DEVELOPMENT OF AN INNOVATIVE NEURAL … · 7/10/2007 Gustavo A. Rengifo 22 Outline Problem...

Gustavo Augusto RengifoThesis Presentation

Advisor: Dr. Hazim ElAdvisor: Dr. Hazim El--MounayriMounayri

Advanced Engineering Manufacturing Laboratory (AEML)Advanced Engineering Manufacturing Laboratory (AEML)Mechanical Engineering DepartmentMechanical Engineering Department

Purdue School of Engineering & Technology, IUPUIPurdue School of Engineering & Technology, IUPUI

April 13April 13thth, 2007, 2007

DEVELOPMENT OF AN INNOVATIVE NEURAL NETWORK MODEL FOR MILLING BASED ON A SYSTEMATIC APPROACH FOR STATISTICAL

DESIGN OF EXPERIMENTS

7/10/20077/10/2007 Gustavo A. RengifoGustavo A. Rengifo 22

OutlineProblem Definition

Previous Work

Current Work

• Overview

• Experiments

• More general ANN model for end milling

• New DOE technique for optimal data collection/sets

• Systematic approach for optimizing process modeling

Results

Conclusions and Future Research


Problem Definition

The End Milling OperationProcessCutting Conditions & Process ParametersUsability

GoalComprehensiveEfficientInexpensive Practical

R.D.C.

A.D.C.

Tool

Workpiece

Spindle Speed

Feed rate


Previous Work Traditional vs. Non-Traditional Techniques

Mathematical/Analytical models:

- Kline [1]: Predicted cutting forces and cutter/workpiece deflection

- Sutherland [2]: Determined chip load for surface error prediction

ANN:

- Elanayar [3]: Predicted surface roughness

- El-Mounayri [4]: Predicted cutting forces using feed, speed and axial depth of cut

Generality: Cutting Conditions & Process Parameters

- Oktem [5]: Predicted surface roughness using cut. speed, and ADC and RDC


Previous Work

Training and Collection of Data

Optimization

Lack of systematic approach

- Oktem [5] used a full factorial DOE to study the effects of cutting parameters on AL end milling

- Ghani [6] performed a three factor full factorial to minimize cutting forces and surface roughness

- Baris [7] investigated the impact of cutting parameters on surface finish using fractional factorial


Experimental Setup

Data Collection

Optimum Data Set

Training Validation

Trained ANNOptimization

of Cutting Parameters

F & Ra

Process Model

Systematic Approach

DOE HGLInput Parameters

Tool DiameterAxial Depth f Cut

Radial Depth of CutFeed per toothCutting Speed

Overview


Overview - Summary

Efficient application of BP ANN to model End Milling

Unique Cutting Force and Surface Roughness Model

Simulation of Cutting Force Components

Implementation of Fractional Factorial DOE

Development of a Systematic Approach based on reliability to train the ANN Model


ExperimentsExperimental Setup for Cutting Force Measurement

3-Component Force Dynamometer

Shielded Connecting cable LabVIEW Application

PC

Charge Amplifier


Experiments Cont’Surface Profile Measurement

Non contact Profilometer: Proscan 2000

Chromatic SensorRes. 0.1 µm

Measurement of Surface Profile at two levels

L1L2


Experimental Setup

Data Collection

Optimum Data Set

Training Validation



F & Ra

Process Model

Systematic Approach




Overview


Experiments Cont’Cutting Experiments

Control Factors

1. Tool diameter

2. Radial depth of cut

3. Axial depth of cut

4. Feed per tooth

5. Cutting speed

System Responses

1. Cutting Forces

2. Surface Profiles

Cutters:

½” & 1” – 1 flute end mill for AL

→ RUNOUT

Material

AL-7075


Experiments Cont’Run Out Effect

Surface Profile using 2 flute cutter[0.2 mm/tooth & 0.5 mm RDC]

0.2 mm


Experiments Cont’Run Out Effect

Surface Profile using 1 flute cutter[0.4 mm/tooth]

0.2 mm


Experiments Cont’Cutting Experiments

Control Factors

1. Tool diameter: ½”, 1”

2. Axial depth of cut: 25%, 50%, 75%, 100%

3. Radial depth of cut: 0.5, 2, 4, 6 [mm]

4. Feed per tooth: 0.1, 0.15, 0.2, 0.25 [mm/tooth]

5. Cutting speed: 90, 110, 150 [mm/min]

2 X 3 X 43

384

experiments

Dv

**1000S

π= SNF **FR =

F…feed per tooth

N…# of flutes

S…Spindle Speed

F.R…Feed Rate

v…Cutting Speed

D…Cutter Diameter

S…Spindle Speed

LevelV1 X LevelV5 X Level V23


Experiments Cont’Cutting Force Measurement

1.27 1.28 1.29 1.3 1.31 1.32 1.33

-250

-200

-150

-100

-50

0

Cutting Forces: Experiment #60: t1a2r1f4v3

Second

Cut

ting

Forc

es [N

ewto

n]

FxFyFz

Force Measurement: Exp# 60:t1=1/2”, a2=50%, r1=0.5mm,

f4=0.25mm/tooth, v3=150mm/min

Force FFT: Exp# 60

20 40 60 80 100 120 140 160 180 2000123

x 107

FFT and Power Spectrum: Experiment#60: t1a2r1f4v3

Forces X

Pow

er

50 100 150 200 2500

5

10

15x 10

5 FFT Forces Y

Pow

er50 100 150 200 250

0

1

2x 10

5 FFT Forces Z

Frequency [Rad/sec]P

ower

62.65 rad/sec3759.6 RPM


Experiments Cont’Surface Profile Measurement

Surface Profile measured: 1L

Photo using CCD CameraScaling Techniques

[0.25mm/tooth]

Approx.

Distance0.5 1 1.5 2 2.5

-5

-4

-3

-2

-1

0

1

2

3

Surface Profile: Experiment #60: t1a2r1f4v3 Level #1

Distance [mm]

Mic

ron

0.5 mm1 µm

Distance

Rou

ghne

ss

Surface Profile measured: 2L0.5 1 1.5 2 2.5

-4

-3

-2

-1

0

1

2

3

Surface Profile: Experiment #60:t1a2r1f4v3 Level #2

Distance mm

Mic

ron

0.5 mm

1 µm

Rou

ghne

ss

Distance


Experimental Setup

Data Collection

Optimum Data Set

Training Validation



F & Ra

Process Model

Systematic Approach




Overview


ANN End Milling ModelBack Propagation Artificial Neural Network: (BP ANN)

BP ANN General Topology

Feed-Forward Phase

Processing Element “PE”Architecture

∑==

n

iiijj IWa

0

)( jl

j aSFY = Yj…Predicted output

SF…Squashing FunctionBack-Propagation Phase

2)(21

jjj Yte −=

IJJJWW T

Told

ijnew

ij ⋅+⋅

−= ⋅

⋅

µδ

E = (e1,…, ej,…ek )

Adaptation: Levenberg-Marquardt

Aj…information

W…Weight

I…Input vector


Experimental Data for Training and Validation

Full Factorial

Experimental Data 384 experiments

75% Training Set (288 exp.)

25% Validation Set (96 exp.)

Data Preprocessing

Cutting Forces: (each component)

1. Amplitude: “Amp”

2. Mean: “Mean”

3. Standard Deviation: “Std”

4. Period (Avg.): “Period”

0 2000 4000 6000 8000 10000 12000 14000-400

-300

-200

-100

0

100

200

300

400

Reading #

Forc

es [N

]

Cutting Forces Fx: Exp#112: t1a3r2f2v1

0 1000 2000 3000 4000 5000 6000-450

-400

-350

-300

-250

-200

-150

-100

-50

0

50

Reading #

Forc

es [N

]

Cutting Forces Fy: Exp.#80: t1a2r3f3v2

Raw DataAdjusted Data

ANN End Milling Model


Experimental Data for Training and Validation (Cont’)

Surface Profiles

1. Surface Roughness: “Ra”

2. Feed Marks: “FeedM”

n

yRa

n

ii∑

= =1

86 86.5 87 87.5 88 88.5 89-5

0

5

10

15

20

25

Position [mm]

Sur

face

Rou

ghne

ss -

Hei

ght [

10-6

m]

Surface Profile: Exp. #80: t1a2r3f3v2

Raw Data2nd order Pol.Adjusted DataFiltered Data



Experimental Data for Training and Validation (Cont’)

Normalization minmin)max(

min)max(*min)( NRR

NNRRN +−

−−=


Topology: End Milling ANN model


Validation Results

0.976035.58Feed Marks

0.4732832.59Ra

0.994846.11Period

0.986969.23Std

0.9848110.43Mean

0.988118.50Amp

Fz

0.995337.38Std

0.991408.72Mean

0.991618.32Amp

Fy

0.992738.53Std

0.9901912.78Mean

0.991538.54AmpFx

R valueAvg. Error ej [%]Output Variable

0 10 20 30 40 50 60 70 80 90 1000

500

1000

1500

2000

2500

3000

Experiment Indices in Testing Set

Forc

e [N

]

Measured vs. Simulated Amplitude Fx in Testing

Error [%] = 8.5422

MeasuredSimulated

Amplitude Fx



Experimental Setup

Data Collection

Optimum Data Set

Training Validation



F & Ra

Process Model

Systematic Approach




Overview


DOE for Optimal Data Sets

Design of Experiments (DOE)

Process of planning the experiments appropriate data

Full Factorial 2 X 3 X 43 = 384 experiments

Screening methodInvestigate effects on the responsesMore efficient High amount of experiments c2

c1

b2

b1a2a1

C

B

A

Full Factorial 2 level DOE: Design Factors: A, B, C

Full Factorial 2k-level DOE


Fractional Factorials

Number of design factors is high

Provides efficient exploration of space – Process behavior

Experimental constraints

Three key ideas:

• Sparsity of effects principle

• Projection property

• Sequential experimentation



Hyper Greco Latin DOE (HGL DOE)

Balanced and orthogonal DOETabular grid “p x p”, p being the # of levelsThree Latin Squares superimposedEach level occurs once and only once in each row/column

Factor: X

CBAD4

BADC3

ADCB2

DCBA1

Factor: Y4321

• Additive model• Effect model

Latin Square Design



Hyper Greco Latin DOE (HGL DOE) (Cont’)

4-level 5 design factor DOE: 16 vs. 45 runs (1024 experiments)

Factor: UA β 3B α 4C δ 1D γ 24B γ 1A δ 2D α 3C β 43C α 2D β 1A γ 4B δ 32D δ 4C γ 3B β 2A α 11

Factor: V4321

What if the design is mixed?

2 X 3 X 43



Hyper Greco Latin DOE (HGL DOE): Layout Rules

Rules:1. Column Axial depth of cut 2. Row Radial depth of cut3. Latin letter Feed per tooth 4. Greek letters Cutting speed5. Numbers Tool Diameter 6. Greek letter equal 0: no fraction7. Number 1-3, 2-4 are same levels 8. Random definition of levels

Radial Depth of Cut

A β 1B α 2C δ 1D γ 24B γ 1A δ 2D α 1C β 23C α 2D β 1A γ 2B δ 12D δ 2C γ 1B β 2A α 11

Axial Depth of Cut4321



Hyper Greco Latin DOE (HGL DOE): Sample Fraction

Cutter diameter: t = 25.4*[0.5 1.0] = [1, 2]Axial depth of cut: a = [0.25 0.5 0.75 1.0] = [1, 2, 3, 4] Radial depth of cut: r = [0.5 2.0 4.0 6.0] = [1, 2, 3, 4]Feed per tooth: f = [0.1 0.15 0.2 0.25] = [A, B, C, D] Cutting speed: v = [0 90 110 150] = [α, β, γ, δ]

1100.20.50.7512.72

900.150.50.525.41

Cutting Speed

Feed per tooth

Radial depth of

cut

Axial depth of cut

Cutter DiameterExp. #

D δ 2C γ 1B β 2A α 11

Axial Depth of Cut4321



Hyper Greco Latin DOE (HGL DOE): Sample Fraction

900.16112.712

1500.260.512.711

1100.2560.2525.410

1100.154112.79

1500.140.7525.48

900.240.2525.47

900.2520.7512.76

1100.120.525.45

1500.1520.2512.74

1500.250.5125.43

1100.20.50.7512.72

900.150.50.525.41

Cutting SpeedFeed per tooth

Radial depth of cut

Axial depth of cut

Cutter DiameterExperiment #



Fractional Factorial Back Propagation ANNIdentify optimal fraction sets to successfully train the modelFull Factorial as a benchmark


Topology: End Milling ANN model


Fractional Factorial Back Propagation ANN

Results: Validation (Overall E)

Fraction Performance Comparison

%100*

)(1

nt

Yt

e

n

iji

jiji

j

∑−

==

%100*12

12

1∑

== jje

E

1510.5522-22-22288 F. F.

1312.1327 - 27252

3612.5426 - 26240

1312.7326 - 26 228

2412.9523 - 23216

1512.9223 - 23204

3113.1922 - 22192

3112.9920 - 20180

2414.1220 - 20168

6213.1218 - 18156

5415.8619 - 19144

2416.3618 - 18132

2117.1218 - 18120

2523.516 - 1696

EpochsE [%]# PE per Hidden Layers# of runs



Validation Results: Fraction of 156 exp.

0.9726.23Feed Marks

0.54244.98Ra

0.99710.95Period

0.99014.95Std

0.98616.21Mean

0.98911.36AmpFz

0.9938.03Std

0.98714.21Mean

0.9909.21Amp

Fy

0.9949.26Std

0.99212.61Mean

0.9939.03Amp

Fx

R valueAvg.Error ej

[%]

Output Variable

0 50 100 150 200 2500

500

1000

1500

2000

2500

3000


Forc

e [N

]

Measured vs. Simulated Amplitude Fx in Testing

Error [%] = 9.031

MeasuredSimulated

Amplitude Fx



How do we know the selected fraction is the optimum set to train and validate the ANN?

Is the fraction set capable to fully represent the end milling process behavior?

Statistical DOE Validation Approach

• Determine best DOE fraction to be statistically comparable to the full factorial fraction

“Process Response Distributions”


Probability Density Function “PDF”: (Fraction of 96 experiments)

0 260.9 575.4 889.8 1204.3 1518.7 1833.2 2147.60

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

Amplitude of Forces in X direction 'Fx'

Freq

uenc

y 'N

(t)'

Frequency distribution of Fx

2625

19

12

6 5

3

Delta(t)=260.9

t1 t2 t3 t4 t5 t6 t7 200 400 600 800 1000 1200 1400 1600 1800 2000 22000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10-3

Force [N]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

Data Distribution "pdf" of Amplitude of Force in X Direction

96 exps

PDFFrequency Distribution at t = 7


tNttCumNtCumNtfpdf

∆∆−−

==*

)()()(


PDF of the End Milling Process

0 500 1000 1500 2000 25000

0.2

0.4

0.6

0.8

1

1.2

1.4x 10-3

Forces [N]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

Data Distribution of Amplitude Force in X direction

12 exps24 exps36 exps48 exps60 exps72 expsFull Factorial

0 500 1000 1500 2000 25000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10-3

Forces [N]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)



0 500 1000 1500 2000 25000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10-3

Forces [N]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)



Amplitude Fx

Experimental fraction size increases



PDF of the End Milling Process

0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

0.5

1

1.5

2

2.5

3

Ra

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

Data Distribution of Surface Rouhgness


0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Ra

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)



0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Ra

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)



Surface Roughness


Experimental fraction size increases


Chi-Square Goodness of Fit Test: Distribution Comparison

∑=

−=

−++

−+

−=

k

j j

jj

k

kk

eeo

eeo

eeo

eeo

1

22

2

222

1

2112 )()(

...)()(χ

Comparison between two distributions:1: Observed (o) 2: Expected (e)

95% confidence level

(χ2) ≤ (χ2)1-α,f1−−= mkf



Distribution Comparison: Fraction vs. Full Factorial Fraction

10.841812.1618

18.861720.7617

21.571626.2116

27.701438.8214

36.131254.2412

57.98983.309

80.207105.257

102.275132.975

126.333159.843

152.941

Ra(χ2)0.95.5=11.1

192.791

Amp Fx(χ2)0.95.6=12.6

χ2Observed Fractionf = 5χ2Observed

Fractionf = 6



0 500 1000 1500 2000 25000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10-3

Force [N]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

Data Distribution of Amplitude of Force in X direction

18th FractionFull Factorial

0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Ra

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

Data Distribution of Surface Roughness

18th FractionFull Factorial

Distribution Comparison: 18th vs. Full Factorial Fractions

Amplitude Fx Surface Roughness



Experimental Setup

Data Collection

Optimum Data Set

Training Validation



F & Ra

Process Model

Systematic Approach




Overview


Basic Idea

Systematic Approach for Optimizing the Modeling

1. Assume the End Milling Process is reliable (based on the definition of Reliability shown below)

2. Determine the Law Probability Distribution of the process (i.e. distribution of the process parameters)

3. Track the distributions of the data set

4. Identify the minimum set as the data set with distribution that fits closely the process distribution as determined in step 2.

Definition of Reliability:

Probability that a system will adequately perform under stated environmental conditions for a specific time.


Law Probability Distributions considered

β

θβ

θθβ ⎟

⎠⎞

⎜⎝⎛−

−

⎟⎠⎞

⎜⎝⎛=

tyt

t ey

ypdf1

)(

⎟⎠⎞

⎜⎝⎛−

= θ

θ

ty

t eypdf 1)(

( ) tyrtt ey

rypdf µµµ −−

Γ= 1

)()(

Weibull

Exponential

Gamma



Fitting Process Parameters to a Law Probability Distribution

600 800 1000 1200 1400 1600 1800 2000 2200 24000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10-3

Force [N]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

Data Distribution Fitting of Amplitude Fx

Response pdfFull FactorialExponential pdfWeibull pdfGamma pdf

200 300 400 500 600 700 8000

0.5

1

1.5

2

2.5

3x 10-3

Force [N]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

Data Distribution Fitting of Std Fx


Amplitude Fx Standard Deviation Fx



400 500 600 700 800 900 1000 1100 12000

0.5

1

1.5x 10-3

Force [N]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

Data Distribution Fitting of Amplitude Fy


80 100 120 140 160 180 200 220 240 260 2800

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10-3

Force [N]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

Data Distribution Fitting of Mean Fy


Amplitude Fy Standard Deviation Fy




200 300 400 500 600 700 8000

0.5

1

1.5

2

2.5x 10-3

Force [N]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

Data Distribution Fitting of Amplitude Fz


50 100 150 200 250 3000

1

2

3

4

5

6

7x 10-3

Force [N]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

Data Distribution Fitting of Std Fz


Amplitude Fz Standard Deviation Fz




36.2647.5010.9314.17Std Fz

43.3055.5013.9514.17Mean Fz

21.8631.787.6514.17Amp. Fz

40.6653.4910.7311.15Std Fy

51.7164.9223.7611.15Mean Fy

37.5649.5812.6711.15Amp. Fy

20.3730.283.9414.17Std Fx

41.0252.6314.0214.17Mean Fx

17.1026.094.8214.17Amp. Fx

GammaWeibullExponential

χ2

χ21-α,f

Degrees of freedom

“f”Response

End Milling Reliability Analysis: Distribution Comparisons

Chi-Square test

95% Confidence Level



Identifying Optimum Fraction

600 800 1000 1200 1400 1600 1800 2000 2200 24000

0.2

0.4

0.6

0.8

1

1.2

1.4x 10-3

Force [N]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

Systematic Approach to find the optimun fraction

Frac #1: ActualFrac #1: ExpFrac #2: ActualFrac #2: ExpFrac #6: ActualFrac #6: ExpFrac #10: ActualFrac #10: Exp



600 800 1000 1200 1400 1600 1800 2000 2200 24000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10-3

Force [N]

Pro

babi

lity

Den

sity

Fun

ctio

n (p

df)

Systematic Approach to find the optimun fraction

Frac #12: ActualFrac #12: ExpFrac #15: ActualFrac #15: ExpFrac #17: ActualFrac #17: ExpFrac #18: ActualFrac #18: Exp

Identifying Optimum Fraction



ResultsFull Factorial ANN:

Extended end milling ANN model (Force + Ra)Training and validation successfully completed. R > 0.9. Improvement with respect to literature. 32% vs. (20% and 53%) (only Ra)

DOE for Optimal Data Sets & Validation

HGL DOE: efficient method of selecting fractions (balanced/orthogonal) Validation 13th fraction: E = 13.12% (Compromise: accuracy, cost and time)End milling behavior captured progressively

Systematic approach for optimizing process modeling

End milling: statistical similarity behavior to exponential distribution (95%)Selection of the optimum fraction can be systematizedSimilar correlation found using AL6061


ConclusionsDevelopment of an efficient and accurate predictive end milling model

• Prediction of cutting force and surface roughness• Reconstruction of force signal components

Implementation of DOE techniques: HGL • Optimization of the data collection process• More design factor levels / orthogonal & balanced experiments

Systematization of the optimum fraction data set selection• Exponential behavior: Chi-Square test + 95% confidence level

Proposed technique is applicable for machining other material types.

Extensive collection of accurate data


Future Work

Extension of the ANN: (Attractive for implementation in industry)• Cutting Parameters: # of cutting flutes, tool geometry• Similar cutting tools: ball end mill, taper end mill

Incorporation of additional process responses (development of self monitoring and control systems)• Flatness, chatter, tool wear

Integration of dynamic effects: • Cutter/workpiece deflection and runout

Extension of the reliability analysis:• Tool/workpiece material and end milling cutter types


AcknowledgementAcknowledgement

Hazim El-Mounayri, Advisor, ME department, IUPUI

Committee Members, ME department, IUPUI

Behnam Imani and Affan Badar

School of Dentistry, Oral Health Research Institute

Colleagues from the AEML, ME department, IUPUI

Family members


ReferencesReferences1. Kline, W. A., DeVor, R. E., and Shareef, I. A., “The prediction of surface accuracy in end milling,”

Journal of Engineering for Industry, Vol. 104, 1982, pp. 272-279.

2. Sutherland, J., and DeVor, R. E., “An improved method for cutting force and surface error prediction in flexible end milling system,” Journal of Engineering for Industry, Vol. 108, 1986, pp. 269-279.

3. Elanayar, S. and Shin, Y. C., “Design and implementation of tool wear monitoring with radial basis function neural networks,” Proceedings of the American Control Conference, Part 3, 1995, pp. 1722 - 1726

4. El-Mounayri, H. and Tandon, V., “An AI-based model for predicting instantaneous cutting force in end milling,” 2002 ASME International Mechanical Engineering Congress & Exposition, 2002

5. Oktem, H., Erzurumlu, T., and Erzincanli, F., “Prediction of minimum surface roughness in end milling mold parts using neural network and genetic algorithm,” Journal of Materials and Design, Vol. 27, 2006, pp. 735-744.

6. Ghani, J.A., Choudhury I.A., and Hassan, H.H., “Application of Taguchi method in the optimization of end milling parameters,” Journal of Materials Processing Technology, 2004, Vol. 145, pp. 84-92.

7. Baris, K., Investigation of the Impact of Cutting Parameters on Surface Finish for a Discontinuous Machining Process, Master’s Thesis, School of Industrial Engineering, University of Tennessee, Knoxville, 2004


Advisor: Dr Hazim ElAdvisor: Dr Hazim El--MounayriMounayri




Question SessionQuestion Session


Advisor: Dr Hazim ElAdvisor: Dr Hazim El--MounayriMounayri




Thanks!!!Thanks!!!


EXTRA!!!!


Training Results

%100*288

)(288

1∑

−

==i

ji

jiji

j

tYt

e

0.987574.21Feed Marks

0.999551.45Ra

0.998931.54Period

0.999963.82Std

0.999076.78Mean

0.998943.78Amp

Fz

0.999222.87Std

0.998375.84Mean

0.998473.29Amp

Fy

0.999443.38Std

0.998966.38Mean

0.999283.18Amp

Fx

R valueAvg. Error ej [%]Output Variable



Training Results (Cont’)

0 50 100 150 200 250 3000

500

1000

1500

2000

2500

Experiment Indices in Training Set

Forc

e [N

]

Measured vs. Simulated Amplitude Fx in Training

Error [%] = 3.1783

MeasuredSimulated

0 50 100 150 200 250

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8


Sur

face

Rou

ghne

ss [1

0- 6 m

]

Measured vs. Simulated Surface Roughness Ra in Training

Error [%] = 1.4486 Measured

Simulated

Amplitude Fx Surface Roughness



Validation Results (Cont’)

0 10 20 30 40 50 60 70 80 90 100-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5


Sur

face

Rou

ghne

ss [1

0- 6 m

]

Measured vs. Simulated Surface Roughness Ra in Testing

Error [%] = 32.5918

MeasuredSimulated

0 10 20 30 40 50 60 70 80 90 100

0.1

0.15

0.2

0.25


Feed

per

toot

h [m

m/to

oth]

Measured vs. Simulated Feed Marks Testing

Error [%] = 5.5818

MeasuredSimulated

Surface Roughness Feed Marks



Training Results: Fraction of 156 exp.

0.9993.99Feed Marks

0.9990.63Ra

0.9991.38Period

0.9993.91Std

0.9996.86Mean

0.9993.87Amp

Fz

0.9992.60Std

0.9987.34Mean

0.9983.30Amp

Fy

0.9993.20Std

0.9996.61Mean

0.9993.43AmpFx

R valueAvg.Error ej [%]

Output Variable

0 20 40 60 80 100 120 140 1600

500

1000

1500

2000

2500


Forc

e [N

]

Measured vs. Simulated Amplitude Fx in Training

Error [%] = 3.4323MeasuredSimulated

Amplitude Fx



Training Results: Fraction of 156 exp. (Cont’)

0 20 40 60 80 100 120 140 1600

0.5

1

1.5


Sur

face

Rou

ghne

ss [1

0- 6 m

]

Measured vs. Simulated Surface Roughness Ra in Training

Error [%] = 0.63207MeasuredSimulated

0 20 40 60 80 100 120 140 1600.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0.28

Experiment Indices in Training SetFe

ed p

er to

oth

[mm

/toot

h]

Measured vs. Simulated Feed Marks in Training

Error [%] = 3.9864Measured

Simulated




Validation Results: Fraction of 156 exp. (Cont’)

0 50 100 150 200 250-0.5

0

0.5

1

1.5

2

2.5

3

3.5


Sur

face

Rou

ghne

ss [1

0- 6 m

]

Measured vs. Simulated Surface Roughness Ra in Testing

Error [%] = 44.9807

MeasuredSimulated

0 50 100 150 200 2500.05

0.1

0.15

0.2

0.25

0.3

Experiment Indices in Testing SetFe

ed p

er to

oth

[mm

/toot

h]

Measured vs. Simulated Feed Marks in Testing

Error [%] = 6.2295

MeasuredSimulated




Reliability:

Probability that a system will adequately perform under stated environmental conditions for a specific time.

Reliability, operational reliability, inherent reliability, probability of survival

Probability of failure

)()( tFtTP =≤ 0≥t

)()(1)( tTPtFtR >=−=



Probability Density Function “PDF”

∫∫∞

=−=−=t

tdfdftFtR ττττ )()(1)(1)(

0

tNttCumNtCumNtfpdf

∆∆−−

==*

)()()(

tNttNtNtfpdf

∆∆+−

==*

)()()(



0.4718170.781817

0.5517160.751716

1.0411101.471110

1.48982.0598

1.73872.6087

13.27761.7276

1.58542.4454

3.354316.1743

2.82324.8932

6.0821

Ra(χ2)0.95.5=11.1

-21

Amp Fx(χ2)0.95,6=12.6

χ2Exp. F.Obs. Ff = 5χ2Exp. F.Obs. Ff = 6

Distribution comparison between consecutive fractions


DEVELOPMENT OF AN INNOVATIVE NEURAL … · 7/10/2007 Gustavo A. Rengifo 22 Outline Problem...

Documents

Transcript of DEVELOPMENT OF AN INNOVATIVE NEURAL … · 7/10/2007 Gustavo A. Rengifo 22 Outline Problem...