In practice, it is usually difficult to obtain the physical model of nonlinear, rotor-bearing systems due to uncertain nonlinearities. In order to solve this issue to conduct the analysis and design of nonlinear, rotor-bearing systems, in this study, a data driven NARX (Nonlinear Auto-Regressive with exogenous inputs) model is identified. Due to the lack of the random input signal which is required in the identification of a system′s NARX model, for nonlinear, rotor-bearing systems, a new multi-harmonic input based model identification approach is introduced. Moreover, the identification results of NARX models on the nonlinear, rotor-bearing systems are validated under different conditions (such as: low speed, critical speed, and over critical speed), illustrating the applicability of the proposed approach. Finally, an experimental test is conducted to identify the NARX model of the nonlinear rotor test rig, showing that the NARX model can be used to reproduce the characteristics of the underlying system accurately, which provides a reliable model for dynamic analysis, control, and fault diagnosis of the nonlinear, rotor-bearing system.

This brief presents a new framework for the identification of nonlinear autoregressive (AR) models with exogenous inputs (NARX) model for design (NARX-M-for-D), which represents NARX of engineering systems where the model coefficients are represented explicitly as a function of the physical parameters that can be adjusted for the system design. The framework is concerned with identifying a common structure of the NARX model which is shared by all design configurations, and with identifying the nonlinear static maps that link these design parameters with NARX coefficients. The problem of the common structure identification is solved via extended forward orthogonal regression, after which a joint regression problem is formulated to determine the explicit relationships between NARX coefficients and physical parameters for the system. Using sparse regression methods allows simultaneous detection of a compact structure of the NARX model and design parameter maps. The reduced structure improves model generalization in design parameter space which is instrumental for the application of the identified model in the system design. The performance of the framework is evaluated on a benchmark model and on the experimental data from dynamic testing of auxetic foams. An example of evaluating the output frequency response from the identified model demonstrates how the proposed framework can be used to assess dynamical properties of engineered systems in the design process.