Chiradeep Sen

Evaluation of the functional basis using an information theoretic approach

Abstract A metric for computing the 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. 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 the 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.

Topological Information Content and Expressiveness of Function Models in Mechanical Design

In this paper, two approaches for computing the topological information content of function models in mechanical engineering design are developed and compared. Previously a metric for computing information content of functions and flows within function models was proposed. Here this metric is adapted to compute the information contained in the resulting connections of flows between functions in a function model. The first approach is based on uniform unconditional probability of a flow connecting any two functions within the model. The second approach is based on additional knowledge that the functions and flows in a model have limited compatibility, thereby reducing the choices for origin and destination functions for each flow. This additional knowledge is represented using a new graphical representation supported by syntactical grammar rules. Both approaches are then applied to an example function model. Comparison between the approaches shows that the inclusion of compatibility knowledge increases the expressiveness of function representations and reduces the uncertainty of function models.Copyright

A protocol to formalise function verbs to support conservation-based model checking

This paper proposes, demonstrates, and validates a protocol to formalise mechanical function verb definitions to support automated analysis of early design concepts, specifically, physics-based model checking using the conservation laws. Present graph-based function structures rely on controlled vocabularies of verbs and nouns to model functions and flows. Currently, all vocabularies define these terms in plain text, allowing inconsistent interpretation and term usage in models, thus making the models unsuitable for formal computational reasoning. To address this limitation, two types of model-level consistencies – topological and conservational – are identified through model examination as critical requirements for physics-based reasoning. A protocol is then demonstrated to evolve three verbs – Branch, Distribute, and Convert_Energy – from their textual definitions into formal classes that include the necessary information elements to support this reasoning. These verbs are used to construct function models, which are then used to simulate reasoning by computer algorithms, thus validating that the definitions indeed support conservation-based model checks at the conceptual level.

An empirical study of the expressiveness of the functional basis

Abstract Function models are frequently used in engineering design to describe the technical functions that a product performs. This paper investigates the use of the functional basis, a function vocabulary developed to aid in communication and archiving of product function information, in describing consumer products that have been decomposed, analyzed, modeled functionally, and stored in a Web-based design repository. The frequency of use of function terms and phrases in 11 graphical and 110 list-based representations in the repository is examined and used to analyze the organization and expressiveness of the functional basis and function models. Within the context of reverse engineering, we determined that the modeling resolution provided by the hierarchical levels, especially the tertiary level, is inadequate for function modeling; the tertiary terms are inappropriate for capturing sufficient details desired by modelers for archiving and reuse, and there is a need for a more expressive flow terms and flow qualifiers in the vocabulary. A critical comparison is also presented of two representations in the design repository: function structures and function lists. The conclusions are used to identify new research opportunities, including the extension of the vocabulary to incorporate flow qualifiers in addition to more expressive terms.

COMPLEXITY AS A SURROGATE MAPPING BETWEEN FUNCTION MODELS AND MARKET VALUE

The purpose of this paper is to investigate if early stage function models of design can be used to predict the marketvalue of a commercial product. In previous research, several metrics of complexity of graph-based product models have been proposed and suitably chosen combinations of these metrics have been shown to predict the time required in assembling commercial products. By extension, this research investigates if this approach, using new sets of combinations of complexity metrics, can predict market-value. To this end, the complexity values of function structures for eighteen products from the Design Repository are determined from their function structure graphs, while their market values are procured from different vendor quotes in the open market. The complexity and value information for fourteen samples are used to train a neural net program to define a predictive mapping scheme. This program is then used to predict the value of the final four products. The results of this approach demonstrate that complexity metrics can be used as inputs to neural networks to establish an accurate mapping from function structure design representations to market values to within the distribution of values for products of similar type.

Empirical Examination of the Functional Basis and Design Repository

This paper investigates the use of functional basis within the design repository through the observation of eleven functional models. It also examines the amount of information contained in the functional model of a hair dryer at various hierarchical levels. Two experiments show that the secondary level of the functional basis hierarchy is used most often because the secondary level provides significantly more information than the primary level, and the tertiary level does not provide enough additional information to be useful.

An Entropic Method for Sequencing Discrete Design Decisions

This paper presents a mathematical model for quantifying uncertainty of a discrete design solution and to monitor it through the design process. In the presented entropic view, uncertainty is highest at the beginning of the process as little information is known about the solution. As additional information is acquired or generated, the solution becomes increasingly well-defined and uncertainty reduces, finally diminishing to zero at the end of the process when the design is fully defined. In previous research, three components of design complexity—size, coupling, and solvability—were identified. In this research, these metrics are used to model solution uncertainty based on the search spaces of the variables (size) and the compatibility between variable values (coupling). Solvability of the variables is assumed uniform for simplicity. Design decisions are modeled as choosing a value, or a reduced set of values, from the existing search space of a variable, thus, reducing its uncertainty. Coupling is measured as the reduction of a variables search space as an effect of reducing the search space of another variable. This model is then used to monitor uncertainty reduction through a design process, leading to three strategies that prescribe deciding the variables in the order of their uncertainty, number of dependents, or the influence of on other variables. Comparison between these strategies shows how size and coupling of variables in a design can be used to determine task sequencing strategy for fast design convergence.

Information Generation in the Design Process

This paper proposes and demonstrates a protocol for measuring information generated throughout a design process. The intent is to provide a consistent approach to allow the comparison of different design procedures and processes. The proposed method divides the design process into requirement, function, and component domains occurring within design iterations. To measure information or complexity in each of these domains, the elements describing the domains are counted and their mappings within and across the domains are computed. The results show that the proposed protocol and information metrics produce data points of comparable order across all domains under different design situations. Furthermore, it is shown that within-domain-coupling and across-domain-coupling metrics should be accommodate the continual increase in element count size without hiding relative changes in information generation throughout the process. When this correction is applied, it is observed that across-domain-coupling displays a decaying process of converging and diverging towards a steady state level. This presents possible support for the concepts of modeling the design process as a series of convergent and divergent processes while also suggesting that such oscillation may not be necessary.Copyright

Physics-based reasoning in conceptual design using a formal representation of function structure graphs

This paper validates that a previously published formal representation of function structure graphs actually supports the reasoning that motivated its development in the first place. In doing so, it presents the algorithms to perform those reasoning, provides justification for the reasoning, and presents a software implementation called Concept Modeler (ConMod) to demonstrate the reasoning. Specifically, the representation is shown to support constructing function structure graphs in a grammar-controlled manner so that logical and physics-based inconsistencies are prevented in real-time, thus ensuring logically consistent models. Further, it is demonstrated that the representation can support postmodeling reasoning to check the modeled concepts against two universal principles of physics: the balance laws of mass and energy, and the principle of irreversibility. The representation in question is recently published and its internal ontological and logical consistency has been already demonstrated. However, its ability to support the intended reasoning was not validated so far, which is accomplished in this paper.

Automotive lightweight engineering: a method for identifying lazy parts

This paper presents a method for evaluating the lightweightedness of a vehicle, specifically addressing those components whose primary purpose is to aid in manufacturing and assembly rather than to provide end-user function. Seven laziness indicators are described. These indicators are used to evaluate individual vehicle components to aid in identifying mass reduction potential and focus the attention of designers on components or assemblies with high potential for mass reduction. This method is applied to a complete automotive vehicle, demonstrating a mass savings potential of the overall vehicle of approximately 5% of the total mass of the vehicle.