Optimization Function for Costs (fminbnd)

Hi,

I have to optimize the cost using the fminbnd function

I am getting a scalar error while the code runs the fminbnd function. Can anyone help me debug

%%An example of Matlab code
clc;clear;
format long;

%%Constants
hf_H2   = 0;
hf_O2   = 0;
hf_H2Og = -244820;
sf_H2   = 130.68;
sf_O2   = 205.14;
sf_H2Og = 188.72;
cp_H2O  = 33.7;
cp_H2   = 29.5;
cp_O2   = 329.0;
Tref    = 298;
Ru      = 8.314;
T       = 353;
n       = 2;
F       = 96487;
p_H2    = 1;
p_O2    = 0.21;
a_H2O   = 1;
po      = 1;
delT    = T-Tref;

%%Calculate Nerst Reversible Cell Potential

% Calculate Gibbs Free Energy
delH = hf_H2Og+cp_H2O*delT - (hf_H2+cp_H2*delT) - 0.5*(hf_O2+cp_O2*delT);
delS = sf_H2Og+cp_H2O*log(T/Tref) - (sf_H2+cp_H2*log(T/Tref)) - 0.5*(sf_O2+cp_O2*log(T/Tref));
delG = delH - (Tref * delS);

% Reversible voltage
Ero = -delG/(n*F);

% Nerst Expression for voltage
Eo=Ero+(Ru*T/n/F)*log((p_H2/po)*(p_O2/po)^0.5);

%%Populating matrix for calculations
V_mdl = @(a,I)(Eo-Ru*T/F*log((I+a(4))/a(1))+Ru*T/2./F*log((a(2)-(I+a(4)))/a(2))-I*a(3));
I_exp = [0,2.5,5,10,20,40,60,80,100,200,400,600,800,1000,1200];
V_exp = [0.986615,0.950774,0.951704,0.916295,0.910731,0.90338,0.857798,0.853067,0.851497,0.799984,...
    0.730907,0.689608,0.638525,0.57848,0.440924];
Irange = min(I_exp):1:max(I_exp);

%%Initial guess & Brute-force minimize error function

a(1)=0.5; %Io: Reference exchange current density mA/cm2
a(2)=1200.00; %I_lim: Limiting current density mA/cm2
a(3)=2.5e-4; %total resistance kohm*cm2
a(4)=21.0; %cross-over current density mA/cm2

g = @(a) norm(V_mdl(a,I_exp)-V_exp);
ahat = fminsearch(g,a); % Values Calculated
V_cell = @(I) V_mdl(ahat,I);

%%Plotting and figures
figure(1)
scatter(I_exp,V_exp,'ok','MarkerFaceColor','b')
hold on
plot(Irange,V_cell(Irange),'-r','linewidth',2)
grid on
title('H_{2} - O_{2} Proton Exchange Membrane Fuel Cell - Voltage vs Current Density')
xlabel('Current Density [i, mA/cm^2]')
ylabel('Voltage [V]')
legend('Polarization Curve','Location', 'Best');
R=V_cell(Irange);

%%Calculation of power
i=0;
P_out=zeros;
for j=1:1201
    P_out(j)= V_cell(j)*i;
    i=i+1;
end
Pmax=max(P_out);

%%Plotting Power
figure(2)
hold on
title('H_{2} - O_{2} Proton Exchange Membrane Fuel Cell Power')
xlabel('Current Density [i, mA/cm^2]');
ylabel('Power Density [W/cm^2]');
plot(Irange,P_out,'-b','linewidth',2);
legend('Power Curve','Location', 'Best');
grid on
axis([0 1200 0 600])
Max_Power=max(P_out)
Max_cdp=Irange(P_out==Max_Power)

%%Calculation of Efficiency
i=0;Eta_tot=zeros;
for j=1:1201
    Eta_fc=(V_cell(j)/Eo);
    Eta_fuel=(i/(i+ahat(4)));
    Eta_tot(j)=Eta_fc*Eta_fuel;
    i=i+1;
end
Current=zeros;
for j=1:1201
P_kWh_req=80000*100;
P_kWh_fc=80000/1000*Max_Power;
Area_fc=P_kWh_req/P_kWh_fc;
Install_cost(j)=Area_fc*1500*10000;

Current(j)=j*Area_fc/1000/(j/(j+ahat(4)));
Mol_H2(j)=j*80000*3600/2/96458;
Mass_H2=Mol_H2(j)*2/1000;
Fuel_cost(j)=Mass_H2*4;

end

%%Plotting Efficiency
figure(3)
hold on
title('H_{2} - O_{2} Proton Exchange Membrane Fuel Cell Efficiency')
xlabel('Current Density [i, mA/cm^2]');
ylabel('Efficiency [\eta]');
plot(Irange,Eta_tot,'-r','linewidth',2);
legend('Efficiency Curve','Location', 'Best');
grid on
axis([0 1200 0 1])
Max_Eff=max(Eta_tot)
Max_cde=Irange(Eta_tot==Max_Eff)

%%Optimize(minimize) Cost
for j=1:1201
f=@(j) Install_cost+Fuel_cost ;
[low,high]=fminbnd(f,1,1201)
end

Answer 1

[John D'Errico]

READ THE ERROR MESSAGE!

fminbnd expects scalar input, and the function MUST return scalar output.

numel(f(1))
ans =
        1201

Does f return a scalar? NO.

Return to step 1. READ THE ERROR MESSAGE. Think about what it is telling you. While I have no idea what the function f SHOULD be doing, it is not doing what fminbnd expects.

Admittedly, I also have no idea what you think lines like this are there for:

j=linspace(0,1200,1)
j =
      1200

So for someone else to try to debug code that has random statements in it like that is next to impossible.

[DIP]

f takes 2 vectors as arguments. i cant really understand,im fairly new to matlab.

[DIP]

the two costs I need to optimize are in the form of two 1x1201 vectors .

[DIP]

i used a counter linspace j because the value of the costs depend on current j.

[DIP]

for f function -> Install_cost and Fuel_cost are two vectors whose sum needs to be minimized. I have no clue how to do so. The section till the calculation of these variables is correct but I cant find a way to minimize the sum.

[DIP]

Maybe I have defined the function handle wrongly. ive tried all combinations but i keep getting errors

[DIP]

What i basically need is to debug this part of the code

for j=1:1201
f=@(j) Install_cost+Fuel_cost ;
[low,high]=fminbnd(f,1,1201)
end