# How to count active faults in a specific time interval

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Kwaku Junior on 20 Apr 2022
Commented: Mathieu NOE on 21 Apr 2022
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 CommentsShowHide 1 older comment
Kwaku Junior on 20 Apr 2022
my mistake , i meant show 0 there is no fault

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
Mathieu NOE on 20 Apr 2022
My pleasure !

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')
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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