The Process Model to Aid Innovation of Products Conceptual Design 01

Expert Systems with Applications 37 (2010) 3574–3587

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Expert Systems with Applications

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The process model to aid innovation of products conceptual design

Wenqiang Li a, Yan Li a,*, Jian Wang b, Xiaoying Liu a

a School of Manufacturing Science & Engineering, Sichuan University, Chengdu 610065, People’s Republic of Chinab School of Aerospace & Aircraft Engineering, Faculty of Engineering Kingston University, Friars Avenue Roehampton Vale, London SW15 3DW, UK

a r t i c l e i n f o a b s t r a c t

Keywords:Conceptual designInnovative strategiesProcess mappingExtension reasoningMathematical model

0957-4174/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.eswa.2009.10.034

* Corresponding author. Tel.: +86 28 85406946; faxE-mail address: [email protected] (Y. Li).

Currently, designers often pay little attention to integrated innovation during the design process of prod-ucts. In addition, the product assistance design systems mainly focus on the detailed design phrase andthe construction function of mathematics models are often been neglected. In order to solve these prob-lems, this paper proposes a conceptual design process model to aid multi-stage innovation of productdesign based on the integration of the essential rules of the Axiomatic Design (AD) model, Function–Behaviour–Structure (FBS) model, and the guideline of functional creative thinking logics. By utilisingthe function tree and functional structure tree as the mediums to express the design information andby applying the conflict solving strategies of Extensic theory, the conceptual design process is definedas an integrated system with five stages and four mappings. The integrated logical processes of thismodel are described with mathematical language. Thus, the whole transformation from design experi-ences to design principles and to mathematical model finally to aided design system is realized perfectlyin the proposed process model. The meaningful exploration on the nature and practical processes of prod-uct conceptual design is carried out in this research.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

The product development process is a transform process fromcustomer requirements to a physical structure while consideringthe various design constraints. During the transform process, thestage of conceptual design is the most important one. It not onlydetermines the innovation level of the final product but also com-mits 70–80% of the funds. In addition, any design defect in the con-ceptual design is very difficult to correct in detail design and willincur further cost in the future (Francis, Tay, & Jinxiang, 2002).The product conceptual design process includes a set of technicalactivities, which are the refinement of customer requirements intodesign functions, new concept development, and embodimentengineering of a new product.

Under the notion of customer-driven design, the essential partof the conceptual design process is ensuring the ability of productfunctions meets customer’s requirement(s) (Henry, Bing, Felix, &Ralph, 2002; Lin, Wang, Chen, & Chang, 2008). Researchers haveproposed many conceptual design methods, which can be classi-fied into three categories based on focal points and tools used: de-sign models according to design criterion of product, designmodels based on design strategies of product and design modelsadopting artificial intelligence. (1) For the first group, conceptual

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design process of product is defined as the mapping process amongdifferent design domains.A certain canonical format is chosen torepresent the design information, and the innovation of productdesign is supported by mapping processes among different do-mains, such as the Axiomatic Design (AD) model proposed bySuh (2001), the Sycle design model proposed by Kobayashi(2006) and the Technology System Forecasting model proposedby Mann (2003). (2) For design models based on the design strat-egies, the design process is regarded as a decision-making process.The innovation process of product can be implemented throughvarious design strategies among design units. For example, theFunction–Behaviour–Structure (FBS) model proposed by Gero andKannengiesser (2007), the agent-based model proposed byCampbell, Cagan, and Kotovsky (2000) and the attribute-baseddecision-making model proposed by Wang (2001). (3) For designmodels adopting artificial intelligence, the design process isregarded as a process of resolving different design conflicts. Itcan be realized effectively with various innovative tools springingfrom intelligence techniques, such as the case-based reasoningmodel proposed by Therani Madhusudan, Zhao, and Marshall(2004), the rule-based reasoning model proposed by Burattini, DeGregorio, and Tamburrini (2002), the design catalogues reasoningmodel proposed by Peien, Shuai, Yong, Shuangxia, and Bin(2002), the analogy-based reasoning model proposed by Goel andBhatta (2004), the fuzzy neural network and the genetic algorithmreasoning model proposed by Hsiao and Tsai (2005) and the Exten-sic reasoning model proposed by Cai, Yang, and He (2003).

W. Li et al. / Expert Systems with Applications 37 (2010) 3574–3587 3575

At the same time, many design assistance systems have beendeveloped, which include:

(1) A knowledge-based system developed by Zhang, Tor, andBritton (2001): a concept variants are generated firstly andan expert system shell, called C Language Integrated Produc-tion System, is used to aid the quantitative phase of conceptevaluation. It performs the product design based on variousdesign rules and eliminates the explosion phenomenon ofdesign projects effectively during the design process.

(2) An agent system developed by Campbell et al. (2000): soft-ware agents are interacted to achieve the function solving,and then by combining unique problem solving strategies,these agents are able to generate solutions to open-endeddesign problems. This model has been implemented to solvegeneral electromechanical design problems currently.

(3) A case system developed by Han and Lee (2006): a computa-tional framework for design synthesis is provided by imitat-ing the common design method of reviewing past designs toobtain solution concepts for a new design problem. Feasibledesign alternatives are generated by combining virtual func-tion generators using some adaptation rules.

(4) A FBS system developed by Umeda, Ishii, and Yoshioka(1996): since FBS Model can support functional design notonly in the analytical phase but also in the synthetic phase.Simultaneity, a computer tool called subsystem QualitativeProcess Abduction System is developed. It can realize theanalogism innovation between different design fields fleetly.

(5) A Scheme builder system developed by Bracewell and Sharpe(1996): a design environment called Schemebuilder which isa comprehensive of software tools aimed at supporting thedesigner in the rapid development of product design modelsin the conceptual, through embodiment stages of design.

(6) A character system developed by Brownsboro and Noort(2004): unlike current modelling systems, it provides a mul-tiple-view feature modelling can adequately support an ownview on a product for each phase. Each view contains a fea-ture model of the product specific for the correspondingphase.

(7) A restriction system developed by Kulak, Durmusoglu, andTufekci (2005) and an environment system developed byXu, Sun, and Pan (2001) integrate the design environmentinto design process and make the design result meets thepractice accurately. All these design assistant systems areto complete the requirement functions of a product basedon certain functional solving strategies and the expressingform of design information.

However, in these design models and assistant systems alwayspay more attention to the practical methods or systems of productdesign and emphasise partial optimization of the design process.The research of integrated innovative strategies of product designhas been ignored. In addition, few mathematical models have beenproposed to represent their research theoretically, which restrictsthe expression of the innovative process from a microscopic viewas the mathematical form can express the essence of design pro-cess quantificationally and accurately.

In an attempt to rectify these deficiencies, this paper proposes aconceptual design model aiding multi-stage innovation of theproduct by means of the hierarchy frame of information descrip-tion model and based on the internal driven regulations of theAD and FBS models. The different innovative strategies in differentdesign stages are discussed respectively. The logic process of thedesign model framework is presented mathematically, in whichthe integrated transform from design experience to design princi-ple, then, to the mathematical model, finally to assistance design

system is presented in this paper. These provide an explorationinto the effective practical supports of conceptual design and alsoestablish a foundation for the conceptual design assistant system’sdevelopment.

2. The design process based on multi-stage innovation

The purpose of conceptual design is to realize the requirementfunctions of a product and the essence is innovation. How to sup-port the innovative design effectively has become the priority con-sideration in the conceptual design process. Those design modelsdiscussed above can all realize some innovation to new designproducts through various means. For example, the product innova-tions in the criterion model are achieved through the conversionmappings among design domains. The product innovations in thestrategies model are achieved through various decisions and theartificial intelligence model achieve it through different intelligenttools. In the sections below, the three kinds of typical design mod-els referred to in this paper will be discussed in detail.

In the AD model (Suh, 2001), the design process is carried out byzigzagging mappings between the customer domain, function do-main, physical domain and process domain. This model describesan integrated design framework and general design regulations ofthe product design process, but lacks a specific strategy to deal withthe innovative process of design. In the FBS model (Vermaas &Dorst, 2008), every design task is decomposed into three stages:establishing a requirement function, searching functional struc-tures and recomposing functional structures. The model providesan effective means for conceptual design process by utilising behav-iours of the products as the information bridge, adopting causalmapping between design elements as the driver to implementexploration of the innovative space of the products. The disadvan-tage of this model is paying much attention to innovative strategiesof the product but neglect the representation ability of the modelfor the whole design process. As a conflict resolving theory in thecross-disciplinary, the focuses of Extensic are the expansion meth-ods, expansion rules and expansion operation of the conflicts. Thefundamental theory is based on extension set theory of matter-ele-ment and extension logics, which provides an effective mode ofthinking and a concrete operational process to solve contradictoryproblems in the design process of product by the rhombus thinkingmethod of transformation operations (Cai et al., 2003).

Considering the characteristics of the above design models andconflict resolving strategies, this paper combines the three methodstogether and attempts to create a fusion of their advantages. Itbuilds an integrated process of conceptual design with the goodexpression framework of the AD model and realizes various crea-tive solutions of requirement functions according to the decision-making behaviours between design units in the FBS model. At thesame time, the conflict resolving strategies of Extensic theory areincorporated into the model to deal with various design conflicts.Finally, an integrated conceptual design model aiding multi-stageinnovation of products is proposed. The whole process is definedas a multi-stage mapping process among the customer require-ments domain, principle solution domain, functional structures’ do-main, extension structures’ domain, and design project domain,shown in Fig. 1. Different innovative strategies are implementedin the different mapping processes to enable the design process ofthe product to be performed with multi-stage innovation.

In the mapping processes, the customer requirements domain isthe target descriptive set of design products which meets customerrequirements. These need to be abstracted into the standard formof functions to adapt the design process. The principle solution do-main is the scientific principle set used to achieve various designfunctions. It spans different academic boundaries to create a

Fig. 1. The multi-stage mapping processes of product design.

3576 W. Li et al. / Expert Systems with Applications 37 (2010) 3574–3587

perfect product. The functional structures’ domain is the physicalstructures’ set produced from a certain scientific principle andthere always exists some partial conflict structures which do notmeet the design constraints. Extending and perfecting those con-flict structures is necessary to obtain a satisfying design project.The extension structure’ domain is the satisfied functional struc-tures’ set in which the structures meet the design constraints aftervarious extending conversions. The design project domain is thevarious effective design path set in which a product satisfyingthe design constraints can be obtained. Through the multi-stagemapping process, the fluxion of design information can be realizedsmoothly in the design process. Furthermore, the scientific princi-ples are introduced as the innovative means and the conflictresolving strategies of Extensic theory are incorporated into the de-sign process, making up for the deficiency of the information breakand the limited innovative means in AD model. In the followingsections, we will describe the transformation process of creativethinking in the multi-stage mapping process.

2.1. The innovative strategies in design process

Product innovative design is a superior design process whichperforms design along with various creative thinking strategiesand is built on the foundation of routine design. The creative think-ing strategies are usually classified into three categories: exploringa new conceptual space, transforming an existent conceptualspace, and recomposing a familiar conceptual space. They areimplemented by mapping processes between different conceptualdesign domains (Vermaas & Dorst, 2007).

As discussed above, in this paper, the design process is definedas an integrated mapping system with five stages and the designinformation can be conveyed among the different design domains.It provides a broad space for the implementation of creative think-ing strategies. The mapping processes among the design domainsare shown as follows:

(1) The mapping from the customer requirements domain to theprinciple solution domain: The aim of this mapping is tosearch for primary principle solutions which fulfil the mainrequirement functions of customers by means of functionmatching methods. In this process, the conceptual solutionspace is extended adequately so that customers’ require-ments are satisfied by attempting various scientific princi-ples. Consequently, the variety and innovation of theultimate design project can be decided in this process.

(2) The mapping from the principle solution domain to the func-tional structures’ domain: Taking the principle solution asthe information bridge, a function model and correspondingfunctional structures’ model can be built based on the pri-mary principle solutions. After evaluating the functionalstructures’ model according to the design requirements,some partial function conflicts and functional structures’conflicts are identified and confirmed. The transformationfrom the holistic conflict space to partial conflict space willbe realized and the design space will be further extended.

(3) The mapping from the functional structures’ domain to theextension structures’ domain: As for all the conflict func-tional structures existing in the design model, they will beeliminated by the extension mechanism of Extensic theory.Different extending conversions are used from the conflictelements to their solutions, it can realize the extension andinnovation of design process further.

(4) The mapping from the extension structures’ domain to thedesign project domain: After optimized assembly of theextension structures’ solutions, an optimal conceptual solv-ing path is developed based on the evaluation strategiesabout the least design information and shortest solving path.It will realize a finally design project place and provide anend-result to the multi-stage innovation.

From the perspective of function, this conceptual design modelincluding four mapping processes reflects the transform relation ofthe multi-stage innovation of a new product. They are coherentfrom the customer requirements domain to the design project do-main and the solution range of every mapping process is the defi-nition domain of the next mapping process. Therefore the designinformation conveyed in the whole design process has good conse-cution. This kind of mapping model between domains uses themapping rules of the AD model and applies different innovativestrategies according to the characteristics of the different designstages. It not only puts forward a kind of design approach in con-sistent with the thinking logic of the design process, but also pro-vides an efficient and high level concrete means to develop acreative product.

2.2. The description of the conceptual design process

The conceptual design model can be logically described as atransformation of the customer requirements to a product thatbest meets those requirements wherein the design law is deduced(Karuppoor, 2003). There are always two non-mathematical ap-proaches to describe the processes. One is the semantic descriptionwith words or languages such as detailed task lists. It is abstractand systematic. The other is the non-semantic description withblock diagrams and entities such as flow charts. It is figurativeand visible. In contrast, the mathematical model possesses themerits both of them. It can simplify the abstract semantic informa-tion by rigorous symbols and logic, and also changes the non-semantic process framework into the structure of a mathematicalmodel, which enables the descriptive process to be clear and accu-rate. In addition, by means of the computer’s supportive manage-ment of the conceptual design process, and depending on theoutstanding communication quality of mathematical model, thedesigners’ thinking can be transferred into the computer system,which provides a foundation for the development of the computerlanguage. Moreover, it can abstract accurate design norm from theblurry design experience and make general designer acquaint thedesign process quickly. Therefore, it is meaningful to establish amathematical model of the design process with good structurewhich will benefit to the designers in understanding the essenceof the conceptual design process and developing an assistance sys-tem for the conceptual innovation of product design. In the follow-ing section, the conceptual design model with multi-stageinnovation will be further described mathematically.

3. Mathematical descriptions in the multi-stage innovationmodel

The conceptual design process of products is a mapping processfrom customer requirements to the design project. Supposing Rc as

W. Li et al. / Expert Systems with Applications 37 (2010) 3574–3587 3577

the customer requirement set, F as the function set and S as thefunctional structures’ set, and mapping Rc to S on the basis of F, asatisfied design project X can be yielded, which can be written as:

X ¼ FðRc ! SÞ ð1Þ

The conversion process of Eq. (1) is the essence of product design.However, this conversion process in practice is always complicatedand different conversion strategies will be adopted in different de-sign models. In this paper, the design process is defined as an inte-grated system which includes five arbitrary design stages and four

mapping processes. The five design stages are Rc; FH; S_; S^; X and

the four mapping processes are RC ! FH; F

H! S

_; S_! S

^and S

^! X,

where FH

is the set of primary principle solutions which match themain function requirements of customers. S

_is the set of conflict

functional structures derived from the function’s decompositionand S

^is the corresponding set of extended functional structures.

The four mapping processes are described below:

The first mapping : KR : Rc ! FH

or : FH¼ KRðRcÞ ð2Þ

This is a divergent mapping process with the aim of searching var-ious scientific principles to match the main requirement functionsof customers. Since the requirements knowledge KR at this stage

is blurry and uncertain, the primary principle solution FH

is usuallynot unique. The more scientific principles that are found, the higherthe innovative level of a product.

The second mapping : KF : FH! S

_or : S

_¼ KFðF

HÞ ð3Þ

This is a convergent mapping process. After applying the reasoning

design of the FBS model to the principle solution FH

, a function modeland functional structure model is set up. Comparing the relation-ship between the functional structures’ model and the customerrequirements and design constraints, the conflict functional struc-

tures’ set S_, which requires further optimization, is confirmed. In

this mapping, KF is the restriction knowledge of the design process.

The third mapping : KT : S_! S

^or : S

^¼ KTðS

_Þ ð4Þ

This is a divergent mapping process with the restrictions on therequirement functions and design process. The aim of this mappingprocess is to convert all the conflict functions and conflict functionalstructures into extension functional structures by the conflict reso-lution theory of Extensic. In this mapping, KT is the various reasonknowledge in Extensic, S

^is the extension functional structures after

conversion.

The fourth mapping : KV : S^! X or : X ¼ KV ðS

^ÞP H ð5Þ

This is a convergent mapping process and its essence is an evalua-tion process. Based on the convergent mapping, the evaluation

knowledge KV been acted on S^

in this process. Here, KV ðS^ÞP H

means that the functional structures S^

satisfies design requirementsafter conversion, and KV ðS

^Þ < H mean the opposite. H denotes the

entropy confirmed in advance.From the four mapping processes discussed above, we can see

that the aim of product design is to enable a design project X sat-isfying the requirements, which can be expressed mathematicallyas:

RC ¼ KV ðS^[ F^Þ ¼ ½X� ð6Þ

In this formula, [X] denotes all the characteristic knowledge of X.Substituting Eq. (6) into Eqs. (2)–(5), we can get Eq. (7):

X ¼ KV ðKTðKFðKRðð½X�ÞÞÞÞÞ ð7Þ

From Eq. (7), the starting point of conceptual design is the productcharacteristic knowledge related to the design requirements, andthe design target is to obtain new knowledge set. The new knowl-edge set will become the knowledge resource for this and/or othernew designs later. Therefore, the re-creation process based on theexisting knowledge is the essence of product design and is a veryimportant element of the design as well. From the aforementionedmapping processes, it can be easily concluded that this design mod-el is composed of double cycles from divergent thinking to conver-gent thinking, shown in Fig. 2. The first and second stageinnovations are achieved in the first alternation which realizes theinnovation for principles on the whole. The third and fourth stageinnovations are achieved in the second alternation which realizesthe deep-level innovative design of the product in some local re-spects. This design-thinking model has two advantages. First, itcan avoid the premature convergence of the design space at theearly design stage and also ensures that the distributed scientificprinciples can support the innovation of the design effectively. Inaddition, it can effectively eliminate the explosion phenomenonwhich is difficult to forecast during the reorganization process ofthe design scheme. In the following section, taking some key prob-lems in the conceptual design process into account, the solving pro-cess of the specific design scheme will be elaborated.

4. The key techniques in the multi-stage innovation model

All conceptual design models consist of two key techniques thatare the expression of design information and the solution ofrequirement function. Because both of them are restricted by themodel of customer requirements, there are three focuses in a con-ceptual design model. In order to describe the multi-stage concep-tual design process clearly, this paper will discuss the designprocess from these three aspects, which are: establishing the cus-tomer requirements, expressing the design information and pro-ducing the design project.

4.1. Establishing design requirement functions of customer

As above explanation about the conceptual design process, thecommence point is customer requirements. Because they are usu-ally expressed with certain human language which can be blurry,the customer requirements cannot be regarded as the designrequirements directly used in design process. Therefore, a modelis required to clarify and clearly define the customer requirementsin order to convert them into the concrete design parameters. As akind of conceptual descriptive method for the essential require-ments of an existing object, function is very suitable for represent-ing the design requirements. Therefore, the design requirementsare generated in the form of function based on customer require-ments in the following two steps.

4.1.1. Classifying the customers requirementsCustomers provide requirements for designers in terms of qual-

ity, cost, and environment and so on. The information is usuallyprovided in human language i.e. words and/or sentences, such as‘‘the product is light in weight” and ‘‘the price is low”. Since theseexpressions, without any fidelity differences in their level of signif-icances, are too blurry to guide the design process and define thepreferential level of the design, they must be analysed and classi-fied firstly. Fuzzy set theory has strong ability in tackling abstract,uncertain and un-quantitative information, and can be used to de-scribe the design information quantificationally and effectively.After classifying and prioritising the requirements informationof customers by fuzzy set theory, the essential and important

Fig. 2. Double divergent and convergent processes.

3578 W. Li et al. / Expert Systems with Applications 37 (2010) 3574–3587

requirements can be separated from the surplus/redundant andsubsidiary requirements, which clearly reflect the true intentionsof customers (Laszlo, David, Dirk, & Wim, 2008). Let Rc denotethe clarified customer requirements.

4.1.2. Abstracting and normalising customer requirementsBecause of designers’ experience, habits and design concept,

different designers will hold different interpretations on thecustomer requirements, which is likely to cause many prejudicesand unreal constrains being introduced into the design process inadvance. Therefore, the customer requirements should be ab-stracted in rigorous language to smash the fetters of the traditionaldesign ideology and limitations of the subjectivity and contin-gency. It is necessary to represent the customer’s essential require-ments emphatically to ensure smoothly transform from thecustomer requirement space to the design knowledge space. Itcan furthest guarantee to grasp the core of customer’s require-ments by using design requirement function to represent theessence of customer’s requirements. Therefore, the fault restric-tions can easily be identified and eliminated. The design solutionspace can be constructed in the highest level. (Rc)+ denotes thedesign requirement functions and can be derived from the stan-dardization of customer’s requirements.

ðRcÞþ ¼ RðRcÞ ð8Þ

where the R is the normalise operator. Based on Kirschman’s clas-sification method according to basic functions, different objects andaction status are described in terms of four basic function types,namely, Motion, Control, Power and Enclosures (Kirschman & Fadel,1998), each of which has the respective basic feature set. However,this classification only focuses on the technical characteristics ofproduct but disregards the non-technical characteristics. Neverthe-less, the design process should be comprehensive and integrateddesign features. Therefore, in this paper, the characteristics of cus-tomer requirements in conceptual form is taken into account, a syn-thetic functions is introduced into the design process to describethe non-technical characteristic of product, such as the field charac-teristics, application characteristics and so on as a complementaryto Kirschnman’s method. Consequently, the design requirementfunctions become five basic functions which are Motion Function(MF), Control Function (CF), Power Function (PF), Enclosures Func-tion (EF) and Synthetic Function (SF). Further more, each basic func-tion set includes multi-level more basic functions. Finally, everycustomer requirement can be defined by a combination functionset of the five types of basic function sets. Each basic function is ex-

pressed in the form of ‘‘function operation method + function oper-ation object” and comprised of a sentence with ‘‘verb+noun” such as‘‘deliver machine energy”, ‘‘separate impurity”, etc.

R ¼ ðMF; CF; PF; EF; SFÞ; MF ¼ ðMFV ;MFNÞ;CF ¼ ðCFV ; CFNÞ . . . ð9Þ

Among the motion function MF, MFV, MFN means the functionaloperation method and functional operation object of the basicmotion function respectively. For example:

MFV ¼ ðbring; switch; change; transfer; consumeÞ;MFN ¼ ðelectric-energy; mechanical-energy; other-energyÞ;

Similarly, each basic functions of CF, PF, EF, SF have their own morebasic functional operation method set and functional operationobject set.

In order to express and manage the basic function set of the de-sign’s requirements efficiently, each function set is expressed withthe form of power set which its element is a sub-function set, i.e.lower level set is embed in the higher level set. The higher levelelement in a set denotes more abstract function, while the elementin a lower level set represents specific function. In this way, thecustomer requirements can be established through the five basicfunction sets successfully and the conversion from the customers’requirement space to designers’ concept space can be accom-plished. The ith customer requirement can be uniquely describedas a set of basic function set, shown in Eq. (10).

Rci

� �þ ¼ MFik;CFi

k; PFik; EFi

k; SFik

� �\ ðk 6 kmaxÞ;

k ¼ 1;2; . . . ; kmax ð10Þ

Then

ðRcÞþ ¼Xm

i¼1

Rci

� �þ; i ¼ 1;2; . . . n ð11Þ

In Eqs. (10) and (11), kmax denotes the maximal decomposing levelof function and n is the number of customer requirements.

4.2. The representation model for design information

In conceptual design, it is necessary to define a model, which iscompletive and conductive to innovation design, representingproduct design information to describe the whole design process.Under the function of the environment, the realization of the

Fig. 3. The tree-like structures of product function.

W. Li et al. / Expert Systems with Applications 37 (2010) 3574–3587 3579

customer requirement function runs through the entire designprocess, in this paper product functions information is used asexpression of information representing the product design process.The original customer requirements are the design target. How-ever, they are normally general, complex, regardless of the hierar-chy and lack of focused and practical accuracy and are impossibleto be represented by single functional structures. Therefore, thehierarchical approach is introduced to decompose the original cus-tomer requirement functions into sub-functions which will bedealt with gradually in different design levels. In order to describethe relationship of product design information in different designstages accurately, a notion of function tree and functional struc-tures tree is introduced with tree-layer structures. This informa-tion expressive model can not only describe the design conflictsin each stage flexibly and unanimously, provide support for elimi-nating the conflicts effectively, but also lay a foundation for imple-menting the product function innovation layer by layer during thedesign process. The top down representing tree proposed by Csa-bai, Stroud, and Xirouchakis (2002) is used for the expressive mod-el of product function, notated as F, which can be written as:

F ¼ fFði; k; jÞji; k ¼ 1;2; . . . ;n; j ¼ 1;2; . . . mg;Fk

i ¼ fFði; k; jÞjj ¼ 1;2; . . . mg ð12Þ

where F(i,k, j) is the most top level of function tree, i is the ith sub-function of F. k is the decomposition layer number and j is the func-tion sequence of sub-function F(i,k) in layer k. Fk

i represents all ofthe function tree in layer k. The function tree is shown in Fig. 3.

According to the reasoning theories of FBS (Karuppoor, 2003),the continuous decomposition of functions will inevitably lead tothe corresponding decomposition of functional structures. Similarto the function expressive model, the functional structures’ modelalso can be expressed as:

S ¼ fSði; k; jÞji; k ¼ 1;2; . . . ; n; j ¼ 1;2; . . . mg;Sk

i ¼ fSði; k; jÞjj ¼ 1;2; . . . ;mg ð13Þ

where S(i,k, j) is the root functional structures of functional struc-tures tree and Fk

i are all functional structures tree in layer k.Following the tree-layer description of the function and func-

tional structures, the design information in each conceptual designstage can be expressed by the basic function tree and basic func-tional structures tree.

4.3. An innovation project produced from multi-stage mapping

The essential target of conceptual design is to get an innovationproject plan which can meet the customer requirements in compli-ance with design constraints. The conceptual design model with

multi-stage innovation proposed in this paper achieves this targetwith the following four mapping processes.

4.3.1. The mapping of searching for function’s principle solutionAlthough innovation is the essence of product design, high-level

innovation is usually difficult to fulfil due to the knowledge limita-tions of the designer, particularly in situations requiring designknowledge across multiple disciplines. During the process ofimplementing certain kinds of requirement functions, having moreknowledge in achieving a certain kind of functions is more likely toobtain novel principle solutions and provide a wide range of designsolutions to the new product. In this paper, the scientific principleset, which can realize the design requirement functions, are classi-fied into different classes according to Kirschman’s classificationmethod. It is expressed in the form of ‘‘verb+noun”, where the verbdenotes the operations of a scientific principle, such as input, out-put, deliver, guide, etc. The noun denotes the objects of operations,such as gas, liquid, voice, electricity, magnetism, caloric, etc. Theverb can be simply denoted as V and the noun as N. In this way,the similar principle solutions of function are combined together,and the corresponding principle solution trees are set up on the ba-sis of the function trees. The high-level nodes of the tree are thoseabstract principle solutions, which are used for implementing gen-eral functions, and the leaf nodes of the tree are the most specificprinciple solutions, which are utilised to realize concrete functions.Using the mapping mechanism between scientific principles anddesign requirement functions, a satisfied principle solution fromthe scientific principle tree can be found efficiently.

There are many mathematic ways (Amir & Yoram, 2005; Hris-hikesh & Suh, 2004) to search for a scientific principle satisfyingthe requirements in the resource tree. In this paper, a correlation

function, rðxÞ ¼ qðx0 ;X0ÞDðx;X0 ;XÞ

of Extensic’s theory, is introduced to ex-

press the level of similarity between any two nodes in functionspace and used to search and realize the principle solution of afunction. Fig. 4, the extendable matter-element semantic informa-tion pattern, is used to illustrate the searching principle, which alsoshows that the searching process of the principle solution is theissue of semantic matching between extended semantic informa-tion. The semantic pattern of information can be expressed as an

array M ¼ ½Rc; FH;r;r0;K�. In this array, r is the dependent level

between the verbs of Rc and FH

. r0

is the dependent level between

the nouns of Rc and FH

. The Possible level K Rci ; F

H

i

� �between Rc

i

and FH

i can be obtained by the following equation:

K Rci ; F

H

i

� �¼X5

i¼1

rðVi;V0iÞ � r Ni;N

0i

� �ð14Þ

cR

FΘ

'( , )i iV Vσ

iV

'iV

jV

'jV

jN

'jN

jN

'jN

( , )cK R FΘ'( , )j jV Vσ

Fig. 4. The extendable matter-element semantic information pattern.

3580 W. Li et al. / Expert Systems with Applications 37 (2010) 3574–3587

The unequal equation K Rci ; F

H

i

� �P U will chose F

H

i as the principle

solution to meet the requirement functions of customer, where Uis the entropy determined as prior.

4.3.2. The confirming mapping of conflict functional structuresThere will be many principle solutions based on the entropy U

and each principle solution has theirs own characteristics. There-fore, when a principle solution is used to establish the concretefunctional structure’s system, some partial matching conflictsbetween functional structures and design constraints are likely toappear. Resolving those conflicts will guarantee the smooth perfor-mance of the design process. In this paper, the causal mappingmechanism of the FBS model is adopted as the reasoning tool toaccomplish the functional structures analysis of a principlesolution. After the iteration of the multi-level mappings betweenfunctions, behaviours and functional structures of the FBS model,a functional structures tree which has the same structural viewas the design function tree is yielded. By comparing the matchingstatus between the functional structures tree and the design func-tion tree, the conflict functional structures, which need furtherextension, will be identified. Following top down strategy, from ab-stract to practical and general to partial, the decomposed tree ofthe functional structures is established. Then an integrated designroute to realize the principle solution can be found and the partialconflicts requiring extension are also located in the design model.Meanwhile, a vast innovative space is created by the multi-layermappings among design elements. The construction process offunctional structures’ systems, commencing from a principle solu-tion, are expressed by the following mathematic form:

DecðFH; B; SÞ

fi ¼ 0; k ¼ 0; j ¼ 0;

REPEATfi ¼ iþ 1; k ¼ kþ 1; j ¼ jþ 1;

sðFki

H

¼ ff kij jj ¼ 1;2; . . . ; nÞg;

8f kij 2 sðFk

i

H

Þ; nðf kij Þ ¼ bk

ij;

s Bki

� �¼ bk

ijjj ¼ 1;2; . . . ;nn o

;

8bkij 2 s Bk

i

� �; n bk

ij

� �¼ sk

ij;

8skij 2 s Sk

i

� �;

IF skij R Ln; THEN n sk

ij

� �¼ Fkþ1

ij ;

UNTIL 8skij 2 s Sk

i

� �; sk

ij 2 Ln;

TreeðFH;B; SÞgg

where s is the decomposing operator and n is the reasoning opera-tor. Ln is the basic functional structures’ set which can be realizeddirectly. In this process, the realized structures of behaviours are

employed as a basis to check the completion of decomposition.When every decomposed sub-function is realized by a set of basicfunctional structures, the reasoning process is completed. Then,

the final Tree ðFH;B; SÞ is the final functional structures tree that is

derived from the various reasoning mappings. Comparing the dis-crepancy between the functional structures tree and design con-straints, as well as the function conflicts between the primalprinciple solution, design requirement and the corresponding struc-tures conflicts are figured out, which sets up a target for furtherextension of the structures, shown as below.

Fki

_

¼ Fði; k; jÞ l rdk ; Sk

i

_

¼ Sði; k; jÞ l Fki

_

ð15Þ

where ‘‘l” means the design conflict between two design units.

4.3.3. The extending mapping of conflict functional structuresAfter the mapping process above, the conflict functional struc-

tures with design constraints can be confirmed. The extension ofthe partial conflict functional structures’ set is the further optimi-zation with respect to the principle innovative solution. In this pa-per, Extensic’s (Cai et al., 2003) theory of resolving conflicts is usedto deal with these kinds of partial conflicts. According to theexpression theory of Extensic, the conflict functional structures’set Sk

i

_

should be firstly expressed in the form of an ordered triadR ¼ ðN; c;vÞ. It is the basic element for describing things, calledmatter-element and the matter-element of Sk

i

_

is RLkSj

_

(k = 1,2,n;j = 1,2, . . . ,m), shown in Eq. (16).

RLS

_¼

NLkS1

_

CLk1S1

VLk1S1

CLk2S1

VLk2S1

..

. ...

CLkjSj

VLkjSj

26666664

37777775

NLkS2

_CLk

S2VLk

S2

..

. ... ..

.

NLkSn

_CLk

SnVLk

Sn

266666666666666664

377777777777777775

ð16Þ

where RLkS1

_

is the child matter-element of RLS

_; NLk

Sjis the represents of

RLkS1

_

; CLkSj

is the characteristics of RLkSj

_

; VLkSj

is NLkSj

0s measure about the

characteristics CLkSj

. Lk is the character number in the kth layer ofthe conflict structures Sk

i

_

. Si is the number of the sub-functionalstructures.

Supposing RLS

_as the conflict matter-element which needs trans-

formation, and T as extendable transformation, the transformation

process of RLS

_can be present as follows:

TðRLS

_Þ ¼ TðRLk

S1

_

;RLkS2

_

; . . . ;RKkSn

_

Þ

¼ ðT1ðRLkS1

_

Þ; T2ðRLkS2

_

Þ; . . . ; TkðRLkSn

_

ÞÞ; k ¼ 1;2; . . . n ð17Þ

where T1,T2, . . . ,Tk are the extendable transformations which meetthe design requirements.

According to the dependent principle of Extensic, any active

conversions Tu of matter-element RLkSi

_

will cause the compelled con-

versions Tx of dependent matter-element RLkSj

_

. We note the trans-

formation T as T ¼ TuTx

� . Supposing RL

S

^as the resulting matter-

element after conversions, the conversion process can be shownas follows:

W. Li et al. / Expert Systems with Applications 37 (2010) 3574–3587 3581

RLS

^¼ TðRL

S

_Þ ¼

Tu

Tx

� �

RLkSi

_

RLkSj

_

24

35 ¼ TuðRLk

Si

_Þ

TxðRLkSj

_Þ

24

35 ¼ RLk

Si

^

RLkSj

^

24

35 ð18Þ

By virtue of various extendable strategies and extendable conver-sions, various contradictions and conflicts of the functional struc-tures of Sk

i

_

can be resolved from the perspective of dynamicchange through the transform from infeasibility to feasibility andfrom opposition to coexist.

The reasoning knowledge set KTk in this mapping stage in-

cludes not only the practical reasoning methods of the extensiontheory but also the rule knowledge of regularities and rules L in aspecial design field. The need of human–computer interactionsupport in this stage represents the significance of human influ-ence in the conceptual design process. It can be said that the rea-soning knowledge in this mapping stage refers to all thecorrelative knowledge which can satisfy the design process andcan be defined as:

KTk ¼ r Sk

i � Fki

H !

[ L ð19Þ

where r is the reasoning operator. When all the extensions fromthe conflict functions to extended functions are completed, the ex-tended functions can be assessed by the evaluation operator, whichis the final phase of conceptual design.

4.3.4. The evaluating mapping of extension functional structuresFollowing the extension mappings, many design project plans

will be yielded. It can be regarded as the second divergent opera-tion in the design process and can enhance the innovation in de-tailed level. However, in order to get an optimal design projectplan, these divergent design solutions are required to be integratedthrough a convergent process to complete the evaluation on thesolution space. In this work, using a hierarchical extension evalua-tion method by comparing satisfactory level between the designproject and design requirement, the convergent process is accom-plished, which is explained as follows:

(1) Establish the evaluation standards. According to the actualdemands, an evaluation standard that can comply with thetechnical and economic requirements is set up. Then, theevaluation measures set M = (M1,M2, . . . ,Mn) is proposed,where Mi = (Ni,ci,Vi) is the normal eigenvector and Ni is theevaluation field of the eigenvector.

(2) Decide the weighing coefficients of evaluation condition. Theweighing coefficients a = (a1,a2, . . . ,an) of each child mat-

ter-element NLkSi

^

ði; k ¼ 1;2; . . . mÞ towards the normal eigen-vector M1,M2, . . . ,Mn is worked out. In order to set theweighing coefficients reasonably, a layer analysis methodbased on the relativity and correlation between the evalua-tion objections are applied.

(3) Establish the dependent functions. The level of excellence Ki

for each child matter-element NLkS1

^

;NLkS2

^

; . . . ;NLkSm

^

regardingthe Mi is figured out.

Kij ¼ ðKiðNLkS1

^

Þ;KiðNLkS2

^

Þ; . . . ;KiðNLkSm

^

ÞÞ ði ¼ 1;2; . . . ;nÞ ð20Þ

where the calculation of KiðNLkSi

^

Þ should be accomplished by

(4) Calculate the advantageous level. The advantageous level of RLS

^

regarding each evaluation standard

M1;M2; . . . ;Mn is : CðRLS

^Þ ¼ aKðNLk

Si

^

Þ ¼Xm

i¼1

aiKij ðj ¼ 1;2; . . . ;mÞ

ð21Þ

The resulting matter-element RLS

^with the highest advanta-

geous level is chosen to enable the design project meet thedesign requirements perfectly.

The whole mapping process can be summarised in Fig. 5, thedesign frame. There are four main parts in this frame. Firstly, con-structing the design requirements and searching for the main func-

tion principle solution FH

on the basis of customer requirements.Secondly, establishing the functional structures’ model based onthe principle solution by the reasoning mechanism of FBS anddefining the conflict functions and conflict functional structures’set by comparing the functional structures’ model with the designconstraints. Thirdly, according to the Extensic theory, extension ofthe partial functional structures’ conflicts to an extension struc-tures’ solution. Finally, evaluating and recomposing the extensionstructures’ solution to reach a final design project.

4.4. The mathematical frame of multi-stage innovation design

Therefore, the framework of a conceptual design process withmulti-stage innovation is developed. Next, an integrated mathe-matical model of the design process will be presented. This modelincludes 6 steps.

Step 1: Collect the customer requirements Rci and convert it to the

design requirement functions set Rci

� �þaccording to Kirs-chman’s classification method, the five types of basic func-tion sets.

Step 2: Accomplish the mappings from requirement functions setto a primal principle solution F

Hbased on the requirement

functions Rci

� �þ.Step 3: Apply function analysis on the principle solution set F

Hto

obtain a corresponding functional structures’ model. Com-pare the functional structures’ model with the design con-

straints to identify the conflict functions Fki

_

and conflict

functional structures Ski

_

.Step 4: Expand the functional structures’ conflicts of Sk

i

_

to theextension functional structures by the extensible reason-ing conversions of Extensic.

Step 5: Evaluate the extension functional structures Ski

^

to get thesatisfied structures’ set S½s�i according to the requirementfunctions Rc

i

� �þ.Step 6: Recompose the structures’ set S½s�i and corresponding func-

tion set F ½f �i to reach the final satisfied projects’ set andthen, evaluate X.

These steps can be expressed mathematically as follows:

1. 8Rci ; Rc

i

� �þ¼ MFik;CFi

k;PFik;EFi

k;SFik

� �\ðk6kmaxÞ; ðRcÞþ¼

Pmi¼1 Rc

i

� �þ;

2. 8 Rci

� �þ; 9KR

k ; Fki

H

¼ KRk Rc

i

� �þ;KðF

HÞ ¼

Pmi¼1r Vi;V

0i

� �� rðNi;N

0iÞP H;

3. 8Fki ;8Sk

i ;Fki

H

¼ Fði;k; jÞ; Ski ¼ Sði;k; jÞ; 9KF

k ;Fki

_

¼ Fði;k; jÞ l Rci

� �þ;

Ski

_¼ Sði;k; jÞ l Fk

i

_

;

4. 8 Fki

_

;8Ski

_

; 9KTS ; KT

S ¼ r Ski � Fk

i

� �[ L; Fk

i

^

¼ KTkðF

ki

_

Þ; Ski

^

¼ KTkðS

ki

_

Þ;

5. 9S½s�i 2 Ski ; 9F

½f �i 2 Fk

i ; 9Kvk ; S½s�i ¼ Kv

k ðSki

^

Þ; F ½f �i ¼ Kvk ðF

ki

^

Þ;

6. X�¼Pn

i¼1ðS½s�i [ F ½f �i Þ; X ¼ KV ðX

�Þ;

The aforementioned conceptual design process is an iterativeprocess which incorporates the design requirements, productdescription and functions reasoning into the process. In iteration,the results obtained from the previous design cycle will be usedas the input for the next cycle. It is an endless evolving process

[ ]fF

dR

[ ]sS

F∨

S∧

X

[ ]fF

dR

[ ]sS

F∨

VK

VK

RK FK TK

VK

Fig. 6. The reduplication process of design.

Fig. 5. The model framework of multi-stages innovation design process.

3582 W. Li et al. / Expert Systems with Applications 37 (2010) 3574–3587

from low-level to high-level, requiring more and more multi-disci-plinary knowledge. Finally, it will develop a huge and infinite de-sign system with a continuous learning mechanism, as shown inFig. 6.

According to the design thinking regulations, the FBS model andconflicting resolution theory of Extensic, the paper elaborates aconceptual design method using mathematical language, whichis based on double divergent–convergent processes. This methodconverts the vague qualitative description into a quantitativedescription so that it can represent the design process accurately.The next section will illustrate the process by an example of emer-gent cutting off valve.

5. Case studies

The top gas pressure recovery turbine (TRT), electricity genera-tion unit of a blast-furnace, is a well-known and valuable pieceequipment for energy regeneration. The project is proposed to uti-lise the waste gas and pressure to be generated from the steel pro-duction processes of an existing hot roll workshop within the steelproduction area, and generate power with the installation of toppressure recovery power generation units (Huanrong, 2005). Inthis piece of equipment, the pressure energy and thermal energyof the blast furnace’s top gas are recovered to drive the generatorto generate electricity by their expansion acting in the turbine. It

Fig. 7. The equipment of blast-furnace top pressure recovery turbine unit.

Table 1The scientific principles of move solid matter.

W. Li et al. / Expert Systems with Applications 37 (2010) 3574–3587 3583

not only recovers the former wasted energy, but also reduces thenoise and vibration in the reduction valve. The scheme of thisequipment is shown in Fig. 7.

The emergency cutting off valve is pivotal equipment in TRT.The main function of this equipment is to cut the blast-furnace coalgas in pipe rapidly when something wrong happens in order toprotect the whole system. In the following presentation, the designprocess of the emergency cutting off valve will be elaborated toillustrate the proposed design model. The design parameters of itare listed below:

The maximal flux of coal gas: 10–60 m3/h.The maximal intake pressure: 3 bar.The outtake pressure: 0.8 bar.The maximal intake temperature: 240 �C.The period to cut off: 1 s.The manner of switch: slow opening, slow shutting, quick shut-ting and moving.The capability demands: high reliability and high pollutionresistance.The next will present the conceptual design of this emergencycutting off valve based on the process model of multi-stageinnovation proposed in this paper.

5.1. Searching for function’s principle solution

The first step is to analyse the customer’s requirements andsearch various scientific principle methods to implement the mainfunctions. The purpose of emergency cutting off valves is to regu-late the flux of coal gas by moving the valve plate position of thebutterfly valve, so it can be abstracted as the requirement function

‘‘moving solid material”. According to the mapping mechanismfrom the requirement function to the principle solution, some sat-isfied scientific principles which can fulfil the functions are pickedout from the scientific principles base in the form of ‘‘verb+noun”,as shown in Table 1 (Runhua, 2002).

Because there are many principle solutions which can meet thefunctions requirements, in order to reduce the time of the trial-and-error method, the extensible dependent function r(x) is usedto choose the optimal principle solution. After setting an enact-ment entropy U0, the principle solutions which can satisfy theenactment entropy can be found by calculating the possible levelbetween the ‘‘moving solid material” functions from the scientificprinciples base. These principle solutions include the electrorhe-ological effect, fluid effect, forced vibration effect, magnetic effect,aerodynamic effect and so on. They provide different directions forthe design target and can be realized from some practical func-tional structures’ models according to the reasoning strategies ofFBS.

5.2. Confirming of conflict functional structures

Taking the electrorheological effect as an example of principlesolution, we can establish a functional structures’ model to fulfilthe function of ‘‘moving solid material”. The implementation ofthis principle is converting the electric power into other forms ofenergy and driving the valve plate of the emergent cutting offvalves to move. According to the existing design experience, elec-tric power is firstly converted into hydraulic pressure energy to fin-ish the concrete function model. Here, the function model ofemergency cutting off valves is described in the form of a functiontree which combines the function design model ‘‘verb+noun” and

Fig. 9. The functional structures tree of emergent cutting off valve.

Fig. 8. The function model of emergent cutting off valve.

3584 W. Li et al. / Expert Systems with Applications 37 (2010) 3574–3587

‘‘input flow + output flow”, shown in Fig. 8. By this way, not onlycan the function principle of the function operation steps be specif-ically obtained, but also the detail realization process modallypresented.

According to the function model of Fig. 8, a correspondingfunctional structures’ model can be developed such as Fig. 9.However, this design project at this state cannot satisfy all designrequirements. We need to compare it with the design constraintsand ascertain the conflict functional structures. Following someanalysis, the functional structures in this state can meet mostof design constraints except for pollution resistance. This is be-cause the hydraulic oil is used as the medium of energy transferand it will touch the dust in coal gas during the work of hydrau-

lic components. The friction among the components will influ-ence the stability of design project seriously. So, it can beconcluded that the functional structures of energy transfer arethe design conflicts in this project, shown in the shadowed areaof Fig. 9.

5.3. Extending of conflict functional structures

In order to make the design project satisfy the design con-straints, the conflict functional structures in the design projectshould be eliminated. There are two ways to solve these conflicts.One is to reduce the density of blast-furnace coal gas. This is costlyin capital and the implementation technology is very different as

Fig. 10. The matter-element framework of emergent cutting off valve.

W. Li et al. / Expert Systems with Applications 37 (2010) 3574–3587 3585

well. Another way is to extend the conflict functional structures bythemselves. The second method is chosen in this paper and theconflict structures are disposed by the conflicting resolution theoryof Extensic. According to the extensible condition of Extensic, theconflict functional structures should firstly described as the formof matter-element, shown in Fig. 10.

In the matter-element framework, the matter-element of en-ergy transfer is the conflict matter-element, and it can be describedas:

R_¼

Energy Hydraulic cylinder Pluuger barrel

Control box Control valve

Oil resource L-HM

2664

3775 ð22Þ

The extensible reasoning methods can be used to enable the energytransfer matter-element to meet the design constraints of pollutionresistance. The extensible reasoning methods include radiation,implication, relationship, addition, deletion and so on. They providevarious solving directions and approaches to eliminate designconflicts.

According to the extending conversion method that a matterhas many characteristics, called one matter many characteristics:(N,c,v) � j{(N,c1,v1), (N,c2,v2), . . . , (N,cn,vn)}, the divergent natureof matter-elements is chosen for the energy transfer matter-ele-ment R2

2

_. Through the reasoning of radiation, many viable methods

which can eliminate the pollution conflict are found, such as mag-netic field, air-actuated, and heat energy.

R22

_�

Energy transfer Solenoid Doughnut

Ferromagnet Steelbar

Spring Common

26664

37775;

8>>><>>>:

�

Energy transfer Pneumatic crock Doughnut coil

Control box Control valve

Air resource Air

26664

37775; . . . ;

�

Energy transfer Heat resource High temperature air

Gas storage equipment Cylinder

� � � � � �

26664

377759>>>=>>>;¼ R2

2

^

ð23Þ

A method is picked to remove the function conflict of energy trans-fer from the various divergent solutions. It should be presented inthe form of specific corresponding functional structures. By the vir-tue of the underlying reasoning principles of Extensic, the concretefunctional structures’ solution can be yielded from the reversethinking. This process can be shown below

R22

^¼

Energy Solenoid Doughnut

Ferromagnet Steel bar

Dynamical pring Common

264

375

(

Energy transfer Canula Metal tube

Lead Nichrome

Ferromagnet Steel bar

Electrical resource Alternating current

266664

377775

(

Energy tansfer Canula length 30 cm

Canula material Steel

Lead diameter 2 cm

Lead material Nichrome

Ferroagnet length 10 cm

Ferromagnet material Steel bar

Voltage 220 V

26666666666664

37777777777775

( � � � ð24Þ

There are always some relationships among the design matter-ele-ments, so the active reasoning conversions of a certain matter-ele-ment will lead to the compelling conversion of some other relatedmatter-elements. Because the medium of energy transfer is chan-ged from hydraulic oil to magnetic force, the corresponding mat-ter-element of energy control matter-element will be changedfrom the hydraulic control valve to the magnetic control switch.The energy transfer matter-element should be changed by passiveconversion, as shown below

R22

�U

¼ TðR22

�U

Þ ¼Tj

Tx

" #

¼

Tj

Energy transfer Hydraulic cylinder Plunger barrel

Hydraulic Control valve

Oil resource L-HM

2664

3775

Tx

Cut-off valve Bearing Ball valve

gear Bevel gear

Valve body Butterfly valve

2664

3775

2666666666664

3777777777775

¼

Energy transfer Solenoid Mongline

Ferromagnet Steel bar

Spring Common

2664

3775

Cut-off valve Bearing Bushing valve

Gear Bevel gear

Valve body Butterfly valve

2664

3775

2666666666664

3777777777775

ð25Þ

Fig. 11. The function model of emergent cutting off valve subject extending conversion.

Fig. 12. The final improved result of emergent cutting off valve.

3586 W. Li et al. / Expert Systems with Applications 37 (2010) 3574–3587

R33

�U

¼ TðR33

�U

Þ ¼Tj

Tx

�

¼

Tj

Oil Oil box Entirety typeHydraulic L-HMOil filter Network

Hydraulic pump Vane oil pump

26664

37775

Hydraulic control box Electromagnetic valve CommonThrottle valve 2 : 1

Reversing valve 3 : 1Pressure reducing valve Common

26664

37775

Hydrocylinder Hydraulic cylinder Plunger barrelPiston PlungerRack Common

264

375

26666666666666666666664

37777777777777777777775

¼

Magnetic force Solenoid MonglineFerromagnet Steel bar

Altemating current 220 V

264

375

Control element Switch Two�way typeConnecting rod Common

Resistance Temperature sensing

264

375

2666666664

3777777775ð26Þ

5.4. Recomposing of extension functional structures

Based on the outcomes yielded from the various extending con-versions, the hydraulic drive system is substituted by a controlcubicle system. While the electric current passes the solenoid,the magnetic field is generated inside the solenoid. The intensityand direction of magnetic field depends on the intensity and direc-tion of the voltage or current. Changing the intensity and directionof magnetic field, the ferromagnet can move in different directionsand with different speed. It enables the valve to slowly turn on,slowly cut off, quickly cut off and slide. The function model ofEmergency cutting off valves subject to the extending conversionis shown in Fig. 11.The corresponding functional structures thathave realized the function of energy transfer also meet all designconstraints. After assembling the optimal functional structures,the final improved result of the emergent cutting off valve can bereached, shown in Fig. 12.

Comparing the improved system with the original system, 1/3of elements and interactions are decreased, the harmful actionsare eliminated, the system structure is simplified and the cost is re-duced. From the point of view of system performance, the negativeeffects inherent to the hydraulic system, such as the pollution ofoil, the flow resistance of oil and the unreliability of hydraulic

W. Li et al. / Expert Systems with Applications 37 (2010) 3574–3587 3587

meter, etc, are removed by replacing the hydraulic drive systemwith an electromagnetic drive system.

6. Conclusion

In this paper, based on the general process of conceptual design,the innovation strategies applied in each design stage are discussed.Based on hierarchical design information expression and doubledivergent–convergent reasoning mechanism, an integrated concep-tual design model to aid multi-stage innovation of product is pro-posed. In the conceptual design field, this has been activelyexploring and practice on the decision making of an innovation de-sign plan and on the description of the general design process. Theinnovations of this paper are as follows. (1) An integrated designprocess model of conceptual design from customer requirementsto design projects plan is proposed based the double divergent–con-vergent design reasoning. (2) Different innovative strategies in eachstage of the design process are discussed and they are implementedusing the different extendable methods of Extensic theory. (3) Thehierarchic and progressive design process is described by the designinformation of function tree and functional structures tree. The es-sence of conceptual design is revealed from the microscopic point ofview. (4) The whole design process is described by sophisticatedmathematic language, in which a valid prototype framework ofthe computer aided conceptual design systems is set up.

There are still some areas that need further work. Therefore, (1) Acomputer assistant system based on this design model will bedeveloped and in this model the process information in the designwill be managed effectively and the sustainment of multi-stageinnovations will be realized during the whole design process. (2)A better visual man–machine interface will be established and a pulland push mechanism of design knowledge will be finished then.

Acknowledgements

This work has been supported by the National Natural ScienceFoundation, China (Grant No. 50875180), and the National High-Tech. R&D Program for, China (Grant No. 2006AA04Z102).

References

Amir, Z.-A., & Yoram, R. (2005). SOS – Subjective objective system for generatingoptimal product concepts. Design Studies, 26(5), 509–533.

Bracewell, R. H., & Sharpe, J. E. E. (1996). Functional descriptions used in computersupport for qualitative scheme generation‘Schemebuilder’. AIEDAM, 10(4),333–345.

Brownsboro, W. F., & Noort, A. (2004). Multiple-view features modelling for integralproduct development. Computer-Aided Design, 36(10), 929–946.

Burattini, E., De Gregorio, M., & Tamburrini, G. (2002). Hybrid expert systems: Anapproach to combining neural computation and rule-based reasoning. ExpertSystems, 1315–1354.

Cai, W., Yang, C., & He, B. (2003). Entension logic accidence. Publish of science [inChinese].

Campbell, M. I., Cagan, J., & Kotovsky, K. (2000). Agent-based synthesis of electro-mechanical design configurations. ASME Journal of Mechanical Design, 122(1),61–69.

Csabai, A., Stroud, I., & Xirouchakis, P. C. (2002). Container spaces and functionalfeatures for top-down 3D layout design. Computer-Aided Design, 34(13),1011–1035.

Francis, E., Tay, H., & Jinxiang, Gu (2002). Product modelling for conceptual designsupport. Computers in Industry, 48(2), 143–155.

Gero, J. S., & Kannengiesser, U. (2007). A function-behaviour-structure ontology ofprocesses. AIEDAM, 21(3), 295–308.

Goel, A. K., & Bhatta, S. R. (2004). Use of design patterns in analogy-based design.Advanced Engineering Informatics, 18(2), 85–94.

Han, O. H., & Lee, K. (2006). A case-based framework for reuse of previous designconcepts in conceptual synthesis of mechanisms. Computers in Industry, 5(4),305–318.

Henry, C. W., Bing, J., Felix, T. S., & Ralph, W. L. (2002). An innovative scheme forproduct and process design. Journal of Materials Processing Technology, 123(1),85–92.

Hrishikesh, D. V., & Suh, N. P. (2004). Mathematical transforms in design: Case studyon feedback control of a customizable automotive suspension. CIRP Annals –Manufacturing Technology, 3(1), 125–128.

Hsiao, S.-W., & Tsai, H.-C. (2005). Applying a hybrid approach based on fuzzy neuralnetwork and genetic algorithm to product form design. International Journal ofIndustrial Ergonomics, 35(5), 411–428.

Huanrong, Z. (2005). Power test and analysis for TRT at Baosteel. Iron Making,24(S1), 96–99 [in Chinese].

Karuppoor, S. S. (2003). Tools for innovation and conceptual design. DissertationAbstracts International 65–07(B), Ravinder Chona.

Kirschman, C. F., & Fadel, C. M. (1998). Classifying for function for mechanicaldesign. ASME Journal of Mechanical Design, 120(3), 475–482.

Kobayashi, H. (2006). Systematic approach to eco-innovative product design basedon life cycle planning. Advanced Engineering Informatics, 20(2), 113–125.

Kulak, O., Durmusoglu, M. B., & Tufekci, S. (2005). A complete cellularmanufacturing system design methodology based on axiomatic designprinciples. Computers & Industrial Engineering, 48(4), 765–787.

Laszlo, F., David, M., Dirk, V., & Wim, D. (2008). Application of fuzzy numericaltechniques for product performance analysis in the conceptual and preliminarydesign stage. Computers & Structures, 86(10), 1061–1079.

Lin, M.-C., Wang, C.-C., Chen, M.-S., & Chang, C. A. (2008). AHP and TOPSISapproaches in customer-driven product design process. Computers in Industry,59(1), 17–31.

Mann, D. L. (2003). Better technology forecasting using systematic innovationmethods. Technological Forecasting and Social Change, 70(8), 779–795.

Peien, F., Shuai, Z., Yong, C., Shuangxia, P., & Bin, H. (2002). Research on featuremodelling and solving process of complex function. China MechanicalEngineering, 3(4), 308–311 (in Chinese).

Runhua, T. (2002). Innovative design: Problem solving theory of TRIZ. Publisher ofManufacture (in Chinese).

Suh, N. P. (2001). Axiomatic design – Advances and application. Oxford UniversityPress.

Therani Madhusudan, J., Zhao, Leon, & Marshall, B. (2004). A case-based reasoningframework for workflow model management. Data & Knowledge Engineering,50(1), 87–115.

Umeda, Y., Ishii, M., Yoshioka, M., et al. (1996). Supporting conceptual design basedon the function-behavior-state modeler. AIEDAM, 10(4), 275–288.

Vermaas, P. E., & Dorst, Kees (2007). On the conceptual framework of John Gero’sFBS-model and the prescriptive aims of design methodology. Design Studies,28(2), 133–157.

Vermaas, P. E., & Dorst, K. (2008). On the conceptual framework of John Gero’s FBS-model and the prescriptive aims of design methodology. Design Studies, 28(2),133–157.

Wang, J. (2001). Ranking engineering design concepts using a fuzzy outrankingpreference model. Fuzzy Sets arid Systems, 119(1), 161–170.

Xu, Y., Sun, S., & Pan, Y. (2001). Constraint-based distributed intelligent conceptualdesign environment and system model. In IECON’O1: The 27th annual conferenceof the IEEE Industrial Electronics Society (pp. 2105–2110). Denver, USA: IEEE.

Zhang, W. Y., Tor, S. B., Britton, G. A., et al. (2001). EFDEX: A knowledge-based expertsystem for functional design of engineering systems. Engineering withComputers, 17(4), 339–353.