Identify random repetitive patterns
Finding repeating but not periodically repeating patterns of an unknown template which you expect the algorithm to identify is a hard problem.  Nature typically doesn't shut off all the other patterns that may be present for our convienance either.  

Signals have sources or generating mechanisms. It would help if you had some idea how your patterns are generated.

The concept of noise can be helpful because what isn't noise might very well be signal.

I would approach a problem as a time series that corresponds to an ODE and try to learn the ODE.

One way to do this would be to construct a phase space representation, that is something like $x(t)$ and $y(t)=dx(t)/dt$. If the noise is low using central differences can give a good approximation to the derivative of your time series. A phase space plot might identify orbits and limit cycles produced by your pattern.

These ideas are common in chaos theory and I would search Google accordingly

As an example https://en.m.wikipedia.org/wiki/Van_der_Pol_oscillator