Abstract
In this paper, a gradient descent algorithm is proposed for the parameter estimation of multi-input and multi-output (MIMO) total non-linear dynamic models. Firstly, the MIMO total non-linear model is mapped to a non-completely connected feedforward neural network, that is, the parameters of the total non-linear model are mapped to the connection weights of the neural network. Then, based on the minimization of network error, a weight-updating algorithm, that is, an estimation algorithm of model parameters, is proposed with the convergence conditions of a non-completely connected feedforward network. In further determining the variables of the model set, a method of model structure detection is proposed for selecting a group of important items from the whole variable candidate set. In order to verify the usefulness of the parameter identification process, we provide a virtual bench test example for the numerical analysis and user-friendly instructions for potential applications.
Highlights
Because a total non-linear model can provide a very concise representation for complex non-linear systems and has good extrapolation characteristics, it has attracted the attention of academic research and applications
Compared with the polynomial non-linear auto-regressive moving average with exogenous input (NARMAX) model, the total non-linear model is an extension of the polynomial model, which can be defined as the ratio of two polynomial expressions [1,2,3]
Zhu and Billings have done a lot of research work on the parameter identification of a total non-linear model [7,8], and they put forward the parameter estimation method of a total non-linear model based on a back-propagation (BP) algorithm in 2003
Summary
Because a total non-linear model can provide a very concise representation for complex non-linear systems and has good extrapolation characteristics, it has attracted the attention of academic research and applications. Compared with the polynomial non-linear auto-regressive moving average with exogenous input (NARMAX) model, the total non-linear model is an extension of the polynomial model, which can be defined as the ratio of two polynomial expressions [1,2,3]. The introduction of denominator polynomials makes the NARMAX model non-linear in parameters and regression terms. Compared with the polynomial model, the model identification and the controller design of the total non-linear model are much more challenging [4,5]. In view of the difficulty of parameter estimation of a total non-linear model, using simple and effective algorithm and machine learning should be considered for extracting the information from measurement data
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