sliding window algorithm for time-series data

I have sample data and sampling frequency . Sample data points are 27900 and sampling frequency is 600 hz . I want to apply slidding window concept for my data. I want divide all data into set of 5 sec each with overlap of 4 sec. (i.e. 0-5, 1-6, 2-7, etc.). Please help me to apply slidding window concept.

Answer 1

[Mathieu NOE]

HELLO

see demo below - second section implement a overlap method

all the best

clc
clearvars

% dummy data
data = rand(320,3); % data must be column oriented (number of rows = number of samples)
buffer = 25;    % nb of samples for averaging 

%% zero overlap averaging (unweighted)
[m,n] = size(data);

for ci=1:fix(m/buffer)
    start_index = 1+(ci-1)*buffer;
    stop_index = min(start_index+ buffer-1,m);
    time_index(ci) = round((start_index+stop_index)/2);  % time index expressed as sample unit (dt = 1 in this simulation)
    avg_data(ci,:) =mean(data(start_index:stop_index,:));  % 
end

figure(1),
plot(time_index,avg_data,'+-');

% return

%% averaging with overlap  
clearvars
% dummy data
data = rand(320,3);

buffer = 25;  % nb of samples in one buffer (buffer size) 
overlap = 10; % overlap expressed in samples

%%%% main loop %%%%
[m,n] = size(data);
shift = buffer-overlap;    % nb of samples between 2 contiguous buffers  
for ci=1:fix((m-buffer)/shift +1)
    start_index = 1+(ci-1)*shift;
    stop_index = min(start_index+ buffer-1,m);
    time_index(ci) = round((start_index+stop_index)/2);  % time index expressed as sample unit (dt = 1 in this simulation)
    avg_data(ci,:) = mean(data(start_index:stop_index,:));  % 

end

figure(2),
plot(time_index,avg_data,'+-');

[Sameer Sayyad]

@Mathieu NOE Thanks sir. Can you please explain me (time_index(ci)) code line. Because I have frequency and number of samples from which I can create time step coloun. So can I use that Time step coloum in this code.

Thank you

[Mathieu NOE]

hello Sameer

you are speaking about the time vector which is associated with your raw data (sampled at 600 Hz)

when I do buffer averaging , the output data have a different time spacing (increment) which depends on the buffer and overlap :

in my code, each buffer of data is associated with the time index around the middle of the buffer (for example , if my buffer has 11 samples , then I associate this buffer with the 6th sample (center position of the buffer) , then I do the buffer averaging and this value is associated with the 6th sample time index

hope this answer your question

[Mathieu NOE]

That looks nice , have you another question ?

[Sameer Sayyad]

% clear window

clc;

clear all;

% % import xls or csv file

axial_Depth_1 = xlsread('E:\SIT\Datasets\TOOL WEAR DATASET OF NUAA_IDEAHOUSE\+-¦½-²+¦\Data collection of variable cutting parameters\Variable axial cutting depth\1');

%fz: feed per tooth= 0.03 ; n: spindle speed= 1200; ap: axial cutting depth=1; ae: radial cutting depth=3.0

%extract data in respective sensors sensors

Axial_cutting_force= axial_Depth_1 (:,1:1);

[m,n] = size(Axial_cutting_force);

buffer = 600;

for ci=1:fix(m/buffer)

start_index = 1+(ci-1)*buffer;

stop_index = min(start_index+ buffer-1,m);

time_index(ci) = round((start_index+stop_index)/(2*buffer)); % time index expressed as sample unit

% 1. mean (Average)

Mean_Axial_cutting_force(ci,:) = mean(Axial_cutting_force(start_index:stop_index,:)); %

% 2. rms (Root mean square), Value that generally tends to get bigger as the degree of fault increases

RMS_Axial_cutting_force(ci,:) = rms(Axial_cutting_force(start_index:stop_index,:));

% 3. std(x)(Standard Deviation)

std_Axial_cutting_force(ci,:) = std(Axial_cutting_force(start_index:stop_index,:));

%4. Peak (Maximum value of signal absolute value)

Peak_Axial_cutting_force(ci,:) = max(Axial_cutting_force(start_index:stop_index,:));

%5. Skewness (The asymmetry of the probability density function of the signal)

Skewness_Axial_cutting_force(ci,:) = skewness(Axial_cutting_force(start_index:stop_index,:));

%6. Kurtosis (The sharpness of the probability distribution of the signal)

kurtosis_Axial_cutting_force(ci,:) = kurtosis(Axial_cutting_force(start_index:stop_index,:));

%7. Crest factor (The ratio of peak values to the RMS of a signal)

CF_Axial_cutting_force(ci,:) = Peak_Axial_cutting_force(ci,:)/RMS_Axial_cutting_force(ci,:);

%8. Clearance factor (Peak value divided by the square of root mean)

CL_Axial_cutting_force(ci,:)= (Peak_Axial_cutting_force(ci,:)/(RMS_Axial_cutting_force(ci,:))^2);

%9.Shape factor (RMS divided by mean)

SF_Axial_cutting_force(ci,:) = (RMS_Axial_cutting_force(ci,:)/ Peak_Axial_cutting_force(ci,:));

%10. Impulse factor (The ratio of peak values to the mean of a signal)

IF_Axial_cutting_force(ci,:)= (Peak_Axial_cutting_force(ci,:)/ Mean_Axial_cutting_force(ci,:));

%11. Peak to peak (The difference between maximum and minimum values of the signal)

Max_Axial_cutting_force (ci,:)= max(Axial_cutting_force(start_index:stop_index,:));

Min_Axial_cutting_force (ci,:)= min(Axial_cutting_force(start_index:stop_index,:));

P2P_Axial_cutting_force(ci,:)= (Max_Axial_cutting_force (ci,:)- Min_Axial_cutting_force (ci,:));

end

figure(1),

subplot (3,4,1)

plot(time_index,Mean_Axial_cutting_force,'+-', 'color','r');

title('Mean Axial Cutting Force'); grid on

xlabel('Time (Sec)')

ylabel('Mean Axial force in N')

subplot (3,4,2)

plot(time_index,RMS_Axial_cutting_force,'+-','color','b');

title('RMS Axial cutting force'); grid on

xlabel('Time(Sec)')

ylabel('RMS Axial cutting force in N')

subplot (3,4,3)

plot(time_index,std_Axial_cutting_force,'+-','color','g');

title('Std. Dev. Axial cutting force'); grid on

xlabel('Time(Sec)')

ylabel('std axial cutting force in N')

subplot (3,4,4)

plot(time_index,Peak_Axial_cutting_force,'+-','color','m');

title('Peak Axial cutting force'); grid on

xlabel('Time(Sec)')

ylabel('Peak Axial cutting force in N')

subplot (3,4,5)

plot(time_index,Skewness_Axial_cutting_force,'+-','color','r');

title('Skewness Axial cutting force'); grid on

xlabel('Time(Sec)')

ylabel('Skewness Axial cutting force in N')

subplot (3,4,6)

plot(time_index,kurtosis_Axial_cutting_force,'+-','color','b');

title('kurtosis Axial cutting force'); grid on

xlabel('Time(Sec)')

ylabel('kurtosis Axial cutting force in N')

subplot (3,4,7)

plot(time_index,CF_Axial_cutting_force,'+-','color','g');

title('Crest factor of Axial cutting force'); grid on

xlabel('Time(Sec)')

ylabel('CF of Axial cutting force in N')

subplot (3,4,8)

plot(time_index,CL_Axial_cutting_force,'+-','color','m');

title('Clearance factor of Axial cutting force'); grid on

xlabel('Time(Sec)')

ylabel('CL of Axial cutting force in N')

subplot (3,4,9)

plot(time_index,SF_Axial_cutting_force,'+-','color','r');

title('Shape factor of Axial cutting force'); grid on

xlabel('Time(Sec)')

ylabel('SF of Axial cutting force in N')

subplot (3,4,10)

plot(time_index,IF_Axial_cutting_force,'+-','color','b');

title('Impulse factor of Axial cutting force'); grid on

xlabel('Time(Sec)')

ylabel('IF of Axial cutting force in N')

subplot (3,4,11)

plot(time_index,P2P_Axial_cutting_force,'+-','color','g');

title('Peak to Peak value of Axial cutting force'); grid on

xlabel('Time(Sec)')

ylabel('P2P of Axial cutting force in N')

% return

[Sameer Sayyad]

Is it correct?

time_index(ci) = round((start_index+stop_index)/(2*buffer));

[Mathieu NOE]

yes

maybe I should emphasize that this is an index , means it about samples , not time is seconds

if you want to have it in seconds divide time_index by your sampling rate

[Sameer Sayyad]

Okay. Thank you so much sir.

[Alyaa Ghazi]

This was very helpfull to me also. Thanks alot.