Averaging Hysteresis Data - how to do it?

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

Answer 1

[Mischa Kim]

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.

[Giuseppe Naselli]

Hi Mischa,

thanks for the hint, it works as I wanted a part 2 things listed below. (see picture)

1. The fitting result is fine, but I wish my fitting curve to pass through zero. How can I do that?
2. How can I create a variable (.mat, 1-column vector) which contains the fitted data?

Thanks in advance

Regards,

G

[Giuseppe Naselli]

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]

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!