Optimise a reference that cuts my curve into 2 equal sections

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fadi awar 2022-2-12

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编辑： Matt J 2022-2-12

Hello,

I am collecting data from excel, then basic idea is that i want to determine a constant value line that cuts my curve into 2 eqaual sections (area above the line and the curve = area under).

The objective is to determine the value of the red line.

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Matt J 2022-2-12

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https://ww2.mathworks.cn/matlabcentral/answers/1648335-optimise-a-reference-that-cuts-my-curve-into-2-equal-sections#answer_894710

编辑：Matt J 2022-2-12

在 MATLAB Online 中打开

 %t= time, X=consumption, x=unknown midline
 
 tc=t-t(1);
 Xc=cumtrapz(t,X);
 
 x=optimvar('x');
 sol=solve( optimproblem('Objective',x,'Constraints',Xc-x*tc<=90,'ObjectiveSense','minimize') );
 lb=sol.x; %lower bound
 sol=solve( optimproblem('Objective',x,'Constraints',10<=Xc-x*tc,'ObjectiveSense','maximize') );
 ub=sol.x; %upper bound
 
 if lb>ub
  disp 'Problem is infeasible'
 else
     
  xunc=trapz(t,X)/(t(end)-t(1)); %unconstrained solution
  
  x=min(max(xunc,lb),ub); %constrained solution
  
 end

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Matt J 2022-2-12

编辑：Matt J 2022-2-12

You probably need to upgrade your Matlab version.

If you cannot upgrade, you can try my revised version.

fadi awar 2022-2-12

Yeah, this one worked.

Thank you for your help!

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William Rose 2022-2-12

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https://ww2.mathworks.cn/matlabcentral/answers/1648335-optimise-a-reference-that-cuts-my-curve-into-2-equal-sections#answer_894530

@fadi awar,

If you mean that the area between the red line and the blue curve abve the line equals the area between the red line and the blue curve below the line, then the height of the red line is simply the mean value of the blue line data.

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dpb 2022-2-12

Attach the data as a .mat file.

Just looking at the graph, I'd venture it isn't possible to meet the constraints that the integral of the area be <95 when the magnitudes of the integrand are in the thousands. Just by a very crude approximation of the leftmost area (brown?) as roughly a rectangle of height ~(2800-1800) and a duration of 12, the integral would be roughly 1000*12 --> 12,000. Unless there's a very small scaling factor to be applied, it "just ain't a-gonna' happen".

fadi awar 2022-2-12