Integrated Identification of the Nonlinear Autoregressive Models With Exogenous Inputs (NARX) for Engineering Systems Design

• Published in: IEEE transactions on control systems technology Vol. 31; no. 1; pp. 394 - 401
• Main Authors: Kadochnikova, Anastasia, Zhu, Yunpeng, Lang, Zi-Qiang, Kadirkamanathan, Visakan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Autoregressive models; Autoregressive processes; Auxetic materials; Benchmark testing; Biological system modeling; Coefficients; Configuration management; Design parameters; Design-parameter-dependent model; Dynamic tests; Frequency response; Indexes; modeling for design; nonlinear system identification; Parameter identification; Physical properties; Predictive models; Presses; Regression; regularized least squares (LS); sparse structure detection; System analysis and design; Systems design
• ISSN: 1063-6536; 1558-0865
• DOI: 10.1109/TCST.2022.3171130

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.