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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
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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:
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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.
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Type-2 FLS
13
(Mendel, 2001)
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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
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* 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
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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
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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
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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.)
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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
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Application of type-2 TSK fuzzy logic in mechanical manufacuring
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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.
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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
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Every time when cutting length reached 10 mm, the machine was stopped to manually measure the tool wear parameter (VBB).
Type-1 Parameters
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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
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Type-2 Parameters
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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
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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.
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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
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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.
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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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