A model validation scale based on multiple indices

Abstract

Validation of an estimated model is not a trivial task because it depends on the purpose of the model, which usually defines the most important features of the model. Thus, in a validation process, the use of diverse tools that exploit different domains is recommended. Here, with this aim, a scale for model validation is proposed that combines the Normalized Root Mean Square Error (NRMSE) with two new indices: the coherence-based index and the fourth-order cross-cumulant index. The proposed scale was used for the validation of three models: the Logistic Map, the Duffing-Ueda oscillator, and the Buck converter. The results demonstrated that the proposed model validation scale produces a more complete validation process that takes into account both time and frequency information and provides robustness against Gaussian noise.

Hybrid Method Based on NARX models and Machine Learning for Pattern Recognition

“…System Identification is an experimental approach that aims to identify and adjust a mathematical model of a system, based on experimental data that record the behavior of system inputs and outputs (Billings, 2013;Aguirre, 2007). In particular, the interest in nonlinear system identification has received a lot of attention from researchers since the 1950s and many relevant results have been developed (Wei et al, 2004;Nepomuceno and Martins, 2016;Ferreira et al, 2017). A model representation constantly employed is the NARX model (Nonlinear Au-toRegressive with eXogenous inputs), consisting of a mathematical model based on differential equations.…”

Classificação de Distúrbios na Qualidade de Energia Usando Modelagem Logística-NARX Multinomial

“…Uma vez determinada a estrutura do modelo, deve-se estimar seus parâmetros, que pode ser realizada usando o método tradicional dos Mínimos Quadrados, Gradiente Descendente e Metropolis-Hastings algorithm (Baldacchino et al, 2012). Por fim, a validação do modelo pode ser realizada mediante testes de correlação estatística, que verificam a validade dos modelos de entrada e saída identificados (Ferreira et al, 2017). Em resumo, a identificação de sistemasé um processo que cria um modelo parcimonioso que satisfaz um conjunto de testes de acurácia e validade.…”

Structure selection based on interval predictor model for recovering static non‐linearities from chaotic data

“…It has been widely recognised the importance of identification for control as a research area that deals with modelling, the design of experiments, identification of dynamic models appropriate for control design and evaluation of the quality of estimated models [1–4]. Although the quality of models, also known as model validation, has been evaluated in many different ways and numerous works have been published [5–7], it is also well known that non‐linear systems pose challenging difficulties to find a suitable model. For instance, it has been known for a number of years that most conventional approaches for model validation are not attractive when the models are chaotic [8].…”