Model identification for machine system design, design optimization, and manufacturing planning is an important method that has high prediction accuracy and could become an essential stage in practical applications. In this paper, an effective fuzzy model identification algorithm for mechanical system design is developed. First, a fuzzy c-regression model clustering algorithm, in which hyperplane-shaped cluster representatives are utilized to provide a mathematical tool to partition the input–output space reasonably, is introduced. Then, an enhanced cluster validity criterion, in which the structural information hidden in the clusters can be reflected in the index, is proposed to choose the optimal number of clusters. In the proposed architecture, an improved Takagi–Sugeno fuzzy model is proposed to describe the system. Two illustrative examples under various conditions are provided, and their performances are indicated in comparison with other published works. In comparison to these fuzzy works, the proposed fuzzy model identification requires fewer fuzzy rules and a shorter tuning time.

References

1.
Baruch
,
I.
,
Flores
,
J. M.
,
Martinez
,
J. C.
, and
Garrido
,
R.
, 2000, “
A Multi-Model Parameter and State Estimation of Mechanical Systems
,”
Proceedings of the 2000 IEEE International Symposium on Industrial Electronic
,
Cholula, Puebla
(Dec. 2000), pp.
700
705
.
2.
Yang
,
J.
,
Zhang
,
D.
, and
Li
,
Z.
, 2007, “
Modeling and Identification for High-Speed Milling Machines
,”
IEEE International Conference on Automation Science and Engineering 2007
,
Scottsdale, AZ
(Sept. 2007), pp.
346
351
.
3.
Lloyd
,
B. A.
,
Szekely
,
G.
, and
Harders
,
M.
, 2007, “
Identification of Spring Parameters for Deformable Object Simulation
,”
IEEE Trans. Vis. Comput. Graph.
,
13
(
5
), pp.
1081
1094
.
4.
Yao
,
L.
,
Gu
,
B.
,
Haung
,
S.
,
Wei
,
G.
, and
Dai
,
J. S.
, 2010, “
Mathematical Modeling and Simulation of the External and Internal Double Circular-Arc Spiral Bevel Gears for the Nutation Drive
,”
ASME J. Mech. Des.
,
132
(
2
),
p.
021008
.
5.
Chow
,
T. W. S.
, and
Tan
,
H. -Z.
, 2000, “
HOS-Based Nonparametric and Parametric Methodologies for Machine Fault Detection
,”
IEEE Trans. Ind. Electron.
,
47
(
5
), pp.
1051
1059
.
6.
Garbone
,
G.
,
de Novellis
,
L.
,
Commissaris
,
G.
, and
Steinbuch
,
M.
, 2010, “
An Enhanced CMM Model for the Accurate Prediction of Steady-State Performance of CVT Chain Drives
,”
ASME J. Mech. Des.
,
132
(
2
),
p.
021005
.
7.
Zhou
,
H.
, 2010, “
Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model
,”
ASME J. Mech. Des.
,
132
(
11
),
p.
111003
.
8.
Iwasaki
,
M.
,
Miwa
,
M.
, and
Matsui
,
N.
, 2005, “
GA-Based Evolutionary Identification Algorithm for Unknown Structured Mechatronic Systems
,”
IEEE Trans. Ind. Electron.
,
52
(
1
), pp.
300
305
.
9.
Liu
,
D.-P.
, 2006, “
Parameter Identification for Lugre Friction Model Using Genetic Algorithms
,”
International Conference on Machine Learning and Cybernetics 2006
,
Dalian, China
(Aug. 2006), pp.
3419
3422
.
10.
Van
,
H. I.
,
Rovid
,
A.
,
Szeidl
,
L.
, and
Varlaki
,
P.
, 2006, “
Identification and Reconstruction of Car Body Deformation Applying Tensor Product Models
,”
Intenational Conference on Intelligent Engineering Systems 2006
,
London
(Sept. 2006), pp.
98
101
.
11.
Zhang
,
S.
,
Chen
,
T.
, and
Yang
,
H.
, 2007, “
Reconstruction of Natural Crack Shapes From the ECT Signals by Using an Artificial Neural Networks Forward Model and an Optimization Approach
,”
International Conference on Mechatronics and Automation 2007
,
Harbin
(Aug. 2007), pp.
276
281
.
12.
Gaspar
,
P.
, and
Nadai
,
L.
, 2007, “
Parameter Estimation of Coupled Road-Vehicle
,”
International Workshop on Soft Computing Applications 2007
,
Oradea, Romania
(Aug. 2007), pp.
199
204
.
13.
Messer
,
M.
,
Panchal
,
J. H.
,
Krishnamurthy
,
V.
,
Klein
,
B.
,
Yoder
,
P. D.
,
Allen
,
J. K.
, and
Mistree
,
F.
, 2010, “
Model Selection Under Limited Information Using a Value-of-Information-Based Indicator
,”
ASME J. Mech. Des.
,
132
(
12
),
p.
121008
.
14.
Sendrescu
,
D.
,
Marin
,
C.
,
Petre
,
E.
,
Popescu
,
D.
, and
Roman
,
M.
, 2010, “
Nonlinear Identification of a Rotating Flexible Beam
,”
IEEE International Conference on Automation Quality and Testing Robotics 2010
,
Cluj-Napoca
(May 2010), Vol.
1
, pp.
1
5
.
15.
Yamei
,
W.
,
Hui
,
Z.
,
Zhongmian
,
Y.
,
Jiaguang
,
S.
, and
Paul
,
J.-C.
, 2010, “
Reconstructing 3D Objects From 2D Sectional Views of Engineering Drawings Using Volume-Based Method
,”
International Conference on Shape Modeling International 2010
,
Aix-en-Provence
,
France
(June 2010), pp.
13
24
.
16.
Jiang
,
S.
, and
Zheng
,
S.
, 2010, “
Dynamic Design of a High-Speed Motorized Spindle-Bearing System
,”
ASME J. Mech. Des.
,
132
(
3
),
p.
034501
.
17.
Takagi
,
T.
, and
Sugeno
,
M.
, 1985, “
Fuzzy Identification of Systems and Its Applications to Modeling and Control
,”
IEEE Trans. Syst. Man Cybern.
,
15
, pp.
116
132
.
18.
Hathaway
,
R. J.
, and
Bezdek
,
J. C.
, 1993, “
Switching Regression Models and Fuzzy Clustering
,”
IEEE Trans. Fuzzy Syst.
,
1
, pp.
195
204
.
19.
Wang
,
L.
, and
Yen
,
J.
, 1999, “
Extracting Fuzzy Rules for System Modeling Using a Hybrid of Genetic Algorithms and Kalman Filter
,”
Fuzzy Sets Syst.
,
101
, pp.
353
362
.
20.
Yen
,
J.
, and
Wang
,
L.
, 1998, “
Application of Statistical Information Criteria for Optimal Fuzzy Model Construction
,”
IEEE Trans. Fuzzy Syst.
,
6
, pp.
362
371
.
21.
Yen
,
J.
, and
Wang
,
L.
, 1999, “
Simplifying Fuzzy Rule-Based Models Using Orthogonal Transformation Methods
,”
IEEE Trans. Syst. Man Cybern.
,
29
, pp.
13
24
.
22.
Setnes
,
M.
, and
Roubos
,
H.
, 2000, “
GA-Fuzzy Modeling and Classification: Complexity and Performance
,”
IEEE Trans. Fuzzy Syst.
,
8
, pp.
509
522
.
23.
Yangmin
,
L.
,
Yugang
,
L.
,
Xiaoping.
L.
, and
Zhaoyang
,
P.
, 2004, “
Parameter Identification and Vibration Control in Modular Manipulators
,”
IEEE/ASME Trans. Mech
,
9
(
4
), pp.
700
705
.
24.
Kumar
,
M.
,
Arndt
,
D.
,
Kreuzfeld
,
S.
,
Thurow
,
K.
,
Stoll
,
N.
, and
Stoll
,
R.
, 2008, “
Fuzzy Techniques for Subjective Workload-Score Modeling Under Uncertainties
,”
IEEE Trans. Syst., Man, Cybern., Part B: Cybern.
,
38
(
6
), pp.
1449
1464
.
25.
Bonjour
,
E.
,
Dulmet
,
M.
,
Deniaud
,
S.
, and
Harmel
,
G.
, 2009, “
A Fuzzy Method for Propagating Functional Architecture Constraints to Physical Architecture
,”
ASME J. Mech. Des.
,
131
(
6
),
p.
061002
.
26.
Kyoung
,
K. A.
, and
Ho
,
P. H. A.
, 2010, “
Inverse Double NARX Fuzzy Modeling for System Identification
,”
IEEE/ASME Trans. Mech.
,
15
(
1
), pp.
136
148
.
27.
Aboukheir
,
H.
, 2010, “
Closed Loop Identification Using Takagi Sugeno Models
,”
IEEE Lat. Am. Trans.
,
8
(
3
), pp.
199
204
.
28.
Xie
,
X. L.
, and
Beni
,
G. A.
, 1991, “
Validity Measure for Fuzzy Clustering
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
13
, pp.
841
846
.
29.
Kung
,
C. C.
, and
Su
,
J. Y.
, 2007, “
Affine Takagi-Sugeno Fuzzy Modelling Algorithm by Fuzzy C-Regression Models Clustering With a Novel Cluster Validity Criterion
,”
IEE Proc.-D: Control Theory Appl.
,
1
(
5
), pp.
1255
1265
.
30.
Anderson
,
D. T.
,
Bezdek
,
J. C.
,
Popescu
,
M.
, and
Keller
,
J. M.
, 2010, “
Comparing Fuzzy, Probabilistic, and Possibilistic Partitions
,”
IEEE Trans. Fuzzy Syst.
,
18
(
5
), pp.
906
918
.
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