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International Journal of Computer IntegratedManufacturing

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Integrating views of properties in models of unitmanufacturing processes

Peter Denno & Duck Bong Kim

To cite this article: Peter Denno & Duck Bong Kim (2015): Integrating views of propertiesin models of unit manufacturing processes, International Journal of Computer IntegratedManufacturing, DOI: 10.1080/0951192X.2015.1130259

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Integrating views of properties in models of unit manufacturing processes

Peter Denno * and Duck Bong Kim Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA

( Received 4 November 2014; accepted 15 August 2015 )

This paper investigates the potential advantages and dif culties of integrating predictive model equations in models of unit manufacturing processes. The method described uses metamodels and semantic web technology to relate equations, asobjects, to downstream activities. The potential advantages of this include enhanced knowledge re nement and reuse,traceability, model veri cation and agility in production activities. In an example usage, the authors apply the method to thedevelopment and downstream usage of predictive models of a selective laser sintering process. Use of equations as objectsenables linking them with supporting evidence, property de nitions and dimensions in an engineering notebook paradigm.Model-based interpretation of the equations enables composition in trade studies and mapping to downstream process parameter optimisation.

Keywords: modelling methodology; predictive models; design of experiments; unit manufacturing processes; ontologies

1. Introduction

The evolution towards an industrial internetwill enable morene-grained control over the resources, both physical and

informational, used in industrial operations (General Electricand Accenture 2015). Predictive model equations, expres-sing a relationship among state variables, process controlsvariables and a response variable, are such informationresources. Oftentimes, however, the intent of these equationscannot be accurately interpreted outside the software toolandanalysis where the equation is established. This paper con-siders new means of sharing knowledge expressed as pre-dictive model equations. It also suggests the advantages andchallenges of doing so. Sharing and composing predictivemodel equations, for example, to produce a surrogate modelor optimisation, requires knowledge of what is beingexpressed. Key to that is grasping what is intended by each property referenced as a variable of the equation. The authorscall the intended meaning of a property its ‘ property sense ’ .Property sense is analogous to the notion of word senseemployed in ordinary dictionaries (Wikipedia 2015). Thisanalogy is not perfect however; whereas there may be littlerelation among the senses of a word, the various senses of a property may be united by a common general de nition.

That de nition may include dimensionality, and propertysenses may be distinguished by differences in units of mea-sure, measurement conditions, provenance and propositionalattitude. The value of a property may be expressed by anumber, a range of values, a distribution of values or amathematical expression that might reference other propertyvalues. Information providing property sense can be used todetermine the validity of using the property in a given

analytical context. In this work, predictive model equationsare represented as structured information objects that can beintegrated with ontology-based information describing the property sense of each of the variables. This paper arguesthat rigorous representation of property sense and propertyrelations is necessary if mathematically formulated informa-tion (MFI) is to be elevated into new roles.

The contribution of this paper to the literature is (1) ananalysis of the requirements that must be met to elevateMFI to new roles, (2) a discussion of how these require-ments can be met and (3) a discussion of standards-based

research prototype tools available to further explore the problem space. MFI, properly organised, will serve thegoals of the industrial internet by providing more agile useof analytical tools, eschewing tool application protocolinterfaces (APIs) and graphical user interfaces in favour of lightweight services and an engineering notebook para-digm. This paper contributes to that goal.

Throughout this paper, ideas are illustrated with anexample in selective laser sintering. Selective laser sinter-ing is a powder-bed additive manufacturing (AM) processin which, iteratively, a thin layer of metal powder isapplied to the top of the work piece and is bonded to it with laser heating. The laser-beam focus area is typicallyvery small compared to the area of the top of the work piece; so, the beam is made to run paths over the layer,sintering the area under the beam as it goes. Scan speed isthe speed at which the beam moves over the part andhatch distance is the distance between parallel paths.The case study concerns the use of experimental designto develop predictive models of the laser sintering process.

*Corresponding author. Email: peter.denno@nist.gov

International Journal of Computer Integrated Manufacturing , 2015http://dx.doi.org/10.1080/0951192X.2015.1130259

This work was authored as part of the Contributor ’ s of cial duties as an Employee of the United States Government and is therefore a work of the United States Government. Inaccordance with 17 USC. 105, no copyright protection is available for such works under US Law.

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The authors also suggest how the representation of the predictive models as web-linked equation objects facili-tates veri cation of the analysis and downstream use of the knowledge.

The paper is organised as follows. Section 2 discussesrelated work. Section 3 discusses the essential require-

ments of the methodology in terms of semantic interoper-ability, data modelling and system design. Section 4illustrates use of the methodology in an example problemin which experimental design is used to establish predic-tive models of an AM process (Michopoulos, Lambrakos,and Iliopoulos 2014 ). The example demonstrates howinformation from production facility sources is integratedinto an IPython notebook (ipython.org 2014 ) where theanalyses are performed. Of course, application of themethodology is not limited to this usage scenario.

2. Related work

Our goal is to provide functionality similar to that of theProcess Analytical Technology (PAT), but for discretemanufacturing rather than pharmaceuticals. The goals of PAT were rst described by the US Food and DrugAdministration (US FDA 2004 , Scott and Wilcock 2006 ). Rathore et al. describe PAT as ‘ a system for design-ing, analysing, and controlling manufacturing throughtimely measurements (i.e., during processing) of criticalquality and performance attributes of raw and in-processmaterials and processes, with the goal of ensuring nal product quality. ’ (Rathore, Bhambure, and Ghare 2010 ).Though it appears that PAT has been implemented, there islittle record of it in the literature. The authors are not aware of any implementation of it that emphasises themanagement of symbolic, mathematically formulatedinformation, our key contribution.

Concerning the management of MFI, the authors use anotebook paradigm and web-based data. Andrejev et al.(2013 ) integrated MATLAB (MathWorks 2014 ) with aScienti c SPARQL Database Manager and SciSPARQL, providing array operations, function views, expressionsand de nition of external functions for scienti c comput-ing and laboratory data management. Our goals andapproach differ however; we seek to support manufactur-ing. We do so by integrating symbolic expressions withmetamodels and property ontologies.

One of our goals is to facilitate integration betweenanalytical tools and production information infrastructure.Our approach to this problem emphasises the use of toolmetamodels and mapping technologies. Terkaj et al.sought similar goals, but they used an integrated frame-work, including a Virtual Factory Manager and VirtualFactory Data Model (Tolio et al. 2013 , Terkaj, Pedrielli,and Sacco 2012 ).

The authors believe that there is great value to industryand the research community in using existing technical

infrastructure wherever possible. Our work uses standards:Web Ontology Language (OWL) (W3C 2012 ), TheResource Description Framework (RDF) query language,SPARQL (W3C 2013 ), Meta Object Facility (OMG 2011 )and queries, views, and transformations (QVT) (OMG2011 ). The work can be implemented entirely in open

tools, including IPython notebooks (ipython.org 2014 ),the Eclipse Modelling Framework (Eclipse Foundation2014 ) and ontology editors such as Protégé (StanfordCenter for Biomedical Informatics Research 2014 ).

3. Modelling properties and predictive modelequations

3.1. The value of sharing predictive model equations

Predictive model equations can serve key roles in produc-tion. The equations express enduring knowledge of therelationships between inputs and outputs. Physics-based predictive models can be tested for consistency with estab-lished knowledge; they may eventually become part of theestablished conceptual schema. Empirically derived pre-dictive models can be re ned through established statisti-cal techniques, and uncertainty in the delity of the t can be quantitatively expressed. Figure 1 depicts the variousroles that predictive model equations play in manufactur-ing operations. As depicted, baseline unit process controlscan be established through process knowledge expressedas these equations; the knowledge can be re ected in process plans. A unit process response (the measuredvalue, not the predicted value) can be viewed as a dis-turbance in downstream process steps. Likewise, a

response to disturbances from outside the system bound-ary (lower left of the gure) can be formulated by com- posing equations in an analysis or optimisation leading toimproved control of the process. For example, in a selec-tive laser sintering process, equations predicting the tensilestrength, surface roughness and conformity to designdimensions can be combined for this purpose. Such inte-grated viewpoints are useful to process optimisation,whereas the viewpoints of individual response functionsare useful to ‘ what if ’ investigation. Abstraction and com- position over unit process responses yield key perfor-mance indicators (lower right of gure).

3.2. The challenges of sharing predictive model equations

Predictive model equations can be represented as struc-tured information objects expressed as an equivalence between a function of state and process control variables, xi and ui, respectively, and a response variable yi, that is, as f i( x1 , . . . xn ,u1 , . . . , um) = yi. In the interpretation of the equa-tion, in order to make sense of what is being asserted, eachof the variables must be related to concepts used in the

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industrial process that the equation models. To make useof the information asserted by the equation reliably, onemight need to know for each value represented by avariable:

● The measurement conditions and certainty by whichthe value is known. Information about the measure-ment condition itself may include the method of measurement, and how the method was veri ed.

● The provenance of the values, for example, from

sensor readings, supplier datasheets or referencedata. Knowledge of provenance can sometimeserve as a substitute or shorthand for knowledgeof measurement conditions.

● The value – space representation, providing knowl-edge of a structure from which values can bederived, such as a distribution, a point cloud, bounds on a value or an equation.

Associated with property values must also be dimension-ality, units of measure and propositional attitude. The propositional attitude (Quine 1960 ) of variables mayvary. A function f i, and the response variable, yi, used todenote it express a belief about the consequences of vary-ing the state and control variables. In the context of thefunction as an abstraction, both the control and state vari-ables may be viewed as expressing hypothetical context.However, when using the equation to recommend a courseof action, the state variables express belief derived throughmeasurement processes and the control variables expressintention. These differences in propositional attitude areimportant distinctions governing how the variables might be used. For this reason, conceptualisations denoted by

variables with differing propositional attitude must betreated as distinct objects.

Moving beyond this abstraction reveals problems.Oftentimes, equations are isolated in analytical softwaretools and property sense information buried in datasheetsand engineering reports. In light of these problems, theauthors suggest an approach that, in shorthand, might bereferred to as ‘ equations as objects ’ . Pragmatically, it is asit sounds: a matter of information modelling. But philoso- phically, it is a stance on epistemics in engineering, sug-gesting what is required to enable sharing of MFI acrossanalytical tools, engineering reports and datasheets.

Information should be organised to forms that max-imise its usefulness. Due to the idiosyncrasies of MFI,some of which were mentioned above, special considera-tions must be made in organising it. The next three sec-tions discuss, in turn, (1) how MFI should be organised todraw inferences from it (semantic interoperability), (2)how it can be to integrate with other production informa-tion resources (data model integration) and (3) how it can be re ned and versioned (system design).

3.2.1. Semantic interoperabilityShared understanding is essential to collaborative work.MFI can be shared among participants and tools that havea shared understanding of the properties represented bythe variables. Property sense acts as constraints on the useand interpretation of properties; additional contextualinformation acts as constraints on the use and interpreta-tion of equations. To verify an analytical model, one must ascertain that the correct property sense is being applied toeach of its variables (Mitre 2014 ). Similarly, one must

Figure 1. Roles of properties and equations in control and knowledge re nement.

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ascertain that the use of equations does not violateassumptions about where that equation is valid. For exam- ple, one might possess a predictive model equation that relates the yield strength of some part to process para-meters applied in making that part. (e.g. the yield strengthof the part is a function of the laser power and scan speed

applied.) It would be unreasonable to rely on this yieldstrength equation in a process optimisation that varied thealloy as a design parameter; the equation represents theyield strength of a particular alloy. The goal of semanticinteroperability is to provide model veri cation, andthereby to enable effective sharing of MFI.

Constraints on properties and equations may beexpressed in an ontology. Ontologies providing this mayneed to be extensive and expressive; but the return oninvestment may be large. An ontology describing thesenses of properties relevant to production will typicallyhave many de nitions for the same basic term. Amongthose many de nitions, only a few might be appropriate in

a given analytical context; but, interrelating terms acrossdisciplines enables multidisciplinary processes (Zhanget al. 2009 ). To illustrate the diversity of meaning, con-sider the notion of laser power, which may be intended toexpress a requirement (of a machine that possesses a laser,or of a process that requires use of a laser), or a measuredvalue of an actual machine (see Figure 2 ). Laser power may be expressed in watts, and may be a measure of theelectrical power used or optical power delivered. Whenthe value concerns electrical power, it may refer to just the

power delivered to the laser diodes or it may include lossin the power supply (Paschotta 2014 ). Process knowledge,for example, predictive model equations, may describehow some phenomena, such as melting, respond tochanges under laser power.

Typically, analytical tools only bind the one sense of

each property that they use in calculation. It is proble-matic that tools usually do this implicitly. For example,a Modelica library of electrical components might usestandard physics-based equations in representing the behaviour of components; but, verifying that fact requires knowledge of Modelica, and facilitating theuse of the fact elsewhere is not within the remit of Modelica. Errors such those in the yield strength exam- ple above abound because of similar sorts of isolation.Given the role of mathematical formulation in engineer-ing and the opportunities that knowledge-based applica-tions present, the isolation of MFI to speci c tools isunfortunate. To automate the integration of these tools,

to verify the composition of modelling viewpoints, or,more generally, to share MFI, a rst step must be torecognise where equivalences and irreducible differencesexist among those things intended to be shared andcomposed.

Engineering typically involves many disparate view- points. Heterogeneity of viewpoint (and form) is com-monplace in representing large bodies of knowledge(Halevy 2005 , Bergman 2014 , Sowa 2000 ).Heterogeneity, in itself, is not a problem. In fact,

Figure 2. Related notions of a term appear in various production resources.

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heterogeneity may be necessary as a means to represent differing perspectives; or it may be a consequence of anef cient shorthand for a method of representing a pro- blem. The challenge that heterogeneity presents is the problem of reasoning in the face of it, which is the problem of knowing the relationships among viewpoints.

Given that ontologies are speci ed formally, there is rea-son to hope that automated means can be applied to this problem. Ontology matching is the process of identifying,across viewpoints, where similarity exists, and wheredifferences are inherent and irreducible. Automated ontol-ogy matching has been an area of intense study with onlyminimal success (OM-2013 2013 ). However, thoughautomated ontology matching may provide a solution inthe future, it is not an adequate solution for engineeringand MFI in the near term. Speci cally, the problem is that contextual clues that would guide matching are oftentimesmissing. Denno and Thurman ( 2005 ) describe nineaspects of properties, which are used in engineering deci-

sion making, that together provide an epistemic basis for belief in the integrity of properties in the context of their use. These aspects include (1) associativity across views(knowledge of reuse of a property in other views), (2)authority (knowledge that the value originates with areliable source), (3) origin in requirements (knowledgethat the property traces to requirements), (4) origin in process (knowledge of the process from which the valuewas derived), (5) logical consistency (knowledge of thetype and interpretation constraints) and (6) measurement conditions (quanti cation of uncertainty in measurement and computation). Applying automated ontology match-ing in this context must account for these disparateaspects. Unfortunately, these aspects are not currently(and not easily) encoded as formal database structures.Therefore, until property sense in recorded, much of thecurrent work automating ontology mapping is of limitedvalue towards composing MFI.

3.2.2. Data model integration

A data model (or database model) concerns how informa-tion is physically organised, for example, as relationaltables, as objects, or as documents (GITTA 2014 ). Assuggested above, MFI can be organised as objects built from variables and relations. Each variable denotes a property; property sense is associated as ontology-baseddata, that is, variables reference uniform resource identi-

ers to OWL (W3C 2012), statements.A body of knowledge that is subject to vigorous

research is also subject to intense revision. Such is thecase currently with AM, where phenomena are not yet well-understood and models are frequently re ned andrevised. The challenge, from a data modelling perspective,in this regard is to avoid disruptive reconceptualisation. Disruptive reconceptualisation is a defect in the design of

an information technology system where minor changes inthe domain supported by the system necessitate its rede-sign. A good data model should prevent disruptive recon-ceptualisation by anticipating how the underlyinginformation is apt to evolve.

To illustrate the problem, suppose a predictive model

for laser sintering has established a relationship betweenthe tensile strength of the fabricated part and powder-metal average particle size. This predictive model maynot perform well when used with powder from a newsupplier that possesses the same average particle size but a very different distribution of particle sizes. Re nement of the model calls for re nement of the notion of particlesize, but only in cases where knowledge of particle-sizedistribution is available. To treat a particular notion of particle size as ‘ owned ’ or ‘ contained ’ by the powder-metal class invites the need to reconceptualise.

Solutions to disruptive reconceptualisation centre oncareful management of the relations among classes, prop-

erties and instances. Parsons and Wand recommend a two-layered data model where instances are not statically clas-si ed by their properties (Parsons and Wand 2000 ).Applying these ideas, Masin et al. ( 2013 ) distinguishclassi cation by containment , a pattern of informationmodelling where classes serve as containers for a xedset of properties, from class i cation by property , a patternwhere properties can be attributed to objects in a manner that is mostly independent of the object ’ s classi cation.Masin et al. note that metamodels of engineering toolstend to follow a classi cation-by-containment pattern of information modelling. This is consistent with what the paper asserted earlier that tools bind the one sense of each property that they use in calculation. Further, they (andParson and Wand) suggest that viewpoint integration isenhanced by transformation of information to the classi -cation-by-property pattern.

In this work, the authors adopt the classi cation-by- property discipline primarily by modelling properties inthe RDF (W3C 2014b ). RDF, which underpins the OWL,forces representation into triples, linking a subject to anobject using a property. Modelling information in RDF issimilar to modelling it in relational fth normal form, wherea relational table is de ned for each property (Date 2012).Beyond employing the normalisation inherent to RDF, theauthors ’ approach requires that value – space representationsare not directly associated with classes. For example, metal powder has a grain-size property but potentially manyvalue – space representations. Commitment to a value –

space representation is only made in the context of softwaretools and supporting technology.

3.2.3. System design

The nal dimension of the challenge of maximising theutility of MFI concerns systems-level issues These issues

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include (1) the mechanics of interrelating MFI amongmodel viewpoints, tool viewpoints, object representationand web representation, and (2) allowing association of versioning information.

MFI does not reside on the web comfortably. Thesyntax of mathematical formulae imposes structural com-

plexity that makes its manipulation by web-based techni-ques unwieldy. Further, semantic web-based inference onMFI is not common. Yet, the semantic web is designed toovercome isolation and as a means to integrate sharednotions of properties across a manufacturing enterprise,the web is ideal. A typical use case for MFI, annotatingvariables with the intended property sense, combinesobject and web representations. An object representationof an equation may originate with use of an analytical tool.The authors developed a metamodel of Modelica (Fritzon2011 ), (Tiller 2014 ) for the purpose of capturing object- based models of Modelica equations. When an equation isde ned in Modelica syntax, it is parsed to a collection of

objects; and, in the context of the tool use, the intendedsense of properties is associated with variables as weblinks. In order to make the equation available (e.g. for model composition), the method maps the structure to webOWL objects. The details of this procedure are describedin the Section 4 example.

Mapping property information to the web may entailthe need to track versions. The example earlier of there nement of the metal-powder particle-size representa-tion is typical in this regard. More generally, versioningmay be required wherever contingent information such asengineering change interrelates with MFI. Versioning of linked data is problematic; the web is replete with brokenlinks, many a consequence of versioning. In the authors ’

work, some web data are a mirror on object-based datathat is identi ed uniquely by universally unique identi er,or by other means such as part number, process occur-rence, etc. In principle, where the object-based data aremanaged by a product lifecycle management (PLM) sys-tem, it should be possible to navigate from the PLMviewpoint on the information to the web-based mirror of it. In practice, however, this may not provide equivalent

PLM functionality. Oftentimes, inquiry originates from aconceptual viewpoint, rather than a product-based or pro-cess-based one. ManuTerms (Ameri et al. 2014 ) is anexample of an RDF-based thesaurus of manufacturingterms that facilitates inquiry originating in a conceptualviewpoint. Where contingent information links to concep-

tual information such as provided by ManuTerms, the fact that the contingent information is also linked to a PLMviewpoint might not be helpful; the path originating in aconceptual viewpoint may be broken. Additional means of managing versions must be sought.

Another means of managing versions relies solely onweb-based data. Vesse et al. describe a system based on theidea of reifying RDF triples (Vesse, Hall, and Carr 2010). Inrei cation, the original relation is expressed as a collectionof relations about a (typically anonymous) object. Theintroduced object provides the opportunity to provide ver-sion-speci c information about the original relation.

4. Example usage

4.1. Process overview

Presented below is an example usage of the authors ’

method of managing MFI. In the example, a predictivemodel of a selective laser sintering AM process is devel-oped. Currently, adequate physics-based theoretical mod-els of the process do not exist. In lieu of theoreticalmodels, empirical predictive models are developed basedon experimental data originating in work by Gong et al.(2013 ). A somewhat similar approach is described byJeang, Li, and Wang ( 2010 ) but uses simulation to gen-erate the experimental data.

Predictive models of three phenomena were investi-gated: part density, surface roughness and geometric tol-erance. For simplicity of exposition, only the part densityresponse is discussed. Taguchi method (NIST 2015c )screening experiments identi ed three signi cant factorsthat might affect part density (see Figure 3 ). These experi-ments used three levels for each factor and assumed nointeractions among the factors.

Figure 3. Density response. Eight factors were studied in screening experiments. An asterisk indicates signi cant factors. Factors areused differently in experiments and production.

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Note that factors x1 through x4 in the gure concern process, and x5 through x8 concern material properties. In production, typically, the composition of the alloy varieswith each supplier and shipment; it is not ‘ set ’ but mea-sured. In a production setting, adjustment of the four process variables is a practical means of in uencing the

process; adjustment of the material properties is not. Thus,the predictive models bridge process and material con-cerns in ways that make it useful to manage everyday production, especially when knowledge provided by the predictive models is integrated in an optimisation process.This becomes signi cant in production reuse of the equa-tions; variables referencing production measurements of raw material characteristics should be made available for modi cation, so that a response to variations in thesecharacteristics can be put into effect.

Next, a quadratic regression model for part density(Equation (1)) is developed using experiments based ona 3-factor Box – Behnken design. In Equation (1), yk is a

response variable, β are coef cients, x are input variables(explanatory variables) and ε k is an error term. 3-factor Box – Behnken design requires 15 experiments (NIST2014 ). In a model-based production environment, theseexperiments can be speci ed using process plans, where plan tasks specify values of the explanatory variablesconsistent with the experiment run. A process planmodel was developed. It enabled speci cation of the AM process parameters in one task and inspection processes inother tasks. The plan tasks occurrences reference datacollected. For example, dimensional tolerances and sur-face roughness can be collected in the form of QualityInformation Framework Results (DMSC 2014 ). The link-ing of (1) experiments to process occurrences and (2) process occurrences to outcome data enable automated

means to access experimental data and easier veri cationof the experimental process.

yk ¼ β k ; 0 þ Xn

i¼ 1

β k ; i xi þ Xn

i¼ 1

β k ; ii x2i

þ X Xn

j ¼ 2 ; i<j β k ; ij xi x j þ ε k (1)

Ordinary least squares t of the data provided thecoef cients, β k ,0 , β k ,i, β k ,ii, β k ,ij , for each of the three predictive models, k = {1,2,3}.

4.2. Implementation

The authors used IPython notebooks (ipython.org 2014 ), aQVT-r mapping engine (OMG 2011 ) and web services toimplementation this example. The complete IPython note- book for the work is available (NIST 2015a ). Object-based

models were mapped to OWL content using mappingsspeci ed in the Ontology De nition Metamodel (ODM)(OMG 2014 ). Use of ODM with Uni ed ModelingLanguage (UML) provides a frame-like language(Chungoora, Canciglieri, and Young 2010 ). ODM alsospeci es a mapping from UML to Common Logic.Though the present word does not use Common Logic,access to it provided by ODM may have value in expres-sing concepts dif cult to express in OWL (Palmer et al.2013 ). Use of IPython notebooks enabled exible interac-tion with supporting software. Python scienti c libraries provided functionality for regression analysis, matrixmanipulation, design of experiments and visualisation of data. The architecture of the solution is depicted inFigure 4 . The QVT-r mapping engine is part of a

Figure 4. System overview.

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component called the Modelegator that maintains no long-term persistent knowledge of engineering reports (or any-thing else), but maintains knowledge of a session interact-ing with the report using an HTTP session cookie (IETF2011 ).

Narrative of the process begins assuming screening

experiments have been performed and key factors identi-ed. Discussion focuses on how part density responds toscan speed, layer thickness and oxygen content. An appro- priate form of the response equation and experimentaldesign, in this case, are, respectively, quadratic formwith no 3-factor interaction and Box – Behnken design.Appropriate parameter values for the 15 experimentsrequired by 3-factor Box – Behnken design are selected.These values are re ected in process plans used to executethe experiments. Retrieval of the experimental data isshown in Figure 5 . The data are retrieved by means of a python function that is provided by identi ers of the process plan and task within that plan.

A text-based form of the equation is communicated tothe Modelegator through a Python call (see Figure 6 ).Communicating with Python using web services, theModelegator parses the equation into a collection of objects specifying an equation in the form of a Modelicametamodel equation (NIST Github 2015 ) and respondswith a label (e.g. Equation (1)) than can be used through-out the session to refer to that equation.

The next step in the process is to link the responsevariable ( Y den ) and the explanatory variables ( x1 , x2 and x3 )with property sense information. The variable could also be associated with sources of its value (not applicable inthis case). This task is depicted in Figure 7 .

The response data are tted to a quadratic using thePython Statsmodels library (Statsmodels 2014 ), providingthe β coef cients. If the t reported by Statsmodels isacceptable, the completed, response-model equation can be registered. Access to it is then always available through

the engineering report, among other means. The equationcan then be integrated with other response function intrade-off analysis and optimisation, implemented in other engineering reports. Registration of the completed predic-tive model is depicted in Figure 8 .

5. Conclusion

The paper describes a method of managing knowledgefrom predictive model equations that treats MFI as web-available symbolic information. Our method associates property descriptions from an OWL ontology with equa-tion variables, providing the intended sense of the proper-ties. The paper describes requirements and solutions inthree key areas: semantic interoperability, data modellingand systems design.

The method facilitates veri cation, model integrationand collaborative work. The key challenge in each of these

three tasks is con rming that the information used incomposition is as intended. Model veri cation veri esthat the senses of properties and context of equations,composed in the model are as intended. Model integrationveri es that the composition of component viewpointsinvolves compatible properties. Collaborative work is pos-sible only where participants agree on the meaning of terms (including properties) used in communication.When all relevant distinctions of the properties are forma-lised and made available, each of these tasks is facilitated.

The method facilitates knowledge re nement. When anassertion is written down and acted upon, use may serve tofurther support or diminish belief. Predictive model equa-tions are an actionable formulation of process knowledgewhere this effect can be exploited. However, making best use of MFI requires addressing issues of meaning represen-tation, data modelling and systems design as described.With these challenges addressed, disruptive

Figure 5. Retrieving density response from experiments.

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reconceptualisation is minimised and strongly held belief can be integrated into the broader conceptual schema.

Our long-range plans for this work include elaboratingan ontology for AM processes in collaboration withresearchers in that area. The authors also intend to focusmore on integrating MFI with analytical-tool metamodels.The authors envisage an environment where complexengineering tools can be driven not by APIs (whichrequire recondite skills), but by template-based mappingsto a metamodel of the tool.

Our near-term plans for the work include replacing useof our Modelica-based equation model with an equationmodel that provides a wider spectrum of mathematicaloperators and notation. MathML (W3C 2014a ) is a possible

substitute. Our Modelica metamodel is not only too limitingfor our planned work, but it produces a complex, syntacti-cally-organised, collection of objects typical of classi cation by containment. Our next version will use QVT-r to map a presentation form such as MathML to a more concise formspeci c to the engineering problem (e.g. to a quadraticregression formula). The authors also believe there is valuein providing scripts for the engineering reports of commonly performed tasks. This could facilitate integration with ana-lytical tools while making use of notebooks less open-ended.

‘ Equations as objects ’ facilitates the composition of MFI into analyses such as optimisations. As researchers at an agency involved with standards, the authors haveinitiated discussion with industry on the idea of providing

Figure 6. Registering a predictive model equation in the IPython notebook.

Figure 8. Associating parameters and saving the completed equation.

Figure 7. Registering variables and their intended sense.

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a metamodel for mathematical programming languages(NIST 2015b ) such as the Optimisation ProgrammingLanguage (Van Hentenryck 1999 ).

Disclosure statement

No potential con ict of interest was reported by the authors.

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