MATLAB: How to fit this data

curve fittingdata fittingfitnlmMATLAB

Hi everyone,
I am struggling with the following problem:
I have a dataset (Map3D.mat file is included) for which I am trying to fit a function where I have 3 variables and one value for a combination of these 3 variables.
The variables are engine power, altitude and speed. The value is the fuel consumption of the engine. I want to fit this fuel consumption data with a function in such a way that engine power, altitude and speed are input variables and fuel consumption is the output variable. Is this possible? I have been trying stuff with fitnlm but I cannot get it working. I dont get how I can change my data structure to the required format. The Map3D.mat file is structured as follows: 7x21x4 (speed x power x altitude). With a speedvector from as Speed = 0:10:60, a powervector as Power = 5:10:205 and an altitudevector as Altitude = [0 300 600 700].
Currently I found a workaround with the interp3 function which works okay, however it increases the computation time of my code significantly compared to a function evaluation because it gets called often as it is within an iteration loop. I also expect my code to converge faster with a function which fits the desribed dataset.
I am really looking forward to see what you guys think!
Toon

Best Answer

Your model function contains some redundant terms that should be merged. Below you find the code to estimate your parameters and how to use that fit. Note that your model returns inf for most parameter sets for the cases where speed is 0. How to deal with that is up to you.
You should note that fminsearch is fairly sensitive to the initial guess, so if you have better ones you might not even have to remove the speed==0. It is also possible to implement bounds by letting the OLS return inf for fit values outside of an allowed range.
%load data from mat file
Map3D=load('Map3D');Map3D=Map3D.Map3D;
Speed = 0:10:60;
Power = 5:10:205;
Altitude = [0 300 600 700];
[S,P,A]=ndgrid(Speed,Power,Altitude);
%remove all speed==0 since that returns a value of inf when evaluated
L_speed_nonzero=S~=0;
[P,S,A,Map3D]=deal(P(L_speed_nonzero),S(L_speed_nonzero),...
    A(L_speed_nonzero),Map3D(L_speed_nonzero));
b_initial_guess=[-10 0.1 -200 -0.05 50 40];
%objective least squares function (requires scalar/vector input)
OLS=@(b,x,y,z,v) sum((MyFun(b,x,y,z) - v).^2);
opts = optimset('MaxFunEvals',50000, 'MaxIter',10000);
% Use fminsearch to minimise the 'OLS' function
b_fitted=fminsearch(OLS, b_initial_guess(:), opts,S(:),P(:),A(:),Map3D(:));
clc
fprintf('b_fitted=[')
fprintf('%.4e ',b_fitted)
fprintf('];\n')
%%
%you can calculate the predicted values like this:
%(copied from before, but you should keep it as a variable)
b_fitted=[1.6348e+02 1.0524e-05 -3.2690e-03 6.0934e-08 -1.8714e-04 5.3567e-01 ];
Speed = 0:10:60;
Power = 5:10:205;
Altitude = [0 300 600 700];
[S,P,A]=ndgrid(Speed,Power,Altitude);
predicted_value=MyFun(b_fitted,S,P,A);
%check quality of fit:
real_value=load('Map3D');real_value=real_value.Map3D;
delta=predicted_value-real_value;
delta(i
sinf(delta))=[];
fprintf(['difference between non-inf fitted values and true values ',...
    'is:\nmean= %.2e\nabs max= %.2e\n\n'],mean(delta),max(abs(delta)))
function val=MyFun(b,Power,Speed,Altitude)
% val = Power.^-b(1) ...
%     +b(2) ...
%     +b(3)*Speed.^2 ...
%     +b(4).*Speed ...
%     +b(5) ...
%     +b(6)*Altitude.^2 ...
%     +b(7)*Altitude ...
%     +b(8);
val = Power.^-b(1) ...
    +b(2)*Speed.^2 ...
    +b(3).*Speed ...
    +b(4)*Altitude.^2 ...
    +b(5)*Altitude ...
    +b(6);
end
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