Identifying start of non-periodic cycles in Matlab

Question

I am trying to identify the start of a cycle which would be characterized by the maximum value. Although the data appears to be periodic, there is not a set number of points so I can't just break up the data into points of 50 and search for the max. However, I do know that the cycle cannot repeat before 20 pts (pt_limit) have elapsed which might be used a check. There is also not a trigger for the data due to the limitations of the DAQ hardware. I've included a few cycles below, but the actual data set will contain thousands of these quasi-periodic cycles.
Here is an example (sorry in advance for the longer data set):

data = [9147    9147    9513    9696    9696    9940    10093   10093   10246   10520   10520   10520   10795   10947   10947   11222   11772   11772   9452    4049    4049    4049    599 111 691 691 1515    2309    2309    2309    3072    3683    3683    4415    4995    4995    5453    5453    6063    6063    6643    7162    7162    7468    7742    7742    7742    8200    8536    8536    8841    9116    9116    9238    9543    9543    9543    9818    10001   10001   10246   10551   10551   10673   10673   10673   10917   10917   8749    4049    4049    1057    722 722 722 1210    2004    2004    2828    3683    3683    4293    4293    4751    4751    5270    5728    5728    6155    6643    6643    6643    7071    7437    7437    7712    8048    8048    8353    8353    8689    8689    9024    9269    9269    9513    9909    10215   10215   10215   10368   10673   10673   11008   11192   11192   11039   7864    7864    7864    2828    661 661 661 1332    1332    2309    2309    2950    2950    3683    4507    4507    5117    5667    5667    5667    6094    6521    6521    6949    7437    7437    7864    7864    8169    8169    8322    8689    9086    9086];  
dt = [0 diff(data)];  
t_thresh = -0.5;       % threshold to identify changes (exclude noise)  
ind = find(dt < t_thresh);  
figure
set(gcf,'position',[50 50 (1080) (675)])
ax(1) = subplot(2,1,1);
plot(data, '.')
xlim([-5 155])
grid on
ax(2) = subplot(2,1,2)
plot(dt, '.')
grid on
hold on
plot(ind, dt(ind), 'ro')
xlim([-5 155])
linkaxes(ax,'x')

The data often contains repeat points which makes just looking for large changes in the derivative difficult.
The solution of this problem with the included data set would be:

cycle_ind = [18 68 116]

Thanks for the help

Any help would be greatly appreciated.

Answer 1

I would try filtering the data then looking for sign changes in the derivative, rather than thresholding it.

B = fir1(8,0.5);
newData = filtfilt(B,1,data);
dt = [0 sign(diff(newData))];
ddt = -[0 diff(dt)];
localMaxima = data(ddt>0);
idx = find(ddt>0);
plot(1:length(data),[data;newData;ddt*max(data)])