Fuzzy Wavelet Neural Network Using a Correntropy Criterion for Nonlinear System Identification

Recent researches have demonstrated that the Fuzzy Wavelet Neural Networks (FWNNs) are an efficient tool to identify nonlinear systems. In these structures, features related to fuzzy logic, wavelet functions, and neural networks are combined in an architecture similar to the Adaptive Neurofuzzy Inference Systems (ANFIS). In practical applications, the experimental data set used in the identification task often contains unknown noise and outliers, which decrease the FWNN model reliability. In order to reduce the negative effects of these erroneous measurements, this work proposes the direct use of a similarity measure based on information theory in the FWNN learning procedure. The Mean Squared Error (MSE) cost function is replaced by the Maximum Correntropy Criterion (MCC) in the traditional error backpropagation (BP) algorithm. The input-output maps of a real nonlinear system studied in this work are identified from an experimental data set corrupted by different outliers rates and additive white Gaussian noise. The results demonstrate the advantages of the proposed cost function using the MCC as compared to the MSE. This work also investigates the influence of the kernel size on the performance of the MCC in the BP algorithm, since it is the only free parameter of correntropy

Human lower extremity joint moment prediction: A wavelet neural network approach

Joint moment is one of the most important factors in human gait analysis. It can be calculated using multi body dynamics but might not be straight forward. This study had two main purposes; firstly, to develop a generic multi-dimensional wavelet neural network (WNN) as a real-time surrogate model to calculate lower extremity joint moments and compare with those determined by multi body dynamics approach, secondly, to compare the calculation accuracy of WNN with feed forward artificial neural network (FFANN) as a traditional intelligent predictive structure in biomechanics. To aim these purposes, data of four patients walked with three different conditions were obtained from the literature. A total of 10 inputs including eight electromyography (EMG) signals and two ground reaction force (GRF) components were determined as the most informative inputs for the WNN based on the mutual information technique. Prediction ability of the network was tested at two different levels of inter-subject generalization. The WNN predictions were validated against outputs from multi body dynamics method in terms of normalized root mean square error (NRMSE (%)) and cross correlation coefficient (ρ). Results showed that WNN can predict joint moments to a high level of accuracy (NRMSE 0.94) compared to FFANN (NRMSE 0.89). A generic WNN could also calculate joint moments much faster and easier than multi body dynamics approach based on GRFs and EMG signals which released the necessity of motion capture. It is therefore indicated that the WNN can be a surrogate model for real-time gait biomechanics evaluation