A Latent Restoring Force Approach to Nonlinear System Identification
This work addresses a significant challenge in engineering for system identification, but it appears incremental as it builds on existing restoring force surface approaches.
The paper tackles the challenge of identifying nonlinear dynamic systems by proposing a Bayesian filtering approach to extract and model an unknown nonlinear restoring force, demonstrating effectiveness in both simulated and experimental benchmark datasets.
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.