The process of engineering design involves moving through different levels of abstraction of the design problem and solution. During this cycle, the use of analogies has been shown to be a powerful mechanism for the development of a design solution. These design analogies are often drawn from systems that embody a similar function-flow-performance metric combination. Yet, most existing design tools focus not on these abstract representations, but instead focus on functional, linguistic descriptions of the systems. This paper focuses on several significant concepts that are essential to the exploitation of function-flow-performance based comparisons of design analogies.
Engineers often abstract complex ideas into the realm of mathematics and use these
abstractions to predict the performance of designed artifacts. It is not uncommon for
designers to proceed through multiple rounds of abstraction and de-abstraction in the
development of a design solution. During this process, the use of analogies by
experienced designers is well-known. Novice designers often lack the experience that
allows expert designers to identify and employ these analogies. However,
computational systems that may be able to assist novice and experienced designers explore new
realms of analogies are of increasing interest to the engineering design community.
Most efforts to date have focused on linguistic approaches, but in this paper, we
discuss an approach based on the Functional Modeling as design problem abstraction
technique. Use of this approach reveals novel insights into the complex world of
analogies and how a formalized approach to abstraction may benefit the search for
tools for computational analogy generation.
Studies of the activities of designers indicate that previous experience is used to
identify solutions to many design problems [
The established tools and approaches for analogy generation generally rely upon
linguistic pattern matching to keywords. Linguistic resources can be explained in terms
of patterns and contextual exploration based on syntactic and semantic constraints [
The WordTree Method begins with the identification of key function(s) within the
problem. Once identified, the user systematically represents the functions in a tree
with the verbs associated with each individual function. The individual verbs are
identified by specifying a broad-spectrum of verbs that are similar or analogous in
meaning. These verbs can be identified either from the designer’s knowledge base or
through a linguistic pattern match repository, such as WordNet [
The WordTree Method is a tool that aids in the identification of additional analogies across analogous domains. These various domains allow for a connection to be made between the problem and externalities of the existing design domain. The WordTree database provides analogies that are maintained and continually grows past design solutions where novice engineers can be aided in their goal towards developing a unique solution to a design problem. An example using the WordTree Method is shown in Figure 1.
AskNature.org is a community generated online database of biomimetic entries [
The DRACULA tool has several aspects that are similar to other analogy search tools. First, DRACULA is a design analogy tool similar to the WordTree method and AskNature database. With an understanding of the revised functional basis to establish appropriate functions and flows, DRACULA can produce related results from its design repository. Since the foundation of this approach involves functional abstraction concepts, that is the next topic of discussion.
A common abstraction tool used by design engineers is the creation of a functional
model. A functional model consists of flows (energy, material, and signal)
representing the inputs and outputs of the model, which are acted upon by functions (verb-noun
descriptors), resulting in changes to the flows. Both the Functions and the Flows are
described using a limited vocabulary of terms known as the Revised Functional Basis
[
The key benefit of a functional modeling abstraction to the design engineer is the separation of function (what must be done) from form (how it is done). This abstraction process can reveal analogous forms that accomplish the same function. Through a de-abstraction process, these alternate forms can be integrated into a new design solution that becomes an analogy to the original design concept.
Generating analogies from a function-flow-performance representation does require the application of several concepts to reveal the foundational core of elements within a functional representation. 3.1
Not all functions within a functional model have the same level of significance to the performance of the design. The functions whose performance is crucial to the effective performance of the design are termed “Critical Functions”. Selecting an appropriate form solution for these functions significantly affects the performance of the overall design. Critical Functions are candidates for design analogies. 3.2
Associated with the critical functions are certain flows (Material, Energy or Signal) whose management is significant to the performance of the device. Just as some functions are more important within the functional model than other functions, some flows are more significant to the performance of the design solution than other flows. These flows are designated as “Critical Flows” and are also candidates for design analogies. 3.3
The performance of different design solutions can be evaluated by examining how the critical flow(s) are modified by the critical function(s). Each of these measurements represents a Key Performance Parameter (KPP) that is often defined in the context of the design problem. For instance, a design problem may be to increase lift on an airfoil while reducing drag. The KPP could be expressed as the drag coefficient, the lift coefficient, or the lift to drag ratio. However, each of these expressions is a different way of measuring the effectiveness of the function “guide air” on the flows “air” and “kinetic energy” within a function structure, such as that shown in Figure 2. When taken together, the Critical Functions, Critical Flows, and KPPs represent a functional chain of critical design elements. This chain is defined as a “Critical Chain” within a functional model. One or more functional chains may exist within a functional model. These chains represent an opportunity to identify design analogies based on elements of function, flow, and performance. Furthermore, these chains also can be compared to identify analogies based on elements of Chain Similarity and Chain Architecture. To discuss these elements, we will use the critical chain in Figure 3 as the basis for comparison. Chain similarity is a measure of the similarity in function (and potentially also in flow) between two chains. Obviously, two chains with the exact same functions (and flows) would exhibit perfect similarity (as defined in Eq. 1) and would be analogies to each other. However, similarity does not need to be complete in order to be significant. For instance, the left example in Figure 4 exhibits partial similarity while the right example exhibits perfect similarity. The greater the similarity between two chains, the stronger the potential for a viable design analogy. Due to relationships between functions, perfect similarity is not required for a viable analogy to exist.
ChainA ∩ ChainB = ChainA = ChainB (1) where:
ChainA = is the chain of a red circle, yellow diamond, and blue square ChainB = is the chain of a yellow diamond, blue square, and a red circle.
Partial similarity can mean that only one function is shared between two chains. Conceptually, even a total lack of similarity can exist, due to conceptual relationships between descriptions in the revised functional basis. 3.6
The left example in Figure 4 exhibits perfect similarity but distinctly different chain architecture. Chain Architecture is also a factor in identifying analogy matches between critical chains. Even simple linear chains of three or four functions can exhibit a number of distinct architectures including: Identical, Mirror, Disordered, Mirrored Disordered and Unique. Taken as a whole the left example in Figure 4 exhibits a Disordered architecture where the yellow diamond precedes the blue square, but the red circle does not exhibit a common relationship to the other functions. The subchain of the yellow diamond preceding the blue square is an identical architecture, just as is the right example red circle followed by the yellow diamond in the right example. Figure 5 provides examples of the different architectures.
The study of chain architecture is very interesting. Not only do different
architectures exist even for fairly simple linear chains, but critical chains also exhibit
additional more complex topologies including trees and potentially rings. Some of these
architectural forms result in very close analogies as the order of functions in a
functional model is not necessarily unique [
The effectiveness of similarity and architecture comparisons on critical chains can be
evaluated using the aforementioned concepts to develop critical chains. Through
studies of prior analogy implementations such as [
The first metric, Similarity, measures the similarity of two chains. Because chains may be of different lengths in the comparison, Similarity is defined in Eq. 2 as: (2) (3) (4) Similarity = 2(FcnShared)
LC1+LC2 where:
FcnShared = The number of functions two chains have in common LC1 = The total chain length of the input LC2 = The total chain length of the source required to cover all common functions.
The next metric, Identical, shown in Eq. 3, is nearly identical to the Similarity metric, with the exception that its numerator is based on whether or not the chains share the same function order. If the functions in the same location in the chain are the same, the FcnSharedOrder is 1, otherwise it is 0. Thus, if the functions do not share an identical order, the metric value is zero. This evaluation begins with the first shared function in the chains.
Identical =
LC1+LC2
Similarly, the calculation for the Mirrored metric, Eq. 4, is also nearly the same as that in Eq. 3. However, in this metric, the FcnSharedInverse term compares the ith function to the m - ith function in the chain where m is the length of the chain. If the terms are the same, the expression is equal to 1, otherwise its value is zero. Thus, the metric is 1 if and only if the chains have the same number of terms in opposite orders.
Mirrored =
LC1+LC2
The Disordered and Deredrosid (i.e. Mirror Disordered), Eq. 5 and 6, metrics assign a value to the location of each shared function from the input chain (IFP) to the source chain (SFP), resulting in the average position differences two chains. Disordered = Deredrosid = n ∏ i n ∏ i 11| IFPi-SFPi + 1 |
n | n-IFPi-SFPi + 1 | n where: n = the number of matched functions IFPi = the position of input function i SFPi = the position of source function i.
The last metric is the Unique metric, which is based upon the average of the Disordered and Deredrosid metrics as shown in Eq. 7.
Unique = 1
Disordered + Deredrosid 2
All of the metrics range from 0 to 1 and represent an initial attempt to measure similarity and architecture between functions in critical chains. Similar efforts can be developed to also incorporate flows in the evaluations. 4.2
Our evaluation of these criteria consisted of an evaluation of known analogies versus simply random chain comparisons. If the metrics are detecting analogies, then their averages should deviate from the average of chain comparisons as shown in Table 1.
In the set of known analogies, we discovered (after the fact) that we did not have a mirrored analogy included in the study. Therefore, we do not have valid results to present concerning this criterion and thus it was omitted from Table 1. Based on the data in Table 1, the criteria appear to be measuring the presence of analogies. Further research into the analogies within the random sample that appear to be previous unidentified analogy matches is still needed to better understand and to further refine the proposed criteria. 5
Based on this research, the use of Functional Models as an abstraction tool and the basis for identifying and matching analogies prior to de-abstraction appears to be a promising new approach. Further understanding and refinement of the criteria employed to date are necessary. In addition, the formulation of functional models exhibit varying use of grammars, syntax and levels of abstraction. Understanding and employing these stylistic differences will be important in the continued development of analogy matching tools based upon this abstraction approach.
Of course, functional models are not the only abstraction approach available and
employed by engineers. Modeling forms such as SysML, Control Diagrams, and
Bond Graphs offer alternative modes of abstraction that may also lead to attractive
outcomes when used for analogy matching. Additionally, there a multiple approaches
to functional modeling, such as Goel’s Structure−Behavior−Function [
The authors would like to acknowledge the work of their graduate students, Peter Morgenthaler, Dr. Briana Lucero, and Peter Ngo in the development of this research, as well as the financial support of the National Science Foundation through Awards No. CMMI-1304383 and CMMI-1234859. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.