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.

中文翻译：

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非线性系统辨识的潜在恢复力方法

非线性动态系统的识别仍然是整个工程领域的重大挑战。这项工作提出了一种基于贝叶斯滤波的方法来提取和识别系统中未知非线性项的贡献，这可以看作是恢复力表面类型方法的替代观点。为了实现这种识别，非线性恢复力的贡献最初被建模为高斯过程。该高斯过程被转换为状态空间模型，并与系统的线性动态组件相结合。然后，通过滤波和平滑分布的推断，可以提取系统的内部状态和非线性恢复力。拥有这些状态，可以构建非线性模型。