Hierarchical least squares algorithms for single-input multiple-output systems based on the auxiliary model

Xiang, Lili; Xie, Lihua; Liao, Yuwu; Ding, Ruifeng

doi:10.1016/j.mcm.2010.05.025

Cited by 30 publications

(16 citation statements)

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“…Using this idea, the following two steps are involved in forming the regression matrix Φ in (4). Firstly, the RBF centers c j are determined by randomly selecting M(M ≤ N) samples from the training data.…”

Section: Determining the Centers And Widths Using The Elmmentioning

confidence: 99%

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A multi-output two-stage locally regularized model construction method using the extreme learning machine

et al. 2014

Neurocomputing

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. (2014). A multi-output two-stage locally regularized model construction method using the extreme learning machine. Neurocomputing, 128, 104-112. DOI: 10.1016/j.neucom.2013 Published in: Neurocomputing Document Version: Peer reviewed version Queen's University Belfast -Research Portal: Link to publication record in Queen's University Belfast Research Portal Publisher rights NOTICE: this is the author's version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Vo. 128, 2014 General rights Copyright for the publications made accessible via the Queen's University Belfast Research Portal is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights.Take down policy The Research Portal is Queen's institutional repository that provides access to Queen's research output. Every effort has been made to ensure that content in the Research Portal does not infringe any person's rights, or applicable UK laws. If you discover content in the Research Portal that you believe breaches copyright or violates any law, please contact openaccess@qub.ac.uk. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractThis paper investigates the construction of linear-in-the-parameters (LITP) models for multi-output regression problems. Most existing stepwise forward algorithms choose the regressor terms one by one, each time maximizing the model error reduction ratio. The drawback is that such procedures cannot guarantee a sparse model, especially under highly noisy learning conditions. The main objective of this paper is to improve the sparsity and generalization capability of a model for multi-output regression problems, while reducing the computational complexity. This is achieved by proposing a novel multioutput two-stage locally regularized model construction (MTLRMC) method using the extreme learning machine (ELM). In this new algorithm, the nonlinear parameters in each term, such as the width of the Gaussian function and the power of a polynomial term, are firstly determined by the ELM. An initial multi-output LITP model is then generated according to the termination criteria in the first stage. The significance of each selected regressor i...

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Section: Determining the Centers And Widths Using The Elmmentioning

confidence: 99%

“…For example, multi-innovation stochastic gradient [3] and hierarchical least squares algorithms [4] have been proposed for multi-output systems. Gradient-based and least-squares-based iterative estimation algorithms for MIMO systems have also been proposed [5].…”

Section: Introductionmentioning

confidence: 99%

A multi-output two-stage locally regularized model construction method using the extreme learning machine

et al. 2014

Neurocomputing

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“…Recently, new hierarchical least squares algorithms and hierarchical stochastic gradient algorithms were developed for multivariable equation error systems using the hierarchical identification principle [36,37]. Xiang, et al presented a hierarchical least squares algorithm for single-input multiple-output systems based on the auxiliary model [38]; Han, et al proposed a hierarchical least squares based iterative identification for multivariable systems with moving average noises (i.e., multivariable CARMA-like models) [39]. On the basis of the work in [39], this paper studies the hierarchical gradient based iterative parameter estimation method for multivariable output error moving average systems using the hierarchical identification principle.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems

Zhang

Ding

Liu

2011

Computers & Mathematics with Applications

107

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a b s t r a c tAccording to the hierarchical identification principle, a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems (i.e., multivariable OEMA-like models) which is different from multivariable CARMA-like models. As there exist unmeasurable noise-free outputs and unknown noise terms in the information vector/matrix of the corresponding identification model, this paper is, by means of the auxiliary model identification idea, to replace the unmeasurable variables in the information vector/matrix with the estimated residuals and the outputs of the auxiliary model. A numerical example is provided.

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“…Many estimation/identification algorithms were reported for different systems, e.g., the hierarchical estimation algorithms for multivariable systems [14,15], the multi-innovation estimation algorithms for linear systems [16][17][18][19][20][21][22][23][24][25]. Moreover, Shi and Fang presented a Kalman filter based identification method to estimate parameters for systems with randomly missing measurements in a network environment [26] and Shi et al discussed Kalman filter based adaptive control for networked systems with unknown parameters and randomly missing outputs [27].…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation for nonlinear dynamical adjustment models

Xiao

Yue

2011

Mathematical and Computer Modelling

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a b s t r a c tA recursive generalized least squares algorithm and a filtering based least squares algorithm are developed for input nonlinear dynamical adjustment models with memoryless nonlinear blocks followed by linear dynamical blocks. The basic idea is to use the filtering technique and to replace the unknown terms in the information vectors with their estimates. The simulation results show the performance of the proposed algorithms.

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Hierarchical least squares algorithms for single-input multiple-output systems based on the auxiliary model

Cited by 30 publications

References 50 publications

A multi-output two-stage locally regularized model construction method using the extreme learning machine

A multi-output two-stage locally regularized model construction method using the extreme learning machine

Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems

Parameter estimation for nonlinear dynamical adjustment models

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