Robustness of nonlinear parameter identification in the presence of process noise using control-based continuation

In this study, we consider the experimentally obtained, periodically forced response of a nonlinear structure in the presence of process noise. Control-based continuation is used to measure both the stable and unstable periodic solutions, while different levels of noise are injected into the system. Using these data, the robustness of the control-based continuation algorithm and its ability to capture the noise-free system response are assessed by identifying the parameters of an associated Duffing-like model. We demonstrate that control-based continuation extracts system information more robustly, in the presence of a high level of noise, than open-loop parameter sweeps and so is a valuable tool for investigating nonlinear structures.

Investigating the Influence of Fluid-Structure Interactions on Nonlinear System Identification

A complex fluid-structure interaction can often create nonlinear dynamic behaviour in the structure. This can be better estimated using nonlinear modal analysis, capable of identifying and quantifying the nonlinearity in the structure. In this study, the case of a vibrating beam submerged in liquid using a nonlinear parameter identification method is presented. This system is considered as an alternative propulsion mechanism, hence understanding the interaction between the fluid and the structure is necessary for its control. Here, impulse signals are used to characterise the numerical and experimental dynamics response of the system. Since the transient responses contain of a multi-component vibratory signals, a vibration decomposition method is used to separate the time response signals based on the dominant amplitude in the frequency response function. The separated time-series signals are then fitted to the nonlinear identification method to construct the backbone and damping curves. The modal parameters obtained from experimental data are then used as a base for the development of the analytical models. The analytical approaches are based on the Euler-Bernoulli beam theory with additional mass and quadratic damping functions to account for the presence of the fluid. Validations are carried out by comparing the dynamic responses of the analytical and experimental measurements demonstrating the accuracy of the model and hence, its suitability for control purposes.

A linear regularization method for a nonlinear parameter identification problem

In order to obtain regularized approximations for the solution

Nonlinear System Identification Using Quasi-ARX RBFN Models with a Parameter-Classified Scheme

Quasi-linear autoregressive with exogenous inputs (Quasi-ARX) models have received considerable attention for their usefulness in nonlinear system identification and control. In this paper, identification methods of quasi-ARX type models are reviewed and categorized in three main groups, and a two-step learning approach is proposed as an extension of the parameter-classified methods to identify the quasi-ARX radial basis function network (RBFN) model. Firstly, a clustering method is utilized to provide statistical properties of the dataset for determining the parameters nonlinear to the model, which are interpreted meaningfully in the sense of interpolation parameters of a local linear model. Secondly, support vector regression is used to estimate the parameters linear to the model; meanwhile, an explicit kernel mapping is given in terms of the nonlinear parameter identification procedure, in which the model is transformed from the nonlinear-in-nature to the linear-in-parameter. Numerical and real cases are carried out finally to demonstrate the effectiveness and generalization ability of the proposed method.