Double integration of the acceleration signals to obtain displacment signals

Hi,

In order to obtain the displacement signals from the acceleration data, The following steps are used to convert the acceleration data to achieve the displacement values:

1- The acceleration signals are filtered [High pass filter]

2- The cumtrapz is applied to integrate the displacement to obtain the velocity

3- The velocity signals are filtered [High pass filter]

4- Finally, the filtered signals of velocity is integrated to get the displacement signals.

The concern is still about the correct methods and the accuracy of the results which are obtained.

Please have look at the Matlab Program as stated below; If there any comments and contribution regarding the proposed methodology please do not hesitate to shear us your experience, Thank you

%%accelerations are integrated twice to produce displacements

clear all

close all

clc

time = load('D:\Users\Desktop\time.txt');

acc = load('D:\Users\Desktop\data.txt');

figure

plot(time,acc)

xlabel('Time (sec)')

ylabel('Acceleration (mm/sec^2)')

%%Design High Pass Filter

fs = 8000; % Sampling Rate

fc = 0.1/30;  % Cut off Frequency

order = 6; % 6th Order Filter

%%Filter  Acceleration Signals

[b1 a1] = butter(order,fc,'high');

accf=filtfilt(b1,a1,acc);

figure (2)

plot(time,accf,'r'); hold on

plot(time,acc)

xlabel('Time (sec)')

ylabel('Acceleration (mm/sec^2)')

%%First Integration (Acceleration - Veloicty)

velocity=cumtrapz(time,accf);

figure (3)

plot(time,velocity)

xlabel('Time (sec)')

ylabel('Velocity (mm/sec)')

%%Filter  Veloicty Signals

[b2 a2] = butter(order,fc,'high');

velf = filtfilt(b2,a2,velocity);

%%Second Integration   (Velocity - Displacement)

Displacement=cumtrapz(time, velf);

figure(4)

plot(time,Displacement)

xlabel('Time (sec)')

ylabel('Displacement (mm)')

[RogerLM]

Hi,

thank you for this code. I just have a question, how do you choose the cut-off frequency of the high pass filter ? Thank you !

[Philippe Corner]

You have to produce the FFT of the signal, and analyse the frequency where is concentrate the magnitude.. that's the cut-off frequency

[Keith Walker]

what do you mean by "concentrate the magnitude" ? if i am interested in velocity/displacement @ low frequency range 30-35Hz, is the fc, same for both velocity and acceleration ?

[AJ]

Awesome!!!

Thank you very much!

Very useful

[Jose Sosa Lopez]

Thank you, I'll use it

[Samuel Hudson]

Would you be willing to provide a sample of data that works in this code?

Answer 1

[UTS]

Any comments, Thanks

[Matthew Nijsten]

Hi there, so if i put an array of 2498x1 acceleration points into this code it will output me 2498x1 respective data points

Answer 2

[as k]

Its working ıts working , Thank you so much my friend . Really saved my life today. I hope the sun may always shine upon your path.

Answer 3

[as k]

One more thing , we usually measure disp. in mm and those calculation above give us result ,generally, in meters so this is just a reminder.

Answer 4

[Hasan Siddiqui]

What units does the original accelerometer data need to be in originally? I have data collected from an arduino that is a 10 bit voltage reading from 0-1023. Does it need to be converted to the range of the accelerometer in gs first (-3g to 3g)?

Answer 5

[Adi Negoro]

I'm newbie,

how to understand the "fc=0.1/30; % Cut off Frequency"?

[kingsley mah]

i would like to know this also

[Tsai Han Hao]

this is what I'm confused about

[Vincent den Ouden]

From the butterworth doc;

"For digital filters, the cutoff frequencies must lie between 0 and 1, where 1 corresponds to the Nyquist rate—half the sample rate or π rad/sample."

so in this case (0.1/30)*4000 = 13.3 rad/s if I understand correctly.

[Desmond Dunggat]

@Vincent den Ouden Can you share to me the document? This is my email: [e-mail]

Thank you in advance!

[Vincent den Ouden]

just write 'doc butter' in matlab and itll bring you to the documentation.

[Desmond Dunggat]

@Vincent den Ouden so actually the filter designed above is Butterworth filter is it? Not High Pass filter?

[Vincent den Ouden]

the term butterworth says more something about the idea/characteristics behind the filter, and in the case of the butterworth the idea is to have the most flat frequency response possible in the passband (frequencies that you want). The filter itself can be lowpass/highpass or bandpass.

Answer 6

[Aashish Sah]

Hi,

I have one question regarding this code. I have acceleration data in terms of g, so I multiply by 9.8 to get in terms of ms^-2. The displacement should then be in terms of m. However, when I apply the filter to my acceleration data, it normalizes the data. For example, the max and min of raw acceleration data is [10.5, 9.6] ms^-2 and after I apply the filter I get [0.68 -0.56]. It seems that filtering process normalizes the raw data between -1 and 1.

This introduces an issue for me since I wish to compare the actual displacement from different accelerometer sensors.

Any suggestions?

[Broc Sommermeyer]

This code is designed to measure the velocity and displacement that are a function of time dependent acceleration by applying the high pass filter to remove the constant gravity value of 1g. Fourier series representation of periodic signals would break down a(t) into a constant term and an infinite sum of sine and cosine terms. The filter removes the constant term and any sine and cosine terms that have a frequency lower than the cutoff frequency fc. If you want to look at the complete accelerometer data including gravity remove the filter from the code.

Answer 7

[Joven Chou]

awesome codes