A200908-1045

Study on Modular Design of Complex Products Based on the Triple Fusion of Function/Feature/Knowledge1

Li Baotong, Hong Jun

State Key Laboratory for Manufacturing Systems Engineering,

Xi’an Jiaotong University, Xi’an, (710049)

[email protected]

Abstract A modular design methodology based on functional feature analysis is proposed to remedy the existing deficiency in modeling of the design process for complex structural components. In this approach, a partitioning is firstly performed for the complex structural components by mapping the functions to structures layer by layer. Based on this partition, a comprehensive design matrix is then developed to identify the key design mode which is driven by the special function. The design process is also programmed by analyzing the coupled information on both the functional and structural hierarchies. Then, the integrated knowledge model based on object-oriented method and hybrid inference method is constructed, in this model, knowledge can be organized at hierarchical classification and expressed with different forms. Finally, this method has been verified through a case study on an automobile cylinder block. The results indicate that this method is effective in the reduction of design process complexity in product development. In addition, it also supports variable parameters, which is a favorable feature for potential changes of products. Keywords: Functional Feature Partition, Knowledge Unit, Comprehensive Design

Matrix, Knowledge Model

1 Introduction

There are a large number of complex structural components existing in today’s industrial products,

such as large pump, marine crank and automobile engine. Because the design of this kind of

components often requires multi-disciplinary knowledge, it is very difficult to achieve significant

innovation within a short period of time. According to the statistics in industries, only about 20% of

OEM’s investment is on new design while about 80% is on the reuse of existing products, with or

without modification[1]. In order to obtain rapid product development, it is necessary to accumulate

and inherit the existing knowledge during the design process. An effective modular design knowledge

model for complex structural components is of great importance [2~4].

The modular design concept was formally proposed in the 1950s and it has subsequently attracted

more and more attention. G. Brunetti et al [5] proposed an approach towards a feature-based integrated

modular design model. Liang Hou et al [6] developed an object-oriented approach to package the

1 * Sponsored by：1. National Natural Science foundation of China (No. 50675173); 2. National Education Department

Doctor Fund (No. 20060698038)

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modular design knowledge. Robert B. Stone et al [7]introduced a methodology for representing a

modular design model in a quantitative manner. GAO Fei et al [8] presented rules of function module

partition for creative design, which were formalized and quantified based on generalized directed

graph and improved house of quality. Gunnar Erixon et al [9] proposed a proven methodology for

product design using the concept of “module drivers”, which could set up independent assembly units

for each module that can be precisely adapted to the requirements of the actual module. P.Gu et al [10]

developed an integrated modular design methodology for achieving multiple objectives. The

methodology identified the factors related to the objectives, and clustered components into modules

using a genetic algorithm based technique.

All the achievements mentioned above mainly focus on how to package the design knowledge based

on modules. However, for a complex structure, the design knowledge and in-depth analysis of the

design characteristics are often missing or difficult to do. Particularly, it is very difficult to describe

the complex structural components comprehensively. This paper presents a way to map the complex

structural components design process into comprehensive design matrix and package the design

knowledge with modules based on the functional feature partition tree. The approach is implemented

in an integrated design knowledge framework, which helps to achieve rapid development of product

structures. The paper is organized into six sections. After an overview of the related work in Sect.1, a

functional feature partition framework is presented in Sect. 2. Section 3 focuses on the modeling of

functional structures in all levels. Section 4 presents the modeling method for design knowledge based

on object-oriented technique and hybrid inference engine. Section 5 illustrates the method with a case

study on an automobile cylinder block design. Section 6 presents the conclusions, finally.

2 Functional Feature Partition of Complex Structural Components

The design of complex structural components often involves various types of functional structures

which are mutually coupled. In order to simplify the process without loss of design information, a

functional feature partition is used. In this partition, complex structural components are decomposed

into many relatively simple parts by mapping the functions to structures layer by layer. In this way, the

complex integral design model is transformed into the simple partial design model.

2.1 Figures and tables

Each function of a complex structural component is called its branch function. Unit function is the

basic unit obtained by partitioning the sub-functions contained within the branch function layer by

layer until it cannot be further subdivided. A complex structural component possesses branch

function f and it is formed by coupling lower-level functions 1f , 2f , 3f … nf , which can be

represented as

1 2 nf f f f

1 2 ( 1, 2, )i i i inf f f f i n

if ij if f ，then if is called unit function.

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In complex structural components, the structure s , which is used for accomplishing each branch

function f , is called functional structure. Similar to the function partitioning, the functional structure

is partitioned layer by layer and the minimal feature unit with independent function is called

functional feature. Suppose there is a functional structure s and its constitution is shown as:

1 2 ns s s s

1 2 ( 1, 2, )i i i ins s s s i n

if 1 2i con ns f f f f and

ijs ( 1, 2, )if i n , then is is defined as functional feature.

Knowledge unit is a kind of description set which reflects the design feature and knowledge inference

method of the corresponding functional structure, which is shown as follow:

KU= (ID, DesUnit, ConRules, ConsceProc, ParaSet, RuleSet)

In the formula: (1) ID is the identifier; (2) DesUnit is the literal description; (3) ConRules is the

activation condition of knowledge unit; (4) ConsceProc is the knowledge inference method; (5)

ParaSet is the design parameter set; (6) RuleSet is the design rule set of the knowledge unit.

There are many ways to partition the functional structures. This paper focuses the method of

constructing the design knowledge model for complex structural components. Thus, it requires that the

functional structure should present the positive design idea well. Due to the fact that there are many

different functional structures which are similar in geometry, if structural perspective is used in the

partition, the positive design idea would not be represented well. On the other hand, if functional

perspective is used in the partition, more emphasis would be made on the different functions of those

structures which are similar in geometry.

In this paper, the function is used as the starting point to accomplish the partitioning of complex

structural components (as Fig.1 shows). This method is consistent with the thinking logic of positive

design. In addition, it may avoid the disjunction of function design and structure partitioning, such that

it is beneficial to the packaging of design knowledge.

2.2 A knowledge modelling framework for product design

The product design can be represented as three aspects by using knowledge unit, viz. functional

structure model, design parameters and rule constraints. The functional structure model is a physical

object which includes conceptual design information, the design parameters are the property

description of the physical object, and the rule constraints are a set of relationship supporting the

functional structure model and design parameters. Based on these, this section presents a knowledge

modelling framework for product design which regards the knowledge unit as a uniform mechanism

of description, definition and basic organization for design knowledge. This model involves three

major processes, namely, functional feature partitioning, knowledge unit extraction and design

synthesis. Figure 2 shows the architecture of this model.

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Figure 1: The packaging model of design knowledge

Figure 2: System architecture of the product design knowledge model

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3 Modelling of Functional Structures in All Levels

During the design process, there are three relationships between the functional structures, namely,

independence, decoupling, and coupling. For two functional structures A and B, independence means

the change of A (or B) does not influence the change of B (or A); decoupling means the change of A

(or B) influences that of B (or A), but does not do contrariwise; coupling means the change of A (or B)

influences that of B (or A) and vice versa, and it will provoke the iterative design consequentially.

One effective tool of researching the iterative design process is the Design Structure Matrix (DSM). In

the matrix, each row and column correspond a certain functional structure, and the elements represent

the design information for the functional structures. Fig.3 shows these three relations.

DSM supplies an effective solving thought for the modelling of complex structural components, but

the traditional DSM merely describes the relationship between the functional structures qualitatively

just on the structural hierarchy. So it can not further reveal the correlative information from the

functional hierarchy. In order to excavate these information thoroughly, this section will construct the

comprehensive design matrix on the basis of the above functional feature partition tree.

Figure 3: Three relations between functional structures

3.1 Function-oriented modeling of DSM

Function-oriented modelling of DSM is the process of developing the design structure matrix (DSM1)

by analyzing the coupling degree on the functional hierarchy. This section introduces the HOQ (House

of Quality) model to build the functional influence matrix (as Fig.4 shows). Then, it can further

transform this matrix to obtain the Function-oriented DSM1.

( 1,2,i i )n shows the weight of function if , and it can be determined by using the method of

“analytic hierarchy process, AHP”[11];

( 1,2, ; 1,2, )ijr i n j m shows the influence degree of function if on structure js . There are four

levels（5、3、1、0） to represent the degree of high、medium、low and no influence in sequence, and

it can be determined by analyzing the mapping relation through the functional feature partition tree.

ij m nr

R shows the functional influence matrix;

Finally, the function-oriented DSM1 can be obtained by using the method of “quantity product,

. ij m nf

DSM1

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1

1

1 mij

l li ljl

i j

fr r i j

M

(1) 1

maxm

li ljij l

M r r

(2)

In the formula, ijf —the coupling degree between

is and js on the functional hierarchy;

lir —the influence degree of

function lf on structure is ;

l —the weight factor of function lf .

2f if nf

1s 2s js ms

1s 2s js ms

1

i

2

n

1f

1f

2f

if

nf

11r 12r 1jr 1mr

21r 22r 2jr 2mr

1ir 2ir ijr imr

1nr 2nr njr nmr

Figure 4: Function-oriented Modeling of DSM

3.2 Structure-oriented modeling of DSM

Structure-oriented modeling of DSM is the process of developing the design structure matrix (DSM2)

by analyzing the coupling degree on the structural hierarchy (as Fig.5 shows).

( 1,2, ; 1,2,ij )s i n j m shows the coupling degree between is and js on the structural hierarchy.

There are five levels (1、0.1、0.03、0.01、0) to represent the degree of high、medium、low、negligibility

and no coupling in sequence.

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The structure-oriented DSM2 can be obtained by using the method of AHP, . ij m ns

DSM2 =

Based on this, the comprehensive design matrix, namely, CDM could be obtained by synthesizing the

above matrices, that is CDM=DSM1+DSM2.

1f

2f

1s

2s

if js

nf ms

… …

… …

… …

… …

… …

1s 2s js ms

1s 11s 12s 1 js 1ms

2s 21s 22s 2 js 2ms

js 1js 2js jjs jms

ms 1ms 2ms mjs mms

Functional feature partition tree

Figure 5: Structure-oriented Modeling of DSM

3.3 Identification of design mode

In order to optimize the iterative design process, it is necessary to further identify the key design mode

which has significant influence on the design process.

Make a decomposition of the comprehensive design matrix CDM to obtain the eigenvalue and

eigenvector:

-1CDM = LΛL (3)

In the formula: Λ is the eigenvalue-diagonal matrix, L is the eigenvector matrix.

According to the Perron-Frobenius’s matrix theory, when the real part of the eigenvalue is positive, the

larger the value is, the more contribution to the iterative effect in the design process the corresponding

design mode would make. Fig. 6 shows the process of identifying the design mode.

2ml1mlms

11l 12l

22l

2il

1il

2il

iil

mil

1ml

2ml

iml

mml

1

2

i

m

21l

1il

1nf

kf

1f 1s

2s

nf

is

Figure 6: Identification of design mode

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a) For example, Let i be the i th eigenvalue of the CDM, and it corresponds to the i th column

vector of matrix L , namely, the i th design mode ( )iL ;

b) Then, suppose that iil is the most significant element in ( )iL , and it corresponds to functional

structure is ;

c) Based on these, combined with the mapping relation in the functional feature partition tree, it can

be clearly identified that the i th design mode is driven by function kf ;

d) Finally, according to this method, the key design mode would be easily identified by analyzing

the most significant eigenvalue of the matrix CDM.

The programming of functional structure design process includes two aspects, namely, the vertical

design process and the transverse design process. For the vertical design process, based on the

functional feature partition tree, the design information could be transmitted from the superior

functional structure to its subordinate one until the functional feature. For those functional structures

in the same level, the transverse design process is programmed based on the comprehensive design

matrix CDM. Define unit row vector as a , then:

Tind CDM a (4)

outd a CDM (5)

In the formula: is the input state vector, is the output state vector. ind outd

The vector describes the status of information input in the design process, and its element

shows the amount of information which is supplied by the other functional structures for the design of

functional structure

ind ~in id

is . The vector describes the status of information output in the design process.

Its element shows the amount of information which is supplied by functional structureoutd

~ioutd is for

the design of the other functional structures.

Therefore, the ratio of the corresponding element in and reflects the design priority, the

smaller the ratio is, the higher prior grade it has. So the programming of functional structures

transverse design process could be accomplished according to the ranking result.

ind outd

4 Modeling of the design knowledge

In order to match the design feature of the product functional structure model, a case-based and

rule-based knowledge inference system is adopted, in which the case base building is improved by

utilizing the functional feature partitioning technology. Based on this partition, a united decomposing

structure for product design case is constructed and figured with a design case tree which matches to

the functional structure tree (shown in figure 7). This kind of system is greatly beneficial to CBR,

based on this matching relationship between design case tree and functional structure tree, we can

easily extract the similar case to organize a new design scheme. In this hierarchical searching model, if

there is no suitable design case accorded with the matching requirement, the system will extract the

most similar case and then modify the master model to get the conclusion set by utilizing RBR.

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The corresponding modeling driven mechanism can be established based on the combination of

product functional structure model and design knowledge inference engine (shown in Figure 7), the

concrete steps are as follow:

Figure 7: Knowledge inference engine and modeling driven mechanism

Step 1: Construct the knowledge unit of the functional structure according to the product functional

structure model, then establish the knowledge unit library by integrating these knowledge units at all

levels through design knowledge inference;

Step 2: The overall function object sends message to trigger the branch function object who judges the

operation to analyze and calculate the mapping relationship between product functions and structures,

and then select the functional structure object which meets the searching requirements;

Step 3: The functional structure object sends message to trigger the knowledge unit library that

conducts the operation to extract and apply the corresponding design information into the constraint

solving, and then determine the design parameters which meet the constraint requirement;

Step 4: Utilize the secondary development module of CAD software system such as Catia/GII and

Pro/Toolkit. Then, carry on parametric designs of the functional structure design module under

VC++/VB development environment, repeat the above steps until the completion of all the design

modules.

5 Case Study

Take the cylinder block of automobile engine for example, as shown in Figure 8. There are different

types of rib reinforcements, cleaning holes, bearing saddle bores, water jacket and oil channels

distributed within the structure. In addition, the different types of horizontal and vertical baffle plates

in engine, which, together with different types of constraints existing among the features, makes the

spatial relationship quite complicated.

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cylinder crankcase

Cylinder block

water/oil pump rib reinforcement

oil channel

water jacket

exhaust passage cleaning hole

Figure 8: Cylinder block of automobile engine

Through the analysis of its function, the block functions can be partitioned into 3 types, namely, basic

functions, auxiliary functions and other functions. Basic function refers to the original function

assumed in engine operating principle; auxiliary function coordinates with basic function and ensures

its normal operation; other functions mainly refer to adjustive functions designed to meet

manufacturing requirement other than basic function and auxiliary function. Figure 9 shows the

functional feature partition of the cylinder block at its first level.

Based on the partitioning result, the structure design matrix DSM1 and DSM2 can be developed by

the method presented in section 3. The comprehensive design matrix CDM can then be obtained by

synthesizing the two matrices:

1.000 0.099 0.000 0.150 0.000 0.000 0.000

0.099 1.000 0.005 0.064 0.000 0.000 0.000

0.050 0.005 1.000 0.015 0.000 0.021 0.000

0.155 0.069 0.000 1.000 0.000 0.000 0.000

0.005 0.015 0.000 0.000 1.000 0.000 0.000

0.000 0.005 0.036 0.000 0

CDM =

.005 1.000 0.000

0.005 0.000 0.000 0.000 0.000 0.000 1.000

The key design mode can be identified through the eigenvalue analysis of the comprehensive design

matrix.

As shown in Table one, the key eigenvalue is 1.216. The significant elements of its corresponding

eigenvector are -0.616 and -0.588, which correspond to cylinder crankcase and oil channel

respectively. Finally, through the mapping relationship between function and structure we can

conclude that the key design mode is driven by the source function.

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Figure 9: The functional feature partition of cylinder block

Table 1 Result of eigenvalue analysis

Eigen

value

Eigen

vector

Functional

structure Branch function

1.000 -0.616 1s : crankcase 1f :source

1.216 -0.459 2s :water pump 2f : linkage

0.843 -0.198 3s :water jacket 3f : cooling

0.942 -0.588 4s :oil channel 4f :lubricating

0.971 -0.046 5s :rib reinforcement 5f :intensifying

1.027 -0.045 6s :cleaning hole 6f : cleaning

0.999 -0.142 7s :exhaust passage 7f : airing

Then, the input/output state vector can be obtained based on the comprehensive design matrix,

according to the ranking result of in outd d , we can easily accomplish the planning of the design

process. Table 2 shows the planning results.

Table 2 Planning results of design process

Information 1s 2s 3s 4s 5s 6s 7s

ind 2.49 2.34 2.18 2.45 2.04 2.09 2.10

outd 2.71 2.39 2.08 2.46 2.01 2.04 2.00

in outd d 0.92 0.98 1.05 0.99 1.01 1.02 1.05

Planning 1s 2s 4s 5s 6s 3s 7s

Finally, the cylinder block can be divided into 4 layers, which includes totally 252 functional feature

modules. The design parameters and rules of each functional feature could be represented with frames

based on the functional feature partition tree. Through knowledge acquisition, it adopts a uniform

expression to conduct rule representation as follow:

Other functions

Auxiliary functions

Basic functions

2 :f linkaging

1 :f source

6 :

3 :f cooling

4 : f cleaningf lubricating

5 :f intensifying

7 :f airingwater/oil pump 2:s

1:s crankcase

3:s water

jacket

4 :s oil

channel

6 :s cleaning

hole

7 :s exhaust

passage

rib

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Rule (RuleNo, <Conclusion expression>, [CondNo], [ConcluNo], Reliability)

Cond (CondNo, <Condition expression>).

Then, all of the rules are compiled into fact base and rule base (shown in table3 and table4), which are

expressed by utilizing the object-oriented methods:

Class Rule {

Private: // Rule’s attribution

Char RuleNo [10]; // Rule number

Char CondNo [100]; // Condition number

Char ConcluNo [100]; // Conclusion number

Float Reliability; // Rule confidence

Public: // Rule inference

Rule (RuleNo [10], CondNo [100], ConcluNo [100], Reliability); //Initialization

~Rule ( ); // Destructor function

Void SelectRule (CondNo [500]); //Calling method}

During the operation of the system, users first determine the design requirements and objectives. Then

the system makes use of CBR to perform model retrieval, and makes inference using the expert

system’s equation for similarity computing. The main model that best meets the requirements is

extracted and RBR is then used to modify this model. Finally, the system generates a command stream

file based on the inferred parameter values, submits it to the background program for modeling and

displays the results on the user interface. Figure10 shows the design process and the software

implementation of the cylinder block.

Table 3 Fact base

FactNo Fact description

1 Engine type: A=“Liner Gasoline”

2 Cylinder diameter: D= diameter

3 MainDia=(0.65~0.7)*D

4 ConDia=(0.60~0.65)*D

5 MainDia/ConDia[a, b]

6 Accord with the crank design criterion

┇ ┇

Table 4 Rule base

RuleNo CondNo CondNo … ConcluNo Reliability

R0001 1 2 / 3、4 0.90

R0002 5 / / 6 1

┇ ┇ ┇ ┇ ┇ ┇

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Figure 10: The practical design example of the cylinder block

4 Conclusions

This paper presents a method of constructing the modular design knowledge model for complex

structural components. Firstly, the initial conceptual design module of the complex structural

component is decomposed based on its function. Secondly, the comprehensive design matrix is

obtained. With this matrix, the feature description and system modelling on the coupling relation

between modules are accomplished during the product development process. According to the

correlation analysis, the key design mode can be clearly identified. At the same time, the design

process of functional structures can also been designed and programmed. Finally, the design

knowledge can be represented by a set of frames based on the functional feature partition tree. The

method has been used in a case study of the cylinder block, in which the positive design idea runs

through the whole design process. It appears that the application of this method can improve

efficiency in the product development process for complex structural components.

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Author Brief Introduction：

Li Baotong P.H.D. Candidate State Key Laboratory for Manufacturing Systems Engineering

School of Mechanical Engineering Xi'an Jiaotong University Xi'an 710049, China E-mail: [email protected]


http://std.xjtu.edu.cn/english/key_3.php

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A200908-1045