Multivariate Nonlinear Problem With vector & matrix unknown inputs

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Ahmed Ghamdi 2019-9-21

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https://ww2.mathworks.cn/matlabcentral/answers/481464-multivariate-nonlinear-problem-with-vector-matrix-unknown-inputs

评论： Matt J 2019-9-27

采纳的回答： Matt J

Hello,

Problem description:

I have oil flow rate observed (qo_obs) and I have a model to calculate oil flow rate (qo_cal).

The model to find qo_cal is somewhat complex, and it invloved three unknowns: f, tau, and V.

f is a 9x16 matrix, tau is a 9x1 vector, V is a 9x1 vector.

each of the unkowns above has its own constraints, such as:

Sum of every column of f = 1, (How do I even write this constraint?)

any tau >0

0< V<C, where C is some constant I know.

Now I want to find the values of these unkowns that will yield minimum of (qo_obs-qo_cal)^2

What solver to use? and how?

Thanks,

采纳的回答

Matt J 2019-9-21

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/481464-multivariate-nonlinear-problem-with-vector-matrix-unknown-inputs#answer_392904

编辑：Matt J 2019-9-21

在 MATLAB Online 中打开

It's very easy to set up all the variables and constraints with the problem-based approach.

f=optimvar('f',[9,16]);
tau=optimvar('tau',[9,1],'LowerBound',zeros(9,1));
V=optimvar('V',[9,1],'LowerBound',0,'UpperBound',C);
prob=optimproblem('ObjectiveSense','minimize');
prob.Constraints.fconstraint=sum(f)==1;
prob.Objective=_____________

Once you've defined your objective, just do

sol=solve(prob)

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Ahmed Ghamdi 2019-9-23

在 MATLAB Online 中打开

Hey Matt, thanks for following up,

I have found out how to get the values of f, I need to type

sol.f

and if I want a particular value of f, say f(1,1) I type

sol.f(1,1)

But my problem is that now I try to find values of the other optimized values, tau and Vp, when I type sol.tau or sol.Vp I get

>> sol.tau
Reference to non-existent field 'tau'.
>> sol.Vp
Reference to non-existent field 'Vp'.

Below is my code

%% Assume values for f & tau
f = zeros(9,16);
tau = zeros(9,1);
for i=1:9
    tau(i,1) = 10;
    for j=1:16
    f(i,j) = 0.1111;
    end
end
%% Assume values for Vp
Vp = zeros(9,1);
for j=1:9
        Vp(j) = 10^5;
end
%% Start calculating oil rate
for j=1:9
    for k=2:120
        krw(k,j) = krw_endpoint*((Sw(k,j)-Swr)/(1-Swr-Sor))^n1;
        kro(k,j) = kro_endpoint*((1-Sw(k,j)-Sor)/(1-Swr-Sor))^n2;
        fw(k,j) = (krw(k,j)/uw)/((krw(k,j)/uw)+(kro(k,j)/uo));
        fo(k,j) = 1-fw(k,j);
        Mt(k,j) = krw(k,j)/uw+kro(k,j)/uo;
        for i=1:16
            press_sup(i) = f(j,i)*All_Inj_qw(k,i); %here i use f
        end
        summation = sum(press_sup);
        qt(k,j) = qt(k-1,j)*exp((-dt(k))/(tau(j)/Mt(k,j)))+(1-exp((-dt(k))/(tau(j)/Mt(k,j))))*summation; %here I use tau
        qo(k,j) = qt(k,j)*fo(k,j);
        So_avg(k,j) = So_avg(k-1,j)-dt(k)/Vp(j)*(((So_avg(k-1,j)*(cf+co))/ct)*(summation-qt(k,j))-qo(k,j)); %here I use Vp
        Q(k) = (Q(k-1)+summation)/Vp(j);
        So_outlet(k,j) = So_avg(k-1,j)+Q(k)*(1-fw(k,j));
        Sw(k+1,j) = 1-So_outlet(k,j);
    end
end
%% Calculate Error
for j=1:9
    for k=1:120
        Error(k,j) = (qo(k,j)-All_Prod_qo(k,j))^2;
    end
end
Total_Error = sum(Error);
%% Optimization Problem for finding optimized f,tau, and Vp
prob=optimproblem('ObjectiveSense','minimize');
f=optimvar('f',[9,16],'Type','continuous','LowerBound',0,'UpperBound',1);
tau=optimvar('tau',[9,1],'Type','continuous','LowerBound',zeros(9,1));
Vp=optimvar('Vp',[9,1],'Type','continuous','LowerBound',0,'UpperBound',1.6895e+07);
prob.Constraints.fconstraint=sum(f)==1;
prob.Objective = Total_Error;
sol = solve(prob);

Also, when I check my problem by typing

show(prob)

this what comes out

>> show(prob)
  OptimizationProblem : 
	Solve for:
       f
	minimize :
       1703960721.818
       

why isn't MATLAB solving for tau and Vp, why only f?

Ahmed Ghamdi 2019-9-27

Thanks Matt,

my code is working fine, but fmincon takes 7 hours to run. Is this normal? Also, are there more advanced algorathims better than fmincon?

Matt J 2019-9-27

There is no normal. It depends in part on how much time it takes to execute your Objective function code. I see in your code that you have done no vectorization at all - everything is done with for-loops. It is plausible to me that that would make execution time very long.

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