Converting acceleration data to displacement data using FFT results in Zero-drift

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Johann Vormadal 2024-5-23

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https://ww2.mathworks.cn/matlabcentral/answers/2121921-converting-acceleration-data-to-displacement-data-using-fft-results-in-zero-drift

评论： Johann Vormadal 2024-5-29

I have a (n x 1) vector containing acceleration data from a sensor and I am trying to obtain the displacement by:

performing an FFT
Convert acceleration to displacement in the frequency domain by dividing by -omega^2
performing an IFFT to get back to the time domain.

The idea is to make a conversion which doesn't result in any Zero-drift, but all my attempts so far result in the oscillation being superimposed on a very low frequency wave (See figure attached), and I can't tell where this low frequency oscillation is coming from. The result should be a near sinusoidal wave centred around zero.

Below is a (slightly modified) snippet from my code. The sensor data (Ch5) is attached as a .mat file.

    Tinterval = 0.000625;
    Length = length(Ch5);
    SamplingFrequency = 1/Tinterval;
    Frequency = SamplingFrequency*(0:Length-1)/Length;
    Omega = 2*pi*Frequency;  
    ConversionFactor = -(Omega.^2).';
    ConversionFactor(1,:) = 1; %To avoid dividing by zero
    % Base Data
    RawData = Ch5;
    Data = RawData - mean(RawData);
    FourierTransform = fft(Data);
    Y_accel_base = ifft(FourierTransform).';
    dY_base = abs(ifft(FourierTransform./ConversionFactor)).';

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Mathieu NOE 2024-5-27

hello

doing it by fft/ifft is a requirement or just an idea ?

also notice that the raw data is not zero mean, so you're going to have drift on first integration then a parabolic trend on the 2nd integration

Johann Vormadal 2024-5-28

Hi,

In my code I remove my DC offset before applying the fft.

The requirement is to have zero drift. the fft/ifft seems to be the best way to acheive this (in theory).

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Answer 1

Mathieu NOE 2024-5-27

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2121921-converting-acceleration-data-to-displacement-data-using-fft-results-in-zero-drift#answer_1463846

在 MATLAB Online 中打开

Ch5 data.mat

FYI, a very simple time domain approach - assuming we don't care about the DC values , only the dynamic portion of the data is of interest

results may be even refined by adding some high pass filtering if you really need it

load('Ch5 data.mat')

dt = 0.000625;

fs = 1/dt; % sampling rate

acc = Ch5;

samples = numel(acc);

t = (0:samples-1)*dt;

% remove DC value

acc = acc - mean(acc);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

velocity = cumtrapz(dt,acc);

velocity = detrend(velocity); % baseline correction

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

disp = cumtrapz(dt,velocity);

disp = detrend(disp); % baseline correction

%

figure(1)

subplot(311),plot(t,acc);

title('accel'); ylabel('m/sÂ²');xlabel('time (s)');

subplot(312),plot(t,velocity);

title('velocity'); ylabel('m/s');xlabel('time (s)');

subplot(313),plot(t,disp);

title('disp'); ylabel('m');xlabel('time (s)');

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Mathieu NOE 2024-5-29

have to try a few other options , like :

Finding the velocity from displacement - MATLAB Answers - MATLAB Central (mathworks.com)

Converting acceleration to displacements records - File Exchange - MATLAB Central (mathworks.com)

there are probably more ...

Johann Vormadal 2024-5-29

Thank you for those links!

Those also use the fft method, but their code is slightly different and much more elegant. I will try and emulate them, and see if it solves my problem.

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Converting acceleration data to displacement data using FFT results in Zero-drift

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