Prediction and simulation errors in parameter estimation for nonlinear systems

Aguirre, Luís A.; Barbosa, Bruno Henrique Groenner; Braga, Antônio de Pádua

doi:10.1016/j.ymssp.2010.05.003

Cited by 30 publications

(19 citation statements)

References 41 publications

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“…3, the simulationbased index (denoted I s ) provides a sharp and precise classification of the regressors. This is very much in line with a number of previous results in the literature (see, e.g., Aguirre et al, 2010, Connally, Li, & Irwin, 2007and Piroddi & Spinelli, 2003.…”

Section: Evaluating the Regressor Importancesupporting

confidence: 93%

“…Accordingly, if employed for parameter estimation in perfect model matching conditions (i.e., the model structure coincides with that of the system generating the data), no bias is experimented. On the other hand, the MSS process is much more affected by this choice of input signal, as observed in several works (Aguirre et al, 2010;Piroddi & Spinelli, 2003). This occurs because such an input produces a slowly varying output, causing the difference between adjacent output samples to be very small.…”

Section: Evaluating the Regressor Importancementioning

confidence: 94%

“…The exponential transformation is also useful in the MSS task, since it tends to amplify the differences between models with similar performance, so that even small improvements can be detected. For further generality and in analogy with Aguirre, Barbosa, and Braga (2010), one can employ the following combined performance index:…”

Section: Parameter Estimation and Student's T-testmentioning

confidence: 99%

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A randomized algorithm for nonlinear model structure selection

2015

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The identification of polynomial Nonlinear Autoregressive [Moving Average] models with eXogenous variables (NAR[MA]X) is typically carried out with incremental model building techniques that progressively select the terms to include in the model. The Model Structure Selection (MSS) turns out to be the hardest task of the identification process due to the difficulty of correctly evaluating the importance of a generic term. As a result, classical MSS methods sometimes yield unsatisfactory models, that are unreliable over long-range prediction horizons. The MSS problem is here recast into a probabilistic framework based on which a randomized algorithm for MSS is derived, denoted RaMSS. The method introduces a tentative probability distribution over models and progressively updates it by extracting useful information on the importance of each term from sampled model structures. The proposed method is validated over models with different characteristics by means of Monte Carlo simulations, which show its advantages over classical and competitor probabilistic MSS methods in terms of both reliability and computational efficiency

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Section: Evaluating the Regressor Importancesupporting

confidence: 93%

Section: Evaluating the Regressor Importancementioning

confidence: 94%

Section: Parameter Estimation and Student's T-testmentioning

confidence: 99%

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A randomized algorithm for nonlinear model structure selection

2015

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“…Several EA-based approaches for system identification have been proposed in the literature. A majority of the proposed approaches use EAs to determine the appropriate model complexity within a fixed class of dynamical models (for e.g., see [7]- [12]), or just use EAs to solve the underlying non-linear estimation problem (e.g., see [13], [14]). Alternatively, EAs can be used to build models from a basic set of elements without a prior specification of the structure of the model (e.g., see [15]- [17]).…”

Section: Introductionmentioning

confidence: 99%

Data-driven Modelling of Dynamical Systems Using Tree Adjoining Grammar and Genetic Programming

Khandelwal

Schoukens

Tóth

2019

2019 IEEE Congress on Evolutionary Computation (CEC)

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State-of-the-art methods for data-driven modelling of non-linear dynamical systems typically involve interactions with an expert user. In order to partially automate the process of modelling physical systems from data, many EA-based approaches have been proposed for model-structure selection, with special focus on non-linear systems. Recently, an approach for data-driven modelling of non-linear dynamical systems using Genetic Programming (GP) was proposed. The novelty of the method was the modelling of noise and the use of Tree Adjoining Grammar to shape the search-space explored by GP. In this paper, we report results achieved by the proposed method on three case studies. Each of the case studies considered here is based on real physical systems. The case studies pose a variety of challenges. In particular, these challenges range over varying amounts of prior knowledge of the true system, amount of data available, the complexity of the dynamics of the system, and the nature of non-linearities in the system. Based on the results achieved for the case studies, we critically analyse the performance of the proposed method.

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“…As an extreme alternative to the one-step-ahead prediction error, we can consider simulation error, which is often interpreted as ∞-step-ahead prediction error. It has been observed in [14] and [15] that simulation error is more sensitive to model errors in non-linear systems than prediction error. However, estimating model parameters using simulation error leads to a non-convex optimization problem, in general.…”

Section: B Performance Criterionmentioning

confidence: 99%

Grammar-based Representation and Identification of Dynamical Systems

Khandelwal

Schoukens

Tóth

2019

2019 18th European Control Conference (ECC)

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In this paper we propose a novel approach to identify dynamical systems. The method estimates the model structure and the parameters of the model simultaneously, automating the critical decisions involved in identification such as model structure and complexity selection. In order to solve the combined model structure and model parameter estimation problem, a new representation of dynamical systems is proposed. The proposed representation is based on Tree Adjoining Grammar, a formalism that was developed from linguistic considerations. Using the proposed representation, the identification problem can be interpreted as a multiobjective optimization problem and we propose a Evolutionary Algorithm-based approach to solve the problem. A benchmark example is used to demonstrate the proposed approach. The results were found to be comparable to that obtained by stateof-the-art non-linear system identification methods, without making use of knowledge of the system description.

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Prediction and simulation errors in parameter estimation for nonlinear systems

Cited by 30 publications

References 41 publications

A randomized algorithm for nonlinear model structure selection

A randomized algorithm for nonlinear model structure selection

Data-driven Modelling of Dynamical Systems Using Tree Adjoining Grammar and Genetic Programming

Grammar-based Representation and Identification of Dynamical Systems

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