**3.1 Case-based reasoning**

Fig. 13 shows case-based reasoning (CBR) operations. CBR compares cases in an analogue way. First, CBR compares a new case with cases in a case database and searches for the most similar case.

Knowledge-Based Engineering Supporting Die Face Design of Automotive Panels 29

3. Revise: Based on the reuse assessment, designers revise the proposed solution when

4. Retain: The final assessment result for a stamping die design for an automotive sheet

Differing from rule-based reasoning, CBR does not require a set of explicitly defined mathematical models, rules, or logic. Thus, CBR is suitable for problems with general rules

When comparing cases, algorithms (Watson & Marir, 1994; Tor et al., 2003) are used to assess similarity among cases, and CBR uses significant features to describe a case (Fig. 15),

> n A B i ii i 1 n i i 1

w

.

i f and <sup>B</sup> i f

w s(f , f ) <sup>S</sup>

f , A B i i 0 s(f , f ) 1

i i s(f , f ) 1 if A B

i i

f f ; otherwise, A B

metal part for future reference is stored and reference cases are recorded.

compares each case with given weights, and finally determines total similarity.

i f and <sup>B</sup> i

.

A B

max(f f )

i f and <sup>B</sup> i

f f

i i

When features are represented numerically, the similarity between features <sup>A</sup>

When features are represented non-numerically (e.g., Boolean value or textual description),

i i s(f , f ) 0 if A B

In this study, KBE and CBR are combined to provide designers with guidance from similar

f is A B

necessary.

that cannot be systemized.

Fig. 15. Data structure of feature recognition

The algorithm for determines similarity is

i i s(f , f ) : similarity between features <sup>A</sup>

A B i i i i A B

**3.2 Determining similarity of sheet metal panels** 

wi : weight of each feature A

f : the th i feature of case A A B

s(f , f ) 1

similarity between feature <sup>A</sup>

panels when designing a new panel.

i

would be

i i f f .

S : similarity between case A and case B, 0 S 1

Fig. 13. Reasoning process of case-based reasoning

Typically, CBR has the following four procedures (4R) (Fig. 14):


Fig. 14. The CBR cycle (Kendal & Creen, 2007)


Differing from rule-based reasoning, CBR does not require a set of explicitly defined mathematical models, rules, or logic. Thus, CBR is suitable for problems with general rules that cannot be systemized.

When comparing cases, algorithms (Watson & Marir, 1994; Tor et al., 2003) are used to assess similarity among cases, and CBR uses significant features to describe a case (Fig. 15), compares each case with given weights, and finally determines total similarity.

Fig. 15. Data structure of feature recognition

$$\text{The algorithm for determines similarity is } \mathbf{S} = \frac{\sum\_{i=1}^{n} \mathbf{w}\_i \times \mathbf{s}(\mathbf{f}\_i^{\land}, \mathbf{f}\_i^{\land})}{\sum\_{i=1}^{n} \mathbf{w}\_i}.$$

S : similarity between case A and case B, 0 S 1

wi : weight of each feature A

28 Industrial Design – New Frontiers

1. Retrieve: After feature recognition of an automotive sheet metal panel, CBR compares the features with those in the case database, assesses the similarity among cases, and

2. Reuse: Designers can decide whether a retrieved case is appropriate for reuse and

Matching

Matched case

Retrieve

Adapt?

Yes No

Reuse

Retain

Knowledge and adaption rules

> Closest case

> > Suggest solution

Case base

New case

Fig. 13. Reasoning process of case-based reasoning

Retain

Fig. 14. The CBR cycle (Kendal & Creen, 2007)

Learn

Typically, CBR has the following four procedures (4R) (Fig. 14):

which manufacturing method should be a reference.

retrieves the most similar case as a reference for the design process.

i f : the th i feature of case A A B

i i s(f , f ) : similarity between features <sup>A</sup> i f and <sup>B</sup> i f , A B i i 0 s(f , f ) 1

When features are represented numerically, the similarity between features <sup>A</sup> i f and <sup>B</sup> i f

$$\text{woodd be } \text{s(f}^{\wedge}, \text{f}^{\wedge}) = 1 - \left| \frac{\text{f}^{\wedge} - \text{f}^{\wedge}}{\max(\text{f}^{\wedge} - \text{f}^{\wedge})} \right| \dots$$

When features are represented non-numerically (e.g., Boolean value or textual description), similarity between feature <sup>A</sup> i f and <sup>B</sup> i f is A B i i s(f , f ) 1 if A B i i f f ; otherwise, A B i i s(f , f ) 0 if A B i i f f .

#### **3.2 Determining similarity of sheet metal panels**

In this study, KBE and CBR are combined to provide designers with guidance from similar panels when designing a new panel.

Knowledge-Based Engineering Supporting Die Face Design of Automotive Panels 31

Next, the maximum entry cd S among the n-1 pieces of product-out face parts of each sheet metal is found and marked as <sup>2</sup> S ; the entries that are similar to the th c product-out face of A and those that compared with the th d product-out face of B are removed. Eventually, each feature of product-out face A that matched those of product-out face B are found

11 12 1 1

*s sss*

*s sss*

... ...

*d m*

*d m*

... ...

... ...

... ...

k 1 k

. If one calculates the similarity

f is a non-

. As the difference between n and m

21 22 2 2

... ... ... ... ... ...

... ... ... ... ... ...

*n n nd nm*

1 S S <sup>n</sup> .

i i s(f , f ) 0 . Items 23 6 f ,f , ,f are numerical ones

*s sss*

*c c cd cm*

*s sss*

(a) (b)

This comparison is repeated, such that, 34 m S ,S , ,S (n m) can be derived and, finally,

In this approach, when the numbers of product-out face areas differ (n m) between sheet

increases, the similarity between parts A and B decreases. If A and B have the same number

numerical item representing the existence of undercuts. If both sheet metals parts have an

A B i i i i A B

between each item with weights, overall similarity between two sheet metal parts is

Table 1 shows the similarities between product-out face areas. In this table, 1

s(f , f ) 1

n

A B

max(f f )

f f

i i

1 2

1 2

(Fig. 17)

1 2

1 2

undercut, then A B

and their similarity is defined as

n A B i ii i 1 n i i 1

w

.

w s(f , f ) <sup>S</sup>

11 12 1 1

*s sss*

*s sss*

*s sss*

*s sss*

... ...

*b m*

*b m*

Fig. 17. Accessing similarities between features of A and that of B

the similarity between sheet metal A and B can be determined as <sup>m</sup>

... ...

... ...

... ...

metal parts A and B, the maximum similarity is m

of product-out face areas, maximum similarity is 1.

i i s(f , f ) 1 ; otherwise, A B

2. Similarities between product-out face areas

21 22 2 2

... ... ... ... ... ...

... ... ... ... ... ...

*n n nb nm*

*a a ab am*

Before comparisons, one should first define "similar" for two sheet metal parts. One approach (Tor et al., 2003) is to use part features, geometries, topologies, and materials to describe panels, meaning that this method compares the "appearance" of sheet metal parts. However, in this study, locating sheet metal panels that are similar in terms of manufacturing processes is more important than locating those with similar appearances. This is because sheet metal parts that have a similar appearance may be made with different manufacturing processes and, on the other hand, sheet metal parts that have different appearances may have similar manufacturing processes. For instance, two significantly different product-in face parts may have been shaped by the same drawing operation, meaning these differences do not guarantee differences in the manufacturing process. When comparing two sheet metal parts, the product-in face part should not be considered because it does not significantly affect manufacturing processes. However, the product-out face part significantly affects manufacturing processes. Thus, this study compares product-

out face sheet metal parts to locate cases with similar manufacturing processes.

The parts are compared using a cross-reference method to calculate similarity.

#### 1. Cross reference

Each sheet metal part has uncertain number of product-out face areas. Take sheet metal parts A and B as an example; this study first cross-references each product-out face part (Fig. 16).

Fig. 16. Cross-reference between sheet metal A and B

Here, ij S is defined as the similarity between the th i product-out face area of panel A and

the th j product-out face area of panel B and 1in 1 j m . An n x m matrix can be derived as


The maximum entry ab S is then found and marked as 1 S and then a1 a2 am S ,S , ,S and 1b 2b nb S ,S , ,S are removed.

Before comparisons, one should first define "similar" for two sheet metal parts. One approach (Tor et al., 2003) is to use part features, geometries, topologies, and materials to describe panels, meaning that this method compares the "appearance" of sheet metal parts. However, in this study, locating sheet metal panels that are similar in terms of manufacturing processes is more important than locating those with similar appearances. This is because sheet metal parts that have a similar appearance may be made with different manufacturing processes and, on the other hand, sheet metal parts that have different appearances may have similar manufacturing processes. For instance, two significantly different product-in face parts may have been shaped by the same drawing operation, meaning these differences do not guarantee differences in the manufacturing process. When comparing two sheet metal parts, the product-in face part should not be considered because it does not significantly affect manufacturing processes. However, the product-out face part significantly affects manufacturing processes. Thus, this study compares product-

out face sheet metal parts to locate cases with similar manufacturing processes. The parts are compared using a cross-reference method to calculate similarity.

Fig. 16. Cross-reference between sheet metal A and B

j product-out face area of panel B and

.

Each sheet metal part has uncertain number of product-out face areas. Take sheet metal parts A and B as an example; this study first cross-references each product-out face part (Fig. 16).

Here, ij S is defined as the similarity between the th i product-out face area of panel A and

 

The maximum entry ab S is then found and marked as 1 S and then a1 a2 am S ,S , ,S and

1in 1 j m

. An n x m matrix can be derived as

 

1. Cross reference

the th

11 12 1 m 21 22 2 m

 

 

SS S SS S

n1 n2 nm

1b 2b nb S ,S , ,S are removed.

SS S

Next, the maximum entry cd S among the n-1 pieces of product-out face parts of each sheet metal is found and marked as <sup>2</sup> S ; the entries that are similar to the th c product-out face of A and those that compared with the th d product-out face of B are removed. Eventually, each feature of product-out face A that matched those of product-out face B are found (Fig. 17)

Fig. 17. Accessing similarities between features of A and that of B

This comparison is repeated, such that, 34 m S ,S , ,S (n m) can be derived and, finally, the similarity between sheet metal A and B can be determined as <sup>m</sup> k 1 k 1 S S <sup>n</sup> . In this approach, when the numbers of product-out face areas differ (n m) between sheet metal parts A and B, the maximum similarity is m n . As the difference between n and m increases, the similarity between parts A and B decreases. If A and B have the same number of product-out face areas, maximum similarity is 1.

2. Similarities between product-out face areas

Table 1 shows the similarities between product-out face areas. In this table, 1 f is a nonnumerical item representing the existence of undercuts. If both sheet metals parts have an undercut, then A B i i s(f , f ) 1 ; otherwise, A B i i s(f , f ) 0 . Items 23 6 f ,f , ,f are numerical ones

and their similarity is defined as A B A B i i i i A B i i f f s(f , f ) 1 max(f f ) . If one calculates the similarity

between each item with weights, overall similarity between two sheet metal parts is

$$\mathbf{S} = \frac{\sum\_{\mathbf{i}=1}^{n} \mathbf{w}\_{\mathbf{i}} \times \mathbf{s} (\mathbf{f}\_{\mathbf{i}}^{\wedge}, \mathbf{f}\_{\mathbf{i}}^{\wedge})}{\sum\_{\mathbf{i}=1}^{n} \mathbf{w}\_{\mathbf{i}}}.$$

Knowledge-Based Engineering Supporting Die Face Design of Automotive Panels 33

Fig. 18. Design process integrated with case-based reasoning

Fig. 19. Fender A

Connecting line


Table 1. Similarity of items of product-out face
