📄 多元非线性回归分析 方法原理说明.htm
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<p class=MsoNormal align=center style='text-align:center'><b><span
style='font-size:16.0pt;mso-bidi-font-size:12.0pt;font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>多元非线性回归分析</span></b><b><span
style='font-size:16.0pt;mso-bidi-font-size:12.0pt'> </span></b><b><span
style='font-size:16.0pt;mso-bidi-font-size:12.0pt;font-family:宋体;mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>方法原理说明</span></b><b><span
lang=EN-US style='font-size:16.0pt;mso-bidi-font-size:12.0pt'><o:p></o:p></span></b></p>
<p class=MsoBodyTextIndent>现在的非线性回归方法种类很多，本程序主要采用的方法和原理说明如下：</p>
<p class=MsoNormal style='margin-left:46.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2;
tab-stops:list 46.0pt'><![if !supportLists]><span lang=EN-US style='font-size:
14.0pt;mso-bidi-font-size:12.0pt;font-family:宋体'>1.<span style='font:7.0pt "Times New Roman"'>
</span></span><![endif]><span style='font-size:14.0pt;mso-bidi-font-size:12.0pt;
font-family:宋体'>随机爬山法<span lang=EN-US>:<o:p></o:p></span></span></p>
<p class=MsoNormal style='margin-left:28.0pt;text-indent:-28.0pt;mso-char-indent-count:
-2.0;mso-char-indent-size:14.0pt;mso-char-indent-size:14pt'><span lang=EN-US
style='font-size:14.0pt;mso-bidi-font-size:12.0pt;font-family:宋体'><span
style="mso-spacerun: yes"> </span><span style="mso-spacerun:
yes"> </span>程序不断的按参数的取值范围随机产生一组组的参数，然后按程序使用者设定的回归模型计算，找出其中和数据符合最好的一组参数，接着按当前最优参数设定新的缩小的参数取值范围，不断重复这个过程直到参数取值范围足够小，这样就确定了参数的值。<o:p></o:p></span></p>
<p class=MsoNormal style='margin-left:46.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2;
tab-stops:list 46.0pt'><![if !supportLists]><span lang=EN-US style='font-size:
14.0pt;mso-bidi-font-size:12.0pt;font-family:宋体'>2.<span style='font:7.0pt "Times New Roman"'>
</span></span><![endif]><span style='font-size:14.0pt;mso-bidi-font-size:12.0pt;
font-family:宋体'>网格爬山法<span lang=EN-US>:<o:p></o:p></span></span></p>
<p class=MsoBodyTextIndent2>这和“随机爬山法”不同的地方是程序先把参数取值区域按参数精度分割成许多块（就像打网格），从每一块区域的中心产生一组参数，这样参数值的分布比较平均，其他地方与“随机爬山法”相同。</p>
<p class=MsoNormal style='margin-left:46.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2;
tab-stops:list 46.0pt'><![if !supportLists]><span lang=EN-US style='font-size:
14.0pt;mso-bidi-font-size:12.0pt;font-family:宋体'>3.<span style='font:7.0pt "Times New Roman"'>
</span></span><![endif]><span style='font-size:14.0pt;mso-bidi-font-size:12.0pt;
font-family:宋体'>最速下降法<span lang=EN-US>:<o:p></o:p></span></span></p>
<p class=MsoNormal style='margin-left:28.0pt;text-indent:27.0pt;mso-char-indent-size:
14pt'><span style='font-size:14.0pt;mso-bidi-font-size:12.0pt;font-family:宋体'>随机选定一组参数初值<span
lang=EN-US>,按给定的模型函数可以找出每个参数的最佳前进方向,如果前进方向与上一次前进方向一致就加大前进步长,如果前进方向不一致就缩小前进步长,这样不断的迭代就可以找到最佳参数值(有可能是局部最佳值)。程序在找出一个最佳值后还会继续运行，重新随机选定参数初值进行计算。<o:p></o:p></span></span></p>
<p class=MsoNormal style='margin-left:46.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2;
tab-stops:list 46.0pt'><![if !supportLists]><span lang=EN-US style='font-size:
14.0pt;mso-bidi-font-size:12.0pt;font-family:宋体'>4.<span style='font:7.0pt "Times New Roman"'>
</span></span><![endif]><span style='font-size:14.0pt;mso-bidi-font-size:12.0pt;
font-family:宋体'>最速下降网格爬山法<span lang=EN-US>:<o:p></o:p></span></span></p>
<p class=MsoNormal style='margin-left:28.0pt;text-indent:27.0pt'><span
style='font-size:14.0pt;mso-bidi-font-size:12.0pt;font-family:宋体'>最速下降网格爬山法是最速下降法和网格爬山法的混合使用，就是在每块小区域中使用最速下降法找出局部最优值。<span
lang=EN-US><o:p></o:p></span></span></p>
<p class=MsoNormal style='margin-left:46.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo2;
tab-stops:list 46.0pt'><![if !supportLists]><span lang=EN-US style='font-size:
14.0pt;mso-bidi-font-size:12.0pt;font-family:宋体'>5.<span style='font:7.0pt "Times New Roman"'>
</span></span><![endif]><span style='font-size:14.0pt;mso-bidi-font-size:12.0pt;
font-family:宋体'>基因算法<span lang=EN-US>:<o:p></o:p></span></span></p>
<p class=MsoNormal style='margin-left:28.0pt;text-indent:27.0pt'><span
style='font-size:14.0pt;mso-bidi-font-size:12.0pt;font-family:宋体'>基因算法（统称为进化计算）是通过模拟自然界的生物进化过程来解决实际问题的一种方法，它是一种通用的问题求解方法。程序采用一种编码技术（程序中采用的是浮点表示方案）来表示问题的解，并将每个编码看作一个个体，算法维持一个一定数目的编码集合，称为种群，并通过对种群中的每个个体进行某些遗传操作来模拟进化过程，最终获得一些具有较高性能指标的编码。程序把算法中的编码称为基因，基因的表现型就是问题的解。<span
lang=EN-US><o:p></o:p></span></span></p>
<p class=MsoNormal style='margin-left:28.0pt;text-indent:27.0pt'><span
style='font-size:14.0pt;mso-bidi-font-size:12.0pt;font-family:宋体'>进化是由四个操作组成的连续过程：繁殖、变异（基因变异、交叉）、竞争和选择；程序中采用的遗传算子主要有：一致变异、非一致变异、单点一致交叉、启发式交叉、一般算术交叉和完全算术交叉。<span
lang=EN-US><o:p></o:p></span></span></p>
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12.0pt;font-family:宋体'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p>
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12.0pt;font-family:宋体'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p>
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12.0pt;font-family:宋体'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p>
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12.0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p>
<p class=MsoNormal align=center style='text-align:center'><span lang=EN-US
style='font-size:9.0pt;mso-bidi-font-size:12.0pt'><a href="多元非线性回归分析%20帮助主题.htm"><span
style='font-family:宋体;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>帮助主题</span></a><o:p></o:p></span></p>
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12.0pt;font-family:宋体'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p>
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