Averaging Hysteresis Data - how to do it?

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Giuseppe Naselli
Giuseppe Naselli 2013-12-16
评论： Fede 2024-2-7
Hi All,
below damper Force Vs Velocity for a typical 2-way adjustment damper is shown and as expected a typical hysteresis shape is obtained. We could imagine the data as the sum of 2 curves: one curve is given when the velocity goes from NEGATIVE to POSITIVE and the other is obtained when the velocity goes from POSITIVE to NEGATIVE
I want to use this damper data on my vehicle dynamics model and in order to speed up the processing time (as there are 4 dampers) I would like to extrapolate a curve with the following features
  • Only one line
  • This line should pass the middle of the two curves (a sort of average, an ideal damper with no hysteresis)
I would appreciate some suggestions on how to tackle this problem. how would you do that?
Many thanks for you help
(DATA attached)
Thanks in advance
G

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Mischa Kim
Mischa Kim 2014-1-4
Hello Guiseppe, try to use curve fitting. In MATLAB, go to the Apps tab and find the Curve Fitting app (in the math, statistics and optimization folder). Select as X and Y data Velocity and Force, respectively. Smooth Splines will probably work pretty well, you can also adjust the smoothness/roughness of the fit.
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Giuseppe Naselli
Giuseppe Naselli 2014-1-9
ok so I foundthe way of creating the variable with only the fitted data
Basically I used the following script
load('Force-Velocity.mat'); % Load the data to fit
Fit_of_the_Data = fit(Velocity, Force, 'smoothingspline', 'SmoothingParam', 0.025) % Create a smoothing spline fit with the parameter I specified
Data_fitted = feval(Data_Fit,Velocity);
The Data_fitted variable is what I was looking for.
NOw the last step is to find how I can say to the command "fit" to generate a curve which goes to zero
Help please :)
G
Fede
Fede 2024-2-7
Ciao @Giuseppe Naselli, I found a way to do this without curve fitting toolox, as follows:
Let's assume you have your datain (x,f) format, meaning displacement and force:
% First, I calculate the index at which the data turns, to separate up and down curves:
% hystereis turning point:
[x_turning, idx] = max(x_data);
x_up = x_data(1:idx);
f_up = f_data(1:idx);
x_down = x_data(idx:end);
f_down = f_data(idx:end);
% plot(x_up, f_up, 'o')
% plot(x_down, f_down, 'x')
% Then, Filter to only keep unique values:
%Keep unique values:
[x_up,ia,~] = unique(x_up);
f_up = f_up(ia);
% plot(x_up,f_up, '.');
[x_down,ia,~] = unique(x_down);
f_down = f_down(ia);
% plot(x_down,f_down, '.');
% Fit curves for each segment:
nQueryPoints= 100;
xx_up = linspace(min(x_up), max(x_up), nQueryPoints); % Generating points for smooth curve
yy_up = interp1(x_up,f_up,xx_up);
% plot(xx_up, yy_up, 'r');
xx_down = xx_up; % Note: I take the same query points as xx_up, to be ale to later calculate average value :)
yy_down = interp1(x_down,f_down,xx_down);
% plot(xx_down, yy_down, 'g');
% Calculate Average value:
xx_avg = xx_up;
yy_avg = (yy_up+yy_down)./2;
plot(xx_avg, yy_avg, '--b');
It doesn't give you a spline, but it's something!

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