A Bayesian approach to model change propagation mechanisms

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A Bayesian28th approach to model change propagation mechanisms CIRP Design Conference, May 2018, Nantes, France Shirin Mirdamadib , Sid-Ali Addouchea,* , Marc Zolghadrib

A new methodology to analyze the140,functional and93100 physical architecture of QUARTZ Laboratory & IUT de Montreuil, rue de la nouvelle France, Montreuil, France Laboratoty & Supmca, 3 Rue Fernand Hainaut, 93400 Saint-Ouen, France existing productsQUARTZ for an assembly oriented product family identification Corresponding author. Tel.: +33-66-438-5563. E-mail address: [email protected] aa

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Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat Abstract École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France Engineering Changes (EC) are often the answers the designers think of while dealing with new performance targets or customers needs and

*expectations, Correspondingregarding author. Tel.: +33 3 87 37 54 30; E-mailsecurity, address: [email protected] functionality, aesthetics, etc. Engineering change management (ECM) techniques look to predict or control

these consequences within an existing system or product, to limit the generated cost and required efforts to integrate such changes. Engineering change management (ECM) techniques look to predict or control these consequences within an existing system or product, to limit the generated cost and required efforts to integrate such changes. This paper addresses the issue of enhancing the ability of the ”change evaluation” through Abstract the suggested technique. We propose a methodology that covers change analysis and evaluation from change’s objective initialization to formulation of recommendation based on system engineering framework (ANSI/EIA-649 1998). We use a modeling technique based on influence In today’s able business environment, theuncertainty trend towards more varietyinand customization is will unbroken. Duethat to this development, theability need of diagrams to integrate different levels (on product dependencies) a unique model. It be shown the models offer the to agile andchange reconfigurable systems emergedthe to cope withFinally, variousthese products and product families. design and way optimize production analyze impacts production but also allow to synthesize system. results can be obtained in aTo very efficient which gives the systems as of well as use to choose optimal product matches,way product methodsofare needed. Indeed, oftothe knowngo/no-go methodsdecision. aim to possibility their during athe design meeting in a practical at theanalysis very beginning a change project and most mainly support analyze a product or one product family on the physical level. Different product families, however, may differ largely in terms of the number and © 2018 The Authors. Published Elsevier This iscomparison an open access the CC BY-NC-ND license nature ofThe components. This fact by impedes anLtd. efficient and article choice under of appropriate product family combinations for the production c 2018  Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/3.0/) system. A new methodology is proposed to analyze existing of products inCIRP view Design of theirConference functional and physical architecture. The aim is to cluster Peer-review under responsibility of the scientific committee the 28th 2018. Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. these products in new assembly oriented product families for the optimization of existing assembly lines and the creation of future reconfigurable Keywords: ChangeBased engineering ; Bayesian System engineering assembly systems. on Datum Flownetwork Chain,; the physical structure of the products is analyzed. Functional subassemblies are identified, and a functional analysis is performed. Moreover, a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the similarity between product families by providing design support to both, production system planners and product designers. An illustrative example of a nail-clipper is used to explain the proposed methodology. Anbased industrial case study two product of steering columns of products [3]. on Product familyfamilies is a group of related prod1. Introduction thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. ucts that share common features, components, and subsystems, © 2017 The Authors. Published by Elsevier B.V. and satisfy a variety of market niches. Specifically, the product When the needs and expectations of customers change in Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018.

terms of functionality, aesthetics and safety, the solution that is Engineering Changes (EC). These dereaches consensus Keywords: Assembly; Design method; Family identification mands can be initiated by any external or internal stakeholder, during design, re-design or upgrade of the system. But they can also be launched during any other phases of the system’s life1.cycle. Introduction It is well-known that the change impacts are propagated in cascade, from sub-systems to sub-systems leading to further Due to the Engineering fast development the domain of modifications. change in management (ECM) communication an ongoing trend of digitization techniques hopeand to anticipate these consequences withinand an digitalization, manufacturing are facing existing system or product, enterprises to restrain the createdimportant cost and challenges in today’s market environments: continuing expected endeavors to incorporate such changes. aAmong them tendency towards reduction of product development and some methods rely on product structure or functionstimes or more shortened lifecycles. Ulrich In addition, is anthe increasing generally product its architecture. in [1]there defines product demand of customization, at thethesame timeofinaaproduct global architecture as the ”schemebeing by which function competition competitors all over This the world. This (1) trend, is allocated with to physical components”. is to define the which is inducing the development macro tobetween micro arrangement of functional elements; (2)from the mapping markets, in diminished lot components; sizes due to and augmenting functionalresults elements and physical (3) the product varieties (high-volume to low-volume production) [1]. specification of the interacting physical components interfaces. To cope with this augmenting variety as well as to be able to identify possible potentials existing Researchers andoptimization practitioners define there in the the product famproduction system, it is important have adesign precise knowledge ily architecture [2] through producttofamily and platform-

platform is a set of common parts, subsystems, interfaces, and manufacturing processes that are shared among a set of products [4]. Such commonality or reusability is an efficient solution for the product family architecture and limits the change propagation effects. However, a change triggered in a shared of the product range characteristics manufactured and/or component could leadand to redesign in much other components assembled in this system. In this context, the main The challenge in and products, propagated through the interfaces. ”go” or modelling and analysis now not only to cope with single ”no-go” decision on theiscommitted change is then based on products, a limited product range or existing product the analysis of ”return on investment” comparing fromfamilies, one side but to beextent able tothrough analyzeknown and topropagations compare products to define the also impacts’ and risk of unnew product families.toIt other can bedependent observed sub-systems that classicaland existing known propagations from product regrouped in on function of clients or features. the otherfamilies side theare awaited return such investments. The sysHowever, assembly oriented product hardlyto to engifind. tem engineering community offers a families holistic are approach Onchanges the product family level, products differ with mainly in two neer through an EIA standard dealing ”Configumain the number of components and[5]. (ii)The the rationcharacteristics: management” (i) (CM), cf. (ANSI/EIA-649 1998) type of components (e.g. mechanical, standard provides guidelines to buildelectrical, industrialelectronical). support tools methodologies considering mainly single products forClassical CM. Research works have also focused on diverse activities or solitary,and already product families the to support equip existing ECM. This standard definesanalyze the change product structure on a through physicalthree levelmain (components which management process activities:level) (1) Change causes difficulties regardingandancoordination, efficient definition and identification, (2) Evaluation (3) Implemencomparison of different product families. Addressing this tation and verification.

2212-8271 © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license c 2018 The Authors. Published by Elsevier B.V. 2212-8271  (http://creativecommons.org/licenses/by-nc-nd/3.0/) 2212-8271 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the of 28th 2018. Peer-review under responsibility of scientific the scientific committee theCIRP 28thDesign CIRP Conference Design Conference Peer-review under responsibility of the committee of the 28th CIRP Design Conference 2018. 2018. 10.1016/j.procir.2018.03.309

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This paper addresses the second activity in which that we are looking to enhance the ability of the ”change evaluation” through the suggested technique. This research reported here addresses first of all the modeling of dependencies of an existing design and secondly the performing changes propagation during redesign. The state of the art is structured according to this decomposition. Both topics are addressed either through data or knowledge-based learning approaches. In the third section, the main concepts of the general framework defined for such modeling are put forward. This framework is based on System Engineering (SE) and the vocabulary is in line with the SE standards and mainly ANSI/EIA-632. The framework and the related tools are then illustrated thanks to a simple re-design case in section four. 2. State of the art Let us consider the system architecture [6] made of the hierarchy of physical structure and functions adding the mapping between them. ”Functions are discrete actions necessary to achieve the system’s objectives. The functions will ultimately be performed or accomplished through use of equipment, personnel, facilities, software, or a combination.” [7]. We can add the structure of needs and requirements. Requirement is defined by ANSI/EIA-632 [8] as something that governs what, how well, and under what conditions a product will achieve a given purpose [9]. According to this, the global view of a product or system is resumed in left side of Fig. 1.

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Fig. 1. Product-data model (left) and Various linkages in adjacency matrices (right)

The x-axis shows the product-data evolution through four successive ”states”. A state represents a set of data related to the product-to-be. In accordance with the ANSI/EIA-632, these states are named here, Needs (N), Requirements (R), Logical representation (L) and Physical representation (P). The needs are transformed into requirements that define what should be designed. The logical state contains required models to understand fully how the product will run and the physical model defines the structure of the product linked to the requirements and the logical models. This is the product design process, seen from the state point of view and called in short the NRLP model. The z-axis represents the hierarchy levels and the y-axis corresponds to the population of each hierarchy level. Any piece of the product-data model is then identified thanks to three values. The instance refers to a distinct element which belongs to a given layer of a given state (ex. engine or each door of a car). Otherwise, the product data model (PDM) is represented by G = (V, E). N ∪ R ∪ L ∪ P represents the set of all vertices which belong to one of four sets of nodes, N, R, L or P. The partial adjacency matrices NN, RR, LL and PP define the 1

intra-state linkage of each sets of nodes. The partial adjacency matrices NR, RP, RL and LP define the inter-states linkage according to ANSI/EIA-632 description of design process. The linkage within each state could be bidirectional: NN, RR, LL and PP while the dependencies modeled by matrices NR, RP, RL and LP unidirectional and therefore these latter matrices are strictly upper triangular, see right side of Fig. 1. 2.1. The existing models of dependencies identification In the product design field, dependencies identification is approached from different angles. Either solely geometrical dimension is addressed [10], or the reasoning goes further toward functional [11] or even behavioral aspects [12]. FunctionBehavior-Structure (FBS) is one of the most used models in the engineering context. The aim is to explain, using functional reasoning (FR), how an artefact’s structure and behaviors can satisfy intended functions. What is called behavior in FBS models can be regarded as what satisfy high-level functions. It is in the same spirit that [13] propose a methodology inspired by conceptual graphs [14] and functional trees. Most of these research works fall within the context of redesign and use historical design information. To represent and better synthetize the dependencies, matrix forms are intensively used. Design Structure Matrices (DSMs) [15] can provide indications as to how changes may propagate through a system, or how each feature/component/function/etc. is affected by others. Each cell in the DSM matrix may contain a numerical or binary representation of links. For inter-layer dependencies QFD-like matrices are also commonly used to put forward highly affected (affecting) functions or design architectural zones [16]. Dependencies identification and modeling should be used properly for change propagation, directly influenced by these latter ones. Anyhow the reference model presented in section above, is broad enough to fit any method mentioned in this section. 2.2. EC propagation literature survey Many research works proceed to change propagation based on DSM. We propose a brief review of Change Prediction Method (CPM) [17] as one of the best ranked ECM method according to a very exhaustive literature review proposed by [18]. CPM is an approach who uses DSM to capture and quantify (subjectively) component dependencies and to calculate the change propagation risk between components: 1. The product is decomposed into its components or subsystems. 2. The direct dependencies between components are captured in a DSM. 3. The indirect dependencies (up to six steps) are computed using forward CPM algorithm to deduce the combined risk of change propagation. 4. This combined and reordered risk matrix can be used by different stakeholders to support ECM decisions. However some research works integrate functional reasoning with change propagation to reinforce the results [18–20]. We discuss merely the most recent work based on FBS Linkage. As stated earlier [18] proposed a comparative analysis of existing ECM methods in the literature. Firstly, the extent of the



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analysis and secondly the comprehensive established benchmark criteria are the reason why we rely on this analysis. The major CPM drawback is the fact that only one level of the system at a time can be analyzed. It can support all kind of changes affecting components but initiated changes to functions and behaviors must be translated to component changes. This aggregation makes the propagation difficult to follow (lack of visibility). This approach is totally unidirectional and does not support omnidirectional of change propagation.MDM is used to evaluate different change alternatives, as a decision making tool. [21] demonstrates on a common example that dependencies identification through FBS results in higher overall risk value comparing to CPM. This is explained by the increase of number of indirect links in the multi-layered FBS linkage model compared to single-layered CPM model. The most impacting components, behaviors, and sub-functions can be extracted from MDM. However, updating and readjustment of the models obtained through these methods is not a trivial task. Risk factors shall be modified or re-determined for each component update and the overall risk should be recalculated. To analyze redesign solutions designers should detect violated constraints, and determine the impact of design modifications. One of the most cited techniques supporting constraint negotiation is the one proposed by [22]. Authors define a design problem as a set of constraints which are expressed by functional relations among design variables. To solve the design problem, the subjective knowledge, experience and desires of the designer are used to determine the value of decision variables for the first design solution. However, by propagating these values to the constraints and goals, it is possible to verify if one or several constraints are violated. In this case, it becomes necessary to make them evolve towards the conflict resolution while answering the goals and reaching the better performance among feasible solutions. Using such techniques is based on formal knowledge (equations) that links the system parameters together. Even if it remains a very powerful alternative to CPMlike approaches, it requires the existing of all the expert knowledge, mainly in the forms of mathematical relations to be able to propagate changes within the system. This could become very complex for a system for which the formal knowledge is not available or the study level (first steps of the re-design) is not worthwhile to go through such a complex model. 2.3. Analysis of the related works The related works describes in previous section, gave an overview of the most cited ECM techniques. The main drawbacks that can be figure out from these methods: 1. 2. 3. 4.

What-if Analysis and impact determination. One change and impacts. Multivariable/bivariate dependency. Performance and attributes modifications.

To deal with these drawbacks, we rely in our research on causal networks where it is possible to answer the need of simultaneous changes integration and if properly used, they allow designers to synthesize system. Indeed, two principal families of causal graphic networks are distinguished in the literature: probabilistic and possibilistic [23]. Formalism used here concerns Bayesian network (BN). One of the main advantages of

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BN is their adaptability. They allow the consideration of the time with dynamic BN. BN are as well able to incorporate utility (cost function), constraint, and decision nodes, becoming a real decision making tool [24]. Change propagation is addressed by BN especially in software systems [25]. The objective is to formalize the uncertainty through the system and thus to identify which other elements of the software system will likely change as well. A change request is a user’s specification of which element(s) they wish to change [26]. As will be discussed later in this paper, the probabilistic view of change propagation encourages the use of Bayesian Belief network, based on conditional probability. 3. Proposed methodology This paper aims to propose an comprehensive approach enough to support all kind of changes and thus to cover an important range of levels of system decomposition. The methodology has two main axes, dependencies identification and modeling, and change propagation. For the first axe, we are strongly inspired by so-called ”Requirement relationships” introduced in EIA-632 standard [8] and developed by [9], linking needs, requirement, logical solutions and physical solutions (NRLP), see right side of Fig. 2. These relationships are valid for both design and redesign processes. The proposed approach is composed of five major steps: Initialization: This step is to clarify the study objectives and intended changes, and to identify key performance indicators used to judge as to the success or failure of the improvement project or to define a degree of achievement. At this stage, users, designers or stakeholders determine desired changes. Change can target functions/requirements and also design choices. Intended changes can be architectural, structural, behavioral, functional or even non-functional (aesthetic, security, ...). Dependencies and (their) constraints identification and modeling: This can take place in full agreement within the framework of the EIA-632 standard. The goal is to integrate the needs in the process of (re)-design. To do so the NRLP approach determines the guidelines but is not always enough, to objectively identify direct and indirect dependencies between Needs – Requirements – Logical solutions – Physical solutions. The following section provides guidelines for this step. Change propagation: This step use identified dependencies, specify the model, and restrict if possible the search space in order to gain tractability. The propagation technique let the initial change to be introduced into the system, regardless of the hierarchy level or state. Verification and Validation of models: In this step one should (1) ensure that the resulting model is well established (respecting specifications and recommendations of the conceptual model) and (2) confirm the correspondence between the model and reality/ Change scenarios experimentation : It a step when pronostic and design synthesis are done. Prognostic adresses change impact analysis and design synthesis is an activity that develops a physical architecture (a set of product, system, and/or software elements) in such a way as to achieve a design solution capable of satisfying the stated requirements within the limits of the performance prescribed.

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While we talk about an existing product to redesign, it is most of the time easier (more intuitive) to construct the dependencies model by approaching the system in a top-down manner. All the more so these models are developed during design process (eg. functional analysis) and thus are available for an existing product. However, the analysis can be top-down or bottom-up. Following the initialization step, regarding to initiated change, one can use one or more adapted tools, models and methods for dependencies identification. Among these tools we can mention conceptual graphs, functional trees, FBS, Function analysis system technique diagram, ... To study the behaviors (logical solution layer in NRLP) we can consider, for example, dynamic, mechanical and thermal models of all or part of the system. In this case awaited performance and constraint, arising from functional requirements, should be assessed to logical solutions. The physical state of system is defined by a set of alternative solutions ensuring the requirements, specified in previous state(s). To meet the technical requirements of the system and the performances of the logical solution, adequate models and studies must be conducted. The more the links binding the two layers are explicit, the more the choice of the physical solution is reliable. Physical solution should ensure this requirement. In other words, we should be able to demonstrate (formally, via simulation, etc.) whether or not the requirement is fulfilled. The resolution of conflict and obtaining consensus would play an important role for alternative selection. This consensus becomes all the more difficult to find in view of inter layer links. The scenarios should be evaluated via objective or subjective indicators. It should be noted that even (initially) subjective requirements satisfaction, can be assessed through indicator. Otherwise when the links between parameters are not established objectively, the experts’ knowledge should be used to express them. Whatever the tool and indicator, we must ensure the top-down and bottom-up traceability between all the successive layers. Next section goes further and discusses system modeling principals regarding the proposed methodology needs.



Fig. 2. Assembling two bike tubes

and total length are (geometrical/behavioral) parameters to ensure the comfort, stability, transmission and transformation of movement. The assembly is considered from its compression resistance, aesthetic and cost. They are considered as needs and are represented on x-axis in Fig. 3. The knowledge modeling allowed to represent the dependencies between the parameters and the performances. In proposed model the compression resistance, apart the vertical force applied to the surface of the tubes, depends on the thickness, overlap and naturally the materials from which the (external and internal) tubes are made, see different floors in Fig. 3. The tubes can be viewed by users and therefore it has an aesthetic impact. This is linked to the materials of external and internal tubes from one side but also on the way that these two tubes are assembled, tube’s diameters and total length. Total length depends on tubes lengths and their overlap, see blue links. In sum there are four constraints that link parameters together: (1) the maximum total length of the assembled tubes is defined by the height of the bike user, (2) the maximum and minimum backlash between the tubes required for their adjustment and assembly, (3) the junction between the two tubes can be done either by welding or pasting depending on the nature of the materials, and (iv) the recommended minimum overlap of tubes to ensure the resistance. It is decided to use Iron, Aluminium or Composite. The tubes may not be made from the same materials. The Fig. 3 represent the dependencies identified for this situation and the constraints mentioned above, based on the model presented in left side of Fig. 1. Through the next section we put forward the reasons why Bayesian Network seems to be appropriate to fit to the methodology proposed in section 3, and the needs mentioned in terms of modeling.

4. Methodology implementation

4.1. Bayesian Networks

Given an instigating change supposed or observed on a parameter, we would like to compute how other parameters of the model would vary. When supposing a potential change, we associate with the parameter a probability of occurrence while observing a change means certainty about the change. Based on the reference model presented in section 2, nodes of the graph represent model parameters. We do distinguish between nodes classes. Using the vocabulary suggested by [22], nodes represent : decision variables, design goals, intermediate variables, design specifications or requirements and finally constraints. Let us exemplify the system, modeling design problem, through a simple example of two tubes assembled together by adequate assembly permanent or non-permanent technique as welding or clamping. These tubes are bike saddle’s seat post and bike frame’s seat tube (vertical tube under the rider’s seat), see Fig. 2. The obtained assembly will be under a variable compression stress. The four structural parameters, intrinsic to each respectively external and internal tubes are diameter, length, thickness, and material: D; L; T; M and d; l; t; m. The overlap

The models we are going to manipulate are graphs that have to deal with uncertainties. The uncertainties in the context of change propagation are related to dependency degree between two parameters (or even their independencies) or their causality. To obtain these models, we rely in this paper on expert knowledge and expertise where, the uncertainties reflect the experts’ beliefs. According to [27], ”the main tool for dealing with degrees of belief is probability theory”. One of the main tools that model uncertainties associated with graphs is the Bayesian Theory. Hereafter, we are going to provide a very brief overview of this theory to make the further developments understandable. The growing interest about the Bayesian theory is tiedup with their ability to model two types of relations, namely causality and co-occurrence, by a graph on which probability inference can be applied. While the causality shows a causeeffect relationship, the association represents the co-occurrence of linked events modeled by random variables represented by nodes. Formally, a Bayesian network, noted BN, is a directed acyclic graph with directed edges. The nodes are represented by discrete or continuous random variables. Bayesian Belief



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Network, BBN, associates probabilities to random variables for prediction and diagnostic.

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4.2. Bayesian Network structure construction There no any rule or task hierarchization for building BN structure from NRLP-Dependencies graph (NRLP-DG). However, it is suitable to start from lower physical level of elements and advancing primarilly towards needs direction on X,Y plan and then, enhancing hierarchy level Z step by step while exploring X,Y plan. In the case study, only level z=3 is concerned related to NRLP Bike element. Added performance indicators that are intrinsic to the performance that we want to observe during the change engineering and are : (37) Total lenght ; (38) Int. tube volume ; (39) Assembly technique ; (40) Overlap ; (41) Ext. tube volume. We consider that these indicators contribute directly or indirectly to enhance (12) Tube aesthetic level, (13) Tube resistance an (14) Tube cost like shown in Fig. 4. The cost and decision nodes related to the re-design choices are to be added by the experts. The figure does not shown them for graph readability reaisons.

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Nice bike Well-designed frame Reasonable price bike Well-designed handlebar Nice pedals Confortable bike Aesthetic forms Aesthetic colours Reliable bike Resistant frame Reasonable frame cost Well-designed frame tube Resistant frame tube Reasonable frame tube cost Aesthetic tubes structure Aesthetic tubes assembly Resistant assembly technique Resistant tubes structure Reasonable material cost Reasonable fab. Cost Tubes material impact on aesthetique

(22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41)

Tubes geometry impact on aesthetique Tubes assembly impact on aesthetique Assembly technique impact on resistance Tubes geometry impact on resistance Tubes material impact on resistance Materials cost Assembly techniques cost l – Lenght interior t – Thickness interior d – Radius Interior m – Material Interior M – Material Exterior L – Lenght Exterior T – Thickness exterior D – Radius exterior Total lenght Int. tube volume Assembly technique Overlap Ext. tube volume

Fig. 3. NRLP dependencies graph for two bike tubes

Having defined performance nodes 1 linked to design parameters, BBNs can be used as a recommendation system, to evaluate different scenarios, being given the observations and constraints. Structure learning may not be trivial but once completed is relatively easy to update or modify. Contrary to the methods based on Design Structure Matrices (DSMs), BBNs propose prognostic but also diagnostic, or even both at the same time while the initiated change’s layer requires. Prognostic, or impact analysis, is to verify the consequence of change decisions (solutions), regarded as causes, on requirements and needs satisfaction level, considered as effects, or on the related ongoing decisions. Contrariwise, the diagnostic, or system synthesis, purpose is to explore, based on established needs and requirements (effects), the design solution space (causes) to better predict the change alternatives. In next section we will provide some details and modeling tips relative to the bike’s vertical R as self-sustained Artube under saddle. We use BayesiaLab tificial Intelligence software.

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Fig. 4. BN Structure obtained from NRLP-DG

4.3. Completing BN structure As exposed before external and internal tubes are associated each to four structural parameters represented by Bayesian nodes; length, diameter, thickness, and material. Among these, length, diameter, and material are considered as parent (root) nodes in our model. Some corrections by the expert can be useful required as the dependence between the diameter and the thickness of the tube (arc between t and d as well as T and D. The other example is to involve the parameters t, d and D in the evaluation of the level of geometric aesthetics of the tube (node 22 in Fig. 4). The two lengths’ parameters are parents for Overlap-length and Total-length nodes. It is supposed that Overlap impacts the Total-length. Two other nodes put constraints on these two parameters. A constraint node is a node used to express a constraint relationship that must be true between multiple nodes (e.g. Total-length should not exceed 1000mm). Providing Total-length node with the equation linking the four latter parameters, (T otal length = Length ext + Length int − Overlap) probability tables are filled automatically. However, the user should fill conditional probability table corresponding to overlap node, see area (a) in Fig. 4. Note that internal and external tubes’ thickness are supposed to be impacted by their mutual diameters, the larger the tube’s

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diameter, the thicker the tube’s body. However, we must ensure the assemblability of the tubes. The assembly of the tubes could be feasible if Diameter Ext-Thickness ext-Diameter Int < 0 & Diameter Ext-Thickness ext-Diameter Int ≤ 0.1, see area (b) in Fig. 4. As stated before three materials are eligible for both tubes material nodes; Iron, Aluminum or Composite. Three assembly techniques are as well suggested to join the tubes; welding, bonding, clamping. The relative likelihoods are providing via expertise. Two constraint nodes are appended to external and internal tube’s material and assembly techniques nodes: (1) the possible material combination motivated by common practice, (2) the feasible assembly techniques for each material combination. Note that Assembly technique’s likelihood node is not adequate to exclude non-feasible technique-material combination, see area (c) in Fig. 4. We have introduced so far the structural parameters. Besides, three functional parameters are intended to integrate the scope of this study; cost, resistance, and aesthetic. The current system is not complex enough to address behavioral parameters. However structural and high-level functional parameters should be linked. These links are rarely mathematically established, particularly for subjective performances such as aesthetic. In this case the conditional probability tables (CPT) should be fulfilled based on expertise. 5. Discussion and perspectives This paper addressed the modeling of dependencies of an existing design and the performing changes propagation during redesign. We shown how identifying and reducing or controlling unavoidable change propagation paths early enough and this, with theoretical framework. The main concepts of the general framework defined for such modeling are put forward. This framework is based on System Engineering (SE) in line with the SE standards, especially ANSI/EIA-632. The framework and the related tools are then illustrated thanks to a simple redesign case. For this, we used BN as the main modeling tool as a knowledge-based framework and having the ability to deal with uncertainty related to re-design considerations. Such tool allows us modeling change propagation structure of system redesign in order to make pronostics and/or system synthesis. The limits of this proposal are related to the important work that the experts must do to build the Bayesian network and the inability to evaluate multiple solutions at the same time. For the first limit, the further works will concern existant facilitation and size reduction algorithms related to BN. For the second limit, BN will be enhanced to ”Influence Diagram” in order to perform simulation of different change scenarii with related forecasted costs. References [1] Ulrich, K.. Fundamentals of Product Modularity. In: Management of Design. Dordrecht: Springer Netherlands; 1994, p. 219–231. doi:10.1007/978-94-011-1390-8 12. [2] Martin, M.V., Ishii, K.. Design for variety: a methodology for understanding the costs of product proliferation. In: The 1996 ASME Design Engineering Technical Conferences and Computers in Engineering Conference. California; 1996,. [3] Jiao, J., Simpson, T.W., Siddique, Z.. Product family design and platformbased product development: a state-of-the-art review. Journal of Intelligent Manufacturing 2007;18(1):5–29. doi:10.1007/s10845-007-0003-2.

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