Type-2 Takagi-Sugeno-Kang Fuzzy Logic System and Uncertainty in Machining

Qun REN

Director - Luc BARON, Ph. D. & Marek BALAZINSKI, Ph. D.

Mechanical engineering department

École Polytechnique de Montréal

13th April, 2012 Ph. D. Defence

Outline

Introduction Literature review High order interval type-2 TSK FLS Application Conclusions & future perspectives

2

Outline

Introduction Uncertainty in machining Objectives

Literature review High order interval type-2 TSK FLS Application Conclusions & future perspectives

3

Uncertainty in machining

4

Metal machining has been requested to be more productive, more versatile and ever higher precision.

Uncertainties in machining become a focus point Conventional methods need a large number of cutting experiments and additional

assumptions in many circumstances for effective uncertainty handling. Artificial intelligence methods have played an important role in modern modeling

and monitoring systems. Nowadays, type-2 fuzzy logic is the only artificial intelligent which can handle

uncertainties associated with the system.

Objectives

Distinguishing the differences between type-2 TSK system and its type-1 counterpart.

Developing a generalized type-2 TSK FLS and high order

TSK FLS - architecture, inference engine and design method.

Proposing a reliable type-2 fuzzy tool condition estimation method based on information of uncertainty in AE signal.

5

Outline

Introduction Literature review

Fuzzy logic Type-1 TSK FLS Type-2 TSK FLS

High order interval type-2 TSK FLS Application Conclusions & future perspectives

6

Fuzzy logic

7

TSK FLS (1988)

Fuzzy logic (cont.)

8

Fuzzy Sets (1965)

Linguistic approach (1968 & 1973)

Qualitative modeling (1979-1993)

Linguistic control (1974)

Mamdani FLS (1974)

TSK FLS (1988)

TSK FLS

9

A systematic approach to generating fuzzy rules from a given input-output data set.

(Takagi & Sugeno 1985; Sugeno & Kang, 1988)

Fuzzy set

Mathematic function

TSK FLS (cont.)

10

TSK FLS

Structure identification

Parameter identification

• Number of rules • Variables involved in the rule premises as

cluster centers and deviation of Gaussian membership functions

• Membership function parameters • Consequent regression coefficients

Zero order: First order: The curse of dimensionality:

11

TSK FLS (cont.)

m MFs

n variables

The number of rules increases exponentially with the number of input variables and the number of membership functions (MFs) per variable .

TSK FLS (cont.)

High order:

Reduce drastically the number of rules needed to

perform the approximation;

Improve transparency and interpretation in many high dimensional situations.

12

Type-2 FLS

13

(Mendel, 2001)

13

Type-2 FLS

14 14

BOOK

JOURNAL CONFERENCE

Type-2 TSK FLS

First-order type-2 TSK FLSs (Liang and Mendel 1999)

15

Type-2 Fuzzy set

Mathematic function

Fuzzy number Fuzzy

number

first order polynomial

function

Differences between Type-1 and Type-2 TSK FLS

16

* there are M rules and each rule has p antecedents

Outline

Introduction Literature review High order interval type-2 TSK FLS Application Conclusions & future perspectives

17

High Order Type-2 TSK FLS

18

BEST STUDENT PAPER

High order type-2 TSK FLS (cont.)

Aim : To handle uncertainties within FLS. To overcome the problem of dimensionality;

High order type-2 TSK FLS

== High order type-1 TSK FLS

+ First order type-2 TSK FLS 19

High order type-2 TSK FLS (cont.)

Generalized IT2 TSK fuzzy system

20

Zero order type-2 TSK FLS m=0 constant

First order type-2 TSK FLS

first order polynomial function m=1

Higher order type-2 TSK FLS

more than second order polynomial function m≥2

High order type-2 TSK FLS (cont.)

Second-order type-2 TSK FLS

21

Type-2 Fuzzy set

Mathematic function

Fuzzy number Fuzzy

number Fuzzy

number Fuzzy

number Fuzzy

number

Second order polynomial

function

High order type-2 TSK FLS (cont.)

22

Original system Type-1 TSK model

Uncertainty?

Subtractive clustering

Type-2 TSK model End

EXPANDING Cluster center

Consequent parameters

Yes

No

Is this the best model?

Yes

No

Type-1 fuzzy approach

Type-2 fuzzy approach

Type-2 TSK Fuzzy System

23

Outline

Introduction Literature review High order interval type-2 TSK FLS Application

Conclusions & future perspectives

24

Application of type-2 TSK fuzzy logic in mechanical manufacuring

25

Application of type-2 TSK fuzzy logic in mechanical manufacuring

26

Type-1

First order type-2

High order type-2

• To propose a reliable type-2 fuzzy tool condition estimation method based on information of uncertainty in AE signal.

• To prove that high order IT2 TSK FLS has the capability to reduce the number of rules to identify the same system as that of a first order.

Uncertainty estimation for cutting acoustic emission

• To distinguish the difference between type-2 TSK system and its type-1 counterpart

Sources of Acoustic Emission (AE)

Since 1977 Frequency range of AE

is much higher than that of machine vibrations and environmental noises

AE from process changes like tool wear, chip formation can be directly related to the mechanics of the process.

Along with the scale of precision machining becomes finer and closer to the dimensional scale of material properties, microscopic sources become very significant.

27

Experimental setup Cutting Tools:

KY Diamond : RNMN Diamond PCD.

Diameter: 0.5” New Kind of Poly Crystalline Diamond

SECO CNMG. Carbide.

New type of coating ( confidential)

BOEHRINGER CNC Lathe.

The TiMMC material: 10-12% TiC particles in matrix of Ti-6Al-4V2.5” diameter in dry machining conditions

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Tool cutting speed: 80 m/min Cutting depth: 0.15mm Cutting feed: 0.1mm.

• 5~8s : tool is approaching the workpiece and gradually reaching the cutting depth.

• 8~30s is the continuous cutting period, containing the main information.

• After 30s, the cutting tool leaves the surface of workpiece.

AE Signal

29

Every time when cutting length reached 10 mm, the machine was stopped to manually measure the tool wear parameter (VBB).

Type-1 Parameters

30

Cutting section

(mm) 0 ~ 10 10 ~ 20 20 ~ 30 30 ~ 40 40 ~ 50

Number of data

sets 5500 8200 5700 4500 4000

Number of rules 24 23 29 24 22

standard deviation 1.1209 0.9016 1.034 1.1932 1.0606

cluster radius 0.22 0.15 0.15 0.2 0.15

accept ratio 0.5 0.3 0.5 0.4 0.5

reject ratio 0.15 0.1 0.1 0.15 0.15

squash factor 0.15 0.15 0.1 .05 0.1

Type-1 Model output

31

Type-2 Parameters

32

Cutting section (mm) 0 ~ 10 10 ~ 20 20 ~ 30 30 ~ 40 40 ~ 50

Spread percentage of cluster centers

(1.0e-004 *)

0.3330

0.9217

0.6325

0.9322

0.4259

0.3005

0.8890

0.0174

0.1481

0.9592

0.7145

0.3065

0.8281

0.8079

0.9093

0.6428

0.6287

0.1185

0.9190

0.6240

0.2576

0.9513

0.0462

0.0209

0.5078

0.7136

0.6977

0.8935

0.7012

0.9373

0.0109

0.8197

0.0343

0.5162

0.6533

0.7541

0.2800

0.6031

0.8888

0.6432

0.7861

0.4911

0.4035

0.8774

0.7082

0.8265

0.0107

0.3465

0.5575

0.2998

0.1591

0.6653

0.6842

0.7924

0.3486

0.2501

0.3450

0.3286

0.9275

0.7561

0.2882

0.6062

0.7661

0.8462

0.9020

0.5957

0.0685

0.2180

0.8694

0.4142

0.6612

0.7832

0.2479

0.5544

0.2296

0.0069

0.7841

0.4867

0.4648

0.1313

0.8864

0.6746

0.8352

0.6565

0.9839

0.9798

0.2502

0.6246

0.7282

0.4982

0.8498

0.1909

0.1241

0.0028

0.1530

0.5342

0.5106

0.3852

0.3106

0.0036

0.4820

0.1206

0.5895

0.2262

0.3846

0.5830

0.2518

0.2904

0.6171

0.2653

0.8244

0.9827

0.7302

0.3439

0.5841

0.1078

0.9063

0.8797

0.8178

0.2607

0.5944

0.0225

Spread percentage of consequent parameters 0.02 0.02 0.02 0.02 0.02

Type-2 output

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(a) From 0mm to 10 mm (b) From 10mm to 20 mm

(c) From 20mm to 30 mm

(e) From 40mm to 50 mm

5 10 15 20 25 30370

380

390

400

410

420

430

440

outp

ut(v

)

time (s)

AverageUpperLower

10 12 14 16 18 20 22 24 26 28360

380

400

420

440

460

480

500

520

outp

ut(v

)

time (s)

AverageUpperLower

(d) From 30mm to 40 mm

5 10 15 20 25 30380

390

400

410

420

430

440

450

460

470

outp

ut(m

v)

time (s)

AverageUpperLower

5 10 15 20 25 30380

390

400

410

420

430

440

450

460

470

outp

ut(m

v)

time (s)

AverageUpperLower

10 15 20 25 30 35320

330

340

350

360

370

380

390

400

410

outp

ut(m

v)

time (s)

AverageUpperLower

Variations in Modeling Results

34

Cutting Length (mm)

Variations (mv)

VB

(mm)

Upper boundary and identified AE

(V1)

identified AE and lower boundary

(V2)

Upper boundary and lower boundary

(V3)

identified AE and raw AE

(V4)

MAX MIN MAX MIN MAX MIN MAX MIN

0 ~10 1.1092 0.0262 1.0257 0.0003 2.1350 0.0108 136,8040 0.0670 0.050

10 ~20 4.7649 0.0214 4.5361 0.0006 9.3011 0.0018 287.8089 0.1597 0.100

20 ~ 30 5.9340 0.0604 5.660 0.0155 11.5940 0.0759 92.8960 0.1784 0.146

30 ~ 40 4.2204 0.0270 3.9954 0.0007 19.3474 0.0296 117.3628 0.1980 0.196

40 ~ 50 12.6305 0.0210 12.0973 0.0001 24.7279 0.0040 128.2942 0.0464 0.373

Tool Wear Assessment

Along with the increasing of uncertainty in AE signal, the development of wear is continuous and monotonically increasing.

During initial cutting period (0~40 mm), AE signal varies in accordance with the initial stages of wear occurring.

The period with significant variations (40~50 mm) corresponds to the period of relatively rapid wear or failure of cutting tool.

AE signal is associated with cutting tool wear, even catastrophic tool failure.

35

Maximum and minimum variations Tool wears

Raw AE Signals

36 Fig. 3 Raw AE signal from cutting process

5 10 15 20 25 30250

300

350

400

450

500

550

600

Time (s)

Ram

AE

(mv)

First Order Type-2 Fuzzy Modeling

37

Rule Number

Spreading Percentage of Cluster Center

1 0,00458% 2 0,00722% 3 0,00339% 4 0,00401% 5 0,00527% 6 0,00894% 7 0,00778% 8 0,00069% 9 0,00279% 10 0,00379% 11 0,00865% 12 0,00420% 13 0,00240% 14 0,00598% 15 0,00479% 16 0,00899% 17 0,00935% 18 0,00818% 19 0,00709% 20 0,00743% 21 0,00900% 22 0,00065% 23 0,00336% 24 0,00004%

5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

mem

bers

hip

func

tion

degr

ee

upperlowerprinciple (type-1)

5 10 15 20 25 30370

380

390

400

410

420

430

440

outpu

t(v)

time (s)

AverageUpperLower

Second Order Type-2 Fuzzy modeling

38

5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

Input

mem

bers

hip

func

tion

degr

ee

upperlowerprincipal (type-1)

Rule

Number

Spreading Percentage of

Cluster Center

1 0,00141%

2 0,00951%

3 0,00883%

4 0,00437%

5 0,00835%

6 0,00325%

7 0,00368%

8 0,00795%

9 0,00099%

10 0,00952%

11 0,00001%

5 10 15 20 25 30360

370

380

390

400

410

420

430

440

outp

ut(v

)

time (s)

AverageUpperLower

Comparison

39

• Second order IT2 TSK FLS has less rules than that of first order FLS to obtain the similar performance,.

• Higher order IT2 TSK FLS has the capability to reduce the number of rules needed to perform the approximation,

Outline

Introduction Literature review High order interval type-2 TSK FLS Application Conclusions & future perspectives

40

Conclusions Type-2 fuzzy modeling has better performance than that of its type-1

counterpart.

The interval output of type-2 approach provides the information of uncertainty in machining, which could be of great value to decision maker to investigate tool wear condition.

High order type-2 TSK FLS is able to reduce the number of rules needed to perform the approximation, and improve transparency and interpretation in many high dimensional situations.

The estimation of uncertainties can be used for proving the conformance with specifications for products or auto-controlling of machine system.

41

Triangle Quasi Type-2 Gaussian MF

Future Perspective A reliable on-line type-2 fuzzy TCM base on AE can be developed for high

precision machining. Type-2 FLSs is widely used for different aspects of mechanical engineering. Type-2 FLS, which is more robust to uncertainty, will be gradually

developed.

Comparative analysis can be done with the FLSs from other structure identification approach and parameter learning algorithm.

More examples are in need to verify the performance of the high order type-2 FLS to draw a convincing conclusion.

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Thank You!

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