Non-linear model approximation and reduction by new input-state Hammerstein block structure

Functional electrical stimulation (FES) has been widely used in limb rehabilitation. The first step for the precision rehabilition is to clarify the variation of limb angle induced by FES. In this study, an electric stimulator and an inertial sensor are used to build a human body experimental platform. Motion characteristics of ankle angle induced by electrical stimulation pulse variation are obtained through experiment. The obtained ankle angle characteristics are used to train a neural network-based Hammerstein (H) model and the model parameters are identified by the genetic algorithm, which can effectively predict the ankle angle change induced by electrical stimulation. The structural parameters of the H model are adjusted according to the normalized root mean square error value (NRMSE) of the training data. The 10-fold cross-validation is used to verify the feasibility and effectiveness of the model. Experimental results show that the neural network-based H model can effectively predict the output change of the ankle angle induced by the electrical stimulation pulse, and its root mean square error (RMSE) and NRMSE are 2.78 ± 0.33 • and 23.70 ± 1.77%, respectively. Therefore, the proposed model can provide a theoretical basis for predicting ankle angle change in an electrical stimulation closed-loop control system.INDEX TERMS Functional electrical stimulation, ankle angle, Hammerstein model, neural network, genetic algorithm.

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“…The H model [26], [27] consists of a static nonlinear function followed by a linear dynamic subsystem, as shown in Fig. 1.…”

Section: A Hammerstein Model Of Neural Network 1) Hammerstein Modelmentioning

confidence: 99%

Estimating the Ankle Angle Induced by FES via the Neural Network-Based Hammerstein Model

et al. 2019

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“…This section provides an example of a chemical reaction process to demonstrate the effectiveness of the proposed method. The multivariable process is a continuous stirred tank reactor (CSTR) [28], as illustrated in Fig. 7.…”

Section: Examplementioning

confidence: 99%

Bias compensation based recursive least squares identification algorithm for multivariable Hammerstein nonlinear systems

Lyu,

Wang,

et al. 2024

Preprint

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The multivariable Hammerstein nonlinear system contains the sum of bilinear parameters, which is not a regression form. By using the special properties of binary signals, we can transform the sum of bilinear parameter matrices into two different models, achieving the parameter separation for parallel nonlinear subsystems and a linear subsystem. In order to improve the accuracy of parameter identification, this paper uses a biased correction technique to compensate a biased recursive least squares estimates. Then, a bias compensation based recursive least squares algorithm is proposed to separately identify the parameters of a linear subsystem and parallel nonlinear systems. The numerical simulation indicate that the proposed algorithm has a higher accuracy than recursive least squares and over-parametrization based identification algorithms. The multivariate Hammerstein nonlinear system is implemented on a case study from the process industry namely the continuous stirred tank reactor. The accuracy of the prediction is improved by a biased correction term.

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“…For this, block-oriented nonlinear models which are composed of linear dynamic block and static nonlinear functions for instance Hammerstein model and Wiener model have been performed on account of their simple structures. The two nonlinear models can approximate nonlinear dynamics of many practical industrial processes applications [1][2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Data‐driven Learning Algorithm of Neural Fuzzy Based Hammerstein‐Wiener System

Luo

et al. 2021

Journal of Sensors

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A novel data-driven learning approach of nonlinear system represented by neural fuzzy Hammerstein-Wiener model is presented. The Hammerstein-Wiener system has two static nonlinear blocks represented by two independent neural fuzzy models surrounding a dynamic linear block described by finite impulse response model. The multisignal theory is designed for employing Hammerstein-Wiener system to separate parameter learning issues. To begin with, the output nonlinearity parameters are learned utilizing separable signal with different amplitudes. Furthermore, correlation analysis method is implemented for estimating linear block parameters using separable signal inputs and outputs; thereby, the interference of process noise is effectively handled. Finally, multi-innovation learning technology is introduced to improve system learning accuracy, and then, multi-innovation extended stochastic gradient algorithm is obtained for optimizing input nonlinearity and noise model using multi-innovation technique and gradient search method. The simulation results display that presented data-driven learning approach has the availability of learning Hammerstein-Wiener system.

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Non-linear model approximation and reduction by new input-state Hammerstein block structure

Cited by 18 publications

References 23 publications

Estimating the Ankle Angle Induced by FES via the Neural Network-Based Hammerstein Model

Estimating the Ankle Angle Induced by FES via the Neural Network-Based Hammerstein Model

Bias compensation based recursive least squares identification algorithm for multivariable Hammerstein nonlinear systems

Data‐driven Learning Algorithm of Neural Fuzzy Based Hammerstein‐Wiener System

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