Investigation of the Interpretability of Three Function Structure Representations: A User Study

2009 ◽  
Author(s):  
Jonathan Thomas ◽  
Chiradeep Sen ◽  
Gregory M. Mocko ◽  
Joshua D. Summers ◽  
Georges M. Fadel
Keyword(s):  
User Study ◽  
Research Effort ◽  
Functional Model ◽  
Two Dimensions ◽  
Controlled Vocabulary ◽  
Product Analysis ◽  
Functional Models ◽  
Physical Form ◽  
Functional Representations ◽  
Function Models

Function models are used during the conceptual design phase of the design process to model the intended use or objective of a product, independent of the products physical form. Function models also aid in guiding design activities such as generating concepts and allocating design team resources. Recent research effort have focused on the formalization of function models through a controlled vocabulary and archival of functional representations in computer-based repositories. However, the usefulness and interpretability of these function models has not fully been explored. This paper presents the results of a user study to ascertain the interpretability of functional representations at three levels of abstraction. In this interpretability is defined as the ability to identify the product based on a functional representation. These function models vary in abstraction in two dimensions: (1) the number of function within the model and (2) the specificity of the terms used within the functional models. Sixteen mechanical engineering graduate students are asked to identify the products from the functional models in these three abstraction levels. In addition to identifying the product, students are asked to record time and list any keywords in the functional model that help them to choose a product. Analysis of the results indicates that interpretability of a functional model increases substantially by using free language terms over a limited functional vocabulary and environmental context of the product. Additionally, the number of functions within the functional model correlates with the identification of similar products.

Development of a Functional Basis for Design

1999 ◽  
Author(s):  
Robert B. Stone ◽  
Kristin L. Wood
Keyword(s):  
Classification Scheme ◽  
Mechanical Design ◽  
Functional Model ◽  
Coding System ◽  
Structure Generation ◽  
Functional Basis ◽  
Product Function ◽  
Functional Models ◽  
Functional Representations ◽  
Architecture Development

Abstract Functional models represent a form independent blueprint of a product. As with any blueprint or schematic, a consistent language or coding system is required to ensure others can read it. This paper introduces such a design language, called a functional basis, where product function is characterized in a verb-object (function-flow) format. The set of functions and flows is intended to comprehensively describe the mechanical design space. Clear definitions are provided for each function and flow. The functional basis is compared to previous functional representations and is shown to subsume these attempts as well as offer a more consistent classification scheme. An example is provided for using the functional basis to form a functional model. Applications to the areas of product architecture development, function structure generation, and design information archival and transmittal are discussed.

Functional Similarity at Varying Levels of Abstraction

2010 ◽  
Author(s):  
Benjamin W. Caldwell ◽  
Gregory M. Mocko
Keyword(s):  
Clustering Algorithm ◽  
Consumer Products ◽  
Controlled Vocabulary ◽  
Functional Similarity ◽  
Concept Generation ◽  
Levels Of Abstraction ◽  
Similarity Metric ◽  
Conceptual Design Phase ◽  
Functional Models ◽  
Function Models

Function modeling is often used in the conceptual design phase as an approach to capture a form-independent purpose of a product. Current research efforts have focused on the formalization of functional models, development of function-based design repositories, and concept generation based on a quantitative functional similarity metric. In this paper, three levels of abstraction of function models are obtained by including supporting functions, excluding supporting functions, and applying abstraction rules to function models of 128 products in a design repository. The similarity of these products is computed using the Functional Basis controlled vocabulary and a matrix-based similarity metric. A matrix-based clustering algorithm is then applied to the similarity results to identify groups of similar products. A subset of these products is then studied to further compare the three levels of abstraction and to validate the results. Similarity between consumer products depends on the level of abstraction of the models, with higher levels of abstraction producing better results.

scholarly journals Adjustment models for multivariate geodetic time series with vector-autoregressive errors

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Boris Kargoll ◽  
Alexander Dorndorf ◽  
Mohammad Omidalizarandi ◽  
Jens-André Paffenholz ◽  
Hamza Alkhatib
Keyword(s):  
Least Squares Method ◽  
Functional Model ◽  
Expectation Maximization Algorithm ◽  
Two Dimensions ◽  
Vector Autoregressive ◽  
Wide Range ◽  
Engineering Geodesy ◽  
Cross Correlations ◽  
T Distribution ◽  
Multivariate T

Abstract In this contribution, a vector-autoregressive (VAR) process with multivariate t-distributed random deviations is incorporated into the Gauss-Helmert model (GHM), resulting in an innovative adjustment model. This model is versatile since it allows for a wide range of functional models, unknown forms of auto- and cross-correlations, and outlier patterns. Subsequently, a computationally convenient iteratively reweighted least squares method based on an expectation maximization algorithm is derived in order to estimate the parameters of the functional model, the unknown coefficients of the VAR process, the cofactor matrix, and the degree of freedom of the t-distribution. The proposed method is validated in terms of its estimation bias and convergence behavior by means of a Monte Carlo simulation based on a GHM of a circle in two dimensions. The methodology is applied in two different fields of application within engineering geodesy: In the first scenario, the offset and linear drift of a noisy accelerometer are estimated based on a Gauss-Markov model with VAR and multivariate t-distributed errors, as a special case of the proposed GHM. In the second scenario real laser tracker measurements with outliers are adjusted to estimate the parameters of a sphere employing the proposed GHM with VAR and multivariate t-distributed errors. For both scenarios the estimated parameters of the fitted VAR model and multivariate t-distribution are analyzed for evidence of auto- or cross-correlations and deviation from a normal distribution regarding the measurement noise.

Validation of Function Pruning Rules Through Similarity at Three Levels of Abstraction

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Benjamin W. Caldwell ◽  
Gregory M. Mocko
Keyword(s):  
Conceptual Design ◽  
Clustering Algorithm ◽  
Controlled Vocabulary ◽  
Design Activity ◽  
Conceptual Level ◽  
Levels Of Abstraction ◽  
Similarity Metric ◽  
Level Of Abstraction ◽  
Design By Analogy ◽  
Function Models

Function modeling is often used in the conceptual design phase as an approach to capture a form-independent purpose of a product. Previous research uses a repository of reverse-engineered function models to support conceptual-based design tools, such as similarity and design-by-analogy. These models, however, are created at a different level of abstraction than models created in conceptual design for new products. In this paper, a set of pruning rules is developed to generate an abstract, conceptual-level model from a reverse-engineered function model. The conceptual-level models are compared to two additional levels of abstraction that are available in a design repository. The abstract models developed through the pruning rules are tested using a similarity metric to understand their usefulness in conceptual design. The similarity of 128 products is computed using the Functional Basis controlled vocabulary and a matrix-based similarity metric at each level of abstraction. A matrix-based clustering algorithm is then applied to the similarity results to identify groups of similar products. A subset of these products is studied to further compare the three levels of abstraction and to validate the pruning rules. It is shown that the pruning rules are able to convert reverse-engineered function models to conceptual-level models, better supporting design-by-analogy, a conceptual-stage design activity.

Functional Models With Inherent Behavior: Towards a Framework for Safety Analysis Early in the Design of Complex Systems

2016 ◽  
Author(s):  
Matthew G. McIntire ◽  
Elham Keshavarzi ◽  
Irem Y. Tumer ◽  
Christopher Hoyle
Keyword(s):  
Design Process ◽  
Functional Model ◽  
Behavioral Model ◽  
Safety Analysis ◽  
State Machine ◽  
System Component ◽  
State Transitions ◽  
Failure Behavior ◽  
State Machines ◽  
Functional Models

This paper represents a step toward a more complete frame-work of safety analysis early in the design process, specifically during functional modeling. This would be especially useful when designing in a new domain, where many functions have yet to be solved, or for a problem where the functional architecture space is large. In order to effectively analyze the inherent safety of a design only described by its functions and flows, we require some way to simulate it. As an already-available function failure reasoning tool, Function Failure Identification and Propagation (FFIP) utilizes two distinct system models: a behavioral model, and a functional model. The behavioral model simulates system component behavior, and FFIP maps specific component behaviors to functions in the functional model. We have created a new function-failure reasoning method which generalizes failure behavior directly to functions, by which the engineer can create functional models to simulate the functional failure propagations a system may experience early in the design process without a separate behavioral model. We give each basis-defined function-flow element a pre-defined behavior consisting of nominal and failure operational modes, and the resultant effect each mode has on its functions connected flows. Flows are represented by a two-variable object reminiscent of a bond from bond graphs: the state of each flow is represented by an effort variable and a flow-rate variable. The functional model may be thought of as a bond graph where each functional element is a state machine. Users can quickly describe functional models with consistent behavior by constructing their models as Python NetworkX graph objects, so that they may quickly model multiple functional architectures of their proposed system. We are implementing the method in Python to be used in conjunction with other function-failure analysis tools. We also introduce a new method for the inclusion of time in a state machine model, so that dynamic systems may be modeled as fast-evaluating state machines. State machines have no inherent representation of time, while physics-based models simulate along repetitive time steps. We use a more middle-ground pseudo time approach. State transitions may impose a time delay once all of their connected flow conditions are met. Once the entire system model has reached steady state in a timeless sense, the clock is advanced all at once to the first time at which a reported delay is ended. Simulation then resumes in the timeless sense. We seek to demonstrate this modeling method on an electrical power system functional model used in previous FFIP studies, in order to compare the failure scenario results of an exhaustive fault combination experiment with similar results using the FFIP method.

Modality and representation in analogy

2008 ◽  
Vol 22 (2) ◽  
pp. 85-100 ◽  
Author(s):  
J.S. Linsey ◽  
K.L. Wood ◽  
A.B. Markman
Keyword(s):  
Prior Knowledge ◽  
English Language ◽  
Functional Model ◽  
Cognitive Mechanisms ◽  
Support Design ◽  
Design Problems ◽  
Functional Models ◽  
Current Design ◽  
Design By Analogy ◽  
General Semantic

AbstractDesign by analogy is a powerful part of the design process across the wide variety of modalities used by designers such as linguistic descriptions, sketches, and diagrams. We need tools to support people's ability to find and use analogies. A deeper understanding of the cognitive mechanisms underlying design and analogy is a crucial step in developing these tools. This paper presents an experiment that explores the effects of representation within the modality of sketching, the effects of functional models, and the retrieval and use of analogies. We find that the level of abstraction for the representation of prior knowledge and the representation of a current design problem both affect people's ability to retrieve and use analogous solutions. A general semantic description in memory facilitates retrieval of that prior knowledge. The ability to find and use an analogy is also facilitated by having an appropriate functional model of the problem. These studies result in a number of important implications for the development of tools to support design by analogy. Foremost among these implications is the ability to provide multiple representations of design problems by which designers may reason across, where the verb construct in the English language is a preferred mode for these representations.

Experimental Studies Assessing the Repeatability of a Functional Modeling Derivation Method

2003 ◽  
Vol 125 (4) ◽  
pp. 682-693 ◽  
Author(s):  
Mark A. Kurfman ◽  
Michael E. Stock ◽  
Robert B. Stone ◽  
Jagan Rajan ◽  
Kristin L. Wood
Keyword(s):  
Design Research ◽  
Functional Model ◽  
Experimental Studies ◽  
Testing Procedure ◽  
Research Literature ◽  
Functional Modeling ◽  
Skill Levels ◽  
Functional Models ◽  
Model Derivation ◽  
Derivation Method

This paper presents the results of research attempts to substantiate repeatability and uniqueness claims of a functional model derivation method following a hypothesis generation and testing procedure outlined in design research literature. Three experiments are constructed and carried out with a participant pool that possesses a range of engineering design skill levels. The experiments test the utility of a functional model derivation method to produce repeatable functional models for a given product among different designers. In addition to this, uniqueness of the functional models produced by the participants is examined. Results indicate the method enhances repeatability and leads designers toward a unique functional model of a product. Shortcomings of the method and opportunities for improvement are also identified.

A Comparison of Vector and Network-Based Measures for Assessing Design Similarity

2020 ◽  
Author(s):  
Ananya Nandy ◽  
Andy Dong ◽  
Kosa Goucher-Lambert
Keyword(s):  
Functional Model ◽  
Similarity Measures ◽  
Current Function ◽  
Surface Level ◽  
Graph Similarity ◽  
Functional Models ◽  
Design By Analogy ◽  
Computational Systems ◽  
The Impact ◽  
Target Design

Abstract In order to retrieve analogous designs for design-by-analogy, computational systems require the calculation of similarity between the target design and a repository of source designs. Representing designs as functional abstractions can support designers in practicing design-by-analogy by minimizing fixation on surface-level similarities. In addition, when a design is represented by a functional model using a function-flow format, many measures are available to determine functional similarity. In most current function-based design-by-analogy systems, the functions are represented as vectors and measures like cosine similarity are used to retrieve analogous designs. However, it is hypothesized that changing the similarity measure can significantly change the examples that are retrieved. In this paper, several similarity measures are empirically tested across a set of functional models of energy harvesting products. In addition, the paper explores representing the functional models as networks to find functionally similar designs using graph similarity measures. Surprisingly, the types of designs that are considered similar by vector-based and one of the graph similarity measures are found to vary significantly. Even among a set of functional models that share known similar technology, the different measures find inconsistent degrees of similarity — some measures find the set of models to be very similar and some find them to be very dissimilar. The findings have implications on the choice of similarity metric and its effect on finding analogous designs that, in this case, have similar pairs of functions and flows in their functional models. Since literature has shown that the types of designs presented can impact their effectiveness in aiding the design process, this work intends to spur further consideration of the impact of using different similarity measures when assessing design similarity computationally.

An Investigation Into the Effectiveness of an Algorithmic Approach to Teaching Functional Modeling

2013 ◽  
Author(s):  
Robert L. Nagel ◽  
Matt R. Bohm ◽  
Julie S. Linsey
Keyword(s):  
Engineering Design ◽  
Positive Impact ◽  
Functional Model ◽  
Preliminary Evidence ◽  
Algorithmic Approach ◽  
Functional Models ◽  
Grammar Rules ◽  
Approach To Teaching ◽  
Teaching Function

The consideration of function is prevalent across numerous domains as a technique allowing complex problems to be abstracted into a form more readily solvable. In engineering design, functional models tend to be of a more generalized nature describing what a system should do based on customer needs, target specifications, objectives, and constraints. While the value of function in engineering design seems to be generally recognized, it remains a difficult concept to teach to engineering design students. In this paper, a study on the effectiveness of an algorithmic approach for teaching function and functional model generation is presented. This paper is a follow-up on to the 2012 ASME IDETC paper, An Algorithmic Approach to Teaching Functionality. This algorithmic approach uses a series of grammar rules to assemble function chains which then can be aggregated into a complete functional model. In this paper, the results of a study using the algorithmic approach at Texas A&M in a graduate level design course are presented. The analysis of the results is discussed, and the preliminary evidence shows promise toward supporting our hypothesis that the algorithmic approach has a positive impact on student learning.

scholarly journals Function modeling combined with physics-based reasoning for assessing design options and supporting innovative ideation

2017 ◽  
Vol 31 (4) ◽  
pp. 476-500 ◽  
Author(s):  
Hossein Mokhtarian ◽  
Eric Coatanéa ◽  
Henri Paris
Keyword(s):  
Functional Model ◽  
Mathematical Framework ◽  
Functional Modeling ◽  
Design Problems ◽  
Academic Communities ◽  
Functional Representations ◽  
Incremental Improvement ◽  
Design Options ◽  
Structural Blocks

AbstractFunctional modeling is an analytical approach to design problems that is widely taught in certain academic communities but not often used by practitioners. This approach can be applied in multiple ways to formalize the understanding of the systems, to support the synthesis of the design in the development of a new product, or to support the analysis and improvement of existing systems incrementally. The type of usage depends on the objectives that are targeted. The objectives can be categorized into two key groups: discovering a totally new solution, or improving an existing one. This article proposes to use the functional modeling approach to achieve three goals: to support the representation of physics-based reasoning, to use this physics-based reasoning to assess design options, and finally to support innovative ideation. The exemplification of the function-based approach is presented via a case study of a glue gun proposed for this Special Issue. A reverse engineering approach is applied, and the authors seek an incremental improvement of the solution. As the physics-based reasoning model presented in this article is heavily dependent on the quality of the functional model, the authors propose a general approach to limit the interpretability of the functional representations by mapping the functional vocabulary with elementary structural blocks derived from bond graph theory. The physics-based reasoning approach is supported by a mathematical framework that is summarized in the article. The physics-based reasoning model is used for discovering the limitations of solutions in the form of internal contradictions and guiding the design ideation effort.

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