Contents
clear all;
clc;
experiment data prepare
load experiment data
xe=[ 20 30 40 50 60 70 80 90 100];
ye=[ 5.15689154037705 0.928210336705772 0.700609434233889 0.704872737425338 ...
0.929915657982351 1.08311696243415 1.23512850785578 0.790118971937154 0.3996003996004];
r = 1300;
normalization of the data
ysum=sum(ye,2);
yenorm=ye/ysum;
Approximation
pstart=[15.9979606024077,0.377418721825493,14.2739695461521,30.5699098632726,1.11502799929318,1.24510665791401;];
[params,fval] = fminsearch(@(par)odeesol(par,xe,r,yenorm),pstart, optimset('TolX',1e-10,'TolFun',1e-10, 'MaxFunEvals', 1e8, 'MaxIter', 3e3, 'PlotFcns', @optimplotfval,'Display','iter'));
Iteration Func-count min f(x) Procedure
0 1 0.0946399
1 7 0.0946399 initial simplex
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Optimization terminated:
the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-10
and F(X) satisfies the convergence criteria using OPTIONS.TolFun of 1.000000e-10
data output
k01=params(1);
k02=params(2);
f2=params(3);
phi0=params(4);
f12=params(5);
f1=params(6);
[TOUT,YOUT] = ode45(@(t,y) -(phi0*k01*exp(t/f1)+exp(t/f12)*exp(t/f2)*k02)/(phi0+exp(t/f12))*y/r,xe,1);
y_f=((phi0*k01.*exp(TOUT./f1)+exp(TOUT./f12).*exp(TOUT./f2).*k02)./(phi0+exp(TOUT./f12))).*YOUT/r;
y_f=y_f/sum(y_f,1);
figure(1)
plot(xe,y_f*ysum,'r+-',xe,ye,'ko-','LineWidth',2);
set(gca,'FontSize',16);
xlabel('Rupture force (pN)');
ylabel('Frequency (%)');
