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标题: 急~求一个Matlab曲面拟合算法~高手帮帮忙 [打印本页]

作者: BaoXieWang1 时间: 2010-12-29 21:01
标题: 急~求一个Matlab曲面拟合算法~高手帮帮忙
很急，高手们给点意见，帮帮忙~我先谢谢大家了
拟合的函数是
x(1)*exp(-(t(1)-129)^2/(2*x(2)^2)-(t(2)-7.5)^2/(2*x(2)^2))/(2*pi*x(2)^2)+x(3)*exp(-(t(1)-129)^2/(2*x(4)^2)-(t(2)-7.5)^2/(2*x(4)^2))/(2*pi*x(4)^2)
就是两个加权正态函数叠加
拟合的数据点是
X=[129,140,108.5,88,185.5,195,105.5,157.5,107.5,77,162,162,117.5];(横坐标)
Y=[7.5,141.5,28,147,22.5,137.5,85.5,-6.5,-81,3,-66.5,84,-38.5];（纵坐标）
Z=[6,2,4,2,4,2,2,1,1,2,1,6,1];（函数值）
我想直接用拟合函数或者最小二乘函数lsqnonlin和lsqcurvefit，但是数据是三维的用不了
所以我就把问题转化为非线性最优化问题
目标函数（就是把函数在每个点的值减去函数值求平方和，展开了，各位大侠可以不用看了）
y=(x(1)*exp(-(140-129)^2/(2*x(2)^2)-(141.5-7.5)^2/(2*x(2)^2))/(2*pi*x(2)^2)+x(3)*exp(-(140-162)^2/(2*x(4)^2)-(141.5-84)^2/(2*x(4)^2))/(2*pi*x(4)^2)-2)^2+(x(1)*exp(-(108.5-129)^2/(2*x(2)^2)-(28-7.5)^2/(2*x(2)^2))/(2*pi*x(2)^2)+x(3)*exp(-(108.5-162)^2/(2*x(4)^2)-(28-84)^2/(2*x(4)^2))/(2*pi*x(4)^2)-4)^2+(x(1)*exp(-(88-129)^2/(2*x(2)^2)-(147-7.5)^2/(2*x(2)^2))/(2*pi*x(2)^2)+x(3)*exp(-(88-162)^2/(2*x(4)^2)-(147-84)^2/(2*x(4)^2))/(2*pi*x(4)^2)-2)^2+(x(1)*exp(-(185.5-129)^2/(2*x(2)^2)-(22.5-7.5)^2/(2*x(2)^2))/(2*pi*x(2)^2)+x(3)*exp(-(185.5-162)^2/(2*x(4)^2)-(22.5-84)^2/(2*x(4)^2))/(2*pi*x(4)^2)-4)^2+(x(1)*exp(-(195-129)^2/(2*x(2)^2)-(137.5-7.5)^2/(2*x(2)^2))/(2*pi*x(2)^2)+x(3)*exp(-(195-162)^2/(2*x(4)^2)-(137.5-84)^2/(2*x(4)^2))/(2*pi*x(4)^2)-2)^2+(x(1)*exp(-(105.5-129)^2/(2*x(2)^2)-(85.5-7.5)^2/(2*x(2)^2))/(2*pi*x(2)^2)+x(3)*exp(-(105.5-162)^2/(2*x(4)^2)-(85.5-84)^2/(2*x(4)^2))/(2*pi*x(4)^2)-2)^2+(x(1)*exp(-(157.5-129)^2/(2*x(2)^2)-(-6.5-7.5)^2/(2*x(2)^2))/(2*pi*x(2)^2)+x(3)*exp(-(157.5-162)^2/(2*x(4)^2)-(-6.5-84)^2/(2*x(4)^2))/(2*pi*x(4)^2)-1)^2+(x(1)*exp(-(107.5-129)^2/(2*x(2)^2)-(-81-7.5)^2/(2*x(2)^2))/(2*pi*x(2)^2)+x(3)*exp(-(107.5-162)^2/(2*x(4)^2)-(-81-84)^2/(2*x(4)^2))/(2*pi*x(4)^2)-1)^2+(x(1)*exp(-(77-129)^2/(2*x(2)^2)-(3-7.5)^2/(2*x(2)^2))/(2*pi*x(2)^2)+x(3)*exp(-(77-162)^2/(2*x(4)^2)-(3-84)^2/(2*x(4)^2))/(2*pi*x(4)^2)-2)^2+(x(1)*exp(-(162-129)^2/(2*x(2)^2)-(-66.5-7.5)^2/(2*x(2)^2))/(2*pi*x(2)^2)+x(3)*exp(-(162-162)^2/(2*x(4)^2)-(-66.5-84)^2/(2*x(4)^2))/(2*pi*x(4)^2)-1)^2+(x(1)*exp(-(117.5-129)^2/(2*x(2)^2)-(-38.5-7.5)^2/(2*x(2)^2))/(2*pi*x(2)^2)+x(3)*exp(-(117.5-162)^2/(2*x(4)^2)-(-38.5-84)^2/(2*x(4)^2))/(2*pi*x(4)^2)-1)^2+(x(3)*exp(-(129-162)^2/(2*x(4)^2)-(7.5-84)^2/(2*x(4)^2))/(2*pi*x(4)^2)-6)^2+(x(1)*exp(-(162-129)^2/(2*x(2)^2)-(84-7.5)^2/(2*x(2)^2))/(2*pi*x(2)^2)-1)^2
但是我用fmincon解不了这个最优化问题，大规模算法，中规模算法都不行，请问应该怎样才能解这个问题

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