Features in the time domain are the most frequently used for myoelectric classification, given that they do not need a transformation because they are based on the amplitude of the signal [28]. This type of features is widely used because they are simple to obtain and have a low computational cost [15], [22], [29]. To this effect, the features used in this work were: i) the root mean square (RMS) value, calculated through expression (2), ii) the mean absolute value (MAV), obtained through (3), iii) the number of zero crossings, which was calculated by means of (4), iv) the integral of the signal through the calculation of (5), and v) the signal power, which is obtained through the use of (6).

Figure 3. Figure 3. Angular positions of the wrist joint performed Source: Own elaboration

Root mean square:

Multiple studies in literature have mathematically modeled the EMG signal as a random process [30]. The RMS value provides the best probability of estimating the EMG amplitude during muscle contractions under conditions of constant force and fatigue-free contraction [30]. Its value is used to quantify the electrical signal since it is the reflection of the physiological activity in the motor units

(2)

where M is the number of samples of signal x and x_m is the value of signal x at time instant m.

Mean absolute value:

It is estimated from the sum of the absolute values and the measurement of the contraction levels of the sEMG signal, representing the contractile force of the muscle [31].

(3)

as in expression (2), M is the number of samples of signal x and x_m is the value of signal x at time instant m and the operator |.| represents absolute value.

Zero crossings (ZC):

Zero crossings count the number of times the signal passes through the zero line, that is, how many times has it gone from a negative value to a positive value and vice versa. The threshold is added to reduce the effect of noise [32].

(4)

x_m is the value of signal x at time instant m.

Integral of the signal (IEMG):

It is the sum of the absolute value of the sEMG signal amplitude. It is normally used to indicate the onset of muscle contraction in clinical applications. It is related to the trigger point of the signal sequence [33]

(5)

as in previous expressions, M is the number of samples of signal x and x_m is the value of signal x at time instant m.

Signal power:

This value is obtained by adding the power of the interval of the signal under study [30], using the expression:

(6)

where M is the number of samples of signal x and x_m is the value of signal x at time instant m.

After extracting this group of features, each signal window is represented by a five-value vector given by the features described above. Since each angular position was measured simultaneously by five electrodes, each one of these positions will then be represented by a vector of 25 features for this particular group.

The modeling of a time series can be determined through parameters that represent said signal. Thus, it has been reported in literature that the amplitude of an EMG signal is stochastic in nature and can be represented by an autoregressive (AR) model. AR models are widely used in pattern recognition from sEMG signals [15], [29]. In this type of model, the coefficients are used as a prediction model that describe each sample xi of the sEMG signal as a linear combination of previous samples plus a residual wi [34] and is represented by:

(7)

where 𝑎k is the k-th coefficient of the AR model, n is the order of the model, and w is Gaussian residual noise. A sixth order model was used for this work because previous studies have shown that this type of model is best suited for the representation of sEMG signals [34] and [35]. The Levinson-Durbin recursion was used to calculate the coefficients using the autocorrelation sequence according to [36]. Upon completion, a vector of seven values is obtained, which represents the signal window. This process was performed for each electrode used in the acquisition.

In order to use the signal representation in terms of both time and frequency, this type of technique has been used in recent decades since Englehart’s work [37]. One of the most widely used forms is DWT, where the signal is broken down through filters and analyzed in different frequency bands with different resolutions that provide approximation and detail information in the time and frequency domains simultaneously.

The calculation of the discrete wavelet transform is an implementation of the wavelet transform using a discrete set for scales and translations, obeying defined rules, and decomposing a signal x[n] into a set of mutually orthogonal wavelets. The calculation process to obtain the decomposition of a signal x[n] through the DWT is analogous to the use of a filter bank [38] (see figure 4); for this purpose, we can represent this decomposition as:

(8)

where uk[u] is each of the decompositions of input signal x[n], h1,1[n] is the scaled and displaced mother wavelet, and L is the number of decomposition levels. In this case, the signals used as bank input were each of the windows previously described in the preprocessing subsection. The structure of the filter bank is comprised by a dyadic tree with two filters, a low-pass one and a high-pass one, and a subsampling by two in each branch, according to the number of filters used. For this case, three levels and a daubechies4 mother wavelet were used, based on the values and parameters recorded in the literature [28], [36], [39]. Likewise, as reported in these works, the mean, standard deviation, and power values were calculated and used as features for each level obtained. There is a vector of 12 features for each electrode used in the acquisition for this group of features.

Figure 4. Figure 4. Filter banks to attain signal decomposition using a three-level DWT. HP: High pass, LP: Low pass Source: Own elaboration

There are different artificial neural network models according to their architecture and training mode. For this work, multilayer perceptron (MLP) was chosen to perform the classification task due to its capabilities to establish relationships between input-output vectors in a supervised learning procedure, which in turn is due to its ability to learn complex nonlinear patterns by adjusting its synaptic weights that link artificial neurons with nonlinear activation functions [41].

MLP models have shown good results in the classification of sEMG signals, which is why they have been chosen to perform the task of position differentiation [19], [42]. In this work, a two-layer architecture was chosen: a hidden one and an output one. The number of inputs is established by the group of features to be used in training (table 1); the number of neurons in the hidden layer was found through experimentation, varying from one to ten neurons, and the number of neurons in the output is determined by the five angular positions of the wrist. Figure 5 shows the model used for classification, where all connections between neurons are forward connections. The activation functions of neurons were hyperbolic tangent in the hidden layer and a softmax function in the output layer.

The training algorithm is resilient backpropagation [43], which shows a higher speed due to its modification based on the sign of the gradient. The maximum number of training epochs was set to 800, with a root mean square error as a cost function because its convergence was found through experimentation. Among the training stoppage criteria, the maximum number of epochs, a training error of zero, and premature stoppage were considered, with an observation window of 250 iterations.

Figure 5. Figure 5. Neural network model used for classification Source: Own elaboration

This machine learning technique, used for pattern recognition and classification, is a development of statistical learning theory [44]. Vector support machines, as it was mentioned in the introduction, have been used to work in conjunction with sEMG signals. Their main function is in the differentiation stage, mainly in the detection of neuromuscular pathologies [19], [36], [45], [46], [47], [48]. In this case, the parameter adjustment of the SVM models was performed in a similar way as done with neural networks. Four folds as those described above were also used, again performing cross-validation between the different features and five classes. Taking into account that this technique, by nature, has a binary classification [36], it was necessary to establish a multiclass SVM, which would evaluate one class against all the others.

Initially, SVM models were developed for a classification given by a linear function [44], [48], and it is for this reason that it is necessary to perform a non-linear transformation through a kernel function. So, said transformation allows the SVM to perform a linear classification of a data set that originally did not have this characteristic. The kernel function projects data from a low dimension space to a larger dimension space, and it is in said new space that the initial formulation of the model is used with a linear two-class classification [49]. For this work, the following kernel functions were used: radial base function (RBF), polynomial, and quadratic, given that the basic linear function of the SVM yielded poor results. All these non-linear kernels allow for faster training, which facilitates the convergence of the algorithm, and also for the obtainment of a similarity between input vectors and their combinations and the suppression of as many support vector multipliers as possible, thus minimizing the number of support vectors required for classification.