Integrating Acceleration Data Matlab

Hi there,

I have the acceleration vs. time data that is attached. When I plot it, I get the following:

I want to integrate it to get the Velocity vs. Time graph but I do not know how to do this. I have tried trapz() but it only gives some weird linear graph.

If someone could let me know how to do this that would be greatly appreciated.

Cheers.

Answer 1

[Alan Stevens]

Try

v = cumtrapz(X2(:,1),X2(:,2));
plot(X2(:,1),v)

[Timo Mayer]

Hi Alan,

thanks for the reply, I get the following:

It seems a bit off since it is only going into the negative, and only going up to 4. did you scale the units?

Cheers.

[Alan Stevens]

Have a look at the help file for cumtrapz. In the form cumtrapz(x,y) it calculates the cumulative integral of y with respect to x using trapezoidal integration.

I suspect you just used

plot(X2(:,2))

whereas if you'd used

plot(X2(:,1),X2(:,2))

you would have had the x-axis going from 0 to 4.

Also, look closely at your original plot. You can see that the dense part of the plot lies slightly below 0, so the acceleration tends to be mostly negative.

[Timo Mayer]

Thanks, I got it working now with cumtrapz as can be seen below but it seems the exponential line is adding everything together with absolute values but the other line is actually what I want, as it adds what is above the line and substracts what is below. Any idea how I can get only this bottom line and not the exponential one?

My code is below:

close all
z = cumtrapz(X2);
h = cumtrapz(z);

figure
plot(X2)
title('Acceleration (m/s^2) vs. Time (ms)')
xlabel('Time (ms)') 
ylabel('Acceleration (m/s^2)')
 
figure
plot(z,'r')
title('Velocity (m/s) vs. Time (ms)')
xlabel('Time (ms)') 
ylabel('Velocity (m/s)')

Cheers.

[Alan Stevens]

Your "exponential" curve is simply the cumulative integral of the time!!

You need to use, say

t = X2(:,1);
accn = X2(:,2);
vel = cumtrapz(t,accn);

to be clear.

The time intervals are not constant, so technically

cumtrapz(accn)

on its own, is not velocity

.

[Timo Mayer]

Ok thanks, I understand now that I need to include time when using the trapezoidal rule. I now have the following results. Do those look correct to you?

How can I remove the second blue line from the original data?

Here is my code:

t = X2(:,1);
accn = X2(:,2);
vel = cumtrapz(t,accn);
dis = cumtrapz(t,vel);

figure
plot(X2)
title('Acceleration (m/s^2) vs. Time (ms)')
xlabel('Time (ms)') 
ylabel('Acceleration (m/s^2)')
 
figure
plot(vel,'r')
title('Velocity (m/s) vs. Time (ms)')
xlabel('Time (ms)') 
ylabel('Velocity (m/s)')


figure
plot(dis,'k')
title('Displacement (m) vs. Time (ms)')
xlabel('Time (ms)') 
ylabel('Displacement (m)')

Cheers.

[Alan Stevens]

Instead of

figure
plot(X2)
title('Acceleration (m/s^2) vs. Time (ms)')
xlabel('Time (ms)') 
ylabel('Acceleration (m/s^2)')

use

figure
plot(t,accn)
title('Acceleration (m/s^2) vs. Time (ms)')
xlabel('Time (ms)') 
ylabel('Acceleration (m/s^2)')

Similarly, I would use

plot(t,vel)

and

plot(t,dis)

for clarity.

[Timo Mayer]

Great, thank you very much, now it looks much better!