Comparison between Cascade Forward and Multi-Layer Perceptron Neural Networks for NARX Functional Electrical Stimulation (FES)-Based Muscle Model

Abstract

This paper presents the development and comparison of muscle models based on Functional Electrical Stimulation (FES) stimulation parameters using the Nonlinear Auto-Regressive model with Exogenous Inputs (NARX) using Multi-Layer Perceptron and Cascade Forward Neural Network (CFNN). FES stimulations with varying frequency, pulse width and pulse duration were used to estimate the muscle torque. About 722 data points were used to create muscle model. One Step Ahead (OSA) prediction, correlation tests and residual histogram analysis were performed to validate the model. The optimal Multi-Layer Perceptron (MLP) results were obtained from input lag space of 1, output lag space of 43 and hidden units 30. The MLP selected a total of three terms were selected to construct the final model, which producing a final Mean Square Error (MSE) of 1.1299. The optimal CFNN results were obtained from input lag space of 1, output lag space of 5 and hidden units 20 with similar terms selected. The final MSE produced was 1.0320. The proposed approach managed to approximate the behavior of the system well with unbiased residuals, which CFNN showing 8.66% MSE improvement over MLP with 33.33% less hidden units.