📄 3．3．3 模糊神经网络的遗传学习算法.htm
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<P>3．3．3 模糊神经网络的遗传学习算法</P></TD></TR>
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<P>在模糊神经网络中，也可以采用遗传学习算法对参数进行学习。在这一节中，用一个具体的例子说明遗传学习算法在模糊神经网络参数学习中的情况及其结果。
</P>
<P>一、一些基本概念</P>
<P>在这一节中，假设所考虑的模糊量是实数模糊集。为了简单起见，这些实数模糊集表示为：A、B、……、W、V。模糊量A在x处的隶属度表示为A(x)。</P>
<P>模糊量A的<SPAN
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<P>A[α]={x|A(x)<SPAN
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<P>下面给出三角模糊数的定义：</P>
<P>由3个数字a<b<c所定义的N称为三角模糊数，并且有如下性质：</P>
<P>1．当x<SPAN
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<P>当x＝b时，N(x)=1。</P>
<P>2．在[a，b]区间，从(a，0)到(b，1)，y＝N(x)是一条直线段；</P>
<P>在[b，c]区间，从(b，1)到(c，0)，y＝N(x)是一条直线段。</P>
<P>同理，可以给出三角形模糊数定义：</P>
<P>由3个数字a<b<c所定义的N称为三角形模糊数，并且有如下性质：</P>
<P>1．当x<SPAN
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<P>当x＝b时，N(x)=1。</P>
<P>2．在[a，b]区间，y＝N(x)是一条单调增曲线；</P>
<P>在[b，c]区间，y＝N(x)是一条单调减曲线。</P>
<P>无论是三角模糊数或三角形模糊数，都表示为：N＝(a/b/c)。</P>
<P>如果a<SPAN
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<P>模糊数N的模糊测度表示为f<SUB>uzz</SUB>(N)，并且有：</P>
<P>f<SUB>uzz</SUB>(N)＝b—a</P>
<P>如果有f<SUB>uzz</SUB>(M)<SPAN
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<P>如果有M(x)<SPAN
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<P>二、模糊神经网络结构</P>
<P>在这一节中，所给出的模糊神经网络是三层前向网络，它的输人，权系数都是模糊数。模糊神经网络的结构如图3—13中所示。</P>
<P align=center><IMG height=212
src="3．3．3 模糊神经网络的遗传学习算法.files/6.3.3.38.gif" width=500 border=0></P>
<P align=center>图3-13 模糊神经网络</P></TD></TR>
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<P>在图3—13中，输入X．权系数w，v是三角模糊数，输出Y和目标T可以是三角形模糊数。 </P>
<P>除了输入层之外，所有的神经元都有激发函数y＝f(x)，并且f是连续从R到[-t,t]的非单调减映射，t是正整数，R是实数域。</P>
<P>在隐层中，第i个神经元的输入为I<SUB>i</SUB>，有：</P>
<P>I<SUB>i</SUB>=X.W<SUB>i</SUB>, 1<SPAN
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style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>4
(3.146)</P>
<P>而第i个神经元的输出为Z<SUB>i</SUB>：</P>
<P>Z<SUB>i</SUB>=f(I<SUB>i</SUB>),
1<i<4
(3.147)</P>
<P>在输出层，输出神经元的输入为I<SUB>0</SUB></P>
<TABLE cellSpacing=0 cellPadding=0 width="80%" align=center border=0>
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src="3．3．3 模糊神经网络的遗传学习算法.files/6.3.3.39.gif" width=316 border=0></TD>
<TD width="22%">(3.148)</TD></TR></TBODY></TABLE></TD></TR>
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<TD width="100%" height=489>
<P>而在输出层产生的输出为Y </P>
<P>Y=f(I<SUB>0</SUB>)
(3.149)</P>
<P>为了对模糊神经网络进行学习，所用的训练数据为</P>
<P>(X<SUB>1</SUB>,T<SUB>I</SUB>),1<SPAN
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<P>其中：T<SUB>I</SUB>是在x<SUB>1</SUB>为输入时所需的输出。</P>
<P>学习中，实际输出为Y<SUB>1</SUB>， 1<SPAN
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<P>图3—13中所示的模糊神经网络的学习问题就是在输人为x<SUB>1</SUB>时，找寻最优的权系数W<SUB>i</SUB>，V<SUB>i</SUB>，使实际输出Y<SUB>l</SUB>逼近于T<SUB>1</SUB>，1<SPAN
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<P>三、模糊神经网络的遗传学习算法</P>
<P>遗传算法是一种直接随机搜索方法，它的主要步骤包括编码、选择、交叉、变异等。其原理在3．2节中已说明。在这里只对优化过程的目标函数及一些参数加以介绍。</P>
<P>1．模糊救</P>
<P>因3—13所示的模糊神经网络，优化的目的是找寻最优的权系数W<SUB>i</SUB>、V<SUB>i</SUB>：</P>
<P>W<SUB>i</SUB>=(W<SUB>i1</SUB>/W<SUB>i2</SUB>/W<SUB>i3</SUB>)
(3.150)</P>
<P>V<SUB>i</SUB>=(V<SUB>i1</SUB>/V<SUB>i2</SUB>/V<SUB>i3</SUB>)
(3.151)</P>
<P>其中：1<SPAN
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<P>W<SUB>i2</SUB>=(W<SUB>i1</SUB>+W<SUB>i3</SUB>)/2</P>
<P>V<SUB>i2</SUB>=(V<SUB>i1</SUB>+V<SUB>i3</SUB>)/2</P>
<P>从上两式可知：只要知道W<SUB>i1</SUB>、W<SUB>i3</SUB>和V<SUB>i1</SUB>、V<SUB>i3</SUB>，就可以确定权系数W<SUB>i</SUB>和V<SUB>i</SUB>。因此，遗传算法只需对模糊权系数W<SUB>i</SUB>、V<SUB>i</SUB>的支持集进行追踪寻优即可。因此，群体的个体编码表示为P：</P>
<P>P=(W<SUB>11</SUB>,W<SUB>13</SUB>,......,V<SUB>41</SUB>,V<SUB>43</SUB>)
(3.152)</P>
<P>P的编码采用二进制数。</P>
<P>2．遗传算法的有关参数</P>
<P>遗传算法的参数主要有3个，它们分别是群体数s，交叉车c，变异率M。一般是按经验进行选取。在这里，这些参数确定如下：</P>
<P>S＝2000</P>
<P>C=0．8</P>
<P>M＝0．0009</P>
<P>3．优化的目标函数</P>
<P>设Y<SUB>1</SUB>的<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">α</SPAN>截集为Y<SUB>1</SUB>[<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">α</SPAN>]，有</P>
<P>Y<SUB>l</SUB>[α]=[y<SUB>l1</SUB>(α),y<SUB>l2</SUB>(α)]
(3.153)</P>
<P>设T<SUB>l</SUB>的α截集为T<SUB>l</SUB>[α]，有</P>
<P>T<SUB>l</SUB>[]=[t<SUB>l1</SUB>(α),t<SUB>l2</SUB>(α)]
(3.154)</P>
<P>α<SPAN
style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">∈</SPAN>{0,0.1,0.1,......,0.9,1.0}</P>
<P>则定义</P>
<TABLE cellSpacing=0 cellPadding=0 width="80%" align=center border=0>
<TBODY>
<TR>
<TD width="70%"><IMG height=43
src="3．3．3 模糊神经网络的遗传学习算法.files/6.3.3.40.gif" width=288 border=0></TD>
<TD width="30%">(3.155)</TD></TR>
<TR>
<TD width="70%"><IMG height=39
src="3．3．3 模糊神经网络的遗传学习算法.files/6.3.3.41.gif" width=284 border=0></TD>
<TD width="30%">(3.156)</TD></TR></TBODY></TABLE></TD></TR>
<TR>
<TD width="100%" height=45>
<P>E=E<SUB>1</SUB>+E<SUB>2</SUB> </P>
<P>遗传算法的目的就是寻找恰当的权系数Wi，Vi的值趋于0。</P>
<P>4．模糊神经网络的激发函数</P>
<P>图3—13所示的模糊神经网络中，隐层和输出层的激发函数f的意义如下：</P>
<TABLE cellSpacing=0 cellPadding=0 width="80%" align=center border=0>
<TBODY>
<TR>
<TD width="70%"><IMG height=80
src="3．3．3 模糊神经网络的遗传学习算法.files/6.3.3.42.gif" width=256 border=0></TD>
<TD width="30%">(3.157)</TD></TR></TBODY></TABLE></TD></TR>
<TR>
<TD width="100%" height=349>
<P>其中：t是正整数，一般根据应用情况选择t的值。由于输出的目标模糊数T在[-1，1]区间之内，故在输出层中t的值通常取1。
<P>四、学习情况</P>
<P>采用遗传算法对图3—13的模糊神经网络进行学习之后，可得出在不同输入输出要求下的学习结果。在这里给出一些具体的学习结果。</P>
<P>1．基本概念</P>
<P>(1)相同模糊度</P>
<P>如果对于输入X<SUB>1</SUB>和目标T<SUB>I</SUB>，存在：</P>
<P>f<SUB>uzz</SUB>(X<SUB>I</SUB>)＝f<SUB>uzz</SUB>(T<SUB>I</SUB>)， 1<SPAN
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style="FONT-SIZE: 10.5pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-bidi-font-family: 'Times New Roman'; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA">≤</SPAN>L</P>
<P>则称输入和输出有相同模糊度，亦称等模糊。</P>
<P>(2)过模糊</P>
<P>如果对于输入X1和目标T1，存在：</P>
<P>f<SUB>uzz</SUB>(X<SUB>I</SUB>)<f<SUB>uzz</SUB>(T<SUB>I</SUB>),
1<SPAN
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