Why fmincon does not minimize the objective function

Dear all, I have experiment data X1+X2, where in the model x_1=F/K1, F=K2*x_2+T*K2*x_2(dot), x_2(dot) is the first derivative of x_2 with respect to time. I want to determine the parameters K1,K2. F is the force from the experiment. so I determine x_2 by using Rung-Kutta 4th order method by proving initial condition of K2 and also for K1 for x_1. After getting x_1 and x_2 from initial guess of K1,K2, I find the error between experiment and model by e=(x1+x2) (experiment)-(x_1+x_2)(model). Then I use fmincon to minimize this error. Unfortunately, fmincon doesn't work. It doesn't minimize the error and it keeps value of K1,k2 the same as initial condition (There is no error in my code, fmincon runs but it just doesn't minimize error). Thus could you please help me related to this problems, I am looking forward to hearing from all of you soon. I will send you by matlab code if it is needed.

Best regards; S. Van

[Christoforos Rekatsinas]

Hello,

Did you manage to solve the problem?

Answer 1

[Walter Roberson]

fmincon is a local minimizer, not a global minimizer. If the initial conditions are even just slightly more favorable than the immediately adjacent locations, then fmincon may get stuck there.

We would need your code to make more detailed suggestions.

[Van S]

Thank you very much for your suggestion . Here is my code

function [estimate,model,existflag,fval,funcCount]=parameter_prediction(t,f,K1,K2,X_loading)
options=optimset('MaxFunEvals',1e6,'MaxIter',1e5,'TolFun',1e-27,'TolX',1e-27,'Display','iter','Algorithm','sqp','PlotFcns' , @ optimplotfval);
 model=@parameters;
 start_point=[K1 K2];
 lb=[0 0];        
 ub=[];  
 A=[];
 b=[];
 Aeq=[];
 beq=[];
 nonlcon=[];
 global j h T
 [estimate,fval,existflag,output]=fmincon(model,start_point,A,b,Aeq,beq,lb,ub,nonlcon,options); 
  funcCount=output.funcCount; 
  function[e,Fittedcurve]=parameters(para) 
         K1=para(1);
         K2=para(2);

      for i=1:j-1;
      F=@(y) (f/T*K2)-y/T; 
      y(1)=0;
      k_1=h*F(y(i));
      k_2=h*F(y(i)+k_1/2);
      k_3=h*F(y(i)+k_2/2);
      k_4=h*F(y(i)+k_3);
      y(i+1)=y(i)+(1/6)*(k_1(i)+2*k_2(i)+2*k_3(i)+k_4(i));
        x_1=f(1:i+1)/K1;   
      end
      X= x_1+y(i+1);
      Fittedcurve= X;    
      error1=Fittedcurve-X_loading; 
      sse1=(error1.^2);
      e=sum(sse1);
    end   
  end

This one is the main script :

clear all
close all
clc
global h j T
data=xlsread('Experiment data',1); % load data from excel
t=data(:,1); % load time
x=data(:,2); %load the displacement
f=data(:,3);% load the impact loading
N=length(t); % number of data 
fmax=max(f); % maximum force
xmax=max(x);  % maximum displacement
xlast=x(end); % displacement due to ratchet component
K3=fmax/xlast; % spring k3 in the ratchet component
j=find(f==fmax);
q=find(x==xmax);
t1=t(j); % time corresponding the maximum load
t2=t(q); % time corresponding the maximum displacement
T=t2(1)-t1(1); % delay time between loading and displacement
dt=t(2)-t(1);
x3_loading=f(1:j)./K3; % displacement of ratchet component at loading part
x3_unloading=xlast; % displacement of ratchet at unloading part
xloading=x(1:j); % total displacement at unloading part
x_12_loading=(xloading-x3_loading); % displacement at fast and slow component

K1=30; K2=25; C2=T*K2; % initial value for k1 and k2
h=dt;
y=zeros(j(1),1);
k_1=zeros(j(1),1);
k_2 =zeros(j(1),1);
k_3=zeros(j(1),1);
k_4=zeros(j(1),1);
[estimate,model,existflag,fval,funcCount]=parameter_prediction(t,f,K1,K2,x_12_loading);
[e,Fittedcurve]=model(estimate);
for i=1:j(1)-1     
    F=@(y) (f(i)/T*K2)-y/T; 
    k_1(i)=h*F(y(i));
    k_2(i)=h*F(y(i)+k_1(i)/2);
    k_3(i)=h*F(y(i)+k_2(i)/2);
    k_4(i)=h*F(y(i)+k_3(i));
    y(i+1)=y(i)+(1/6)*(k_1(i)+2*k_2(i)+2*k_3(i)+k_4(i));  
end
x_12=f(1:i+1)/K1+y;
plot(t(1:i+1),x_12)

hold on
Fittedcurve= x_12;
error=Fittedcurve-x_12_loading; 
sse=(error.^2);
e=sum(sse);    

plot(t(1:i+1),Fittedcurve,'r',t(1:i+1),sse,'b')
plot(t(1:i+1),x_12_loading) 
legend('x12 loading','Fitting','Error')

I am looking forward to hearing from you soon !

Best regards;

S. Van

[Walter Roberson]

You do not appear to be using fmincon ?

I think we will need some sample data.

[Van S]

I made a mistake for last time, now I have edited to use fmincon in my code. I could not attach my excel file. Could you please give me your email address. Thank you very much !

Best regards;

[Walter Roberson]

You can zip the data file and attach that.