Computers in Industry 64 (2013) 68–79

B-Cube, behavioural modelling of technical artefacts

Vicente Chulvi *, Rosario Vidal 1

GID, Dpt. Enginyeria Mecanica i Construccio, Universitat Jaume I, Av. Sos Baynat s/n, E-12071 Castellon, Spain

A R T I C L E I N F O

Article history:

Received 19 January 2011

Received in revised form 25 September 2012

Accepted 2 October 2012

Available online 23 October 2012

Keywords:

Knowledge management

Behaviour

Functional design

FBS

Ontology

A B S T R A C T

A new model, B-Cube, is described for managing knowledge at the behaviour level of the function–

behaviour–structure framework. The model proposes a three-dimensional approach to the behavioural

modelling of technical artefacts using definitions based mainly on the meta-ontology DOLCE as concepts

of behaviour.

The present work aims to show how these terms and those from the NIST functional basis can

complement each other in functional design. It is assumed that this model achieves similar objectives

with behaviours to those obtained by the NIST functional basis with functions, i.e. the representation of

behaviours in CAD and KBS, a scheme for the modelling of behaviours and a universal set of behaviours.

The modelling language IDEF was adapted to be able to produce a graphic example of the modelling of

technical artefacts in the FBS framework using B-Cube terminology at the behaviour level.

� 2012 Elsevier B.V. All rights reserved.

Contents lists available at SciVerse ScienceDirect

Computers in Industry

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1. Introduction

The aim of this article is to present a new model of functionaldesign based on the function–behaviour–structure (FBS) frame-work that can be implemented in a solution-synthesis system andact as a link between different libraries of software applications.This model proposes a three-dimensional approach that usesdefinitions as behaviour concepts. It is assumed that this modelachieves similar objectives with behaviours to those obtained bythe NIST (National Institute of Standards and Terminologies)functional basis with functions, i.e. the representation of beha-viours in Computer Aided Design (CAD) and Knowledge BasedSystems (KBS), a scheme for the modelling of behaviours and auniversal set of behaviours. It is able to solve, a priori, theshortcomings encountered in previous research when trying tolink functional design with TRIZ-based Computer Aided Inventing(CAI) tools [1], e.g. loss of information within the use of taxonomiesat the functional level (such as ambiguities, synonyms andfunctions without correlations). The present work aims to showhow these terms and those from the NIST, the ReconciledFunctional Basis (RFB) [2], can complement each other infunctional design. The B-Cube (Behaviour Cube) model is basedmainly on the meta-ontology of DOLCE (Descriptive Ontology forLinguistic and Cognitive Engineering) [3,4] and on Garbacz’sfunctional development of it [5,6].

* Corresponding author. Tel.: +34 964729252; fax: +34 964728106.

E-mail addresses: chulvi@emc.uji.es (V. Chulvi), vidal@emc.uji.es (R. Vidal).1 Tel.: +34 964729252; fax : +34 964728106.

0166-3615/$ – see front matter � 2012 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.compind.2012.10.001

The concepts of function and behaviour, as part of the FBSframework [7,8], are at the core of our research. The FBS frameworkis widely used among designers for design process analyses, as it iscapable of representing the evolution of the design state from thestudy of protocols [9]. More recently, Gero and many otherresearchers have extended the study of FBS representation [10–15]. Within this framework, function is the abstract purpose thedesign is oriented towards. When the function is carried to a lowerlevel of abstraction and defines how the device or its componentswill be related to the uses for which they are employed and designed,we are defining the term behaviour. Devices and their parts havephysical structures and these structures and their relation with theenvironment determine the behaviours, which are in turn related tothe functions of the device [5,16–18].

The FBS framework allows computational modelling to becarried out, that is, software applications can be produced that areable to use search and explore procedures in order to find andcombine design-solving procedures for a problem represented byfunctions. Thus, several authors have tried to develop approachesand software applications to implement FBS-based procedures[19], while others have attempted to model function and/orstructure libraries to be implemented in functional reasoningprocesses [20–24]. The possibilities of these systems have beenincreased by function classifications achieved by means ofhierarchies [16] and the use of taxonomies.

A taxonomy consists of a group of concepts and relationshipsthat are organised hierarchically and whose concepts can bearranged as classes with sub-classes [25]. Taxonomies wereintroduced into the industrial world by Gershenson and Stauffer[26], but Szykman et al. [27] were the first to differentiate

V. Chulvi, R. Vidal / Computers in Industry 64 (2013) 68–79 69

functions with their extensive review of function terminologieswithin the engineering context from 1976 until 1998. Since then,several function taxonomies [28,29], as well as behaviour [5,30–32] and structure taxonomies [33] have been developed. In thecase of function taxonomies, the most significant are thoseprovided by the NIST [2] and those based on DOLCE [6,34].

The RFB allows overall product functions (especially from theelectromechanical and mechanical domain) to be modelled as setsof connected elementary sub-functions. Function is described in averb–object form and represented by a black-box operation onflows of materials, energies and signals. A sub-function is alsodescribed in verb–object form but it is represented by a well-defined basic operation on well-defined basic flows of materials,energies and signals. The black-box operations on general flowsrepresenting product functions are derived from costumer needsand the basic operations and basic flows representing sub-functions are arranged in libraries. Some authors have remarkedthat the descriptions of operations-on-flows may be betterunderstood as representing the behaviour of products and theircomponents rather than functions [16,35,36].

The RFB supports a number of engineering tasks, including thearchiving, comparison and communication of functional descrip-tions of existing products and the engineering design of newproducts. For example, the RFB has been used to develop and refinea web-based repository of design knowledge. This repository(which includes descriptive product information such as function-ality, physical parameters of components, manufacturing process-es, failure modes and component connectivity) contains detaileddesign knowledge about consumer products and the componentsthey are made up of. Design generation tools, like function–component matrices and design–structure matrices, can be readilycreated from single or multiple products and used in a variety ofways to enhance the design process [37]. The functional basis isapplied even outside the engineering field, for modellingfunctional processes, manual operations and human-centricprocedures [38].

Hence, a formal function representation is needed to supportfunctional modelling, which helps to clarify the meanings of termsand also to support representation of device knowledge forautomated reasoning [39]. In this regard, research efforts are beingmade to move functional basis towards a functional modellinglanguage [40]. Another line of research is the work of Garbacz [6],who reviewed the RFB and refined it formally, with the help ofthe conceptual framework of the DOLCE ontology [3]. This line ofresearch served as the inspiration for our model, B-Cube, whichis introduced in the present article.

Furthermore, in Section 7 a graphical modelling approach isproposed to model technical artefacts in the FBS framework byadapting the modelling language IDEF4 [41] and using the B-Cube’sterminology for the representation of behaviours. The aim is toachieve an intuitive, easy-to-understand model that can be used byany designer and also to represent the examples that are includedat the end of this article to provide a clearer illustration of howbehaviours are modelled with B-Cube. A more complex example ofa functional design expressed using the B-Cube model’s terminol-ogy can be seen in [42], where the authors defended the usability ofthis kind of model to establish a link between functional design andCAI tools.

2. Functions and behaviours

Despite the importance of function and behaviour in engineer-ing design, there are still some fundamental ambiguities andconfusion regarding their definition. The disadvantage of lackingconceptual consensus becomes an important issue when func-tional and behavioural descriptions have to be shared. This occurs

when, for instance, designing is modelled as a procedure in whichexisting knowledge about the relations between the functions,behaviour and physical structure of artefacts is partially retrievedfrom knowledge bases. In such cases, having a common set ofdefinitions is essential [43].

Chandrasekaran distinguishes between two general approachesto defining the functions of technical artefacts, called thefunctional representation approach and the functional modellingapproach [35]. The two approaches involve performing researchthat is mutually complementary. First, functional representationresearch provides the basic layer for the device ontology in aformal framework that helps to clarify the meanings of terms suchas function and structure, as well as supporting representation ofthe device knowledge for automated reasoning. Second, functionalmodelling research provides another layer in the device ontologyby attempting to identify behaviour primitives that are applicableto subsets of devices, with the hope that functions can be describedin those domains with an economy of terms. This can lead to usefulcatalogues of functions and devices in specific areas of engineering.With increased attention to formalisation, work on functionmodelling can provide domain-specific terms for function repre-sentation research in knowledge representation and automatedreasoning.

Functional modelling and functional representation mightmerge over time. Ontologies of the sort being developed byfunction modellers are certainly going to be useful for deviceknowledge representation because the current body of represen-tational primitives in artificial intelligence does not have terms forthe properties, behaviours and functions of devices in specificdomains [35].

In relation to the functional representation approach, Chan-drasekaran and Josephson [44] isolated five meanings of behaviourand two of function. The meanings of behaviour are characterisedusing the primitive notion of state variable:

� Behaviour as the value of some state variable of the artefact or arelation between such values at a particular instant.� Behaviour as the value of a property of the artefact or a relation

between such values.� Behaviour as the value of some state variable of the artefact over

an interval of time.� Behaviour as the value of some output state variable of the

artefact at a particular instant or over an interval.� Behaviour as the values of all the described state variables of the

artefact at a particular instant or over an interval.

The two meanings of function distinguished by Chandrasekaranand Josephson are called the device-centric and environment-centric meanings. Without going into detail, a device-centricfunction of an artefact is a behaviour of the artefact that is selectedand intended by some agent (in device terms). It is a function thatis described in terms of the properties and behaviours of theartefact only. An example of a device-centric function is ‘makingsound’ in the case of an electrical buzzer. An environment-centricfunction is, in contrast, an effect or an impact of this behaviour ofthe artefact on its environment, provided that this effect or impactis selected and intended by some agent (the ‘why’ of the device).This kind of function is conceptually separate from the artefact thatperforms or is expected to perform the function. Thus, ‘enabling avisitor to a house to inform the person inside the house thatsomeone is at the door’ is an environment-centric function of thebuzzer.

Functional modelling includes the functional basis model byStone and Wood [45] and the RFB [2]. Stone and Wood modelledthe overall product functions of technical artefacts, especially fromthe electromechanical and mechanical domain, as sets of

Table 1Extract of the Reconciled Functional Basis [2].

Primary function Secondary function Tertiary function

Branch Separate Divide

Extract

Remove

Distribute

Channel Import

Export

Transfer Transport

Transmit

Guide Translate

Rotate

V. Chulvi, R. Vidal / Computers in Industry 64 (2013) 68–7970

connected elementary sub-functions. An overall product functionof an artefact is defined as a general input/output relationship ofthe artefact having the purpose of performing an overall task, andis represented by a black-box operation on flows of materials,energies and signals. A sub-function performs a part of that overalltask and is represented by a well-defined basic operation on well-defined basic flows of materials, energies and signals, which arearranged in libraries that list all the possible basic operations andbasic flows.

Deng [16] attempts to address the problem of integrating thepurpose and the operation functions (sub-functions) in thefunctional modelling approach with function and behaviour inthe functional representation approach by restricting the designsto the conceptual stage of mechanical products. According to Deng,the function at the same level of abstraction as behaviour is theoperational function and it can be more specifically referred to asan action function, which is defined as ‘a physical interactionbetween two objects of interest, each of which may be acomponent of a design or the design itself and its environment’.Hence, function can be semantically classified into two types: apurpose function and an action function. A purpose function is ‘adescription of the designer’s intention or the purpose of a design’,whereas an action function is ‘an abstraction of intended anduseful behaviour that an artefact exhibits’. In the same line,Vermaas [36] argued that the operations-on-flows descriptions(sub-functions), as used by Stone and Wood, may be betterunderstood as representing the behaviour of products and of theircomponents.

3. Reconciled Functional Basis

The RFB [2] is a reconciliation and integration of othertaxonomies but mainly of the research conducted at the NIST[27] and the functional basis effort [45]. The main aim of the NIST isto develop a formal representation of functions with a hierarchicalvocabulary of standardised terminologies, focused on mechanicaldesign.

The NIST’s work stems from three specific needs: therepresentation of functions in Computer Aided Design (CAD), afixed scheme for modelling functions and a universal set offunctions performed by mechanical systems. The greatest achieve-ments reached by NIST are reduced ambiguity and increaseduniformity. To reduce ambiguity they defend that the more termsare used to refer to the same concept (synonyms), the greater thenumber of different ways to model a given concept there will be.Increased uniformity attempts to facilitate the exchange offunction information among different applications.

The RFB follows Pahl and Beitz’s [46] classic paradigm bydefining artefact functions in terms of flows. Pahl and Beitz defineda function as a relation between an input and an output of anartefact (under a specific goal). A flow is either a conversion ofmaterial, a conversion of energy or a conversion of signal.

This hierarchically organised vocabulary arranges the termsonto three levels of specification. The higher-level term providesfull coverage of the meaning of the terms included in this class.Moreover, terms at the same level within the same class aremutually exclusive. Table 1 shows an extract of the RFBtaxonomy.

Garbacz [6] criticised the RFB for having a number of differentshortcomings such as a lack of principles with which to explainthe three divisions, a lack of exclusivity, a lack of exhaustivenessin some divisions, and problems with ambiguity in terms andexamples. Garbacz proposed the philosophical category of states

of affairs (SoA) as the most adequate conceptual category ofartefact functions and the use of the DOLCE ontologicaltaxonomy [3].

4. Dolce ontology

DOLCE [3] is presented as an upper-level ontology or meta-ontology. In order to understand the development of the B-Cubemodel, it is necessary to start by defining some concepts belongingto DOLCE (Fig. 1) that were used to develop the B-Cube model,namely the descriptions of endurant (ED), perdurant (P) andquality (Q).

An endurant is an entity, all the parts of which are presentwhenever the entity is present at any time in its existence, that is,the entity is wholly present throughout time. This meaningcorresponds to the definition of structure in the FBS framework, soendurants are used as elements (artefacts or parts) that behavioursare related to. Since the B-Cube model refers to the behaviour level,endurants do not appear in the model directly because they arerelated to the structure level. Despite this, endurants help to definethe input of the B-Cube and, hence, the distinction betweenphysical endurants (PEDs) and non-physical endurants (NPEDs) isstill meaningful. PEDs correspond to tangible structures like ahuman person, a bottle or a screwdriver, while NPEDs correspondto the abstract domain, like a legal person, a social agent or a rolecarried out by a human.

A perdurant (P) was originally defined as an entity that is notwholly present over time, that is, not all its parts are presentthroughout all the time in which the entity is present. A perdurant‘happens’ in time, so during all the time that the entity is present,only some temporal parts of it are present at any given moment. InB-Cube, perdurants refer to the kind of behaviour that the structure(endurant) carries out. Thus, perdurants are necessary but on theirown are not enough to describe behaviours. The list of perdurantsprovided by DOLCE seems to cover all the needs in B-Cube in thisrespect. These perdurants are achievement, accomplishment, stateand process. Furthermore, if we look at the work of Garbacz [6], itcan be seen that he agrees with these definitions and applies themto define the sub-taxonomy of participation functions, where theyare understood as occurring when an endurant participates in aperdurant.

Fig. 2 shows the classification algorithm of these termsaccording to the DOLCE definition: cumulative (or stative) iswhen the mereological sum of two cases of the same typemaintains that same type. For example: an occurrence of corrosionis cumulative since the sum of two instances of corrosion is still anoccurrence of corrosion. Within cumulative occurrences, wedistinguish between states and processes according to home-omericity. Homeomeric is when all the temporal parts aredescribed by the same expression used for the whole occurrence,so corroding is classified as a state but shaping is classified as aprocess, since there are (very short) temporal parts of a shapingthat are not themselves shaping. Non-cumulative (or eventive)occurrences are classified according to their atomicity. Atomic iswhen the case is immeasurably short in time, that is, it has noproper parts. Thus, the event is an achievement if it is atomic,

Fig. 1. The DOLCE ontology [3].

V. Chulvi, R. Vidal / Computers in Industry 64 (2013) 68–79 71

otherwise it is called an accomplishment. So ‘to switch off’ isatomic (t ! 0), while ‘to extract’ is non-atomic (the process ofextracting something is clearly supposed to be >0).

Finally, qualities are defined as the basic entities that can bemeasured and are inherent to other entities (endurants orperdurants). Thus, every entity has a certain number of qualitiesthat define it. DOLCE distinguishes between physical qualities(PQs), abstract qualities (AQs) and temporal qualities (TQs). PQsare those that are inherent in PEDs (e.g. the weight, the position inspace or the energy state). DOLCE provides only one definitionwithin this group (spatial location), but it leaves the group open tonew parameters, that is, it explicitly makes room for othermembers in some of its divisions. Garbacz [6] took advantage ofthis fact to increase the number of PQs to three, with the addition oftopological connectedness and energy. However, these threeconcepts do not fulfil all the needs that B-Cube generates in orderto define all behaviours. For this reason the concept of the blackbox model, defended by several authors and in agreement with the

Perdurant

State Process

Cumula�ve?

Homeomeric?

Yes

Yes

No

Fig. 2. Classification algorithm of perdu

research conducted by NIST, is used here [40,46,47]. This modelemphasises the fact that for each different kind of flow, when it actsover a specific function that is represented by a black box withinput and output flows, this function displays a different behaviourdepending on the type of flow that has acted on it. It can thereforebe deduced that the three kinds of flows, e.g. energy, signal andmaterial, are suitable for defining behaviours and, consequently,these terms can be added to the group of PQs. To sum up, the PQsused in B-Cube are:

� Spatial location: related to the position of a PED in space. Movingan object belongs to this category.� Topological connectedness: concerned with the sort of connec-

tion at the topological level on which the PED is located. Breakingor joining an object corresponds to this group.� Energy: refers to the energy state of the PED. Freezing water or

charging a battery are examples of behaviours classified withinthe energy group.

Achievement Accomplishment

Atomic?

Yes

No

No

rants according Masolo et al. [3].

Fig. 3. Axes for the representation of behaviours.

Fig. 4. B-Cube model.

V. Chulvi, R. Vidal / Computers in Industry 64 (2013) 68–7972

� Material: related to the physical magnitude or material propertyof the PED that is affected by the perdurant. Increasing theweight or changing the colour of an object is examples thatcorrespond to this group.� Signal: related to actions involving PEDs when they act as signals.

Examples could be increasing a wave or a mobile phone that issending a signal.

On the other hand, when behaviour is related to an NPEDinstead of a PED, it must be defined by an AQ. Although bothDOLCE’s and Garbacz’s work defines AQs as those related to NPEDs,it does not put forward any value for them, since this region doesnot affect the artefacts themselves. Thus, the AQ region is set asidefor future work.

TQs are those that are inherent in perdurants. They refer to theway that PQs or AQs are affected by perdurants over time. As in thecase of PQs, DOLCE provides only one definition within this group,temporal location (TL), and it leaves the group open to newparameters. But in this case, instead of increasing the group’sparameters, Garbacz [6] developed TL with the terms initial SoAand final SoA. In the B-Cube model, TL is taken as being equal to TQin order to take advantage of Garbacz’s approach. Thus, initial SoAis defined as a behaviour which a perdurant performs byeliminating or reducing an initial PQ, e.g. cooling an object makesit lose its initial energy. Final SoA works in the opposite way, that is,the PQ is obtained (or increased) as a consequence of theperdurant. Thus, heating an object causes it to obtain a finalenergy. In order to cover all the range of behaviours, it is necessaryto add a term to describe those which do not act by reducing orincreasing PQ. For example, converting energy does not change theenergy level (First Law of Thermodynamics), but nonetheless it is abehaviour that needs to be described. This new term has beencalled immutable SoA. At this point it is important to emphasisethat the application of the definition of TL in the PQ spatial locationneeds to be carried out in agreement with the other terms. It istherefore easy to see that initial SoA in energy means that theenergy is present at the beginning and the action decreases it; intopological connectedness, it means that the object is connectedinitially and then loses this connection. But it may not be so easy toperceive how TL affects spatial location, because an object alwayshas a position in space. Thus, by analogy to other terms, TL is arelative position. In other words, initial SoA means that the initialposition of an object is close to another element and the actionseparates the object. In the same way, when an object hastopological connectedness with another, they are closer than ifthey had lost that connection, although this occurs on amicroscopic scale.

5. B-Cube

B-Cube is a model for representing knowledge on thebehaviours layer within the function–behaviour–structure frame-work based on the DOLCE ontology. The basic idea when using theDOLCE ontology is that a behaviour b of a technical artefact a in aperdurant e, where a perdurant is an entity that is only partiallypresent at any time it is present, is the specific way in which a

occurs in e [43].Although Borgo [43] formalised artefact functions as intended

behaviours, in this state of the research the authors preferred touse Deng’s concept of purpose function [16] in the function layerand to use the RFB taxonomy directly for such functions.

In the previous section we described the terms endurant (ED),physical (PED) and non-physical (NPED), perdurant (P), physicalqualities (PQs), abstract qualities (AQs) and temporal qualities(TQs) as they are used in the B-Cube model. Endurants weredefined as structures or elements. A structure that is carrying out a

function has a specific behaviour, so it is used as input in B-Cube. Asthe number of endurants in the universe tends to infinity, it doesnot seem to be practical to classify behaviour in classes. But it hasbeen shown that endurants are related to qualities (PEDs to PQs,and NPEDs to AQs) and these exist in a finite number. Therefore,PQs and AQs describe the X-axis of the B-Cube. In the present articlethe X-axis will refer only to its physical part, since, as said above, theabstract part has been set aside for future work. On the other hand,perdurants were defined as ‘the kind of behaviour’ and so, bydefinition, perdurants can be used to define a behaviour. They areassigned to the Y-axis. Moreover, TLs were also related to theprevious terms, since they were defined as the ‘direction’ in which aperdurant affects a PQ. As a result, TLs are set on the Z-axis, and theycomplete the three dimensions needed to build all the vectors thatdefine behaviours in the B-Cube model. Fig. 3 shows the frameworkof the B-Cube model with the three axes that make up the model andwhere the previously mentioned values will be allocated.

Therefore, behaviour is now represented as (xi, yj, zk), where xi

refers to the PQ affected by the behaviour, yj is the kind ofperdurant, and zk means the temporal location of the perdurant.Fig. 4 represents the physical part of the B-Cube model with all itsvalues, which is better explained in Table 2. So, for example, ablowtorch that is used to weld pipes has a main behaviour (2, 3, 3).That is, X = 2 = topological connectedness, due to the fact thatwelding refers to a physical state of connection. Y = 3 = accom-plishment, from the algorithm in Fig. 2 it can be seen that weldingpipes is non-cumulative, because to weld a pipe + to weld a

Table 2Definition of B-Cube terms.

Axis Value Term Significance Examples

X (physical quality) 1 Spatial location Position of a PED in space Move an object

2 Topological

connectedness

The kind of connection at a topological level on which a PED finds itself Break an object

Join an object

3 Energy Energetic state of a PED Freeze water

Charge a battery

4 Material A physical magnitude of the PED that is affected by the behaviour Increase weight

Change colour

5 Signal Actions referred to PEDs when they act as signals Increase a wave

A mobile phone

sending a signal

Y (perdurant) 1 Process The behaviour is cumulative and non-homeomeric To run

2 State Cumulative and homeomeric To sit

3 Accomplishment Non-cumulative and non-atomic To give a lecture

4 Achievement Non-cumulative and atomic To break a glass

Z (temporal location) 1 Initial SoA The behaviour makes the initial PQ or AQ reduce or disappear To cool an object

2 Immutable SoA The behaviour does not vary the degree or quantity of PQ or AQ affected by it To convert energy

3 Final SoA The behaviour makes the degree or quantity of PQ or AQ increase or appear To warm an object

Table 3Examples of two different behaviours that perform the function ‘remove’.

FRB Remove Remove

B-Cube (2, 1, 1) (2, 2, 1)

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pipe = to weld two pipes, and it is non-atomic, because to weldpipes requires more than an instantaneous action. And Z = 3 = finalSoA, because of the fact that topological connectedness is notpresent at the beginning, but it is obtained in the end.

The B-Cube model can also present an abstract part, which isnot represented in the RFB, by using AQs instead of PQs. NIST doesnot take the abstract actions into consideration because it isfocused on mechanical design. This fact is of no importance whendesigning physical objects, devices or artefacts, where the NISTfunctional basis works perfectly well, but the abstract part of B-Cube leaves an important door open to organisational and processdesign. Here there are some structures that can act as physicalthings, but they can also support an abstract behaviour or role[48,49], like the case of human beings or artificial intelligencedevices.

6. B-Cube version of Reconciled Functional Basis

The B-Cube model was deployed with each of the possiblevalues for the three axes X, Y and Z (according to Table 2) and asearch was conducted for each of these elements to find the verbthat fitted the secondary and tertiary levels of the RFB taxonomybest. Despite the fact that tertiary level terms are supposed to beincluded in secondary level ones, the usage of both levels toestablish correlations is justified for two main reasons. First, thelevel of abstraction expected to be achieved with the B-Cube modelmakes the slight differences in meanings between levels quiteimportant. And the second reason is the fact that NIST also usesthese levels when establishing correlations with other taxonomies[2].

Correlations were made by taking the B-Cube terms one by one.For each of these terms, a function from the NIST functional basis issought for which the behaviour can be a concrete action of itsabstract meaning. As a result of these correlations, we canappreciate that one function verb from the RFB can be performedin several specific ways, that is, through different behaviours, in B-Cube. Table 3 shows an example of two different ways of carryingout the same function expressed by the RFB verb ‘remove’. Bothstructures (objects or substances) act by causing the target to loseits initial (Z = 1) topological connectedness (X = 2), but while thesander machine entails a long-term continuous and non-homeo-meric process (Y = 1), ambient corrosion acts in a long-termcontinuous homeomeric way (Y = 2).

Another case is that two different verb functions in the RFB canlead to the same behaviour in B-Cube. This happens when one ofthe possible ways to achieve a function can be described by the

same three properties as another one. For example, when thefunction ‘translate’ means a process (Y = 1) of moving an object inspace (X = 1) without a defined direction, that is, neitherapproaching nor moving away (Z = 2), the behaviour is the sameas the function ‘rotate’, where it acts as a process of spinning anobject, and so it neither approaches nor moves away from thereference point. This does not mean that the B-Cube model lacksunambiguity. On the contrary, it aims to increase the specificitypresented by the FRB, since the term ‘translate’ could also mean tobring the object closer (Z = 3) or to move it away (Z = 1). The simpleword ‘translate’ can also be understood as a movement carried outin a more instantaneous way (Y = 4).

Table 4 shows the assignments of the B-Cube terms to RFBverbs. The third column shows other corresponding terms in orderto make it easier to grasp the specific meaning of each behaviour. Inthe same table it can be seen that there are some behavioursrepresented in the B-Cube model that have no correlation with theRFB, since the behaviours in B-Cube were defined by combiningtheir possible parameters, which ensures that no term or meaningcan be omitted.

B-Cube was built from the DOLCE meta-ontology, meaning thatthere is knowledge hidden inside the term, or taxon. Thus, thefunctional basis is a taxonomy, which means that the tertiary classterm ‘join’ belongs to the secondary level group ‘couple’, which is atthe same time a part of the primary group ‘connect’. As can be seenin Fig. 5, when we structure the B-Cube terms hierarchically, theyare systematically repeated. But this is because it is not a simpleclassification. Here, each chosen branch provides the final termwith a specific and unambiguous meaning. This is one reason fordefending the idea that the path is more important than the finalterm in the B-Cube model. As a result, when we are talking aboutthe path (2, 4, 3), we are referring to an action that affects thetopological connectedness (X = 2) of an object, in a non-cumulativeand atomic way (Y = 4), and which makes the object achieve thatconnectedness (Z = 3), regardless of the name we have chosen to

Table 4Assignment of B-Cube terms to RFB verbs.

B-Cube RFB Other correspondences

(1, 1, 1) Remove; extract Bail out

(1, 1, 2) Translate; rotate Move; vibrate; spin;

(1, 1, 3) Implant; insert; install

(1, 2, 1) Repel; keep separated

(1, 2, 2) Allow DOF; secure Not allow DOF; hold up; orient

(1, 2, 3) Attract; keep close

(1, 3, 1) Guide; remove Shift

(1, 3, 2) Position Align, orient

(1, 3, 3) Introduce; put in; approach

(1, 4, 1) Separate; export

(1, 4, 2) Stop Locate

(1, 4, 3) Import Reach

(2, 1, 1) Remove Carve; polish; clean; erode

(2, 1, 2) Stabilize Stabilize

(2, 1, 3) Secure; couple Fix; fuse; bind; screw

(2, 2, 1) Remove Cleave; corrode

(2, 2, 2) Contain Protect; shield

(2, 2, 3) Mix

(2, 3, 1) Separate Disjoin; disincrust

(2, 3, 2) Inhibit; secure Insulate; retain

(2, 3, 3) Join Assemble

(2, 4, 1) Divide Split; tear; rip; disincrust

(2, 4, 2) Block

(2, 4, 3) Link Touch; prick; stick; attach

(3, 1, 1) Collect Consume

(3, 1, 2) Transmit; convert Conduct; channel; transform

(3, 1, 3) Convert Generate; energize

(3, 2, 1) Convert Cool; freeze; condense; solidify

(3, 2, 2) Store Conserve; transform

(3, 2, 3) Convert Warm; evaporate; melt

(3, 3, 1) Unload; discharge

(3, 3, 2) Regulate Regulate

(3, 3, 3) Load; charge

(3, 4, 1) Prevent Switch off; stop; turn off

(3, 4, 2) Guide Switch

(3, 4, 3) Actuate Switch on; turn on

(4, 1, 1) Shape Compact; compress

(4, 1, 2) Condition; shape Adapt; prepare; deform

(4, 1, 3) Expand; stretch; enlarge

(4, 2, 1) Decrement Reduce; dampen; weaken

(4, 2, 2) Measure

(4, 2, 3) Increment Magnify; strengthen; increase

(4, 3, 1) Decrement Decrement; attenuate

(4, 3, 2) Change Normalize; adjust

(4, 3, 3) Increment Amplify

(4, 4, 1) Decrease

(4, 4, 2) Change Invert

(4, 4, 3) Increase

(5, 1, 1) Display; export Emit

(5, 1, 2) Transfer Identify

(5, 1, 3) Detect; import

(5, 2, 1) Display

(5, 2, 2) Transmit Conduct; guide

(5, 2, 3) Sense

(5, 3, 1) Display Emit

(5, 3, 2) Process Compare

(5, 3, 3) Indicate Record; register; import

(5, 4, 1) Indicate Show

(5, 4, 2) Process Check

(5, 4, 3) Measure Locate

V. Chulvi, R. Vidal / Computers in Industry 64 (2013) 68–7974

designate that path. By definition, several terms such as ‘touch’,‘prick’, ‘stick’, ‘attach’, ‘link’, ‘join’, and others can fit that meaning,but the same terms can also be understood as another pathdepending on the user. This is one of the main problems thatauthors find when trying to set up a taxonomy, as could be seen inthe work on the RFB set of functions carried out by Hirtz et al. [2].There, it can be seen how several terms belonging to correspon-dences appear in different positions within the reconciledtaxonomy, depending on the author’s perception of it. For example,one author can understand the verb ‘join’ as (2, 3, 3), another as (2,1, 3) and a third one as (2, 4, 3), but the way this final joined state is

achieved is different. Hence, a single word could be set for eachterm within a taxonomy or ontology just to make the model easierto understand, but for the time being it seems better to keep avector terminology in order to avoid the ambiguity that may bepresent in the interpretation of one simple verb.

7. Graphical modelling

In order to represent the models graphically, the authorsresorted to the concepts of the IDEF3 [50] and IDEF4 [41] modellinglanguages. IDEF3 is oriented towards process design and IDEF4towards the design of objects.

The basic IDEF4 box, which has rounded corners, was selectedto represent functions. The same kind of box was chosen torepresent behaviours, but in this case a band was added on the left-hand side in order to differentiate them from functions. Regardingstructures, the basic IDEF4 box, which has square corners, wastaken in this case. Structures regarding solution design andenvironment restrictions are differentiated by means of a bandalong the left-hand side added to the latter, as in the case offunctions and behaviours. All these boxes have their headerdivided into two differently sized spaces, the wider one for thename of the function/behaviour/structure and the narrower onefor its number and level, as in the IDEF3 modelling language. Thisname function, behaviour or structure corresponds to the purposefunction in the NIST RFB taxonomy in the case of representingfunctions, to the terms of the B-Cube model when representingbehaviours, and structures are called by their usual names as theyappear in dictionaries. On the other hand, the numbers that areused in the boxes are simple units for first level components (1, 2,3, . . .), tens for the second level, where the first digit corresponds tothe preceding first level component, hundreds for the third level,and so on. Thus, for example, a behaviour numbered 11 is the firstbehaviour derived from the behaviour labelled as 1. Numbers aresituated in the upper right corner in the case of functions andstructures, and in the upper left corner in the case of behavioursand restrictions, so as to be able to differentiate between thembetter. The body of the boxes is also divided into two parts, but inthis case the division is horizontal. The upper part is for showingthe active attributes in the design being represented, while thelower part is used to show the rest of the possible but not activeattributes. Additionally, if the box is represented with a blackshadow, it means that this function/behaviour/structure com-prises a sub-diagram. A sub-diagram is defined as a high-detailrepresentation of one part of a diagram. For example, a wheel canbe a complete part of the diagram representing a bicycle, while itcan present a sub-diagram where it is sub-divided into its smallerparts: rim, tyre, spokes, and so forth. Sub-diagrams are representedon separate sheets and each numbering in that new diagram ispresented as a numbered scheme with the first digit indicating thesource component. For example, if structure 3 has a sub-diagram,all structures within this new diagram are preceded by a 3 (3.1, 3.2,3.21, . . .). Fig. 6 shows the four different kinds of boxes.

These boxes are represented in three layers corresponding tofunction, behaviour and structure (restrictions are represented inthe same layer as structures). Different kinds of relationshipsbetween different components of the diagram are shown in Fig. 7.Functions represent their correspondence with behaviours bymeans of arrows. The relations between one behaviour and thoseon a lower level can be represented in two different ways,depending on whether the new lower behaviour is caused orrequired by the upper-level one. The relation of a behaviour causedby the previous one is represented by a line that ends in a blacktriangle, and the relation of a behaviour required by the previousone is represented by a line that ends in a white triangle. Therelations between behaviours and structures or restrictions are

Fig. 5. Extract from the B-Cube ontology.

V. Chulvi, R. Vidal / Computers in Industry 64 (2013) 68–79 75

represented with a line with a small box like the ones used in IDEF3to indicate the ‘and’ and ‘or’ sentences, but in this case an ‘O’ willappear inside the boxes if the structure or restriction is the objectof the corresponding behaviour and an ‘S’ if it is the subject.

Fig. 6. Box representations for functions, b

Furthermore, the letters ‘O’ and ‘S’ also have a subscript with thenumber of the corresponding behaviour that affects the structuresor restrictions, in order to make the diagram easier to understand.Lastly, also with the aim of simplifying the diagrams, two implicit

ehaviours, structures and restrictions.

Fig. 7. Relationships between the different components of the diagram model.

V. Chulvi, R. Vidal / Computers in Industry 64 (2013) 68–7976

behaviours commonly present in all artefacts are representedthere directly without the need for the corresponding behaviourboxes. These behaviours are (2, 2, 2), which refers to the state ofone structure containing another one, and (2, 2, 3), referring to thestate of one structure attached to another one. The first case isrepresented by an upper-lower level relation between structuresin the form of a simple line. The second case is represented bydrawing the two boxes joined by one side.

Fig. 8. Representation of the sch

8. Examples

Two examples are given in this section in order to clarify the useof the B-Cube model together with the RFB for design knowledgerepresentation within an FBS framework.

The first example is a sander machine (Fig. 8). The purposefunction is ‘remove’, which is on the third level of the RFB (Table 1)derived from the second level function ‘separate’, which in turn

eme of a sander machine.

Fig. 9. Representation of the scheme of a guillotine paper cutter.

V. Chulvi, R. Vidal / Computers in Industry 64 (2013) 68–79 77

stems from the first level function ‘branch’. From the correspon-dence between terms shown in Table 4 it can be seen that thisspecific function can be performed in four different ways: (1, 1, 1),(1, 3, 1), (2, 1, 1), and (2, 2, 1). As the action of the sander affects thetopological connectedness of the object (for example, the surface ofa piece of wood) and not its position in space, the value of X must be2. Moreover, the way the action is performed can be considered acumulative and non-homeomeric process, that is, Y = 1, so the onlybehaviour remaining is (2, 1, 1). Topological connectedness ispresent at the beginning of the action and is lost while it is beingperformed (Z = 1), so the choice that was made is the correct one. Itcan be seen in the image that the structure that performs thisbehaviour is the sanding wheel, which is connected to a casing thatcontains a motor. This motor moves the sanding wheel in a (1, 1, 2)way, that is, the behaviour affects the spatial location (X = 1) with acontinuous process (Y = 1), but neither approaching nor moving itaway (Z = 2), just rotating it. This motor needs to be powered, so astructure capable of conducting energy is needed. The wire fulfilsthese requirements, since it performs the behaviour related to thestate (Y = 2) of allowing the energy flow (X = 3) without increasingor decreasing it (Z = 2). Lastly, the casing that is connected to thewire and the sanding wheel, and which contains the motor, isthe part that is held by the user and represented by the behaviour(1, 2, 2).

The second example is the case of a guillotine paper cutter. InFig. 9 it can be seen that the main function is represented by theRFB verbs ‘branch’/‘separate’/‘divide’, so it shares first and secondlevels of the taxonomy with the last example, but it is different inthe third-level term. Searching for correlations in Table 4, the onlyB-Cube term corresponding to ‘divide’ is (2, 4, 1), since it affects thetopological connectedness (X = 2) in a non-cumulative andinstantaneous way (Y = 4) and it causes loss of the initialtopological connectedness (Z = 1). The structure chosen forcarrying out this behaviour is a blade, which has a handle atone end in order to protect users from hurting themselves whenusing it. This use is represented by the behaviour (1, 4, 3), thatis, the user changes the spatial location (X = 1) of the handle in a

non-cumulative and instantaneous way (Y = 4) in order to move itcloser to the paper (Z = 3).

9. Conclusions

The main objective achieved in the present work is to develop amodel for representing, managing and modelling knowledge onthe behaviour level of the function–behaviour–structure frame-work. This model is supposed to be clear and unequivocal and it isfocused on optimising and automating decision-making in theproduct design process by means of knowledge managementtechniques or tools. It is also aimed at achieving better knowledgetransfer by minimising the loss of information.

In the present article, the B-Cube model represents thebehaviour level and it acts as the link between the functionlevel, represented by NIST’s Functional Basis, and the structurelevel. The comparison between the NIST functional basis and theB-Cube model in Section 6, where B-Cube was expanded in eachof the possible values for the three axes and the best secondaryand tertiary levels of the RFB taxonomy were assigned (ifpossible) to each vector, allows several conclusions to be made.The first one is that, while terms in the functional basis aregeneric, the ones in the B-Cube are more specific, since itrequires the behaviours. This higher level of concretenesspresented by behaviours has shown that there are possibleactions that are not reflected in the NIST functional basis. Thisfact could also act as a check for the NIST functional basis, so thecombinatory property of the B-Cube model ensures that nomeaning is omitted.

Another way to explain this difference in level of specificitybetween the NIST functional basis and the B-Cube model is that,while the former is clearly a taxonomy, B-Cube acts more like anontology. This seems logical because B-Cube was built from theDOLCE meta-ontology. As can be seen in Fig. 5, each chosen branchprovides the final term with a specific meaning. This is one reasonfor defending the idea that the path is more important than thefinal term in the B-Cube model. A single word could be set for each

V. Chulvi, R. Vidal / Computers in Industry 64 (2013) 68–7978

term, just to make the model easier to understand, but for the timebeing it seems better to keep the vector terminology in order toavoid the ambiguity that may be present in the interpretation ofone simple verb.

The importance of behaviour lies in its concreteness (in contrastto the generality of function) and also in its direct relation withstructures. In the B-Cube model, behaviours are defined by a (x, y, z)vector, which offers several advantages. On the one hand, itprovides more information than a single taxon, since there arethree defining parameters instead of one. On the other hand,vectors do not have the ambiguity that may be present in theinterpretation of taxa and, moreover, it is easier for softwareapplications to manage vectors. As has been seen earlier, bymanaging 12 factors (five X-values, four Y-values and three Z-values), B-Cube is able to represent 60 different but comprehen-sively defined kinds of behaviour. This low number of factors to bemanaged will make software applications easier to build and fasterto work with.

This fact opens up the chance of enabling the implementation ofsoftware tools that support behavioural modelling within the FBSframework, while at the same time achieving the objective ofdeveloping a common basis of standardised terms for the exchangeof behaviour-based information. The possibilities of the B-Cubemodel include its use in KBS to automate the design process andlinking this kind of system with other CAD, CAM or CAI toolsthrough model libraries in order to improve it, as can be seen inparallel work [42], where the authors defended the usability of thiskind of model to establish a link between functional design and CAItools with an example. Future work will study these openpossibilities.

Following the DOLCE’s structure in the development of themodel, it can be seen that similar results can be achieved with therole behaviours if the abstract qualities are considered instead ofthe physical qualities. Future work will also be oriented in thisdirection, as it is considered that functional design including rolebehaviours can lead to new horizons in the fields of artificialintelligence and videogames.

Acknowledgements

This work was supported by the Spanish Ministry of Educationand Science (ref. DPI2006-15570-C02-00) and the European Fundfor Regional Development (FEDER).

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Vicente Chulvi is Professor at the Department of

Mechanical Engineering and Construction at the Uni-

versitat Jaume I of Castellon. Chulvi earned a BSc in

Mechanical Engineering (2001), an MSc in Mechanical

Engineering (2007) and a PhD in Engineering (2010).

Rosario Vidal is Chair of Engineering Projects. For the

past 15 years she has held different academic positions

at the Universitat Jaume I in the Department of

Mechanical Engineering and Construction. She is

director of the GID (Engineering Design Group). Vidal

earned a BSc in Industrial Chemical Engineering (1990),

an MSc in Mechanical Engineering (1993) and a PhD in

Engineering (1996).

Industry 64 (2013) 68–79 79