modelfrf, experiment, naturel frequecies, magnitude

When I plot the experiment data with modalfrf, the units on the vertical axis are not correct. I gave the result for the experiment with figure 1 and the numerical results with figure 2. I think figure 2 is correct and figure 1 is wrong. Where is my mistake?

B1=xlsread('excel.xlsx',1);
x = B1(1:10000,3:3);
f = B1(1:10000,4:4);

dt = 0.0001;
Fs = 1/dt;
N = 10000;
t = dt*(0:N-1);

wind = hann(N/2);

[frf,f] = modalfrf(f,x,Fs,wind);

plot(f,20*log10(abs(frf)))

[dpb]

I don't see anything to complain about -- I hadn't realized there was a modal frf function in SP TB; I haven't done much of that sort for a while, so "know nuthink!" about it per Sgt Schultz but it appears it outputs the plot in linear scale and you've converted to a power/dB axis. Somewhat more conventional, but if you got the expected amplitudes, what's to complain?

[Gloria]

Thanks for reply. two figure must be match. The values of x axis true bu obviously I have a mistake when I change displacements which are time depentt to dB.

Answer 1

[Mathieu NOE]

hello

I plotted the time data for channels combos 3/4 (and 1/2)

both shows single (low) frequency sinus type data - so this is not what I expected for a modal frf - I was expecting to see random, random burst , sine dwell (chirp) , but not a lonely fixed freq sinus

not a surprise that the computed frf is completly misleading

also the amplitude of x and f are of very different orders of magnitudes : x is in the 10^-5 and f in the 10^5 , so a ratio like this cannot give a frf modulus like the "good" figure 2 would show between 10^-7 and 10^-4.

[Gloria]

Now I understood thank you. Can I ask something else? I have data of experiment but data is recorded with 1 Hz gaps and data length is 1005 lines. How can I see natural frequencies? I can only see the frequency range until 0.5 Hz.

[Gloria]

And the data of experiment is acceleration. I mean I have acceleration(m/s^2) and Force (N). How can I found naturel frequencies :(

[Mathieu NOE]

hello again

can you share yor data file ?

[Gloria]

I appreciate for your help. I need to do this to prove the validity of the numerical model.

First column is axial acceleration m/s^2 and second and third column are axial pressures.And data step is 1 Hz. I found my first mistake they are pressures not force. Shaft diameter is 0.086 m.People who help me for the experiment told me that I need to take the difference between the two columns to calculate the force, but I don't really trust them. So I shared both column so maybe we can get reasonable answer. Tne naturel frequencies are Numerical method 763,1496,1987 and 2562 Hz :(

[Mathieu NOE]

hello

I did a couple of investigations (spectrograms, averaged spectra, coherence analysis) , but the nature of your signals are strange to me ... I assume that you are exciting your structure through hydraulic pressure and measuring the response by the accel , but as you can see below in the figure 6 , the coherence between the accel and each one of the pressure signal is very low in almost the entire frequency range, so I wonder how one could do a proper modal extraction with uncoherent signals. How do you generate them ?

FYI, my code below

N = 1000;

B1=xlsread('excel2.xlsx',1);
accel = B1(1:N,1);
Pr1 = B1(1:N,2);
Pr2 = B1(1:N,3);

dt = 0.0001;
Fs = 1/dt;
N = 1000;
t = dt*(0:N-1);

figure(1); 
subplot(2,1,1),plot(t,accel)
title (' accel ');
subplot(2,1,2),plot(t,Pr1,'b',t,Pr2,'r')
title (' Pr1 (b) , Pr2 (r) ');
xlabel('time (s)');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 2 : time / frequency analysis : spectrogram demo
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
nfft = N/4;
wind = hann(nfft);
OVERLAP = 0.95;
NOVERLAP = floor(nfft*OVERLAP);

[sg1,fsg,tsg] = specgram(accel,nfft,Fs,wind,NOVERLAP);  
[sg2,fsg,tsg] = specgram(Pr1,nfft,Fs,wind,NOVERLAP);  
[sg3,fsg,tsg] = specgram(Pr2,nfft,Fs,wind,NOVERLAP);  
% FFT normalisation and conversion amplitude from linear to dB (peak)
sg1_dBpeak = 20*log10(abs(sg1))+20*log10(2/length(fsg));     % NB : X=fft(x.*hanning(N))*4/N; % hanning only
sg2_dBpeak = 20*log10(abs(sg2))+20*log10(2/length(fsg));     % NB : X=fft(x.*hanning(N))*4/N; % hanning only
sg3_dBpeak = 20*log10(abs(sg3))+20*log10(2/length(fsg));     % NB : X=fft(x.*hanning(N))*4/N; % hanning only

% plots spectrograms
figure(2);
imagesc(tsg,fsg,sg1_dBpeak);colormap('jet');
axis('xy');colorbar('vert');grid
title([' Spectrogram (accel) / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(fsg(2)-fsg(1)) ' Hz ']);
xlabel('Time (s)');ylabel('Frequency (Hz)');

figure(3);
imagesc(tsg,fsg,sg2_dBpeak);colormap('jet');
axis('xy');colorbar('vert');grid
title([' Spectrogram (Pr1) / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(fsg(2)-fsg(1)) ' Hz ']);
xlabel('Time (s)');ylabel('Frequency (Hz)');

figure(4);
imagesc(tsg,fsg,sg3_dBpeak);colormap('jet');
axis('xy');colorbar('vert');grid
title([' Spectrogram (Pr2) / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(fsg(2)-fsg(1)) ' Hz ']);
xlabel('Time (s)');ylabel('Frequency (Hz)');

% Averaged fft spectrum = linear average of spectrograms along the time
% axis
accel_spectrum = mean(sg1_dBpeak,2);
Pr1_spectrum = mean(sg2_dBpeak,2);
Pr2_spectrum = mean(sg3_dBpeak,2);

figure(5);
plot(fsg,accel_spectrum,'b',fsg,Pr1_spectrum,'r',fsg,Pr2_spectrum,'m');grid
title (' Autospectrum :  accel (b) , Pr1 (r) ,  Pr2 (m) ');
legend('accel','Pr1','Pr2');
xlabel('Freq (Hz)');

[frf1,freq] = modalfrf(Pr1,accel,Fs,wind,NOVERLAP);
[Cxy1,freqC] = mscohere(Pr1,accel,wind,NOVERLAP,nfft,Fs);
[frf2,freq] = modalfrf(Pr2,accel,Fs,wind,NOVERLAP);
[Cxy2,freqC] = mscohere(Pr2,accel,wind,NOVERLAP,nfft,Fs);

figure(6);
subplot(2,1,1),plot(freq,20*log10(abs(frf1)),'b',freq,20*log10(abs(frf2)),'r')
title (' FRFs :  accel / Pr1 (b) , accel / Pr2 (r) ');
subplot(2,1,2),plot(freqC,Cxy1,'b',freqC,Cxy2,'r');
title (' Coherence :  accel / Pr1 (b) , accel / Pr2 (r) ');
xlabel('Freq (Hz)');

[Gloria]

Thank you so much. As you said ; we stimulated structure through hydraulic pressure and measured the accelerations.I also have time dependent displacement values.I guess the frequency range was not scanned during the experiment so we can not see the naturel frequencies.Thank you very much for your time.I guess I can not see natural frequencies.

[Mathieu NOE]

you have to introduce some wide frequency range excitation signals , like random (white noise ) or chirps , but do not rely on "operationnal" background noise or narrow band signals like sines to get accurate models

have a good day