacts are new, or as good as new (D=1), an initial arc wear takes place. This process is rapid (two or three months) and fairly independent on the interrupting conditions. On the other hand, when the contacts are in degradation state D=2 the value of the interrupted current heavily influences the transition time toward state D=3, in which the contacts ability to interrupt the current is compromised. Table 1 summarizes the expert assessments, which lies on the fuzzification of the transition time shown in Figure 7. The number of previous maintenances is considered as a factor that can influence the quality of a repair. The universe of discourse is partitioned by means of two fuzzy sets, "Low" and "High" respectively, as shown in Figure 4.

Table 2 summarizes the expert"s assessment for what concerns the likelihood that a repair either will reduce the degradation state (L 2 ) or leave it as it currently is (L 0 ).

Parameter evaluation

Table 3 summarizes the values of the parameters used in the simulation. The failure rates of the exponential distributed failure times in the three degradation states are  1 = 1.0e-6 h -1 ,  2 = 2.1e-5 h -1 and  3 = 2.5e-2 h -1 , respectively.

RESULTS

Figures 8 shows the results of the CBM model built according to the procedure described above. These results are provided by MC simulation of 5000 trials with the mission time of the component set to 15 working years. The computational time for each simulation is a mere few seconds on a regular desktop computer.

The average unavailability reaches a minimum in correspondence of II=3500 working hours. Further investigations show that this minimum corresponds to the situation in which an inspection takes place just before the component enters the third degradation state.

CONCLUSION

We have proposed a method to use the information elicited from an expert to build a maintenance model of a generic electrical component, which is then simulated in order to optimize the maintenance policy.

One key feature of the model lies in its capability of accounting for the actual working conditions in which the component operates. This capability comes from the fact that the aging process of the component is deduced step-by-step by means of interviews, in which the expert"s experience on components working in different conditions with different aging behaviors is captured and made exploitable for modeling. In this setting, we have largely resorted to FL to represent and propagate the imprecision associated to the qualitative sentences of the expert.

Figure 1 :

 1 Figure 1: Example of time evolution of the effective age depending on the component working conditions through the age speed .

Figure 2 :

 2 Figure 2: Depending on the IFs, the expert specifies the age speed by giving the transition time between one degradation state and the following one.

Figure 4 :

 4 Figure 4: Fuzzification of the number of repairs already done.

Figure 5 :

 5 Figure 5: Overview of the Medium Voltage test network.

Figure 6 :

 6 Figure 6: Fuzzy set definition for the environment, according to the interrupted current.

5. 4

 4 Figure 7: Fuzzification of the transition time.

Figure 8 :

 8 Figure 8: Average unavailability as a function of the II.

  , A. Balestrero, M. Compare

	Energy Department, Politecnico di Milano, Italy
	E. Zio
	Energy Department, Politecnico di Milano, Italy
	Ecole Central Paris-Supelec, France
	L. Benetrix, A. Despujols
	EDF R&D, Chatou, France

Table 1 :

 1 Expert"s estimation of the transition time.

		Environment
		Good Medium Heavy
	Transition time D=1→D=2	Very small
	Transition time D=2 →D=3 High Medium Small

Table 2 :

 2 Likelihood of the two possible outcomes of a repair, as a function of the number of repairs already done.

		Number of repairs already done
		Low	High
	L 0	Low	High
	L 2	High	Low

Table 3 :

 3 Summary of the simulation parameters.

	Quantity	Expert's assessment
	Inspection duration [h]	8
	Maintenance duration [h]	8
	Scheduled Replacement duration	16
	Replacement duration after failure [h]	40