Moukhtar El

Zemmouri

Hicham Behja

Abdelaziz Marzak

Brigitte Trousse

Ontology-Based Knowledge Model for Multi-view KDD Process

Keywords: KDD process, viewpoint, domain knowledge, ontology, CRISP-DM, OWL

Knowledge Discovery in Databases (KDD) is a highly complex, iterative and interactive process that involves several types of knowledge and expertise. In this paper we propose to support users of a multi-view analysis (a KDD process held by several experts who analyze the same data with different viewpoints). Our objective is to enhance both the reusability of the process and coordination between users. To do so, we propose a formalization of viewpoint in KDD and a Knowledge Model that structures domain knowledge involved in a multi-view analysis. Our formalization, using OWL ontologies, of viewpoint notion is based on CRISP-DM standard through the identification of a set of generic criteria that characterize a viewpoint in KDD.

INTRODUCTION

Knowledge Discovery in Databases (KDD) is a highly complex, iterative and interactive process, with a goal-driven and domain dependent nature [START_REF] Fayyad | The KDD process for extracting useful knowledge from volumes of data[END_REF]. It involves three main steps (data preprocessing, data mining and post-processing) with many decisions made by the analyst (see Figure 1). The complexity of KDD is mainly due to the nature of the analyzed data (distributed, incomplete, heterogeneous, etc.) and the nature of the process itself (since the KDD is by definition interactive and iterative).

Given this complexity of KDD, the analyst faces two major challenges. On the one hand, he must manipulate prior domain knowledge to better understand the data and the business objective. On the other hand, he must be able to choose, configure, compose and execute tools and methods from various fields (e.g., machine learning, statistics, artificial intelligence, databases) to achieve goals. The first challenge involves analyzed domain knowledge, while the second involves the analyst domain knowledge (see Figure 1). Figure 1. Interaction between KDD and the two types of domain knowledge. Analyzed domain knowledge is used during the early stages of the process; mainly to understand and prepare data. Analyst domain knowledge is used during the latter stages to choose, configure and execute data mining methods, and to evaluate extracted patterns [START_REF] Behja | Prise en compte des points de vue pour l'annotation d'un processus d'Extraction de Connaissances à partir de Données[END_REF].

A multi-view KDD process is usually held by one or more experts who consequently manipulate several types of knowledge and know-how. They will have different objectives and preferences, different competences, and different visions of analyzed data, KDD methods and functions. In brief, they have different viewpoints. In this context, the KDD process will be guided by the analyst's viewpoint [START_REF] Behja | Prise en compte des points de vue pour l'annotation d'un processus d'Extraction de Connaissances à partir de Données[END_REF] and several types of knowledge and expertise are incorporated.

Figure 2 below shows an example of a multi-view analysis of data from an e-learning system (mainly: log files, database, and courses material). These data can be analyzed by different actors of the system (learners, teachers, administrator, marketing …). The objective of a teacher (e.g., evaluation of a course) is not the same as the administrator's one (e.g., ensuring system reliability). Attributes used for evaluating a course are different from those used for studying the reliability. Similarly, chosen data mining methods, techniques and tools will be different, and the interpretation of data mining results depends on the analyst's viewpoint. Therefore, it is fundamental to take into account the viewpoint of each analyst and incorporate the two types of domain knowledge in the KDD process. In this paper we propose to assist the users of a multi-view KDD process. Our objective is to enhance both the reusability of the process and coordination between its different users. We propose a formalization of viewpoint notion in KDD following a knowledge engineering approach: eliciting, structuring, and formalizing information and knowledge involved in a multi-view analysis [START_REF] Schreiber | Knowledge engineering and management: The CommonKADS methodology[END_REF]. Elicitation will be based on CRISP-DM standard [START_REF] Chapman | CRISP-DM 1.0 Step-by-step data mining guide[END_REF] to identify a set of generic criteria that characterize a viewpoint in KDD. Knowledge involved in a multi-view analysis will be structured as a knowledge model containing four hierarchical sub-models: domain model, task and method model, viewpoint model and viewpoint organizational model. The viewpoint sub-model will be formalized using Ontologies in OWL 1 (Web Ontology Language) language.

The remainder of the paper is organized as follows. Section 2 presents the state-of-the-art in supporting users of KDD process using ontologies. Section 3 gives our definition of viewpoint in KDD, its situation in relation to other approaches in knowledge engineering, and our proposed set of generic criteria that characterize a viewpoint in KDD. Then, in section 4 we present our knowledge model integrating viewpoints. In this section we also present our OWL formalization of the viewpoint sub-model. Finally section 5 draws some conclusions and opens up new avenues for future work.

RELATED WORK

Several related works have addressed the complexity of KDD with different approaches with the aim of supporting both expert and novice users using ontologies. Most of these approaches offer the user the advantage to explore the large space of valid data mining processes [START_REF] Bernstein | Towards intelligent assistance for a data mining process: an ontology based approach for cost-sensitive classification[END_REF][START_REF] Diamantini | Ontology-driven KDD process composition[END_REF], to discover and access distributed data mining services [START_REF] Euler | Publishing operational models of data mining case studies[END_REF][START_REF] Diamantini | Ontology-driven KDD process composition[END_REF], to reuse successful data mining experiences [START_REF] Morik | The MiningMart approach to knowledge discovery in databases[END_REF], etc. but without taking into account the multi-view aspect of a KDD analysis.

One of the first ontologies proposed to support users of KDD is DAMON (Data Mining ONtology) [START_REF] Cannatro | A data mining ontology for grid programming[END_REF], that is designed to simplify the development of distributed KDD applications on Grids. DAMON ontology concerns only the data mining phase of a KDD process, and offers a taxonomy for discovering tasks, methods and tools deemed more suitable for a given data mining goal.

In MiningMart project [START_REF] Morik | The MiningMart approach to knowledge discovery in databases[END_REF] a case-based reasoning (CBR) system to support end users during data preprocessing is proposed. This system is based on a metamodel (called M4) of KDD preprocessing chains that contains ontology for describing conceptual domain knowledge. In the same project, [START_REF] Euler | Publishing operational models of data mining case studies[END_REF] proposes a web-based platform (which is a case base containing MiningMart successful experiences) to publicly display preprocessing models in a structured way, together with descriptions about their business domains, goals, methods and results. [START_REF] Bernstein | Towards intelligent assistance for a data mining process: an ontology based approach for cost-sensitive classification[END_REF] propose an Intelligent Discovery Assistant (IDA) for valid data mining processes enumeration and ranking. IDA focuses mainly on preprocessing and data mining phases of the KDD process. It is based on a formal ontology that contains input/output, preconditions constraint, and performance (accuracy, complexity, and comprehensibility) of each data mining operator. This ontology allows selection and composition of data mining operators suitable for user's data and goal. A similar approach is proposed by [START_REF] Diamantini | Ontology-driven KDD process composition[END_REF] in a project called KDDVM (KDD Virtual Mart), which is a web services based system that aims to support users in the design of valid KDD process. It represents KDD operations as services which can be "annotated, introduced, accessed, described, composed and activated". KDDVM is based on KDDONTO ontology and concerns only data preprocessing and data mining steps.

A recent European project (e-LICO 2 : e-Laboratory for Interdisciplinary Collaborative Research in Data Mining and Data-Intensive Science) deals with the problem of supporting users of KDD in a collaborative way [START_REF] Hilario | Ontology-based metamining of knowledge discovery workflows[END_REF]. One of the products of this project is eProPlan [START_REF] Kietz | eProPlan: A tool to model automatic generation of data mining workflows[END_REF], an ontology based environment for planning KDD workflows. It is based on two ontologies DMWF-DMOP and uses IA planning techniques to automatically generate KDD execution plan for solving data mining problems. DMWF (Data Mining Work Flow Ontology) formalizes IO-objects, operators, goals, tasks and methods as well as the decomposition of tasks into methods and operators (this ontology is equivalent to our OntoECD ontology described in [START_REF] Zemmouri | OntoECD : une ontologie pour le processus d'ECD[END_REF]). DMOP (Data Mining Optimization Ontology) provides a unified conceptual framework for analyzing data mining tasks, algorithms, models, datasets, workflows and performance metrics, as well as their relationships.

Our approach focuses on the reusability and coordination between multi-users of a KDD process, rather than the automatic generation of KDD execution plan. In addition, we cover the whole phases of the KDD process (cf. 6 phases suggested by CRISP-DM standard in Figure 4).

A VIEWPOINT-BASED APPROACH IN KDD

The concept of viewpoint is a polysemic word introduced in knowledge representation since the 70s by [START_REF] Minsky | A framework for representing knowledge[END_REF], especially for modeling and design of complex systems that are inherently multi-view. Since then, several proposals have focused on the meaning, representation, interpretation and confrontation of viewpoints, sometimes with different names (e.g., perspective, context, opinion, view, etc.).

The multi-view approach has been used in various fields: in object-oriented methods and languages VBOOM (View Based Object Oriented Method) [START_REF] Kriouile | VBOOM : une méthode orientée objet d'analyse et de conception par points de vue[END_REF] and VBOOL (View-Based Object Oriented Language) [START_REF] Marcaillou-Ebersold | Intégration de la notion de points de vue dans la modélisation par objets : le langage VBOOL[END_REF], in view programming [START_REF] Mili | Views: A framework for feature-based development and distribution of OO applications[END_REF], in the O2VIEWS object databases [START_REF] Abiteboul | Objects and views[END_REF], in software process [START_REF] Finkelstein | Viewpoint oriented software development[END_REF] and also in UML [START_REF] Nassar | VUML : une extension UML orientée point de vue[END_REF].

The concept of viewpoint was also addressed implicitly or explicitly by a large community of knowledge engineering. Especially in object knowledge representation languages like KRL [START_REF] Bobrow | An overview of KRL, a knowledge representation language[END_REF] and its improvement LOOPS [START_REF] Bobrow | LOOPS: data and object oriented Programming for Interlisp[END_REF], ROME [START_REF] Carré | Multiple and evolutive représentation in the ROME language[END_REF] and its extension to Frames FROME [START_REF] Dekker | Multiple and dynamic representation of frames with points of view in FROME[END_REF], and TROPES [START_REF] Marino | Raisonnement classificatoire dans une représentation objets multi-points de vue[END_REF]; in the context of multi-expertise modeling in designing complex systems such as spacecrafts [START_REF] Trousse | Viewpoint management cooperative design[END_REF] and in developing multi-expert knowledge bases with C-VISTA [START_REF] Ribière | A Viewpoint model for cooperative Building of an Ontology[END_REF], and MVP [START_REF] Bach | Construction d'un web sémantique multi-points de vue[END_REF].

According to the works and areas mentioned above, the definition of viewpoint notion varies. For example [START_REF] Ribière | A Viewpoint model for cooperative Building of an Ontology[END_REF] have classified definitions of the concept viewpoint into two categories which correspond to two possible interpretations: perspective and opinion. Perspective viewpoints refer to different conceptual positions from which different experts examine an object (system, knowledge base, problem…). This allows one "to index consensual descriptions of the same object by different experts" [START_REF] Ribière | A Viewpoint model for cooperative Building of an Ontology[END_REF], and also to access a subset of relevant information or knowledge from a given viewpoint. Opinion viewpoints refer to opinions given by experts on the object. Opinion viewpoints are closely related to the expert and take account of his experience, knowledge, task, etc.

Viewpoint in KDD

We propose, in this paper, to make explicit the notion of viewpoint in KDD. In fact KDD is a complex process (complex system) most often held by several experts (i.e. multi-view). The definition we propose for the notion of viewpoint in KDD is inspired from knowledge engineering (knowledge involved during a KDD analysis) and takes into account the two facets perspective and opinion defined by [START_REF] Ribière | A Viewpoint model for cooperative Building of an Ontology[END_REF].

Definition:

A viewpoint in KDD is an interface allowing [START_REF]W3C Consortium[END_REF] access to a subset of domain knowledge (analyzed domain knowledge and analyst domain knowledge) and leading the analyst to achieve his goals, [START_REF]LICO Project[END_REF] capture the logic of reasoning and trace of major decisions made by the analyst during a KDD process (i.e. capture the semantics of the process).

Thus the viewpoint of the analyst allows him to filter the relevant expert domain knowledge according to his vision on analyzed data, on application domain, on the domain of KDD (tasks, methods, algorithms, tools…), and according to his objective.

The specification of an analyst viewpoint is based on the instantiation of a set of generic criteria that may fall into three components: analyzed domain, analyst domain, and context of analysis (see Figure 3).

Figure 3. Components of a viewpoint in KDD.

To identify these three components of viewpoint, we were inspired by viewpoints in second-order cybernetics: observed object, observer and context of observation (Ben [START_REF] Ahmed | Safe Next : une approche systémique pour l'extraction de connaissances de données[END_REF]. This is a systemic approach of a multi-view KDD process that we analyze from three viewpoints: analyzed domain viewpoint (observed object), analyst domain viewpoint (observer), and context of analysis.

To identify generic criteria that characterize a viewpoint in KDD, we were based on the CRISP-DM standard CRISP-DM. This point is discussed in the next sub-section.

Generic criteria of viewpoint in KDD

Our objective in this paper is to formalize the definition of viewpoint in KDD. For this, we will first identify a set of generic criteria that characterize a viewpoint in KDD. Once instantiated, these criteria define an analyst viewpoint. This viewpoint will guide the execution of the KDD process, and then keep trace of reasoning and major decisions made by the analyst.

The criteria of a viewpoint are called generic "if they are not instantiated" [START_REF] Ribière | A Viewpoint model for cooperative Building of an Ontology[END_REF]) (e.g. KDD_Task is a generic criterion), they are called specific criteria if they are instantiated (e.g. KDD_Task = "Description" is a specific criterion). The criteria are generic also if they are independent of the application domain, and of the data mining tools and techniques. For this reason, we have found useful to elicitate these generic criteria based on CRISP-DM standard. Genericity of criteria will be ensured by the level of abstraction and description of KDD process according to CRISP-DM.

In fact, CRISP-DM (Cross-Industry Standard Process for Data Mining) [START_REF] Chapman | CRISP-DM 1.0 Step-by-step data mining guide[END_REF]) is a process model and a methodology that describes commonly used approaches to conduct a data mining project. CRISP-DM process model focuses on the life cycle of a KDD project; it does not rely on a particular application domain, data mining technique or tool. CRISP-DM methodology is described in terms of a hierarchical set of tasks organized at four levels of abstraction: phase, generic task, specialized task, and process instance (from generic to specific). At the top level, the life cycle of a KDD project is organized into six phases as depicted in Figure 4. [START_REF] Chapman | CRISP-DM 1.0 Step-by-step data mining guide[END_REF].

In each phase of the process, the analyst must perform a number of tasks. According to the knowledge required for each task, we can distinguish: tasks that require analyzed domain knowledge, tasks that rely on analyst domain knowledge, his skills and expertise, and tasks that rely on business objectives and criteria for validating the results of the process (models).

Based on these tasks, we have identified the set of generic criteria that we draw in Table 1, and formalize in the next section.

KNOWLEDGE MODEL FOR MULTI-VIEW KDD PROCESS

According to CommonKADS project [START_REF] Schreiber | Knowledge engineering and management: The CommonKADS methodology[END_REF] a knowledge model is "a specification of the information and knowledge structures and functions involved in a knowledge-intensive task". It gives an implementation-independent description of knowledge involved in a task. A knowledge model is composed of three types of knowledge that are subject of separate models with specific modeling primitives: domain knowledge, tasks and methods (Charlet et al., 2000).

Our knowledge model integrating the viewpoint notion (see Figure 5) consists of four hierarchical sub-models structured in domain knowledge and strategic knowledge according to [START_REF] Aussenac-Gilles | Acquisition et ingénierie des connaissances : tendances actuelles[END_REF]. Domain level describes the domain concepts and their relationships. The strategic level is based on the domain level and expresses how a task will be achieved. In this paper, we will focus much more on the description and formalization of the viewpoint model in figure 5.

Domain Model

Domain knowledge is knowledge about application domain that is necessary to execute methods. The domain model provides conceptualization of studied domain concepts and also the various relations between them. It describes the analyzed domain knowledge in terms of manipulated data and the analyst domain knowledge in terms of tasks performed, methods selection, configuration and composition. In our context of KDD, we consider domain model as an ontology used to index manipulated data and their attributes.

Task and Method Model

This model describes the KDD process in terms of tasks and methods. Tasks are performed by methods. A task is a description of what must be done in the application in terms of goals and sub-goals. The methods describe how a goal can be achieved in terms of a series of operations and an order of execution.

We have formalized this model as a generic semi-formal ontology OntoECD [START_REF] Zemmouri | OntoECD : une ontologie pour le processus d'ECD[END_REF]. OntoECD conceptualizes methods and functions of KDD process regardless of the application domain and the structure of data to improve reusability.

Viewpoint Model

Viewpoint model is a conceptualization of the generic criteria introduced in section 2. These criteria are independent of the task and the application domain. They allow modeling the vision of the analyst on manipulated data, the objective of analysis, and part of the expertise required for decisions made during the analysis.

Modeling viewpoint in KDD will promote coordination and understanding between different experts in a multi-view analysis. It also promotes the reuse of analysis according to a given viewpoint (this is possible thanks to annotations of KDD process that we introduced in [START_REF] Behja | Viewpoint-based annotations for knowledge discovery in databases[END_REF]).

To formalize the viewpoint model, we have chosen OWL (Web Ontology Language) due to its expressiveness compared with XML Schema and RDF(S), and to its representational and inferring capacity. Figures 6, 7 and 8 draw a subset of classes' hierarchy and relations of viewpoint in KDD.

Figure 6. Class hierarchy of viewpoint in KDD.

A viewpoint in KDD is composed of three parts (see Figure 6): the analyst domain viewpoint which describes actions and decisions taken by the analyst in terms of KDD task (verification, description, or prediction), selected KDD methods, and criteria for validating methods. The analyzed domain viewpoint describes the analyst vision on analyzed domain in terms of selected data and relevant attributes for the analysis. The context viewpoint describes business objectives of the project and criteria for validating the results (models).

The main part of the analyst domain viewpoint is actions and decisions made to construct a KDD execution plan (see Figure 7). A KDD execution plan consists of a set of selected methods (data preparation and modeling according to CRISP-DM). Each method has some constraints (pre-and post-conditions) and a set of parameters. Modeling methods have models as output. The analyst has to select, configure and execute methods according to the KDD task, and available data. The main part of analyzed domain viewpoint (see Figure 8) is the description of analyzed data and the effects of executed methods on data. Analyzed data have some properties: format, source, quality (missing values, errors…), and quantity (number of attributes, number of rows…). Each selected and executed method by the analyst has a transformational effect on data and their properties. The instantiation of these classes characterizing a viewpoint in KDD is considered as an analyst viewpoint's definition. This viewpoint will guide the execution of the process and allow keeping trace of decisions made by the analyst.

Viewpoints Organizational Model

In a multi-view analysis, it is important to emphasize the interaction and interdependence between various analyses according to different viewpoints. The viewpoints organizational model (see Figure 5) requires the identification of a set of relations between viewpoints like: equivalence, exclusion, complementarity, composition, subsumption. These relations are under study and development.

CONCLUSION

In this paper we have presented a formalization of the concept of viewpoint in KDD that integrates both analyzed domain knowledge and analyst domain knowledge. This multi-view approach of KDD will promote coordination and understanding between different experts in a multi-view analysis, and also the reuse of analysis according to a given viewpoint. For example there will be some complementarities between the viewpoint "evaluation" of a teacher, and the viewpoint "reliability" of the administrator (see Figure 2). Also a teacher will reuse the analysis of another teacher (i.e. one can use the same KDD execution plan of another to evaluate his/her course materials).

Figure 9 below shows the current version of a platform that we are developing to support multi-view analysis. It is able to interact with a user (a teacher in this example) to define his viewpoint by instantiating some of the generic criteria defined in this paper (context, KDD_Task, Selected_Data, relevant attributes) and then guide him in the selection, configuration and execution of KDD methods based on the collection of algorithms Weka 3 . Our system is supported by the Jena 4 Toolkit and its SPARQL query engine. It is architected as a Web Services Architecture [START_REF] Zemmouri | Architecture web service d'un processus d'ECD multiutilisateur[END_REF]. As future works, we plan to develop the organizational model for defining relationships between viewpoints, and allowing the reasoning on viewpoints. We also plan to develop the aspect of assessment of methods and models that are not treated in depth in this paper.

Figure 2 .

 2 Figure 2. Multitude of viewpoints to analyze data from an e-learning system. The teacher may have as an objective the "evaluation of learning rate of a course", description as KDD task, and may use (IP, UserLogin, Date, URL, Status, and Referrer) as attributes. While the administrator may have as an objective "ensuring the reliability of the system", prediction as KDD task, and may use (IP, Date, URL, Status, and UserAgent) as attributes.

Figure 4 .

 4 Figure 4. CRISP-DM reference model[START_REF] Chapman | CRISP-DM 1.0 Step-by-step data mining guide[END_REF].

Figure 5 .

 5 Figure 5. Knowledge Model for a multi-view KDD process.

Figure 7 .

 7 Figure 7. Class hierarchy for analyst domain viewpoint.

Figure 8 .

 8 Figure 8. Class hierarchy for analyzed domain viewpoint.

Figure 9 .

 9 Figure 9. Definition of a teacher viewpoint to analyze data (HTTP log files) of an e-learning platform.

Table 1 .

 1 Selected generic criteria of a viewpoint in KDD based on CRISP-DM.

		Analyzed domain viewpoint	Analyst domain viewpoint	Context viewpoint
		Business area
	Business understanding	Project resources +Data +Knowledge +personnel +computing Risks -Contingencies Constraints Requirements, Assumptions,	KDD Task KDD success criteria +Model accuracy +Model performance Assessment of tools and techniques Initial project plan +Model complexity	Business objective Business success criteria Costs and Benefits
		Terminology
		Data locations
		Datasets (list)
		Sources
	understanding	Problems Data description + Data format + Data quantity -number of fields -number of records -number of classes	Collect methods Selection criteria Data exploration +Basic statistical
	Data	+ Attributes list (names) + attribute data types
		Data quality
		+ has missing values
		+ has inconsistent values
		+ has outlier values
			Data cleaning method
	Data preparation	Dataset Data selection method Data selection criteria Derived Attributes Merged data Reformatted data	+missing handling +outliers handling +duplicates handling +errors handling Data Transformation +Method
			+Parameters
	Modeling	Modeling assumptions +Data format +Data quality Test Design +Options +Training Dataset +Test Dataset +Validation Dataset	Modeling Technique Parameter settings +Parameter, +Value Model (Final Model Location) Model description +Estimated Model Accuracy Model Assessments +Model Quality -DM success criteria achieved
	Evaluation		Approved Model Improvement suggestions Decision List of possible actions	Business success criteria achieved
	Deployment		Deployment plan Monitoring plan Maintenance plan Final report Final presentation Experience documentation


Moukhtar El

Zemmouri
email: ezemouri@yahoo.fr

Hicham Behja
email: h_behja@yahoo.com

Brahim Ouhbi
email: ouhbib@yahoo.co.uk

Brigitte Trousse
email: brigitte.trousse@inria.fr

Abdelaziz Marzak
email: marzak@hotmail.com

Youssef Benghabrit
email: you_benghabrit@yahoo.fr

Goal Driven Approach to Model Interaction between Viewpoints of a Multi-view KDD Process

Keywords: component, KDD process, Viewpoint, Goal analysis, Ontologies, SWRL I

A data mining project is usually held by several actors (domain experts, data analysts, KDD experts …), each with a different viewpoint. In this paper we propose to enhance coordination and knowledge sharing between actors of a multiview KDD analysis through a goal driven modeling of interactions between viewpoints. After a brief review of our approach of viewpoint in KDD, we will first develop a Goal Model that allows identification and representation of business objectives during the business understanding step of KDD process. Then, based on this goal model, we define a set of relations between viewpoints of a multi-view analysis; namely equivalence, inclusion, conflict and requirement.

INTRODUCTION

In recent decades, enterprises' information systems become more and more flooded by all kind of data: structured (databases, data warehouse), semi-structured (XML, server log files), and unstructured data (raw text, multimedia data). This has created new challenges for companies and for the scientific community. Including, how to understand and analyze such a mass of data to extract knowledge. Hence, KDD (Knowledge Discovery in Databases [START_REF] Fayyad | The KDD Process for Extracting Useful Knowledge from Volumes of Data[END_REF]) have rapidly changed from a research area into an industry standard (i.e. CRISP-DM: Cross-Industry Standard Process for Data Mining [START_REF] Shearer | The CRISP-DM model: the new blueprint for data mining[END_REF]). In [START_REF] Kurgan | A survey of Knowledge Discovery and Data Mining process models[END_REF], Kurgan and Musilek draw up a comprehensive survey of knowledge discovery and data mining standard process models.

But, available data mining tools (commercial as well as free tools) support end-users only with graphical and/or manual construction of KDD execution plans. This is done without taking into account analyst viewpoint and coordination within organization (coordination between domain experts, data analysts, and KDD experts). But this is time consuming, cost sensitive, and requires good experience and prior knowledge of data mining domain to successfully conduct a KDD project.

Our objective in this paper is to model and formalize interactions between different viewpoints of a multi-view KDD process (a KDD process held by several experts who analyze the same data with different viewpoints). This is done by introducing a set of semantic relations between viewpoints.

Our formalization is based on a goal driven approach and will allow us to enhance coordination, knowledge sharing and mutual understanding between different actors of a multi-view analysis, and reusability in terms of viewpoint of successful data mining experiences within an organization.

In the reminder of this introductory section we briefly recall our approach of viewpoint in KDD to fix definitions and context of our work. This approach was initiated by Behja et al. [START_REF] Behja | Prise en compte des points de vue pour l'annotation d'un processus d'Extraction de Connaissances à partir de Données[END_REF] [START_REF] Behja | Plateforme objet d'évaluation orientée point de vue d'un système d'information[END_REF] as part of Behja's doctoral thesis in the context of France-Morocco cooperation (Software Engineering Network) 1 .

A multi-view KDD process is usually held by one or more users who consequently manipulate several types of knowledge and know-how. They will have different objectives and preferences, different competences, and different visions of analyzed data, KDD methods and functions. In brief, they have different viewpoints. In this context, the KDD process will be guided by the analyst viewpoint [START_REF] Behja | Prise en compte des points de vue pour l'annotation d'un processus d'Extraction de Connaissances à partir de Données[END_REF] and several types of knowledge and expertise are incorporated (analyzed domain knowledge and analyst domain knowledge).

Figure 1. Multitude of viewpioints to analyse data from an e-learing system [START_REF] Zemmouri | Ontology-based Knowledge Model for Multi-view KDD Process[END_REF].

Figure 1 shows an example of a multi-view analysis of data from an e-learning system (that consists of HTTP log files, platform database, and courses material). These data can be analyzed by different actors of the system (teachers, learners, administrator, marketing, KDD expert, data miner). The objective of a teacher (e.g. improve quality of a course) is not the same as the administrator's one (e.g. ensure system reliability). Attributes used for evaluating a course are different from those used for studying the reliability. Similarly, chosen data mining methods, techniques and tools will be different, and interpretation/deployment of data mining results depends on the analyst's viewpoint. Therefore, it is fundamental to take into account the viewpoint of each analyst and interaction between different viewpoints.

In previous works we have developed a Knowledge Model for multi-view KDD process [START_REF] Behja | Plateforme objet d'évaluation orientée point de vue d'un système d'information[END_REF] which is "a specification of the information and knowledge structures and functions involved [during a multi-view analysis]" [START_REF] Schreiber | Knowledge Engineering and Management: The CommonKADS methodology[END_REF]. As shown in figure 2, our Knowledge Model integrating the viewpoint notion consists of four hierarchical sub-models structured in domain knowledge and strategic knowledge. Domain level describes the domain concepts and their relationships. The strategic level is based on the domain level and expresses how a task will be achieved. The Domain Model concerns the studied domain concepts and the various relations between them. In our applicative context, that contains an e-learning ontology, platform database and HTTP log file structure. Task and Method Model describes the KDD process in terms of tasks and methods. We have formalized this model as a generic semi-formal ontology OntoECD [START_REF] Zemmouri | OntoECD : une ontologie pour le processus d'ECD[END_REF]. Viewpoint Model is a conceptualization of a set of generic criteria that characterize a viewpoint in KDD [START_REF] Zemmouri | Ontology-based Knowledge Model for Multi-view KDD Process[END_REF]. These generic criteria were identified based on CRISP-DM reference model and formalized as a viewpoint ontology in OWL.

In this paper we will mainly focus on the development of the Viewpoint Organizational Model.

The remainder of the paper is organized as follows. In section 2 we will give a state of the art of works related to supporting users of KDD and managing knowledge in such process especially using ontologies. In section 3, we will develop a goal model that represents business objectives of different actors of a multi-view analysis, and formalize two types of relations between goals: AND/OR decomposition, and positive/negative influence. We will also illustrate our goal model within an example in e-learning. Based on this goal model, in section 4, we will define a set of semantic relations between viewpoints in KDD, especially: equivalence, conflict, and requirement. As stated before, the main purpose of these relations is to provide a means of coordination and mutual understanding between viewpoints actors. In section 6, a case tool implementation to validate our approach is presented. Finally, we will draw some learned lessons in conclusion.

II. RELATED WORK

"An analyst is usually not a KDD expert but a person responsible for making sense of the data using available KDD techniques. Since the KDD process is by definition interactive and iterative, it is a challenge to provide a high-performance, rapid-response environment that also assists users in the proper selection and matching of appropriate tools and techniques to achieve their goals" [START_REF] Fayyad | The KDD Process for Extracting Useful Knowledge from Volumes of Data[END_REF]. This was a statement of Fayyad et al. in 1996 highlighting the challenge of supporting both expert and novice users of KDD due to its complexity. We notice also that during a KDD process (a data mining project according to CRISP-DM vocabulary) there will be several actors (domain expert, data analyst, data miner …). The question we address in this paper is how to provide a framework allowing these actors to collaborate, share knowledge (about business domain and data mining techniques), and reuse each others' experiences.

Several works and standards have addressed the complexity of KDD with different approaches with the aim of supporting both expert and novice users. Most of these approaches are based on ontologies (either domain ontologies, or data mining ontologies). They offer the user the advantage to explore the large space of valid data mining processes [START_REF] Bernstein | Towards intelligent assistance for a data mining process: an ontology based approach for cost-sensitive classification[END_REF][10], to discover and access distributed data mining services [START_REF] Euler | Publishing Operational Models of Data Mining Case Studies[END_REF][10], to reuse successful data mining experiences [START_REF] Morik | The MiningMart approach to knowledge discovery in databases[END_REF], etc. But without taking into account the multi-view aspect of a KDD analysis.

One of the first ontologies proposed to support users of KDD is DAMON (Data Mining ONtology) [START_REF] Cannatro | A data mining ontology for grid programming[END_REF] that is designed to simplify the development of distributed KDD applications on Grids. DAMON ontology concerns only the data mining phase of a KDD process, and offers a taxonomy for discovering tasks, methods and tools deemed more suitable for a given data mining goal.

In MiningMart project [START_REF] Morik | The MiningMart approach to knowledge discovery in databases[END_REF] a case-based reasoning (CBR) system to support end users during data preprocessing is proposed. This system is based on a meta-model (called M4) of KDD preprocessing chains that contains ontology for describing conceptual domain knowledge. In the same project, Euler [START_REF] Euler | Publishing Operational Models of Data Mining Case Studies[END_REF] proposes a web-based platform (which is a case base containing MiningMart successful experiences) to publicly display preprocessing models in a structured way, together with descriptions about their business domains, goals, methods and results.

Bernstein et al., [START_REF] Bernstein | Towards intelligent assistance for a data mining process: an ontology based approach for cost-sensitive classification[END_REF] propose an Intelligent Discovery Assistant (IDA) for valid data mining processes enumeration and ranking. IDA focuses mainly on preprocessing and data mining phases of the KDD process. It is based on a formal ontology that contains input/output, preconditions constraint, and performance (accuracy, complexity, and comprehensibility) of each data mining operator. This ontology allows selection and composition of data mining operators suitable for user's data and goal. A similar approach is proposed by Diamantini et al., [START_REF] Diamantini | Ontology-driven KDD process composition[END_REF] in a project called KDDVM (KDD Virtual Mart), which is a web services based system that aims to support users in the design of valid KDD process. It represents KDD operations as services which can be "annotated, introduced, accessed, described, composed and activated". KDDVM is based on KDDONTO ontology and concerns only data preprocessing and data mining steps.

A recent European project (e-LICO 2 : e-Laboratory for Interdisciplinary Collaborative Research in Data Mining and Data-Intensive Science) deals with the problem of supporting users of KDD in a collaborative way [START_REF] Hilario | Ontology-based meta-mining of knowledge discovery workflows[END_REF]. One of the products of this project is eProPlan [START_REF] Kietz | eProPlan: A tool to model automatic generation of data mining workflows[END_REF], an ontology based environment for planning KDD workflows. It is based on two ontologies DMWF-DMOP and uses IA planning techniques to automatically generate KDD execution plan for solving data mining problems. DMWF (Data Mining Work Flow Ontology) formalizes IO-objects, operators, goals, tasks and methods as well as the decomposition of tasks into methods and operators (this ontology is equivalent to our OntoECD ontology described in [START_REF] Zemmouri | OntoECD : une ontologie pour le processus d'ECD[END_REF]). DMOP (Data Mining Optimization Ontology) provides a unified conceptual framework for analyzing data mining tasks, algorithms, models, datasets, workflows and performance metrics, and their relationships.

Our approach of supporting KDD users focuses on the reusability, coordination, and knowledge sharing between multi-users of a KDD process, rather than the automatic generation of KDD execution plan. In addition, we cover the whole phases of the KDD process (cf. 6 phases suggested by CRISP-DM reference model [START_REF] Shearer | The CRISP-DM model: the new blueprint for data mining[END_REF]).

In previous works we have addressed mainly three issues: integration of domain knowledge [START_REF] Zemmouri | Ontology-based Knowledge Model for Multi-view KDD Process[END_REF], annotation of KDD in terms of viewpoint [START_REF] Behja | Viewpoint-based Annotations for Knowledge Discovery in Databases[END_REF], and viewpoint characterization and modeling [START_REF] Zemmouri | Ontology-based Knowledge Model for Multi-view KDD Process[END_REF].

In this paper we propose to focus on modeling interactions between viewpoints of multi-view KDD process. For this, our proposed model will be based on a goal driven approach [START_REF] Anton | Goal based requirements analysis[END_REF].

III. GOAL MODEL FOR MULTI-VIEW KDD PROCESS

Goal driven analysis consists of the identification, modeling and analysis of goals and objectives that guide decisions and strategies of an organization at different levels. Goals are also defined to be a logical mechanism for identifying, organizing and justifying requirements [START_REF] Anton | Goal based requirements analysis[END_REF].

Goal models have been used in Software Engineering [START_REF] Anton | Goal Identification and Refinement in the Specification of Information Systems[END_REF] [19] and Data Warehousing [START_REF] Giorgini | Goal-oriented requirement analysis for data warehouse design[END_REF] [21] [START_REF] Kumar | Stakeholders Driven Requirements Engineering Approach for Data Warehouse Development[END_REF] in order to represent users requirements, business objectives and design qualities. Indeed, eliciting requirements (as high level goals) early in the development process is crucial [START_REF] Nuseibeh | Requirements engineering: a roadmap[END_REF]. Requirements can be functional or non-functional. Non-functional requirements (also known as quality requirements) are defined as attributes or constraints of the system such as performance, security, and reliability [START_REF] Glinz | On Non-Functional Requirements[END_REF]. 2 e-LICO Project, http://www.e-lico.eu/ Goal models are recognized also to be useful for knowledge management systems which focus on strategic knowledge representation and reasoning [START_REF] Jarvis | Semantic Models for Knowledge Management[END_REF] [START_REF] Giorgini | Formal Reasoning Techniques for Goal Models[END_REF]. In this case, goals are used to represent strategic objectives of an organization and to analyze and keep track of events and trends that may influence positively or negatively these objectives.

A. Generic goal model for multi-view KDD process

In the context of multi-view KDD process we propose to use the goal-driven approach to identify and represent business objectives (this is recognized to be the first task of the first step of CRISP-DM reference model) of a multi-view KDD process and to model interactions between viewpoints of stakeholders of these objectives. This will provide users with a methodological assistance during the business understanding step of KDD and make business objectives persistent for the other steps (especially evaluation and deployment of data mining results). In fact, as is the case for requirements traceability and persistence in data warehousing [START_REF] Khouri | Towards a Method for Persisting Requirements and Conceptual Models in Data Warehousing Context[END_REF] and software development [START_REF] Aybuke | Engineering and Managing Software Requirements[END_REF], we support here the necessity of storing early defined business objectives. Their presence can guide many decisions and solve many problems encountered at different stages of a KDD analysis. The persistence of goals, in our approach, is intended also to be a complement of metadata schema introduced by Behja et al. [START_REF] Behja | Viewpoint-based Annotations for Knowledge Discovery in Databases[END_REF][5] to annotate and keep track of multi-view analysis.

Our proposed generic goal model for multi-view KDD process, represented as OWL ontology, is depicted in figure 3: During a data mining project, an analyst (actor of the system) may have one or more goals (these goals are considered as a part of the context associated with his/her viewpoint [START_REF] Zemmouri | Ontology-based Knowledge Model for Multi-view KDD Process[END_REF]). A goal can be either functional or nonfunctional. Functional goals reflect business objectives, while non-functional goals reflect constraints of the system (such as security, reliability, and performance) or technical constraints on the execution of KDD methods (such as accuracy, cost sensitivity, comprehensibility, runtime, number of techniques that form the execution plan, etc.). As an example: "Improve quality of a course" is a functional goal, "ensure reliability of the e-learning platform" is a non-functional one.

A goal may have two attributes (Data Type Property in OWL vocabulary) priority and label. Label indicates if a goal is satisfied or denied [START_REF] Giorgini | Formal Reasoning Techniques for Goal Models[END_REF]. Priority indicates if a goal is mandatory or optional [START_REF] Khouri | Towards a Method for Persisting Requirements and Conceptual Models in Data Warehousing Context[END_REF].

A goal is proposed by an actor (KDD expert, domain expert, and data miner are example of actors) and is measured by some success criteria.

In goal-driven approach, two types of reflexive relations (Object Property in OWL vocabulary) between goals are defined (especially for reasoning purposes) [START_REF] Giorgini | Formal Reasoning Techniques for Goal Models[END_REF]: sub-goal relation and influence relation. Notice that binary decomposition is not a restriction since it can be easily generalized into n-ary decomposition.

Sub-goal relation

Influence relation: this type of relation models situations

where a goal contributes positively or negatively towards the satisfaction/denial of another goal. It is described to be more qualitative relation than AND, OR-decomposition [START_REF] Giorgini | Formal Reasoning Techniques for Goal Models[END_REF].

Influence relation has 4 sub-relations that are labeled (+, -, ++, and --) with the following semantic:

 +(G, G') : if G is satisfied then G' is partially satisfied.  -(G, G') : if G is satisfied then G' is partially denied.  ++(G, G') : if G is satisfied then G' is fully satisfied.  --(G, G') : if G is satisfied then G' is fully denied.
To formalize these relations, we define the following SWRL rules: posInfluence(?x,?y) ˄ satisfied(?x) → partSatisfied(?y) negInfluence(?x,?y) ˄ satisfied(?x) → partDenied(?y) posPosInfluence(?x,?y) ˄ satisfied(?x) → fullSatisfied(?y) negNegInfluence(?x,?y) ˄ satisfied(?x) → fullDenied(?y) 3 SWRL: A Semantic Web Rule Language Combining OWL and RuleML, http://www.w3.org/Submission/SWRL/ Where (posInfluence, negInfluence, posPosInfluence, and negNegInfluence) represent respectively influence relations (+, -, ++, and --) in OWL.

B. An example

In this subsection we will illustrate through an example in our applicative context e-learning. This example will be considered as an instance of the goal model presented in the previous sub-section.

Assume that we want to conduct a data mining project to analyze data from a web based e-learning platform. According to CRISP-DM methodology [START_REF] Chapman | CRISP-DM 1.0 Stepby-step data mining guide[END_REF], the first and critical step of the project is business understanding, where business objectives must be identified, analyzed and then transformed into data mining tasks. In our case study, examples of such business objectives are: "improve course quality" form the teacher viewpoint, "manage users' relationship" from the marketing viewpoint, and "ensure reliability of the platform" from the admin viewpoint (see figure 1).

These business objectives are modeled using goals and goal relations (AND/OR decomposition, +/-influence) as illustrated in figure 4 below. The teacher goal "improve course quality" is ANDdecomposed to "restructure the course" and "diversify content and activities", and is positively influenced by the admin goal "ensure reliability of the platform" (i.e., satisfaction of the latter contribute positively towards the satisfaction of the former). The admin goal "ensure reliability of the platform" is AND-decomposed to "secure users data", "use multi-site access", and "detect and prevent HTTP attacks".

The decomposition and refinement of goals continue until we have sub-goals that are tangible [START_REF] Giorgini | Formal Reasoning Techniques for Goal Models[END_REF] (i.e., they can be analyzed using a simple KDD task).

One of the main issues in goal-driven analysis is goals identification. Even if there exist some attempts to guide the identification of goals (like eliciting goals from scenarios, eliciting goals by refinement, and eliciting goals by reuse [START_REF] Rolland | Modeling Goals and Reasoning with Them[END_REF]). We argue that, in the context of KDD, the assistance of domain experts is necessary to guide and validate the identification of goals and influences between them.

IV. VIEWPOINTS INTERACTION

In most modeling paradigms for information systems (such as Entity Relationship modeling, Object Oriented modeling, and Conceptual Graphs), relations between objects are recognized to have a predominant role. In particular, relations express dependency between entities of a conceptual model. In addition, during a multi-view analysis, it is important to emphasize the interaction and interdependence between the various analyses according to different viewpoints. It is therefore necessary for our approach of knowledge representation in a multi-view KDD process to provide opportunities for expressing such interaction and dependency in terms of relations.

Based on the presented goal model and relationships between goals we introduce some relations between viewpoints of a multi-view analysis. The main purposes of these relations are to enhance coordination and mutual understanding between viewpoint stakeholders, and to allow reusability of KDD process in terms of viewpoint.

Let VP 1 and VP 2 be two different viewpoints during a multi-view analysis, G 1 ={G 11 , G 12 , …, G 1n } goals associated with VP 1 , G 2 ={G 21 , G 22 , …, G 2m } goals associated with VP 2 , {g 11 , g 12 , …, g 1i } a subset of G 1 , and {g 21 , g 22 , …, g 2j } a subset of G 2 . We define and formalize equivalence, inclusion, conflict, and requirement relations between VP 1 and VP 2 as follow:

 Equivalence: VP 1 is equivalent to VP 2 if:
Satisfaction of all of the goals associated with VP 1 implies satisfaction of all of the goals associated with VP 2 and vice versa. The equivalence relation serves mainly the purpose of reusability of KDD process in terms of viewpoint. In fact, it may be benefit within an organization to reuse successful data mining experiences to achieve different business objectives (goals) associated to different viewpoints (actors). This is done by comparing only the goal models associated with VP1 and VP2 without considering the technical details of the KDD execution plans.

The conflict, inclusion and requirement relations can be used to provide methodological assistance to a KDD user to achieve his/her goals. Especially tasks to be avoided in the case of conflict with another VP, or tasks to be partially reused in the case of inclusion and requirement.

V. IMPLEMENTATION OVERVIEW

To validate our approach, we are implementing a case tool in Java language that can be used by KDD users to design valid KDD process by reusing existing ones. As illustrated in figure 5, our assistant consists of 5 main components: a graphical user interface, a case based reasoner, a rule based reasoner, a KDD case base, and OWL ontologies. OWL ontologies and rule base give a formal representation of knowledge involved during a KDD analysis, while the KDD case base holds detailed annotations [START_REF] Behja | Viewpoint-based Annotations for Knowledge Discovery in Databases[END_REF] about successful data mining experiences (data sources characterization, goals instances, used data mining methods and their parameters, etc.). The case based reasoner provides a set of similar KDD cases based on the analyst definition of viewpoint (that includes goals identification and data sources) and using the previously defined relations between viewpoints. Reusability/adaptation of a KDD case is carried out by the inference capabilities of the rule based reasoner, which based on FaCT ++ reasoner [START_REF] Fact++ | FaCT++ OWL-DL reasoner[END_REF] and SWRL.

VI. CONCLUSION

To support users of multi-view KDD process within an organization, we have proposed a goal-based formal framework to model and formalize business objectives and interactions between viewpoints of a multi-view KDD process.

At first we have presented a goal model to identify and represent business objectives during the business understanding step of KDD. We defined also two reflexive relations within goals: AND/OR decomposition and influence relation. A precise semantic has been given for these relations as well as a formalization using SWRL language. This goal model has the benefit of assisting users during the early stage of the KDD process to clearly define business objectives of the data mining project, and then to make them persistent. This persistence will guide decisions at different steps of the KDD process, especially during the evaluation and deployment of data mining results.

Then, to formalize interaction and interdependence between various analyses according to different viewpoints, we have presented a set of semantic relations between viewpoints. We have defined equivalence, inclusion, conflict, and requirement relations. These relations allow us to enhance coordination, knowledge sharing and mutual understanding between different actors of a multi-view analysis, and reusability in terms of viewpoint of successful data mining experiences within an organization.

Finally we argue that our approach has the benefit of minimizing the cost of developing new KDD analyzes (since we can develop new analyzes from earlier), and providing a methodological assistance during KDD steps (especially about tasks and choices to be reused or avoided). The evaluation of our proposal is conducted by implementing a case tool and analyzing data and viewpoints from an e-learning system.

Figure 2 .

 2 Figure 2. Knowledge Model for a multi-view KDD process [5].

Figure 3 .

 3 Figure 3. Generic Goal Model for multi-view KDD process.

  consists of the decomposition of a general goal into more specific sub-goals. For this relation two main sub-relations are used: AND and OR decomposition. Semantic of these relations is as follow: If a goal G is AND-decomposed into sub-goals G 1 , G 2 , …, G n , then if all of the sub-goals are satisfied so is goal G.  If a goal G is OR-decomposed into sub-goals G 1 , G 2 ,…, G n , then if at least one of the sub-goals is satisfied so is goal G. To formalize these relations, in the case of binary decomposition, we define the following SWRL 3 rules: AND decomposition: satisfied(?G1) ˄ satisfied(?G2) → satisfied(?G) OR decomposition: satisfied(?G1) → satisfied(?G) satisfied(?G2) → satisfied(?G)

Figure 4 .

 4 Figure 4. Example of a goal model for analysing a web based e-learining system.

  satisfied(?G11) ˄ … ˄ satisfied(?G1n) → satisfied(?G21) ˄ … ˄ satisfied(?G2m) satisfied(?G21) ˄ … ˄ satisfied(?G2m) → satisfied(?G11) ˄ … ˄ satisfied(?G1n)

Figure 5 .

 5 Figure 5. Architecture overview of our implementing tool.

  VP 1 includes VP 2 if: Satisfaction of some of the goals associated with VP 1 implies satisfaction of all of the goals associated with VP 2 .

	 Requirement:
	VP 1 requires VP 2 if:
	Satisfaction of some of the goals associated with VP 1
	requires satisfaction of all of the goals associated with
	VP 2 .
	satisfied(?g11) ˄ … ˄ satisfied(?g1i) ←
	satisfied(?G21) ˄ … ˄ satisfied(?G2m)
	satisfied(?g11) ˄ … ˄ satisfied(?g1i) →
	satisfied(?G21) ˄ … ˄ satisfied(?G2m)
	 Conflict:
	VP 1 is in conflict with VP 2 if
	Satisfaction of some of the goals associated with VP 1
	implies denial of some of the goals associated with VP 2 .
	satisfied(?g11) ˄ … ˄ satisfied(?g1i) →
	denied(?g21) ˄ … ˄ denied(?g2j)

 Inclusion:

http://raweb.inria.fr/rapportsactivite/RA2003/axis/uid81.html


B Candelon
email: b.candelon@maastrichtuniversity.nl

G Gaulier

C Hurlin

Extreme Financial cycles $

Keywords: Financial extreme cycles, Extreme value theory, cycles financiers extr mes, théorie des valeurs extrèmes. JEL codes: C22, G00

This paper proposes a new approach to date extreme financial cycles. Elaborating on recent methods in extreme value theory, it elaborates an extension of the famous calculus rule to detect extreme peaks and troughs. Applied on United-States stock market since 1871, it leads to a dating of these exceptional events and calls for adequate economic policies in order to tackle them. Cet article élabore une nouvelle méthodologie de datation des cycles financiers extrêmes. S'appuyant sur la théorie des valeurs extrêmes, il étend la "calculus rule" afin de détecter les pics et les creux exceptionnels. Appliquée sur des séries financières américaines depuis 1871, cette méthode permet de mieux appréhender les mouvements extrmes et d'y apporter le cas écheant les réponses les plus adéquates.

Introduction

Since the seminal paper of [START_REF] Burns | Measuring Business Cycles[END_REF], the economic literature has proposed numerous methodologies 1 to detect peaks and troughs in order to date the recession and expansion phases of the business cycle. Such a dating delivers practitioners with the adequate information to correctly time economic policies, insuring hence an optimal stabilization effect.

Nevertheless, academic literature has neglected two important dimensions.

First, similarly to economic activity, stock markets also exhibit periods of persistent rises or falls, i.e. so-called "bulls" and "bears". While it has been recognized by the financial practitioners for a long time, it has attracted the attention from the academic community only in the recent past. [START_REF] Pagan | A Simple Framework for Analysing Bull and Bear Markets[END_REF], and [START_REF] Candelon | On Measuring Synchronization of Bulls and Bears: The Case of East Asia[END_REF] scan the cross country synchronization of bull and bear phases. Gómez Biscarri and Pérez de [START_REF] Gomez Biscarri | Bulls and Bears: Lessons from some European Countries[END_REF], and [START_REF] Edwards | Stock Market Cycles, Financial Liberalization and Volatility[END_REF] focus on the structural change in cyclical stock market synchronization. Chen (2009) considers bear markets as a key variable to forecast, and investigates the role of macroeconomic variables to predict bear markets. Second, a bull (resp. a bear) phase can be sufficiently rare to be classified as extreme asking for exceptional accommodating economic policies. This is in particular the case during financial crises, where fluctuations on the stock markets are severe. The analysis of exceptional bulls and bears has thus only been scarcely investigated (Candelon andHenin, 1995 or Candelon and[START_REF] Candelon | Testing for Exceptional Bulls and Bears: A Non-Parametric Perspective[END_REF] to name but a few). This paper proposes to tackle both issues, offering a new approach to evaluate exceptional parts of the financial cycles, based on the extreme value theory (EVT), in particular on the paper of [START_REF] Hartmann | Asset Market Linkages in Crisis Periods[END_REF].

In Section 2, the behavior of extreme phases of financial cycles is scrutinized. It begins with the definition of financial cycles' peak and troughs. The new framework to measure of extreme phases can then be presented. Elaborating on EVT, it aims at estimating two thresholds beyond (resp. below) which an extreme bull (resp. bear) can be characterized. It is noticeable that such an approach relies on the conditional probability of exceeding a upper (resp. lower) threshold, differing hence on methods considering unconditional measures. Beyond being very easy to implement, our approach presents also the advantage to allow for different thresholds for exceptional bulls and bears, authorizing hence for asymmetry among the extreme financial cyclical phases. Section 3 is devoted to the empirical analysis where the extreme phases of the U.S. stock market are investigated, whereas Section 4 concludes.

Extreme Financial Cycles

Characterizing financial cycles

Let us consider a series of stock market prices (y t ) and its associated real financial returns (r t = ∆y t ). The simplest rule to detect a peak (resp. a trough) in considering as a peak (resp. a trough) of a series r t at time t, if r t > 0 and r t+1 < 0 (resp. r t < 0 and r t+1 > 0). This approach is often referred as the calculus rule. In other words, the existence of a turning point is associated with a change in the sign of the first derivative. It is possible to illustrate graphically this rule where the clouds of points are represented in a space (r t , r t+1 ). For ease of convenience, (r t , r t+1 ) are drawn from two independent standard normal distributions and have a dimension T = 1, 000.

It turns out that potential peaks are located in the south-east quadrant whereas potential trough are in the north-west (N-W) quadrant. In the two remaining quarters, i.e. south-west (S-W) and north-east (N-E), there is no change in the first derivative, which is identical. An acceleration is nevertheless detectable if the angle is larger the 45 o , as |r t+1 | > |r t |. In such a case, a situation of excess growth (resp. excess loss) can be observed in the north-east (N-E) (resp. south-west, S-E, quadrant). This representation is often labeled as the clockwise approach.

Characterizing extreme financial cycles

Turning points are then characterized by the quadrant they are belonging to. Besides, the distance from the origin indicates there strength. Typically, the further they are from the origin, the most severe would be the cycle phase associated to the turning point. Formally, the distance form the origin can be written as d t = (r 2 t + r 2 t+1 ), and then d t increases with |r t+1 | and |r t |. In Figure 1, two troughs i and j are considered, and it is immediately noticeable that d j < d i indicating that the turning point i is more extreme than the turning point j. Such a result can be drawn even if r i,t = r j,t , highlighting that the distance measure has a conditional dimension. Empirically, it can be rewritten in terms of conditional probability. The probability of occurrence of i (P (r t < q 1 , r t+1 > q 2 )) is lower than the one of j. A turning point will be considered as extreme if for the given thresholds (q 1 , q 2 ), this joint-probability is lower than α an criterion of severity, which is generally set up to 5% or 1%.

The thresholds can be endogenously obtained via the following minimization problem:

M in q1,q2 P (r t < q 1 , r t+1 > q 2 ) = α.

(1)

It is straightforward to notice that the set of points satisfying ( 1) is infinite and corresponds to the values q 1 , q 2 defining the contour at α% of the cloud of points. 2 The contour line at 5% is represented in Figure 2 for the two independent standard normal distributions. It is possible to see that the contour line, which is usually an ellipse, becomes a circle when considering two independent normal distributions for r t and r t+1 . When returns would depart from the i.i.idness hypothesis, the contour line would not be a circle anymore. For example, in a case of a simple AR(1) process with a positive coefficient, the ellipse will be oriented from the south-west to the north-east.

Additional constraints are then required to obtain an unique solution. We therefore imposed that each unconditional probability should be also extreme P (r t > q 1 ) = P (r t+1 < q 2 ) = p. Graphically, such a constraint consists in imposing a minimum angle on the x-and y-axis, in order to reduce the possible set of q 1 , q 2 . Hence, the program boils down to: M in (p,q1,q2) s.t.    P (r t < q 1 ) = p P (r t+1 > q 2 ) = p P (r t < q 1 , r t+1 > q 2 ) = α.

(2)

The optimal thresholds q * 1 and q * 2 are then located on Figure 2 and turn out to be symmetric as we are considering two independent symmetric distributions.

The troughs are located thus in the North-West area delimited by q * 1 and q * 2 . Straetmans et al. ( 2004) elaborates a statistical framework to test for such a hypothesis of symmetry.

Similarly, it is possible to set up program for extreme peak as follows:

P eak : M in (p,q1,q2) s.t.
   P (r t > q 1 ) = p P (r t+1 < q 2 ) = p P (r t > q 1 , r t+1 < q 2 ) = α.

(3)

Empirical example

To illustrate the outlined method, we consider the historical yearly database Applying the program defined by ( 2) to (3), we obtain the estimates for q * 1 and q * 2 for α=(1% and 5%). 5 They are reported in Table 1 and the corresponding periods of extreme peaks and troughs are gathered in Table 2.

3 Data correspond to an Update of those presented in Chapter 26 of Market Volatility, R. Shiller, MIT Press, 1989, andIrrational Exuberance, Princeton 2005. Time series are freely available at the following address : http : //www.econ.yale.edu/ shiller/data.htm.

4 A potential extension of this method could be devoted to assess the properties of our approach in the presence of such patterns.

5 Programs are freely available at www.runmycode.com. 1930 1935 1938 1946 1963 1974 1988 1991 2001 T rough 1936 1959 1964 1976 1983 1992 1996 2004 1886 1923 1935 1940 1947 1988 2003 2010 T rough 1897 1931 1933 1939 1968 1976 1996 2002 α = 1% P eak 1923 2003 T rough 1897 1939 1976 We first notice that the estimated thresholds are decreasing with α, the measure for severity, matching the idea that the more conservative the severity criterion is, the higher the thresholds are and the less numerous the exceptional peaks/troughs are detected. 6 The unconditional probability p presents an opposite evolution, corroborating its positive relationship with the severity criterion.

α = 5% α = 1% p q * 1 q * 2 p q * 1 q * 2 T rough 0.
α = 5% α = 1% p q * 1 q * 2 p q * 1 q * 2 T rough 0.
Second, it turns out that thresholds q * 1 and q * 2 present almost the same absolute value but opposite sign (except for SP at 5%) , supporting hence the symmetry hypothesis.7 Exceptional peaks and troughs conditions are then identical, indicating that their number should not differ too much. This is what we observe in Table 2, where we detect 8 or 9 exceptional peaks and troughs at 5% and 2 or 3 at 1%. Third, the interpretation of the extreme financial cycles since 1871 reveals interesting features: For both series (SP and PER) extreme peaks are very frequent during the first part of the XX th century 1920-1946 (4 out of 9 extremes peaks are detected for SP and 4 out of eight for PER) and since 1987 (3 out of 9 for both series) when α is fixed to 5%. The exceptional peak recently observed corresponds to the well known high tech bubble, usually called dot.com bubble, whereas the peaks in the early 1900's are related to the great depression fluctuations. The difference between series appear when considering a 1% threshold.

In such a case, peaks in SP are all located in the recent years whereas 1923 is also extreme for the price earning ratio. This stylized fact is straightforward when looking at Figures 3 a) and b): The real stock price skyrocketed last 30 years, where the price earning ratio remains stable. This discrepancy is also noticeable when analysing exceptional troughs at 1%. Exceptional troughs are following a different path. They appear to be more severe in the recent years (1988, 1991, and 2001) for SP but not for PER (1897, 1939 and 1976). This stylized fact constitutes an interesting feature of the recent years: extreme stock prices associated with relatively price earning ratios. Besides, Such it has consequence in term of economic policy, as it would suggest that recent the troughs in SP are rather extreme and should be tackled using specific stabilization policies and not the traditional ones.

Conclusion

This paper proposes a deeper analysis of extreme financial cycles. Elaborating on recent method in extreme value theory, it proposes an extension of the famous calculus rule to detect extreme peaks and troughs. This method presents also some interesting potential byproducts as the detection of outliers in stationary time series. In the present paper, it is applied on United-States stock market since 1871. The dating of the exceptional peaks and troughs clearly indicates that the last thirty years are extreme for real stock prices but to a much lesser extend for Price Earning Ratio. This discrepancy constitutes an interesting feature of the recent years. Such findings also reveal that traditional stabilization policies implemented to limit the occurrence of extreme bulls or bears in stock prices fails. It thus paves the way for future research analysing optimal stabilization policies.

Figure 1 :

 1 Figure 1: Clouds of points issued from two independent normal distributions.

Figure 2 :

 2 Figure 2: Contour line and measure of severity.

  for U.S. Stock Price Data (y t ) proposed by Shiller 3 covering the period 1871-2011. Data are considered on yearly frequency in order to avoid specific problems associated with high frequency time series, such as conditional heteroscedasticity.4 Besides, we consider that a fluctuation can be defined as bulls or bears only if its length exceeds a year. Two series are considered: First the real stock price (SP), defined as the ratio of the stock market composite index over the Consumer price index and the Price Earning ratio (PER). They are represented on Figures 3 a) and b).

Figure 3 :

 3 Figure 3: Historical data, United-States, 1871-2011

Table 1 :

 1 Thresholds for rt

Real Stock Prices (SP)

Table 2 :

 2 Exceptional Peaks and troughs

		221 -2.473 2.600 0.171 -3.529	2.990
	P eak	0.136 3.937 -3.925 0.021 10.899 -11.761

The reader can also consider the contour line as the frontier out of which α% of the points are left out.

A similar pattern is observed when considering a 10% threshold. For sake of space, this result is not reported but is available from the authors upon request.

A formal test a la[START_REF] Hartmann | Asset Market Linkages in Crisis Periods[END_REF] could be performed to formally test for such an hypothesis.


Associate Professor, Farouk Fardoun

PHD Oussama Ibrahim

Assaad Zoughaib

DYNAMIC MODELING OF AN AIR SOURCE HEAT PUMP WATER HEATER

Keywords: Heat pump, Dynamic modeling, Water heating, Simulation 1

This paper presents a dynamic simulation model to predict the performance of an air source heat pump water heater (ASHPWH). The mathematical model consists of submodels of the basic system components i.e. evaporator, condenser, compressor, and expansion valve. These submodels were built based on fundamental principles of heat transfer, thermodynamics, fluid mechanics, empirical relationships and manufacturer's data as necessary. The model simulation was carried out using MATLAB software. Refrigerant R134a with two different reservoir volumes 150L & 200L are investigated. Additionally, different ambient air temperatures are considered. Results show that the rate of hot water production increases as the water reservoir volume decreases and the integrated COP increases as the ambient temperature increases.

INTRODUCTION

In Mediterranean countries such as Lebanon, electric water heaters are often used to generate hot water. Electric water heaters are usually simple, but not desirable in view of energy efficiency since the overall efficiency, in converting a potential energy of fossil fuels into electric energy and then into thermal energy, is quite low. Compared to those water heaters, heat pump water heating systems can supply much more heat just with the same amount of electric input used for electric water heaters. The ASHPWH absorbs heat from the ambient air and injects it into a water storage reservoir. The use of an air source heat pump (ASHP) leads to a high sensibility of the performance to the local ambient temperature. Moreover, reaching low ambient temperatures close to 0°C, and even below, presents the disadvantage of frost formation on the evaporator, and leads to higher technical complexity due to the required defrosting. The cost of a simple ASHP (with no defrost system) is much lower, which is an advantage permitting a higher interest of this technology in developing countries. According to a UNDP (UNDP 2005) study concerning climatic zoning for buildings in Lebanon, Lebanon was divided into four climatic zones; Zone 1: Coastal, Zone 2: Western Mid-Mountain, Zone 3: Inland Plateau, and Zone 4: High Mountain. Five weather files were created based on data from five meteorological stations (Beirut & Bayssour for zone 1, Qartaba for zone 2, Zahle for zone 3, Cedars for zone 4). Two files were created for the zone 1, since this zone has the highest population density. Based on these weather files, it was observed that during the winter season (Jan., Feb., March), the ambient temperature doesn't fall below zero in zones 1 & 2 on the contrary of zones 3 & 4. These investigations show that a simple ASHP could be an interesting alternative to electrical water heaters for zones 1 & 2 in Lebanon (covering about 80% of the population). Therefore, this paper presents a dynamic model of a simple ASHPWH that is used to assess its seasonal performance in the Lebanese context.

Several dynamic models of heat pumps have been developed, but few of them dealt with heat pump water heaters. Chi and Didion (Chi and Didion 1982) developed a model using a moving boundary-lumped parameter formulation for a residential air-to-air heat pump system. The momentum equation was also included in the heat exchanger models. [START_REF] Macarthur | Unsteady compressible two-phase flow model for predicting cyclic heat pump performance and a comparison with experimental data[END_REF] presented a model of vapor-compression heat pumps. The heat exchangers were modeled with detailed distributed formulations, while the expansion device was modeled as a simple fixed orifice. Fu et al. (Fu et al. 2003) presented a dynamic model of air-to-water dual-mode heat pump with screw compressor having fourstep capacities. The dynamic responses of adding additional compressor capacity in stepwise manner were studied. [START_REF] Kima | Transient thermal behavior of a water heater system driven by a heat pump[END_REF]) presented a dynamic model of a water heater system driven by a heat pump, finite volume method was applied to describe the heat exchangers, and lumped parameter models were used to analyze the compressor and the hot water reservoir, where dynamic simulations were carried out for various reservoir sizes. Rasmussen and Alleyne [START_REF] Rasmussen | Dynamic Modeling and Advanced Control of Air Conditioning and Refrigeration Systems[END_REF] developed an air to air heat pump system using moving boundary-lumped parameter approach for the heat exchangers. [START_REF] Techarungpaisan | Modeling of a split type air conditioner with integrated water heater[END_REF]) presented a steady state simulation model to predict the performance of a small split type air conditioner with integrated water heater. The model used a rotary compressor and a capillary tube.

MATHEMATICAL MODEL

The typical ASHPWH used in this study is shown in figure 1. It is composed of the major components of the heat pump system, namely compressor, evaporator, condenser and throttling device in addition to a hot water reservoir. Static models are chosen to simulate the actuator components, since the dynamics of compressors or expansion devices are generally faster than those of the heat exchangers, where the compressor is considered as an adiabatic reciprocating one and the throttling device is considered as an electronic expansion valve. Concerning the heat exchangers, lumped parameter, moving boundary dynamic models are chosen. The modeled evaporator is a tube and fins heat exchanger type, while a shell and tube heat exchanger is chosen for the condenser, where the refrigerant flows inside the tubes.

Figure 2: P-h Diagram of the 7-point cycle 2.1 Compressor

There are three key parameters that are of interest in the compressor model. They are compressor mass flow rate (m ), outlet enthalpy (h ), and electrical input power (W ), the mass flow rate is given by:

m V ( 1 )
Where P h , f P

Assuming an adiabatic compression process with an isentropic efficiency, the outlet enthalpy is given by:

h h h ( 2 )
Where h h P s , s s P h and f P

Based on the discharge enthalpy, the compressor useful power (W ) is calculated as follows:

W m h h ( 3 )

Expansion valve

There are two key parameters expected out of the valve model, the mass flow rate and the outlet enthalpy.

The mass flow rate is given by:

m C P P ( 4 )
Where C m P P

Assuming an isenthalpic process, the outlet enthalpy is given by: h h ( 5 )

Heat exchangers

The dynamics of a vapor compression system are assumed to be dominated by the dynamics of the heat exchangers. The heat exchanger transient models can be generally classified into three groups: lumped parameter models, discretized models, and moving boundary models. In this work, the moving boundary approach is chosen to model both the evaporator and condenser because of its capability to capture important dynamics due to the complex heat exchanger behavior while preserving the simplicity of lumped parameter models.

To derive governing differential equations suitable for simulation, we will begin with the governing partial differential equations (PDEs) for fluid flow in a tube. After applying a few simplifying assumptions, these PDEs can be integrated along the length of the heat exchanger to remove the spatial dependence and yield several ordinary differential equations (ODEs). The assumptions made are: (1) the heat exchanger is assumed to be a long, thin, horizontal tube;

(2) The refrigerant flowing through the heat exchanger tube is modeled as a one-dimensional fluid flow; (3) Axial conduction of refrigerant is neglected;(4) Pressure drop along the heat exchanger tube due to momentum change in refrigerant and viscous friction is neglected; thus the equation for conservation of momentum is not needed. The partial differential equations for conservation of refrigerant mass and energy are illustrated in equations 6 & 7 shown below:

u ( 6 ) u h q f u u (7)
Where u is the fluid velocity vector, f is the body force vector, q is heat flux vector, is the stress tensor, and is the shear stress tensor.

By applying the assumptions outlined previously, these equations are simplified to onedimensional PDEs illustrated in equations 8 & 9. Additionally an equation for the conservation of heat exchanger wall energy is given in Equation 10.

( 8 )

p T T ( 9 ) C A p T T p T T ( 1 0 )
Figure 3 shows a schematic of an evaporator. By the phase of refrigerant, an evaporator can be divided into two distinct parts: two-phase region, and superheat region. For the condenser, there is an additional part: subcooled region. lumped parameters are assumed to be associated with each fluid region. Several assumptions are made regarding the lumped parameters. In the first region, the fluid properties are determined by assuming a mean void fraction. Void fraction is defined as the ratio of vapor volume to total volume, and has long been used to describe certain characteristics of two-phase flows. Thus, and so forth. In the second region, average properties are assumed, i.e. h , T T P h , and P h .

The mean void fraction used in this study is found in [START_REF] Rasmussen | Dynamic Modeling and Advanced Control of Air Conditioning and Refrigeration Systems[END_REF]:

log
Where a S and b a

x , x : refrigerant quality at inlet & outlet of two-phase region respectively

The slip ratio S is calculated by Zivi relationship:

S

Following the Leibniz's integration rule [START_REF] Rasmussen | Dynamic Modeling and Advanced Control of Air Conditioning and Refrigeration Systems[END_REF], equations ( 8), ( 9) & ( 10) can be integrated over each region to give the governing equations for the conservation of refrigerant mass, refrigerant energy, and heat exchanger wall energy respectively.

Conservation of Refrigerant Mass (Two-Phase and Superheated Regions)

A L P A L m m (11)
A L P A L h A L m m ( 1 2 )
Conservation of Refrigerant Energy (Two-Phase and Superheated Regions)

A L P h A L m h m h A T T ( 1 3 ) h A L P h A L h h h A L m h m h A T T ( 1 4 )
Conservation of Wall Energy (Two-Phase and Superheated Regions)

C V T A T T A T T ( 1 5 ) C V T L A T T A T T (16)
Defining the state vector x L P h T T and algebraically combining the equations ( 11) through ( 16), the governing equation of evaporator dynamics reduces to the following compact state space form:

z z z z z z z z z z z x m h h A T T m h h A T T m m A T T A T T A T T A T T (17)
Expressions of all elements in matrix [z] are given in the Appendix A.

Similar derivation can be carried out for the condenser dynamics resulting in Equation of the form D x = f, with state vector x L L P h T T T .

Water reservoir

The water reservoir stores heated water ready for being supplied to the demand site. The condenser coil is installed inside the water reservoir in a spiral form. As the refrigerant is forced to circulate through the condenser coil, the water temperature in reservoir is raised due to heat rejected from the refrigerant.

For the sake of modeling, several assumptions are made as follows: (1) uniform temperature in the hot water reservoir (stratification is not considered), ( 2) no external heat loss from the reservoir wall, and ( 3) the total amount of hot water in the reservoir is conserved (No water consumption during heating process) It should be noted that the mean water temperature (T ) is first initialized at the beginning of the calculation procedure, the new value of mean water temperature (T ) will be calculated from Eq. ( 18). If T does not agree with the target hot temperature value, the new value is used in the next step of iteration. This procedure is repeated until T reaches a pre-specified value, usually 60 .

T T

Heat transfer coefficients

The single-phase refrigerant side heat transfer coefficient is computed from the well known Dittus-Boelter correlation:

Nu 0 023Re 0 8 Pr n

Where n = 0.4 for heating and n = 0.3 for cooling of refrigerant

The heat transfer coefficient of the two-phase region inside the condenser (Fu et al. 2003) is calculated by the correlations as follows:

Nu 5 03Re The heat transfer coefficient of the two-phase region inside the evaporator [START_REF] Granryd | REFRIGERATING ENGINEERING[END_REF]) is given by: Nu 10 2 Re 2 k f 0 4

Where k f

The water-side natural convection heat transfer coefficient (ASHRAE, 2001) is given by:

Nu 0 13Ra 0 33 if Ra > 10^8 Nu 0 56Ra 0 25 if Ra < 10^8
The air-side heat transfer coefficient (Fu et al. 2003) is given by: w

SYSTEM SIMULATION

The purpose of simulating an ASHPWH is to predict the performance of the unit under certain working conditions.

Input and output parameters

The input parameters shown in table1 are: 1) Geometrical parameters of the heat exchangers.

2) Initial temperatures of water and air.

3) Air flow rate. 4) Water reservoir volume. 5) Compressor theoretical displacement (swept volume). 6) Expansion valve constants 7) Initial state vector in both heat exchangers

The output parameters are: 1) Condensing and evaporating pressures /temperatures.

2) Heating and cooling capacities.

3) Temperature of water in reservoir. 4) Refrigerant mass flow rate of the compressor. 5) Electrical power input to the compressor. 6) Refrigerant mass flow rate of the expansion valve.

Simulation methodology

The most important steps solution algorithm are: 1) Input geometrical parameters.

2) Initialization of state variables.

3) The condensing pressure is updated as a result of the comparison between the mass flow rates of compressor and expansion valve. 4) A backward difference approach is used to calculate the partial derivatives existing in the governing equations. 5) The under-relaxation method is used to achieve convergence. 6) The evaporating pressure is updated in order to control the amount of superheating. 7) Refrigerant properties of are calculated using REFPROP software.

Results and Discussion

The model is coded into MATLAB simulation program and used to predict system parameters of interest such as hot water temperature, condensing and evaporating pressures, heating capacity, electrical power input and coefficient of performance COP. The figures below show some of the simulated results at 15 ambient air temperature.

Figure 4 shows the evolution of condensing and evaporating pressures. The condensing pressure rises gradually from the beginning to the end of simulation which is due to the continuous increasing of water temperature.

In figure 5, the input electrical power rises gradually from 400 W to 770 W since the condensing temperature is rising; however, the heating capacity decreases gradually with time. Water temperature data, several ambient temperatures have been chosen to simulate the performance of the ASHPWH corresponding to the integrated COP over a whole reservoir heating cycle. In figure 8, it is observed that the integrated COP increases as the ambient air temperature increases. Thus, as the ambient temperature rises, more energy can be pumped to the water reservoir and accordingly quite important savings in time and energy are obtained. The model was based on fundamental principles of heat transfer, thermodynamics, fluid mechanics, empirical relationships and manufacturer's data as necessary. Simulating the system with the two water reservoir volumes showed that the evolution of all studied parameters were almost the same except for the time needed to reach the pre-specified water temperature (60 ). Moreover, it has been shown that the integrated COP increases as the ambient temperature increases. Finally, for the selected Lebanese zones (1 & 2), the expected annual value of the integrated COP will vary from 5 to 6 leading to a very high efficiency compared to other hot water production means.

A 7 -

 7 point cycle model, shown in figure 2, is chosen to simulate the entire cycle using the refrigerant R134a with two different water reservoir volumes (150L & 200L).

Figure 3 :

 3 Figure 3: Evaporator with two fluid regions (Rasmussen and Alleyne 2006)

FigureFigure 5 :

 5 Figure 4: Condensing and evaporating pressures with 200L reservoir 0 2000 4000 6000 8000 10000 12000 200 400 600 800 1000 1200 1400 1600 1800 2000

Figure 6 :Figure 7 :

 67 Figure 6: Water temperature with 200L reservoir

Figure

  Figure 8: Integrated COP versus ambient temperature

  ., and D. Didion, Jr. 1982. "A simulation model of the transient performance of a heat pump", International Journal of Refrigeration. 5(3) pp. 176-184. Fu L., G. Ding and C. Zhang, Jr. 2003. "Dynamic simulation of air-to-water dual-mode heat pump with screw compressor", Applied Thermal Engineering 23 pp. 1629-1645.

Figure 1: Air source heat pump water heater Nomenclature List of symbols Variable Explanation

						Unit
	A			Area
			Convective heat Transfer Coefficient
	Cp			Specific Heat
				Efficiency
	COP		Coefficient of performance
				Mean Void Fraction
	h			Enthalpy
	e			Internal energy
	L			Length		m
				Mass Flow Rate
	P			Pressure		Pa
	p			Perimeter		m
	Q			Heat		w
				Density
				velocity
	T			Temperature		K
	dt			Time step		s
	g			Gravitational acceleration
	k			Thermal conductivity
			Coefficient of thermal expansion
				Dynamic viscosity
	D			Diameter		m
				Speed of compressor	rps
	Subscripts		Dimensionless Numbers
	Variable	Explanation	Symbol	Explanation	Relation
	1,2,3 a	Air	Region	Gr	Grashof number	Gr	L g	T
	e c cs f g i	Evaporator Condenser Cross section Saturated liquid Saturated gas Inner, inside	Nu Pr Re	mean Nusselt number Prandtl number Reynolds number	Nu Pr Re	D k C k wD
	int k	Intermediate Compressor	Ra	Rayleigh number	Ra Gr Pr
	o.out	Out
	R	Refrigerant
	v	Valve, volumetric
	w	Wall
	wat	Water
	s	Saturated
	isen	Isentropic

Table 1

 1

		: Simulation Inputs
	Parameter	Value	Unit
	Degree of super heating	5
	Degree of subcooling	5
	Initial water temperature	20
	Water set temperature	60
	Air input temperature	15; 18; 21; 24; 27; 30; 31.5
	Volume of water reservoir	200 (150)	L

th IEA Heat Pump Conference 2011, 16 -19 May 2011, Tokyo, Japan

th IEA Heat Pump Conference 2011