Suggestions for Future Work

53

54

REFERENCES

Amen, M. (2001). Heuristic methods for cost-oriented assembly line balancing: A comparison on solution quality and computing time. International Journal of Production Economics, 69 (3), 255-264.

Andrew, K. (1992). Intelligent design and manufacturing. New York: John Wiley &

Sons Inc.

Anjum, M. F., Tasadduq, I., & Al-Sultan, K. (1997). Response surface methodology: A neural network approach. European Journal of Operational Research, 101, 65-73.

Ben-Arieh, D., Kumar, R. R., & Tiwari, M. K. (2004). Analysis of assembly operations’ difficulty using enhanced expert high-level colored fuzzy Petri net model. Robotics and Computer-Integrated Manufacturing, 20, 385-403.

Boart, P. (2005). Life cycle simulation support for functional products. M.Sc. thesis, Luleå University of Technology, SWEDEN.

Bourjault, A. (1984). Contribution á une approche méthodologique de l’assemblage automatisé: Elaboration automatique des séquences opératoires, Unpublished doctoral dissertation, Faculté des Sciences et des Techniques de l’Université de Franche-Comté, France.

Chen, C. L. P. (1990). Neural computation for planning and/or precedence-constraint robot assembly sequences. In: Proceedings of the International Conference on Neural Networks. 127-142. San Diego, CA.

Chen, R. S., Lu, K. Y., & Tai, P. H. (2004a). Optimization of assembly plan through a three-stage integrated approach. International Journal of Computer Applications in Technology, 19(1), 28-38.

Chen, R. S., Lu, K. Y., & Tai, P. H. (2004b). Optimizing assembly planning through a three-stage integrated approach. International Journal of Production Economics, 88, 243-256.

Chen, W. C., & Hsu, S. W. (2007). A neural-network approach for an automatic LED inspection system. Expert Systems with Applications, 33(3), 531-537.

Chen, W. C., Tai, P. H., Deng, W. J., & Hsieh, L. F. (2008). A three-stage integrated approach for assembly sequence planning using neural networks. Expert Systems with Applications, 34, 1777-1786.

Cheng, C. S., & Tseng, C. A. (1995). Neural network in detecting the change of process mean value and variance. Journal of the Chinese Institute of Industrial Engineers, 12 (3), 215-223.

Clive, L. D., & Patric, L. (2009). Engineering Design: a project-based introduction.

55 USA, John Wiley & Sons.

Crowson, R. D. (2006). Assembly Processes: finishing, packaging, and automation.

Taylor & Francis, New York.

De Fazio, T. L., & Whitney, D. E. (1987). Simplified generation of all mechanical assembly sequences. IEEE Transactions on Robotics and Automation, 3(6), 640-658.

Eng, T. H., Ling, Z. K., Olson, W., & Mclean, C. (1999). Feature-based assembly modeling and sequence generation. Computers & Industrial Engineering, 36, 17-33.

Fogel, D. B. (1991). An information criterion for optimal neural network selection.

IEEE Transaction on Neural Network, 2(5), 490-497.

Gu, P., & Norrie, D. H. (2006). Intelligent Manufacturing Planning. USA, Chapman &

Hall.

Gu, P., & Yan, X. (1995). CAD-directed automatic assembly sequence planning.

International Journal of Production Research, 33(11), 3069-3100.

Guo, Y. W., Li, W. D., Mileham, A. R., & Owen, G. W. (2009). Applications of particle swarm optimization in integrated process planning and scheduling. Robotics and computer-integrated manufacturing, 25, 280-288.

Haupt, R. L. (2004). Practical genetic algorithms. 2nd ed. USA, Wiley-Interscience Publication.

Haykin, S. (1999). Neural Networks: A comprehensive foundation. Canada, Prentice Hall.

Henrioud, J. M., Relange, L., & Perrard, C. (2003). Assembly sequences, assembly constraints, precedence graphs. In: Proceedings of the fifth IEEE symposium on assembly and task planning, France, July 10-11, 90-5.

Holland, W. V., & Bronsvoort, W. F. (2000). Assembly features in modeling and planning. Robotics and Computer Integrated manufacturing, 16, 277-294.

Homen de Mello, L. S., & Sanderson, A. C. (1991a). Representations of mechanical assembly sequences. IEEE Transactions on Robotics and Automation, 7(2), 211-227.

Homen de Mello, L. S., & Sanderson, A. C. (1991b). A correct and complete algorithm for the generation of mechanical assembly sequence. IEEE Transactions on Robotics and Automation, 7(2), 228-240.

Hong, D. S., & Cho, H. S. (1995). A neural network based computational scheme for generating optimized robotic assembly sequences. Engineering Application Artificial Intelligence, 8(2), 129-45.

56

Huang, G. Q. (1996). Design for X: Concurrent Engineering Imperatives. London, Chapman & Hall.

Huang, G. Q., & Mak, K. L. (1997). The DFX shell: a generic framework for developing design for X tools. Robotics & Integrated Manufacturing, 13 (3), 271-300.

Hush, D. R., & Horne, B. G. (1993). Progress in supervised neural networks. IEEE Signal Processing Magazine, January, 8-39.

Kai, Y., & Basem, E. H. (2003). Design for Six Sigma: a roadmap for product development, McGraw-Hill, New York.

Kalpakjian, S. (1992). Manufacturing process for engineering materials. 2nd ed. USA, Addison-Wesley.

Khaw, J. F. C., Lim, B. S., & Lim, L. E. N. (1995). Optimal design of neural network using the Taguchi method. Neurocomputing, 7, 225-245.

Kroll, E. (1994). Intelligent assembly planning on triaxial products. Concurrent Engineering: Research and Applications, 1(2), 311-319.

Kulon, J., Broomhead, P., & Mynors, D. J. (2003). Applying knowledge-based engineering to traditional manufacturing design. International Journal of Advanced Manufacturing Technology, 30, 945-951.

Kuo, T. C., Huang, S. H., & Zhang, H. C. (2001). Design for manufacture and design for‘X’: Concepts, applications, and perspectives. Computers & Industrial Engineering, 41, 241-260.

Lai, H. Y., & Huang, C. T. (2004). A systematic approach for automatic assembly sequence plan generation. International Journal of Advanced Manufacturing Technology, 24, 752-763.

Lee, K. (1999). Principles of CAD/CAM/CAE systems. USA, Addison-Wesley.

Lee, S. (1989). Disassembly planning by subassembly extraction. In: M.A., Proceedings of the third ORSA/TIMS Conference on flexible manufacturing systems (pp. 383-388). Cambridge.

Levitin, A. V. (2007). Introduction to the design and analysis of algorithms. 2nd ed.

USA, Addison-Wesley.

Lim, S. S., Lee, B. H., Lim, E. N., & Ngoi, B. K. A. (1995). Computer-aided concurrent design of product and assembly processes: a literature review, Journal of Design and Manufacturing, 5, 67-88.

Lin, A. C., & Chang, T. C. (1993). An integrated approach to automated assembly planning for three-dimensional mechanical products. International Journal of

57 Production Research, 31(5), 1201-1227.

Liu, Y., Liu, W., & Zhang, Y. (2001). Inspection of defects in optical fibers based on back-propagation neural networks. Optics Communications, 198(4-6), 369-378.

Lotter, B. (1989). Manufacturing assembly handbook, Butterworths, London.

Lu, C., Wong, Y. S., & Fuh, J. Y. H. (2006). An enhanced assembly planning approach using a multi-objective genetic algorithm. Journal of Engineering Manufacture, 220, 255-272.

Maier, H. R., & Dandy, G. C. (1998). Understanding the behaviour and optimising the performance of back-propagation neural networks: an empirical study.

Environmental Modelling & Software, 13, 179-191.

Marian, R.M., Luong, L.H.S., & Abhary, K. (2003). Assembly sequence planning and optimisation using genetic algorithms. Applied Soft Computing, 2(3), 223-253.

Mascle, C., & Zhao, H. P. (2008). Integrating environmental consciousness in product/process development based on life-cycle thinking. International Journal of Production Economics, 12, 5-17.

McDonald, D. B., Grantham, W. J., Tabor, W. L., & Murphy, M. J. (2007). Global and local optimization using radial basis function response models. Applied Mathematical Modelling, 31, 2095-2110.

Murata, N., & Yoshizawa, S. (1994). Network information criterion-determining the number of hidden units for an artificial neural network model. IEEE Transaction on Neural Network, 5, 865- 872.

Nof, S. Y., Wilhelm, W. E., & Warnecke, H. J. (1997). Industrial Assembly. Chapman

& Hall, London.

Onoda, T. (1995). Neural network information criterion for optimal number of hidden units. Proceedings of the IEEE International Conference on Neural Networks, 1, 270-280.

Prasad, B. (1997). Concurrent engineering fundamentals: Integrated product development. New Jersey, Prentice-Hall.

Ramos, C., Rocha, J., & Vale, Z. (1998). On the complexity of precedence graphs for assembly and task planning. Computers in Industry, 36, 101-111.

Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1996). Learning representations of back- propagation errors. Nature(London), 323, 533-536.

Sage, A. P. (1990). Concise encyclopedia of information processing in systems and organizations. New York, Pergamon.

Santos, M. S., & Ludermir, B. (1999). Using factorial design to optimize neural

58

networks, International Joint Conference on IEEE Neural Networks, 2, 857-861.

Washington, DC.

Saridakis, K. M., & Dentsoras, A. J. (2008). Soft computing in engineering design- A review. Advanced Engineering Informatics, 22, 202-221.

Sinanog˘lu, C. (2006). A neural predictor to analyze the effects of metal matrix composite structure (6063 Al/SiCp MMC) on journal bearing. Industrial Lubrication and Tribology, 58(2), 95-109.

Smith, G. C., & Smith, S. S. F. (2002). An enhanced genetic algorithm for automated assembly planning. Robotics and Computer-Integrated Manufacturing, 18, 355-364.

Su, Q. (2009). A hierarchical approach on assembly sequence planning and optimal sequence analyzing. Robotics and Computer-Integrated Manufacturing, 25, 224-234.

Tai, P. H. (1997). Feature-based assembly modeling for assembly sequence planning of three-dimensional products. Unpublished master’s thesis, Cranfield University, UK.

Tripathi, M., Agrawal, S., Pandey, M. K., Shankar, R., & Tiwari, M. K. (2009). Real world disassembly modeling and sequencing problem: Optimization by Algorithm of Self-Guided Ants (ASGA). Robotics Computer-Integrated Manufacturing, 25(2009), 483-496.

Wang, J. F., Liu, J. H., & Zhong, Y. F. (2005). A novel ant colony algorithm for assembly sequence planning, International Journal of Advanced Manufacturing Technology, 25, 1137-1143.

Yao, S., Yan, B., Chen, B., & Zeng, Y. (2005). An ANN-based element extraction method for automatic mesh generation. Expert Systems with Applications, 29, 193-206.

Yin, Z. P., Ding, H., & Xiong, Y. L. (2004). A virtual prototyping approach to generation and evaluation of mechanical assembly sequences. In: Proceedings of the Institution of Mechanical Engineering, January, 218, 87-102.

59

APPENDIX A Wheel Illustration Over a Full CE System

Prasad addresses a number of fields to illustrate how a full Concurrent Engineering (CE) system will work as shown in Fig. 39. The successful DFX is based on dedicated CE implementation and whole realization.

Figure 39. PPO&IPD wheel illustration over a full CE system.

60

1

2

6 9 12

5

8

4 7 10

11

GS1 GS2 GS3

13 16

14

3 22 21

17

20 23

24 25

26

27

18

28

15 19

APPENDIX B

Representation of ASP Development Process

Step 1.

Figure 40. Car three-axis deployment of Above graph.

Above-X Above-Y

Above-Z

2 5

2 6 9 1 2

1 3 1 4

1 8

5 8 1 1

2 2 2

4 7 1 0

2 1 2 4

2 3 1 7

1 9 2 0

1

2 8 2 7

S A G B 3

2 2

2 6

1 5 1 6

2

61

16 1 3 22

13 14 25 27 28 26

4 10 11 12 21 15

17 9 6 8 5 7 20 19 18

23 2 24

No Parts’ name 1 MB(MainBody) 2 CP(ChassisPan) 3 DG(DriveGear) 4 GS1_1(GearSet1_1) 5 GS1_2(GearSet1_2) 6 GS1_3(GearSet1_3) 7 GS2_1(GearSet2_1) 8 GS2_2(GearSet2_2) 9 GS2_3(GearSet2_3) 10 GS3_1(GearSet3_1) 11 GS3_2(GearSet3_2) 12 PO(Power)

13 LBW(LeftBackWheel) 14 LFW(LeftFrontWheel) 15 BS1(BaseScrew1) 16 BS2(BaseScrew2) 17 PP1(PowerPack1) 18 PP2(PowerPack2) 19 PPS1(PowerPackScrew1) 20 PPS2(PowerPackScrew2) 21 RA(RearAxis)

22 RD(RearDiff)

23 RBW(RightBackWheel) 24 RFW(RightFrontWheel) 25 SL(Spoiler)

26 SP1(Spring1) 27 SP2(Spring2) 28 SR(SteeringRack)

3DG

SAGB

21RA ²³RBW

22RD ¹³LBW

14LFW

2CP

28SR

27SP2

1MB

24RFW

25SL

26SP1

16BS2

15BS1

Figure 41. Creating a correct car explosion graph via Above graph rule

Step 2. Basepart: 2CP

Figure 42. Car sub- relational model graph (RMG) on level 1

62

2CP

26SP1 27SP2 22RD 14LFW 25SL

24RFW

1MB SAGB 3DG

21RA

28SR 13LBW

23RBW

15BS1 ₁₆BS2

Spatial constraint

17PP1

GS3

GS1 GS2

17PP1

GS3 GS2

GS1

12PO ₁₈PP2

19PPS1 20PPS2

12PO

18PP2

19PPS1

20PPS2

GS2

GS3

17PP1

GS1

18PP2

19PPS1

20PPS2

12PO

Step 3: Basepart: 17PP1 (SAGB)

Spatial constraint

2CP

22RD

3DG

SAGB

28SR

21RA

13LBW

14LFW

24RFW

26SP1

27SP2

25SL

1MB

23RBW

15BS1

16BS2

Figure 44. Car sub- RMG and APD on SAGB

Figure 43. Car assembly precedence diagram (APD) on level 1

63

Spatial constraint

6GS1_3

10GS3_1

12PO

4GS1_1

7GS2_1

11GS3_2

5GS1_2

8GS2_2

9GS2_3

Step 5. Key connections:

6G S 1 _ 3

1 0G S 3 _ 1

4G S 1 _ 1

7G S 2 _ 1

1 1G S 3 _ 2

8G S 2 _ 2

9G S 2 _ 3

1 7P P 1

1 8P P 2 9G S 2 _ 3

8G S 2 _ 2

7G S 2 _ 1

6G S 1 _ 3

5G S 1 _ 2

4G S 1 _ 1

1 1G S 3 _ 1

1 2P O

1 0G S 3 _ 2

1 7P P 1

1 8P P 2

1 9P P S 1

2 0P P S 2

6GS1_3

10GS3_1

12PO

4GS1_1

7GS2_1

11GS3_2

5GS1_2

8GS2_2

9GS2_3

17PP1 18PP2

20PPS2 19PPS1

9G S2_3

8G S2_2

7G S2_1

6G S1_3

5G S1_2

4G S1_1

11G S3_1

12PO

10G S3_2

Figure 45. Sub- RMG and APD on car Gear Set Step 4. Base part: 9GS2_3 (Gear Set)

Figure 46. Car sub- RMG and APD on level 2

64

Step 6. Key connections: 2CP ¹⁷PP1 ³DG ⁵GS1_2

2CP 22RD 3DG 17PP1 9GS2_3 ₈GS2_2 7GS2_1

4GS1_1

5GS1_2

6GS1_3

10GS3_1

11GS3_2

28SR

16BS2

21RA ¹³LBW 23RBW 14LFW

24RFW 26SP1 ₂₇SP2 25SL 1MB

12PO ¹⁸PP2

19PPS1 ²⁰PPS2

15BS1 C40

C39

C21

C22

C23

C24 C25

C26 C27 C29 C28

C30

C32 C31 C33

C34

C36 C35

C37 C38

C2

C3 C4

C5 C6

C7

C8

C9

C10 C11

C12 C13

C14 C15

C16 C17 C18

C19

C20

C1

3DG

21RA

23RBW

22RD

13LBW

14LFW

2CP

28SR

27SP2

1MB

24RFW

25SL

26SP1

16BS2

15BS1

6GS1_3

10GS3_1

12PO

4GS1_1

7GS2_1

11GS3_2

5GS1_2

8GS2_2

9GS2_3

17PP1 18PP2

20PPS2 19PPS1

Figure 47. Car complete- RMG and APD

65

13

14

11

12

15 2 9 16

1

6 10

17

3

5 4

8

7

66

No Part name

1 MA(MotorbikeAxle) 2 MB1(MotorbikeBearing1) 3 MB2_1(MotorbikeBearing2_1) 4 MB2_2(MotorbikeBearing2_2) 5 MB3_1(MotorbikeBearing3_1) 6 MB3_2(MotorbikeBearing3_2) 7 MH1(MotorbikeHandlE1) 8 MH2(MotorbikeHandlE2) 9 MMB1(MotorbikeMainBody1) 10 MMB2(MotorbikeMainBody2) 11 MN(MotorbikeNut)

12 MPN(MotorbikePin) 13 MPE(MotorbikePlate) 14 MS(MotorbikeScrew) 15 MW1(MotorbikeWheel1) 16 MW2(MotorbikeWheel2) 17 MW3(MotorbikeWheel3)

13

9 10

15

Above-X

7 13

11 15

10 2

9

14 8

6

17

3

10

9

4

16

5

1

12

Above-Y

2 15 7

13 12

8

1

5 16 4

9 10 11

3 17 6

14

2 15 7

13 12

8

1

5 16 4

9 10 11

3 17 6

14

Figure 48. Motorbike three-axis deployment of Above graph

Figure 49. Creating a correct Motorbike explosion graph via Above graph rule

67 Base part: 9MMB1

C1

C2 C3

C4 C5

C6 C7

C8 C9 C10

C12 C11 C13

C14

C15 C16

C17

C18 C19 C20

C21 C22

2MB1

12MPN ₁₅MW1

13MPE

7MH1 ₈MH2

9MMB1 ₁₀MMB2

14MS ₁₁MN

1MA

5MB3_1 ₆MB3_2

16MW2 4MB2_2 3MB2_1 17MW3

7 13

11

15 10

2

14 9

6 17

3

8 4

16

5 1

12

7 13

11 15

10 2

14 9

6 17

3

8 4

16

5

1

12

7 13

11 15 10

2 14 9

6 17 3

8 4

16

5

1 12

7 13

11 15 10

2 14 9

6 17

3

8 4 16

5

1 12

Figure 50. Motorbike Sub- RMG and APD

68

APPENDIX C Data Matrix of KBE-based ASP System

Product Name: Toy Car

69

70 Product Name: Toy Motorbike

71

72

);

( ) ( )

(

n y n x n

W_kj = × _k × _j

Δ

η

);

(ω ε

∇

= g

T

wn

w

w ⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

∂

∂

∂

∂

∂

= ∂

∇ ...

2 , 1,

. n point at the evaluated ector

gradient v the

is (n) and parameter, rate

learning or

size

step the called constant positive

a is where n

n 1

n

) (

; ) ( ) ( ) (

ω η

η ω

ω

g



− g

= +

y

y x

x n

W_kj( )= ( _j − )( _k − );

Δ η

hypothesis Covariance

APPENDIX D

Statistical Learning Theory and BP Algorithm

A learning theory of NN-based statistical characterization addresses how to control the generalization ability of a supervised learning machine, which is capable of implementing a set of input-output mapping functions. A neural network is a massively parallel distributed processor composed of processing units of stored useful experiential knowledge. It resembles the human brain in two respects (Haykin, 1999):

1. Knowledge is obtained by the network through a powerful learning process.

2. Interneuron connection strengths, called synaptic weights, are dedicated to storing the acquired knowledge.

Hebbian learning is known as Hebb’s basis of learning, which is the most famous of all learning rules. A Hebbian synapse is a time-dependent, highly local, and strongly interactive mechanism of interest to make synapse efficient. The simplest formula of Hebbian learning can be denoted as follows:

Where

x

and

y

imply the time-averaged values of the pre-synaptic signal xj and post-synaptic signal

y

_k, respectively; n is the time step or epoch.

Method of steepest descent:

where ∇ is the gradient operator, and ω is weight vector.

The steepest descent algorithm is formally described by

73

) ( ) ( ) ( ) 2 / 1 ( ) ( ) ( ))

( (

)) ( ( )) 1 ( ( )) ( (

; 0 ) ( ) ( ) (

n n

H n n

n

 g

n ating

Differenti

n n

n



 n n H n g

T

T ω ω ω

ω ε

ω ε ω

ε ω

ε ω

Δ Δ

+ Δ

≈ Δ

− +

= Δ

= Δ

+

) ( ) ( )

(

) ( ) ( ) 1 ( );

( ) ( )

(

1 1

n g n H

 n







n n

 n n

g n H n

−

−

−

=

Δ +

= +

−

= Δ

ω

ω ω

ω ω

) ( )

(  e i

W

∑

n

=

=

1 2

2 1

i

ε

) ˆ( ) ( ) ) (

) ( ) (

(

) ( ) ( ) ( );

( )

(

) ( );

( )

(

n g n e n n x

W n W

n x W

n e

n W n x n d n n e

W W n e

n e W

W

W W

n e n

e W

T

=

−

∂ =

⇒ ∂

−

∂ =

∂

−

∂ =

= ∂

∂

∂

=

) ( )

Hence, (

) ( ) ) (

) ( (

) ( ctor weight ve the

respect to with

ating Differenti

n.

at time measured

signal error the is ) ( 2

1 ₂

ε ε

ε ε

) ( )

(

; ) ( ) ( )

(n 1 ω n ηg n  ω n ηg n

ω + = − Δ =−

ctor.

weight ve the

around loop

feedback the

is n and

parameter, rate

-learning the

is where n

1 n

) ˆ(

; ) ( ) ( ) ˆ( ) ˆ (

ω η η

ω

ω + = + x n e n 

operator.

delay -unit the is 1

n

n) =Ζ⁻¹[ˆ( + )];Ζ⁻¹

ˆ( ω

ω

⎥⎥

⎥⎥

⎥⎥

⎥⎥

⎥

⎦

⎤

⎢⎢

⎢⎢

⎢⎢

⎢⎢

⎢

⎣

⎡

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

=

∇

=

2 2

2 2

1 2

2 2 2

2 2

1 2

2

1 2

2 1

2 2

1 2

2

m m m

m m



...





...

...

...

...









...



) ( H

ω ε ω

ω ε ω

ω ε

ω ω

ε ω

ε ω

ω ε

ω ω

ε ω

ω ε ω

ε

ω ε

) n ( )

n ( ) 1 n ( ) n

( ω ω ηg

ω = + − =−

Δ ; This form is error-correction rule, where

) 1 n ( +

ω is its updated value, and ω(n) is the old value of the weight vector.

The matrix H (n) is the m×m Hessian matrix of ε (ω) as represented below.

Where )H⁻¹(n is the inverse of the Hessian ofε (ω).

Gauss-Newton method is applicable to a cost function that is expressed as the sum of error squares.

Least-Mean-Square (LMS) algorithm is based on the use of instantaneous values for the cost function, namely,

74 . )]

( [

; )]

ˆ( [

∞

→

→

∞

→

→

n as constant n

solution.

Wiener is

n as n

2

0 0

e

 ε

ω ω

ω ε

X1(n)

X₂(n)

X_m(n)

………

Bias, b

∫

Output Layer Input Layer

w1

w2

w_m

Hard Limiter

) ϕ(v v

neuron of

field local induced or

input limiter hard

the is

1

ν ν w x_i b;

m

i

i +

=

∑

=

. (n) signal, error the of value ous instantane the

is n 2 n

n) 1e²_k( );E( ) e_k

(

E =

larning.

of rate the determines that

parameter)

rate -learning (say the

constant positive

a is where n

n

n η η

ω_kj( )= e_k( )x_j( ); Δ

The objective is achieved by minimizing a cost function or index of performance, E (n).

The step-by-step adjustments to the synaptic weights of neuron k are continued until the system reaches a steady state (i.e., the synaptic weights are essentially stabilized). The learning process described herein is obviously referred to as error-correction learning; belong to a closed-loop feedback system.

Let w_kj(n denote the value of synaptic weight ) w_kj of neuron k excited by element x_j(n of the signal vector ) x n( ) at time step n.

The delta rule (or Widrow-Hoff rule): the adjustment Δw_kj(n) applied to the synaptic weight w_kj at time step n is defined by

The delta rule may be stated as: the adjustment made to a synaptic weight of a neuron is proportional to the product of the error signal and the input signal of the synapse in question.

75

………………

X₁(n)

X₂(n)

X_m(n)

Bias, b

ϕ(.)

Output Layer

Input Layer

W_k1(n)

W_km(n)

)

k(n

X_j(n) ν y_k(n)

) ( d_k n

) ( y ) ( d ) (

e_k n = _k n − _k n

W_k2(n)

W_kj(n)

−1

) y ( y y

y

y y y . y y e

e ' y y e

y ] e [ ' y

] e . y e ' y [ ' y y ; e y

e y y

j j

j j

j j j

j j j

j j

j

j j

j j

j j

j

j j j

j

j j

j j

−

− =

− = +

− + =

=

⇒

= +

=

− +

− +

=

⇒

= +

−

−

−

−

−

−

−

−

1 1 1 1 1

1 1 1

0 1

1

υ υ υ

υ

υ υ

υ υ

) ( )

( )

( _{kj kj}

kj n 1 ω n ω n

ω + = +Δ ; X(n)=[+1,x1(n), x2(n), …xn(n)]^T W(n)=[+1,W1(n), W2(n), …Wn(n)]^T; b (n): bias

)]

( y ) ( d [ ) ( )

(n+1 =ω n +η n − n

ω x(n); 0<η<1;

y(n)=sgn [W^T(n)X(n)] ; d(n):desiredresponse ;y(n):actual response A commonly used form of nonlinearity is defined by the logistic function.

neuron.

the of output

the is and j, neuron of

) bias the plus inputs synaptic

all of sum weighted the

(i.e., filed local induced the

is ); exp(

1 1

j j

j j

y





y υ

υ

−

= +

Back-Propagation Algorithm

The error signal at the output of neuron j at iteration n

j.

neuron for signal function the

is n

j;

neuron for response desired

the is n n n

n

) ( y

) ( d );

( y ) ( d ) ( e

j j j j

j = −

The total error energy

∑

∑

∈ =

=

= ^N

n av

c j

) N (

) ( );

( e )

( j

1

2 1 n

n 2 n

n 1 ε ε

ε

76

ϕ(.) )

j(n

ν y_j(n)

) ( d_j n

) ( e_j n

−1

) ( y ) ( )

(n n n

0

i i

ji

j

∑

=

= ^mω ν

) ( y ) ( )

( )) ( ) (

( ) ( ) y ( y ) ( d ) ( e

) ( y )) ( ( ) ( e ) ( y )) ( ( ) )(

( e

) (

) . (

) (

) ( . y ) ( y

) ( . e ) ( e

) ( ) (

) (

j ' j j

j j

j j

j j ' j j j

j ' j j

ji j

j j

j j

j ji

n n n

, n n

, n n n

n where

n n n

-n n 1

n

n n n

n n

n n

n n

n

calculus of

rule chain the to According

0

i i

ji

j

∑

=

=

∂ =

− ∂

=

=

−

=

∂

∂

∂

∂

∂

∂

∂

= ∂

∂

∂

m ω ν

υ υ ϕ

υ ϕ υ

ϕ

ω υ υ

ε ω

ε

)) ( ( ).

( e

) (

) ( . y ) ( y

) ( . e ) ( e

) ( )

( ) ) (

(

j ' j j

j

n n

n n n

n n

n n

n n gradient Local

j j j

j j

j

υ ϕ

υ ε

υ δ ε

=

∂

− ∂

∂

− ∂

∂

− ∂

∂ =

− ∂

=

. neuron

of signal input the is parameter,

rate learning the

is where n

n n

correction Weight

j

i j

j ji

y );

( y ).

( . )

( ηδ η

ω =

Δ

Activation functionϕ_j(υ_j(n)): 1. Sigmoid nonlinearity

neuron.

hidden the

is j n 1

n n

n n

1 n 0

and m

- 0, a n 1

n 1

)];

( y )[

( ay )) ( ( ))

( ( ) ( y

) ( y )

( ));

( a )) exp(

( (

j j

j ' j j

j j

j j

j

−

=

⇒

=

≤

≤

∞

<

<

∞

− >

= +

υ ϕ υ

ϕ

υ υ υ

ϕ _j

j

) ( ) ( )]

( y )[

( ay ) ( ) ( )) ( ( )

( _kj

k k j

j kj

k k j

'

j n n n n 1 n n n

j n ϕ υ δ ω δ ω

δ ⁼

∑

^{= −}

∑

2. Hyperbolic tangent function

77

Data Structure for NeuroSolutions

X1(n)

X2(n)

X5(n)

Bias, b

ϕ(.)

Output Layer

Input Layer

W61(n)

Wkm(n)

) n

10( ν

X3(n) y_j(n)

) ( d_j n

) ( e_j n

W62(n)

Wkj(n) −1

Wji(n)

Hidden Layer X4(n)

Bias, b

) n

6( ν

) n

7( ν

) n

8( ν

) n

9( ν

)]

( y a )][

( y a a[ )) b ( b ( (

ab )) ( b ( ab

)) ( (

) ( y )

(

; ) ( )) a

( b exp(

)) ( b a exp(

)) ( (

j j

j ' j

j j

j

n n

n tan

-1 n

Sech n

1 n 1 and m -

0, b a, ) n (b tanh n

1

n . 1

n

2

2 = = − +

=

≤

≤

∞

<

<

∞

>

− = +

−

= −

j j

j

j j

j

υ υ

υ ϕ

υ

υ υ υ υ

ϕ

) ( ) ( )]

( y a )][

( y a a[ )) b ( ( ) ( e )

( _kj

k k j

j j

' j

j n n n n n n

j n ϕ υ δ ω

δ ^{= = − +}

∑

An example for BPNN Algorithm using NeuroSolutions package can be seen below: assume that there are five inputs: the value of assembly incidence (AI), total penalty value (TPV), feature number (FN), weight and volume, which are crucial criteria for assembly sequence planning, and the output variable is a global optimal assembly sequence.

The above BPNN architecture with weights and bias as follows.

78

Compared with BPNN implementation using C and KF programming

The performance of C programming is much better than that of KF programming, and both programs are listed below.

[C programming]

// back2.cpp : //

#include "stdafx.h"

#include <stdio.h>

#include <stdlib.h>

#include <math.h>

#define Ntest 17

#define Ninp 5

#define Nhid 14

#define Nout 1

#define weight_file "d:\\5925007\\myvc\\xorTrain.wei"

#define test_file "d:\\5925007\\myvc\\xorTest.txt"

#define recall_file "d:\\5925007\\myvc\\xor.rec"

int _tmain(int argc, _TCHAR* argv[]) {

FILE *fp1,*fp2,*fp3;

float X[Ninp],T[Nout],H[Nhid],Y[Nout];

float W_xh[Ninp][Nhid],W_hy[Nhid][Nout];

float Q_h[Nhid],Q_y[Nout];

float sum,mse;

int Itest;

int i,j,h;

/*--- open files ---*/

fp1=fopen(weight_file,"r");

fp2=fopen(test_file,"r");

fp3=fopen(recall_file,"w");

if (fp1==NULL) {

puts("File not exist !!");

getchar();

exit(1);

}

if (fp2==NULL) {

puts("File not exist !!");

getchar();

exit(1);

}

79 /*--- input weights from weight_file ---*/

fseek(fp1,0,0);

for (h=0;h<Nhid;h++) for (i=0;i<Ninp;i++)

fscanf(fp1,"%f",&W_xh[i][h]);

for (j=0;j<Nout;j++)

for (h=0;h<Nhid;h++)

fscanf(fp1,"%f",&W_hy[h][j]);

for (h=0;h<Nhid;h++)

fscanf(fp1,"%f",&Q_h[h]);

for (j=0;j<Nout;j++)

fscanf(fp1,"%f",&Q_y[j]);

/*--- Testing ---*/

fseek(fp2,0,0);

for (Itest=0;Itest<Ntest;Itest++) {

/*--- input one testing example ---*/

for (i=0;i<Ninp;i++)

fscanf(fp2,"%f",&X[i]);

for (j=0;j<Nout;j++)

fscanf(fp2,"%f",&T[j]);

// for (i=0;i<Ninp;i++) { // printf("x[i]=");

// printf("%-8.2f",X[i]);

// }

/*--- comput H,Y ---*/

for (h=0;h<Nhid;h++) {

sum=0.0;

for (i=0;i<Ninp;i++){

// printf("w[%d][%d]=",i,h);

// printf("%-8.2f",W_xh[i][h]);

sum=sum+X[i]*W_xh[i][h];

// printf("sumA[%d]=",h);

// printf("%-8.2f",sum);

}

// printf("sum[%d]=",h);

// printf("%-8.2f",sum);

H[h]=(float)1.0/(1.0+exp(-(sum-Q_h[h])));

//H[h]=(float)(exp(sum-Q_h[h])-exp(-(sum-Q_h[h])))/(exp(sum-Q_h[h])+exp(-(sum-Q_h[h])));

// printf("H[%d]=",h);

// printf("%-8.3f",H[h]);

// printf("Q_h[%d]=",h);

// printf("%-8.3f",Q_h[h]);

80 }

for (j=0;j<Nout;j++) {

sum=0.0;

for (h=0;h<Nhid;h++)

sum=sum+H[h]*W_hy[h][j];

Y[j]=(float)1.0/(1.0+exp(-(sum-Q_y[j])));

//Y[j]=(float)(exp(sum-Q_y[j])-exp(-(sum-Q_y[j])))/(exp(sum-Q_y[j])+exp(-(sum-Q _y[j])));

// printf("Y[%d]=",j);

// printf("%-8.5f",Y[j]);

}

/*--- compute the mean_square_error ---*/

mse=0.0;

for (j=0;j<Nout;j++)

mse+=(T[j]-Y[j])*(T[j]-Y[j]);

/*--- Write the results to recall_file ---*/

printf("T[j]= ");

fprintf(fp3,"T[j]= ");

for (j=0;j<Nout;j++) { printf("%-8.2f",T[j]);

fprintf(fp3,"%-8.2f",T[j]);

}

printf("Y[j]= ");

fprintf(fp3,"Y[j]= ");

for (j=0;j<Nout;j++) { printf("%-8.5f",Y[j]);

fprintf(fp3,"%-8.5f",Y[j]);

}

printf(" mse= %-8.4f\n\n",mse);

fprintf(fp3," mse= %-8.4f",mse);

fprintf(fp3,"\n");

} /*--- end of recalling for total teat examples ---*/

fclose(fp1);

fclose(fp2);

fclose(fp3);

getchar();

return 0;

}

[KF programming]

#! NX/KF 5.0

DefClass: recursion (ug_base_part);

(Number)Ncycle:1;

81

(Number)Ntrain:45;

(Number)Ninp:5;

(Number)Nhid:14;

(Number)Nout:1;

(Number)eta:0.5;

(Number)alpha:0.9;

(Number)etao:0.7;

(Number)alphao:0.1;

(String) train_file:"D:\NXKF\BB\Proposal\Assembly_Sequencing\train_file.xls";

(String)weight_file:"D:\NXKF\BB\Proposal\Assembly_Sequencing\weight_file.xls";

(String)mse_file:"D:\NXKF\BB\Proposal\Assembly_Sequencing\mse_file.xls";

(List)fp1:@

{

$openExcel << ug_excel_open_file(train_file:, read);

$Bracket << Loop{

For $i from 1 to 6;

For $Read is ug_excel_read_range($openExcel, 1, 1, $i, Ntrain:,$i);

For $sublist is subList($Read,6,Length($Read)+5);

For $MakeNumber is loop{

For $j from 1 to length($sublist);

For $Make is MakeNumber(nth($j,$sublist));

collect $Make;

};

Collect $MakeNumber;

};

$closeFile << ug_excel_close_file($openExcel, True);

$Bracket;

};

(List)ReadTextList:@

{

$openExcel << ug_excel_open_file(weight_file:, read);

$Read << ug_excel_read_range($openExcel, 1, 1, 1, -1,1);

$sublist << subList($Read,6,Length($Read)+5);

$MakeNumber << loop{

For $j from 1 to length($sublist);

For $Make is MakeNumber(nth($j,$sublist));

collect $Make;

};

$closeFile << ug_excel_close_file($openExcel, True);

$MakeNumber ; };

##################################################################

(Method Boolean) writeMethod:(integer $fileOpen, integer $WorkID, integer $rowStar, integer

$colStar, integer $rowEnd, integer $colEnd, List $data)

@{

$write << ug_excel_write_range($fileOpen, {$WorkID, $rowStar, $colStar, $rowEnd, $colEnd} +

$data);

};

(String)dW_hy_file:"D:\NXKF\BB\Proposal\Assembly_Sequencing\dW_hy.xls";

(Uncached any)ALearning:loop{

For $Icycle from 1 to Ncycle:;

Do StoreValue(0, self:, mse);

For $Trainingtimes is ATrainingtimes:+1;

Do StoreValue($Trainingtimes, self:, ATrainingtimes);

For $Icycle2 is loop{

82

For $Itrain from 1 to Ntrain:;

For $HideNet is loop{

For $h from 1 to Nhid:;

For $Sum is 0;

For $HideNet1 is loop{

For $i from 1 to Ninp:;

For $Sum is $Sum+nth($Itrain,nth($i,X:))*nth($i,nth($h,W_xhList:));

Sum $sum;

};

For $HideNet2 is 1.0/(1.0+exp(-($HideNet1-nth($h,Q_hList:))));

Do StoreValue($HideNet2, self:,nth($h,HStoreList:));

append{$HideNet2};

};

For $YoutputNet is loop{

For $j from 1 to Nout:;

For $Sum is 0;

For $YoutputNet1 is loop{

For $h from 1 to Nhid:;

For $Sum is $Sum+nth($h,H:)*nth($j,nth($h,W_hyList:));

Sum $sum;

};

For $YoutputNet2 is 1.0/(1.0+exp(-($YoutputNet1-Q_y_1:)));

Do StoreValue($YoutputNet2, self:,nth($j,YStoreList:));

append{$YoutputNet2};

};

For $delta_y is loop{

For $j from 1 to Nout:;

For $delta_y1 is nth($j,Y:)*(1.0-nth($j,Y:))*(nth($Itrain,X6:)-nth($j,Y:));

Do StoreValue($delta_y1, self:,nth($j,delta_yStoreList:));

append{$delta_y1};

};

For $delta_h is loop{

For $h from 1 to Nhid:;

For $Sum is 0;

For $delta_h2 is loop{

For $j from 1 to Nout:;

For $Sum is $Sum+nth($j,nth($h,W_hyList:))*nth($j,delta_y:);

Sum $sum;

};

For $delta_h3 is nth($h,H:)*(1.0-nth($h,H:))*$delta_h2;

Do StoreValue($delta_h3, self:,nth($h,delta_hStoreList:));

append{$delta_h3};

};

For $dw_hy is loop{

For $j from 1 to Nout:;

For $dw_hy2 is loop{

For $h from 1 to Nhid:;

For $dw_hy3 is etao:*nth($j,delta_y:)*nth($h,H:)+alphao:*nth($j,nth($h,dw_hyList:));

Do StoreValue($dw_hy3, self:,(nth($j,nth($h,dw_hyStoreList:))));

append{$dw_hy3};

};

append{$dw_hy2};

};

For $dQ_y is loop{

For $j from 1 to Nout:;

For $dw_hy2 is -etao:*nth($j,delta_y:)+alphao:*dQ_y_1:;

Do StoreValue($dw_hy2, self:, dQ_y_1);

append{$dw_hy2};

83

};

For $dw_xh is loop{

For $h from 1 to Nhid:;

For $dw_xh2 is loop{

For $i from 1 to Ninp:;

For $dw_xh3 is eta:*nth($h,delta_h:)*nth($Itrain,nth($i,X:))+alpha:*nth($i,nth($h,dw_xhList:));

Do StoreValue($dw_xh3, self:,(nth($i,nth($h,dw_xhStoreList:))));

append{$dw_xh3};

};

append{$dw_xh2};

};

For $dQ_h is loop{

For $h from 1 to Nhid:;

For $dQ_h2 is -eta:*nth($h,delta_h:)+alpha:*nth($h,dQ_hList:);

Do StoreValue($dQ_h2, self:,nth($h,dQ_hStoreList:));

append{$dQ_h2};

};

For $W_hy is loop{

For $j from 1 to Nout:;

For $W_hy2 is loop{

For $h from 1 to Nhid:;

For $W_hy3 is nth($j,nth($h,W_hyList:))+nth($j,nth($h,$dw_hy));

Do StoreValue($W_hy3, self:,(nth($j,nth($h,W_hyStoreList:))));

append{$W_hy3};

};

append{$W_hy2};

};

For $Q_y is loop{

For $j from 1 to Nout:;

For $Q_y2 is Q_y_1:+nth($j,$dQ_y);

Do StoreValue($Q_y2, self:, Q_y_1);

append{$Q_y2};

};

For $W_xh is loop{

For $h from 1 to Nhid:;

For $W_xh2 is loop{

For $i from 1 to Ninp:;

For $W_xh3 is nth($i,nth($h,W_xhList:))+nth($i,nth($h,$dw_xh));

Do StoreValue($W_xh3, self:,(nth($i,nth($h,W_xhStoreList:))));

append{$W_xh3};

};

append{$W_xh2};

};

For $Q_h is loop{

For $h from 1 to Nhid:;

For $Q_h2 is nth($h,Q_hList:)+nth($h,$dQ_h);

Do StoreValue($Q_h2, self:,nth($h,Q_hStoreList:));

append{$Q_h2};

};

For $mse is loop{

For $h from 1 to Nout:;

For $mse1 is mse:+(nth($Itrain,X6:)-nth($h,Y:))*(nth($Itrain,X6:)-nth($h,Y:));

Do StoreValue($mse1, self:, mse);

append {$mse1};

};

For $IcycleNumber is $Icycle;

collect{$IcycleNumber};

};

For $openExcel is ug_excel_open_file(weight_file:, Write);

在文檔中 中 華 大 學 博 士 論 文 (頁 67-98)