Surface roughness analysis from raw data

Hello! I need some help with this: I have roughness values of a surface, and now I want to filter the values in order to differentiate between roughness and waviness. I read I should use FFT and short and long wave filtering but I am a bit lost with it. Find attached the data (first column is length (milimeter) and second roughness value (micrometer)). I guess the first column could be considered as time... Any help is welcome! Thanks in advance.

Answer 1

[Mathieu NOE]

hello

this is a starter , to do the spectral analysis of your data

then you can use some low / high or bandpass filters to filter your analog signal according to your cut off frequencies (and filter order)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

filename = ('nominalprofile.txt'); 
data = readmatrix(filename); % 2 channels : Time + signal
time = data(:,1);
dt = mean(diff(time));
signal = data(:,2); % select here one or several channels 
Fs = 1/dt; % sampling rate 

[samples,channels] = size(signal);

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% define filters (optionnal) 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% low pass filter %
option_LPF = 0;     % 0 = without low pass filter  , 1 = with low pass filter
    fc_lpf = 100;       % LPF cut off freq
    N_lpf = 5;           % filter order

% high pass filter %
option_HPF = 0;     % 0 = without high pass filter  , 1 = with high pass filter
    fc_hpf = 100;       % HPF cut off freq
    N_hpf = 5;           % filter order

% bandpass filter %
option_BPF = 0;     % 0 = without bandpass filter , 1 = with bandpass filter
    f_low = 50;      % lower cut off freq Hz
    f_high = 500;      % higher cut off freq Hz
     N_bpf = 5;           % filter order
     
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 1000;    % 
OVERLAP = 0.75;

 %% apply filters 
 % low pass filter section %%%%%%
if option_LPF ~= 0
    w0_lpf = 2*fc_lpf/Fs;
    % digital notch (IIR)
    [b,a] = butter(N_lpf,w0_lpf);
    % now let's filter the signal 
    signal = filter(b,a,signal);
end

% high pass filter section %%%%%%
if option_HPF ~= 0
    w0_hpf = 2*fc_hpf/Fs;
    % digital notch (IIR)
    [b,a] = butter(N_hpf,w0_hpf,'high');
    % now let's filter the signal 
    signal = filter(b,a,signal);
end

% band pass  filter section %%%%%%
if option_BPF ~= 0
    [b,a] = butter(N_bpf,2/Fs*[f_low f_high]);
    signal = filter(b,a,signal);
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 1 : time domain plot
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1),plot(time,signal);grid on
title(['Time plot  / Fs = ' num2str(Fs) ' Hz ']);
xlabel(' length (milimeter) ');ylabel('roughness value (micrometer)');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 2 : averaged FFT spectrum
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[freq, sensor_spectrum] = myfft_peak(signal,Fs,NFFT,OVERLAP);

figure(2),semilogy(freq,sensor_spectrum);grid on
df = freq(2)-freq(1); % frequency resolution 
title(['Averaged FFT Spectrum  / Fs = ' num2str(round(Fs)) ' Hz / Delta f = ' num2str(df,3) ' Hz ']);
xlabel('1/length (1/mm)');ylabel('roughness value (micrometer)');



function  [freq_vector,fft_spectrum] = myfft_peak(signal, Fs, nfft, Overlap)
% FFT peak spectrum of signal  (example sinus amplitude 1   = 0 dB after fft).
% Linear averaging
%   signal - input signal, 
%   Fs - Sampling frequency (Hz).
%   nfft - FFT window size
%   Overlap - buffer percentage of overlap % (between 0 and 0.95)

[samples,channels] = size(signal);

% fill signal with zeros if its length is lower than nfft
if samples<nfft
    s_tmp = zeros(nfft,channels);
    s_tmp((1:samples),:) = signal;
    signal = s_tmp;
    samples = nfft;
end

% window : hanning
window = hanning(nfft);
window = window(:);

%    compute fft with overlap 
 offset = fix((1-Overlap)*nfft);
 spectnum = 1+ fix((samples-nfft)/offset); % Number of windows
%     % for info is equivalent to : 
%     noverlap = Overlap*nfft;
%     spectnum = fix((samples-noverlap)/(nfft-noverlap));	% Number of windows

    % main loop
    fft_spectrum = 0;
    for i=1:spectnum
        start = (i-1)*offset;
        sw = signal((1+start):(start+nfft),:).*(window*ones(1,channels));
        fft_spectrum = fft_spectrum + (abs(fft(sw))*4/nfft);     % X=fft(x.*hanning(N))*4/N; % hanning only 
    end
    fft_spectrum = fft_spectrum/spectnum; % to do linear averaging scaling

% one sidded fft spectrum  % Select first half 
    if rem(nfft,2)    % nfft odd
        select = (1:(nfft+1)/2)';
    else
        select = (1:nfft/2+1)';
    end
fft_spectrum = fft_spectrum(select,:);
freq_vector = (select - 1)*Fs/nfft;
end

[ana ramirez de las heras]

Hello!! Thank you very much for your answer.

I was looking for something a bit less complicated, because I want to understand the process. I have differents data sets and the first one (the one I attached) gives no results when FFT is performed. The other one shows something but not what I was expecting to see:

Trying to follow the matlab help example but with my data I got to this:

Any clue of what I should review? find attached the program and the second data set.

Thank you again!!

[Mathieu NOE]

hello

yes this code works fine (with both files). Now the x label is not Herz (1 / second) but the inverse of a length (1/ length)

maybe you feel more confortable with the x axis in log scale so the long "wavelength" defaults are easier to see (long wave = lower values of (1/ length)

% %% demo code for fft
% Fs = 8000/2;          % Sampling frequency (number of samples/sampling time)                 
% T = 1/Fs;             % Sampling period       
% L = 8000;             % Length of signal
% t = (0:L-1)*T;        % Time vector
% X = 0.7*sin(2*pi*50*t) + sin(2*pi*120*t);



%% application to our case

filename = ('nominalprofile2.txt'); 
S = readmatrix(filename); % 2 channels : Time + signal
time = S(:,1);
dt = mean(diff(time));
X = S(:,2); % roughness signal
Fs = 1/dt; % sampling rate 

[samples] = length(X);

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

figure;
plot(t,X)
title('Signal')
xlabel('length (mm)');
ylabel('Roughness value (um)')


Y = fft(X);

P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);

f = Fs*(0:(L/2))/L;
figure;
semilogx(f,P1) 
title('Single-Sided Amplitude Spectrum of X(length)')
xlabel('1/length (1/mm)');
ylabel('Roughness value (um)')