Problem in fmincon solver
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Hello all,
My aim is to solve for complicated non linear system of equations defined as follows:
Unknown variables: epsi, da, dr, phi1, Jr, Ja
Known variables: alpha= 40 deg, Z=16, Kn=4.5080*10(^5), Fr=Fa=17800
Equations are defined as follows:
epsi = 0.5 * (1 + da*tan(alpha) / dr)
phi1 = cosinv (-da*tan(alpha) / dr)
Jr=integration from -phi1 to phi1 of (1/(2*pi)) * (1 - (0.5/epsi) * (1-cos(theta) ) )^(1.5) * cos(theta)
Ja=integration from -phi1 to phi1 of (1/(2*pi)) * (1-(0.5/epsi) * (1-cos(theta) ) )^(1.5)
Fr / Fa = (Jr * cos(alpha)) / (Ja * sin(alpha))
To solve for these system of equations I am using fmincon function available in matlab..
My Matlab code is as follows:
Z=16, KN1=4.5080e5; Fr=Fa=17800; alpha=40;
%optimization for load distribution
%KN1=Kn(5);
%for i=1:1:length(Kn)
[dr, Epsi]=opt();
function [dopt,EPSI] = opt()
dr0=[0.08; 0.1];
lb=[0, 0];
ub=[1, 1];
Options=optimset('Algorithm','active-set','Display','Iter');
dopt=fmincon(@myfun,dr0,[],[],[],[],lb,ub,@mycon,Options);
EPSI=myfun(dopt);
end
function epsi=myfun(dr)
epsi=0.5*(1+dr(1)*tand(alpha)/(dr(2)));
end
function [c,ceq]=mycon(dr)
c=abs(-dr(1)*tand(alpha)/dr(2))-1;
phi1=acos(-dr(1)*tand(alpha)/dr(2));
epsi=0.5*(1+(dr(1)*tand(alpha)/dr(2)));
c=-1+(0.5/epsi).*(1-cos(phi1));
funr=@(theta)(1/(2*pi)).*(1-(0.5/epsi).*(1-cos(theta))).^(1.5).*cos(theta);
Jr=quad(funr,-phi1,phi1);
funa=@(beta)(1/(2*pi)).*(1-(0.5/epsi).*(1-cos(beta))).^(1.5);
Ja=quad(funa,-phi1,phi1);
ceq=real(Jr)*cosd(alpha)/(real(Ja)*sind(alpha))-Fr/Fa;
%c=[];
end
When I run this code, I am getting the optimized value of dr as [-0.0001, 0.0011]. This value is clearly beyond limiting values of dr. I am specifying lower bound of dr as [0,0]. I am unable to understand why Matlab is not considering specified boundaries. As well, my final answer is dependent on initial guess. If I change my initial guess then my final answer changes. Can somebody please help to resolve these issues??
Thanks in advance,
Nikhil
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