I ask for help please colleagues

I have a pair of input and output data. My goal is to find a polynomial function that best fits the data. For that I need polynomials of various orders (linear, quadratic, cubic,... up to degree 10). In the matlab program I have, I can get the polynomials one at a time and plot them separately. My problem is: How can I run my program, get the curves of different orders (linear, quadratic, cubic,...), plot them on the same graph and label each curve. I know I should use the "for-loop" but I'm facing difficulties for several days.Can someone help please?

Thanks in advance.

Milagre MANHIQUE

My matlab code is:

clear;
clc;
load manufacturerdata

x=manufacturerdata.windspeed; % Wind speed data in m/s
y=manufacturerdata.power; % Wind turbine output power in Watt.

F=input('Enter the order of the desired polynomial: ');

n=length(x);
N=F+1; % For dimension of matrix A, for Ax=B.

A=zeros(N,N);
for i=1:N
    for j=1:N
        A(i,j)=sum(x.^(i+j-2));
    end
end

B=zeros(N,1);

for k=1:N
    B(k)=sum((x.^(k-1)).*y);
end

U=A\B;
Coefficient=[U(2,1) U(1,1)]

% Displaying the desired polynomial
disp('The desired polynomial function fitted to the manufacturer data is: P(x)= ')

for k=N:-1:2
    fprintf('+(%.4fx^%d)', U(k), k-1)
end

fprintf('+(%.4f)\n', U(1))

% Plotting  the curve fitted to the data
p=flip(U);
x=linspace(x(1),x(n),100);
y=polyval(p,x);
c1=plot(x,y,'-r');
hold on
c2=plot(x,y,'-.');
ylim([0 1000])

title('Output power fitting curve for manufacturer data');
xlabel('Wind speed (in m/s)');
ylabel('Output Power (in kW)');

legend([c1,c2], 'Manufacturer P(v)','Fitted P(v) curve','Location','NorthWest')

[Image Analyst]

You forgot to attach manufacturerdata.mat. Why not use polyfit()?

Obviously the highest order polynomial will fit your training data best (lowest residuals) but may not be best for data not used to train it.

[Milagre MANHIQUE]

I used the polyfit command as you advised me, it gave me some way to solve my problem. With this command it seems to me that there is a light at the bottom of the tunnel.

Thanks for the tip, it's been useful

Milagre MANHIQUE

Answer 1

[Milagre MANHIQUE]

Using polyfit as I was advised, I ended up finding this solution, it gave what I really wanted, but I found it to be a somewhat rudimentary or primitive way, I believe it is possible to use loops (for, while...) and produce the same solution.I need to improve my skills in using loops, but if anyone can give a tip, I would welcome and appreciate.

Thank you for help

The code is:

load manufacturerdata

load winddata.mat %Reference wind speed, v (in km/h).

% Manufacturer data

x=manufacturerdata.windspeed;

y=manufacturerdata.power;

p1 = polyfit(x,y,1);

p2 = polyfit(x,y,2);

p3 = polyfit(x,y,3);

p4 = polyfit(x,y,4);

p5 = polyfit(x,y,5);

p6 = polyfit(x,y,6);

p7 = polyfit(x,y,7);

p8 = polyfit(x,y,8);

p9 = polyfit(x,y,9);

p10 = polyfit(x,y,10);

f1 = polyval(p1,x);

f2 = polyval(p2,x);

f3 = polyval(p3,x);

f4 = polyval(p4,x);

f5 = polyval(p5,x);

f6 = polyval(p6,x);

f7 = polyval(p7,x);

f8 = polyval(p8,x);

f9 = polyval(p9,x);

f10 = polyval(p10,x);

plot(x,y,'bp',x,f1,'k:',x,f2,'.-',x,f3,x,f4,x,f5,x,f6,...

x,f7,x,f8,x,f9,x,f10)

title('Output power fitting curves for manufacturer data');

xlabel('Wind speed (in m/s)');

ylabel('Output Power (in kW)');

ylim([-50 1000])

legend('data','1^{st} degree','2^{nd} degree','3^{rd} degree',...

'4^{th} degree','5^{th} degree','6^{th} degree','7^{th} degree',...

'8^{th} degree','9^{th} degree','10^{th} degree','location','southeast')