A way to sort data using for loops and newton-rhapson calc so data can be readily called

Hello,

I have a program file that executes a Newton Rhapson script for a Heat Pump. I am trying to run two "for" loops for Ae and Ac for a range or parameters to optimize cost. I would like to be able to run the Ae and Ac loops, then have Ae, Ac, Cost, and the Newton solved parameters stored in a matrix. Once the "for" loops are done, then determine the row with the minimum cost and the associated parameters. The code is below:

if true
  % Program Constants
  maxiter = 50;
  epsilon = 0.001;
  nsys = 9;   %Number of System Equations (and unknowns)

    % System Constants
    toa = 0;     %Outside Air Temp, Deg C
    tea = 24;    %Exhaust Air Temp, Deg C
    woa = 5;     %Outside Air Flow Rate, kg/s
    wea = 5;     %Exhaust Air Flow Rate, kg/s
    tsupply = 35;%Supply Air Temp, Deg C
    Uc = 25;     %Condensor Heat Transfer Rate, W/m^2 K
    Ue = 25;     %Evaporator Heat Transfer Rate, W/m^2 K
    cpea = 1.006;%kJ/kg C
    cpoa = 1.006;%kJ/kg C
    for Ae = 1.58:0.01:1.7;
        for Ac = 1.48:0.01:1.6;

    % Define System Equations

     % Evaporator
     % wea*(tea-to)*cpea-Qe = 0
     F1 = @(x) wea*(tea-x(4))*cpea-abs(x(2));
     % tea+(te-tea)(1-exp((-Uc*Ae)/(wea*cpoa)))-t0 = 0
     F2 = @(x) tea+(x(5)-tea)*(1-exp((-Ue*Ae)/(wea*cpea)))-x(4);

     % Condensor
     % woa*(ti-toa)*cpoa-Qc = 0
     F3 = @(x) woa*(x(6)-toa)*cpoa-x(3);
     % toa+(tc-toa)(1-exp((-Uc*Ac)/(woa*cpoa)))-ti = 0
     F4 = @(x) toa+(x(7)-toa)*(1-exp((-Uc*Ac)/(woa*cpoa)))-x(6);

     % Compressor
     % W + Qe - Qc = 0
     F5 = @(x) x(1)+abs(x(2))-x(3);
     % Qe/W-COP = 0
     F6 = @(x) (abs(x(2))/x(1))-abs(x(8));
     % 7.24+0.352te-0.096tc-0.0055tetc-COP = 0
     F7 = @(x) 7.24+0.352*x(5)-0.096*x(7)-0.0055*x(5)*x(7)-abs(x(8));

     %Resistance Heating
     % woa*(tsupply-ti)*cpoa-Qr = 0
     F8 = @(x) woa*(tsupply-x(6))*cpoa-x(9);

     % Overall System Energy Balance
     % W+Qe-Qc-Qr = 0
     F9 = @(x) x(1)+abs(x(2))-x(3)-x(9);

     %Construct Matrix F
     F = {F1,F2,F3,F4,F5,F6,F7,F8,F9};

     % Initial Guesses and Construction of Matrix x
     x(1) = 3;     %W
     x(2) = 3;     %Qe
     x(3) = 3;     %Qc
     x(4) = 11;    %to
     x(5) = 10;    %te
     x(6) = 9;     %ti
     x(7) = 10;    %tc
     x(8) = 2;     %COP
     x(9) = 1;     %Qr
     %Iterative calculations
     nloop=0;
     nconverg=0;
     i = 1;

     while nloop<maxiter

     %Derivative Matrix
     dFidxj=zeros(nsys,nsys);

         for i=1:1:nsys
             for j=1:1:nsys

            fx=F{i};
            xj=x;

            %Function after the point
            xj(j)=x(j)+epsilon/2;
            y1=fx(xj);

            %Function before the point
            xj(j)=x(j)-epsilon/2;
            y0=fx(xj);

            %Derivation in the point
            dFidxj(i,j)=(y1-y0)/epsilon;
        end
    end
    for i=1:1:nsys
       j=F{i};
       D(i,1)=j(x);
    end
    %Calculate Error    
    A=inv(dFidxj);
    error=A*D;
    dx=error';
    %Finding new iteration    
    x=x-dx;
        %While loop counter        
        nloop=nloop+1;
        nconverg=nconverg+1;

Converging criteria (error < epsilon)

        maxdx=max(abs(error));

        if maxdx<epsilon
            nloop=maxiter;
        end
    end    
    i = i + 1;

    Cost = 50*Ae+50*Ac+120*x(1)+0.03*4000*6.145*(x(9)+x(1))
    end
end

end

I would like the data to be stored such that column one is Cost, Column Two is the value of Ae, Column three the value of Ac, etc for all parameters. My attempts at this have not gone so well. Does anyone know of a means to do this?

Thanks

Answer 1

[Guillaume]

With this sort of question, it's better to reduce your code sample to the minimum required to understand the question. I've skimmed most of it but I believe this is what you want:

AeValues = 1.58:0.01:1.7;
AcValues = 1.48:0.01:1.6;
numParameters = 3 %other than cost, Ac, Ae. For you to replace
CostAndParams = zeros(numel(AeValues)*numel(AcValues), 3 + numparameters);
rowindex = 1;
for Ae = AeValues
   for Ac = AcValues
      %... do your calcs ... 
      Cost = ...
      CostAndParams(rowindex, :) = [Cost Ac Ae ...]; %replace ... by other parameters
      rowindex = rowindex + 1;
   end
end

Afterward, I would store the data in a table to make it more explicit what the columns are:

CostTable = table(CostAndParams, 'VariableNames', {'Cost', 'Ac', 'Ae', ...});

Answer 2

[Galen]

Guillaume, this worked great. Thanks!