Hierarchical recursive least squares algorithms for Hammerstein nonlinear autoregressive output‐error systems

Kang, Zhen; Ji, Yan; Liu, Ximei

doi:10.1002/acs.3320

Cited by 82 publications

(50 citation statements)

References 89 publications

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“…[78][79][80][81] By combining the recursive identification methods with different search methods, different identification algorithms can be derived, such as the stochastic gradient algorithms, the recursive least squares algorithms, and the Newton recursive algorithms. [82][83][84] Compared with the latter two types of algorithms, the stochastic gradient algorithms have higher computational efficiency because the inverse of the matrix is not required. 85 Hence, in this part, we use the gradient algorithms to identify the unknown parameters of the established inner model.…”

Section: Dynamic Nonlinear Inner Model Identificationmentioning

confidence: 99%

A novel dynamic nonlinear partial least squares based on the cascade structure

Wang

2022

Intl J Robust & Nonlinear

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For the collinearity problem of input variables in actual industrial process modeling, a novel dynamic nonlinear partial least squares (PLS) approach is presented to solve this problem. In the proposed method, a novel cascade structure which is composed of an autoregressive exogenous model and a radial basis function neural network is introduced as the inner model of the conventional PLS method, so that the newly established PLS method has both dynamic and nonlinear characteristics. In this improvement, an external model for extracting the latent variables of input and output is established through the original PLS model, which eliminates the collinearity between original dependent variables, and then the aforementioned cascade framework is employed to describe the dynamic and nonlinear relationships between the input and output score variables. Furthermore, in order to estimate the unknown parameters of the established dynamic nonlinear inner model, a stochastic gradient algorithm and a forgetting factor stochastic gradient algorithm are presented. Additionally, a simple cross validation method is used to determine the orders of the inner model. Finally, a numerical simulation example and an application example are given to demonstrate the effectiveness of the proposed approach.

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Section: Dynamic Nonlinear Inner Model Identificationmentioning

confidence: 99%

A novel dynamic nonlinear partial least squares based on the cascade structure

Wang

2022

Intl J Robust & Nonlinear

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“…Recursive identification is to modify the previous parameter estimates based on the information brought by the new data. It has the advantage of high computational efficiency and is suitable for online identification 41‐43 . However, general recursive identification algorithms such as the recursive least‐squares algorithm and the stochastic gradient algorithm only use the latest data and innovation to correct the parameter estimation in each recursive calculation, which limits the estimation accuracy to a certain extent.…”

Section: Introductionmentioning

confidence: 99%

“…It has the advantage of high computational efficiency and is suitable for online identification. [41][42][43] However, general recursive identification algorithms such as the recursive least-squares algorithm and the stochastic gradient algorithm only use the latest data and innovation to correct the parameter estimation in each recursive calculation, which limits the estimation accuracy to a certain extent. In recent years, some advanced identification ideas such as the data filtering technique, the hierarchical identification idea, and the multi-innovation theory combined with the classical identification methods have been widely used in identification issues of linear and nonlinear systems, [44][45][46] among which the multi-innovation theory updates the parameter estimates with the newest data group, which has been confirmed as an effective way for optimizing the performance of the identification algorithms.…”

Section: Introductionmentioning

confidence: 99%

Filtering‐based multi‐innovation recursive identification methods for input nonlinear systems with piecewise‐linear nonlinearity based on the optimization criterion

Fan

Liu

2022

Optim Control Appl Methods

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Piecewise-linear nonlinearity is an effective representation for hard nonlinearities such as saturation, dead zone, and backlash, which can be also used as a general tool for approximating nonlinear characteristics. For the input piecewise-linear output-error autoregressive systems, we develop a parametric expression of the piecewise-linear nonlinearity through a switching function and position functions, and derive the identification model of the system by using the key item separation. Based on the optimization criterion, an auxiliary model-based multi-innovation recursive generalized least-squares algorithm is deduced for estimating the unknown parameters according to the obtained model. Since the system is disturbed by colored noise, we introduce the data filtering technique from a view point of improving the parameter estimation accuracy. The filtering identification model of the system is derived and a filtering-based multi-innovation recursive generalized least-squares algorithm is proposed. The simulation example demonstrates the effectiveness of the proposed algorithms and shows that the filtering-based multi-innovation recursive generalized least-squares algorithm has better identification performance.

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“…[1][2][3][4] The identification of the nonlinear system is the basis of nonlinear system control. [5][6][7][8] There exist various types of nonlinear systems in engineering. Therefore, the identification of nonlinear systems is very important and has attracted continuous attention of researchers.…”

Section: Introductionmentioning

confidence: 99%

Bias compensated stochastic gradient algorithm for identification of an ARX‐type nonlinear rational model and its application in modeling of the dynamic of the cellular toxicity

Jing

Kiely

Luxton

2022

Intl J Robust & Nonlinear

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Nonlinear rational model (NRM) is a generalized nonlinear model, the NAR-MAX model and Volterra model can be regarded as its special cases. In this article, the parameter identification of a class of nonlinear rational models is studied. Due to the coupling of the model output and the information vector, the parameter identification of the NRM is very challenging. To reduce the complexity of the identification, the stochastic gradient algorithm is used. However, the estimate given by traditional stochastic gradient algorithm is biased. To obtain unbiased estimation, the bias is calculated by using the observations and the previous estimate and then compensated to the biased estimate. A variable factor considering the estimation error is introduced to speed up the algorithm. Theoretical analysis shows that the proposed algorithm can obtain an unbiased estimate and has the complexity of O(n). The proposed algorithm is validated by a numerical example and is applied in modeling the dynamics of the cellular toxicity using the tetra-ethyl ammonium chloride. Results show that the proposed algorithm can obtain an accurate estimate for the nonlinear rational model with less computation.

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Hierarchical recursive least squares algorithms for Hammerstein nonlinear autoregressive output‐error systems

Cited by 82 publications

References 89 publications

A novel dynamic nonlinear partial least squares based on the cascade structure

A novel dynamic nonlinear partial least squares based on the cascade structure

Filtering‐based multi‐innovation recursive identification methods for input nonlinear systems with piecewise‐linear nonlinearity based on the optimization criterion

Bias compensated stochastic gradient algorithm for identification of an ARX‐type nonlinear rational model and its application in modeling of the dynamic of the cellular toxicity

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