??????????????? An improved approach to automatically build fuzzy model rules

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??????????????? An improved approach to
automatically build fuzzy model rules

• ??? (Nai-Jian Wang)
• ?????????
• ????????????
• ???????

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Outline

• Motivations
• The concept of system identification
• The improved algorithm
• Simulations and Discussions
• Conclusions and Future Works

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Motivation

• Only I/O data
• Model construction
• I/O relation
• Modification

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The concept of system identification
Structure Identification I a Input candidates
Structure Identification I b Input variables
Structure Identification II a Number of rules
Structure Identification II b Partition of input space
Parameter Identification Parameter Identification
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Takagi and Sugenos model
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Sugeno and Yasukawas model
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Fuzzy modeling
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To decide the number of rules
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Fuzzy C-means clustering
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To determine the number of rules
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Coarse fuzzy modeling

• Fuzzy C-Regression Model (FCRM)
• Premise parameters generation
• Consequent parameters generation

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Fuzzy C-Regression Model (1)
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Fuzzy C-Regression Model (2)
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Premise parameters generation (1)
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Premise parameters generation (2)
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Premise parameters generation (3)
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Premise parameters generation (4)
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Consequent parameters generation
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Fine tuning
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The steepest decent method
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The gradient of objective function (1)
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The gradient of objective function (2)
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The gradient of objective function (3)
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Stop condition
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Example 1 (1)
Rule
3.095 3.201 3.518 -0.249 -0.265
1.477 1.511 3.518 -0.249 -0.265
2.751 2.406 6.504 -0.672 -0.469
2.072 2.156 6.504 -0.672 -0.469
2.828 2.437 4.842 -0.381 -0.421
1.831 1.839 4.842 -0.381 -0.421
2.667 2.805 4.136 -0.387 -0.357
1.026 1.369 4.136 -0.387 -0.357
2.897 2.544 5.052 -0.559 -0.243
2.005 1.924 5.052 -0.559 -0.243
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Example 1 (2)
The optimal parameters
Rule
3.806 2.842 5.165 -1.094 -0.224
0.957 1.471 5.165 -1.094 -0.224
2.767 1.853 4.741 -1.117 -1.072
1.080 0.657 4.741 -1.117 -1.072
2.023 2.682 3.671 -0.572 -0.884
0.590 1.323 3.671 -0.572 -0.884
2.973 3.221 3.447 -0.317 -0.551
0.951 1.120 3.447 -0.317 -0.551
2.894 2.363 8.415 -0.376 -0.785
1.984 2.230 8.415 -0.376 -0.785
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Example 1 (3)
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Example 2 (1)
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Example 2 (2)
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Example 3 (1)
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Example 3 (2)
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Conclusions and Future Works

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• ??FCM??????
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Least-squares estimator