Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains

By Stephen A. Billings. 2013

1,017 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

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Citations in the corpus

Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems (2018, background): “…in the context of identifying nonlinear dynamics, there exist several deterministic and probabilistic tools including radial basis functions [6], neural networks [7], Gaussian processes [8, 9, 10, 11, 12], and nonlinear auto-regressive models such as NARMAX [13] and recurrent neural networks [14].”
The Challenge of Machine Learning in Space Weather: Nowcasting and Forecasting (2019, methodology): “An algorithm to identify the most important terms is the so-called FROLS (Forward Regression Orthogonal Least Square) algorithm (Billings, 2013; Billings et al., 1989), which is used in combination with the error reduction ratio index to measure the significance of each candidate model term.”
A lower bound error for free-run simulation of the polynomial NARMAX (2016, methodology): “Billings (2013) presents a extensive list of these techniques.”
Model selection for dynamical systems via sparse regression and information criteria (2017, methodology): “Nonlinear autoregressive moving average models with exogenous inputs (NARMAX models) have also been used for systems identification in conjunction with information criteria [30,31].”
Constrained sparse Galerkin regression (2016, methodology): “…theory (Mezić 2005, 2013) and variants (Tu et al. 2014; Williams, Kevrekidis & Rowley 2015), cluster reduced-order modelling (CROM) (Kaiser et al. 2014), NARMAX (Glaz, Liu & Friedmann 2010; Zhang et al. 2012; Billings 2013; Semeraro et al. 2017) and network analysis of fluids (Nair & Taira 2015).”
On Model-Free Adaptive Control and Its Stability Analysis (2019, background): “System (1) is a general description of large classes of the nonlinear systems and lots of system models can be shown as a special case of this model, such as the bilinear systems [42], Hammerstein model [43], DARMA model [44], and so on.”
Data-driven decomposition analysis and estimation of link-level electric vehicle energy consumption under real-world traffic conditions (2017, methodology): “In this study, we selected the vehicle speed and applied the cross-correlation technique (Billings, 2013) to synchronize these two data sources.”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (2017, background): “The Multivariate Polynomial Regression (MPR) is an extension of the linear and multilinear regressions which allows us to model nonlinear interaction between independent variables [Billings, 2013, Chen and Billings, 1989, Vaccari, 2003].”
Probabilistic Recurrent State-Space Models (2018, background): “State-Space Models (SSMs) are one popular class of representations (Billings, 2013), which describe a system with input u t and output y t in terms of a latent Markovian state x t .”
A comprehensive review of digital twin — part 1: modeling and twinning enabling technologies (2022, methodology): “In a NARMAX model, the noise sequences (i.e., k, k−1,⋯ , k−e ) are also included in g(⋅) in addition to past values of exogenous inputs and the response (Billings 2013).”
Sparse identification of nonlinear dynamics for model predictive control in the low-data limit (2017, methodology): “…models, including state-space models from the eigensystem realization algorithm (ERA) [13] and other subspace identiﬁcation methods, Volterra series [14–16], autoregressive models [17] (e.g., ARX, ARMA, NARX, and NARMAX [18] models), and neural network models [19–22], to name only a few.”
Neural Granger Causality (2021, methodology): “A nonlinear autoregressive model (NAR) allows x t to evolve according to more general nonlinear dynamics [25] x t ¼ g ð x <t 1 ; . . . where x <ti ¼ . . . ; x ð t (cid”