Romain Pinquié
email: romain.pinquie@ensam.eu

Philippe Véron
email: philippe.veron@ensam.eu

Frédéric Segonds
email: frederic.segonds@ensam.eu

Nicolas Croué
email: nicolas.croue@keonys.com

Requirement mining for model-based product design

Keywords: requirements, unstructured, extraction, classification, natural language processing, NLP, supervised learning, machine learning

PLM software applications should enable engineers to develop and manage requirements throughout the product's lifecycle. However, PLM activities of the beginning-of-life and end-of-life of a product mainly deal with a fastidious document-based approach. Indeed, requirements are scattered in many different prescriptive documents (reports, specifications, standards, regulations, etc.) that make the feeding of a requirements management tool laborious. Our contribution is two-fold. First, we propose a natural language processing (NLP) pipeline to extract requirements from prescriptive documents. Second, we show how machine learning techniques can be used to develop a text classifier that will automatically classify requirements into disciplines. Both contributions support companies willing to feed a requirements management tool from prescriptive documents. The NLP experiment shows an average precision of 0.86 and an average recall of 0.95, whereas the SVM requirements classifier outperforms that of naive Bayes with a 76% accuracy rate.

Introduction

Context

Requirements engineering is one of the most critical product lifecycle management (PLM) activities. Indeed, it is well-documented that the cost to fix errors increases as the project and product mature (INCOSE, 2015b;[START_REF] Stecklein | Error cost escalation through the project life cycle[END_REF]. Figure 1 illustrates how the committed lifecycle's cost significantly increases with the time. The study of systems engineering effectiveness carried out by [START_REF] Elm | A study of systems engineering effectiveness -initial results[END_REF] showed that requirements-related factors had a moderately strong relationship to project performances. Moreover, in their analysis of the effectiveness of software defection detection using peer reviews, [START_REF] Selby | 4.4.2 measurement-driven systems engineering using Six Sigma techniques to improve software defect detection[END_REF] discovered that 49.1% of defects were injected during the requirements engineering phase. [START_REF] Standish | Chaos, Technical report[END_REF] already identified requirements engineering as a major cause of software project failure and success. Despite this observation, although a major difference between product data management (PDM) and PLM is the extension of the management activity from the design and manufacturing phases to the entire product's lifecycle, very few papers related to requirements engineering have either been presented at the PLM conferences or published in the International Journal of Product Lifecycle Management (IJPLM). However, requirements engineering has been extensively studied by systems engineering [START_REF] Sommerville | Requirements Engineering. A Good Practice Guide[END_REF][START_REF] Hull | Requirements engineering[END_REF]INCOSE, 2015a) and software engineering [START_REF] Leffingwell | Managing Software Requirements: A Unified Approach[END_REF][START_REF] Aurum | Engineering and Managing Software Requirements[END_REF][START_REF] Chemuturi | Requirements Engineering and Management for Software Development Projects[END_REF][START_REF] Wiegers | Software Requirements[END_REF] practitioners.

Tools are also prone to inequalities. Indeed, there exist various very sophisticated technologies to support the engineering activities that belong to the middle-of-life of a product. 3D geometric modellers, virtual and augmented reality environment, dynamic simulation are standard technologies in industrial design offices. However, the downstream and upstream PLM activities such as requirements engineering still deal with elementary tools like text files, spreadsheets and, at best, relational databases.

Problem

Among the product's lifecycle phases defined by [START_REF] Terzi | Product lifecycle management -from its history to its new role[END_REF], our research study focuses on the requirements analysis phase. Nowadays, a set of requirements is tremendously challenging to develop and manage because of its very large size. For example, at Mercedes-Benz, the size of a building block specification varies from 60 to 2,000 pages and prescribes between 1,000 and 50,000 requirements [START_REF] Houdek | Challenges in automotive requirements management[END_REF]. [START_REF] Langenfeld | Requirements defects over a project lifetime: an empirical analysis of defect data from a 5-year automotive project at Bosch[END_REF] report that, at Bosch, the project to develop a commercial DC-to-DC converter for a mild hybrid vehicle required more than 10,000 requirements. At Sony Ericsson, the total volume of market and platform system requirements exceeds 10,000 [START_REF] Regnell | Can We Beat the Complexity of Very Large-Scale Requirements Engineering?[END_REF]. At Ericsson Microwave Systems, a product that is tailored to customer requests involves between 3,000 and 6,000 requirements, whereas the development of a subsystem involves between 700 and 1,300 requirements [START_REF] Alenljung | Decision-Making Activities in Requirements Engineering Decision Processes: A Case Study[END_REF]. The specification of the FBI Virtual Case file contained more than 800 pages of requirements [START_REF] Goldstein | Who killed the virtual case file?[END_REF]. Among the leading causes of such a staggering increase in the number of requirements we find: the ever-increasing complexity of products and their relentless customisation; the mushrooming accumulation of legal documents; and the geographically dispersed teams through whom products are developed. In addition, requirements are scattered in unstructured prescriptive documents -e.g., Word, PDF, Excel -and a majority -79% according to [START_REF] Mich | Market research for requirements analysis using linguistic tools[END_REF] -are written in unrestricted natural language.

The mushrooming of requirements causes several requirements engineering problems such as the collection, analysis, and traceability of requirements. In this paper, we address two challenges:

1 the extraction of requirements from prescriptive documents 2 the classification of requirements into disciplines.

Extraction of requirements from prescriptive documents

In this study, a prescriptive document is a document that prescribes requirements and which also usually contains informative statements providing contextual information to better interpret the requirements. For instance, Figure 2 is an extract of a prescriptive document, a specification, that is made up of informative statements (in green) introducing functional requirements (in red). Market surveys, reports of interviews with customers, specifications, concepts of operations, business cases or meeting notes can be prescriptive documents. There is no universal definition of what a requirement is. According to the International Council on Systems Engineering (INCOSE, 2015a), a requirement is a formal transformation of one or more needs into an agreed-to obligation for an entity to perform some function or possess some quality within specified constraints. The INCOSE distinguishes a requirement from a need. A need is an agreed-to expectation for an entity to perform some function or possess some quality within specified constraints (INCOSE, 2015a). To put it simply, a need is an ill-defined (incomplete, unverifiable, etc.) prescriptive statement issued by a (sub-)system acquirer, whereas a requirement is a well-defined (complete, verifiable, etc.) prescriptive statement issued by a (sub-)system supplier. By prescriptive statement, we mean a piece of text -a sentence generally -that prescribes a structural or behavioural property [START_REF] Micouin | Property-model methodology: a model-based systems engineering approach using VHDL-AMS[END_REF]) that an object shall own under some potential conditions. There is a derivation phase to transform needs into requirements. For instance, the need 'the user interface shall be user friendly' can be derived into the requirement 'any information shall be accessible within three clicks from each other'. Additionally, there is a third kind of prescriptive statement: constraints. Whereas needs and requirements make certain designs inappropriate for their intended use, constraints make certain design solutions not allowed. The former are usually prescribed by a (sub-)system acquirer or supplier, whereas the latter are prescribed by third-party stakeholders such as regulation authorities or legislations. This segmentation of prescriptive statements into needs, requirements, and constraints is subjective. Labels and underlying concepts vary from one source to another. For instance, needs are sometimes called stakeholder requirements, whereas requirements and constraints are sometimes called system requirements and legal requirements, respectively. Thus, any prescriptive statement can be identified as a requirement with a different qualifying adjective.

When a (sub-)system supplier receives a set of large prescriptive documents, he has no other alternative than to go through the documents to identify the applicable requirements, manually enter them in a requirements management tool, design and verify candidate solutions. Figure 3 illustrates the problem corresponding to the rework task that consists in moving the existing requirements from large prescriptive documents to a requirements management tool. The solution we look for shall be flexible enough to enable (sub-)system suppliers to extract any kind of textual requirements. It shall help to extract and import stakeholder requirements in a database within which their maturity is controlled while deriving them into system requirements. The solution shall also enable suppliers to extract system requirements when reusing in whole or in part a specification from a previous version or a similar existing product. Finally, the solution shall automatically extract legal requirements issued by a third-party.

Being able to automatically extract and import several hundreds or thousands of requirements helps to feed a requirements management tool, but it does not ease their exploitation.

Classification of requirements into disciplines

In the requirements management tool, each domain expert should be able to filter the requirements according to his domain of expertise. For instance, marketers should be able to filter marketing requirements, whereas mechanical engineers should quickly retrieve mechanical ones. In most requirements management tools, analysts can manually specify the value of an attribute standing for the discipline a given requirement belongs to. In this scenario, each time an analyst specifies a new requirement, he also has to input the associated topic. The main problem is the time required to fill one more attribute in addition to the author, version, statement, priority, source, etc. Moreover, if analysts are not domain experts, the categorisation task can also be rather fastidious.

Contribution

Figure 4 illustrates our twofold contribution. First, we propose a natural language processing (NLP) pipeline to extract textual requirements from unstructured and semi-structured prescriptive documents. Second, we show how to implement supervised machine-learning techniques so as to automatically classify requirements into disciplines.

An NLP pipeline to extract requirements

As we will be showing in Section 2.1, although modal verbs are reliable lexical features to identify requirements, the literature review shows that legal terms, as well as the verbs require, need and their derived forms, must be considered too. However, we contend that the solution is still sub-optimal. Indeed, most companies are not aware of, or do not want to follow, systems engineering principles defined in the INCOSE guidelines or IEEE standards, but instead, prefer 'to colour outside the line'. It is therefore usual for them to use verbs that not only express a requirement or a need, but also an expectation, a wish, a hope, a desire, etc. Then, verbs including, but not limited to, expect, need, wish, want or desire also need to be considered. In addition, as there are diverse writing styles, the use of syntactic rules to identify requirements is very likely to be too restrictive in some cases. To follow the principle of parsimony, we propose to enhance the existing lists of prescriptive verbs and to stick to a rule-based classifier that does not sacrifice recall for the sake of precision.

The NLP task of sentence splitting is challenged by the authors' lack of rigour when using lists, bullets, numbering, tables, etc. To limit the side effects of incomplete sentence, we combine the NLP capabilities of the Stanford Parser with the parsing ones of Apache Tika to consider the structure (chapters, sections, footers, headers, lists, tables, etc.) of a prescriptive document.

A machine learning-based classifier to classify requirements

As previously explained, the labelling of requirements with a predefined set of disciplines is a text classification problem. Most supervised techniques that have been proposed to classify requirements face the need for a large enough training set. So far, there are no training sets that we can reuse. PLM being a blend of disciplines, the development of several hundreds or thousands of examples for each discipline would be too time-and-resource consuming. In addition, previous contributions focused on German written requirements only. Thus, we propose to build a supervised classifier for English written requirements. However, instead of asking a supervisor to manually write and classify examples, we propose to automatically generate a training set. The training set is a large set of sentences extracted from handbooks corresponding to disciplines. In our experiment, we have chosen four disciplines:

• mechanical engineering (ME)

• electrical engineering (EE)

• computer science (CS)

• reliability, availability, maintenance and safety (RAMS).

The rest of the paper is organised as follows. Section 2 is a literature review of the existing techniques to extract (Section 2.1) and classify (Section 2.2) requirements. Section 3 describes the NLP pipeline to extract requirements from prescriptive documents (Section 3.1) and the machine learning-based classifier to classify requirements into disciplines (Section 3.2). Section 4 provides experimental results for the NLP pipeline (Section 4.1) and the machine learning-based classifier (Section 4.2). Finally, Section 5 summarises our contributions and gives perspectives for improvements.

Literature review

Recently, information retrieval, NLP, web semantics and text mining techniques have been attracting more attention from academics and industrialists who are challenged by the increasing size of textual data that needs to be collected, stored, analysed and managed in a PLM software application. Relevant research studies, including, but not limited to, [START_REF] Madhusudanan | Evaluation of methods to identify assembly issues in text[END_REF], [START_REF] Jones | Improving Enterprise Wide Search in Large Engineering Multinationals: A Linguistic Comparison of the Structures of Internet-Search and Enterprise-Search Queries[END_REF] and Zhang et al. ( 2016)presented at the last PLM 2015 international conference -or [START_REF] Feldhusen | Enhancement of adaptable product development by computerised comparison of requirement lists[END_REF] have demonstrated the benefits of applying such bodies of knowledge to solve PLM problems. This section gives a broader literature review of the current existing solutions to not only extract textual requirements from prescriptive documents, but also classify them into disciplines.

How can we extract requirements?

A specification S is a couple ( , ), R I where R is a set of requirements and I is a set of informative statements. We notice that very few research studies attempt to automatically distinguish both kinds of statements in unstructured prescriptive documents.

Commercial requirements management tools: commercial requirements management tools do not embed any NLP capabilities. When importing a Word document into IBM Rational DOORS, users choose the decomposition level -none, paragraph, sentence or keyword -he prefers to create similar doors objects. The DOORS and Word documents are twins. Outline level 1-9 are imported as rational DOORS headings objects, whereas tables and bulleted lists become rational DOORS tables and lists, respectively. PLM integrated solutions such as ENOVIA requirements central require manual selections to capture the structure of the document before importing it. Requirements also have to be selected manually. Most requirements management tools propose to distinguish informative sentences from requirements based on a list of keywords that is manually predefined by the user. Users shall therefore know and specify all the inflectional forms of each keyword. Such a solution does not help to maximise recall. Morphological analysis like lemmatisation should be used to remove inflectional endings. Finally, some companies, small and medium-sized business specially, do not want to buy, or cannot afford, such heavy database environments, but prefer a flexible standalone processing tool that can extract requirements at a glance.

Modal verbs: modal verbs such as shall, must and should are key lexical features for identifying requirements [START_REF] Lash | Computational Representation of Linguistic Semantics for Requirement Analysis in Engineering Design[END_REF]. [START_REF] Coatanéa | Requirements Model for Engineering, Procurement and Interoperability: A Graph and Power Laws Vision of Requirements Engineering[END_REF] propose a three-step process to extract requirements from unstructured specifications. The first step is to extract the sentences from a set of documents using a syntactic rule that identifies sentences by looking at capital characters and full stops. The summary report does not give further details; consequently, we can only conclude that the proposition seems sub-optimal. Indeed, although [START_REF] Riley | Some applications of tree-based modelling to speech and language[END_REF] has shown as far back as 1989 that 90% of full stops are sentence boundary indicators, heuristic algorithms suffer from the tokenisation process that requires a lot of hand-coding and domain knowledge [START_REF] Manning | Foundations of Statistical Natural Language Processing[END_REF]. In prescriptive documents, we observe that there are many instances of frequent omissions of full stops. For instance, when tables and bulleted lists are used to collect requirements. Additionally, headings do not usually finish with a full stop and are therefore concatenated with the consecutive sentence. Full stops can also be used in abbreviations or numbers. These pitfalls would not be avoided by a mere rule that only look at capital characters and full stops. Figure 5 gives an example where the extraction of complete sentences is not an easy task. In case A, the heading would be concatenated with both ids and statements in a single sentence. In case B, the sentence would correspond to the whole enumeration. [START_REF] Kof | Natural language processing for requirements engineering: applicability to large requirements documents[END_REF] discussed these sources of incomplete sentences that require a time-consuming manual rephrasing phase: 1.5 working days for an 80-pages specification. Once the identification of the sentence has been done, [START_REF] Coatanéa | Requirements Model for Engineering, Procurement and Interoperability: A Graph and Power Laws Vision of Requirements Engineering[END_REF] use the Stanford parser to identify modal verbs whose POS-tag is 'MD'. Finally, a binary rule-based classifier applies a syntactic rule that labels a sentence as a requirement based on the presence or absence of a modal verb. [START_REF] Bernard | Design: a key stage of product lifecycle[END_REF] reused this solution without stating the potential problems that [START_REF] Kof | Natural language processing for requirements engineering: applicability to large requirements documents[END_REF] and us faced to extract complete sentences from unstructured documents. Although systems engineering best practices recommend to use modal verbs in general and the modal shall in particular, to specify requirements, such a rule is not followed by all companies. Moreover, as explained in Section 1.3.1, in this work, we not only want to collect well-defined requirements, but also ill-defined ones which are often implicitly stated by using prescriptive verbs such as (want, desire, expect, etc.) and derived forms.

Legal terms: legal terms help to identify legal requirements. [START_REF] Breaux | Mining rule semantics to understand legislative compliance[END_REF] developed three lists of syntactic patterns that are commonly used to encode rights, obligations and constraints. More recently, Zeni et al. (2015) have proposed GaiuST, a framework that extracts legal requirements for ensuring regulatory compliance. In their study, they propose to identify rights, anti-rights, obligations and anti-obligations thanks to lexical features too. Their four lists extend the usual list of modal verbs by adding verbs such as permit and require, as well as derived forms like is not required. However, these features exclusively concentrate on legal text. Requirements are not only specified in legal documents -e.g., standards, policies or laws -, but also in reports of interviews, specifications, concepts of operations, business cases or meeting notes whose jargon differs from the legal one.

Syntactic rules: Kang andSaint-Dizier (2013, 2014) implemented 12 syntactic rules for identifying requirements without requiring domain knowledge. In their list, requirements fall into two categories: lexically induced requirements and requirements composed of modal. The former enhances the latter as it adds the verbs require, need and their derived forms such as requires, required, need or needed to the list of modal verbs. Their solution gives promising results as they experienced a precision of 0.97 and a recall of 0.96 on a corpus of 64 pages prescribing 215 requirements.

Rules vs. statistical learning: knowledge engineering and statistical learning are the two main text classification approaches [START_REF] Feldman | Text Mining Handbook: Advanced Approaches in Analyzing Unstructured Data[END_REF]. We did not find any study that proposes to solve the problem of requirements extraction by adopting a machine learning approach. This is not surprising since the main constraint is to obtain a high recall with an acceptable precision, rather than the opposite. Indeed, finding true requirements takes at least an order of magnitude more time than rejecting a false positive. The former requires a tedious manual search, whereas the latter can be done usually in a split second by looking at the claimed requirement. A rule-based approach usually returns a higher recall than a machine learning-based one.

How can we automatically classify requirements into disciplines?

There are two main approaches to regrouping pieces of text -i.e., document, paragraph, sentence, chunk, etc. -into topics: classification or clustering [START_REF] Manning | Foundations of Statistical Natural Language Processing[END_REF][START_REF] Manning | An Introduction to Information Retrieval[END_REF][START_REF] Feldman | Text Mining Handbook: Advanced Approaches in Analyzing Unstructured Data[END_REF].

Classification: given a finite set of categories, the problem of text classification consists in determining which category a given piece of text belongs to. There are two approaches for classifying things: knowledge engineering and machine learning.

A knowledge engineering approach consists in encoding, either declaratively or in the form of procedural classification rules, experts' knowledge about the categories into the system [START_REF] Feldman | Text Mining Handbook: Advanced Approaches in Analyzing Unstructured Data[END_REF]. For instance, one can implement a rule that labels all sentences containing the term computer with the category computer science. Rules can be much more sophisticated regular expressions.

Alternatively, a supervised learning approach consists in using a learning algorithm to estimate a classification function from a set of manually pre-classified examples. An example is made up of a vector of features and a label. The vector of features is a set of key characteristics that describes the things to classify. For instance, if one wants to distinguish interrogative sentences from exclamatory ones, question and exclamation marks, interrogative and emotion words are key features. In addition to the vector of features, each training example is defined by a label that represents the category it belongs to. In the previous example, each sentence has to be manually labelled with the category interrogative or exclamatory. Derived from a learning algorithm, the classification function is used to automatically map an unlabelled text to one or several categories. [START_REF] Sebastiani | Machine learning in automated text categorization[END_REF] gives a detailed introduction to text classification. [START_REF] Ott | Automatic Requirement Categorization of Large Natural Language Specifications at Mercedes-Benz for Review Improvements[END_REF] evaluates several classifiers that classify requirements into topics. Each topic is manually defined as a set of keywords. The best classifier will be used to enable inspectors to clean requirements' defects in parallel. The study states that decision trees and rule-based learning algorithms returned poor results. Therefore, the authors focused on the multinomial naive Bayes (MNB) and the support vector machine (SVM) algorithms. The preprocessing pipeline is not relevant for our problem because the classifier is tuned for German written specifications, whereas our work focuses on English text. One major problem that the research study points out is the difficulty of getting sufficient training examples so as to improve the current recall of 0.8 and precision of 0.6. [START_REF] Knauss | Semi-)automatic categorization of natural language requirements[END_REF] enhanced the previous proposition by comparing three classification approaches: manual, semi-automatic and automatic. The first approach is a manual classification where the user has to assign one or several categories to each requirement. The semi-automatic method automatically classifies a given requirement but requires a confirmation or modification from the user. Finally, the automatic classifier does not require a manual confirmation or modification. The semi-automatic approach is an interesting way of overcoming the cold start problem that is due to a small training set. Indeed, once the semi-automatic classification of a requirement is confirmed or modified by the user, the system adds the requirement to the training set. Although the main ideas are of interest, we cannot directly transpose their method as they also focus on German written specifications.

Clustering: in contrast, clustering is a form of unsupervised learning since a given example is not labelled with a class label. In text mining, clustering algorithms aim at creating clusters of documents where documents within a cluster should be highly similar, and documents in a given cluster should be highly dissimilar from documents in other clusters. [START_REF] Aggarwal | A survey of text clustering algorithms[END_REF] give a survey of text clustering.

There have been many attempts to cluster requirements [START_REF] Duan | Clustering and Its Application in Requirements Engineering[END_REF] to automate various tasks like keywords list development [START_REF] Ko | Using classification techniques for informal requirements in the requirements analysis-supporting system[END_REF], requirements tracing (Duan and Cleland-Huang, 2007a;[START_REF] Sannier | Defining and retrieving themes in nuclear regulations[END_REF], requirements prioritisation and triage [START_REF] Laurent | Towards automated requirements triage[END_REF][START_REF] Duan | Towards automated requirements prioritization and triage[END_REF], detecting cross-cutting concerns (Duan and Cleland-Huang, 2007b), or discovering and improving a prescriptive document's structure [START_REF] Ferrari | Using Clustering to Improve the Structure of Natural Language Requirements Documents[END_REF].

Although unsupervised learning techniques such as clustering and topic modelling are of interest to facilitate the exploitation and management of a large set of requirements, they are not directly suited to our problem as we have predefined categories corresponding to the functional areas of a company.

Extraction and classification of requirements

This section introduces the proposed method to extract and classify requirements. First, we introduce a NLP pipeline that extracts text-based requirements from unstructured and semi-structured prescriptive documents. Second, we show how a machine learning-based classifier can automatically map requirements to disciplines.

Requirements extraction from prescriptive documents

Before introducing the NLP pipeline, we shall clearly distinguish unstructured from semi-structured documents. Digital documents store data that falls into three categories: structured, semi-structured and unstructured [START_REF] Li | Ease: an effective 3-in-1 keyword search method for unstructured, semi-structured and structured data[END_REF][START_REF] Sint | Combining unstructured, fully structured and semi-structured information in semantic wikis[END_REF][START_REF] Abiteboul | Web Data Management[END_REF].

In structured data, one can distinguish the data structure (the schema) from the data itself (an instance). We say that an instance conforms to the schema. Structured data is synonymous with tabular data organised in a matrix where rows and columns correspond to data and attributes, respectively. Requirements management tools such as IBM Rational Doors or Enovia V6 requirements store structured specifications in relational databases.

As the name implies, unstructured data do not have any underlying structure. They are sequences of characters. Unstructured data cannot be stored in tables. Specifications written with software like Word or OpenOffice, or encoded in PDF are unstructured specifications.

Lastly, semi-structured data are blends of structured and unstructured data. Indeed, it is more structured than a raw sequence of characters but less than a table. Usually, semi-structured data can be represented as a tree -e.g., XML format -or as a graphe.g., XMI format. For instance, a specification that complies with the requirements interchange format (ReqIF) (Object Modeling Group, 2016) is semi-structured.

In this study, we concentrate on the extraction of requirements from unstructured and semi-structured prescriptive documents, with an emphasis on the challenging unstructured ones. To do so, we rely on the following NLP pipeline:

Step 1 <Uploading>: the user uploads one or more prescriptive documents. The prototype can process unstructured documents whose format is .doc(x) (Word), .odf (OpenOffice), .pdf (portable document format) and .xls(x) (Excel).

Regarding semi-structured documents, there are various SysML authoring tools and their XML schema definition is very likely to change from one to another.

Our experiment focuses on the requirements diagram edited with Papyrus as it is a commonly used open-source tool. Once saved in XMI format, semi-structured SysML requirements diagram can be uploaded in our prototype. Our solution also supports semi-structured ReqIF specifications exported from a requirements management tool. In this study, we use the ProR open-source editor.

Step 2 <Parsing>: we trigger a specific parser according to the document format (MIME) identified with the Apache Tika API.

If it is an unstructured .doc(x) or .odf document, the parser uses the Apache Tika API to extract the textual content and transform it into .html semi-structured data. We transform the content into HTML because it enables us to get the document's structure by seeking specific HTML tags: header, footer, headings, sections, tables, bullets, numbering, etc. Headings are not only useful to extract complete sentences, but also help to identify the sections which may be used to run NLP tasks in parallel (multi-threading).

If it is an unstructured PDF document, in batch mode, the native capability of Word converts the document from .pdf into .doc. Then, as for .doc, the Apache Tika API converts from .doc into .html. The structure of PDF document is usually lost except for the ones whose native format is Word and partially OpenOffice. Thus, by parsing the new .html semi-structured document, we verify whether the .pdf was generated with Word or OpenOffice. HTML tags such as header, footer or table are of interest for this task. If we find that the .pdf was generated with Word or OpenOffice, then we call the .doc parser; otherwise, we use the .pdf parser that relies on the Apache Tika API and various rules. The second scenario leads to much less accurate results as we lose the document's structure. Fortunately, today, Word and OpenOffice are leading the text processor market.

The .xls(x) parser uses the Apache POI API to parse the textual content of each cell. We make the assumption that analysts follow the requirements writing rules advising that a requirement statement is a single sentence (INCOSE, 2015a); therefore, it is a single cell in the spreadsheet. Each sentences in a cell being a potential requirement statement.

Finally, the .xml parser uses the JDOM parser to parse semi-structured SysML requirements diagrams and ReqIF specifications by extracting the content of XML elements whose tags stand for a requirement statement.

Step 3 <Extract text sections>: we use various regular expressions and analyse HTML tags to clean the HTML document generated in Step 2. For instance, we rebuild complete sentences from bullets and numberings, get rid of the headers, footers, and extract the textual content from tables. We also use a list of keywords such as introduction, scope, table of content, glossary, acronyms, preamble, terminology, appendix, etc. to skip the informative sections that may generate false positive results. Finally, by parsing the HTML document, we can extract the text sections with the associated headings. If the document does not contain any section, then the document itself stands for a single section.

The rest of the process benefits from the NLP capabilities offered by the Java-based Stanford CoreNLP library. Among the various existing NLP libraries (Gate, OpenNLP, etc.), Standford CoreNLP was preferred for several reasons. First, the contributions presented in this paper are part of a larger Java web application. Java as a programming language was therefore mandatory. Second, CoreNLP is one of the most complete NLP library that is actively improved by the Stanford NLP group. Third, the CoreNLP is very well-documented. Finally, the CoreNLP functionalities are also available for Chinese, French, German and Spanish, which will enable us to extend our proposition.

Step 4 <Tokenisation>: the Stanford CoreNLP [START_REF] Manning | The Stanford CoreNLP natural language processing toolkit[END_REF] tokeniser API iteratively tokenises each specification content, that is, it chops the text up into pieces of a sequence of characters that are grouped together as a useful semantic unit for processing, the tokens. For instance, the tokenisation of the statement "The customer requires that the system shall comply with the ISO-15288 standard." returns "The, customer, requires, that, the, system, shall, comply, with, the, ISO-15288, standard, .".

Step 5 <Lemmatisation>: the Stanford CoreNLP lemmatiser API iteratively normalises each token by removing the inflectional ending and returns the dictionary form, the lemma. For instance, lemmatisation reduces the tokens 'requires', 'required' and 'require' to their canonical form 'require'. This not only enables us to increase the recall of the rule-based sentence classifier in

Step 8 <sentence classification>, but also to reduce the vocabulary size that can be of very high dimension.

Step 6 <POS-tagging>: the Stanford CoreNLP POS-tagger API iteratively annotates each token with its grammatical category (noun, verb, adjective, adverb, etc.), the part of speech (POS). Figure 6 shows an example of a labelled sentence. Step 7 <Sentence splitting>: the Stanford CoreNLP Parser API iteratively splits the textual content of each document into sentences. A sentence-lemma matrix stores the sentences in rows and the lemmas in columns.

Step 8 <Sentence classification>: a binary knowledge engineering -a.k.a. rule-basedtext classifier classifies each sentence into 'requirement' vs. 'information'. The matrix of sentence-lemma is traversed, and when the condition "if lemma i of sentence j is a prescriptive verb ∈ {shall, must, should, may, will, have to, require, need, obligate, restrict, provide, permit, mandate, want, expect, wish, desire, crave, demand or recommend}" is true, then the current sentence j is classified as a requirement.

The NLP tasks presented in this section enable users to extract requirements from unstructured and semi-structured prescriptive documents. To date, this capability is part of a standalone JAVA web application, but it could be integrated as a new module or plug-in in commercial requirements management tools.

Once requirements have been extracted, imported and matured in a requirements management tool, designers start the functional, behavioural and physical design synthesis. The 'zigzagging' iterative and recursive process from requirements to design solutions described in the axiomatic design theory of [START_REF] Suh | Axiomatic Design: Advances and Applications[END_REF] should be adopted so as to get the expected results and rise opportunities for innovation [START_REF] Suh | Complexity: Theory and Applications[END_REF]. Nonetheless, when designers deal with a large number of requirements, model-based product design brings about the need to quickly retrieve requirements from the database according to the user's domain of expertise.

Classification of requirements into disciplines

Figure 7 shows that requirements management tools also gives analysts the opportunity to define a range of attributes (e.g., name, title, content, author, source, priority, rationale, cost, etc.) among which one can define a specific attribute to classify requirements into disciplines. Before detailing each step, we shall clearly define our classification problem.

Definition of the classification problem

To formally define our machine learning-based classification problem, we shall consider five elements:

1 A feature vector . i

x Terms is the default form of features in text classification, but it could also be the POS tag of tokens, the results of more sophisticated regular expressions or dimensionality reduction techniques like singular value decomposition, latent semantic indexing or principal component analysis. {( , ), ( , ), , ( , )}

n n x c x c x c = … X
where c i is the class, that is, the discipline, to which the i th requirement belongs to.

The statistical learning classification problem consists in estimating a classification function γ that maps requirements to disciplines:

γ = → X ( 1 )

Automatically generating a training set

According to [START_REF] Manning | An Introduction to Information Retrieval[END_REF], "the biggest practical challenge in fielding a machine learning classifier in real application is creating training data". [START_REF] Ott | Automatic Requirement Categorization of Large Natural Language Specifications at Mercedes-Benz for Review Improvements[END_REF] and [START_REF] Knauss | Semi-)automatic categorization of natural language requirements[END_REF] -18,135, 19,464, 20,183 and 19,699 examples for the ME, EE, CS and RAMS class, respectively. These sentences will finally be transformed into a vector space model. For the sake of simplicity, one can imagine the feature space S as a high dimensional × M sentence-feature matrix, where is the number of sentences and M is the number of features. To transform a given sentence into a vector of features we need to perform a range of natural language pre-processing tasks. In this experiment, we apply tokenisation, case-folding and stop-word removal. Stemming does not usually deliver an additional value but can help to compensate the data sparseness and reduce the computing cost by reducing the vocabulary size [START_REF] Manning | An Introduction to Information Retrieval[END_REF]. Nevertheless, in their experiments of classification at the sentence level, [START_REF] Khoo | Experiments with sentence classification[END_REF] demonstrated that the lemmatisation of tokens was harmful to performance. Therefore, we did not add the lemmatisation task to the pre-processing pipeline. Stemming being even more aggressive than lemmatisation, we have discarded it too. Thanks to the pre-processing pipeline the initial vocabulary size was reduced from 40,729 features, that is, a 77,481 × 40,729 sentence-feature matrix, to 32,885 features.

Features selection and learning algorithms evaluation

Although the pre-processing tasks reduce the vocabulary size, the sentence-feature matrix is still very large and sparse. The larger the matrix, the longer it takes to train the model. Therefore, it is of interest to reduce the size of the matrix to not only compensate the data sparseness, but also reduce the computing cost. Moreover, feature selection consists in selecting a subset of features by avoiding noise features occurring in the training set and using this subset to train a learning algorithm. A noise feature is a feature that increases the misclassification error rate. For instance, if the term temperature has no information about the ME class, but all sentences that contain the term temperature happen to occur in the ME class, then the learning algorithm may produce a classifier that misclassifies new unlabelled requirement statements. When such an incorrect generalisation happens, we say that the classifier overfits the data. In summary, feature selection helps to reduce the training time while preserving, or improving, the accuracy.

There are three main paradigms of feature selection: filter, wrapper and embedded methods [START_REF] Forman | Feature selection for text classification[END_REF]. Although wrapper methods perform best, they are impracticable in our case because of the large size of the initial set of features. Conversely, filtering methods are the most scalable. With filtering methods, the selection of features requires to compute a utility measure A(t i , c i ) for each term t i of the vocabulary against each class c i . The number of features to select depends on the number of features the user wants to keep or a cut-off value of the utility measure. There exist diverse utility measures [START_REF] Forman | An extensive empirical study of feature selection metrics for text classification[END_REF], but the main ones are: mutual information (MI) that is similar to information gain (IG), X 2 and term frequency (TF) [START_REF] Manning | An Introduction to Information Retrieval[END_REF].

TF-based feature selection techniques generally provide less accurate results than X 2 or IG. Moreover, [START_REF] Manning | An Introduction to Information Retrieval[END_REF] point out that no matter which X 2 or IG utility measure is preferred, accuracy does not usually varies significantly. Therefore, we have decided to use IG in our experiment.

The training procedure aims at fitting a classification function that maps requirements to disciplines. In other words, the learning method searches for a good set of parameter values by optimising the misclassification rate criterion. Equation [START_REF][END_REF] shows the definition of the training misclassification rate where ˆi y is the predicted discipline for the i th example in the training set using the approximated classification function ˆ. ( )

1 1 Training misclassification rate n i i i I y y n = = ≠ ∑ ( 2 )
To evaluate the learning algorithms we look at the misclassification rate given in equation (3) on the development set and try to minimise it. The best classifier is the one for which the development misclassification rate is the smallest.

( ) ( )

Development misclassification rate i i Ave I y y = ≠ ( 3 )
In our experiment, we are evaluating two learning algorithms: naive Bayes (NB) and SVM. NB and SVM have been preferred because the former is general enough to be applied to almost any classification problem, whereas the latter usually outperforms other learning algorithms in text classification. The choice of NB and SVM was also motivated by two common trade-offs [START_REF] James | An Introduction to Statistical Learning with Applications in R[END_REF]:

• Bias vs. variance: on the one hand, one can see bias as the error that is introduced by approximating a real life problem to a much simple one. On the other hand, variance is the amount by which the approximated classification function γ would change if we estimate it using a different training set. If a classifier has a high variance, then small changes in the training data can result in a large change in ˆ. γ Therefore, a classifier that has a high variance can perform well on the training set, but its performance on a new set of previously unseen data can be unacceptable. This is the problem of overfitting. The underlying concept behind bias and variance is the flexibility of a learning algorithm. A model is flexible if the approximated classification function γ can fit a wide range of training data closely. A linear function is for instance less flexible than a polynomial function of degree 2. Generally, learning algorithms with low flexibility like NB have high bias but low variance, whereas learning algorithms with high flexibility like SVM have low bias but high variance.

• Prediction accuracy vs. model interpretability: flexible learning algorithms are more interpretable than restrictive ones, because they can produce a smaller range of shapes to estimate the classification function γ. NB exhibits less flexibility than SVM and is therefore less accurate but more interpretable.

In a perfect statistical text classification experiment, we should not look at the test set while developing the classifier, but set aside a development set for testing while our purpose is to find a good value for a parameter, for instance, the number of selected features, the type of kernel function (polynomial or radial), the degree of the kernel function, etc. Then, ideally, at the very end, when all parameters have been set, we should run one final experiment on the test set. In this case, because no information about the test set would be used in developing the classifier, the results of this experiment should be indicative of actual performance in practice and prevent overfitting. To validate the development set, a second researcher, which was not part of this research study, was asked to manually annotate the development set. Figure 9 shows the contingency table that collects the results of both annotators. The contingency table serves to measure the agreement between both annotators by calculating the inter-rater agreement Cohen's kappa score (κ). The observed agreement (P obs ) is equal to 0.934 [equation ( 4)], whereas the expected agreement (P exp ) is equal to 0.251 [equation ( 5)].

Therefore, the kappa score is equal to 0.912, which represents an almost perfect inter-agreement between both annotators [equation ( 6)]. Consequently, there is a shared, objective understanding of the disciplines between both judges. In our experiment, with a weighted average accuracy of 74%, the SVM learning algorithm that was trained with a subset of 2,000 features is the best classifier. Table 2 shows the confusion matrix from which, one could attempt to introduce features that distinguish the mechanical requirements from the electrical requirements, as well as the mechanical requirements from the RAMS requirements. Finally, both curves in Figure 10 illustrate that the number of selected features has a low impact on the accuracy as long as there are at least 1,000 features selected. We were also curious to evaluate the impact of stemming on the accuracy of our best classifier. Therefore, we added the stemming task to the pre-processing pipeline. Although the resulting vector space was different from our previous experiment, we also selected 2,000 features based on the IG utility measure and trained the SVM learning algorithm. The classification function was slightly less accurate as the accuracy was equal to 68.5% confirming the low impact of stemming on classification [START_REF] Manning | An Introduction to Information Retrieval[END_REF]. Consequently, we did not investigate further classifiers including stemming and stuck with the SVM classifier.

Results

Extraction of prescriptive statements

To evaluate the proposed NLP pipeline, we have processed two industrial, unconstrained document-based system specifications.

The first specification specifies an information system to produce global soil moisture data record based on active and passive microwave sensors. This specification is a 106-page document that is freely available on the website of the European Space Agency. It is a Word native PDF document whose structure can be retrieved from its HTML representation. Figure 11 shows that, in this specification, requirements are specified in tables.

The main author of this article, who has a deep understanding of requirements engineering, has manually reviewed the specification and found 194 requirements. Then, we sent the specification down the NLP pipeline that found 194 true-positive requirements leading to the expected recall of 1. However, 72 informative statements have been mistakenly classified as requirements yielding to a precision of 0.73. This first experimental evaluation is satisfactory as we prefer a high recall with an acceptable precision rather than the opposite.

The second specification is a Word document stored on the website of the South African Government's Department of Public Works. It covers the general technical requirements for the equipment, materials, installation, testing, commissioning and maintenance of electrical installations. Figure 12 shows that, in this specification, requirements are specified in raw text.

As with the first specification, the main author has manually found 1,174 requirements. The NLP pipeline found 1,069 requirements among which three were false-positive ones. The number of true-positive statements is equal to 1,066, which leads to a very high precision of 0.99. However, 108 requirements were missed by the NLP pipeline. This results in a recall of 0.90. This 10% rate of false-negative requirements is due to the use of bulleted lists that cannot be retrieved based on the detection of specific HTML tags. Indeed, these lists were manually defined without using the bullets or numbering feature in Word, but with line breaks, parentheses and whitespaces.

The average precision and recall over both documents are equal to 0.86 and 0.95, respectively. Such performances are typical of classifiers developed with a rule-based approach. The recall on specification 1 (1.0) was greater than on specification 2 (0.9) because in specification 1, the modal shall is used to prescribe the requirements, whereas in specification 2, some requirements do not contain any prescriptive term -e.g., "PVC or pitch fibre sleeves are not acceptable -refer to par. 3.10 of the department's standard specification for 'INSTALLATION OF CABLES', Section B6" -and were therefore missed by the prototype. The fact that bulleted lists in specification 2 are defined as raw sequences of characters also has an adverse effect on the recall. The main cause of false-positive results in specification 1 is the use of prescriptive words in informative statements which account for more than a third of the document. Conversely, in specification 2, there are very few informative statements and therefore less chance to mistakenly classify informative statements as requirements. This is the reason why the precision is greater in specification 2 (0.99) than in specification 1 (0.73). Though the style and content of both prescriptive documents differ, the effectiveness of the solution is promising. Nevertheless, the variance, that is the amount by which results would vary if we experience the proposed NLP pipeline using different data sets, needs to be more extensively studied by testing the proposition on numerous prescriptive documents.

Automatic classification of requirements

As explained in the previous section, to prevent overfitting we set aside a development set for testing while our purpose was to tune the parameters of the classifier. We found that the classification function that performs the best on the development set is the one trained with the SVM learning algorithm and 2,000 features. In this section, we run one final experiment on the test set that corresponds to 200 unseen requirements including 50 ME, 50 EE, 50 CS, and 50 RAMS. Because no information about the test set has been used while developing the classifier; the results of this experiment should be indicative of actual performance. Table 3 is the confusion matrix that sums up the results obtained on the 200 examples of the test set with the preferred classifier. The results are slightly better than the ones obtained on the development set. The accuracy is equal to 76% (74% on the development set). The precision (0.78), the recall (0.76) and the F-measure (0.76) are also slightly improved. Since there is no significant difference between the results obtained with the development set and the test set, we can conclude that the classification function is not prone to generalisation error. The only threats to validity are the impartiality of the manual classifications and the definition of finer grained categories. To evaluate the first threat, one could ask to experts coming from different backgrounds (functional area, company, country, etc.) to manually classify the test set so as to finally calculate the inter-rater agreement Cohen's kappa score.

Regarding the second threat, one could study the quality of the solution with further categories (marketing, quality, etc.) and sub-categories (solid mechanics, fluid mechanics, etc.).

Conclusions and further work

This paper proposes:

1 an NLP pipeline to automatically extract requirements from prescriptive documents 2 a machine learning-based text classifier to automatically assign a discipline to a requirement.

To evaluate both contributions we carried out two experiments. In the first one, the NLP pipeline analysed two unstructured specification documents. For the first specification, the NLP pipeline extracted 194 prescriptive statements with a recall of 1 and a precision of 0.73. For the second specification, the NLP pipeline extracted 1,069 prescriptive statements with a recall of 0.9 and a precision of 0.99. The average precision and recall over both documents are 0.86 and 0.95, respectively. In the second experiment, we evaluated the NB and SVM learning algorithms with different pre-processing pipelines and subsets of features. After applying the case-folding, stop-word removal and tokenisation pre-processing tasks and selecting 2,000 features with the information gain utility measure, SVM outperformed other learning algorithms with an accuracy of 0.76.

The NLP pipeline has to be tested on further prescriptive documents issued by different stakeholders. Image processing techniques may also be of interest to analyse unstructured documents within which structural elements such as tables, bulleted lists, etc. cannot be retrieved. Regarding the proposed machine learning-based classifier, the first enhancement will be to increase the size of the test set. Testing of further algorithms such as logistic regression, random forest, tree and neural network is also worth investigating. We have also observed that the classification of a requirement statement is arduous because it contains very few words. For instance, in a manual classification task, one could classify a given requirement statement that contains the words stress and failure in the discipline ME or RAMS. Since requirements that belong to the same topic are often grouped together in a section of the document, the context, that is, the previous and following requirements may improve current results. Another way to overcome this shortcoming is to work out a multi-label classifier that can annotate a requirement statement with, one or several disciplines, or none. For instance, in the previous example, the requirement would be labelled with both ME and RAMS classes. Another way to reduce the misclassification rate of the classifier would be to use a hybrid automatic/manual approach. Once classified, all high-confidence decisions are approved, but all low-confidence decisions are put in a queue for manual revision. After having been revised by an expert, the low-confidence decisions can be used to update the training set and the classifier for obtaining a better approximated classification function. Finally, nowadays, within the data mining discipline, there is a tremendous interest for the deep learning methods. Deep learning is a range of learning algorithms that automatically learn feature representations from raw input. Therefore, instead of hand crafting a training set, one could implement a deep learning algorithm that learns feature representations from an extensive large set of domain-specific documents owned by a company. For instance, [START_REF] Lai | Recurrent convolutional neural networks for text classification[END_REF] studied the use of recurrent convolutional neural networks for text classification. Last but not least, the approach must also be tested in various industrial operational contexts so as to not only identify deviations, but also collect feedback from users.

Figure 1

 1 Figure 1 Committed lifecycle cost against time

Figure 2

 2 Figure 2 Example of a prescriptive document with a set of informative (I) and prescriptive (P) statements (see online version for colours)

Figure 3

 3 Figure 3 Inefficient process that consists in (1) identifying the requirements in large prescriptive documents and (2) rewriting them in a requirements management tool (see online version for colours)

Figure 4

 4 Figure 4 Flowchart that depicts both contributions, (a) the NLP pipeline (b) the classifier (right) (see online version for colours)

Figure 5

 5 Figure 5 Examples of unstructured text for which basic rules based on capital characters and full stops cannot extract complete sentences (see online version for colours)

Figure 6

 6 Figure 6 A sentence whose tokens are annotated with their pos tags (see online version for colours)

Figure 7

 7 Figure 7 A specification with three requirements in the workbench requirements of ENOVIA V6 (see online version for colours)

  set of classes = {c 1 , c 2 , c 3 , c 4 } = {ME, EE, CS, RAMS} where each class corresponds to a discipline. 4 A training example ( , ).

  also mention the difficulty of getting a large amount of labelled requirements.Rather than hand writing and labelling the hundreds or thousands of requirements needed to produce a high-performance classifier, we propose to automatically generate a large amount of training examples.

Figure 8

 8 Figure8Over-simplified illustration that gives the gist of the idea of using handbooks to extract a distribution of keywords that finally serves as features (see online version for colours)

  i th training example was classified correctly; otherwise it was misclassified. The training misclassification rate is nothing more than the fraction of incorrect classifications. The most common approach for approximating the parameters consists in minimising the misclassification rate of the training examples.

  Thus, in addition to the training set used to learn a classification function, the main author of this article manually built a development set by collecting 289 requirements from 15 different industrial specifications and concurrently labelled them manually. The development set is made up of 70 ME, 81 EE, 72 CS and 66 RAMS examples.

Figure 9

 9 Figure 9 4 × 4 contingency table that depicts the annotations of both experts (see online versionfor colours)

Figure 10

 10 Figure 10 Effect of feature set size on the accuracy of the NB and SVM classifiers (see online version for colours)

Figure 11

 11 Figure 11 Extract of the specification 1 (see online version for colours)

Figure 12

 12 Figure 12 Extract of the specification 2 (see online version for colours)

Table 1

 1 gives the weighted average statistics of our experiments with the NB and SVM algorithms, respectively. Because the SMO implementation of SVM is a single-class algorithm, Weka carries out pairwise classification (ME vs. EE, ME vs. CS, ME vs. RAMS, EE vs. CS, etc.) to solve our one-of multi-class classification problem.

Table 1

 1 Results of NB and SVM classifiers according to the number of feature selected

		Accuracy	Precision	Recall	F-measure
	# features
		NB	SVM	NB	SVM	NB	SVM	NB	SVM
	100	0.664	0.567	0.719 0.666	0.664 0.567	0.669	0.557
	500	0.705	0.667	0.726 0.690	0.706 0.668	0.708	0.667
	1,000	0.716	0.723	0.734 0.740	0.716 0.723	0.719	0.725
	1,500	0.712	0.709	0.729 0.725	0.713 0.709	0.715	0.710
	2,000	0.716	0.737	0.734 0.753	0.716 0.737	0.719	0.738
	2,500	0.716	0.705	0.734 0.730	0.716 0.706	0.719	0.707
	3,000	0.712	0.692	0.729 0.720	0.713 0.692	0.715	0.695
	5,000	0.712	0.689	0.729 0.717	0.713 0.699	0.715	0.703
	10,000	0.712	0.698	0.727 0.711	0.713 0.699	0.715	0.701

Table 2

 2 Confusion matrix for the classification function approximated with SVM and 2,000 features evaluated on the development set


Member, IEEE David Florez
email: david.florez@usa.edu.co

Hubert Piquet
email: hubert.piquet@laplace.univ-tlse.fr

R Diez
email: rdiez@javeriana.edu.co

Optimizing the Operation of DBD Excilamps

Keywords: Current control, dielectric barrier discharge (DBD), excimer lamp, ultraviolet (UV)

Dielectric barrier discharge (DBD) excimer lamps are efficient and environmentally friendly sources of ultraviolet (UV). One of the challenges for this technology to be massively adopted is the optimization and effective management of the overall lamp-supply system. Accordingly, a methodology to study the impact of the operating point over the performance and operation of a DBD UV excilamp is developed and experimentally validated. The DBD operating point is parametrically adjusted by means of the power supply current with three independent variables: intensity, frequency, and duty cycle. This methodology allows the determination of the optimal operating point for the particular excilamp under study. These supplying conditions will be later achieved by means of a dedicated electrical generator, which has to be especially designed according to these specifications. It is found that an increment in the current intensity has a positive impact on the lamp efficiency and also leads to the existence of more filamentary discharges. Also, a relation between the energy of the pulse supplied to the DBD and the reactor efficiency can be established. For certain levels of UV power, energy savings on the reactor higher than 50% are attained by proper selection of the operating point.

I. INTRODUCTION

D IELECTRIC barrier discharge (DBD) reactors are char- acterized by key features that make this type of discharge well adapted for its use in a variety of processes in the industry and sciences. Some of the DBD applications are surface treatment [START_REF] Zhang | Surface treatment of polyethylene terephthalate films using DBD excited by repetitive unipolar nanosecond pulses in air at atmospheric pressure[END_REF], lighting [START_REF] Piquet | Pulsed current-mode supply of dielectric barrier discharge excilamps for the control of the radiated ultraviolet power[END_REF], environmental remediation [START_REF] Plaksin | Application of the DBD in the cleaning of diesel engine exhausts[END_REF], [START_REF] Jeong | Removal of gaseous elemental mercury by dielectric barrier discharge[END_REF], medicine [START_REF] Fridman | Blood coagulation and living tissue sterilization by floating-electrode dielectric barrier discharge in air[END_REF], plasma displays [START_REF] Park | Capillary plasma electrode discharge as an intense and efficient source of vacuum ultraviolet radiation for plasma display[END_REF], and jet generation [START_REF] Monge-Dauge | Experimental study coupled with electrical modeling for the consideration of DBD-based plasma jet[END_REF]. The DBD can operate from low to high pressure (>1 bar) [START_REF] Carman | Highpressure (>1 bar) dielectric barrier discharge lamps generating short pulses of high-peak power vacuum ultraviolet radiation[END_REF], which is beneficial for the enhancement of selected electrochemical reactions. It also incorporates the advantages of the low-temperature plasma and can produce filamentary or homogeneous discharges [START_REF] Kogelschatz | Dielectric-barrier discharges: Their history, discharge physics, and industrial applications[END_REF]. The specific set of DBD operating conditions that best fit a particular process is determined by the reactor design and also by the DBD power supply.

DBDs can be powered in a wide range of frequencies (Hz-MHz), current intensities (mA-A), and waveforms (sinusoidal, trapezoidal, square), always in the scale of kilovolts. Unsurprisingly, depending on the values of these parameters, different characteristics of the discharge and performance of the reactor can be achieved; this fact has been already evidenced for different DBD reactors, e.g., DBD-driven ozone generators [START_REF] Amjad | Analysis and implementation of transformerless LCL resonant power supply for ozone generation[END_REF], precipitators [START_REF] Gouri | Study of DBD precipitator energized by a modified square waveform voltage[END_REF], and ultraviolet (UV) excilamps [START_REF] Guivan | Comparative inactivation of Bacillus subtilis spores using a DBD-driven xenon iodide excilamp and a conventional mercury lamp[END_REF].

This paper is mainly focused on DBD-driven excilamps, which are high efficiency and environmentally friendly UV sources, with the potential to replace the traditional mercury-based UV lamps [START_REF] Guivan | Comparative inactivation of Bacillus subtilis spores using a DBD-driven xenon iodide excilamp and a conventional mercury lamp[END_REF], for example, in drinking water treatment applications [START_REF] Florez | Power supplies for the study and efficient use of DBD excimer UV lamps[END_REF]. One of the challenges for this technology to be massively adopted is the optimization and management of the overall lamp-supply system.

In previous studies, a decrease in the excilamp efficiency with the increment of the electrical power delivered to the bulb [START_REF] Höft | Visualization of a coaxial dielectric barrier discharge driven by a sub-ns rising highvoltage pulse and its reflections[END_REF]- [START_REF] Lomaev | Excilamps and their applications[END_REF], as well as an impact of the operating frequency on the UV production [START_REF] Díez | Control of the UV emission of an excimer lamp by means of a current-mode power supply[END_REF], has been found. These results allow to point out that an optimization process of the DBD UV excilamp operating point should lead to maximize the lamp performance (UV production) for a given amount of electrical power. In this work, the DBD operating point is considered only from the perspective of the electrical energy (voltage, current) applied to the DBD. Additional nonelectrical parameters such as the reactor construction, its physicochemical properties (bulb shape, quartz walls, gas mixture), or operating temperature are considered here as constant parameters.

In this paper, a comprehensive study of the operating performances is presented, including measurements of the instantaneous response of the UV radiation, the average UV radiation power density, the parameters of the lamp equivalent electrical model, the lamp efficiency, and the discharge regime as a function of the operating point.

The proposed methodology is presented as follows. In Section II, the DBD operating point and power adjustment is developed, together with the main characteristics of the DBD UV excimer lamp used in this study. In Section III, the experimental bench and the protocols are detailed; here the results are revealed and analyzed, an optimal operating point for the UV excilamp is found, and conclusions are drawn.

II. METHODS AND EQUIPMENT

The proposed methodology relies on the principle that the DBD electrical power can be accurately adjusted if the DBD current is controlled [START_REF] Díez | Control of the UV emission of an excimer lamp by means of a current-mode power supply[END_REF]. As proposed in [START_REF] Florez | Square-shape current-mode supply for parametric control of the DBD excilamp power[END_REF], this current control can be effectively implemented by means of a squareshaped current mode power supply, which is the alternative chosen for this study.

The employed power supply drives an alternate current through the DBD [Fig. 1 (top)] with a versatile almost square-shaped current waveform, adjusted with three independent variables: intensity (J ), frequency ( f DBD ), and duty cycle (D DBD ). Accordingly, these three parameters will be called the degrees of freedom (DOF) of the DBD current. Through these three DOF, the intensity ( J ) and duration (D DBD /2 f DBD ) of the DBD current pulses can be precisely controlled.

The square-shaped current power supply topology consists of a dc two-quadrant current source connected in cascade with a full-bridge inverter; the output of the latter is connected to the DBD through a stepup transformer. A detailed study concerning the design and operation of this DBD power supply topology can be found in [START_REF] Florez | Square-shape current-mode supply for parametric control of the DBD excilamp power[END_REF] and [START_REF] Bonnin | Design of a current converter to maximize the power into homogeneous dielectric barrier discharge (DBD) devices[END_REF].

To achieve the DBD power adjustment, the design of this power supply takes into account the specific requirements of driving a DBD load [START_REF] Florez | Square-shape current-mode supply for parametric control of the DBD excilamp power[END_REF], which are addressed using a DBD equivalent electrical circuit model and taking into account the needs of the final application: here, an efficient control of the emitted UV dose is required.

The simplified DBD model shown in Fig. 2 has proved to be appropriate for the dimensioning of DBD power supplies [START_REF] Bonnin | Design of a current converter to maximize the power into homogeneous dielectric barrier discharge (DBD) devices[END_REF]. Below, for a coaxial DBD excimer lamp as the one represented in Fig. 3, the most important elements of this model are recalled.

In this type of lamp, the bulb confines a gas mixture between two silica walls. These walls, acting as dielectric barriers, are modeled as the equivalent capacitance C d . Before the discharge is produced, the gas can also be modeled as a capacitance (C g ) that is in series with C d .

If properly excited, the voltage across the lamp gas (v Cg in Fig. 2) reaches the breakdown voltage (v th ) at which the discharge takes place and the confined gas conductance abruptly changes; experimental measurements show that v Cg (which waveform is not directly measurable and needs to be computed) remains almost constant as long as the discharge is sustained [START_REF] Díez | Control of the UV emission of an excimer lamp by means of a current-mode power supply[END_REF], with a value near to v th . Most of the effective power is transferred to the DBD during this phase. A comprehensive analysis of the DBD modeling is treated in [START_REF] Díez | Predictive model of a DBD lamp for power supply design and method for the automatic identification of its parameters[END_REF] and [START_REF] Lopez | Parameters identification and gas behavior characterization of DBD systems[END_REF].

As a consequence of this voltage source behavior in the gas (when the discharge is ON), the deterministic way to control the discharge power is by means of controlling its current [START_REF] Florez | Square-shape current-mode supply for parametric control of the DBD excilamp power[END_REF], thus leading to the use of a current-mode approach to power the DBD. This supply, due to the capacitive nature of the DBD, must provide a zero-average current to avoid uncontrolled growth of the DBD reactor voltage and further damage in the supply components.

A. DBD Operating Point and Power Adjustment

In accordance with the considerations exposed before, provided this square-shaped current waveform that flows through the DBD and using the simplified DBD equivalent electrical model (Fig. 2), a theoretical expression for the DBD electrical power, as a function of the three DOF is deduced [START_REF] Zhang | Surface treatment of polyethylene terephthalate films using DBD excited by repetitive unipolar nanosecond pulses in air at atmospheric pressure[END_REF]. The lamp parameters (defined in the previous section) play an important role here as

P DBD = J D D B D v th -4 f DBD C g v 2 th . ( 1
)
From ( 1), it is evident that the three DOF defining the operating point are also available to control P DBD . The usefulness of this property relies on the possibility of accurately adjusting the lamp electrical power at different operating points; consequently, this feature allows the research of a correlation between the values of the DOF and the reactor performance, e.g., the UV power produced by the excilamp.

Regarding the UV instantaneous response in a DBD excilamp, a tight correlation of the lamp current intensity and the UV pulse amplitude is observed. For the operating range of the test, once the lamp ignition is produced, UV radiation is emitted without interruption as long as the current is injected into the lamp. In Fig. 1 (bottom), the experimental DBD current and UV waveform are plotted together to demonstrate this similitude at different operating points. The delay between the beginning of the current and the UV pulses corresponds to the time required to reach the gas breakdown. Once the gas breakdown is produced, the UV pulse starts and its amplitude follows the absolute value of i DBD .

However, one can notice that the initial overshoot in the UV pulse and subsequent oscillations are not observed in the lamp current. In fact, the gas conductance current, i G in Fig. 1, is responsible for the UV production and after gas breakdown i G is not exactly equal to i DBD . However, i G cannot be experimentally measured. With the aim to provide an accurate estimation of i G and by this means, an estimation of the UV production, an identification and estimation algorithm is proposed in [START_REF] Doanh | Estimation of the light output power and efficiency of a XeCl dielectric barrier discharge exciplex lamp using one-dimensional drift-diffusion model for various voltage waveforms[END_REF].

B. DBD Parameters Measurement

Using the current-mode supply presented in the previous section, the DBD load (i.e., the UV excilamp) is excited under different operating points, parametrically adjusting the available DOF: J, D DBD , and f DBD . Then, making use of comparative measurements, the impacts of J and f DBD are analyzed for the following indicators: the excilamp UV power density, the lamp electrical model, and the appearance of the discharge.

The UV radiation as a function of the time (UV instantaneous response in Fig. 1. is registered using a THORLABS PDA-25K photodetector. The measurement of the UV average power density is obtained with the GIGAHERTZ-OPTIK P-9710 radiometer, using a UV-3711-308 sensor head. The radiometer is configured with an integration time of 0.5 s and a dose time of 5 s. The setup of the instruments is detailed in Fig. 3. The DBD current and the voltage electrical signals are acquired using high-speed current probes (Lecroy AP015) and a high-voltage differential probe (Agilent N2891A), respectively; the phase difference between the voltage and current signals is compensated in the oscilloscope, then both signals are multiplied and averaged to obtain the power measurement (averaging time 1 ms).

C. Impact of the Lamp Temperature

In Fig. 4, the UV output power and the lamp surface temperature evolution at natural convection are shown for a given stable operating point. The stabilization of the temperature and UV power needs around 10 min, since the ignition instant. For this particular operating point, a temperature rise of 100 °C in the lamp surface (with natural convection) and a decrease of 14% in the UV power are observed.

According to these results, in order to minimize the impact of the temperature factor in the study, all the measurements are registered when the lamp surface temperature is around 40 °C. Note that the thermal equilibrium is different for each operating point tested in this work, as it depends on the supplied power; however, a fixed temperature is used, considering a final application that sets the lamp temperature, as in water treatment. The rise in the lamp temperature is slowed down thanks to the use of two cooling fans, one for the external electrode and one that forces air through the inner electrode (Fig. 3).

III. RESULTS OF THE PARAMETRIC STUDY

The square-shaped current mode DBD power supply used for this study is able to drive peak currents up to 200 mA in the DBD, within a frequency range from 50 to 200 kHz, a duty cycle from 10%-90%, and a maximum DBD peak voltage of 5 kV. In the following sections, the DBD performance, its equivalent electrical model, and an evaluation of the optimal operating point of the DBD are discussed.

A. Lamp Performance

The DBD excilamp performance is quantified by means of its UV average power density (ρ UV ).

1) Impact of the Current Intensity: For the first experiment, the operating frequency f DBD is held constant (e.g., 50 kHz in Fig. 5), the intensity J is configured at a first set-point value (67 mA), and then, using the current duty cycle D DBD , different values of lamp electrical power P DBD are obtained. According to the voltage and current probe specifications, the accuracy of the electrical power measurements is ±3.02%.

The process is repeated for other values of J , and for each operating point a measurement of the lamp UV power is obtained, showing the impact of the J parameter over the DBD operation. From the radiometer specifications, the obtained UV power density measurement has a maximum error of ±0.5%.

In Fig. 5, different types of lines are used to identify the plots of the same operating frequency.

Three values of frequencies are used: the lower and higher limits of operation of the converter, 50 and 200 kHz, respectively, and an intermediate frequency, 110 kHz. Four current intensities are used with respect to the limiting value of the converter (250 mA) and assuring the lamp ignition in most of the cases (67 mA); the two other currents 128 and 189 mA are intermediate currents. Some combinations do not ignite the lamp (e.g., 200 kHz and 67 mA) and for this reason are not shown in Fig. 5.

From the f DBD = 50 kHz plots (red solid lines) in Fig. 5, a notorious increment in the lamp UV production, for the same electrical power injected into the lamp, is obtained when J is increased from 67 to 128 mA. This increment corresponds to a gain of up to 25% in the UV radiation output.

When the current pulse intensity is increased from 128 to 189 mA, the upward trend in the lamp performance is still advised, but for J above 189 mA a significant gain is not observed anymore. For higher values of f DBD (110 and 200 kHz), this positive impact of the current intensity in the UV production is also verified.

Another characteristic to be noticed is a reduction in the ρ UV -P DBD function slope as P DBD increases. As can be observed in Fig. 5, as the frequency rises, the downward trend in the slope becomes more evident. This reduction in the ρ UV /P DBD ratio with the increase of the injected power corresponds to a reduction in the lamp efficiency, which can be attributed to overexcitation [START_REF] Carman | Computer modelling of a short-pulse excited dielectric barrier discharge xenon excimer lamp (λ~172 nm)[END_REF] or to abrupt gas heating [START_REF] Lomaev | Excilamps based on xenon dimers excited by a barrier discharge[END_REF].

For constant values of P DBD and f DBD , the shape of the discharges becomes more filamentary as the current intensity increases. This can be observed in the pictures in Fig. 6 (Canon PowerShot S5 IS, f/5, 1/2000 sec., ISO-400). All the images in Fig. 6 (top) present the same peak voltage in the lamp and different appearances; therefore, it seems that it is the amplitude of the current and not of the voltage that controls the filament shape.

Accordingly, on the basis of the UV power measurements previously analyzed, the existence of well-defined filaments can be an indicator of high levels of efficiency in the output radiation power. This result complements the experiments presented in [START_REF] Lomaev | Excilamps based on xenon dimers excited by a barrier discharge[END_REF] and [START_REF] Lomaev | Excilamps: Efficient sources of spontaneous UV and VUV radiation[END_REF], where the transition from diffuse channels to clearly defined filaments is studied and associated to a peak in the lamp efficiency.

2) Impact of the Operating Frequency: For the second experiment, f DBD is the parameter to be assessed. With this aim, J is fixed, f DBD is configured at the first operating frequency, and using D DBD , the lamp power is gradually increased. Again, the process is repeated for several values of f DBD acquiring the measurements of interest. The UV output as a function of the injected power for a fixed current intensity is shown in Fig. 7, using a different line type for each J value (e.g., black dashed-dotted plots for 250 mA).

For J = 250 mA and mainly for P DBD < 120 W, a reduction in the UV production (up to 35%) is observed when comparing the 140 and 200 kHz plots. The impact of f DBD over UV radiation for the 50-140 kHz range is negligible. In contrast, the UV output plots obtained for J = 128 and 67 mA (red dashed and blue solid lines, respectively, in Fig. 7) reveal that the smaller the current intensity, the higher the impact of the frequency on the lamp performance.

Accordingly, if this particular DBD excilamp is operated at low levels of power (below 120 W), the best option is to use a frequency smaller than 110 kHz to obtain more UV power per injected electrical power unit.

The pictures in Fig. 6 (bottom) have been taken for a constant P DBD and J value. Each picture corresponds to a different f DBD (50-100 kHz). As can be observed, no change in the visual aspect of the discharge is noticed. The UV power density obtained for these experiments presents a slight decrease of 6% with the increase in f DBD . In conclusion, for the range of this test, the visual aspect of the plasma remains diffuse and the UV production does not change significantly with f DBD . Comparing this behavior with the pictures in Fig. 6 (top), where the change in the discharge from diffuse to filamentary has been accompanied by an increase in the UV power density, a relation between the filamentary appearance of the streamers and a high UV production efficiency is suggested.

B. Lamp Electrical Model

The Lissajous figures, constructed with the DBD chargevoltage trajectory (Fig. 8), are used here for identification of The DBD voltage (v DBD ) in Fig. 8 follows a counterclockwise trajectory as a function of the injected charge, q DBD . The charge is calculated as the integral of the DBD current during a period. Starting from the upper right peak value of v DBD , the voltage decreases linearly with the charge according to the capacitor voltage change

v DBD = 1 C q DBD . (2)
Consequently, the value of the equivalent capacitor is calculated from the parallelogram slope; prior to the gas breakdown the charge is transferred to C d in series with C g , thus this series corresponds to the equivalent capacitor C eq . Once the gas reaches the breakdown voltage v th , the slope becomes equal to C d and the voltage continues to decrease almost linearly until reaching the lamp negative peak voltage-VDBD . Now knowing C d , the value of v th is computed according to the lamp model, using the following equation, with QDBD equal to the absolute value of the maximum charge injected into the lamp:

v th = VDBD - QDBD C d . (3)

TABLE I EQUIVALENT LAMP PARAMETERS

In Fig. 8 (bottom), f DBD is held constant (80 and 170 kHz) and in Fig. 8 (top) a constant J value is used (189 mA). From these trajectories, it is inferred that the slope values (and consequently the equivalent capacitances) are not substantially affected by the changes in the adjusted DOF.

The lamp model parameters, computed for each one of these trajectories, are given in Table I. Using the average value for each of the three parameters to calculate P DBD with (1), a maximum error of only 8% is obtained compared with the DBD power measurement (J = 189 mA, D DBD = 50%, and f DBD = 140 kHz). Accordingly, it is possible to use a fixed DBD model, independent of the three DOF values, to describe the large operating range ( f DBD from 50 to 200 kHz, J from 67 to 250 mA, and D DBD from 10% to 90%), and consequently to design the DBD power supply.

For f DBD = 50 and 80 kHz, an abrupt change in the sign of the curve slope is observed at the breakdown instant, as indicated in Fig. 8 (top). This phenomena, although not considered in the simplified DBD model used here, does not have a significant impact on the validity of this model. A more complete model, including an analysis of the gas conductance can be found in [START_REF] Díez | Predictive model of a DBD lamp for power supply design and method for the automatic identification of its parameters[END_REF]- [START_REF] Doanh | Estimation of the light output power and efficiency of a XeCl dielectric barrier discharge exciplex lamp using one-dimensional drift-diffusion model for various voltage waveforms[END_REF].

C. Optimal Operating Point

The DBD excilamp optimal operating point is defined in this study as the set of DOF (J, f DBD , D DBD ) that obtain a required UV radiation power with the minimum electrical power supplied to the reactor.

Accordingly, from the measurements presented in the previous section, an optimal DBD excilamp operating point (dedicated to the particular lamp under study) has to be found within the studied range.

In order to evaluate the DBD performance, a measurement of the excilamp relative efficiency, η r (1/cm 2 ), in terms of the energy conversion per unit area, is calculated as the conversion ratio between the electrical power injected into the lamp P DBD (W) and the UV output power density ρ UV (W/cm 2 ) (2). This is a relative and not an absolute measurement of the irradiation efficiency since the radiometer only captures part of the entire radiation

η r (1/cm 2 ) = ρ UV P DBD . ( 4
)
Inspired by [START_REF] Razhev | Influence of the specific pump power on the output energy and efficiency of a 223-nm gas-dischargepumped excimer KrCl laser[END_REF] and [START_REF] Boichenko | The effect of the excitation power on the emission efficiency of barrierand glow-discharge pumped exciplex and excimer lamps[END_REF], predicting the existence of an optimal range of discharge energy, the excilamp efficiency has been plotted against the energy transferred to the lamp in each current pulse. This pulse energy (E DBD ) is calculated as

E DBD = P DBD 2 f DBD . ( 5
)
In Fig. 9 (left), the normalized relative efficiency of the lamp is plotted as a function of the supplied pulse energy.

Within the bottom plot, each data point type corresponds to a different J value. According to Fig. 9 (left), the efficiency for the operating points corresponding to the maximum value of J (250 mA) is slightly higher than the others.

In Fig. 9 (top), each data point type means a different operating frequency f DBD . From this figure we find that the maximum efficiency points are obtained for f DBD = 80 kHz. From both graphics, an interesting result from the point of view of the physics of the lamp is found; observe that despite the dispersion of the points, in general the lamp efficiency is very low for E DBD < 300 μJ for the tested values of current frequency and intensity. Note that for f DBD = 50 kHz, no points below 500 μJ are found.

From the results analyzed in Section III-A, to maximize the UV production for a given P DBD value, the minimum value of f DBD should be preferred. This minimum value of f DBD is determined from the point of view of the electrical generator by the maximum tolerated output converter voltage considering, from [13, eq. (2.1.6)], that for a given lamp power, the lamp peak voltage decreases with f DBD From the point of view of lamp efficiency, for a given value of lamp power, the minimum f DBD should be calculated according to (5) to drive a pulse energy higher than 300 μJ.

VDBD = v th + J D D B D 4 f DBD C d . ( 6)
On the other hand, in Section III-A it was shown that for a given lamp electrical power, the UV production is enhanced by increasing the current intensity. However, from Fig. 9 (bottom) it is noticed that an increment of the current amplitude above 189 mA does not contribute with an important gain in the lamp efficiency.

However, the maximum lamp efficiency operating point does not guarantee the production of the UV power required for a given application. Henceforth, in order to obtain this desired ρ UV with high efficiency, Fig. 9 (right) should be used.

These figures show the ρ U V as a function of the lamp electrical power.

To obtain a given value of ρ UV , the optimal operating point is one that requires the least electrical power (P DBD ) (the eftmost data point). For example, if 30 mW/cm 2 of UV power is required, among the operating points highlighted with a circle in Fig. 9, the leftmost operating point provides 27% of energy savings compared with the data point placed at the right limit of the highlighted region. However, it must be noticed that for ρ UV around 18 mW/cm 2 , an energy saving of up to 50% can be afforded by proper selection of the operating point. Accordingly, depending on the UV radiation power required for a particular application, making use of the parametric sweep results shown in Fig. 9, the optimal DBD operating point can be selected.

IV. CONCLUSION

A methodology to quantify the impact of the DBD operating point, over a set of DBD characteristics and allowing to find optimal conditions, was proposed and validated through the study of a particular DBD UV excilamp.

The DBD lamp heating effect over the UV radiation power has been experimentally quantified, indicating the need for performing all the measurements under the same lamp temperature.

As a first result, this study confirms that the amplitude and duration of the UV radiation pulses are governed by the lamp current intensity ( J ) and the current pulse duration, respectively.

Concerning J , we found that the increment of this variable positively affects the DBD excilamp UV production and also promotes the existence of well-defined filaments in the discharge. However, for the particular experimental bench studied here, for J above 190 mA, there is no significant gain in the lamp performance. In contrast, the simplified equivalent electrical model of the lamp is barely affected by the changes in the operating point. Regarding the DBD operating frequency, we found that the lower the values of the DBD power and J , the more visible the negative effect of incrementing the frequency.

The pulse energy of the current supplied to the discharge seems to be correlated to the excilamp performance. For all the tested operating points and for this particular XeCl DBD excilamp, the best performance points have been obtained with energy pulses higher than 300 μJ.

Finally, we point out that the methodology used for this study, incorporating the use of the square-shaped current mode supply, has demonstrated to be a valuable tool for the evaluation of DBD excimer lamps and validates that only by changing the operating point can the lamp performance be drastically improved. According to [START_REF] Lomaev | Excilamps based on xenon dimers excited by a barrier discharge[END_REF], the maximum efficiency conditions can differ depending on the gas mixture of the excilamp; consequently, a comparative study of different types of gas mixture DBD excilamps and other DBD reactors is one of the perspectives of this work.

Fig. 1 .

 1 Fig. 1. DBD current (i DBD ) used for parametric control of the reactor operating point. Theoretical (top) and experimental (bottom) waveforms at different operating frequencies (i DBD : 100 mA/div, v DBD : 2 kV/div, and UV: a.u.).

Fig. 2 .

 2 Fig. 2. DBD excilamp simplified electrical model. The lamp geometry is represented in Fig. 3.

Fig. 3 .

 3 Fig. 3. Experimental bench for measurement and acquisition of the DBD parameters. Top: a-excilamp lateral view, and b-excilamp frontal view.

Fig. 4 .

 4 Fig. 4. DBD excilamp temperature and UV output. f DBD = 100 kHz. D DBD = 60%. J = 110 mA. P DBD = 85 W.

Fig. 5 .

 5 Fig. 5. Impact of DBD current intensity in the UV output for: f DBD = 50 kHz (red solid lines), f DBD = 110 kHz (blue dashed lines), and f DBD = 200 kHz (black dashed-dotted lines).

Fig. 6 .

 6 Fig. 6. Changes in the visual aspect of the discharges. Top: J is increased while f DBD = 70 kHz. Bottom: f DBD is increased while J = 100 mA. P DBD = 80 W for all the pictures.

Fig. 7 .

 7 Fig. 7. Impact of the operating frequency in the UV output for J = 250 mA (black dashed-dotted lines), J = 128 mA (red dashed lines), and J = 67 mA (blue solid lines). the parameters of the simplified DBD model shown in Fig. 2 [2, p. 12].The DBD voltage (v DBD ) in Fig.8follows a counterclockwise trajectory as a function of the injected charge, q DBD . The charge is calculated as the integral of the DBD current during a period. Starting from the upper right peak value of v DBD , the voltage decreases linearly with the charge according to the capacitor voltage change

Fig. 8 .

 8 Fig. 8. DBD charge-voltage plane for different operating points.

Fig. 9 .

 9 Fig. 9. DBD excilamp relative efficiency (left) and UV power (right) as a function of the injected electrical power, with the corresponding lamp operating frequency (top) and lamp current intensity (bottom) of the operating point.

He is currently a Full Professor with the Institut National Polytechnique de Toulouse, where he teaches courses on power electronics and systemic approach in electrical engineering. He is currently involved in research with the Laboratoire Plasma et Conversion d'Energie Laboratory, Toulouse. His current research interests include electrical embedded networks and power supplies for plasma applications.