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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

Rik
on 24 Feb 2020

Edited: Rik
on 24 Feb 2020

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

Alex Sha
on 25 Feb 2020

Hi, toon, how about the model function below:

z = (p1+p2*x+p3*x^2+p4*y+p5*y^2)/(1+p6*x+p7*x^2+p8*x^3+p9*y+p10*y^2);

where x: speedvector, y:Power

Root of Mean Square Error (RMSE): 0.00691844326129822

Sum of Squared Residual: 0.007036134002491

Correlation Coef. (R): 0.998274976728469

R-Square: 0.996552929162226

Adjusted R-Square: 0.996480612990804

Determination Coef. (DC): 0.996552929142504

Chi-Square: 0.0077055307148613

F-Statistic: 4400.72826907425

Parameter Best Estimate

---------- -------------

p1 0.819461830220929

p2 -0.00987471483675952

p3 0.000133551058989172

p4 0.103028178545445

p5 0.00153694829659665

p6 0.00317128381400631

p7 9.70005191197044E-5

p8 3.74684931649973E-6

p9 0.0777991586491392

p10 0.00764599134548915

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