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

Zhou, Hu; Huang, Li-Jeng; Gao, Yueming; Vasić, Željka Lučev; Cifrek, Mario; Du, Min

doi:10.1109/access.2019.2943453

Cited by 10 publications

(7 citation statements)

References 33 publications

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“…In previous modeling studies, the models were often fixedparameter, with low accuracy [19,29,31]. Due to the dynamic characteristics of muscles and their propensity for fatigue, the torque induced by FES exhibited variability and fluctuations [21,32], which is consistent with the Fig.…”

Section: Discussionsupporting

confidence: 77%

“…Since the two blocks of the Hammerstein model correspond to the recruitment of nerve fibers and the subsequent dynamics of muscle contraction [17], it has been widely used for modeling biomechanical systems. In the past, most studies adopted the Hammerstein model with fixed parameters to predict the force and torque under FES [18,19], where the model parameters did not change once the identification was finished. However, the time-varying property of muscles and the occurrence of muscle fatigue may lead to a decrease in the accuracy of models with fixed parameters.…”

Section: Introductionmentioning

confidence: 99%

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An Adaptive Hammerstein Model for FES-Induced Torque Prediction Based on Variable Forgetting Factor Recursive Least Squares Algorithm

Yang,

Li,

et al. 2024

IEEE Trans. Neural Syst. Rehabil. Eng.

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Modeling the muscle response to functional electrical stimulation (FES) is an important step during model-based FES control system design. The Hammerstein structure is widely used in simulating this nonlinear biomechanical response. However, a fixed relationship cannot cope well with the time-varying property of muscles and muscle fatigue. In this paper, we proposed an adaptive Hammerstein model to predict ankle joint torque induced by electrical stimulation, which uses variable forgetting factor recursive least squares (VFFRLS) method to update the model parameters. To validate the proposed model, ten healthy individuals were recruited for short-duration FES experiments, ten for long-duration FES experiments, and three stroke patients for both. The isometric ankle dorsiflexion torque induced by FES was measured, and then the test performance of the fixedparameter Hammerstein model, the adaptive Hammerstein model based on fixed forgetting factor recursive least squares (FFFRLS) and the adaptive Hammerstein model based on VFFRLS were compared. The goodness of fit, root mean square error, peak error and success rate were applied to evaluate the accuracy and stability of the model. The results indicate a significant improvement in both the accuracy and stability of the proposed adaptive model compared to the fixed-parameter model and the adaptive model based on FFFRLS. The proposed adaptive model enhances the ability of the model to cope with muscle changes.

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Section: Discussionsupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

An Adaptive Hammerstein Model for FES-Induced Torque Prediction Based on Variable Forgetting Factor Recursive Least Squares Algorithm

Yang,

Li,

et al. 2024

IEEE Trans. Neural Syst. Rehabil. Eng.

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“…where median(x) is the median of x [33]. The MEPDF is calculated according to Equations ( 25)- (29).…”

Section: Parameter Estimate Of the Nonlinear Blockmentioning

confidence: 99%

“…In order to overcome the above problems, fuzzy system and neural networks system are widely applied to express the nonlinear block in the Hammerstein system since they can approximate the nonlinear block with arbitrary precision [28][29][30]. It should be mentioned that the neuro-fuzzy model (NFM) has stronger nonlinear approximation ability than neural networks and fuzzy systems due to the merits of combining neural network models with fuzzy systems.…”

Section: Introductionmentioning

confidence: 99%

Parameter learning for the nonlinear system described by Hammerstein model with output disturbance

Zhu

et al. 2022

Asian Journal of Control

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A novel parameter learning scheme using multi-signal processing is developed that aims at estimating parameters of the Hammerstein nonlinear model with output disturbance in this paper. The Hammerstein nonlinear model consists of a static nonlinear block and a dynamic linear block, and the multi-signals are devised to estimate separately the nonlinear block parameters and the linear block parameters; the parameter estimation procedure is greatly simplified. Firstly, in view of the input-output data of separable signals, the linear block parameters are computed through correlation analysis method, thereby the influence of output noise is effectively handled. In addition, model error probability density function technology is employed to estimate the nonlinear block parameters with the help of measurable input-output data of random signals, which not only controls the space state distribution of model error but also makes error distribution tends to normal distribution. The simulation results demonstrate that the developed approach obtains high learning accuracy and small modeling error, which verifies the effectiveness of the developed approach.

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“…The proposed model achieved significantly better performance than a polynomial NARMAX model. Zhou et al [ 4 ] studied the response of the human ankle, namely, its angle, to an electrical stimulus. The authors proposed a Hammerstein model based on artificial neural networks to predict the ankle angle.…”

Section: Introductionmentioning

confidence: 99%

Decoding Electroencephalography Signal Response by Stacking Ensemble Learning and Adaptive Differential Evolution

Ribeiro

Silva

Larcher

et al. 2023

Sensors

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Electroencephalography (EEG) is an exam widely adopted to monitor cerebral activities regarding external stimuli, and its signals compose a nonlinear dynamical system. There are many difficulties associated with EEG analysis. For example, noise can originate from different disorders, such as muscle or physiological activity. There are also artifacts that are related to undesirable signals during EEG recordings, and finally, nonlinearities can occur due to brain activity and its relationship with different brain regions. All these characteristics make data modeling a difficult task. Therefore, using a combined approach can be the best solution to obtain an efficient model for identifying neural data and developing reliable predictions. This paper proposes a new hybrid framework combining stacked generalization (STACK) ensemble learning and a differential-evolution-based algorithm called Adaptive Differential Evolution with an Optional External Archive (JADE) to perform nonlinear system identification. In the proposed framework, five base learners, namely, eXtreme Gradient Boosting, a Gaussian Process, Least Absolute Shrinkage and Selection Operator, a Multilayer Perceptron Neural Network, and Support Vector Regression with a radial basis function kernel, are trained. The predictions from all these base learners compose STACK’s layer-0 and are adopted as inputs of the Cubist model, whose hyperparameters were obtained by JADE. The model was evaluated for decoding the electroencephalography signal response to wrist joint perturbations. The variance accounted for (VAF), root-mean-squared error (RMSE), and Friedman statistical test were used to validate the performance of the proposed model and compare its results with other methods in the literature, including the base learners. The JADE-STACK model outperforms the other models in terms of accuracy, being able to explain around, as an average of all participants, 94.50% and 67.50% (standard deviations of 1.53 and 7.44, respectively) of the data variability for one step ahead and three steps ahead, which makes it a suitable approach to dealing with nonlinear system identification. Also, the improvement over state-of-the-art methods ranges from 0.6% to 161% and 43.34% for one step ahead and three steps ahead, respectively. Therefore, the developed model can be viewed as an alternative and additional approach to well-established techniques for nonlinear system identification once it can achieve satisfactory results regarding the data variability explanation.

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

Cited by 10 publications

References 33 publications

An Adaptive Hammerstein Model for FES-Induced Torque Prediction Based on Variable Forgetting Factor Recursive Least Squares Algorithm

An Adaptive Hammerstein Model for FES-Induced Torque Prediction Based on Variable Forgetting Factor Recursive Least Squares Algorithm

Parameter learning for the nonlinear system described by Hammerstein model with output disturbance

Decoding Electroencephalography Signal Response by Stacking Ensemble Learning and Adaptive Differential Evolution

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