Recursive approximation by ARX model: A tool for grey box modelling

Abstract

The presented procedure computes approximate probabilistic models of complex dynamic phenomena recursively with respect to an increasing amount of observed evidence. Measured, fictitious as well as simulated data can be used in combination for obtaining a reasonably conservative approximate model. Thus information from a number of sources can be systematically merged using a refinement of the recently proposed method of Bayesian pooling of imprecise opinions from a variety of experts. It can be applied recursively as the number of treated items grows.The procedure provides (i) a new tool needed for grey as well as black box modelling, (ii) a novel adaptation of probabilistic models and (iii) an approximation of a given model by a simpler one.The general procedure is applied to the autoregressive model with exogenous variables ( A M ) . This example illustrates the adopted approach and conmbutes to the solution of the following tasks: (i) estimation of an appropriate model structure; (ii) incorporation of prior knowledge into the initial conditions of recursive least squares; (iii) construction of a reference for an advanced forgetting technique; (iv) approximation of a complex analytic/simulation model by an ARX model.The behaviour of the procedure is illustrated on typical examples.

Multi-objective symbolic regression for physics-aware dynamic modeling

“…The combination of a priori knowledge with data-driven modeling is not new. Standard graybox modeling methods include a priori information typically in the form of constraints on the model parameters and variables (Tulleken, 1993;Karny et al, 1995;Johansen, 1996;Timmons et al, 1997). For instance, it is well known that the poles of a linear discrete-time model that emerge from a properly sampled stable continuous-time system cannot be situated in the left half complex plane.…”

Multi-objective symbolic regression for physics-aware dynamic modeling

“…The combination of a priori knowledge with data-driven modeling is not new. Standard graybox modeling methods include a priori information typically in the form of constraints on the model parameters and variables (Tulleken, 1993;Karny et al, 1995;Johansen, 1996;Timmons et al, 1997). For instance, it is well known that the poles of a linear discrete-time model that emerge from a properly sampled stable continuous-time system cannot be situated in the left half complex plane.…”

Identificação não-linear caixa-cinza: uma revisão e novos resultados

“…Em (Kárný et al, 1995)é proposto um procedimento, que segundo os autores, fornece (i) uma nova ferramenta tanto para modelagem caixa-preta quanto para caixacinza, (ii) uma inédita adaptação de modelos probabilísticos e (iii) uma forma de reduzir a complexidade do modelo.…”

Multi-objective symbolic regression for physics-aware dynamic modeling

“…The combination of a priori knowledge with data-driven modeling is not new. Standard graybox modeling methods include a priori information typically in the form of constraints on the model parameters and variables (Tulleken, 1993;Karny et al, 1995;Johansen, 1996;Timmons et al, 1997). For instance, it is well known that the poles of a linear discrete-time model that emerge from a properly sampled stable continuous-time system cannot be situated in the left half complex plane.…”

Identificação não-linear caixa-cinza: uma revisão e novos resultados

“…Em (Kárný et al, 1995)é proposto um procedimento, que segundo os autores, fornece (i) uma nova ferramenta tanto para modelagem caixa-preta quanto para caixacinza, (ii) uma inédita adaptação de modelos probabilísticos e (iii) uma forma de reduzir a complexidade do modelo.…”

Multi-objective symbolic regression for physics-aware dynamic modeling

“…The combination of a priori knowledge with data-driven modeling is not new. Standard graybox modeling methods include a priori information typically in the form of constraints on the model parameters and variables (Tulleken, 1993;Karny et al, 1995;Johansen, 1996;Timmons et al, 1997). For instance, it is well known that the poles of a linear discrete-time model that emerge from a properly sampled stable continuous-time system cannot be situated in the left half complex plane.…”

Identificação não-linear caixa-cinza: uma revisão e novos resultados

“…Em (Kárný et al, 1995)é proposto um procedimento, que segundo os autores, fornece (i) uma nova ferramenta tanto para modelagem caixa-preta quanto para caixacinza, (ii) uma inédita adaptação de modelos probabilísticos e (iii) uma forma de reduzir a complexidade do modelo.…”