Critério de correntropia no treinamento de redes fuzzy wavelet neural networks para identificação de sistemas dinâmicos não lineares

The great interest in nonlinear system identification is mainly due to the fact that a large amount of real systems are complex and need to have their nonlinearities considered so that their models can be successfully used in applications of control, prediction, inference, among others. This work evaluates the application of Fuzzy Wavelet Neural Networks (FWNN) to identify nonlinear dynamical systems subjected to noise and outliers. Generally, these elements cause negative effects on the identification procedure, resulting in erroneous interpretations regarding the dynamical behavior of the system. The FWNN combines in a single structure the ability to deal with uncertainties of fuzzy logic, the multiresolution characteristics of wavelet theory and learning and generalization abilities of the artificial neural networks. Usually, the learning procedure of these neural networks is realized by a gradient based method, which uses the mean squared error as its cost function. This work proposes the replacement of this traditional function by an Information Theoretic Learning similarity measure, called correntropy. With the use of this similarity measure, higher order statistics can be considered during the FWNN training process. For this reason, this measure is more suitable for non-Gaussian error distributions and makes the training less sensitive to the presence of outliers. In order to evaluate this replacement, FWNN models are obtained in two identification case studies: a real nonlinear system, consisting of a multisection tank, and a simulated system based on a model of the human knee joint. The results demonstrate that the application of correntropy as the error backpropagation algorithm cost function makes the identification procedure using FWNN models more robust to outliers. However, this is only achieved if the gaussian kernel width of correntropy is properly adjusted.

Efeitos do treino de marcha em esteira com adição de carga ao membro inferior não parético de indivíduos com acidente vascular cerebral: ensaio clínico controlado e randomizado

Introduction: Gait after stroke is characterized by a significant asymmetry between the lower limbs, with predominant use of the non-paretic lower limb (NPLL) over using the paretic lower limb. Accordingly, it has been suggested that adding load/weight to the NPLL as a form of restricting the movement of this limb may favor the use of the paretic limb, reducing interlimb asymmetry. However, few studies have been conducted up to this moment, which only investigated the immediate effects of this practice. Objectives: 1) Investigating whether there is an influence of adding load to the NPLL during treadmill training on cardiovascular parameters and on gait performance of individuals with stroke, compared to treadmill training without load addition; 2) Analyzing the effects of treadmill training with and without load added to the NPLL on kinematic parameters of each lower limb during gait; 3) Analyzing the effects of treadmill training with and without load added to the NPLL on measurements of functional mobility and postural balance of these patients. Materials and Methods: This is a randomized single blinded clinical trial involving 38 subjects, with a mean age of 56.5 years, at the subacute post-stroke phase (with mean time since stroke of 4.5 months). Participants were randomly assigned into an experimental group (EG) or control group (CG). EG (n= 19) was submitted to gait training on a treadmill with the addition of load to the NPLL by ankle weights equivalent to 5% of body weight. CG (n= 19) was only submitted to gait training on a treadmill. Behavioral strategies which included home exercises were also applied to both groups. The interventions occurred daily for two consecutive weeks (Day 1 to Day 9), being of 30 minutes duration each. Outcome measures: postural balance (Berg Functional Balance Scale – BBS), functional mobility (Timed Up and Go – TUG; kinematic variables of 180° turning) and kinematic gait variables were assessed at baseline (Day 0), after four training sessions (Day 4), after nine training sessions (Day 9), and 40 days after completion of training (Follow-up). Cardiovascular parameters (mean arterial pressure and heart rate) were evaluated at four moments within each training session. Analysis of variance (ANOVA) was used to compare outcomes between EG and CG in the course of the study (Day 0, Day 4, Day 9 and Follow-up). Unpaired t-tests allowed for intergroup comparison at each training session. 5% significance was used for all tests. Results: 1) Cardiovascular parameters (systemic arterial pressure, heart rate and derivated variables) did not change after the interventions and there were no differences between groups within each training session. There was an improvement in gait performance, with increased speed and distance covered, with no statistically significant difference between groups. 2) After the interventions, patients had increased paretic and non-paretic step lengths, in addition to exhibiting greater hip and knee joint excursion on both lower limbs. The gains were observed in the EG and CG, with no statistical difference between the groups and (mostly) maintained at follow-up. 3) After the interventions, patients showed better postural balance (higher scores on BBS) and functional mobility (reduced time spent on the TUG test and better performance on the 180° turning). All gains were observed in the EG and CG, with no statistically significant difference between groups and were maintained at follow-up. Conclusions: The addition of load to the NPLL did not affect cardiovascular parameters in patients with subacute stroke, similar to treadmill training without load, thus seemingly a safe training to be applied to these patients. However, the use of the load did not bring any additional benefits to gait training. The gait training program (nine training sessions on a treadmill + strategies and exercises for paretic limb stimulation) was useful for improving gait performance and kinematics, functional mobility and postural balance, and its use is suggested to promote the optimization of these outcomes in the subacute phase after stroke.