  Identification of nonlinear dynamic systems remains a significant challenge
across engineering. This work suggests an approach based on Bayesian filtering
to extract and identify the contribution of an unknown nonlinear term in the
system which can be seen as an alternative viewpoint on restoring force surface
type approaches. To achieve this identification, the contribution which is the
nonlinear restoring force is modelled, initially, as a Gaussian process in
time. That Gaussian process is converted into a state-space model and combined
with the linear dynamic component of the system. Then, by inference of the
filtering and smoothing distributions, the internal states of the system and
the nonlinear restoring force can be extracted. In possession of these states a
nonlinear model can be constructed. The approach is demonstrated to be
effective in both a simulated case study and on an experimental benchmark
dataset.
