Regressor selection with the analysis of variance method

Abstract

Identification of non-linear finite impulse response (N-FIR) models is studied. In particular the selection of model structure, i.e., to find the best regressors, is examined.In this report it is shown that a statistical method, the analysis of variance, is a better alternative than exhaustive search among all possible regressors, in the identification of the structure of non-linear FIR-models. The method is evaluated for different conditions on the input signal to the system. The results will serve as a foundation for the extension of the ideas to non-linear autoregressive processes. Abstract: Identification of non-linear finite impulse response (N-FIR) models is studied. In particular the selection of model structure, i.e., to find the best regressors, is examined. In this paper it is shown that a statistical method, the analysis of variance, is a better alternative than exhaustive search among all possible regressors, in the identification of the structure of non-linear FIR-models. The method is evaluated for different conditions on the input signal to the system. The results will serve as a foundation for the extension of the ideas to non-linear autoregressive processes.

Efficient hinging hyperplanes neural network and its application in nonlinear system identification

“…. , u(k − n a )] T is chosen by trying different values and selecting the one yielding the least validation error, which could be time-consuming [20]. In [21], a structured ANOVA approach has been proposed for regressor and structure selection, which requires large number of data points in high dimension.…”

Identification of non‐linear stochastic spatiotemporal dynamical systems

“…where Y l , is the corresponding lth term of Y , β T l , F l s and e l s are corresponding coefficient vector of the linear part, unknown non-linear mappings and noise terms respectively for N h = N dimensional system that is to be determined directly from the discrete observation data of u(t i , x l ). For more details of the PLM, it can be referred to the references [18,19]. Then, it can be seen that (17b) could be used as a predictor for the finite-element coefficients as the model (18) and (19) are identified by using the observations.…”

“…For more details of the PLM, it can be referred to the references [18,19]. Then, it can be seen that (17b) could be used as a predictor for the finite-element coefficients as the model (18) and (19) are identified by using the observations. B-spline finite-element basis is used here, and let {φ l } N l=0 be the standard l 0 th order B-spline basis.…”

“…Nonlinear system identification is to build a mathematical model with measurement data for non-linear dynamical systems, and many methods have been proposed such as set membership, neural network, orthogonal least square etc [15][16][17][18]. Among those, the kernel learning method is a very promising one, which could realise the best estimation with least number of samples [19,20].…”

Identification of non-parametric FIR non-linear systems with low-degree interactive terms

“…Nonlinear system identification is usually the first step in nonlinear system analysis and design. Despite progress made in recent years in Haber et al (1990); ; Ljung et al (2005); ; Soderstrom et al (2005), development of nonlinear system identification is still in its early stage. In particular, nonparametric nonlinear system identification without a priori structural information poses a very tough problem.…”