1. INTRODUCTION
Functions are used to model designs in a manner that captures
information distinct from, but related to, the physical structure and
behavior of a design solution. A function describes the physical effect
imposed on an energy or material flow by a design entity without regard
for the working principles or physical solutions used to accomplish this
effect. The functional language used in this work is the Functional Basis
developed by Stone and Wood (2000), reconciled
by Hirtz et al. (2002), and tested for utility
(Ahmed & Wallace, 2003; Kurfman et al., 2003). Although a detailed review of
this language is not part of this work, the functional basis describes a
function as a transformation between a set of input flows to a set of
outputs. Here, flows represent energy, material, or signals that flow into
and out of the physical artifact being represented functionally. In this
language, the function for a motor can be represented as
“convert” where the input flow is electrical energy and the
output flow is mechanical rotation. Other languages, concepts, and
definitions of functions are available that take different perspectives
(Umeda & Tomiyama, 1997; Chittaro & Kumar, 1998; Deng,
2002). Hubka and Eder (2001) note that
there are several versions of function definitions, usage, and their
utility. The functional basis is a suitable functional language but an
open problem, and the focus of this work is the specific nature of how
functions are used in design, and particularly, how the mapping of
functionality to physical solutions can and should occur. A key aspect in
this regard is the representation of not only functions but also the other
aspects of design that functions represent or to what these are related.
Wood and Greer (2001) identify the development
of hybrid representations that integrate both functions and other design
specifications as an opportunity for advancing function-based synthesis
methods. The purpose of this work is to present a holistic model for
function-based representations (FBRs) that will serve as a foundation for
an underlying knowledge framework to support the development of artificial
intelligence (AI) design techniques. Toward this end, the objectives of
this work are the following:
- define a formalism for two aspects of FBRs: composition and
mappings;
- examine how the model for FBRs supports design activities; and
- present examples of how computational design methods can benefit
from this formalism.
A common perception is the need for representations of function,
behavior, and structure (Chandrasekaran &
Josephson, 2000; Chang et al., 2000;
Brown, 2003). Behavior, in the sense of physical
events associated with a physical artifact (or hypothesized concept) over
time (or simulated time) as perceived by an observer, is the least
formalized of the three concepts, and addressing this topic is relegated
to future work. Structure is the most tangible concept with various
approaches to partitioning structure into meaningful constituents such as
features (Brown, 2003), Wirk elements (Jensen, 2000), and interfaces (Ullman, 1997) in addition to the widely used
assemblies and components. Depending on the structural definitions used,
different schemes can be prescribed for allocating function to structure.
One of the more formal approaches to dealing with these allocations or
mappings is the development of a functional ontology (Kitamura & Mizoguchi, 1998). Regardless of the
mapping scheme used, the primary significance of functionality is its
independence with structure.
The independence of functionality from particular choices and details
of structure is precisely how functions represent design concepts as an
abstraction from the form or structure of these physical attributes. With
this abstraction, perhaps the most significant, or at least most prevalent
purpose of functional models, is to facilitate freedom in thinking and
reasoning about design solutions without the greater restriction
associated with the structure domain (Pahl &
Wallace, 2002). Both psychological inertia and higher information
content related to the structure domain lead to this restriction.
Functional models in this sense are a lean medium for cognitive
processing, but as Chandrasekaran and Josephson (2000) indicate, especially for computer applications,
this information requires an explicit description of how functional
knowledge is represented.
Two different types of abstractions exist for functional
representations. First is the hierarchy defined in the functional language
itself, such as the three levels of the functional basis (Stone & Wood, 2000). These levels offer a
general-specific classification of function terms. For example, the
function “channel” at the primary level subsumes a more
refined set of functions such as “import” and
“export” at the secondary level. The second type of
abstraction is that of system hierarchy that is sometimes referenced as
aggregation–decomposition or a part-of relation. This refers to the
specification of a functional model where certain high-level functions are
decomposed into lower level functions. The Functional Analysis System
Technique (Miles, 1961; Otto
& Wood, 2001) for developing functional models offers a
hierarchical structure for describing the functionality at multiple levels
of system detail. Similarly, the use of a black box model shows a high
level structure while a functional model provides greater detail. Kitamura
and Mizoguchi (2004) also distinguish between
the above two types of abstraction.
Although benefits of abstraction are readily apparent, the
independence of functionality from structure is complicated by how
functions are allocated to physical solutions particularly in a reverse
engineering or similar mode of analysis. Functional representations,
physical representations, and physical devices themselves exhibit
hierarchical organization and some basic questions are appropriate (Kueneke, 1991). What are the elements of this
information set? Is this set of constructs comprehensive and irreducible?
Given an established composition, how are functions mapped to physical
artifact information? How does this mapping scheme relate to the design
activity being conducted? More broadly, the concern is how the quality of
functional models can be best realized in terms of the composition and
mapping characteristics for various design activities as prescribed in
design methods.
Prior work has addressed the manner in which functionality is
allocated to the various physical system levels in various degrees (Kitamura & Mizoguchi, 1998; Jensen, 2000; Brown, 2003;
Shi & Schmidt, 2003), but the authors are
not aware of a comprehensive treatment of function allocation in a general
context that accounts for the various types of design activities and
conditions in which functional modeling is employed. To understand the
relationship between functionality and the different physical scales on
which functionality is manifested, one task of this research is to examine
the issue of resolution as it applies to functional models.
From a modeling perspective, the quality of information contained in a
model is important because the model must be predictive in ways that
enable design (McAdams & Dym, 2004). In the
specific case of functional modeling, the issue of prediction capability
is perhaps less significant than the issue of facilitating divergent
thinking, at least in a synthesis mode. Similarly, precision and accuracy
in the analysis mode is important because, as prior work shows, functional
models can be used in a reverse engineering approach to archive design
information (Bohm, Stone, & Szykman, 2003)
and to use such archived knowledge for design synthesis (Gietka et al., 2002; Strawbridge et
al., 2002). Clearly, the issues of composition and mappings
propagate beyond reverse engineering to design synthesis when considering
that certain computational synthesis methods rely on data archived from
these reverse engineering analyses. Moreover, functions have already been
related to not only form, but also information of user actions (Janhager, 2003), performance parameters in the form of
equations (Bryant et al., 2001; Yekula et al., 2003), and failure mode data (Tumer & Stone, 2003). It is essential to
understand the composition and mappings of functions and their relation to
design activities because this information is part of the foundation for
function-based methods, and consequently dictates the performance of those
methods.
2. DEVELOPING COMPOSITIONS AND MAPPINGS OF
FBRs
The goal of developing the FBR model is to establish the informational
items relevant to FBR and the relationships among them. As for model
composition, we seek a comprehensive and irreducible set that make up the
hierarchy of terms in both the function and structure domains. The
mappings among these elements is then developed to show how these items
can be associated, stored computationally, and used for automated design
purposes. Much of this task is deciphering how considerable efforts from
prior research can be joined to form a model of FBRs.
2.1. Composition of FBRs
2.1.1. Function
A primary issue for the composition of elements in the function domain
is the concept of resolution. Low resolution implies coarse or abstract
partitioning of functionality where this resolution can be interpreted in
terms of both the functional language and the functional model. For the
resolution within the model, a comparison between a black box model and a
functional model in Figure 1 illustrates this
point with a device designed to tag trees. Here, the black box is a single
function that encapsulates the functionality of the entire functional
model into what is taken to be the overall device function. The process of
decomposing functions into lower level functions can continue until
further decomposition no longer benefits the design activity. This
open-ended interpretation places no restriction on the upper or lower
bounds of resolution where the terms of the Functional Basis can be used
at any resolution level. Selection of best resolution depends of this
design activity, and is examined in Section 2.2.
Different functional model resolutions.
In addition to functions, the term module is a distinct entity that
simply describes a set of functions. Although a single function such as
“convert” is indicated as a module based on the modular
heuristics by Stone et al. (2000), a module is
more commonly a group of two or more functions.
The concepts of modules and functions deal with customer-driven
functions, that is, functions that are directly related to customer needs.
The function “store paper” for a printer is an example.
Supporting functions recently investigated by Bohm and Stone (2004) and referred to as metafunctions by Kitamura and
Mizoguchi (1999), are functions of the physical
artifact acting on itself rather than external flows. Specifically,
supporting functionality is defined as “functions that describe
manufacturing, assembly, and support features present in the embodied form
of a product” (Bohm & Stone, 2004).
For example, the function “secure lid” for a CD holder
describes the action of the compliant mechanism detent of the base as it
acts on the lid by securing it. This distinction between customer-driven
and supporting functionality is significant, and suggests that supporting
functions are another basic entity in the FBR model. The hierarchy of a
functional model is the only factor imposing variations in resolution.
Beyond the resolution of the functional models is the issue of the
functional vocabulary. Three levels of abstraction are specified in the
functional basis for both the functions and flows (Stone & Wood, 2000). No constraints are placed on
how the different levels are used or mixed within a functional model other
than certain restrictions due to the compatibility between functions and
flows. Additionally, the customer needs and type of design problem
influence the choice of resolution level. Despite this flexibility, the
functional basis offers a comprehensive set of customer-driven functions
that offer consistency of function terminology.
2.1.2. Form
Resolution with respect to physical partitions is more complicated.
Here resolution is in terms of the degree of partitioning of a physical
artifact in which the partitioned elements can be associated with one or
more functions. The central issue of physical resolution is the manner in
which a product can be divided along meaningful lines at various degrees
of granularity. This is a description of only how a physical item is
divided and is separate from the issue of how functions are allocated or
associated with the partitioned elements of the product. It may be the
case that while relatively high physical resolution is used, the
allocation of function is kept at a low level of resolution. The issue of
allocation is addressed in Section 2.2.
It is important to note that because functionality of a product is
sometimes specified before the physical artifact exists or is even
conceptualized as in the case of original design, the issue of resolution
and therefore partitioning becomes difficult. In the case of original
design it is irrational to define resolution in terms of the degree of
physical partitioning because nothing yet exists to partition. For
purposes of defining a set of physical elements for the FBR, this problem
is avoided by treating resolution strictly in the context of a descriptive
application such as reverse engineering when the physical device already
exists and the functional model is constructed to represent this
artifact.
As an upper bound of resolution, the complete product or system as a
whole seems the obvious choice. Exploiting this idea, the next issue
becomes the definition of the complete system boundary. Generally, an
individual product can be bounded as a system by its physical boundary,
although certain exceptions apply. Product family design is one exception
where a set of products may make up a system boundary to illustrate the
overall functional behavior of the portfolio rather than individual
products. Additionally, the functional interactions among the members of
the product family may be described if the complete functional model
contains the product family set. A second exception is in the context of
sustainable design or design for the environment. Given the importance of
life-cycle effects in sustainable design, it is desirable to introduce
systems and processes into the system model that would otherwise normally
be outside the system boundary. In this case, the upper bound may include
a wide spectrum of entities ranging from design teams, manufacturing
units, the customer, product take-back facilities, recycling and
refurbishing units, and so forth. From these two exceptions we define a
physical element named metaproduct systems.
Skipping to the opposite end of the resolution spectrum at the
subcomponent level, features (Brown, 2003) or
Wirk elements (Jensen, 2000) are suitable
concepts as they account for functionality at the smallest meaningful
levels with the possible exception of mechanical devices at the micro- or
nanoscale. For example, the tip of a screwdriver clearly exhibits a
function distinct from other portions of the tool, just as the edge of a
knife differs in functionality from the remainder of the blade. Defining
elements that can separate these physical aspects is the task. Wirk
elements are selected here as the low-end physical element because they
are clearly defined as geometrical properties of the designed artifact.
However, to capture the properties of features, as explained by Brown
(2003), that are not readily allocated to a
region of an artifact, these properties are addressed outside the scope of
the physical elements and are discussed in the next section.
Between the upper bound of metaproduct and the lower bound of Wirk
elements, the only intermediate levels that seem meaningful and distinct
are assemblies and components. Each involves a fundamental discontinuity
in the makeup of physical products. These levels are described in Table 1.
Resolution levels and partitioned elements
Selection of the levels in Table 1 is based
on the requirement that each level offer a clearly distinct degree of
resolution. The design data model discussed recently by Aurisicchio et al.
(2003) is based on matrices developed by
Blessing (1994), which include the product,
assembly, and component levels. The proposed levels in Table 1 differ by treating the products as an
assembly. In addition, the Wirk elements are included to address the
subcomponent level. At the low-resolution end, the metaproduct level is
very high level, and offers an overall perspective. The assembly level has
perhaps the widest breadth of the four levels by including all assemblies
whether small modules or major assemblies containing multiple
subassemblies. This broadly applicable level serves as a basis for a
hierarchical approach to function-based product descriptions. The Vehicle
Platform Partitioning System used by General Motors is one industry
example of such a hierarchical strategy in practice today (Bohm, Stock, et al., 2003). Compared with the assembly
level that is applicable down to a component, the component level is
narrowly defined to capture single piece parts. For many original
equipment manufacturer products such as motors, bearings, hydraulic
cylinders, and so forth, these items overall would be captured as an
assembly rather than a component. This approach differs from what is
perceived as conventional practice, which is to treat such items as
“components.” At the finest level of resolution, Wirk elements
discussed by Jensen (2000) are the foundation
for the smallest partitioning that seems reasonable. These elements allow
description of functionality within components. The use of these Wirk
elements enables the description of functionality within components in
terms of geometrical properties. This particular level is rich in
supporting functionality.
2.1.3. FBR model elements
In addition to functional elements and physical elements, a broader
perspective is taken to include three fundamental categories of product
design information in the FBR model. These are the design, performance,
and noise spaces that are respectively described using design variables
(D), noise variables (N), and performance metrics
(P), where each of these is comprehensive and measurable as
described in Otto and Wood (2001). Briefly, the
performance metrics are indicators of design objectives, design variables
represent those items of a design for which a designer has a choice, and
noise variables represent items that are beyond the control of the
designer. Each of these reflects, to various degrees, the behavior of a
design. Customer needs, for example, are accounted for by performance
metrics that reflect the customer need objective. The general format is
P = f (D, N), where D
includes the specification of function and structure as these and other
examples are shown in Table 2. The scope of
relations that are available in this framework is comparable to those
achieved by the “object in the system” approach taken by
Stetter et al. (2001).
Design and noise variables and performance metrics
2.2. Mappings of FBRs
Figure 2 illustrates the combined concepts
of composition and mappings. Here the issue of composition lies in the
type of primitives used across both the function and structure domains in
their respective hierarchies and individual levels of abstraction.
Mappings refer to the associations among these elements and to relevant
factors that constrain the design. These mappings are considered in the
next section.
Elements of function and form as design variables.
Function allocation refers to the mapping or association of function
elements with physical elements. Function allocation is independent of
resolution, but the scheme used to associate functionality with the
physical elements influences the effectiveness of functional modeling. In
this context, the effectiveness of the function allocation scheme is
dependent on the type of design task or activity. The main purpose in
examining function allocation is that previous work does little to address
how allocation should be performed to maximize the effectiveness of
functional modeling. It seems that the allocation strategy is left to the
discretion of the designer. Given the variation in the level of detail
that is possible with different approaches toward allocation, it is
reasonable to assume that this performance can be improved by certain use
of function allocation. A matrix approach for storing function allocation
information is presented, followed by a discussion of allocation with
respect to two prominent design activities: analysis and synthesis.
2.2.1. Adjacency matrix representation for FBR
mappings
Regardless of the scheme used for function allocation, the basic
structure used to store these relations is a graph where an adjacency
matrix can then be formed, as shown in Figure 3.
Such matrices offer a format that is suitable for computation. Examples of
functions to physical elements at different levels are given in Figure 4. In each of these cases, these matrices can
be expanded to include large quantities of archived data from analyses of
existing devices and used to populate a morphological matrix of candidate
physical solutions based on an initial set of functions (Strawbridge et al., 2002). This prior work denotes
these matrices containing archived information as χ matrices, and
this notation is adopted here. In general, χ matrices can be formed
between any two informational items. The correlation of function and
failure modes (Tumer & Stone, 2003) is one
case of an association between design variables and an indicator of
performance metrics. This approach provides a very broad capability for
making associations. Some examples of potential χ matrices include
mappings from functions to assemblies, supporting functions to Wirk
elements, components to their nominal design flexibility, components to
components [design structure matrix (DSM)], modules to
functions, and so forth. Allocating functions with physical solutions at
these different resolution levels (assemblies, components, etc.), allow
separate physical solution searches for each level. For example, physical
solutions at the Wirk element level could be searched to identify
candidate interfaces and, in the process, screen out solutions at other
resolution levels. In addition, this archived data at different resolution
levels can be used to support studies that examine the relation between
functions and their common implementations in terms of physical
resolution.
Function-based associations.
Examples of function associations in χ matrices at four different
resolutions.
2.2.2. Function allocation
Function allocation deals with the issue of resolution used to
associate a functional representation with a physical solution. Resolution
in this sense refers to two items: the level of detail in the functional
model itself, and the physical resolution of the artifact being
represented. A high-resolution functional model would have a large number
of functions to describe the system of interest. Similarly, a
high-resolution description of a physical system would take a
magnification approach to account for the functionality of physical
features at small scales.
One purpose of functional modeling during synthesis is to enhance the
solution search process by providing the designer a means for thinking
about solutions independent of physical form. Outside the scope of
computational approaches, manual use of functions works well when the
following two, somewhat conflicting, constraints are met. First, the
functional model must be sufficiently abstract that normal mental cues
that funnel and restrict the designer to a previously used experience set
are no longer active. This directly facilitates the kind of “outside
the box” thinking that is desirable. The second constraint requires
sufficient descriptive power from the functional model so the solution
presents enough detail to be worthwhile for advancing the design.
These two constraints are representative of two extreme case
approaches that can be employed during function-based synthesis. A small
common DC electric motor is a good example that illustrates both of these
approaches. In the case of a motor, the overall functionality may be
described as simply “convert electrical energy to mechanical
energy.” This allocates a single overall function to the complete
motor assembly that consists of lower level assemblies (housing, armature,
etc.) and components (magnets, bushings, etc.). At the other end of the
spectrum, each function for all levels of detail down to the Wirk element
level could be described. In addition, this entire set could be attributed
collectively to the overall motor assembly. This subsumes all
functionality contained within the motor. Particularly for a motor, the
approach using an overall single function of “convert” is
probably a more effective use of function allocation because these motors
are often selected and purchased rather than designed in-house. However, a
functional model with greater detail may be appropriate for situations
when the motor is custom designed. These two cases are referenced simply
with the level of detail in their approach.
It may seem counterproductive to ever need great levels of functional
detail (e.g., down to and including functionality at Wirk element level)
during design synthesis. However, several factors, which are examined
below in Table 3, could warrant such detail. A
designer may choose to utilize a high level or very detailed approach or
an intermediate level of detail in how functions are allocated. Clearly,
there are distinctions among these approaches, yet little guidance is
presented in the literature for the most effective approach for a
particular design task. Although the best approach is dependent on the
particular circumstances of the designer and the design problem, we
address this issue by examining how different factors affect the
allocation of functions during functional modeling. This provides a
hypothesized effect for the level of functional allocation with respect to
certain design issues that are commonly encountered.
Design issues and effects on function allocation
As an overall observation, the best level of functional detail is
ultimately dependent on the potential benefits that could be gained from
the given detail being considered. Functions at any level chosen should
aid the designer to think, reason, reduce uncertainty, and explore
concepts. It appears that the choice of function allocation in terms of
detail is highly variable and dependent on the particular product, the
type of design being performed, and project constraints such as time
available to the designer.
The particular issue involving the stage of design raises some points
that are not typically addressed when discussing functional modeling.
Normally, function-based synthesis is utilized in the early stages of
design but it is plausible that the benefits of reasoning with functions
can be realized by using a function-based approach throughout the design
process. One consequence of using functional modeling during the later
stages of design is that such an approach accounts for increasing levels
of detail in a design in a manner that still allows a degree of divergent
thinking afforded by the abstraction of functions. For example, the design
of a computer mouse could take advantage of functional modeling by
identifying functions of hand input surfaces. These functions, in turn,
may spawn new ideas for shaping the exterior body and interfaces. Although
relatively high level abstractions and little detail in function
allocation may be necessary during the up-front functional modeling
performed during the early stages of a computer mouse, the embodiment and
detailed design stages could potentially benefit from employing functional
modeling at a fairly detailed level during these later stages. Of course,
the functional modeling used in later stages may be limited in scope and
restricted to particular portions of the design because functional
modeling need not demand a complete and exhaustive model at these later
design stages regardless of the function allocation detail.
2.3. FBR model development summary
The FBR model is a collection of ideas explained in the general
context of design, noise, and performance metrics. These ideas are
individually established largely in prior work but interpreted here in a
manner that define a full scale of resolution in both the function and
physical domains, are explained in a general context of design, noise, and
performance metrics, and offer a matrix approach for storing
function-based and other relevant design information. The FBR model
includes a composition of both function and physical elements that are
comprehensive across the resolution scale of interest and irreducible in
the sense that the distinguishing characteristics of the terms specified
exhibit negligible redundancy. Because these terms are presented in the
context of the broader set of design, noise, and performance parameters,
many relations become readily identifiable. These associations in matrix
form are a consistent and computable format for capturing not only
function-based information as it relates to structure and other
parameters, but also for capturing information between any two meaningful
variables in the FBR model. Discussions are given for the issue of
function allocation in terms of design synthesis; yet, it is clear that
other design tasks are relevant. To understand the role of FBRs throughout
design, the following section examines the FBR model with respect to a
recently developed ontology of generic engineering design activities
(Sim & Duffy, 2003).
3. FBR MODEL IN SUPPORT OF DESIGN
ACTIVITIES
Perhaps the best measure of utility for the FBR model is evidenced by
how the FBR model supports design activities. Despite the above
discussion, which treats only the broad activities of design synthesis, a
much larger set of activities are relevant. To assess the FBR model with
respect to a comprehensive set of activities, the proposed ontology by Sim
and Duffy (2003) is used. Tables 4, 5, and 6 present the assessment of the FBR model where the
first two columns are used from Sim and Duffy (2003) to clearly describe the design activity. In the
second column, the knowledge change refers to the impact that the design
activity imposes on the input knowledge compared to the output knowledge
resulting from the activity. The third column is an estimate of how the
FBR model supports the knowledge change for a given activity. For some
activities, multiple knowledge changes are listed, and when appropriate,
the third column treats these distinctly. In some of these cases, such as
the “decomposing” activity, the FBR support description
applies to the activity overall.
Design definition activities, knowledge changes, and how the FBR model
supports them
Design evaluation activities, knowledge changes, and how the FBR model
supports them
Design management activities, knowledge changes, and how the FBR model
supports them
Based on this assessment, it is apparent that both the design
definition and evaluation categories in Tables 4
and 5 are well supported, while the design
management activities are much less relevant to the FBR model. The support
for the substantial number of design activities implies that the basic
informational items within the FBR model are comprehensive for design over
a broad range of activities. This does not suggest that the FBR model
serves as a design method because no logic, operations, or other
processing actions are part of the model. However, given the relevance of
the model to several design activities, it is reasonable to claim that the
FBR model is a useful foundation for the development of design methods
that could potentially span a large number of design activities.
Specifically, the FBR model in terms of its composition indicates the
specific information that may be useful for a function-based design
method, while the mappings are suggestive of the type of relations that
may be useful. The FBR model also indicates that a matrix-based approach
is a useful format for capturing these relations.
4. FBR INSPIRED METHODS AND
APPLICATIONS
To further explore the FBR model potential, this section examines
specific methods that can benefit from the FBR model. The point is to show
examples of how the concepts from the FBR model (e.g., resolution of
function and physical artifacts; design, noise, and performance
parameters; matrix-based mappings of function and form information) can
inspire and support function-based design methods and applications. First,
two reverse engineering applications are examined where both use the FBR
model for knowledge archival to support analysis type activities, while
the second section examines specific uses of the FBR model to support
synthesis operations in AI applications.
4.1. Reverse engineering knowledge archival for AI:
Computational product analysis and description
4.1.1. Product repositories: Improvements and new
directions
The main purpose of product repositories is to capture and store
design information in a format that facilitates analyses or empirical
studies of historical product data, promotes consistency of design
information, and allows past design data to be reused for design synthesis
activities. Given this purpose, the FBR model indicates that design
information is captured for multiple levels of product abstraction.
Functional models are separated in terms of function, modules, and
supporting functionality in addition to the three abstraction levels
specified in the functional basis language. Similarly, physical data can
be recorded at the metaproduct, assembly, component, and Wirk element
levels to clearly distinguish the physical attribute under consideration.
For example, the combined information of supporting functionality and Wirk
element data allows for capture of functionality for physical
interfaces.
Regardless of the resolution level chosen, the consistency of data
collected is improved by maintaining resolution consistency. This offers
an improvement over current methods in which both the resolution and
allocation of function information may fluctuate during reverse
engineering activities due to the perceived issues of importance from the
person performing the task. In addition to consistency is the issue of
completeness. By capturing product data systematically at each individual
level, a more comprehensive view of the product is achieved. Currently,
several items regarding function and form are captured in the University
of Missouri–Rolla online design repository as shown in Figure 5 (Bohm, Stone, &
Szykman, 2003; Bohm & Stone,
2004).
The jigsaw product information in the design repository.
More generally, the FBR model indicates product data relating function
and form data to performance information is archived. In addition to the
current interest in capturing failure data (Tumer &
Stone, 2003), potentially many additional performance-related
factors could be stored. Similarly, information regarding noise variables
could be correlated with both function and form. As an example, designs
are driven by customer needs, although these customer needs are not
entirely bounded or necessarily reflected directly by customer.
Precipitating events that make up the predesign context are to a great
extent out of the control of the designer and are thus considered noise
variables. For the case of a redesign, certain events would be considered
evolution triggers that drive the design in particular directions.
Examples of these include competitor actions, statutory changes, cyclic
(e.g., annual) changes, and so forth (Van Wie et al.,
2004). A reasonable hypothesis is that elements of this predesign
context are correlated with elements of function and form or changes in
function and form from previous designs. Subsequently, this knowledge
could be used during synthesis activities to generate candidate solutions
in parallel with the conventional approach of using customer needs, as
shown in Figure 6. It is important to note that
this is a supplement to customer needs rather than a replacement.
Bringing design upstream: the use of archived predesign contexts for
synthesis.
4.1.2. Patent description, patent claims data
structure, and automated patent claim discovery
Patents are a particular type of product representation where
descriptions of both function and form at different levels of abstraction
are used to describe an invention and document the boundaries of legal
protection regarding an invention. Although patent content is controlled
as a legal matter, only the basic elements of the patent description and
patent claims are addressed here. As a guideline, clarity and
comprehensiveness are essential to a good claim. Normally a patent will
include several claims that are supported by the description of the
device. In this manner, the claims are an interpretation of the product
description written with specific legal wording and phrasing.
Because of the need for clear and comprehensive descriptions of both
function and form, patent claims are a potential application for
automation of portions of the patent claim process. Although thoroughly
addressing the feasibility of such a goal is well beyond the scope of this
work, the following presents an overview of how the concepts of the FBR
model could be used toward the creation of such an application.
The core of a patent is the portion called simply the
“description” of the invention that is given in both textual
and graphical format. The purpose of this description is to provide
roughly the same information regarding the function and form of the device
as equivalent to that which would be available if the device were
physically in possession of the patent reader. This allows one to
understand very well both the physical form of the invention in terms of
geometry and material, and the manner in which the physical constituents
of the invention act on energy and material and interact with each
other.
The results from this research can be applied to this description. The
actions of the invention noted above describe the invention's
functionality and supporting functionality, respectively. The physical
form is described by the use of assembly, component, and Wirk element
references to physical artifacts at these levels. Ultimately, this is an
expanded and more comprehensive version of the product repository that
currently exists (Bohm, Stone, & Szykman,
2003). For example, a patent description could be comprised of
multiple associations between functions and physical elements in the form
of χ matrices. Based on this description, claims can also be
addressed in a similar manner.
The two main requisites for a claim are clarity and comprehensiveness.
In current practice, claims are written using the format consisting of a
preamble and a body. The preamble simply names the item
that is to be claimed where the body describes the elements that manifest
this claimed item. Consider the patent claim for a mechanical pencil (US
Patent 6,705,789). One specific claim for this patent is stated by the
following:
A mechanical pencil comprising:
a tubular member having a front end and a rear end;
a slide member disposed at the front end of the tubular member for
axial sliding movement therein, the slide member having a lead passageway for
receiving a pencil lead; and
a lead advancement mechanism mounted for axial movement
within the tubular member and having a chuck body for undergoing advancing
movement to advance the pencil lead through the lead passageway of the
slide member and toward the front end of the tubular member and for
undergoing retracting movement toward the rear end of the tubular member,
the chuck body having a plurality of projections for engagement with the
slide member so that the slide member undergoes retracting movement with
the chuck body.
Dissection of this text indicates how functions, supporting functions,
assemblies, components, and Wirk elements are related among each other.
The phrase “a tubular member having a …” is captured by
an association between a component and two Wirk elements. The phrase
“a slide member …” is more complex and requires the use
of both functionality and supporting functionality. Here, a slide member
is associated with supporting functionality of the tubular member. The
slide member is associated with both the functionality of importing
“pencil lead” and the Wirk element of the inner bore or
“lead passageway.” These relations are illustrated in Figure 7, where this collective set of relations is
represented by several matrices. Individually, these matrices are variants
of the χ presented earlier where relations can be defined among the
physical elements and the two types of functionality.
Example relations for a mechanical pencil patent claim.
The graph in Figure 7, representing a claim,
is a subgraph of the graph for the invention description that describes
all the relations among physical elements and functionality. This suggests
that the enumeration and discovery of patent claims for an invention is
the result of searching for subgraphs within the product description that
are unique relative to prior art where such prior art could be stored in a
digital patent repository.
Numerous issues complicate the search for claims with this approach
such as the large amount of data to be searched and the standard needed to
qualify equivalence, similarity, and uniqueness of these candidate claims
during a search operation. Nevertheless, the information content within
the proposed scheme is, as an approximation, quite comprehensive of both
the physical and functional characteristics of mechanical inventions with
respect to the information used in a patent. This suggests that the
underlying information provides sufficient resolution for the requisite
standards to be applied. A benefit of using this approach is that it
establishes clear criteria for patent claims. These criteria could be
helpful for determining the outcome of patent infringement issues. One
reason that patents utilize such lengthy legal descriptions is that patent
claims need to clearly and comprehensively describe the system and the
bounds of legal protection. Employing a computational approach based on a
well-defined scheme of functionality, physical elements, and their
relationships is promising in this regard. As for the process of claim
enumeration, the graph-based representation scheme may serve as a data
structure for searches, but the subgraphs themselves would benefit from a
transformation to a natural language format so that interpretation of
claims can occur in a similar manner as the conventional approach.
4.2. Function-based synthesis operations for AI:
Search, evaluate, and sort
Three specific operations involved in AI applications include
searching, evaluating, and sorting. The following three sections
demonstrate how the FBR model enhances the capabilities of these
operations in computational product design methods.
4.2.1. Searching at multiple levels of
abstraction
A method currently exists for using product data archived in matrix
format to generate candidate physical solutions given some functional
specification (Strawbridge et al., 2002). This
same matrix manipulation process for this technique is demonstrated here
to show how additional information suggested by the FBR model is included
in automated concept generation methods. The first two examples are
illustrated with a redesign case study in which a gas powered nail gun is
adapted to serve as a tree tagging device. In this consulting project, the
design objective is to create a proof of concept prototype to demonstrate
how such a device can give land surveyors the ability to automatically
dispense and attach colored tags to trees without the manual labor of
holding the tag and attaching the tag with a hammer and pouch of nails. An
existing nail gun is selected as a host system following an assessment of
customer needs, the expected activities involved in user operation, and
consideration of other alternative approaches such as staple guns and
human-powered devices similar to hammers. Given this overall system
choice, a functional model is created, as shown in Figure 8. In conjunction with this step, an initial
architecture is proposed and given in Figure 9
for the layout of major modules based on spatial constraints.
The functional model for a tree tagging device.
The initial architecture to integrate with the existing
product.
Given this architecture and functional model, a major task is to
determine how the tags stored on the side of the nail gun can be moved
into place along the nail axis using the energy supplied by the operator
pressing the nail gun against the tree. An illustration of this desired
effect based on two different approaches is shown in Figure 10.
Tag rotation from the storage module to a position in line with the
nail firing axis.
Upon selection of the rotational mode of tag motion, a search can be
made for solutions that achieve this effect based on the desired
functionality of “convert force to torque.” This functionality
is explicitly shown in the functional model. However, the functional model
does not show a more abstract level of functionality that subsumes this
“convert” function along with the “allow degree of
freedom” and others. This more abstract level could be captured in a
singular “convert x-motion to y-motion.”
Generation of these additional functions, like the original functional
model, is simply a brainstorming exercise and not a computational task.
However, the basic problem is that of organizing and aggregating lower
level functions associated with higher level functions (Umeda et al., 1996; Gero &
Kannengiesser, 2004). Here this burden is placed directly on the
designer for mentally developing a functional model and any ancillary
functions derived from the functional model. The two convert functions, at
different levels of functional abstraction, can then be searched for
solutions based on data archived in χ matrices. Associations between
these functions and past solutions consist of those shown in Figure 11. These particular archived solutions are at
an assembly level of abstraction that are interpreted as a working
principle level.
Archived solutions at the assembly level of abstraction.
Given this historical design data, Figure 12
illustrates the matrix multiplication technique given in Strawbridge et
al. (2002) for this search at the assembly level
of structural abstraction. The example χ matrix is premultiplied by a
filter matrix. For clarity, functions excluding the conversion functions
are shown as place holders, although all functions in the functional model
would normally be represented. This process identifies those assemblies
archived in the χ matrix that match the functions designated with a 1
along the diagonal of the filter matrix. Beyond searches for assemblies,
similar searches can be performed at any other level of abstraction
depending on the specific needs of the designer.
The generation of candidate assembly level solutions.
4.2.2. Evaluation and iteration of candidate
solutions
Upon completion of a search, evaluation becomes a key activity to
select, modify, or backtrack to a previous step in the design. The FBR
model suggests that in addition to populating χ matrices with
mappings from function to form, other associations between elements within
the general classes of design variables, noise variables, and performance
parameters can also be formed. Given that failure mode data is classified
as a performance-related issue, the technique for mapping failure mode
data to components is a special case of this more general perspective. In
the nail gun redesign example, it is reasonable to believe that archived
data relating to retrofit type cases would include structural design
solutions for adaptor plates because interfacing old to new is a common
issue among retrofit design scenarios. Figure 13
shows that an adaptor plate is the main element interfacing the prototype
unit with the existing product.
The final proof of the concept.
Specifically, a χ matrix relating the predesign context or
evolutionary trigger of “retrofit” would be related to an
adaptor plate. As a further extension, data could be archived to map such
predesign contexts to the type of design changes that have occurred in the
past. For example, the occurrence of lawsuits (a noise variable) is
correlated and archived with design changes such as “add safety
guard.” Such design changes in general involve adding, changing, or
deleting design elements (function or form). Similarly, these design
changes may also be correlated with certain performance conditions. As a
trivial example, a failing component will likely be correlated with
deleting and subsequent replacement with an alternative. Figure 14 is a schematic for the different general
categories of χ matrices that can be formed from the FBR model. In
this figure, the χs indicate the two items for which associations are
made. By including the mappings to design changes, a loop for design
iteration emerges. If initiated with an existing design, knowing the
performance parameters and predesign context for the product, this loop
can be interpreted as an automated redesign process. Details for
controlling this iteration process for this endeavor is left for future
work. Although not shown in Figure 14,
associations between design variables (e.g., modules to functions) can
also be stored in χ matrices to capture relations such as
hierarchical decomposition of functions similar to that achieved in the
function–means structure that is adopted in the function-based
synthesis methodology of Schemebuilder (Bracewell,
2002).
The relations between various elements in the form of χ matrices
that facilitate computational evaluation and iteration.
4.2.3. Sorting candidate solutions
In the context of automated function-based synthesis, the above two
sections illustrate how candidate solutions are searched given historical
information of past solutions and evaluated given historical information
of the performance from these past solutions. One of the challenges is to
group, sort, or otherwise identify workable solutions from incompatible
ones. Previous work has reported success with clustering strategies based
on similarity of solution (Chakrabarti et al.,
2002). The following presents an outline of a proposed algorithm
for the task of identifying compatible solutions where this compatibility
is based on archived product knowledge of past instances of
component–component relations.
Given a χ matrix for functions to components, functions in the
functional model are mapped to lists of components that are capable of
solving each function. The tree of possible component chains is then
pruned by eliminating component connections that are not feasible
according to component–component compatibility. A schematic of this
process is shown in Figure 15.
A schematic of the proposed method of concept
generation.
Specific χ matrices, including the function–component
matrix (FCM) that describes the function–component relationships
(Fig. 16a) and the DSM that describes the
component–component compatibility (Fig.
16b), coupled with a matrix defining the connectivity from the
functional model (Fig. 16c) can be manipulated
to produce the filtered matrix of design solutions.
(a) Function–component, (b) design structure, and (c) functional
model connectivity matrices.
Rows corresponding to the functions present in the designer's
functional model are extracted from the FCM and multiplied together to
produce matrices of possible component chains linking each pair of
functions together as given in Figure 17.
Matrix multiplication of vectors from the function–component
matrix (FCM) leads to a series of matrices describing possible component
design solutions.
These matrices can then be entered into the function connectivity
matrix as shown in Figure 18 and then filtered
with the DSM to remove component–component combinations that are
incompatible as illustrated in Figure 19. The
matrices generated represent a component tree of design solutions that has
been pruned of infeasible designs. If the component connections of
existing products are used to fill the DSM, then design solutions can be
ranked according to historical occurrence of component connections. In
other words, the most common design solutions to the functional model
would bubble to the top of the list of generated concepts. Other factors,
such as failure modes derived from a separate evaluation step, could also
be used as filters during the sorting stage to help limit and rank design
solutions.
Matrices created from Figure 3 are inserted
into the function connectivity matrix generated from the functional
model.
Cells of the possible design solution matrices are multiplied with
corresponding cells of the design structure matrix (DSM) to produce a
filtered list of design solutions.
5. DISCUSSION AND FUTURE WORK
This work presents a model of FBRs that describes both the functional
and structural elements of this model as they relate to resolution of
knowledge representation. Although these elements have individually been
introduced in prior research efforts, this work identifies a sufficient
and irreducible set of these items in a composite manner that accounts for
a full range of function and structure resolutions applicable in
mechanical design. In addition to the basic items of function and
structure, the FBR model incorporates the broader concepts of design
variables, noise variables, and performance parameters where the
specifications of function and form are subsumed into the set of design
variables. As a whole, this provides a new coherent framework that allows
a great number of associations or mappings to be made between the items
comprising the FBR model. A matrix-based approach is demonstrated as a
computable means for handling these associations. Given the FBR
composition and their mappings, an initial assessment of the model is made
with respect to a comprehensive set of design activities. Potential of the
FBR model is developed further through descriptions of how the concepts of
the FBR are used for both existing and proposed AI methods ranging from
knowledge archival in product repositories to computational synthesis
operations that support concept generation.
A direct benefit of the FBR model is that it clarifies and
demonstrates how function-based information can be related to not only
structure, but also to variables that reflect design performance in a
computable format. Given that product behavior is intimately tied with
performance, the use of performance information as indicated by the FBR
model seems promising for future investigations of product behavior.
Although design synthesis based on archived knowledge is specifically
addressed in this work, another benefit that such archived product
knowledge provides is a convenient source of data for empirical studies.
Development of prescriptive design methods, whether heuristics or advanced
processes, rests on the information gleaned from a descriptive evaluation
of how products are and should be designed. The FBR model presented in
this work is suggestive of many function-based relations that could be
archived in a computational format and examined during an empirical study
to develop this descriptive product information. In addition to empirical
studies, future work should explore and develop AI design methods using
the computational relations that the FBR model provides.
