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Publicly Available Published by De Gruyter November 4, 2015

An Ontology-based Approach for Knowledge Integration in Product Collaborative Development

  • Guodong Yu EMAIL logo , Yu Yang and Xing Qingsong

Abstract

Knowledge integrated model (KIM) is regarded as an effective and critical way to enhance efficiency of product collaborative development (PCD). However, it is much knotty to establish a unified description rule as there exists diverse and heterogeneous designer knowledge. In this paper, an approach based on ontology for KIM is proposed to straightforwardly descript heterogeneous knowledge and achieve a matching of knowledge and design mission objectives easily. First, a KIM of PCD is presented in accordance with the characteristics of product design activities. Hereafter, a knowledge transformation method based on “problem domain – functional domain” model is developed to accurately reflect customer expectations for new products, wherein, knowledge ontology tree including “customer creativity, emotional knowledge, customer needs, and basic knowledge” is constructed to standardize customer needs. Then, a knowledge matching function (KMF) and a Backus–Naur form (BNF) are introduced to measure similarity of request and candidate. Thereafter, a service engine (SE) including KMF and BNF is generated by the knowledge integrated system (KIS). Finally, simulations and experiments illustrate the effectiveness of the proposed methods and models.

1 Introduction

It is an inevitable trend that product innovation design shift from the traditional self-governed mode to open collaborative mode [1], which is mainly manifested in dispersing the risk of innovation and improve the efficiency of innovation [8]. Distributed product collaborative development (PCD) has become an effective way to improve the resource utilization and design efficiency. During the PCD process, participants may be customers, research institutions and professional design engineers, or their combination [17]. Owing to the participants from different backgrounds, their knowledge and expression maybe not unified, which makes knowledge sharing inconvenient between designers [18]. Therefore, how to externalize heterogeneous knowledge with unified specification and integrate it into the collaborative development process are main focuses of this article.

Product development based on knowledge is a process of logical reasoning and configuration based on domain knowledge. This method can integrate all intellectual resources at the most extent, which can greatly contribute to improve the efficiency of development [18]. Actually, since collaborative development was proposed, its huge potential has caused wide attention in academia. Organizational creativity theories, innovation diffusion theory, multichannel innovation mechanism based on the Internet were cited to conduct a study on its effectiveness and feasibility [2, 3, 4, 7, 9, 13, 14, 16, 19, 20, 22]. Büyüközkan put forward a customer knowledge mapping model based on QFD and designed a software for PCD [3]. Gloor established the cooperative innovation organization’s network model, and the dynamic performance of the network was evaluated [8]. Fox established a virtual team work process model [7]. Tseng et al. developed a product consultation configuration system based on multi-attribute negotiation [4, 19]. Wong et al. proposed a decision support tool for apparel coordination by integrating the knowledge-based attribute evaluation expert system [20]. Gruber introduced the principles for the design of ontologies used for knowledge sharing [9]. Anussornnitisarn et al. established a distributed resource allocation model for cooperative and autonomous agents [2]. Parsa and Parand presented a cooperative decision-making method in a knowledge grid environment [14]. Zhen and Jiang put forward a knowledge grid-based knowledge supply mode [22]. Hung et al. developed an interface C framework for semiconductor e-diagnostics systems [13].

Through a comprehensive analysis, how to integrate the designer’s knowledge into the design process is still relatively lacking. Difficulties in this field are mainly concentrated in the following aspects. The designer’s knowledge is characterized by dispersed, diverse, and heterogeneous. A unified description of methods and knowledge integration model to guide knowledge discovery, collection, sorting, and application of the whole process is immature.

With respect to these problems, this paper intends to probe into integrate methods of the distributed knowledge, which aims to explore a strategy effectively organizing, expressing, and sharing knowledge by unified rules to improve knowledge utilization efficiency.

This paper is organized as follows. PCD knowledge integration model is established in Section 1, and then a knowledge transformation method is proposed in Section 2. Afterward, considering ontology theory characteristics of reusing and information interdisciplinary, knowledge description method and service engine model are proposed in Section 3. A design-oriented product knowledge integration management system is presented to verify the integrated model of method in Section 4. Ultimately, a case study of knowledge integration analysis is reported in Section 5.

2 Knowledge Integrated Model

In this paper, knowledge refers to intellectual resources which are effective to PCD. Knowledge comes from the customer, designer, or design organization [11, 16, 17]. Features of knowledge such as ambiguity, dynamic, diversity, development, distribution, personalization, and hidden oriented bring more difficulties for the knowledge integration for product innovation design. Therefore, based on the study of PCD system and knowledge management technology [10, 21], this paper proposes a knowledge integrated model (KIM) for PCD, as is shown in Figure 1, to expect that knowledge can be discovered, collected, excavated, mined, descripted, and shared in PCD.

Figure 1: KIM for PCD.
Figure 1:

KIM for PCD.

Figure 1 shows a KIM for PCD. The model is a four-level 2D structure: the vertical axis is data source level, information level, knowledge level, and application level from top to bottom. The horizontal axis reflects PCD process oriented toward knowledge integrated application. The data source level contains subsystems that provide various information sources. The information level achieves organization and management of the information classification. The knowledge level realizes description and integration of the ontology-based knowledge. The application level integrates and applies the knowledge of PCD process for the key of the transformation from innovation demand to product. Specific integrated applications include knowledge sharing, request, matching, reuse, and support, etc.

Based on the KIM, the innovation team can take advantage of the customer knowledge to clarify the specific objectives of PCD, stimulate product originality, analyze the collaborative issue, and assess the effect of innovative products. Simultaneously, customer knowledge, innovative design methods, and proper innovative tools can bring about generating solutions of product innovation and ultimately form an innovative product based on the KIM. The whole process of KIM is based on the multilevel system via the Internet/Intranet, which also includes the integration of other collaborative tools to meet the specific needs of knowledge integration in PCD. According to the KIM, the key issues to achieve customer knowledge sharing focus on knowledge transformation, mapping, description, integration, and knowledge service.

3 Problem Domain-Oriented Knowledge Transformation Method

Some academics believe that PCD is a process of mapping customer demands to technical indicator [6]. Quality function deployment (QFD), transforming a series of customer demands into product feature, is usually introduced to map between customer demands and product function. However, QFD is confined within the customers’ different needs. With rapid change in market demands, especially the improvement of customers’ expertise skills and awareness of emotion, the knowledge transformation of customer demands for the product function mapping has been unable to satisfy the market requirements [5].

Generally, customers put forward their own demands, opinions, ideas, and preferences starting from their own understanding of domain knowledge under the factors such as interests and budget. Thereby, demand analysis not only includes customer requirements but also includes knowledge of customer product ideas and their product perceptions [15]. Thus, it can be considered that the customer knowledge space determines the direction content and results of the whole process. It should be noted that customer knowledge space contains product functional requirements corresponding to a problem. Therefore, this paper puts forward the concept of the problem domain, a specific area or process that customers describe, express, transform, and solve the problems in PCD under different conditions.

The concept classification of customer knowledge in PCD follows and expands the SBF2 model [17]. Based on the concept level of original product design knowledge, such as function, behavior, flow, and structure, methods transforming problem domain to function domain (PD-FD) is presented in Figure 2.

Figure 2: PD-FD Method.
Figure 2:

PD-FD Method.

As shown in Figure 2, PD-FD includes a problem class involving six attributes: name, description, type, property, relation, and problem-related function. Type provides a vocabulary reference to the problem/function ontology, and the problem/function ontology is divided into six sorts: namely, motion, control, energy, correlation, abstract, and comprehensive, which are the basic problems/function set. Problem type, source, and subject are associated with the type, source, and subject, which all belong to problem property. Problem-related function associates problem with the corresponding function.

The function model includes a function sorts comprising seven attributes: function goal, subfunction, function type, metadata function, objective function, function-related component, and function-related input/output flow, wherein, function represents the relation among parts. Function goal intends design objectives. Subfunction describes the hierarchical relationship between functions. Function type and metadata function provide a reference vocabulary to the problem/function ontology. The function type uses standard function in Ref. [12] to make problem/function ontology expression and classification easier. Objective function associates basic function with the object acted by itself through metadata function. The function-related component and function-related input/output flow, respectively, associate function with corresponding components and flows.

Process of the PD-FD is described as follows:

  • Step 1 Identify the property of the problem domain, including problem name, description, problem, property, relationship, and related function. This step is to lay a foundation for the following analysis, thus, only in an accurate identification of the property, can we obtain desirable results.

  • Step 2 Define sequences of the problems based on importance. In order to obtain the customer’s true intention and ensure that problems with a high importance degree can be mapped to the new product’s final function, the fuzzy set theory and entropy are introduced. The fuzzy set theory is used to express the deviation caused by the incomplete understanding of customers’ need. Entropy is able to explain the dynamic behaviors of each component in CPD.

  • Step 3 Classify and express the problem with functional form. An important problem needs to be expressed in the function form. Classify these problems to different function forms according to the importance based on existing function classification. Then, basic problems or function sets are formed.

  • Step 4 Transform problem-function. Contrary to the difference in customer knowledge, different problem-function transition methods should be considered. For the problem refined from the customer basic knowledge, data mining methods such as clustering, association rules, and regression analysis would be adopted. For customer demands, QFD could be employed. For customer perceptual knowledge, fuzzy cognitive map (FCM) and ant colony algorithm (ACA) would be applied.

The transition of PD-FD is conducive to the description of the knowledge around the problem. This approach is not only able to accurately reflect the customer’s problem and requirements for the new product but also have important meaning to promote PCD team making effective use of knowledge.

4 Ontology-based Theory of Knowledge Description and Service Engine

Owing to the special and non-normative of the designer and customer knowledge, if only based on PDM or XML, the sharing effect will only stay in a syntax level, which is lack of adequate description of semantic information and hardly describe the creative, need, preference, and behavioral characteristic of knowledge. Then, it is difficult to achieve a reasonable inference of knowledge and evaluation. Furthermore, besides complex feature, the owner of the knowledge often uses their individual ways to express under different conditions, which causes that a same concept produces different understanding. Consequently, the interoperability between knowledge is hindered, which may lead to some difficulties in sharing knowledge. As a conceptualization of illustration and description for the concept and relationship, ontology can better compensate for these shortcomings. Object, attribute, and relationship constitute the main structure of ontology [6]. Then, ontology is introduced to realize consistent knowledge description and achieve knowledge integration, sharing, mutual understanding, and mutual operation in the distributed network.

4.1 Knowledge Concept-Ontology Tree Model

Concept and relationship are two units of ontology, where concept is the core, and relationship is used to describe the hypostasis between each fields. Therefore, the ontology tree should be centered on the concept. This paper adopts the top–down method to establish the concept-ontology tree model of knowledge, as shown in Figure 3.

Figure 3: Knowledge Concept–Ontology Tree Model.
Figure 3:

Knowledge Concept–Ontology Tree Model.

In Figure 3, customer demands are helpful for determining innovation goal. Creativity can stimulate innovative ideas of the designer. Customer perceptual cognition contributes to the evaluation of innovation scheme and basic knowledge can unearth the customer preference for innovative product. Based on the previous research results in ontology, knowledge ontology in PCD can be built based on the analysis of the customer knowledge concept ontology tree.

4.2 Ontology Knowledge Description

Definition 1: Knowledge ontology can be expressed as a triple Knowledge=(C, Ds, Rs). C means knowledge domain concept, such as customer idea, customer demands, and feedback; Ds represents nonformal description about the attributes of C; while Rs delineates the “relationship” collection between concepts.

Based on the above definition, OWL (Web Ontology Language) is utilized to describe customer feedback ontology. This paper takes a type of motorcycle frame strength as an example:

  • <owl: ontology about=“Frame strength”>

  • </owl: ontology>

  • <owl: Knowledge Property rdf:ID=“Customer feedback”>

  • <rdfs: range rdf: resource=“Frame”/>

  • </owl: Knowledge Property>

  • <rdfs: comment>Frame strength is weak</rdfs: comment>

  • <rdf: type rdf: resource=“Structure”/>

  • <rdf: subClassOf rdf: resource=“Strength”/>

  • <owl: ontology about=“Frame strength”>

  • </owl: ontology>

  • <owl: Knowledge Property rdf:ID=“customer feedback”>

  • <rdfs: range rdf: resource=“frame”/>

  • </owl: Knowledge Property>

  • <rdfs: comment> to solve the problem of the weak frame strength, improvements or innovation in frame structure must be done</rdfs: comment>

  • <rdf: type rdf: resource=“structure”/>

  • <rdf: subClassOf rdf: resource=“strength”/>

Because of dispersion and diversity of distributed knowledge, an integrated model based on knowledge ontology must be established to achieve and effectively manage and utilize knowledge.

Definition 2: Relationship of Concept and Object can be expressed by a four tuple. Relation=(Type, Object, Des, Weight). Type indicates the relationship type between conceptions, and the relationship type includes part-of, kind-of, same-as, instance-of, attribute-of, and so on; Des means the nonformal description of the relationship; Weight represents the strength of the relationship; Weight value ranges from 0 to 1, and the higher the value, the greater strength of the relationship.

  • <owl:Class rdf:ID=“Frame problem”>

  • <owl:equivalentClass rdf:resource=“# Motorcycle frame problem”/>

  • </owl:Class>

Based on the above definitions, ontology knowledge is integrated based on relationship when the relationship strength between concepts is out of the threshold. It is worth noting that, in the knowledge integration process, different companies or departments may use a different terminology to express the same concept, properties, or individuals. As for these, “owl: equivalentClass”, “owl: equivalentProperty”, and “owl: sameAs” are introduced to describe them, respectively. For example, when the motorcycle frame strength issue raised by the definition customer, some companies may use the “frame problem” to describe it, while other companies may use the “motorcycle frame problem” to describe it; actually, these two concepts are equivalent. To solve this problem, when defining a “frame problem”, equivalence class like “motorcycle frame problem” could be declared as follow:

  • <owl:Class rdf:ID=“frame problem”>

  • <owl:equivalentClass rdf:resource=“#motorcycle frame problem”/>

  • </owl:Class>

In summary, knowledge base can be established based on the description and integration of knowledge ontology. DS=(ds1, ds2, …, dsn) means knowledge base, where dsi denotes knowledge base in different enterprises. The interaction between innovative design team members and client server interface enables team members to access knowledge timely and easily, which makes effective transformation and sharing of knowledge.

4.3 Knowledge Matching Function

Based on the knowledge description, a service engine (SE) is put forward to realize the knowledge sharing. The SE is able to handle customer knowledge requests, complete knowledge matching, as well as the management, updating, modification, and other maintenance services for knowledge base.

Knowledge sharing is represented by a triple (DS, U, K), where U=(url, V) represents the interface model; url indicates corresponding network address with knowledge sharing interface. Then, V=(V1, …, Vn), i=1, …, n, Vi means the property of knowledge sharing interface; K is a returned set of knowledge after submitting a knowledge request through knowledge sharing interface in distributed sites.

Knowledge request and matching can also be expressed as a triple (DS, Us, Kt), where DS represents a knowledge base running in a distributed site; Us indicates a unified knowledge request interface after ds1, ds2, …, dsn integrated, which could be expressed by the formula Us =U1U2⊕…⊕Un; Kt means returned view of result after submitting a knowledge request through unified request interface, which is denoted as Kt=K1K2⊕…⊕Kn, in which ⊕ delineates integration of the request interface based on the interface matching model and the superposition based on logic and semantics.

Combined with PCD process, the designed steps of knowledge request and matching are as follows:

  • Step 1 Identify the knowledge request. Knowledge request is n+1-tuple, denoted as Request=((a1, a2, …, an, f(a1, a2, …, am)). Attributes of each knowledge tuple are a binary mapping <attributename, attributevalue>, indicated by ai.ai indicates the specified matching threshold to support precise and imprecise knowledge. The knowledge tuples meeting a certain threshold can be chosen into the column; besides, ai also refers to the matching level, ordering by a specified criteria of members to meet the needs of multiple knowledge resources.

  • Step 2 Select the matching function f(a1, a2, …, am). Matching function is a constraint equation related to knowledge property, and the knowledge enables f(a1, a2, …, am) to get the maximum, which is the best matching knowledge. Knowledge matching function could be expressed as follows:

    (1)f(a1,a2,,am)=|P(X)P(Y)||P(X)|+|P(Y)||P(X)P(Y)|.

    Here, |P(X)| and |P(Y)| are the number of attributes in the ontology concept tree for the X and Y concept; |P(X)∩P(Y)| means the number of the same attributes in concept X and Y. Meanwhile, each node in the ontology tree is assigned a right weight considering the different levels of concept classification in the ontology tree. According to the concept of the ontology tree X, set m is the number of the node from node to root; i is the number of node X; the weight of the conception of X is the following:

    (2)ρ(X)=1+ik1+mk,

    where k means the exponential factor; generally, k=2. The matching defines considering the position weight of the ontology tree as the following:

    (3)f(a1,a2,,am)=ρ(X)|P(X)P(R)|ρ(R)(|P(X)|+|P(Y)||P(X)P(Y)|)

    where ρ(X) and ρ(R) represent the actual position weight of the request knowledge of X and R.

  • Step 3 Describe the knowledge request. The Backus–Naur form (BNF) is based on the knowledge ontology of knowledge request and is described as follows:

    • <Threshhold>::=<real>

    • <Rank>::=<arithmeticExpression>

    • <requirementExpression>::=<booleanExpression>|<arithmeticExpression>

    • <booleanExpression>::=<booleanExpression><booleanOperator><booleanExpression>

    • |(<booleanExpression>)|<atomicBooleanExpression>

    • <atomicBooleanExpression>::=<attributeName><relationalOperator><value>

    • <booleanOperator>::=‘AND’|‘OR’|‘NOT’

    • <relationalOperator>::=‘>’ | ‘<’ | ‘>=’ | ‘<=’ | ‘= =’| ‘!=’

    • <arithmeticExpression>::=<arithmeticExp><arithmeticOperator>

    <arithmeticExpression>|(<arithmeticExpression>)|<booleanExpression><booleanOperator>

    <arithmeticExpression>|<arithmeticExpression><booleanOperator><booleanExpression>

    |<conceptName>|<attributeName> | <value>

    • <arithmeticOperator>::= ‘+’ | ‘–’ | ‘*’ | ‘/’

    • <conceptName>::=<string>

    • <attributeName>::=<string>

    • <value>::=<integer>|<real>|<boolean>|<string>

  • Step 4 Knowledge matching. The purpose of knowledge matching is to measure the degree of similarity between request knowledge and candidate knowledge. Each knowledge tuple has its own concept and a series of attributes, and each concept owns a name, then attributes can be represented by a tuple <name, value>, where name means a character string, while value represents a numeric or character string. The matching degree can be represented by a number. For example, set n as the matching degree, and 0≤n≤1, n=0 indicates that the two tuples do not match at all, while n=1 means that the two tuples exactly match each other. According to this principle, knowledge matching can be expressed as KMM=(KQ, DS, f, Kt), where KQ means knowledge request; DS indicates candidate knowledge base. The result knowledge set Kt that satisfies the request can be found through the tree-matching function f(a1, a2, …, am) in Equation (3). The BNF grammar is as follows:

    • <CustomerKnowledge>::=<Concept>;<Attribute>|<Resource>;<Attribute>

    • <conceptName>::=<string>

    • <Attribute>::=<attributeName> ‘=’<attributeValue>

    • <attributeName>::=<string>

    • <attributeValue>::=<integer>|<real>|<boolean>|<string>

    • Take the constraints of product innovative design into consideration, the expression as follows:

    • <DesignConstraint>::=<constrainExpression><relationalOperator><constrainExpression>

    • <relationalOperator>::= ‘<’ | ‘>’ | ‘=’ | ‘≤’| ‘≥’

As the knowledge base is established upon unified terminology and concept, it is possible to realize knowledge matching through the above steps. According to knowledge ontology, knowledge request from the innovation team is converted to corresponding concept by registry.

5 Knowledge Integrated System Design

5.1 Framework of KIS

To achieve knowledge sharing in PCD, a KIS is established. The composition of the framework is shown in Figure 4. The system is made up of various types of knowledge server. Customer class includes the customer knowledge base. Product knowledge, product patents, product examples, and product models consist of product categories. Innovative class contains innovative tools, innovative approach, and design knowledge. Each server is an independent knowledge management system, which owns respective knowledge base and ontology. All knowledge and ontology server are connected through the Internet/Intranet to provide clients with the necessary knowledge services.

Figure 4: Framework of KIS.
Figure 4:

Framework of KIS.

5.2 System Development

On the basis of knowledge acquisition, the ontology modeling language is utilized to describe and integrate knowledge on PROTÉGÉ 4.3 DESKTOP. Hereafter, a design knowledge server based on Web Service is created by Simple Object Access Protocol (SOAP) of eXtensible Markup Language (XML). In addition, the ontology server, which is not only responsible for maintaining basic ontology and directories ontology but also serves as a private UDDI registry server, is designed by Java Web Services Developer Pack (JWSDP). B/S architecture is used for browsing or ontology extension. Clients download the ontology file, which is browsed by the Protégé ontology modeling tools, as an attachment via SOAP.

6 Case Study

A motorcycle frame design is taken to illustrate how to integrate the distributed knowledge in collaborative development process.

  • Step 1 Knowledge acquisition and description. Distributed knowledge, such as creative knowledge, customer demand knowledge, product knowledge, constraint knowledge, driven knowledge, selective knowledge, parameter knowledge, and procedural knowledge should be acquired. A motorcycle innovative knowledge base is established based on knowledge representation and integration by OWL. Table 1 shows the parts content of a motorcycle collaborative innovation base. Figure 5 illustrates a knowledge base interface of KIS for collaborative PCD.

  • Step 2 Knowledge matching. Contrary to the problem that strength of frames is weak, an analysis at the motherboard and lugged rear shock absorber is conducted to define the design problem, which is submitted to the knowledge engine service to match. Immediately, some design scheme adopted in other motorcycles to increase the intensity is presented on the KIS.

  • Step 3 Knowledge utilization. Combined with the above knowledge, re-use knowledge base to explore frame needs. Results display: (1) A new structure is required to improve the strength of frames to meet the damping needs. (2) The frame must not be broken under the impact loaded while driving. Then, run the TRIZ tools into its innovation theory, and the software can search out the solutions to the above innovation needs, wherein the device is developed based on “support” innovative principles that not only reinforce the object but support to improve comfort. Whereby, generate innovative solutions to solve customer needs: a reinforcing plate is added after the mainboard suspension parts, and excessive angle should be designed. Simultaneously, a support member connected to the seat rails is installed above the ears on THE damper. The part changes the cantilever beam structure of the ear, which is conducive to improving ear stress condition.

  • Step 4 Evaluate innovation degree based on customer application effect and the appearance of design solutions. In the evaluation of this program, the client application property is defined as the unit dynamic stress generated by a load act while the vehicle is driven on a convex hull road at 18 km/h. Figure 6 illustrates the interface of evaluation of customer knowledge, and in Table 2, the evaluation results are shown. As the data shown in Table 2, a new variable is introduced in the improved scheme, which achieves a great improvement on the stress indicators. Accordingly, the distribution KIM for collaborative product design to motorcycle innovative development is feasible and effective.

Table 1

Knowledge Base.

Customer knowledgeDominant creativity, Customer needs, Customer feedback, R & D knowledge, CRM…
Cases libraryVehicle cases, engine cases, frame cases …
Product features
 ProcessInnovation process, collaborative process, evaluation process, decision-making process…
 RulesVehicle-determined rules, engine-determined rules, frame-determined rules…
 ParametersDimensions, performance, structural parameters…
 ToolsStructural mechanics, material mechanics, ergonomics, TRIZ, CAD, CAE, ProE…
Figure 5: Knowledge Base Interface in KIS.
Figure 5:

Knowledge Base Interface in KIS.

Figure 6: Product Innovation Evaluation in KIS.
Figure 6:

Product Innovation Evaluation in KIS.

Table 2

Product Innovation Evaluation.

Typep/mlAppearance 1Appearance 2Mean stress (MPa)Stress at 0.7 s (MPa)Stress at 10 s (MPa)Innovation degree
Traditional125NullNull2004504000.85
Innovative125Lug supportExcessive angle50210200

7 Conclusions

PCD based on knowledge is different from the design based on customer demands. In order to fully realize the innovation process, integrated customer knowledge management and utilization, in this paper, KIM and its related key technologies have been brought forward for PCD. The KIM was applied to the design of product innovation, which is used to not only consistently describe diverse, heterogeneous knowledge but also achieve to organize, transfer, and share knowledge required in a variety of innovative design activities. PD-FD based on ontology paved an approach to solve the knowledge transformation problem in design activities. Knowledge ontology tree explicates sundry knowledge concept their mutual relations. Knowledge description method and SE based on OWL can easily integrate knowledge to achieve matching of knowledge by KMF and BNF. Using the motorcycle innovation design knowledge, the ontology library verifies the validity and feasibility of KIM.


Corresponding author: Guodong Yu, State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, China, e-mail:

Acknowledgments

This research is sponsored by the National Natural Science Foundation of China under Project No. 71301176, 71401019, 71571023. The authors also thank the Fundamental Research Funds for the Central Universities (Project No. CDJZR12110004) and Specialized Research Fund for the Doctoral Program of Higher Education (Project 20130191120001) for partial support of this work. We are grateful for the constructive suggestions provided by the reviewers, which would improve the paper.

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Received: 2015-5-12
Published Online: 2015-11-4
Published in Print: 2017-1-1

©2017 Walter de Gruyter GmbH, Berlin/Boston

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