  An approach for the identification of discontinuous and nonsmooth nonlinear
forces, as those generated by frictional contacts, in mechanical systems that
can be approximated by a single-degree-of-freedom model is presented. To handle
the sharp variations and multiple motion regimes introduced by these
nonlinearities in the dynamic response, the partially-known physics-based model
and noisy measurements of the system's response to a known input force are
combined within a switching Gaussian process latent force model (GPLFM). In
this grey-box framework, multiple Gaussian processes are used to model the
unknown nonlinear force across different motion regimes and a resetting model
enables the generation of discontinuities. The states of the system, nonlinear
force and regime transitions are inferred by using filtering and smoothing
techniques for switching linear dynamical systems. The proposed switching GPLFM
is applied to a simulated dry friction oscillator and an experimental setup
consisting in a single-storey frame with a brass-to-steel contact. Excellent
results are obtained in terms of the identified nonlinear and discontinuous
friction force for varying: (i) normal load amplitudes in the contact; (ii)
measurement noise levels and (iii) number of samples in the datasets. Moreover,
the identified states, friction force and sequence of motion regimes are used
for evaluating: (1) uncertain system parameters; (2) the friction
force-velocity relationship and (3) the static friction force. The correct
identification of the discontinuous nonlinear force and the quantification of
any remaining uncertainty in its prediction enable the implementation an
accurate forward model able to predict the system's response to different input
forces.
