Question

如何用MATLAB拟合曲线来求参数？

我要计算的是a，b参数，已知c，k，y
其中y=252*a/(2.016129032*10^9)*((cos(k)/sin(k))/c)^b
其中数据为，c=[2.7,2.8,2.9,3,3.1,3.2,3.45,3.7,3.95,4.2,4.45,4.7,4.95,5.2]
k=[ 0,47,93,140,186,279,372,465,558,651];
y=[18.98,27.35,34.86,38.52,38.44,37.73,38.43,43.87,42.77,46.22];
要怎么拟合，才能求出a，b参数啊？求大神指点。

Answer 1

令x＝(cos(k)./sin(k))./c，这个就是xdata向量
y=252/(2.016129032*10^9)*a*x^b

取log得到
log(y)=b*log(x)+log(252/(2.016129032*10^9)*a)
所以log(y)与log(x)是线性关系，用p=polyfit(log(xdata),log(y),1)求出
b=p(1);
a=exp(p(2))/252*(2.016129032*10^9); % 因为log(252/(2.016129032*10^9)*a)=p(2)

所以最终程序是如下：

clear all
c=[2.7,2.8,2.9,3,3.1,3.2,3.45,3.7,3.95,4.2,4.45,4.7,4.95,5.2];
k=[0,47,93,140,186,279,372,465,558,651];
y=[18.98,27.35,34.86,38.52,38.44,37.73,38.43,43.87,42.77,46.22];
xdata=(cos(k)./sin(k))./c;
p=polyfit(log(xdata),log(y),1);
b=p(1);
a=exp(p(2))/252*(2.016129032*10^9);

Answer 2

令x＝(cos(k)./sin(k))./c，这个就是xdata向量
y=252/(2.016129032*10^9)*a*x^b

取log得到
log(y)=b*log(x)+log(252/(2.016129032*10^9)*a)
所以log(y)与log(x)是线性关系，用p=polyfit(log(xdata),log(y),1)求出
b=p(1);
a=exp(p(2))/252*(2.016129032*10^9); % 因为log(252/(2.016129032*10^9)*a)=p(2)

所以最终程序是如下：

clear all
c=[2.7,2.8,2.9,3,3.1,3.2,3.45,3.7,3.95,4.2,4.45,4.7,4.95,5.2];
k=[0,47,93,140,186,279,372,465,558,651];
y=[18.98,27.35,34.86,38.52,38.44,37.73,38.43,43.87,42.77,46.22];
xdata=(cos(k)./sin(k))./c;
p=polyfit(log(xdata),log(y),1);
b=p(1);
a=exp(p(2))/252*(2.016129032*10^9);

Answer 3

可以用优化的方法吧。把a,b做成设计变量，目标函数为：（等式左边-右边）^2，目标最小的时候就求到a跟b了。