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Design of Thinking Design Machine
Design of Thinking Design Machine Nam P. Suh (1). Massachusetts Institute of Technology, Cambridge, MA/USA; Shinya Sekimoto, Toshiba Corporation, KawasakVJapan Received on January 16,1990
The concept of an intelligentmachinewhich generates cre i g n 5 presented. First, the general prOC?SS is described based on the design axioms. According to the axiomat~cdesgn concept, four steps of a 'thinlong desgn machine" are described; definition of functional requirements (FRs), creation of design parameters (DPs), ,a"a'ys's of design solution, and check of final solution. Computer software which deals with each one of the four steps IS discussed. The database required for the design process is also discussed. Using the database or working interactivelywith designers,the system synthesizes the design solutions which satisfy the functional requirementsdefined by the designer. The S ~ Sthen W analyzes the proposed design solutions based on the design axiom 1 (Independence Axiom). When there are many acceptable solutions, the system evaluates them based on the design a x o im 2 (Information Axiom). Finally, the system selects the solution with a minimum information content as the best design solution. KEY WORDS : Design, i n t e l l i machine, creative design, design axioms. database. 1. introduction
Creative processes involved in engineering design are not fully understood. Yet, it is an exciting theme to develop a 'thinking design machine' (IDM) which automatically generates designs or design concepts that are superior to those currently possible in terms of performance, manufacturability, reliability, cost,etc. 'Eventually, through the process of creating TDM, we may be able to provide a better understanding of the cognitive process of human minds. Although many CAD (computer aided design) software programs have been developed, they deal mainly with the later stage of the design process, such as geometric modelling and drawing. To deal with creative processes, the early stage of the design process, i.e. the conceptual design stage, must be systematized for machine processing, since the most critical decisions are made at this stage. The actual design solution depends on the designer's individual knowledge and creative process. To generate creative designs, a TDM must have a broad range of knowledge and a right decision making ability. The purpose of this paper is to describe a concept for such a system that is endowed with both knowledge and decision making principles.
Step 1. Definition of functional requirements. Step 2. ideation or creation of ideas. Step 3. Analysis of the proposed solutions to choase the best solution. Step 4. Checking of the final solution.
2. Concept of Thinking Design Machine
In the first step, a set of FRs are defined in the functional domain in order to satisfy the perceived needs. Then, a set of DPs are selected in order to satisfy the FRs defined in Step 1, which collectively forms a physical entity such as a product or a process. Then, the proposed solutions are analyzedfor acceptability usingthe design axioms and other physical laws and principles. Finally, the fidelity of the final solutii to the original perceived needs is checked. Each one of the steps often involves iteration, which may involve redefining the functional requirements, creation of n8w ideas, and modifying the proposed solutions. Fg.1shows the schematic diagram of a TDM. Depending on the database, it is most likely that TDM will generate many solutions which satisfy Axiom 1. Although these solutions are acceptable from the functional point of view, we must select the best solutions among these by using the InformationAxiom. This step involves the evaluation of the information content of all possible solutions, which will not be dealt with in this paper.
2.1 Design Process
2.2 Design Axioms
The concept of TDM is based on the Axiomatic Design (Suh, 1988,1990).me axiomatic design defines the design as the creation of synthesized solutions that satisfy perceived needs through the mapping between the functional requirements (FRs) and the design parameters (DPs) in the case of product design. The FRs are defined in the functional domain to satisfy the original needs given in the customer domain, while the DPs are created in the physical domain to satisfy the FRs. In the case of process design, the process variable (Ws) are defined in the process domain, but in this paper, we will only be concerned with FRs and DPs. The mapping process from the functional domain to the physical domain is not unique. There can be an infinite number of plausible design solutions. However, not all proposed solutions are good solutions. Therefore, in TDM, these solutions are evaluated based on the design axioms. In accordancewith the axiomatic design concept, the architecture of TDM is divided into the following four steps:
The design axioms are basic principles, based on which we can develop many spedfic methodologies for analysts and problem solving. The TDM uses the following two design axioms:
I
Nwds
I
&
Definition of FRs
Bsponding toeachDP
I I
Axiom 7: The IndependenceAxiom Maintain the independence of functional requirements Axiom 2: The InformationMom Minimize the information content. Axiom 1distinguishes betweengood and bad design, or acceptable and unacceptable design. Axiom 2 is the criterion for selection of the optimum design solutions from among those that satisfy Axiom 1. 2.3 HierarchicalStructure in Design Process There is a hierarchy in both the functional space and the physical space. The design process consists of zigzagging between the hierarchical trees of the two domains shown in Fig.2. The design process is most straightforwardwhen the solution consists of uncoupled designs at each level. When the design is uncoupled, we can deal with each FR of the hierarchical level without considering other FRs of the same and preceding hierarchical levels. When the design is coupled, we must consider the effect of a decision on other FRs and DPs. In TDM, the program finds the solutions by attempting to make a coupled design uncoupled at each hierarchical level (Fig.3).
Cross-term Check
I
Evaluation of the information content
I
Fig.1 Schematic diagram of a Thinking Design Machine'
Annals of the ClRP Vd. 3/1/liW
Fig.2 Hierarchical trees in the functional and physical domains
145
consists of mostly non-zero elements. In this case, we cannot control one FR simply by changing its corresponding DP, since this will affect other FRs. m e design solution clearly violates Axiom 1. A coupled design matrix may be made a decoupled design which has a triangular matrix by selecting new DPs. In some cases, what appears to be a coupled design may be a decoupled design, which can be proven simply by changing the order of the FRs and the DPs. The triangular matrix does fully satisfy Axiom 1, provided that the independence of the FRs can be assured by adjusting the DPs in a particular order. For example, if the design equation is given by Fig.3 Hierarchical approach in coupled design and uncoupled design 3. Architecture of Thinking Design Machlne
The architecture of a TDM must involve at least the first three steps described in 2.1. However, the first step of defining FRs is subjective. m e second and third steps can be dealt with on an objective basis, making the computerization of the design process possible. The computer archlecture can consist of the Ideation Software and the Analysis Software to deal with Steps 2 and 3, respectively. The final software is the Systems Software that can arrange the selected physical components in a systems context so as to yield the desired overall design. 3.1 Establishmentof functional requirements
The design process begins with the establishment of FRs. The FRs are defined in the functional domain to satisfy a given set of needs. This process is subjective, but it is clearly one of the most crical stages in the design. At this step, the system may work interactivelywith the designers. FRs are a set of independent requirements that describe the design objectives. The only restriction for the FRs is that they should be always stated in the functional domain, i.e., FRs must be defined in a solutionneutral environment in a creative design. Since the FRs may be stated in a variety of ways depending on the designer, the software for FRs must have the ability to understand the intention of the designer. As the design task proceeds, the FRs may be changed. Therefore, the system must be flexible enough to accommodate such modifications. The selected set of FRs should not be redundant or depend on each other, since all FRs become independent by definition once they are selected. The number of FRs should be minimal since the proposed design solution becomes increasingly complex with the increase in the number of FRs. In this software, the system finds a set of plausible DPs corresponding to each given FR of a set of {FRs}:
For FR,, the corresponding plausible DPs are.. DP,'. DP,'. DP13,...
For FR,, the corresponding plausible DPs are.. DP;,
...
DP;,
...
If the FR is to transmit rotational motion (FR,), for example, the system may find some DPs such as a gear (DP,'), a timing belt (DP,'), and a chain (DP,?. At this stage, the designer may also propose addlional DPs. Then, the computer program constructs the design matrix which relates FRs and DPs in a design equation as {FR} = [DMI{DP),
........
(11
where the design matrix (DM] represents the relationship between FRs and DPs. The element of the [DM], All, represents the relation between each FRt and DP If the FR, is affected by the DPi, then A#, has a finite value, and if the is not affected by the DPi, then Ar, is zero. For each possible solution, we can write a design equation and a design matrix.
f%,
3.3 The Analysis Software Concept
The remaining question is: Which are acceptable solutions among these [DM]s created by the Ideation Software ?'. This question is answered by the Analysis Software System, which analyzes [DM]s selected by the IdeationSoftware System based on the first design axiom, the Independence Axiom. If [DM] is a diagonal matrix, the proposed design solution satisfies Axiom 1, since each DP, satisfies its corresponding FR, without affecting any other FRs. This kind of design is an uncoupled design. The converse of an uncoupled design is the coupled design, whose design matrix
146
3.4 The System Software Concept
The last step in the design process is the System Software. It arranges the selected physical components so as to make a working coherent physical system. In an uncoupled design, the individual components can be controlled in any sequence. But in a decoupled design, the components must be controlled in the order of the sequence given by the [DM].
3.5 Selection of the Best Design Solution When there are many design solutions that satisfy Axiom 1, they must be evaluated using Axiom 2. This can be done by calculating the information contents. The best solution is the one with the least total information content. The information is defined as
I
........ (3) P where p is the probability of satisfying the given FRs by the specified DPs. Informationcontent is determined by evaluating the system range and the design range. The system range is the capability of the current manufacturing system, whereas the design range is the tolerance specified by the designer. The product is acceptable only when the design range and the design range overlap. m e information content given by Eq.(3) may be expressed as I = log,
For FR, the corresponding plausible DPs are.. DP,'. DP;,
The Analysis Software System has the function of changing the order of the FRs and DPs so as to make the matrix triangular, if possible. The Analysis Software System has also the function of detecting the wrong points of the design, and provide information for improvement of the design if the [DM] is neither triangular nor diagonal.
I =log,--,
3.2 Ideation Software Concept
DP,', DP;,
then we can determine DP, to satisfy FR, without considering the other DPs, since FR, is affected by only DP,. And once we determine DP,, we can determine DP, to satisfy FR, without considering the other DPs, since FR, is affected by only DP, and DP,, and DP, is already determined. Then we can determine DP, to satisfy FR,. This kind of design is a decoupled or quasi-coupled design.
i
system range common range
1
,
........
(4)
where the common range is the overlap area betweenthe system range and the design range. Informationcontent is calculated for each DP. The total information content is the summation of individual information content. 4. Database for Thinking Design Machlne
4.1 Representation of FRs and DPs
To proceed with the design task, the system requires a database. The database should contain sufficient knowledge to make the computer to communicate wiul the designer and to give the designer information about plausible design solutions. Such database should also contain the design knowledge possessed by many designers, since known solutions for a common set of {FRs} constitute a solution to a subset of other FRs. The mode of operation in TDM may require interaction with designers, who may assist in defining functional requirements, and even in creation or ideation of new ideas. In some cases. the idea for a design solution may only be expressed conceptually. The process of stating one's idea in a computer language may force the designer to clarify his/her concept. During the design process. FRs and DPs are expressed using words, a sentence, or a set of sentences. In an ultimate form of TDM, the FRs and the DPs may be stated in an unstructuredway, which wwld then require TDM to have the ability to understand the intended meaning of the designer input. This can be done only if an appropriate database is structured and a proper lexicon is developed. This process resembles the natural language processing. Once a FR is given, the program analyzes the meaning of the FR. and searches
the corresponding DPs from the database. To search for DPs corresponding FRs. parsing and key word search technique can be used. The database contains the technical terms used in engineering design, and their synonyms, antonyms, etc. 4.2 Representation of Design Solutions
To get a creative solution from a computer, we must give it a broad range of knowledge. Databaseof TDM should therefore contains enough knowledge about design solutions. Design solutions are represented by the design equation. To develop the database for design solutions. there could be two ways of representation; one which represents a certain DP and FRs that are satisfied by the given DP, and one which represents a certain FR and DPs that satisfies the given FR. Generally, the same FR is satisfied by a number of physical entities, and one physical entity has many functional aspects. The database for design solutions can be expressed in Prokg as: ...I)
. . . .. . . .
(5)
dp-frrDP',["FRln,"FR2'. ...I)
. . . . . .. .
(6)
fr-dp('FR',['DPl","DPP, or,
iv) Physical phenomena/status
Innovative ideas or designs are often born from the application of a well-known physical phenomenon. A is interesting to develop such a database. In the axiomaticmethodology. any entity m the physical domain could be a DP. Some might be represented as followS: dp-frrpass electric current through filament", ['emit light', "promote oxidation']) dp-frpacuum', ['prevent combustion', 'prevent oxidation"]) dp-frrlighten a certain metal', ['form a charge image']) dp-frrcharge of static-electr.city', ['gather resins carrying an opposite charge"]) dp-frvusion of resins", ['fix resins on paper"]) 5. Matrlx Operation 5.1 Algorithm for changing the order of {FR} and {DP}
The analysis part of TDM has the function of changing the order of FRs and DPs to test if the proposed design matrix can be formed triangular. The algorithm is as follows: i) Find the row which contains one non-zero element, and put the row and the column which contains the element first. According to the arrangement. change the order of {FR} and {DP}, i.e.. if i-th row contains one non-zero element at j-th column, then put i-th element of {FR} first and put j-th element of {DP} first (Fg.4 (i)).
where fr-dp and dp-fr are functors which indicate the nature of the relations. The fr-dp database means a functional requirement 'FR" is satisfied by one of the design parameters 'DPI', "DPP, etc, and the dpfr database means a design parameter 'DP" has functions 'FRY, FRZ', etc. The content of 'DP' or 'FR' may be a string or a set of strings. The dp-fr database and fr-dp database are completely interchangeable in the same hierarchical level of the design. However, there are some fundamental reasons for developing both databases. In actual design process, it is natural to think about DPs that satisfy a given FR. However, the dp-fr database is convenient to evaluate various functional aspects of a DP, such as the side effects, since this information is necessary to construct the [DM]. The database must be updated through a number of actual designs. Two databases are equivalent, but having different types of database increases the probability of finding a new solution.
During the above procedure, If all of the rows contain more than one non-zero elements, the design is coupled. If some rows contain no non-zero elements, then the FRs corresponding to the rows cannot be controlled.
4.3 Database for design solutions
5.2 How to improve the design solution
The database may be constructed in different forms, some of which are illustrated here.
Some design solutions cannot be decoupled by simply reordering the FRs and DPs. Then the Analysis Software System provides suggestions for improving the design solution by examining which nonzero element or which combination of non-zero elements can decouple the [DM]. In the search, the program first tries to decouple the [DM] by making one of the non-zero elements zero. Then, it examines the combinations of two non-zero elements excluding the elements which decouple the matrix alone, and then, examines the combination of three non-zero elements excluding the elements and the pairs of elements which decouple the matrix alone, and so forth. Equation (7) shows an example.
i) Parts/componenfs Mechanicaland electrical parts/components can be considered as DPs. dp-frrgear', ['transmit rotary motion", "change torque', "change revolution']) dp-frrcam', ["transfer rotary motion into reciprocating motion"]) dp-fr('cIutCh', ['transmit and release rotary motion']) dp-frrgeneva", ['convert uniform rotary motion into intermittent rotary motion"]) dp-frrratchet", ['serve as a stop against backward motion", 'provide incremental forward motion']) dp-fr("solenoid", ['establish a magnetic field within a conductor"]) The first element in dp-fro is a DP, and the second element enclosed in is a list of FRs that are satisfied by the DP. The first example means a DP "gear' has such functions as "transfer rotary motion', "change torque", etc. ii) Systems
u
Mechanical and electrical systems may also be DPs which can be represented as follows: dp-fr('pump',['draw fluid in", 'force fluid out", 'put fluid under pressure"]) dp-frcmotor, ['convert electrical energy into mechanicalenergy"]) dp-Wheat pipe', ["transport thermal energy from one place to the other']) iii)Materials
ii) Excluding the first row and column, find the row which contains
one non-zero element, and put the row and the d u m n which contains the element second. Then, put the element of {FR} and {DP} corresponding to the row and column second (Fig.4 (ii)). iii) Repeat the procedure until the last row but one (Fig.4 (iii)).
\:"i
=
FR,
[.,]{:q All
A12
A13
. . . . . . . . (7)
k, 0
0
A32 43
DP3
The [DM] shown in Eq.(7) cannot be decoupled by simply reordering the FRs and DPs. Therefore, the program first examines if the matrix can be decoupled by making A, zero and reordering FRs and DPs according to the algorithm stated in 5.1. Then, it recovers the value of A,, and makes ,, and so fotth. A12zero, and then, recovers the value of A, and makes A In this example, making 4, zero decouples the matrix. Therefore, the program stores 4, as a possible solution which improves the design. After examining each one of the non-zero elements, the program then starts to examine the combinations of two non-zero elements. In this case, the program does not examine the combinations which include 4,. Because. if 4, is zero, the value of other elements, such as 42,does not matter. Furthermore, if the combination of the non-zero elements makes the whde elements of one row or one column zero, the search is
The basic structure for material database is as follows: dp-frrcopper',
['melting point = 1W c ' , 'density=8.9g/cm', 'magnetic property=diamagnetic", 'Young's modulus= l19,300Mpa", 'relative electric conductivity=63.0']) where the functions of material are expressed in terms of mechanical, electrical and chemical properties. Besides the general properties, The knowledge of materials which have spea'al properties could enhance the design solutions. dp-fr("thermoplastic', ["when heated, remain soft and pliable']) dp-fr("viscoelastic", ["transfer mechanical vibration into heat']) dp-frrshape memory alloy', ['when heated, recover original shape"]) dp-fr('selenium', ["vary electrical resistance under influence of light"])
(i)
(iii)
Fig.4 Reordering of { FR} and { DP}
147
stopped. For example, if all elements in the first row become zero, FR, cannot be controlled, and if all elements in the first column become zero, DP, does not work at all and the design matrix should be coupled. Figure 5 shows the answers for the matrix given in Eq.(5). These answ~rsare the ones that do not make any diagonal elements zero, because,in most cases,the diagonal elements are much more important than off-diagonal elements. Ifwe permit to make the diagonal elements zero, we can get six more answers. Once we get the solutions in terms of matrix, we can translete it into the information which has physical meaning. These answers can provide many ideas, and provide the designer with f r u i i l direction of search.
*** Original Design Matrix ***
* Solution (2) : A,=O,
&=O
Solution (3): A,,=O,
A,=O
Solution (1) :4, =O
;=:[ 4, b
:][q DP3
. .. . . . . . (10)
9
Analyzing this design equation as described in 5.2. we gel the following 12 possible solutions. (1) A, =o,4,=o, (2) A, =o, &=o, (4) A,,=O, h = O , (5) A,=O, &=O, (7) A,,=o, b = o , (a) A,,=o, A==O, (10) &=o, &=o, (11) 4,=0,b = o .
(3) A,,=o, 4,=o, (6) A,=O. &=o, (9) 4,=0.&=o, (12) h = o . &=o.
These solutions M i t e the possibility of changing the dd DPs, that is, Pump speed and Nozzle size. However, it is diffcult to select the new DPs which make the old elements zero. Therefore, we concentrate on the solutions that make some of the elements of the third column of the matrix zero. men, the possible solutions are (5) and (7). Using the solution given by (9,i.e., (A, = A, = 0), we should find the new design parameter which controls the functional requirement FR, without affecting the functional requirements FR, and FR,. Similarly using the solution (7),the design equation can be rewritten
as
121
A,,]\ h
= [All 4 1 0
FR,
4 1
k, A,
(A13
Fg.5Three solutions for decoupling the design matrii (shaded areas indicate non-zero elements)
6. Application ol Thinking Oesign Machine to RIM system
This example shows how TDM analyzes the proposed solution, and how it provides the information for improving the design solution. RIM (Reaction injection Molding) machine is a machine for mixing two thermosetting liquid by injectin0 at high speeds. The problem in the original design (Fig.6) is that it is a coupled design because there are fewer DPs than the FRs. (Theorem 1; see Suh.1990). c functional requirements >
FR, = Deliver liquid at high flow rate (0) FR, = Deliver an adequately mixed liquid (X) FR3 = Deliver properly metered liquid (M) c design parameters >
-
DP, Pump speed ON) DP, = Nozzle size (0)
=
........ (11)
DP1] DPz DP3
.
=
In thii case,we should find the new design parameter which contrds the functional requirement FR, without affecting the functional requirements FR, end F&. Baul of the solutions are possible solutions from the mathematical point of view. However, when we consider the solution in the physical domaiin, Eq.(ll) means that we control DP, to satisfy FR,, then DP, to satisfy FR, and finally DP, to satisfy FR,. This sequence is difficult, since DP, (nozzle sue) cannot be easily changed to satisfy FR, (Deliver properly metered liquid). As a result, we obtain the final result that states the following: we should find a new design parameter which controls FR, (Deliver properly metered liquid) without affecting FR, (Deliver liquid at high flow rate) and FR, (Delver an adequately mixed liquid). Figure 7 shows one physical solution. In this example, gear pumps are mechanically coupled to meter the ratio of the liquids. It should be noted that the uncwpled design shown in Fig.7 is just one of many possible uncoupled solutions. When a large number of uncoupled solutions are available, the optimal solution the known solutions is the one with the least infarmation content.
Then, the design matrix is expressed as
Reservoir liquid A
I
liquid B
I where X represents a non-zero element, and 0 represents a zero element. This matrix indicates that FR, is affeaed by DP,, and the other two FRs are affected by both DP, and DP,. In order to improve thiidesign, we haveto find a new DP. When we begin to search for a DP, we have no idea what the new parameter should be. Therefore, the design equation is expressed as
Mechanical Coupling
Pump/Motor Mixing Head
Mixture into Mdd X
O
?
........
Fig.7 Modified design of RIM machine (9)
where ? marks are put in the third column of the [DM], since DP, is an unknown parameter. In order to examine what amibute the new parameter should have, we analyze the following design matrix.
liquid B
Pressure Pump
Pressure Mixing Head
Mixture into Mold Fg.6 Original design of RIM machine
148
7.Conciusion The basic concept of a rhinking design machine" has been presented. The concept of TDM is based on the design axioms. The power of TDM will be a function of the database it contains. Notwithstanding the possible limitations that may be imposed on TDM by the database, the system with the right decision making ability can provide many ideasthat humanengineers may not recognize or conceive. Computers endowed with both a right decision making ability and a rich knowledge database will have the ability to synthesize creative designs that are beyondthe human imagination. Much work needs to be done to achieve the ultimate goal.
References Suh,N.P., "Basic Concepts in Design for Producibiliiy: ClRP Annals, Vol.37, No.2, 1988 Suh,N.P., The Pninciples d Design, Oxford University Press, Oxford, England, 1990
The concept of an intelligentmachinewhich generates cre i g n 5 presented. First, the general prOC?SS is described based on the design axioms. According to the axiomat~cdesgn concept, four steps of a 'thinlong desgn machine" are described; definition of functional requirements (FRs), creation of design parameters (DPs), ,a"a'ys's of design solution, and check of final solution. Computer software which deals with each one of the four steps IS discussed. The database required for the design process is also discussed. Using the database or working interactivelywith designers,the system synthesizes the design solutions which satisfy the functional requirementsdefined by the designer. The S ~ Sthen W analyzes the proposed design solutions based on the design axiom 1 (Independence Axiom). When there are many acceptable solutions, the system evaluates them based on the design a x o im 2 (Information Axiom). Finally, the system selects the solution with a minimum information content as the best design solution. KEY WORDS : Design, i n t e l l i machine, creative design, design axioms. database. 1. introduction
Creative processes involved in engineering design are not fully understood. Yet, it is an exciting theme to develop a 'thinking design machine' (IDM) which automatically generates designs or design concepts that are superior to those currently possible in terms of performance, manufacturability, reliability, cost,etc. 'Eventually, through the process of creating TDM, we may be able to provide a better understanding of the cognitive process of human minds. Although many CAD (computer aided design) software programs have been developed, they deal mainly with the later stage of the design process, such as geometric modelling and drawing. To deal with creative processes, the early stage of the design process, i.e. the conceptual design stage, must be systematized for machine processing, since the most critical decisions are made at this stage. The actual design solution depends on the designer's individual knowledge and creative process. To generate creative designs, a TDM must have a broad range of knowledge and a right decision making ability. The purpose of this paper is to describe a concept for such a system that is endowed with both knowledge and decision making principles.
Step 1. Definition of functional requirements. Step 2. ideation or creation of ideas. Step 3. Analysis of the proposed solutions to choase the best solution. Step 4. Checking of the final solution.
2. Concept of Thinking Design Machine
In the first step, a set of FRs are defined in the functional domain in order to satisfy the perceived needs. Then, a set of DPs are selected in order to satisfy the FRs defined in Step 1, which collectively forms a physical entity such as a product or a process. Then, the proposed solutions are analyzedfor acceptability usingthe design axioms and other physical laws and principles. Finally, the fidelity of the final solutii to the original perceived needs is checked. Each one of the steps often involves iteration, which may involve redefining the functional requirements, creation of n8w ideas, and modifying the proposed solutions. Fg.1shows the schematic diagram of a TDM. Depending on the database, it is most likely that TDM will generate many solutions which satisfy Axiom 1. Although these solutions are acceptable from the functional point of view, we must select the best solutions among these by using the InformationAxiom. This step involves the evaluation of the information content of all possible solutions, which will not be dealt with in this paper.
2.1 Design Process
2.2 Design Axioms
The concept of TDM is based on the Axiomatic Design (Suh, 1988,1990).me axiomatic design defines the design as the creation of synthesized solutions that satisfy perceived needs through the mapping between the functional requirements (FRs) and the design parameters (DPs) in the case of product design. The FRs are defined in the functional domain to satisfy the original needs given in the customer domain, while the DPs are created in the physical domain to satisfy the FRs. In the case of process design, the process variable (Ws) are defined in the process domain, but in this paper, we will only be concerned with FRs and DPs. The mapping process from the functional domain to the physical domain is not unique. There can be an infinite number of plausible design solutions. However, not all proposed solutions are good solutions. Therefore, in TDM, these solutions are evaluated based on the design axioms. In accordancewith the axiomatic design concept, the architecture of TDM is divided into the following four steps:
The design axioms are basic principles, based on which we can develop many spedfic methodologies for analysts and problem solving. The TDM uses the following two design axioms:
I
Nwds
I
&
Definition of FRs
Bsponding toeachDP
I I
Axiom 7: The IndependenceAxiom Maintain the independence of functional requirements Axiom 2: The InformationMom Minimize the information content. Axiom 1distinguishes betweengood and bad design, or acceptable and unacceptable design. Axiom 2 is the criterion for selection of the optimum design solutions from among those that satisfy Axiom 1. 2.3 HierarchicalStructure in Design Process There is a hierarchy in both the functional space and the physical space. The design process consists of zigzagging between the hierarchical trees of the two domains shown in Fig.2. The design process is most straightforwardwhen the solution consists of uncoupled designs at each level. When the design is uncoupled, we can deal with each FR of the hierarchical level without considering other FRs of the same and preceding hierarchical levels. When the design is coupled, we must consider the effect of a decision on other FRs and DPs. In TDM, the program finds the solutions by attempting to make a coupled design uncoupled at each hierarchical level (Fig.3).
Cross-term Check
I
Evaluation of the information content
I
Fig.1 Schematic diagram of a Thinking Design Machine'
Annals of the ClRP Vd. 3/1/liW
Fig.2 Hierarchical trees in the functional and physical domains
145
consists of mostly non-zero elements. In this case, we cannot control one FR simply by changing its corresponding DP, since this will affect other FRs. m e design solution clearly violates Axiom 1. A coupled design matrix may be made a decoupled design which has a triangular matrix by selecting new DPs. In some cases, what appears to be a coupled design may be a decoupled design, which can be proven simply by changing the order of the FRs and the DPs. The triangular matrix does fully satisfy Axiom 1, provided that the independence of the FRs can be assured by adjusting the DPs in a particular order. For example, if the design equation is given by Fig.3 Hierarchical approach in coupled design and uncoupled design 3. Architecture of Thinking Design Machlne
The architecture of a TDM must involve at least the first three steps described in 2.1. However, the first step of defining FRs is subjective. m e second and third steps can be dealt with on an objective basis, making the computerization of the design process possible. The computer archlecture can consist of the Ideation Software and the Analysis Software to deal with Steps 2 and 3, respectively. The final software is the Systems Software that can arrange the selected physical components in a systems context so as to yield the desired overall design. 3.1 Establishmentof functional requirements
The design process begins with the establishment of FRs. The FRs are defined in the functional domain to satisfy a given set of needs. This process is subjective, but it is clearly one of the most crical stages in the design. At this step, the system may work interactivelywith the designers. FRs are a set of independent requirements that describe the design objectives. The only restriction for the FRs is that they should be always stated in the functional domain, i.e., FRs must be defined in a solutionneutral environment in a creative design. Since the FRs may be stated in a variety of ways depending on the designer, the software for FRs must have the ability to understand the intention of the designer. As the design task proceeds, the FRs may be changed. Therefore, the system must be flexible enough to accommodate such modifications. The selected set of FRs should not be redundant or depend on each other, since all FRs become independent by definition once they are selected. The number of FRs should be minimal since the proposed design solution becomes increasingly complex with the increase in the number of FRs. In this software, the system finds a set of plausible DPs corresponding to each given FR of a set of {FRs}:
For FR,, the corresponding plausible DPs are.. DP,'. DP,'. DP13,...
For FR,, the corresponding plausible DPs are.. DP;,
...
DP;,
...
If the FR is to transmit rotational motion (FR,), for example, the system may find some DPs such as a gear (DP,'), a timing belt (DP,'), and a chain (DP,?. At this stage, the designer may also propose addlional DPs. Then, the computer program constructs the design matrix which relates FRs and DPs in a design equation as {FR} = [DMI{DP),
........
(11
where the design matrix (DM] represents the relationship between FRs and DPs. The element of the [DM], All, represents the relation between each FRt and DP If the FR, is affected by the DPi, then A#, has a finite value, and if the is not affected by the DPi, then Ar, is zero. For each possible solution, we can write a design equation and a design matrix.
f%,
3.3 The Analysis Software Concept
The remaining question is: Which are acceptable solutions among these [DM]s created by the Ideation Software ?'. This question is answered by the Analysis Software System, which analyzes [DM]s selected by the IdeationSoftware System based on the first design axiom, the Independence Axiom. If [DM] is a diagonal matrix, the proposed design solution satisfies Axiom 1, since each DP, satisfies its corresponding FR, without affecting any other FRs. This kind of design is an uncoupled design. The converse of an uncoupled design is the coupled design, whose design matrix
146
3.4 The System Software Concept
The last step in the design process is the System Software. It arranges the selected physical components so as to make a working coherent physical system. In an uncoupled design, the individual components can be controlled in any sequence. But in a decoupled design, the components must be controlled in the order of the sequence given by the [DM].
3.5 Selection of the Best Design Solution When there are many design solutions that satisfy Axiom 1, they must be evaluated using Axiom 2. This can be done by calculating the information contents. The best solution is the one with the least total information content. The information is defined as
I
........ (3) P where p is the probability of satisfying the given FRs by the specified DPs. Informationcontent is determined by evaluating the system range and the design range. The system range is the capability of the current manufacturing system, whereas the design range is the tolerance specified by the designer. The product is acceptable only when the design range and the design range overlap. m e information content given by Eq.(3) may be expressed as I = log,
For FR, the corresponding plausible DPs are.. DP,'. DP;,
The Analysis Software System has the function of changing the order of the FRs and DPs so as to make the matrix triangular, if possible. The Analysis Software System has also the function of detecting the wrong points of the design, and provide information for improvement of the design if the [DM] is neither triangular nor diagonal.
I =log,--,
3.2 Ideation Software Concept
DP,', DP;,
then we can determine DP, to satisfy FR, without considering the other DPs, since FR, is affected by only DP,. And once we determine DP,, we can determine DP, to satisfy FR, without considering the other DPs, since FR, is affected by only DP, and DP,, and DP, is already determined. Then we can determine DP, to satisfy FR,. This kind of design is a decoupled or quasi-coupled design.
i
system range common range
1
,
........
(4)
where the common range is the overlap area betweenthe system range and the design range. Informationcontent is calculated for each DP. The total information content is the summation of individual information content. 4. Database for Thinking Design Machlne
4.1 Representation of FRs and DPs
To proceed with the design task, the system requires a database. The database should contain sufficient knowledge to make the computer to communicate wiul the designer and to give the designer information about plausible design solutions. Such database should also contain the design knowledge possessed by many designers, since known solutions for a common set of {FRs} constitute a solution to a subset of other FRs. The mode of operation in TDM may require interaction with designers, who may assist in defining functional requirements, and even in creation or ideation of new ideas. In some cases. the idea for a design solution may only be expressed conceptually. The process of stating one's idea in a computer language may force the designer to clarify his/her concept. During the design process. FRs and DPs are expressed using words, a sentence, or a set of sentences. In an ultimate form of TDM, the FRs and the DPs may be stated in an unstructuredway, which wwld then require TDM to have the ability to understand the intended meaning of the designer input. This can be done only if an appropriate database is structured and a proper lexicon is developed. This process resembles the natural language processing. Once a FR is given, the program analyzes the meaning of the FR. and searches
the corresponding DPs from the database. To search for DPs corresponding FRs. parsing and key word search technique can be used. The database contains the technical terms used in engineering design, and their synonyms, antonyms, etc. 4.2 Representation of Design Solutions
To get a creative solution from a computer, we must give it a broad range of knowledge. Databaseof TDM should therefore contains enough knowledge about design solutions. Design solutions are represented by the design equation. To develop the database for design solutions. there could be two ways of representation; one which represents a certain DP and FRs that are satisfied by the given DP, and one which represents a certain FR and DPs that satisfies the given FR. Generally, the same FR is satisfied by a number of physical entities, and one physical entity has many functional aspects. The database for design solutions can be expressed in Prokg as: ...I)
. . . .. . . .
(5)
dp-frrDP',["FRln,"FR2'. ...I)
. . . . . .. .
(6)
fr-dp('FR',['DPl","DPP, or,
iv) Physical phenomena/status
Innovative ideas or designs are often born from the application of a well-known physical phenomenon. A is interesting to develop such a database. In the axiomaticmethodology. any entity m the physical domain could be a DP. Some might be represented as followS: dp-frrpass electric current through filament", ['emit light', "promote oxidation']) dp-frpacuum', ['prevent combustion', 'prevent oxidation"]) dp-frrlighten a certain metal', ['form a charge image']) dp-frrcharge of static-electr.city', ['gather resins carrying an opposite charge"]) dp-frvusion of resins", ['fix resins on paper"]) 5. Matrlx Operation 5.1 Algorithm for changing the order of {FR} and {DP}
The analysis part of TDM has the function of changing the order of FRs and DPs to test if the proposed design matrix can be formed triangular. The algorithm is as follows: i) Find the row which contains one non-zero element, and put the row and the column which contains the element first. According to the arrangement. change the order of {FR} and {DP}, i.e.. if i-th row contains one non-zero element at j-th column, then put i-th element of {FR} first and put j-th element of {DP} first (Fg.4 (i)).
where fr-dp and dp-fr are functors which indicate the nature of the relations. The fr-dp database means a functional requirement 'FR" is satisfied by one of the design parameters 'DPI', "DPP, etc, and the dpfr database means a design parameter 'DP" has functions 'FRY, FRZ', etc. The content of 'DP' or 'FR' may be a string or a set of strings. The dp-fr database and fr-dp database are completely interchangeable in the same hierarchical level of the design. However, there are some fundamental reasons for developing both databases. In actual design process, it is natural to think about DPs that satisfy a given FR. However, the dp-fr database is convenient to evaluate various functional aspects of a DP, such as the side effects, since this information is necessary to construct the [DM]. The database must be updated through a number of actual designs. Two databases are equivalent, but having different types of database increases the probability of finding a new solution.
During the above procedure, If all of the rows contain more than one non-zero elements, the design is coupled. If some rows contain no non-zero elements, then the FRs corresponding to the rows cannot be controlled.
4.3 Database for design solutions
5.2 How to improve the design solution
The database may be constructed in different forms, some of which are illustrated here.
Some design solutions cannot be decoupled by simply reordering the FRs and DPs. Then the Analysis Software System provides suggestions for improving the design solution by examining which nonzero element or which combination of non-zero elements can decouple the [DM]. In the search, the program first tries to decouple the [DM] by making one of the non-zero elements zero. Then, it examines the combinations of two non-zero elements excluding the elements which decouple the matrix alone, and then, examines the combination of three non-zero elements excluding the elements and the pairs of elements which decouple the matrix alone, and so forth. Equation (7) shows an example.
i) Parts/componenfs Mechanicaland electrical parts/components can be considered as DPs. dp-frrgear', ['transmit rotary motion", "change torque', "change revolution']) dp-frrcam', ["transfer rotary motion into reciprocating motion"]) dp-fr('cIutCh', ['transmit and release rotary motion']) dp-frrgeneva", ['convert uniform rotary motion into intermittent rotary motion"]) dp-frrratchet", ['serve as a stop against backward motion", 'provide incremental forward motion']) dp-fr("solenoid", ['establish a magnetic field within a conductor"]) The first element in dp-fro is a DP, and the second element enclosed in is a list of FRs that are satisfied by the DP. The first example means a DP "gear' has such functions as "transfer rotary motion', "change torque", etc. ii) Systems
u
Mechanical and electrical systems may also be DPs which can be represented as follows: dp-fr('pump',['draw fluid in", 'force fluid out", 'put fluid under pressure"]) dp-frcmotor, ['convert electrical energy into mechanicalenergy"]) dp-Wheat pipe', ["transport thermal energy from one place to the other']) iii)Materials
ii) Excluding the first row and column, find the row which contains
one non-zero element, and put the row and the d u m n which contains the element second. Then, put the element of {FR} and {DP} corresponding to the row and column second (Fig.4 (ii)). iii) Repeat the procedure until the last row but one (Fig.4 (iii)).
\:"i
=
FR,
[.,]{:q All
A12
A13
. . . . . . . . (7)
k, 0
0
A32 43
DP3
The [DM] shown in Eq.(7) cannot be decoupled by simply reordering the FRs and DPs. Therefore, the program first examines if the matrix can be decoupled by making A, zero and reordering FRs and DPs according to the algorithm stated in 5.1. Then, it recovers the value of A,, and makes ,, and so fotth. A12zero, and then, recovers the value of A, and makes A In this example, making 4, zero decouples the matrix. Therefore, the program stores 4, as a possible solution which improves the design. After examining each one of the non-zero elements, the program then starts to examine the combinations of two non-zero elements. In this case, the program does not examine the combinations which include 4,. Because. if 4, is zero, the value of other elements, such as 42,does not matter. Furthermore, if the combination of the non-zero elements makes the whde elements of one row or one column zero, the search is
The basic structure for material database is as follows: dp-frrcopper',
['melting point = 1W c ' , 'density=8.9g/cm', 'magnetic property=diamagnetic", 'Young's modulus= l19,300Mpa", 'relative electric conductivity=63.0']) where the functions of material are expressed in terms of mechanical, electrical and chemical properties. Besides the general properties, The knowledge of materials which have spea'al properties could enhance the design solutions. dp-fr("thermoplastic', ["when heated, remain soft and pliable']) dp-fr("viscoelastic", ["transfer mechanical vibration into heat']) dp-frrshape memory alloy', ['when heated, recover original shape"]) dp-fr('selenium', ["vary electrical resistance under influence of light"])
(i)
(iii)
Fig.4 Reordering of { FR} and { DP}
147
stopped. For example, if all elements in the first row become zero, FR, cannot be controlled, and if all elements in the first column become zero, DP, does not work at all and the design matrix should be coupled. Figure 5 shows the answers for the matrix given in Eq.(5). These answ~rsare the ones that do not make any diagonal elements zero, because,in most cases,the diagonal elements are much more important than off-diagonal elements. Ifwe permit to make the diagonal elements zero, we can get six more answers. Once we get the solutions in terms of matrix, we can translete it into the information which has physical meaning. These answers can provide many ideas, and provide the designer with f r u i i l direction of search.
*** Original Design Matrix ***
* Solution (2) : A,=O,
&=O
Solution (3): A,,=O,
A,=O
Solution (1) :4, =O
;=:[ 4, b
:][q DP3
. .. . . . . . (10)
9
Analyzing this design equation as described in 5.2. we gel the following 12 possible solutions. (1) A, =o,4,=o, (2) A, =o, &=o, (4) A,,=O, h = O , (5) A,=O, &=O, (7) A,,=o, b = o , (a) A,,=o, A==O, (10) &=o, &=o, (11) 4,=0,b = o .
(3) A,,=o, 4,=o, (6) A,=O. &=o, (9) 4,=0.&=o, (12) h = o . &=o.
These solutions M i t e the possibility of changing the dd DPs, that is, Pump speed and Nozzle size. However, it is diffcult to select the new DPs which make the old elements zero. Therefore, we concentrate on the solutions that make some of the elements of the third column of the matrix zero. men, the possible solutions are (5) and (7). Using the solution given by (9,i.e., (A, = A, = 0), we should find the new design parameter which controls the functional requirement FR, without affecting the functional requirements FR, and FR,. Similarly using the solution (7),the design equation can be rewritten
as
121
A,,]\ h
= [All 4 1 0
FR,
4 1
k, A,
(A13
Fg.5Three solutions for decoupling the design matrii (shaded areas indicate non-zero elements)
6. Application ol Thinking Oesign Machine to RIM system
This example shows how TDM analyzes the proposed solution, and how it provides the information for improving the design solution. RIM (Reaction injection Molding) machine is a machine for mixing two thermosetting liquid by injectin0 at high speeds. The problem in the original design (Fig.6) is that it is a coupled design because there are fewer DPs than the FRs. (Theorem 1; see Suh.1990). c functional requirements >
FR, = Deliver liquid at high flow rate (0) FR, = Deliver an adequately mixed liquid (X) FR3 = Deliver properly metered liquid (M) c design parameters >
-
DP, Pump speed ON) DP, = Nozzle size (0)
=
........ (11)
DP1] DPz DP3
.
=
In thii case,we should find the new design parameter which contrds the functional requirement FR, without affecting the functional requirements FR, end F&. Baul of the solutions are possible solutions from the mathematical point of view. However, when we consider the solution in the physical domaiin, Eq.(ll) means that we control DP, to satisfy FR,, then DP, to satisfy FR, and finally DP, to satisfy FR,. This sequence is difficult, since DP, (nozzle sue) cannot be easily changed to satisfy FR, (Deliver properly metered liquid). As a result, we obtain the final result that states the following: we should find a new design parameter which controls FR, (Deliver properly metered liquid) without affecting FR, (Deliver liquid at high flow rate) and FR, (Delver an adequately mixed liquid). Figure 7 shows one physical solution. In this example, gear pumps are mechanically coupled to meter the ratio of the liquids. It should be noted that the uncwpled design shown in Fig.7 is just one of many possible uncoupled solutions. When a large number of uncoupled solutions are available, the optimal solution the known solutions is the one with the least infarmation content.
Then, the design matrix is expressed as
Reservoir liquid A
I
liquid B
I where X represents a non-zero element, and 0 represents a zero element. This matrix indicates that FR, is affeaed by DP,, and the other two FRs are affected by both DP, and DP,. In order to improve thiidesign, we haveto find a new DP. When we begin to search for a DP, we have no idea what the new parameter should be. Therefore, the design equation is expressed as
Mechanical Coupling
Pump/Motor Mixing Head
Mixture into Mdd X
O
?
........
Fig.7 Modified design of RIM machine (9)
where ? marks are put in the third column of the [DM], since DP, is an unknown parameter. In order to examine what amibute the new parameter should have, we analyze the following design matrix.
liquid B
Pressure Pump
Pressure Mixing Head
Mixture into Mold Fg.6 Original design of RIM machine
148
7.Conciusion The basic concept of a rhinking design machine" has been presented. The concept of TDM is based on the design axioms. The power of TDM will be a function of the database it contains. Notwithstanding the possible limitations that may be imposed on TDM by the database, the system with the right decision making ability can provide many ideasthat humanengineers may not recognize or conceive. Computers endowed with both a right decision making ability and a rich knowledge database will have the ability to synthesize creative designs that are beyondthe human imagination. Much work needs to be done to achieve the ultimate goal.
References Suh,N.P., "Basic Concepts in Design for Producibiliiy: ClRP Annals, Vol.37, No.2, 1988 Suh,N.P., The Pninciples d Design, Oxford University Press, Oxford, England, 1990