Reproducing kernel function-based Filon and Levin methods for solving highly oscillatory integral

Geng, Fazhan; Wu, Xinyuan

doi:10.1016/j.amc.2021.125980

Cited by 24 publications

(16 citation statements)

References 29 publications

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“…Compared with the AM‐RLS algorithm, the AM‐HLS algorithm has higher computational efficiency. The proposed methods in this article can be extended to study the parameter identification problems of other nonlinear systems with colored noises 90‐98 and can be applied to other fields 99‐104 such as signal analysis and engineering application systems 105‐111 . In the future work, the further investigation includes the parameter estimation methods of the scalar or multivariable nonlinear systems and the convergence analysis of the proposed algorithms.…”

Section: Discussionmentioning

confidence: 99%

Recursive least squares estimation methods for a class of nonlinear systems based on non‐uniform sampling

Liu

Chen

Ding

et al. 2021

Adaptive Control & Signal

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Summary Many dynamic processes in practice have nonlinear characteristics and must be described by using nonlinear models. It remains to be a challenging problem to build the models of such nonlinear systems and to estimate their parameters. This article studies the parameter estimation problem for a class of Hammerstein‐Wiener nonlinear systems based on non‐uniform sampling. By means of the auxiliary model identification idea, an auxiliary model‐based recursive least squares algorithm is derived for the systems. In order to enhance the computational efficiency, an auxiliary model‐based hierarchical least squares algorithm is proposed by utilizing the hierarchical identification principle. The simulation results confirm the effectiveness of the proposed algorithms.

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Section: Discussionmentioning

confidence: 99%

Recursive least squares estimation methods for a class of nonlinear systems based on non‐uniform sampling

Liu

Chen

Ding

et al. 2021

Adaptive Control & Signal

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“…The simulation results indicate that these two algorithms are effective and the multiinnovation algorithm can provide higher accurate parameter estimation. The proposed approaches in the paper can combine other mathematical tools [60][61][62][63] and statistical strategies [64][65][66][67] and identification methods 68-to study the parameter estimation issues of linear stochastic systems and nonlinear stochastic systems with different structures and disturbance noises [72][73][74][75][76][77][78][79][80][81] and can be applied to literatures such as paper-making systems, information processing, transportation communication systems, and so forth. In the future work, the further investigation includes applying the proposed methods to the parameters estimation of the control systems in the actual industrial processes.…”

Section: Discussionmentioning

confidence: 99%

Filtering‐based recursive least squares estimation approaches for multivariate equation‐error systems by using the multiinnovation theory

Wang

2021

Adaptive Control & Signal

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This article researches the filtering-based parameter estimation issues for a class of multivariate control systems with colored noise. A filtering-based recursive generalized extended least squares algorithm is derived, in which the data filtering technique is used for transforming the original system into two subidentification systems and the least squares principle is used for estimating parameters of these two subsystems. Furthermore, in order to improve the parameter estimation accuracy, the multiinnovation theory is added for deducing a filtering-based multiinnovation recursive generalized extended least squares algorithm.The numerical example confirms that these two proposed algorithms are effective.

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“…However, there are two more interesting aspects are still open: whether the proposed methods can be used to identify the multivariable systems and what optimization strategies should be used to solve the problems of increased computational load caused by the multivariable systems, which are currently under our investigation. The proposed approaches in the article can combine other mathematical tools and statistical strategies and identification methods to study the parameter estimation issues of other linear stochastic systems and nonlinear stochastic systems with different structures and disturbance noises [68][69][70][71][72] and can be applied to literatures [73][74][75][76][77][78][79] such as paper-making systems, information processing, transportation communication systems [80][81][82][83][84][85] and so on.…”

Section: Discussionmentioning

confidence: 99%

Multi‐innovation Newton recursive methods for solving the support vector machine regression problems

Ding

Wang

2021

Intl J Robust & Nonlinear

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The support vector machine has been widely used in binary classification applications because of the simplicity of its implementation. This article proposes an online identification method based on the support vector machine in the field of parameter identification. By substituting the constraint item into the original criterion function to form a new criterion function about the weight vector and the bias item, and then on the basis of the recursive identification methods, the newly established criterion function is minimized by using the Newton search to derive the Newton recursive support vector machine algorithm. Additionally, in order to improve the performance of the Newton recursive support vector machine algorithm, the multi-innovation identification theory is applied to optimize the algorithm, and a multi-innovation Newton recursive support vector machine algorithm is derived. In addition, the convergence and the calculation amount of the proposed algorithms are carefully analyzed in this article.Finally, a numerical simulation example is given to compare the Newton recursive algorithm and the corresponding multi-innovation recursive algorithm. The results show that the algorithms and optimization strategy studied in this article are effective.

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Reproducing kernel function-based Filon and Levin methods for solving highly oscillatory integral

Cited by 24 publications

References 29 publications

Recursive least squares estimation methods for a class of nonlinear systems based on non‐uniform sampling

Recursive least squares estimation methods for a class of nonlinear systems based on non‐uniform sampling

Filtering‐based recursive least squares estimation approaches for multivariate equation‐error systems by using the multiinnovation theory

Multi‐innovation Newton recursive methods for solving the support vector machine regression problems

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