Fminsearch results shows shift from measured curve. How should I solve this?

Question

Amit Das 2023-1-23

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1898920-fminsearch-results-shows-shift-from-measured-curve-how-should-i-solve-this

编辑： Matt J 2023-1-23

I am working with several measurement data which I am reading through matlab and then using Fminsearch to estimate through different model equations to fit with the measurement data. But fminsearch is giving a shift from the measured data as shown in picture. Blue one is the measured curve and orange one is the fminsearch estimation. How should I solve this? I am a beginner so would be helpful with some guidance. Thank you.

My sample of fminsearch:

4 个评论
显示 2更早的评论隐藏 2更早的评论

Amit Das 2023-1-23

编辑：Matt J 2023-1-23

在 MATLAB Online 中打开

I am getting the position and torque values from measurement and then trying to fit the curve with the models. The fminsearch:

sigma_2  = 6.0672e-4;
Fc = 0.6339;
Fs = 2.235;
vs = 87.1746;
Delta=abs(-0.6732);
%             Delta=2.567;
F=torque;
Unrecognized function or variable 'torque'.
ts=1e-3;
%%speed calculation
speed=zeros(length(position)-1,1);
for j=2:1:length(position-1)
    speed(j)=(position(j)-position(j-1))/(time(j)-time(j-1));
end
%%plot
figure(3);plot(time, speed);hold on;
grid on;
xlabel('time in s'); 
ylabel('speed in 1/min'); 
plot(time, position);hold on;
grid on;
xlabel('time in s'); 
ylabel('position in m'); 
v = speed;
%% 2. Identification of LuGre Parameters
%% 2.1 Set starting values for optimization
x_Start=[0.4;0.4];
%% 2.2. Define Fitness-Function
erf=@(x)FitFunction_LuGre(x,Fc, Fs,vs,Delta,sigma_2,time,v, F);
%% 2.3. Perform Optimization
%% 2.3.1 Set Options for NM-Optimizer 
options = optimset('TolX',1e-50,'TolFun',1e-50,'MaxIter', 200000, 'MaxFunEvals', 200000,'PlotFcns',@optimplotfval);
%% 2.3.2 Optimize
[x,fiterr,exitflag,info]=fminsearch(erf,x_Start,options);
sigma_0_est=x(1)
sigma_1_est=x(2)
%% 3. Calculate and plot estimation
%% 3.1 Calculate LuGre
z=0;
for j = 1 : length(time)
    [F_est(j), z] = EQLugre(z, v(j), Fc, Fs, vs, Delta, sigma_0_est, sigma_1_est, sigma_2, ts);
end
figure(2);
plot(time,F_est');hold on;
grid on;
xlabel('time in s'); 
ylabel('Friction Force in Nm'); 
figure(1);
plot(position,F_est');hold on;
grid on;
xlabel('position in m'); 
ylabel('Friction Force in Nm'); 
Fit Function:
function F=FitFunction_LuGre(x,Fs,Fc,vs,Delta,sigma_2,time,speed,torque)
z=0; % Starting value z
ts=time(2)-time(1);
for j = 1 : length(time)
    [M(j), z] = EQLugre(z, speed(j), Fc, Fs, vs, Delta, x(1), x(2), sigma_2, ts);
end
[row_torque,col_torque]=size(torque);
[row_M,col_M]=size(M);
if(row_torque==row_M)&&(col_torque==col_M)
    M=M;
else
    M=M';
end
F=sum(abs(torque-M)).^2;
end

Eq:

function [F, z] = EQLugre(z, v, Fc, Fs, vs, Delta, sigma_0, sigma_1, sigma_2, ts)
r = -(v/vs).^Delta;
g_v = (Fc + (Fs - Fc) * exp(r)) ./ sigma_0;          % eq. 4
z_dot = v - abs(v) .* z ./ g_v;                      % eq. 1 
% note, this is forward euler integration. Your results depend heavily on the size of ts. - Jason Nicholson
z = z + z_dot.* ts;
F = sigma_0 * z + sigma_1 * z_dot + sigma_2.*v;    % eq. 3
end

Matt J 2023-1-23

As you can see above, the code doesn't run. SOme variables have not been specified.

Amit Das 2023-1-23

FrcitionAverage.xlsx

Hi the values needed to run the codes can be found in this excel file. Just run and plot should help.

% Read Measurements

[daten, header]=xlsread("your path");

time =daten(:,1);

position = daten(:,2);

torque = daten(:,3);

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Matt J 2023-1-23

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1898920-fminsearch-results-shows-shift-from-measured-curve-how-should-i-solve-this#answer_1154295

编辑：Matt J 2023-1-23

The x_Start=[1,1] selection looks very arbitrary. If one of the parameters is the oscillation amplitude, it should be closer to 0.4.

Other than that, though, there is too little information to diagnose. We would need to see the full code including the FitnessFunction (and as text, not a screenshot).

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Matt J 2023-1-23

编辑：Matt J 2023-1-23

在 MATLAB Online 中打开

I notice that the least squares prediction F can be written as a linear combination of known things.

Q= abs(v) .* z ./ (Fc + (Fs - Fc) * exp(r));
zdot = v - sigma0*Q;                 
F = sigma0 * (z+zdot.*ts) + sigma1 * z_dot + sigma2.*v;    % eq. 3
  = sigma0*(z  + v) - sigma0^2.*Q.*ts   - sigma0*sigma1.*Q + (sigma1+sigma2)*v
  
  = C1*(z  + v) - C2.*Q.*ts   - C3.*Q + C4*v

So, you can solve for C1 .. C4 by solving a set of linear equations.

Then, from the C coefficients, you can easily solve for sigma0 and sigma1.

Then, you can use that as an initial guess for the original optimization.

请先登录，再进行评论。

Fminsearch results shows shift from measured curve. How should I solve this?

4 个评论
显示 2更早的评论隐藏 2更早的评论

回答（1 个）

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

另请参阅

类别

标签

产品

版本

Community Treasure Hunt

Fminsearch results shows shift from measured curve. How should I solve this?

4 个评论 显示 2更早的评论隐藏 2更早的评论

回答（1 个）

1 个评论 显示 -1更早的评论隐藏 -1更早的评论

另请参阅

类别

标签

产品

版本

Community Treasure Hunt

4 个评论
显示 2更早的评论隐藏 2更早的评论

1 个评论
显示 -1更早的评论隐藏 -1更早的评论