實(shí)驗(yàn)五 用Matlab數(shù)據(jù)擬合課件

用Matlab進(jìn)行數(shù)據(jù)擬合1.多項(xiàng)式曲線擬合:polyfit.y0=polyval(p,x0)p=polyfit(x,y,m)其中,x,y為已知數(shù)據(jù)點(diǎn)向量,分別表示橫,縱坐標(biāo),m為擬合多項(xiàng)式的次數(shù),結(jié)果返回m次擬合多項(xiàng)式系數(shù),從高次到低次存放在向量p中.可求得多項(xiàng)式在x0處的值y0.用Matlab進(jìn)行數(shù)據(jù)擬合1.多項(xiàng)式曲線擬合:poly例1已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy0-0.4470.11.9780.23.280.36.160.47.080.57.340.67.660.79.560.89.480.99.3111.2分別用3次和6次多項(xiàng)式曲線擬合這些數(shù)據(jù)點(diǎn).x=0:0.1:1y=[-0.447,1.978,3.28,6.16,7.08,7.34,7.66,9.56,9.48,9.3,11.2]plot(x,y,'k.','markersize',25)axis([01.3-216])p3=polyfit(x,y,3)p6=polyfit(x,y,6)編寫Matlab程序如下:例1已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy0-0.4470.11.9t=0:0.1:1.2s=polyval(p3,t)s1=polyval(p6,t)holdonplot(t,s,'r-','linewidth',2)plot(t,s,'b--','linewidth',2)gridx=0:0.1:1y=[-0.447,1.978,3.28,6.16,7.08,7.34,7.66,9.56,9.48,9.3,11.2]plot(x,y,'k.','markersize',25)axis([01.3-216])p3=polyfit(x,y,3)p6=polyfit(x,y,6)t=0:0.1:1.2x=0:0.1:1例2用切削機(jī)床進(jìn)行金屬品加工時(shí),為了適當(dāng)?shù)卣{(diào)整機(jī)床,需要測(cè)定刀具的磨損速度.在一定的時(shí)間測(cè)量刀具的厚度,得數(shù)據(jù)如表所示:切削時(shí)間t/h030.0129.1228.4328.1428.0527.7627.5727.2827.0刀具厚度y/cm切削時(shí)間t/h926.81026.51126.31226.11325.71425.31524.81624.0刀具厚度y/cm例2用切削機(jī)床進(jìn)行金屬品加工時(shí),為了適當(dāng)?shù)卣{(diào)整機(jī)床,解:描出散點(diǎn)圖,在命令窗口輸入:t=[0:1:16]y=[30.029.128.428.128.027.727.527.227.026.826.526.326.125.725.324.824.0]plot(t,y,'*')解:描出散點(diǎn)圖,在命令窗口輸入:t=[0:1:16]解:描出散點(diǎn)圖,在命令窗口輸入:t=[0:1:16]y=[30.029.128.428.128.027.727.527.227.026.826.526.326.125.725.324.824.0]plot(t,y,'*')a=-0.301229.3804holdonplot(t,y1),holdoffa=polyfit(t,y,1)y1=-0.3012*t+29.3804解:描出散點(diǎn)圖,在命令窗口輸入:t=[0:1:16]a例2用切削機(jī)床進(jìn)行金屬品加工時(shí),為了適當(dāng)?shù)卣{(diào)整機(jī)床,需要測(cè)定刀具的磨損速度.在一定的時(shí)間測(cè)量刀具的厚度,得數(shù)據(jù)如表所示:切削時(shí)間t/h030.0129.1228.4328.1428.0527.7627.5727.2827.0刀具厚度y/cm切削時(shí)間t/h926.81026.51126.31226.11325.71425.31524.81624.0刀具厚度y/cm擬合曲線為:y=-0.3012t+29.3804例2用切削機(jī)床進(jìn)行金屬品加工時(shí),為了適當(dāng)?shù)卣{(diào)整機(jī)床,例3一個(gè)15.4cm×30.48cm的混凝土柱在加壓實(shí)驗(yàn)中的應(yīng)力-應(yīng)變關(guān)系測(cè)試點(diǎn)的數(shù)據(jù)如表所示1.552.472.933.03已知應(yīng)力-應(yīng)變關(guān)系可以用一條指數(shù)曲線來(lái)描述,即假設(shè)式中,表示應(yīng)力,單位是N/m2;表示應(yīng)變.2.89例3一個(gè)15.4cm×30.48cm的混凝土柱在加壓實(shí)驗(yàn)已知應(yīng)力-應(yīng)變關(guān)系可以用一條指數(shù)曲線來(lái)描述,即假設(shè)式中,表示應(yīng)力,單位是N/m2;表示應(yīng)變.解選取指數(shù)函數(shù)作擬合時(shí),在擬合前需作變量代換,化為k1,k2的線性函數(shù).于是,令即已知應(yīng)力-應(yīng)變關(guān)系可以用一條指數(shù)曲線來(lái)描述,即假設(shè)式中,在命令窗口輸入:x=[500*1.0e-61000*1.0e-61500*1.0e-62000*1.0e-62375*1.0e-6]y=[3.103*1.0e+32.465*1.0e+31.953*1.0e+31.517*1.0e+31.219*1.0e+3]z=log(y)a=polyfit(x,z,1)k1=exp(8.3009)w=[1.552.472.933.032.89]plot(x,w,'*')y1=exp(8.3009)*x.*exp(-494.5209*x)plot(x,w,'*',x,y1,'r-')在命令窗口輸入:x=[500*1.0e-61000*1.0已知應(yīng)力-應(yīng)變關(guān)系可以用一條指數(shù)曲線來(lái)描述,即假設(shè)式中,表示應(yīng)力,單位是N/m2;表示應(yīng)變.擬合曲線為:令則求得于是已知應(yīng)力-應(yīng)變關(guān)系可以用一條指數(shù)曲線來(lái)描述,即假設(shè)式中,在實(shí)際應(yīng)用中常見的擬合曲線有:直線多項(xiàng)式一般n=2,3,不宜過(guò)高.雙曲線(一支)指數(shù)曲線在實(shí)際應(yīng)用中常見的擬合曲線有:直線多項(xiàng)式一般n=2,3,2.非線性曲線擬合:nlinfit.功能:x=lsqcurvefit(fun,x0,xdata,ydata)[x,resnorm]=lsqcurvefit(fun,x0,xdata,ydata)根據(jù)給定的數(shù)據(jù)xdata,ydata(對(duì)應(yīng)點(diǎn)的橫,縱坐標(biāo)),按函數(shù)文件fun給定的函數(shù),以x0為初值作最小二乘擬合,返回函數(shù)fun中的系數(shù)向量x和殘差的平方和resnorm.2.非線性曲線擬合:nlinfit.功能:x=lsqcu例4已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy03.10.13.270.23.810.34.50.45.180.560.67.050.78.560.89.690.911.25113.17求三個(gè)參數(shù)a,b,c的值,使得曲線f(x)=aex+bx2+cx3與已知數(shù)據(jù)點(diǎn)在最小二乘意義上充分接近.首先編寫存儲(chǔ)擬合函數(shù)的函數(shù)文件.functionf=nihehanshu(x,xdata)f=x(1)*exp(xdata)+x(2)*xdata.^2+x(3)*xdata.^3保存為文件nihehanshu.m例4已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy03.10.13.270.例4已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy03.10.13.270.23.810.34.50.45.180.560.67.050.78.560.89.690.911.25113.17求三個(gè)參數(shù)a,b,c的值,使得曲線f(x)=aex+bx2+cx3與已知數(shù)據(jù)點(diǎn)在最小二乘意義上充分接近.編寫下面的程序調(diào)用擬合函數(shù).x=0:0.1:1;y=[3.1,3.27,3.81,4.5,5.18,6,7.05,8.56,9.69,11.25,13.17];x0=[0,0,0];[beta,r,J]=nlinfit(x',y','nihehanshu',x0);例4已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy03.10.13.270.編寫下面的程序調(diào)用擬合函數(shù).x=0:0.1:1;y=[3.1,3.27,3.81,4.5,5.18,6,7.05,8.56,9.69,11.25,13.17];x0=[0,0,0];[beta,r,J]=nlinfit(x',y','nihehanshu',x0);程序運(yùn)行后顯示beta=3.00224.03040.9404編寫下面的程序調(diào)用擬合函數(shù).x=0:0.1:1;程序運(yùn)行后顯例4已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy03.10.13.270.23.810.34.50.45.180.560.67.050.78.560.89.690.911.25113.17求三個(gè)參數(shù)a,b,c的值,使得曲線f(x)=aex+bx2+cx3與已知數(shù)據(jù)點(diǎn)在最小二乘意義上充分接近.說(shuō)明:最小二乘意義上的最佳擬合函數(shù)為f(x)=3ex+4.03x2+0.94x3.此時(shí)的殘差是:0.0912.例4已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy03.10.13.270.f(x)=3ex+4.03x2+0.94x3.擬合函數(shù)為:f(x)=3ex+4.03x2+0.94x3.擬合練習(xí):1.已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy03.10.13.270.23.810.34.50.45.180.560.67.050.78.560.89.690.911.25113.17求用三次多項(xiàng)式進(jìn)行擬合的曲線方程.2.已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy1.617.72.7491.313.14.1189.43.6110.82.334.50.644.9409.13652.436.9求a,b,c的值,使得曲線f(x)=aex+bsinx+clnx與已知數(shù)據(jù)點(diǎn)在最小二乘意義上充分接近.練習(xí):1.已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy03.10.13.27用Matlab進(jìn)行數(shù)據(jù)擬合1.多項(xiàng)式曲線擬合:polyfit.y0=polyval(p,x0)p=polyfit(x,y,m)其中,x,y為已知數(shù)據(jù)點(diǎn)向量,分別表示橫,縱坐標(biāo),m為擬合多項(xiàng)式的次數(shù),結(jié)果返回m次擬合多項(xiàng)式系數(shù),從高次到低次存放在向量p中.可求得多項(xiàng)式在x0處的值y0.用Matlab進(jìn)行數(shù)據(jù)擬合1.多項(xiàng)式曲線擬合:poly例1已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy0-0.4470.11.9780.23.280.36.160.47.080.57.340.67.660.79.560.89.480.99.3111.2分別用3次和6次多項(xiàng)式曲線擬合這些數(shù)據(jù)點(diǎn).x=0:0.1:1y=[-0.447,1.978,3.28,6.16,7.08,7.34,7.66,9.56,9.48,9.3,11.2]plot(x,y,'k.','markersize',25)axis([01.3-216])p3=polyfit(x,y,3)p6=polyfit(x,y,6)編寫Matlab程序如下:例1已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy0-0.4470.11.9t=0:0.1:1.2s=polyval(p3,t)s1=polyval(p6,t)holdonplot(t,s,'r-','linewidth',2)plot(t,s,'b--','linewidth',2)gridx=0:0.1:1y=[-0.447,1.978,3.28,6.16,7.08,7.34,7.66,9.56,9.48,9.3,11.2]plot(x,y,'k.','markersize',25)axis([01.3-216])p3=polyfit(x,y,3)p6=polyfit(x,y,6)t=0:0.1:1.2x=0:0.1:1例2用切削機(jī)床進(jìn)行金屬品加工時(shí),為了適當(dāng)?shù)卣{(diào)整機(jī)床,需要測(cè)定刀具的磨損速度.在一定的時(shí)間測(cè)量刀具的厚度,得數(shù)據(jù)如表所示:切削時(shí)間t/h030.0129.1228.4328.1428.0527.7627.5727.2827.0刀具厚度y/cm切削時(shí)間t/h926.81026.51126.31226.11325.71425.31524.81624.0刀具厚度y/cm例2用切削機(jī)床進(jìn)行金屬品加工時(shí),為了適當(dāng)?shù)卣{(diào)整機(jī)床,解:描出散點(diǎn)圖,在命令窗口輸入:t=[0:1:16]y=[30.029.128.428.128.027.727.527.227.026.826.526.326.125.725.324.824.0]plot(t,y,'*')解:描出散點(diǎn)圖,在命令窗口輸入:t=[0:1:16]解:描出散點(diǎn)圖,在命令窗口輸入:t=[0:1:16]y=[30.029.128.428.128.027.727.527.227.026.826.526.326.125.725.324.824.0]plot(t,y,'*')a=-0.301229.3804holdonplot(t,y1),holdoffa=polyfit(t,y,1)y1=-0.3012*t+29.3804解:描出散點(diǎn)圖,在命令窗口輸入:t=[0:1:16]a例2用切削機(jī)床進(jìn)行金屬品加工時(shí),為了適當(dāng)?shù)卣{(diào)整機(jī)床,需要測(cè)定刀具的磨損速度.在一定的時(shí)間測(cè)量刀具的厚度,得數(shù)據(jù)如表所示:切削時(shí)間t/h030.0129.1228.4328.1428.0527.7627.5727.2827.0刀具厚度y/cm切削時(shí)間t/h926.81026.51126.31226.11325.71425.31524.81624.0刀具厚度y/cm擬合曲線為:y=-0.3012t+29.3804例2用切削機(jī)床進(jìn)行金屬品加工時(shí),為了適當(dāng)?shù)卣{(diào)整機(jī)床,例3一個(gè)15.4cm×30.48cm的混凝土柱在加壓實(shí)驗(yàn)中的應(yīng)力-應(yīng)變關(guān)系測(cè)試點(diǎn)的數(shù)據(jù)如表所示1.552.472.933.03已知應(yīng)力-應(yīng)變關(guān)系可以用一條指數(shù)曲線來(lái)描述,即假設(shè)式中,表示應(yīng)力,單位是N/m2;表示應(yīng)變.2.89例3一個(gè)15.4cm×30.48cm的混凝土柱在加壓實(shí)驗(yàn)已知應(yīng)力-應(yīng)變關(guān)系可以用一條指數(shù)曲線來(lái)描述,即假設(shè)式中,表示應(yīng)力,單位是N/m2;表示應(yīng)變.解選取指數(shù)函數(shù)作擬合時(shí),在擬合前需作變量代換,化為k1,k2的線性函數(shù).于是,令即已知應(yīng)力-應(yīng)變關(guān)系可以用一條指數(shù)曲線來(lái)描述,即假設(shè)式中,在命令窗口輸入:x=[500*1.0e-61000*1.0e-61500*1.0e-62000*1.0e-62375*1.0e-6]y=[3.103*1.0e+32.465*1.0e+31.953*1.0e+31.517*1.0e+31.219*1.0e+3]z=log(y)a=polyfit(x,z,1)k1=exp(8.3009)w=[1.552.472.933.032.89]plot(x,w,'*')y1=exp(8.3009)*x.*exp(-494.5209*x)plot(x,w,'*',x,y1,'r-')在命令窗口輸入:x=[500*1.0e-61000*1.0已知應(yīng)力-應(yīng)變關(guān)系可以用一條指數(shù)曲線來(lái)描述,即假設(shè)式中,表示應(yīng)力,單位是N/m2;表示應(yīng)變.擬合曲線為:令則求得于是已知應(yīng)力-應(yīng)變關(guān)系可以用一條指數(shù)曲線來(lái)描述,即假設(shè)式中,在實(shí)際應(yīng)用中常見的擬合曲線有:直線多項(xiàng)式一般n=2,3,不宜過(guò)高.雙曲線(一支)指數(shù)曲線在實(shí)際應(yīng)用中常見的擬合曲線有:直線多項(xiàng)式一般n=2,3,2.非線性曲線擬合:nlinfit.功能:x=lsqcurvefit(fun,x0,xdata,ydata)[x,resnorm]=lsqcurvefit(fun,x0,xdata,ydata)根據(jù)給定的數(shù)據(jù)xdata,ydata(對(duì)應(yīng)點(diǎn)的橫,縱坐標(biāo)),按函數(shù)文件fun給定的函數(shù),以x0為初值作最小二乘擬合,返回函數(shù)fun中的系數(shù)向量x和殘差的平方和resnorm.2.非線性曲線擬合:nlinfit.功能:x=lsqcu例4已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy03.10.13.270.23.810.34.50.45.180.560.67.050.78.560.89.690.911.25113.17求三個(gè)參數(shù)a,b,c的值,使得曲線f(x)=aex+bx2+cx3與已知數(shù)據(jù)點(diǎn)在最小二乘意義上充分接近.首先編寫存儲(chǔ)擬合函數(shù)的函數(shù)文件.functionf=nihehanshu(x,xdata)f=x(1)*exp(xdata)+x(2)*xdata.^2+x(3)*xdata.^3保存為文件nihehanshu.m例4已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy03.10.13.270.例4已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy03.10.13.270.23.810.34.50.45.180.560.67.050.78.560.89.690.911.25113.17求三個(gè)參數(shù)a,b,c的值,使得曲線f(x)=aex+bx2+cx3與已知數(shù)據(jù)點(diǎn)在最小二乘意義上充分接近.編寫下面的程序調(diào)用擬合函數(shù).x=0:0.1:1;y=[3.1,3.27,3.81,4.5,5.18,6,7.05,8.56,9.69,11.25,13.17];x0=[0,0,0];[beta,r,J]=nlinfit(x',y','nihehanshu',x0);例4已知觀測(cè)數(shù)據(jù)點(diǎn)如表所示xy03.10.13.270.編寫下面的程序調(diào)用擬合函數(shù).x=0:0.1:1;y=[3.1,3