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A posteriori identification of dependencies between continuous variables for the engineering change management

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Abstract

The objective of this document is to contribute to the modelling of engineering changes and their propagation. Usable in preliminary redesign activities, a new approach is suggested that allows greater efficiency. Given a product model, the idea is to use the experiments to calculate in advance the consequences of potential changes in continuous variables. These consequences are collected, analysed and structured in a dependency model, noted \(\langle \varGamma , \varPhi \rangle\), composed of a dependency graph \(\varGamma\) and its associated set of influence functions \(\varPhi\). Bilateral influence functions, associated with arcs, quantify the dependencies between node pairs. Multilateral influence functions, identified by the application of the total differential theorem, define the dependencies between a node and all influential nodes on which it depends. Finally, the relative error is calculated by following the infinitesimal assumption of the total differential for each variables. Our findings show that such a dependency model is informative and allows effective prediction and evaluation of changes. The approach is illustrated by a geometric bicycle model. The results are discussed and future areas of research are finally presented.

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Abbreviations

\(p_i\) or i :

Variable i

n :

Number of variables/nodes

\(x_i^0\) :

Current value of variable i

\({\hat{x}}_i\) :

New value of variable i after change

\(\overline{x_i}\) :

Upper boundary of variable i

\(\underline{x_i}\) :

Lower boundary of variable i

\(\delta _i\) :

Variation of variable i after a change

\(\sigma _i\) :

Sampling step associated to variable i

\(k_i\) :

Number of sampled values of \({\hat{x}}_i\)

\(\varGamma\) :

Dependency graph

\(\varGamma _0\) :

Initial dependency graph

\(\varPhi\) :

Influence functions

\(\phi _{ij}\) :

Bilateral influence function carried out by an edge (i, j)

\(\varphi _j\) :

Multilateral influence function associated with node j

\(d_{ijk}\) :

Value \({\hat{x}}_j\) of variable j according to the kth sampled value of variable i

\(g_{ijk}\) :

Gap between the new value \({\hat{x}}_j\) of variable j after the kth modification of i and its initial value

\(v_{i,j}\) :

Variance of the new values of variable j after the change of variable i

\(b_{i,j}\) :

Binary dependency matrix element

\(q_{i,j}\) :

Quantitative dependency matrix element

\(s_{i,j}\) :

Qualitative dependency matrix element

\(f_{i,j}\) :

Functional dependency matrix element

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Authors and Affiliations

  1. Quartz Laboratory/SUPMECA, 3 rue Fernand Hainaut, 93407, Saint-Ouen Cedex, France

    Mahmoud Masmoudi, Marc Zolghadri & Patrice Leclaire

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  1. Mahmoud Masmoudi
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  2. Marc Zolghadri
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  3. Patrice Leclaire
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Correspondence to Mahmoud Masmoudi.

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Masmoudi, M., Zolghadri, M. & Leclaire, P. A posteriori identification of dependencies between continuous variables for the engineering change management. Res Eng Design 31, 257–274 (2020). https://doi.org/10.1007/s00163-020-00338-5

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