# Grey-box state-space identification of nonlinear mechanical vibrations

arXiv: https://arxiv.org/abs/1804.10758 · HTML: https://mlsanity.com/paper/1804.10758/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2018.

## Built on by (most cited first, 3 of 3)

- [Physics-informed machine learning for Structural Health Monitoring](https://mlsanity.com/paper/2206.15303/) (2022)
- [Decoupling multivariate functions using a nonparametric filtered tensor decomposition](https://mlsanity.com/paper/2205.11153/) (2022)
- [The Benefit of Noise-Injection for Dynamic Gray-Box Model Creation](https://mlsanity.com/paper/2310.01517/) (2023)

## Abstract (arXiv)

The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semi-physical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single-input, single-output (SISO) nonlinear mechanical system and to a single-input, multiple-output (SIMO) geometrically nonlinear beam structure.