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研究生:胡厚楨
研究生(外文):Hou-Jen Hwu
論文名稱:小腦模型類神經網路在函數逼近上之應用
論文名稱(外文):Application of Function Approximation Based on CMAC Neural Network
指導教授:蔡樸生
指導教授(外文):Pu-Sheng Tsai
學位類別:碩士
校院名稱:中華技術學院
系所名稱:電子工程研究所碩士班
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:120
中文關鍵詞:類神經網路函數逼近器小腦模型可微分小腦模型模糊小腦模型學習機制模糊可變學習率。微分型逼近器類神經模型類非線性
外文關鍵詞:Keywords: Neural Network、Function Approximation、Cerebellar Model Articulation Controller(CMAC)、Differentiable CMAC(DCMAC)
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近年來,類神經網路的架構在非線性函數的學習與逼近上,有許多重要的應用,並且獲得良好的效果。本文嘗試以類神經網路的小腦模型為主軸,探討與小腦模型理念相關的可微分型小腦模型類神經網路及模糊小腦模型類神經網路,並且比較對非線性函數逼近的效果。小腦模型類神經網路,它是屬於一系列對映查表法結構,基於快速的學習收斂、完美的逼近效果、極佳的類化特性,加上結構簡單容易以硬體或FPGA加以實現等特性,使得小腦模型成為類神經網路的研究焦點。傳統的小腦模型藉由輸入量化空間、感受場空間、聯想記憶體空間以及權重記憶體的分配,以來平均分配誤差的權重均分法作為遞迴學習方式,來逼近一個非線性的函數。傳統CMAC的超立方塊嵌入均勻分佈函數,導至類神經網路的輸出在每一個量化區間均為等值,造成不可微分的特性。可微小腦模型類神經網路是將可微函數(如高斯函數)嵌入聯想記憶體空間的超立方塊中,形成非定值且可微分的區塊。藉由可微分的特性,權重均分法已經不是學習過程中的唯一方法,取而代之是以最陡坡降法推導網路參數或權重記憶體的內容。至於模糊小腦模型類神經網路的架構與基本的小腦模型類神經網路類似,所不同的是模糊小腦模型針對輸入變數的訓練樣本進行模糊化,引入歸屬函數來實現所謂的口語化規則,並且加入了模糊推論引擎,可大幅減少索引向量的維度,降低計算的負荷。最後,本文提出模糊可變學習率的方法來改善CMAC的學習效能,以小腦模型類神經網路的學習誤差和誤差變化量作為模糊推論引擎的輸入,經由模糊化的過程產生模糊系統的輸出,動態地調整CMAC的學習率。很明顯地,這個方法將大幅提昇函數逼近器的收斂速度。由模擬結果顯示,DCMAC無論在學習精度與速度上呈現最佳的表現,FCMAC雖然在性能上沒有凸出的表現,但是它具有模糊化的強健特性,最適合用在實際控制系統的實現。
Recently, the structures of artificial neural networks (ANNs) have been widely applied to the implementation of function approximators and have been given good results. Based on the learning mechanism of the human cerebellum, Cereberllar Model Articulation Controller (CMAC) is one subclass of the neural networks. Three types of the CMAC architecture, traditional CMAC, differentiable CMAC (DCMAC), and fuzzy CMAC (FCMAC) are investigated for dealing with the function approximation problems in this thesis. In particular, a trained CMAC can approximate nonlinear function in a generalized lookup table style over a domain to any desired accuracy such that the satisfactory performance can be obtained. A complete framework of basic CMAC including input space, receptive-field space, associated memory space, weight memory space, and output space is designed practically. CMAC is an attractive architecture because of its fast learning characteristic, good generalization capabilities, and convergence properties. Its simple structure also enables the CMAC to be easily realized by hardware or FPGA. However, the traditional CMAC uses rectangular basis function in the receptive field, its output is always constant within each quantized state and not differentiable. To overcome this problem, the Differentiable Cerebellar Model Articulation Controller (DCMAC) adopts a differentiable Gaussian basis function embedded in each hypercube structure such that the derivative information of input and output variables can be obtained. The differentiable property has some advantages such as steepest descent method,which can be applied to derive the learning algorithm. By such a new learning algorithm, the learning speed and converge rate is promoted apparently. The merging of CMAC and fuzzy reasoning mechanism, called Fuzzy CMAC (FCMAC), is developed. Intrinsically, the proposed fuzzy CMAC is analogous to the conventional CMAC. Due to possible disturbances on the sensors, the input data may not be exact. To accommodate this fuzziness and simplify the input partition, the structure of FCMAC is designed to reduce the dimension of address index matrix shown in the associated memory and to decrease the computational load in the learning process. To improve the convergence speed of CMAC learning mechanism, an adjustable learning rate, called Fuzzy adaptive learning rate, is then proposed to regulate the scaling factor of weight memory space by the fuzzy inference system, which rapidly drives all initial weight values to the desired ones in each learning process. To demonstrate and compare the performance of the proposed CMAC, DCMAC and FCMAC by simulation results, it is shown that the performance of DCMAC is better than CMAC and FCMAC, but FCMAC with robust feature and simple structure is more suitable in practical implementation.
中文摘要………………………………………………………………………………i
英文摘要………………………………………………………………………………iii
目次……………………………………………………………………………………iv
表目錄 ………………………………………………………………………………vii
圖目錄 ……………………………………………………………………………… ix
符號目錄…………………………………………………………………………… xiv
第一章 緒論…………………………………………………………………………1
第一節 研究動機…………………………………………………………………1
第二節 研究背景…………………………………………………………………2
第三節 本文貢獻…………………………………………………………………8
第四節 論文大綱…………………………………………………………………8
第二章 小腦模型類神經網路 ……………………………………………………11
第一節 CMAC理論基礎 ………………………………………………………11
第二節 一維小腦模型記憶單元之分割……………………………………… 17
第三節 二維小腦模型記憶單元之分割 ………………………………………19
第四節 小腦模型數學表示法 …………………………………………………23
壹 小腦模型類神經網路數學表示法 ………………………………………23
貳 二維小腦模型聯想記憶體的產生 ………………………………………24
参 學習演算法 ………………………………………………………………26
肆 效能評估 …………………………………………………………………26
第五節 模擬結果…………………………………………………………………26
壹 學習流程 …………………………………………………………………26
貳 一維小腦模型類神經網路之筆算學習法 ………………………………29
參 一維CMAC模擬…………………………………………………………39
肆 二維CMAC模擬…………………………………………………………41
第六節 CMAC參數功能說明……………………………………………………59
第七節 CMAC結語………………………………………………………………60
第三章 可微小腦模型類神經網路 ………………………………………………61
第一節 可微分小腦模型類神經網路之原理 …………………………………62
第二節 可微分小腦模型類神經網路之網路結構 ……………………………64
第三節 可微小腦模型類神經網路數學推論 …………………………………66
第四節 可微小腦模型類神經網路學習演算法 ………………………………68
第五節 DCMAC學習流程圖 …………………………………………………71
第六節 模擬結果 ………………………………………………………………73
壹 模擬 III-1…………………………………………………………………73
貳 模擬 III-2 …………………………………………………………………77
第七節 DCMAC結論 ………………………………………………………… 80
第四章 模糊小腦模型類神經網路 ………………………………………………81
第一節 模糊小腦模型類神經網路架構 ………………………………………81
第二節 模糊小腦類神經網路操作方式 ………………………………………83
第三節 模擬結果 ………………………………………………………………87
壹 模擬 IV-1…………………………………………………………………87
貳 模擬 IV-2…………………………………………………………………90
參 模擬 IV-3…………………………………………………………………98
第四節 模糊小腦模型類神經網路總結………………………………………102
第五章 增進小腦模型類神經網路之效能………………………………………103
第一節 可變學習率之網路架構………………………………………………103
第二節 模糊可變學習率之設計………………………………………………105
第三節 模擬結果………………………………………………………………107
第四節 結論……………………………………………………………………118
第六章 結論與未來研究方向……………………………………………………119
第一節 研究結論………………………………………………………………119
第二節 未來研究方向…………………………………………………………120
參考文獻……………………………………………………………………………121
附錄 作者簡介……………………………………………………………………125
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