- The location of data point 1
- The location of data point 2
- Data point 1 is a local maximum (the derivative is equal to zero)
- Data point 2 is a local maximum (the derivative is equal to zero)
fitting curve to two points
7 vues (au cours des 30 derniers jours)
I have this daily load curve " f(x)=342.8+(-4.141*cos(x*0.261))+(-60.26*sin(x*0.261))+(43.46*cos(2*x*0.261))+(-21.9*sin(x*0.261*2)) " I also have data for the two peaks of each day, (ie the two local maxima) with no relation to time.That looks like this:
Day 1 Morning Max 800 Afternoon Max 860 Day 2 Morning Max 900 Afternoon Max 990
I need to adjust the coefficients so that the curve passes through or as close as possible to the data points. I need this to be done for every day for 3 months, so it has to be automated. Any ideas? Thanks in advance.
Richard Willey le 27 Fév 2012
Here's the rub...
When you fit a second order Fourier series, you're estimating values for six different regression coefficients.
In this example you know that
I don't think that you have enough information to generate a unique solution.
Please note: If the fully parameterized daily load curve that you specified has some kind of real world meaning this might allow you to solve your problem. You'd need to design a custom objective function that minimizes some kind of error term between your new coefficients and the existing coefficients, subject to the constraint that data point 1 and data point 2 are local maxima.
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Richard Willey le 24 Fév 2012
From the looks of things, your daily load curve is a particular example of a second order Fourier series.
If you have Curve Fitting Toolbox, its pretty easy to generate a fit. If you don't have Curve Fitting Toolbox, you can solve this same equation using nlinfit in Stats or lsqcurvefit in Optim. However, in either case you'll need to provide starting conditions. (Curve Fitting Toolbox is able to automatically compute the starting conditions for the solvers)
%%Generate a set of random data
X = linspace(1,10,100);
X = X';
% Specify the parameters for a second order Fourier series
w = .6067;
a0 = 1.6345;
a1 = -.6235;
b1 = -1.3501;
a2 = -1.1622;
b2 = -.9443;
Y = a0 + a1*cos(X*w) + b1*sin(X*w) + a2*cos(2*X*w) + b2*sin(2*X*w);
foo = fit(X,Y, 'Fourier2')
Please note: You mention that the only data points that you have available are the peaks in the data series. I'd be leery about using the resulting model to predict anything other than the peak load...