Fit multiple curves in one graph using least squares

Hi all,

I've created yearly power curve for multiple wind farms (with multiple curves in a graph) and I would like to fit these individually - how do I do that? The code is very long for me to copy and paste here but I've used

for yrs = 1: length(years)

and so on..

and then plot(Wind_speed(:,yrs), Pow_ave(:,yrs), '*');

hold on;

and so on...

Thanks!

[Stephan]

As result form the fit function you get an object that can be plotted. If you fit more than one curves give different names to these objects you create and use the

hold on

command like you did with your data. This should work. Here is an example:

load census
curvefit = fit(cdate,pop,'poly3','normalize','on')
plot(curvefit,cdate,pop)
hold on
cdate2 = cdate + 50
pop2 = pop * 0.5
curvefit2 = fit(cdate2,pop2,'poly3','normalize','on')
plot(curvefit2,cdate2,pop2)

This will give you:

If that helped please accept answer, in order to help others finding helpful posts here in the forum.

Best regards

Stephan

[NMans]

Thanks Stephan - however this is plotting multiple curves plus fitting onto one graph. I already have multiple curves in my graph using the for function for every unique year. My question how do I fit each individual curve in my graph. The reason for doing this is I've written my code for 14 wind farms, so my code produces 14 graphs with each one having multiple curves. I should have made that clear.

[Stephan]

Hi,

see my new answer - does this help you? Or did I misunderstand you?

Best regards

Stephan

Answer 1

[Stephan]

Hi,

use the

fit

function for this - see here:

https://de.mathworks.com/help/curvefit/fit.html?s_tid=doc_ta#bto2vuv-5

You can take the several x,y-pairs and fit them individually with this function. Same result you get by using curve fitting app.

Result could look like this (all taken from mathworks.com ):

or for example this

depending on the fitting function you choose.

Best regards

Stephan

Answer 2

[Cathal Cunningham]

You could try fit (allows polynomial line fitting amongst others) or glmfit (Generalized Linear Model Fit) which allows you to define what kind of fit you would like to use.

Answer 3

[Stephan]

Hi,

use this example for your purposes:

% load some example data
load census

% create second sata set
cdate2 = cdate;
pop2 = pop * 0.5;

% fit 2 curves
curvefit1 = fit(cdate,pop,'poly2');
curvefit2 = fit(cdate2,pop2,'poly2');

% create new data from fit objects
X = 1790:1990;
Y1 = curvefit1(X);
Y2 = curvefit2(X);

% plot measured data
a = subplot(2,1,1);
plot(cdate,pop, '*', 'color', 'r')
hold on
plot(cdate2,pop2, 'o', 'color', 'b')

% Plot only the trend lines
b = subplot(2,1,2);
plot(X, Y1, 'color', 'r')
hold on
plot(X, Y2, 'color', 'b')

% same scaling of the subplots
linkaxes([a b], 'xy')

hold off

this gives you:

.

The code snippet:

% fits 2 curves
curvefit1 = fit (cdate, pop, 'poly2');
curvefit2 = fit (cdate2, pop2, 'poly2');

adjusts the curves for both records individually. If I understand you correctly, that's what you want to do:

Calculate an individual curve adaptation for each individual year and repeat this for all 14 wind turbines. For example, if you look at ten years, you'll get a total of 14 charts, each with 10 individually adjusted curves. So in this case you need 140 times the fit function.

Correct?

What you have to do is hand over the corresponding X, Y pairs for each year to the fit function and repeat this process for a new year with a new curve fit.

To execute this in a for loop you could use this code snippet:

% load example data
load census

% preallocate an Array with number of fits you need as columns - here 2
popu = zeros(length(cdata),2);

% fill the data in:
popu(:,1) = pop;
popu(:,2) = pop * 0.5;

% collect all individual fitted curve objects in a cell array
for i = 1:2
    Data{i} = fit(cdate,popu(:,i),'poly2');
end

.

Doing so, will give you a cell Array containing for example 140 individual fits, which you can plot as shown above or like you need.

.

Best regards

Stephan

[NMans]

Thank you so much Stephan - I will try this and get back to you!

[Stephan]

Hi,

hope it works well for your purpose.

Best regards

Stephan

[Stephan]

Still not happy?

Answer 4

[Szu-Yu Lee]

Hi, I guess you are trying to fit a large number of independent equations? MATLAB "fit" function do not support multiple independent curves fitting. I have created a function that takes in a 2D matrix, where each row is a curve to be fitted to some polynomial expression. The function does not use for-loop, so can work on large number of rows in a very short time.

https://www.mathworks.com/matlabcentral/fileexchange/90017-matrix-row-wise-polynomial-fit