How to set proper configuration to obtain peaks of my data

Hi!

I want to extract peaks from my response spectrum for the future modal combination alalysis. My spectras have the following image if I use findpeaks command (this graphic is pretty dominant for one frequency, some others may have different form)

:

I´ve considered using the next settings:

findpeaks(F(:,2),F(:,1),"MinPeakHeight",5,"MinPeakDistance",2)

In this case the results are the following which is what I actually want

Nevertheless, if I change the previous line slightly changing the peak distance I no longer capture the main peak

findpeaks(F(:,2),F(:,1),"MinPeakHeight",5,"MinPeakDistance",1)

Instead it captures one of the first peaks of the data. My question is, how can I configure it so it only captures one peak for a certain X interval and this peak always being the highest value there? As I already mentiones, I have quite a few data sets to analyze and I´d like to make it less manual and avoid changing settings for each case.

Tnank you!

[Mathieu NOE]

hello

IMHO, MinPeakDistance value should be increased and not decreased

also your data seems a bit noisy , so maybe some smoothing would help (smoothdata)

[Andriy Voshchenko]

Smoothing a data isn´t really an option since it reduces the peaks amplitude significally (thos peaks are response for the resonance and i don´t want to "smoothe" them), I just want it to capture the max value in each interval, is it possible?

Increasing peak distance is kinda lazy solution because it works in this case but my natural frequencies are 1.3, 2.6, 3.7. 3.9, etc......... Depending on load case I may have peaks as close as 1Hz, I need to tell the programm to somehow retain only the max one.

The other solution is to create a "for" loop and try to extract peaks in predefined intervals but I don´t really like this solution neither because of the probability of it not detecting/detecting extra peaks depending on my intervals separation.

[Mathieu NOE]

I like to be challenged ... do you have some files with a few representative data ?

... I'd like to see what I can obtain.

Answer 1

[Star Strider]

It would help to have some representative data.

However, since the data are resonances, and the desired result seems to indicate that the peaks are possibly integer harmonics of the greatest peak, one way to approach this is first to take tha max of the data (returning the maximum and its index), and then use the x-value of the maximum (or the index of the maximum, depending on your findpeaks call) to set the 'MinPeakDistance' parameter, perhaps a 90% or so of the x-value or the index value. (Using 'MinPeakProminence' to define the peaks in noisy data might also be an option, however the data do not appear to have much noise. It would be necessary to experiment with that option.)

This involves finding the maximum and its index before calling findpeaks, however that might be the easiest way to get the desired result.

[Andriy Voshchenko]

Thank you for your answer! The solution you are talking about works pretty good in case the peak response is the first resonance. However, the results may vary drastically. Just to give some context, I´m getting the response spectras from Ansys as real + imaginary part of force/moment and amplitude+phase of the displacement. Those response spectras depend on the load case, damping ratio and the point where I observe them (there are a few supports in the structure, usually want to see the reaction forces there and also displacement of some unconstricted point).

For future analysis i want to extract the peak values, so i obtain the absolute value of the complex response

Fcomplex=Freaction(:,2)+i*Freaction(:,3); %complex reactions
Fvalue=abs(Fcomplex); % magnitude

And later on I try to obtain those peaks in order to apply some modal combination technique (CQC, SRSS, ABS). All that just to estimate the peak time response to the load spectra (kinda new in those things so if I´m missing something please let me know)

There are a few cases and each of them contains a few points of interest also. The response spectras may vary a lot, as example

Or also

I was trying to obtain those response peaks somehow and apply the combination methods, what do you think would be the best option?

Now that I think about it, i DO have the modes of the structure so i can just load them on X axis and somehow tell the program to find a peak near that value? How can I do that? Since the peak isnt necessary going to be on the loaded mode shape but +/-error so it has to detect the maximum value in some proximity...... Maybe define that error manually and do something like max(function) on interval [mode-error,mode+error]

I was thinking "findpeaks" could do the work but if there is any other method please let me know.

p.s. Attach the picture of modal analysis of the first 12 modes as example of what values will be included (obviously not all of them have response since the mass participation is very different)

[Image Analyst]

When @Mathieu NOE and @Star Strider asked for representative data, they meant that you should attach your data with the paperclip icon, along with code to read it in to your vector. They did not mean give them a screenshot of a plot and of the numbers in the workspace panel. What can they do with that? Please attach your data so they can continue to help you.

[Star Strider]

My pleasure!

I was using the information provided in the original post.

Just using the data, findpeaks is likely the best option. I have no idea what you are doing beyond that, so I have no further observations. (One possibility might be to estimate the system in state space using the System Identification Toolbox, however I’m not certain that doing that will give you the information you want, especially since I’m not certain what that is.)

Since my approach will obviously not work in the situations illustrated in your latest Comment, and I have no further obseervations, I will delete my Answer in a few minutes.

[Andriy Voshchenko]

Freaction=readmatrix("Freaction.xlsx"); % Frequency, real part and imaginary part

%% Imaginary to real
Fcomplex=Freaction(:,2)+i*Freaction(:,3); %complex reactions
Fvalue=abs(Fcomplex); % magnitude
F=[Freaction(:,1) Fvalue];

%% Find peak values
Fpeaks=findpeaks(F(:,2),F(:,1),"MinPeakHeight",10,"MinPeakDistance",2);
findpeaks(F(:,2),F(:,1),"MinPeakHeight",10,"MinPeakDistance",2) %plot

Sorry @Mathieu NOE, @Star Strider, since my question was more theorical I didn´t include the data at the beginning. Also I´m not sure how useful it will be since I don´t have one big file with all the data. Here are some particular cases if you want to check it out. The format is [Frequency Real_reaction Imaginary_reaction]

[Mathieu NOE]

hello again

a simple comment - so we are trying to locate peaks on response spectra - I assume to define resonance frequencies - but IMO it would be much better if we do the work on transfer functions (aka FRFs : Frequency Response Functions) . Those FRFs are either computed directly from your FFT analyser or simulation tool , or can be performed from time domain data with tfestimate.

As a Noise & Vibration engineer I rarelly rely on output spectras to find structural resonances , it's much more reliable to work on FRF's

so the question is do we have access to both the inputs and outputs of your system and can we do some FRFs computations here before digging in how to use findeaks or any alternative to post - process your data ?

[Andriy Voshchenko]

It´s not about finding the frequencies but the response magnitude of those frequencies. I know what the frequencies are from previous modal analysis and, like I said before, I can just load them on my X axis and check the Y value. The problem here is that the peaks don´t fall exactly on those frequencies, is there a way to tell Matlab to find max value of the function in proximity of each point? Like X +/- 0.1 or 0.05 (I know those are small intervals and one could just assume there is no such error but in resonance proximity they are quite notable).

I guess the best option is to just use findpeaks and check that the program is capturing the data I want for every case, but if there is another solution you can recommend me that would be great also.

Thank you!

[Star Strider]

I am not certain what result you want. The 'MinPeakProminence' option appears to isolate the peaks reasonably well. If these are not the frequencies you want and you want to find amplitude values at different frequencies, those can be interpolated reasonably easily.

Getting the data from findpeaks and displaying it is relatively straightforward —

Freaction = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1043710/Freaction.xlsx');

%% Imaginary to real
Fcomplex=Freaction(:,2)+i*Freaction(:,3); %complex reactions
Fvalue=abs(Fcomplex); % magnitude
F=[Freaction(:,1) Fvalue];

[pks,locs] = findpeaks(F(:,2), 'MinPeakProminence', 5);
Freqs = F(locs,1);

figure
plot(F(:,1), F(:,2))
hold on
plot(F(locs,1), pks, '^r')
hold off
grid
text(F(locs,1), pks, compose('A = %6.1f\nF = %4.1f Hz',[pks, F(locs,1)]), 'Horiz','center', 'Vert','bottom')

.

[Mathieu NOE]

yes you can do a code that search the response peaks within a certain band around the "nominal" frequency given by your modal analysis. now the question is to define that band with enough robustness for all your data

[Andriy Voshchenko]

Thank you for your responses @Star Strider. The MinPeakProminence seems to work pretty good too even thought I don´t fully understant how it´s applied. On the other hand, @Mathieu NOE mentioned the possibility to define a band for each X value I´m interested in and look for the peaks there.This option seems more interesting for me but I don´t really know hoy to code it.

Let´s say I have the previous case and want to find peaks at the X values contained in the excel, how can I do it?

[Mathieu NOE]

hello again

@Andriy Voshchenko

the coding is not complicated but I'm worried that the list of modes is much longer than the number of peaks present in the response spectra as computed by @Star Strider

what do we do with the extra ones ? also the "matching" is not super good between spectra values and modes values

[Star Strider]

That is actually straightforward using the interp1 function:

Freaction = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1043710/Freaction.xlsx');
ModeFreqs  = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1046865/modes.xlsx');

%% Imaginary to real
Fcomplex=Freaction(:,2)+i*Freaction(:,3); %complex reactions
Fvalue=abs(Fcomplex); % magnitude
F=[Freaction(:,1) Fvalue];

[pks,locs] = findpeaks(F(:,2), 'MinPeakProminence', 5);
Freqs = F(locs,1);

Amplitudev = interp1(F(:,1), F(:,2), ModeFreqs);
Mode_Amplitude = table(ModeFreqs, Amplitudev)

Mode_Amplitude = 10×2 table
    ModeFreqs    Amplitudev
    _________    __________

     1.3421        11.299  
     3.6806        16.174  
     3.9112        5.9781  
     3.9429        7.1333  
     4.9696        55.494  
     5.1433        59.957  
     5.3496        74.118  
     6.2745        37.595  
     6.4024        28.312  
     6.8875        14.667  

figure
plot(F(:,1), F(:,2))
hold on
plot(F(locs,1), pks, '^r')
hold off
grid
fpos = get(gcf, 'Position');
set(gcf, 'Position', fpos+[-50 -100 300 200]);                        % Stretch Limits To Inprove Readability
% text(F(locs,1), pks, compose('A = %6.1f\nF = %4.1f Hz',[pks, F(locs,1)]), 'Horiz','center', 'Vert','bottom')
text(ModeFreqs, Amplitudev, compose('  \\leftarrow  F = %4.1f Hz,  A = %6.1f',[ ModeFreqs, Amplitudev]), 'Horiz','left', 'Vert','middle', 'Rotation',90, 'FontSize',8)

The figure is a bit difficult to read because some of the mode frequencies are close together.

.

Answer 2

[Andriy Voshchenko]

That is the best solution so far for spedctras which excitate a lot of modes, Thank you @Star Strider!

Depending on the case I guess I can use a simple findpeaks or a more sophisticated solution you provided.

Also, @Mathieu NOE, answering your questions: you find all the peaks for all the modes and simply filter them (set some minimum frequency and don´t count the results below it) and yeah, I´m aware of the matching problem, there is nothing to do with it since its due to the structural damping and that is where I want the solution actually, to obtain the max value which is close to my freq and not just value for the response for that freq.

I guess with all the info you guys provided I can keep going without problem, thanks a lot!

[Star Strider]

As always, my pleasure!