模糊 c-回歸模型分類之新穎群集驗證準則及其應用

A Novel Validity Criterion for Fuzzy c-regression Model Clustering and its Applications

聶怡芬(Yi-Fen Nieh)

指導教授 ： 龔宗鈞

大同大學/電機資訊學院/電機工程學系所/碩士(2009年)

摘要

模糊c-回歸模型分類演算法(fuzzy c-regression model clustering algorithm)可將資料以線性回歸模型分類且常被使用為辨證複雜非線性系統之工具。直至今日，只有少數針對模糊c-回歸模型分類演算法的群集驗證準則被提出。當各群集資料數不同且群集十分相近時，該群集驗證準則判斷常過於敏銳。因此，我們針對群集具有仿射線性函數型式之模糊c-回歸模型分類演算法提出一新穎群集驗證準則。所提出之群集驗證準則藉由模糊超體積計算模糊c-回歸模型分類之緊緻度(compactness)及獨立度(separateness)以得到最適合之群集數目。
再者，研究一微小但重要之參數－權重指數m (weighting exponent)。當 及 時，應用極限分析探討Bezdek’s partition coefficient與提出之群集驗證準則之特性。數個例子證明此新穎群集驗證準則之效能。
一旦群集數目決定，對於離散非線性系統可藉由模糊辨證方法建立模糊模型。再由梯度陡降法(gradient descent algorithm)為所獲得的模糊模型進行細部調整。以系統化的步驟，用最精簡的模糊規則數目建構出模糊模型。
最後我們採用模糊模型控制器(FMBC)，藉由解線性矩陣不等式(linear matrix inequalities :LMIs)的方法，令受控系統達成 追蹤之控制目標。

關鍵字

模糊 c-回歸模型分類定理 ； 群集驗證準則 ； 模糊超體積

並列摘要

The fuzzy c-regression models (FCRM) clustering algorithm can fit data to locally regression models which are linear in their parameters and be used as a tool to the identification of complex nonlinear systems. To date, only a few cluster validity criteria have been proposed for FCRM clustering algorithm to validate the partitions. They are too sensitive for close clusters with varying data number. Therefore, a new cluster validity criterion for FCRM algorithm with affine linear functional cluster representatives is proposed. The proposed cluster validity criterion calculated the overall compactness with fuzzy hypervolume and separateness of the FCRM partition to determine the appropriate number of clusters.
Furthermore, we examine the role of a subtle but important parameter－the weighting exponent m. The limit analysis is applied to study the behavior of cluster validity criteria for Bezdek’s partition coefficient and the proposed validity criterion. Several simulation examples illustrate the effectiveness and the performance of the novel validity criterion.
Once the number of clusters is determined, we can construct the fuzzy model by fuzzy identification method for discrete-time nonlinear plants. The gradient descent algorithm is then included to adjust the fuzzy model precisely. A fuzzy model with compact IF-THEN rules could thus be generated systematically.
Finally, the fuzzy model based control (FMBC) is adopted to make a class of nonlinear plant with H∞ tracking performance by solving the linear matrix inequalities(LMIs).

並列關鍵字

fuzzy c-regression models clustering algorithm ； cluster validity criterion ； fuzzy hypervolume

參考文獻

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