MATLAB: Fitting Curve To Temperature Data

curve fittingpolyfit

I am trying to fit a curve to temperature data taken over over a period of 48 hours. Looking at this data it seems to osculate similar to a sin function, but I am unsure how to fit a sinus to to this data. I have tried using the polyfit function, but none of those can give me an oscillating function. I have attempted to use a sine curve fitting code found here on MATLAB answers, but have ran into errors. I have attached the data sets I am using. Here is the code I am attempting to use:

yu = max(temp1);
yl = min(temp1);
yr = (yu-yl);                               % Range of ‘y’
yz = temp1-yu+(yr/2);
zx = time_hours(yz .* circshift(yz,[0 1]) <= 0);     % Find zero-crossings
per = 2*mean(diff(zx));                     % Estimate period
ym = mean(temp1);                               % Estimate offset
fit = @(b,time_hours)  b(1).*(sin(2*pi*time_hours./b(2) + 2*pi/b(3))) + b(4);    % Function to fit
fcn = @(b) sum((fit(b,time_hours) - temp1).^2);                              % Least-Squares cost function
options = optimset('MaxFunEvals',100000,'MaxIter',100000);
s = fminsearch(fcn, [yr;  per;  -1;  ym],options)                       % Minimise Least-Squares
xp = linspace(min(time_hours),max(time_hours));
figure(1)
plot(time_hours,temp1,'b',  xp,fit(s,xp), 'r')
grid

I keep getting Nan for s(3) no matter how high I increase MaxFunEvals. The only toolbox I have at my disposal is the Symbolic Math Toolbox. Any suggestions to finding a good fitting oscillating function would be greatly appreciated! Thanks.

Best Answer

You have several options, depending on what you want to do. One is: Curve fitting to a sinusoidal function (link), another is the interpft (link) function.

Related Solutions

MATLAB: Curve fitting to a sinusoidal function

Here’s my suggested solution, using only core MATLAB functions:

yu = max(y);
yl = min(y);
yr = (yu-yl);                               % Range of ‘y’
yz = y-yu+(yr/2);
zx = x(yz .* circshift(yz,[0 1]) <= 0);     % Find zero-crossings
per = 2*mean(diff(zx));                     % Estimate period
ym = mean(y);                               % Estimate offset
fit = @(b,x)  b(1).*(sin(2*pi*x./b(2) + 2*pi/b(3))) + b(4);    % Function to fit
fcn = @(b) sum((fit(b,x) - y).^2);                              % Least-Squares cost function
s = fminsearch(fcn, [yr;  per;  -1;  ym])                       % Minimise Least-Squares
xp = linspace(min(x),max(x));
figure(1)
plot(x,y,'b',  xp,fit(s,xp), 'r')
grid

The elements of output parameter vector, s ( b in the function ) are:

s(1): sine wave amplitude (in units of y)

s(2): period (in units of x)

s(3): phase (phase is s(2)/(2*s(3)) in units of x)

s(4): offset (in units of y)

It provides a good fit.

MATLAB: Damped cosine features in a exponential decay

This produces a reasonable approximation, however the signal appears to be changing its frequency toward the end:

D = load('Ampf.mat');
t = D.Ampf(:,1);
s = D.Ampf(:,2);
s = detrend(s,7);
yu = max(s);
yl = min(s);
yr = (yu-yl);                                                                   % Range of ‘y’
yz = s-yu+(yr/2);
zt = t(yz(:) .* circshift(yz(:),[1 0]) <= 0);                                   % Find zero-crossings
per = 2*mean(diff(zt));                                                         % Estimate period
ym = mean(s);                                                                   % Estimate offset
fit = @(b,x)  b(1) .* exp(b(2).*x) .* (sin(2*pi*x./b(3) + 2*pi/b(4))) + b(5);   % Objective Function to fit
fcn = @(b) norm(fit(b,t) - s);                                                  % Least-Squares cost function
B = fminsearch(fcn, [yr; -1;  per;  -1;  ym])                                   % Minimise Least-Squares
xp = linspace(min(t),max(t));
yp = fit(B,xp);
figure
plot(t, s, '-p')
hold on
plot(xp, yp, '-r')
hold off
grid

It may be necessary to change ‘fit’ to something more closely approximating the process that produced your data. Retain the detrending step in the code.

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