Can I use an unknown number of variables to model my time-series?

I have a bunch of data-sets showing the relationship between two observables, “force” and “time”. See example plot

You see the regularity of the features: There is a region of linearly increasing force, then at some time the force decreases sharply and then it will start to increase again. The number of “peaks” is not constant but typically somewhere between 2 and 10.

I would like to fit each of the increasing regions with a straigt line and have the script figure out when the sudden decrease happens.
I have been following Probabilistic Programming & Bayesian Methods for Hackers where the first example is finding the time where some observable change behavior. Link to the example

The problem is that I don’t know beforehand how many of these changes I have to find. So I can’t just create two linear functions and find the time to switch from one to the other. It needs to be more general.

How should I approach this?