how to curve fit a sine wave to some data

I have been using a open source software package called openFAST to generate some binary files of wind turbine simulations. I then use MATLAB to view the results of the 5MW_Land_DLL.outb files generated by openFAST using the following code:

%% Run this command first
%% Read a binary output file
% Read file
outbfile = '5MW_Land_DLL_WTurb.outb';
[Channels, ChanName, ChanUnit, FileID, DescStr] = ReadFASTbinary(outbfile);
time = Channels(:,1);

This code organizes the data into the matrices etc. like in the image below:

I then use the plot function to generate a graph:

%%CHange the plot number to reflect the parameter in channel names matrix generated from above command.
% Plot Channel 34
iChan=34
figure()
plot(time, Channels(:,iChan))
xlabel('Time (s)')
ylabel([ChanName(iChan) ChanUnit(iChan)])

That looks like :

What I would like to do now is curve fit a sine wave to this plot above so I can get the frequency, the amplitude, phase, and the equation from it.

Is this possible to do?

I have zero experience in MATLAB. The above code was given to me. 🙂 I am not a coder at all.

Thanks

[John D'Errico]

What sine wave? If I look at that curve, I see a slowly varying trend that is arguably a low frequency sine wave. On top of that, I can see faster components, and then some fairly high frequency components.

The point is, you cannot just fit a single sine wave. A fft would tell you that too. There is a lot of stuff happening in there.

[Matt Thomas]

lol, yeah, there is alot of infomation and stuff happening for sure. What about a average sin wave? like a fixed-mean type? i just need something i can work with. OR, anyway to arrange the variable amplitudes into a descending amplitude order? IE, have the highest amplitude shown first, then the next highest, etc etc. and plot a sin wave for each set?

Thanks

[Image Analyst]

@Matt Thomas as I'm sure you know, the Fourier series is a set of sine waves, and if you Fourier transform your data you'll get an array that has the power of your signal in each corresponding sine wave frequency. So essentially you'll have dozens or hundreds of sine waves that, when all summed up, will reconstruct your signal. If you want, you could pick the one frequency with the greatest power and use that one frequency to synthesize a pure sine wave.

[Matt Thomas]

ohhh, ok, how fo i do the FFT so i can see all the dozens or hundreds of frequencies? that would be helpful too.

thanks

[Image Analyst]

Call the fft function and plot its magnitude.

[Matt Thomas]

ok, ill try to figure that out. ill google the syntax. thank you much

[Matt Thomas]

i keep getting an error when using fft.

y=fft( time, Channels(:,iChan))

FFT length must be a nonnegative integer scalar.

thanks

Answer 1

[Matt J]

One way, assuming you have the Curve Fitting Toolbox:

fobj = fit( time, Channels(:,iChan) ,'sin1')

[Matt Thomas]

i do have the toolbox. do i use this code after the plot so it will display the curve and all the information? thanks

[Matt Thomas]

i get this back:

fobj =

General model Sin1:

fobj(x) = a1*sin(b1*x+c1)

Coefficients (with 95% confidence bounds):

a1 = 8960 (8940, 8981)

b1 = 0.003551 (0.003479, 0.003622)

c1 = 0.7699 (0.7623, 0.7776)

which is good, now anyway to see the curve?

EDIT. i used desmos... dang, big wave comin through haha

thank you

[Matt J]

Yes, you can plot fobj using,

https://www.mathworks.com/help/curvefit/cfit.plot.html

Example,

plot(fobj,time,Channels(:,iChan) )

[Matt Thomas]

thank you. i couldnt reply, i was at work till 11pm. thanks for this. illtest it out when im awake haha

[Matt J]

You're welcome, but if it does what you need, please Accept-click thhe answer.

[Matt Thomas]

well, it plots it and works but for sure NOT the results i had in my head haha. I thought it would be more of a tighter and faster sin wave but its nice and slow haha.

when i look at my graph i see a tighter sin wave IE from time 0-15 seconds is a peak, then 15-25 is another peak, and 25-35 is another.

thanks for this. ill see if i can use the data to help me out

[Matt Thomas]

this is what i saw in my head haha