How can I deduce velocity and displacement trends from an acceleration signals

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Guglielmo Giambartolomei
评论： Star Strider 2017-1-19
Hello everyone, I have an acceleration signal from an accelerometer. I wrote a simple script in order to analyse this signal: I plotted the signal in time domain, I performed a frequency domain analysis, I filtered and realigned the signal and at the end I tried to reconstruct velocity and displacement with the cumtrapz function. The code is in the following:
clc;
clear all;
close all;
file_acc='CT4H1X21-2.xlsx';
x_acc=xlsread(file_acc);
%%Time domain analysis of acceleration signal
Fsa=19200;
Ta=1/Fsa;
xa=x_acc(:,3);
Na=length(xa);
ta=linspace(0,Na*Ta,Na);
figure
plot(ta,xa)
grid on
title('Acc. on the sparger')
xlabel('t (s)')
ylabel('xa(t), Acceleration (g)')
%%Frequency domain analysis of accelerometric signal
NFFT2_acc = 2^nextpow2(Na); % Next power of 2 from length of y
Xa=fft(xa-mean(xa),NFFT2_acc)/Na;
fa=Fsa/2*linspace(0,1,NFFT2_acc/2+1);
figure;
plot(fa,2*abs(Xa(1:NFFT2_acc/2+1)))
grid on
title('Single-Sided Amplitude Spectrum of xa(t)')
xlabel('f (Hz)')
ylabel('Xa(f)')
%%Plot the Power Spectral Density of the accelerometric signal
figure;
[pxxa,fxa] = pwelch((xa-mean(xa)),[],[],[],Fsa);
plot(fxa,pxxa);
grid on
title('Power Spectral Density of xa(t)')
xlabel('Frequency (Hz)')
ylabel('Power/Frequency (dB/Hz)')
%%Butterworth filter for accelerometric signal
Fca=150;
Fsa=19200;
[ba,aa]=butter(10,Fca/(Fsa/2));
figure;
freqz(ba,aa)
dataIna=xa;
% Apply the filter to Smooth out the Signal
xafilter=filter(ba,aa,dataIna);
% Overlay the filtered pressure signals on the original signals
% Filtered signal is delayed
figure;
plot(ta,xa,'b',ta,xafilter,'r');
grid on;
title('xa (accelerometric signal)')
xlabel('t (s)')
ylabel('acc. (g)')
legend({'Original xa Signal','Filtered xa Signal'});
%set(gcf,'NumberTitle','Off', 'Name','Filtered Signal vs. Actual Signal');
%%Compare the original accelerometric signal and delay compensated filtered accelerometric signal
figure;
%xfiltfilt = filtfilt(d.sosMatrix,d.ScaleValues,x2);
xfiltfilta=filtfilt(ba,aa,xa);
plot(ta,xa,ta,xfiltfilta);
grid on
title('xa accelerometric signal')
xlabel('t (s)')
ylabel('acc (g)')
legend({'Original xa Signal','Actual xa Signal (filtered and realigned signal)'});
%%Frequency domain analysis of the filtered and realigned accelerometric signal
Xaf=fft(xfiltfilta-mean(xfiltfilta),NFFT2_acc)/Na;
figure;
plot(fa,2*abs(Xaf(1:NFFT2_acc/2+1)))
grid on
xlim([0 150])
title('Single-Sided Amplitude Spectrum of xa(t) filtered and realigned Signal')
xlabel('f (Hz)')
ylabel('Xa(f)')
%%Velocity
acceleration=xfiltfilta*9.80665;
velocity=cumtrapz(ta,acceleration);
figure;
plot(ta,velocity);
grid on
title('Velocity of the sparger from the acceleration signal')
xlabel('t (s)')
ylabel('Velocity (m/s)')
%%Displacement
displacement=cumtrapz(ta,velocity);
figure;
plot(ta,displacement);
grid on
title('Displacement of the sparger from the velocity signal')
xlabel('t (s)')
ylabel('Displacement (m)')
I'm not sure of what I did; in particular I found displacement of the order of meters and this is clearly an error. May someone take a look at my code? Thank you very much.

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采纳的回答

Star Strider
Star Strider 2016-12-19
I am not sure what you did, either.
Without your data, it’s not possible definitively to determine that.
One problem:
xafilter=filter(ba,aa,dataIna);
Use filtfilt! You used it in other parts of your code. It has a maximally flat phase response, so there will be no delays.
Always check your filter performance with the freqz function so that you know that it does what you want it to.
As for the high displacement, you may need to redesign your filter to be a bandpass filter rather than the default lowpass filter. With a bandpass filter, you can completely remove the entire d-c (constant) offset and low-frequency baseline drift. Subtracting the mean as you did here will not do that, because it only removes the d-c offset, not low-frequency baseline drift. The low-frequency baseline drift will also integrate, and could be the reason your displacements are in parsecs rather than microns.
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