# Computing displacement from accelerometer data

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Paul Heineman on 27 Sep 2022
Commented: Cris LaPierre on 27 Sep 2022
Hi,
I am trying to convert my accelerometer data to displacement data through integrating twice, I looked at other questions here and similar questions have been asked and answered however I still dont get a satisfactory answer.
Te problem I have is that I get a displacement of 5*10^-3 which does not make sense from the experiment. I have attached my data for reference.
I import the data from excel, detrend it and then use the function cumtrapz twice.
%Acceleration data
acc = data(:,4); % Add gravity factor ( g to m/sÂ²)
%acc = flip(acc);
acc = detrend(acc); % baseline correction
%Time
tStep = 20/length(acc);
N = length(acc)*tStep;
t = 0:tStep:N;
t(end) = [];
N = length(t);
dt = mean(diff(t));
fs = 1/dt;
% High pass filter
N = 2;
fc = 2;
[B,A] = butter(N,2*fc/fs,'high');
acc2 = filter(B,A,acc);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
velocity = cumtrapz(dt,acc2);
velocity = detrend(velocity); % baseline correction
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp = cumtrapz(dt,velocity);
%disp = detrend(disp); % baseline correction
%
figure(1)
%plot(t,acc);
hold on;
%plot(t,velocity);
hold on;
plot(t,disp);
title('disp'); ylabel('m');xlabel('time (s)');
I am wondering what I do wrong, thanks in advance

Cris LaPierre on 27 Sep 2022
Edited: Cris LaPierre on 27 Sep 2022
I think the first issue is to find the magnitude of the acceleration vector using the data from all 3 axes. From there, you can use cumtrapz with the Time and acceleration data, then Time and the resulting velocity to get position.
Warning: Column headers from the file were modified to make them valid MATLAB identifiers before creating variable names for the table. The original column headers are saved in the VariableDescriptions property.
Set 'VariableNamingRule' to 'preserve' to use the original column headers as table variable names.
data.Properties.VariableNames = ["Time","X","Y","Z","Abs"];
% Combined acceleration
accel = sqrt(data.X.^2 + data.Y.^2 + data.Z.^2);
figure
plot(data.Time,accel)
v = cumtrapz(data.Time,accel);
x = cumtrapz(data.Time,v);
figure
plot(data.Time,v)
figure
plot(data.Time,x)
##### 2 CommentsShowHide 1 older comment
Cris LaPierre on 27 Sep 2022
We would need to know the initial conditions. Perhaps most relevant here would be what the initial displacement of the cantilever beam was, as your data starts with max acceleration in Z

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