Fit multiple curves in one graph using least squares

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NMans on 10 May 2018
Answered: Szu-Yu Lee on 8 Apr 2021
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 on 11 May 2018
Hi,
Best regards
Stephan

Stephan on 10 May 2018
Edited: Stephan on 10 May 2018
Hi,
use the
fit
function for this - see here:
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

Cathal Cunningham on 10 May 2018
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.

Stephan on 10 May 2018
Edited: Stephan on 11 May 2018
Hi,
use this example for your purposes:
% 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
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:
% 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
Stephan on 17 May 2018
Still not happy?

Szu-Yu Lee on 8 Apr 2021
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