How to count active faults in a specific time interval

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hello ,i want to detect faults. if the data ( residual) goes beyond a certain threshold and comes back , it is not a fault so it shows 1 but if the residual goes the threshold for consecutive number of times with a specific time-interval then it shows 1 .When there is no fault , it should show 1 . The fault will be plotted against time . How do i implement this?
  2 Comments
Jon
Jon on 20 Apr 2022
As stated you "show 1" in every case fault or no fault. Do you mean when there is no fault it should "show" 0?

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Accepted Answer

Mathieu NOE
Mathieu NOE on 20 Apr 2022
hello
try this code ; it select segments of data above a given threshold and longer than min_contiguous_samples samples;
% dummy data
samples=10000;
time= 3*(0:samples-1)/samples;
dt = mean(diff(time));
data = max(0,0.03*time+ sin(6*time.^2 -0.5));
fault_signal = zeros(size(time));
%% parameters
min_contiguous_samples = 400; % select segments only if they are at least this length => faulty signal = 1
threshold = 0.5; % 1 = max (100%) of data value
%% main loop %%%%
ind = (data>threshold*max(data)); % find data above threshold
% now define start en end point of segments above threshold
[begin,ends] = find_start_end_group(ind);
length_ind = ends - begin;
ind2= length_ind>min_contiguous_samples; % check if their length is valid (above min_contiguous_samples value)
begin = begin(ind2); % selected points
ends = ends(ind2); % selected points
time2 = time(ind);
data2 = data(ind);
% define the begin / ending x, y values of raw data
time2_begin = time(begin);
data_begin = interp1(time,data,time2_begin);
time2_ends = time(ends);
data_ends = interp1(time,data,time2_ends);
for ci = 1:length(begin)
ind = (time>=time2_begin(ci) & time<=time2_ends(ci));
fault_signal(ind) = 1;
end
figure(1),
subplot(211),plot(time,data,'k',time2,data2,'.r',time2_begin,data_begin,'*c',time2_ends,data_ends,'*m','MarkerSize',12);
xlabel('time');
ylabel('amplitude');
legend('signal',['signal above ' num2str(threshold*100) ' % threshold'] ,'begin points','end points');
subplot(212),plot(time,fault_signal,'k');
xlabel('time');
ylabel('amplitude');
legend('fault signal');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [begin,ends] = find_start_end_group(ind)
% This locates the beginning /ending points of data groups
D = diff([0,ind,0]);
begin = find(D == 1);
ends = find(D == -1) - 1;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function x_rms = my_rms(x)
x_rms = sqrt(mean(x.^2));
end
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More Answers (1)

Jon
Jon on 20 Apr 2022
Edited: Jon on 20 Apr 2022
% set up a small example
thresh = 0.5 % threshold for fault
minCount = 2; % min number of repeated values to be considered a fault
r = rand(1,10) % example vector of residuals
% make logical array with values of residual greater than threshold set
% true
f = r > thresh
% mark beginning and ends of consecutive runs of zeros and ones
d = [true,diff(f)~=0,true]
% find run lengths
n = diff(find(d))
% make vector with run length corresponding to each element
runLength = repelem(n,n);
% just keep run lengths where it is over threshold
runLength = runLength.*f
% assign logical indices for points that are considered faults
isFault = runLength >= minCount
% illustrative plots
idx = 1:numel(r);
plot(idx,r,idx(~isFault),r(~isFault),'og',idx(isFault),r(isFault),'*r')
  5 Comments
Jon
Jon on 20 Apr 2022
Ahh and it wasn't introduced until 2015. The approach above can be done with a little modification just using diffs and cumsums. I would have to think about that a little more though. Is it still of interest?
Otherwise, is there some reason why you can't update your MATLAB, 2013 is almost 10 years old, a lot of advances since then.
Mathieu NOE
Mathieu NOE on 21 Apr 2022
hello again
there are "home made" alternatives to repelem if you don't have it :
see in the code below (expanded)
% set up a small example
thresh = 0.5; % threshold for fault
minCount = 5; % min number of repeated values to be considered a fault
r = rand(1,100) % example vector of residuals
% make logical array with values of residual greater than threshold set
% true
f = r > thresh;
% mark beginning and ends of consecutive runs of zeros and ones
d = [true,diff(f)~=0,true];
% find run lengths
n = diff(find(d));
% make vector with run length corresponding to each element
% runLength = repelem(n,n);
runLength = my_repelem1(n,n); % alternative #1
% runLength = my_repelem2(n,n); % alternative #2
% just keep run lengths where it is over threshold
runLength = runLength.*f;
% assign logical indices for points that are considered faults
isFault = runLength >= minCount;
% illustrative plots
idx = 1:numel(r);
plot(idx,r,idx(~isFault),r(~isFault),'og',idx(isFault),r(isFault),'*r')
%%%%%%%%%%%%%%%%%%%%%% alternatives to repelem %%%%%%%%%%%%%%%%%%%%%
function out = my_repelem1(A,R)
% B = my_repelem1(A, R), returns an array with each element of A
% repeated according to R.
out = cell2mat(arrayfun(@(a,r)repmat(a,1,r),A,R,'uni',0));
end
%%%%%%%%%%%%%%%%%%%%%%
function out = my_repelem2(A,R)
% B = my_repelem1(A, R), returns an array with each element of A
% repeated according to R.
out = cell(1,length(R)) ;
for i = 1:length(R)
out{i} = ones(1,R(i))*A(i) ;
end
out = [out{:}];
end

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