Journal-2010-AIEDAM-Information Content of Function Models Abstract
From Clemson Engineering Design Applications and Research
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[edit] Citation
Sen, C., Caldwell, B., Summers, J.D., Mocko, G., (2010), “Evaluation of the Functional Basis using an Information Theoretic Approach," Artificial Intelligence in Engineering Design Analysis and Manufacturing, vol. 24, no. 1, pp. 87-105 (doi:10.1017/S0890060409990187).
[edit] Abstract
A metric for computing information content of function models in mechanical engineering design is proposed. Function models are graph-based representations used to describe the functionality of engineered artifacts, where the nodes are function verbs and the edges are the objects of action, respectively. The functional basis, a controlled vocabulary of these verbs and nouns organized in a three level hierarchy, is intended to support consistent representation of function models. The Design Repository is a Web-based archive of function models of consumer products described with the functional basis. This paper presents the theoretical underpinnings of a metric for information content of function models, the assumptions required to support it, the definitions of key terms associated with it, and its practical interpretation. Finally, the metric is used to study the usefulness of the functional basis through a series of experiments on function models within the Design Repository. The results of the experiment indicate that the secondary level of the functional basis is the most beneficial to designers, both in terms of information content and information density.
Keywords: Design Repository; Functional Basis; Function Models; Information Content; Information Theory
[edit] Images/Illustration
Information content of verbs in a function model = 
, with xV verbs in the verbs vocabulary and yV verb instances (functions) in the function structure model.
Information content of nouns in a function model = 
, with xN nouns in the nouns vocabulary and yN noun instances (flows) in the function structure model.
As the vocabulary size grows, information obtained from each term grows, but at a diminishing rate, as shown below:
This results into a diminishing information density of the vocabulary, measured as 
.
In this paper, a correlation has been shown to exist between the information content of function models found within the Design Repository ([1]), the information density of the Functional Basis vocabulary levels (3 hierarchical levels), and previous empirical observations (see Conference-2008-DCC-Functional_Basis_Abstract) which shows that the secondary level within the 3-tier vocabulary is the most frequently used in creating models. In that sense, this paper provides a possible theoretical explanation for why product modelers had preferred to use the secondary level over the other levels.
The following figure shows the typical information growth rate within a selected function structure model (a commercial hairdryer product), when each of the three levels of the Functional Basis vocabulary is used to construct the model.
As seen here, while there is a significant increase in information from the primary to the secondary level, information does not necessarily increase from the secondary to the tertiary level, which explains why the secondary level is more preferred by product modelers.
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[edit] Contact Information
Joshua D. Summers, Ph.D.
Associate Professor and CoES IDEaS Professor
Clemson Engineering Design Applications and Research (CEDAR)
Department of Mechanical Engineering
Clemson University
250 Fluor Daniel Building
Clemson, SC 29634-0921
Voice: 864.656.3295
Cell: 864.ME.DX.LAB
Fax: 864-656-4435
Skype: Joshua.d.summers
e-mail: Joshua.Summers@ces.clemson.edu; jsummer@clemson.edu
web: http://www.clemson.edu/ces/cedar/
