Research on athlete skipping surface electromyography and energy consumption based on principal component analysis of wavelet packet

Abstract

EMG signal acquisition is mostly used in medical research. However, it has not been applied in athletes’ sports state recognition and body state detection, and there are few related studies at present. In order to promote the application of EMG signal acquisition in sports, this study combined with the actual needs of athletes to construct an EMG signal acquisition system that can collect athletes’ motion status. At the same time, in order to improve the effect of EMG signal acquisition, a wavelet packet principal component analysis model is proposed. In addition, in order to ensure the recognition efficiency of athletes’ motion state, this paper uses linear discriminant analysis method as the motion recognition assistant algorithm. Finally, this paper judges the performance of this research model by setting up comparative experiments. The research shows that the wavelet packet principal component analysis model performance is significantly better than the traditional algorithm, and the recognition rate for some subtle motions is also high. In addition, this study provides a theoretical reference for the application of EMG signals in the sports industry.

Keywords

EMG signal acquisition athlete wavelet packet master analysis motion recognition

1 Introduction

With the continuous advancement of science and technology, the use of surface electromyography (SEMG) for the recognition of athletes’ movements and training control has become a hot topic. The use of SEMG can not only achieve precise control of the prosthesis, but also enable it to flexibly and freely perform the command actions given by the brain, and it is also beneficial for the athletes to perform daily self-training after the injury [1].

Human hand movements can follow the brain’s instructions for movement, and brain command transmission is transmitted through bioelectrical signals generated by neurons. When the nerve tip receives the transmitted electrical signal, it will issue a command to contract the muscle group associated with the action, thereby affecting the corresponding bone to complete the hand movement [2] sEMG is a bioelectrical signal collected on the surface of the human body, which is closely related to the action of the corresponding muscle group. Therefore, it has a good theoretical basis for recognition by using sEMG opponent’s action, and sEMG-based gesture recognition has great application value for precise control of prosthesis [3].

From the current situation, the application status of SEMG is not good. Different people’s physiological state and skin condition have different effects on SEMG signals. Therefore, it is difficult to establish a standard as a basis for diagnosis. During the process of transmission from the muscle to the surface of the skin, the waveform of the SEMG signal is somewhat distorted due to the filtering effect caused by the volume conductor formed on the surface of the skin. At the same time, volumetric conduction also causes multiple MUAPs of adjacent muscle tissue to overlap each other to generate crosstalk, which is difficult to distinguish. In addition, the external power frequency of 50 Hz will cause a large degree of interference to the measurement of the SEMG signal, and cause serious distortion of the SEMG signal, which brings great difficulty in obtaining an accurate and reliable SEMG signal [4]. Skipping rope is a kind of systemic exercise. It has many patterns, can be simple and complex, easy to learn, and is a kind of aerobic exercise with less time and energy consumption. Skipping rope can play a very good role in enhancing the function of cardiovascular, respiratory and nervous system. It can make blood get more oxygen, keep cardiovascular system strong and healthy. It can accelerate gastrointestinal peristalsis and blood circulation, and promote the metabolism of the whole body.

In summary, the surface EMG signal has important practical application significance for athletes’ muscle rehabilitation engineering and muscle training project application.

2 Related work

The origin of myoelectricity dates back to the mid-1970 s. In 1773, Walsh discovered that the muscle activity of the squid produced certain electrical changes [5]; In 1849, DuBois-Reymond of France discovered that the body’s muscles contracted and also produced electrical activity; In 1922, Gasse and Neweomer used a cathode ray oscilloscope to display electrical signals of muscle activity [6]. Electromyography was initially used only for biofeedback therapy and was later widely used in other fields such as clinical medicine, rehabilitation medicine, sports medicine, and sports science research.

With the maturity of testing techniques and research techniques, surface electromyography plays an extremely important role in the field of sports science research. Moreover, the analysis of surface EMG signals by scholars and experts mainly focuses on time domain and frequency domain analysis. The time domain is the characteristic of myoelectric changes in the time dimension. When performing time domain analysis, the original EMG signal should be digitally processed according to the research needs, but the number of treatments should not be too much, otherwise the signal distortion will be caused. Moreover, common indicators for time domain analysis include: average amplitude, maximum amplitude value, integral myoelectric (iEMG), input percentage (input%), etc. [7]. The frequency domain is a characteristic change of the myoelectric signal in terms of frequency. The data used in the frequency domain analysis must be raw data, and usually the spectrum analysis is performed using Fast Fourier Transform, which is mainly used for the study of muscle fatigue. Common indicators for frequency domain analysis include: surface EMG power spectrum, average power frequency (MPF), median frequency (MF), peak frequency, slope, etc. [8].

In the field of sports research, after a long period of experimental research, scholars have combined the motion characteristics of different sports to carry out the application research of technical movements. For example: jumping sports, football kicking inside the ball, archery technique, Tai Chi fisting, tail jump action, basketball emergency stop jumper, five-line boxing action, swimming freestyle action, taekwondo stretching training, the trampoline jumps on the net, the difficult movements of competitive aerobics, the advancement of the rumba dance, the rowing technique of the rowing boat, the blasting of the ball in the backcourt of the badminton, the different teeing techniques of the tennis ball, the final shot of the hammer, etc. [9].

At present, Chinese scholars have made great achievements in the field of sports research through the research technology of surface electromyography. Liu Yaorong [10] et al. used the electromyography test to study the SEMG changes of the knee flexors and extensors of jumping athletes, and realized the scientific basis of athletes’ strength training; Duan Yifeng [11] studied the characteristics of the oscillating leg muscle electrical signals playing in the football player’s instep, improving the strength and accuracy of passing and shooting; Zhang Xiuli [12] analyzed the muscle strength characteristics of the national archery team athletes and made important contributions to the improvement of the level of archery technology in China; Luo Wei [13] analyzed the relationship between the angle change of the knee joint of Taijiquan and the electromyogram of the lower extremity, and reduced the sports injury of the athlete; Xin Chuming [14] studied the use of electromyography and the changes of knee joint injury in college basketball technical movements, and reduced knee injury by strengthening muscle strength; Wang Song [15] studied the surface electromyography characteristics of the typical action of the five elements of boxing and found the best boxing technique. Fan Nianchun [16] studied the characteristics of freestyle exercise techniques using surface electromyography techniques and understood the characteristics and patterns of muscle activity during freestyle; Huang Yan [17] and others performed PNF stretching training on male Taekwondo athletes, and compared the EMG parameters of the athletes after training. It was found that PNF tensile training can greatly improve the athlete’s ability to lower limb muscle strength. Song Yawei [18] compared the characteristics of athletes’ different muscle groups, found out their advantages and disadvantages, and proposed training methods to enable athletes to better coordinate sports and improve muscle work efficiency; Zeng Yuanyuan [19] studied the surface electromyography characteristics and regularity of the right angle support, the leg support and the Vincent action static control in the difficulty movement of group B of aerobics competition. Its purpose is to provide scientific basis and theoretical guidance for athletes to perform these actions with high quality, so as to effectively promote training and teaching; Gao Chengcheng [20] used the surface electromyography test method to study the basic steps of the Rumba dance, to learn about the characteristics of his muscle exertion, to standardize the movement techniques, to improve the performance of the competition, and to shorten the gap with the world level. Tang Qiao [21] studied the work of the muscles of the male athletes under two kinds of pulling conditions (water full force 2KM and dynamometer full force 2KM). Moreover, the research results can accurately monitor and evaluate the rowing technology and provide good scientific research services for the training practice of rowing sports; Yang Wanli [22] studied the surface electromyography characteristics of badminton players in the back-field evacuation technique, proposed a targeted training method, and improved the rationality of the technology; Guo Quanqing [23] introduced the electromyography technique into the study of tennis movements, improved the program and plan of tennis athletes’ muscle strength training, and conducted different strength training for different batting actions; Yue Guanghua [24] used surface technology to analyze the surface EMG of the main muscle groups of athletes in the final stage of exercise. It can judge the difference between athletes’ muscle strength and sports technology characteristics, provide feedback to the coach in time, and understand the problems that athletes should pay attention to in future training; In order to find the muscle movement law of the knee joint when the athlete climbs, Yang Jianwei [25] used surface electromyography to evaluate the muscle function of the rocker’s knee flexion and extension at different angles, which provided an effective reference value for muscle strength training. In addition, related research has been conducted on many other sports [26, 27].

3 Theoretical basis of the algorithm

3.1 Time domain analysis and its characteristic parameters

Time domain analysis is the most simple and effective method, and the time domain features have the advantages of simple calculation and effective representation of signal characteristics. However, the time domain feature also has certain unstable characteristics and is susceptible to external interference.

By performing mathematical operations and statistics on the time domain signal data, the obtained SEMG features mainly have the average absolute value, the root mean square, the standard deviation, and the mean square error.

(1) Average absolute value

The Mean Absolute Value (MAV) is a typical characteristic parameter in the time domain analysis of the SEMG signal. It can set the threshold by the average absolute value of the surface EMG signal to determine whether the muscle is moving. The definition of the average absolute value is: ${MAV}_{i} = \frac{1}{N} \sum_{k = 1}^{N_{i}} | x_{i, k} | i = 1, 2, \dots I$ (1)

Among them, I is the number of data segments, a is the data of the i-th segment, and N_i is the number of sampling points of the segment, which is set as 100.

(2) Root Mean Square

Root Mean Square (RMS) is a typical characteristic parameter in SEMG signal time domain analysis, which is used to measure the size of SEMG signal. The calculation formula for the root mean square is: ${RMS}_{i} = \sqrt{\frac{1}{N} \sum_{k = 1}^{N_{i}} x_{i, k}^{2}} i = 1, 2, \dots I$ (2)

Among them, I is the number of data segments, a is the data of the i-th segment, and N_i is the number of sampling points of the segment, which is set as 100.

(3) Standard deviation and mean square error

The standard deviation and mean square error can better reflect the dynamic degree of surface EMG signal. Equations (3) and (4) represent the standard deviation and the mean square error formula, respectively. $S_{i} = \sqrt{\frac{1}{N} \sum_{k = 1}^{N_{i}} | x_{i, k} - m_{i} |} i = 1, 2, \dots I$ (3) $S_{i}^{2} = \frac{1}{N_{i}} \sum_{k = 1}^{N_{i}} | x_{i, k} - m_{i} | i = 1, 2, \dots I$ (4) $m_{i} = \frac{1}{N_{i}} \sum_{k = 1}^{N_{i}} x_{i, k} i = 1, 2, \dots I$ (5)

Among them, S_i is the standard deviation, $S_{i}^{2}$ is the mean square error, and m_i is the amplitude average of the data of the i-th segment, I is the number of data segments, a is the data of the i-th segment, and N_i is the number of sampling points of the segment, which is set as 100.

There are certain difficulties in using the traditional time domain analysis method to extract the surface EMG signals. The main performances are as follows:

(1) Because it is difficult to grasp the muscle contraction during the experiment, long-term experiments may cause muscle fatigue and cause the myoelectric signal to be unstable. Therefore, the subject must perform standard actions in the experiment, and the experiment time should not be too long. Moreover, each action is controlled between 1 minute and 2 minutes, and the subject is given 3 to 5 minutes for rest during different actions.

(2) In the process of time domain analysis, due to the existence of external interference signals, extremely weak surface EMG signals are easily submerged by noise in various frequency bands, and whether the surface EMG signal can be effectively extracted becomes an important prerequisite for time domain analysis. Therefore, when collecting surface electromyogram signals, it is indispensable to shape and filter the collected surface EMG signals and remove noise interference.

3.2 Frequency domain analysis and its characteristic parameters

Frequency domain analysis refers to the analysis of the frequency characteristics of a signal. In the frequency domain analysis, the SEMG signal is analyzed by Fast Fourier Transform to obtain the SEMG signal spectrum. The analysis method is a method of decomposing the SEMG signal according to frequency and observes the variation of the SEMG signal at different frequencies by the spectrum of the SEMG signal. The characteristic parameters of the frequency domain analysis mainly include two kinds of median frequency and average power frequency. The median frequency is defined as shown in equation (6):

$\begin{matrix} \int \begin{matrix} f_{mf} \\ 0 \end{matrix} p (f) df & = \int \begin{matrix} + \infty \\ f_{mf} \end{matrix} p (f) df \\ = \frac{1}{2} \int \begin{matrix} + \infty \\ 0 \end{matrix} p (f) df \end{matrix}$ (6)

Among them, f_mf is the median frequency to be sought and p (f) is the power spectrum of the SEMG signal.

The average power frequency is defined as shown in Equation (7): $MPF = \int \begin{matrix} + \infty \\ 0 \end{matrix} fp (f) df / \int \begin{matrix} + \infty \\ 0 \end{matrix} p (f) df$ (7)

Among them, MPF is the average power frequency, and p (f) is the power spectrum of the SEMG signal.

Analysis of SEMG signals using frequency analysis method can be used to study the rate of EMG signaling and muscle fatigue. However, the frequency domain analysis method can only be used to process stationary signals, and it still has limitations in the research and application of SEMG signals.

3.3 Time-frequency domain analysis and its characteristic parameters

The time-frequency domain analysis method is an analysis method for extracting signal features by combining time domain and frequency domain analysis methods. Wavelet Transform (WT) is a typical application method in time-frequency domain analysis. Wavelet transform can extract the local characteristics of the signal, which makes up for the shortcomings in time domain and frequency domain analysis. Moreover, the wavelet transform method combines the advantages of time domain and frequency domain method and has achieved good application effect in bioelectric signal processing. However, domestic and foreign researchers use wavelet transform to analyze and process SEMG signals, which is not mature enough, and is in the research and development stage. The principle of wavelet transform is as follows.

∀f (t) ∈ L² (R), and the continuous wavelet transform of f (t) is:

${WT}_{f} (a, b) = {| a |}^{- 1 / 2} \int \begin{matrix} \infty \\ - \infty \end{matrix} f (t) Ψ (\frac{t - b}{a}) dt, a \neq 0$ (8)

Or inner product form: ${WT}_{f} (a, b) = 〈 f, Ψ_{a, b} 〉$ (9)

In the formula, $Ψ_{a, b} (t) = {| a |}^{- 1 / 2} Ψ (\frac{t - b}{a})$ , a is the scaling factor, b is the translation factor, and Ψ is the base wavelet function.

To make the inverse transformation of Equations (8) and (9) true, Ψ (t) must satisfy the condition:’ $C_{Ψ} = \int \begin{matrix} infty \\ - \infty \end{matrix} \frac{{| \hat{Ψ} (w) |}^{2}}{| w |} dw < \infty$ (10)

In the formula, $\hat{Ψ} (w)$ is the Fourier transform of Ψ (t).

At this time, the inverse transformation is

$f (t) = C_{ψ}^{- 1} \int \begin{matrix} \infty \\ - \infty \end{matrix} \int \begin{matrix} \infty \\ - \infty \end{matrix} ψ_{a, b} (t) {WT}_{f} (a, b) db \frac{da}{{| a |}^{2}}$ (11)

The constant C_Ψ limits the class of the function Ψ that belongs to L² (R) as a “base wavelet”. In particular, if Ψ is required to be a window function, then Ψ must also belong to L¹ (R). Therefore, $\hat{Ψ} (w)$ is a continuous function of R. It can be obtained from equation (10), $\hat{Ψ}$ must be 0 at the origin, that is $\hat{Ψ} (0) = \int \begin{matrix} \infty \\ - \infty \end{matrix} ψ (t) dt = 0$ (12)

Equation (12) shows that the wavelet function must be oscillating.

In order to reconstruct the signal, the variables a, b need to be discretized, usually taking $b = \frac{k}{2^{j}}, a = \frac{1}{2^{j}}; j, k \in Z$ , then ${WT}_{f} (a, b) = 2^{j / 2} \int \begin{matrix} + \infty \\ - \infty \end{matrix} f (t) \bar{ψ} (2^{j} t - k) dt$ (12)

4 Wavelet packet principal component analysis

The wavelet packet principal component analysis is a method for constructing the principal component analysis model for feature extraction based on wavelet packet analysis. The process of extracting two SEMG signal feature matrices using wavelet packet principal component analysis is shown in Fig. 1.

Fig. 1

Wavelet packet master analysis model flow.

Step 1: After the acquired two-way SEMG signals X₁, X₂ are taken by the L-layer wavelet packet transform (WPT), the wavelet packet coefficient matrix S₁, S₂ is obtained. The wavelet packet coefficient matrix $S_{i} = {[S_{0}^{i}, S_{1}^{i}, . . ., S_{2^{L} - 1}^{i}]}^{T}$ , $S_{j}^{i} = [S_{j, 1}^{i}, S_{j, 2}^{i}, . . ., S_{j, C}^{i}]$ is the data of the j-th scale after the wavelet packet transform of the four kinds of action SEMG signals collected by the i-th path. C is the number of wavelet packet coefficient data at each scale. Equation (13) is used to calculate the mean square error of the wavelet packet coefficients of each data segment to obtain the wavelet coefficient feature vectors $y_{0}^{1}, y_{1}^{1}, . . ., y_{2^{L} - 1}^{1}$ and $y_{0}^{2}, y_{1}^{2}, . . ., y_{2^{L} - 1}^{2}$ at each scale, and form the wavelet coefficient feature matrix y₁, y₂. $y_{i} = {[y_{0}^{i}, y_{1}^{i}, . . ., y_{2^{L} - 1}^{i}]}^{T}$ , $y_{j}^{i} = {[y_{j, 1}^{i}, y_{j, 2}^{i}, . . ., y_{j, N}^{i}]}^{T}$ , The root mean square of the wavelet coefficients at each scale is: $y_{j, d}^{i} = \sqrt{\frac{1}{N} \sum_{c = 1}^{N_{d}} {(S_{j, c + N_{d} (d - 1)}^{i})}^{2}}$ (13)

Among them, j = 0, 1, . . . , 2^L - 1, $S_{j, c + N_{d} (d - 1)}^{i}$ is the c + N_d (d - 1)-th data at the jth scale after the wavelet packet transform of the i-th SEMG signal, c = 1, 2, . . . , N_d. N_d is the number of sampling points of the d-th data segment, which is selected as 100, d = 1, 2, . . . , N, N is the number of data segments, C = N_d × N, I = 1, 2, and i is the i-th acquisition channel;

Step 2: After y₁ and y₂ are analyzed by the principal component, the SEMG signal characteristic matrices Y₁, Y₂ are obtained. Step 3 Y₁ and Y₂ are merged into a motion feature matrix Y. After the motion feature matrix Y is obtained, subsequent motion recognition is performed.

Wavelet packet transform is a more detailed signal analysis method developed on the principle of wavelet analysis. The wavelet packet decomposition algorithm is:

We set the scale subspace to V_j, the wavelet subspace to W_j, the wavelet packet scale factor to j, and the coefficient sequence to {h (k)}, {g (k)}. Then, a new space $U_{j}^{n}$ is used to unify the two subspaces V_j and W_j, and ${\begin{matrix} U_{j}^{0} = V_{j} \\ U_{j}^{1} = W_{j} \end{matrix}, j \in Z$ (14)

We define the subspace U_j to be the closure space of the function w_n (t), and $U_{j}^{2 n}$ is the closure space of the function w_2n (t), and both satisfy the following two-scale equation. ${\begin{matrix} w_{2 n} (t) = \sqrt{2} \sum_{k \in Z} h (k) w_{n} (2 t - k) \\ w_{2 n + 1} (t) = \sqrt{2} \sum_{k \in Z} g (k) w_{n} (2 t - k) \end{matrix}$ (15)

In the formula, g (k) = (- 1) ^kh (1 - k), that is, the two coefficients also have an orthogonal relationship [57]. Its equivalent is expressed as: $U_{j + 1}^{n} = U_{j}^{2 n} \oplus U_{j}^{2 n + 1}, j \in Z, n \in Z_{+}$ (16)

The sequence {w_n } _n∈Z constructed by equations (15) and (16) is called a wavelet packet determined by the basis function w₀ (t) = φ (t) and φ (t) is a scaling function. The 3-layer wavelet packet decomposition of the SEMG signal is shown in Fig. 2.

Fig. 2

Wavelet packet three-layer decomposition.

In Fig. 2, (0,0) represents the SEMG raw signal data, denoted as X_i, and i = 1, 2 represents the SEMG data collected by the i-th path. (3,0), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (3,7) n represents the data of the 8 scales of the SEMG signal data after three-layer decomposition of the wavelet packet, which are respectively recorded as the vector $S_{0}^{1}$ , $S_{0}^{2}$ , $S_{0}^{3}$ , $S_{0}^{4}$ , $S_{0}^{5}$ , $S_{0}^{6}$ , $S_{0}^{7}$ , and $X_{i} = S_{0}^{i} + S_{1}^{i} + S_{2}^{i} + S_{3}^{i} + S_{4}^{i} + S_{5}^{i} + S_{6}^{i} + S_{7}^{i}$ .

These eight wavelet coefficient vectors are constructed as wavelet coefficient matrices for single-channel SEMG signals, which are recorded as S_i, $S_{i} = {[S_{0}^{i}, S_{1}^{i}, S_{2}^{i}, S_{3}^{i}, S_{4}^{i}, S_{5}^{i}, S_{6}^{i}, S_{7}^{i}]}^{T}$ . When the subject performs four kinds of movements: fist clenching, punching, wrist inversion and wrist eversion, two SEMG raw signal data and db08 collected from the temporal and temporal wrist flexors of the subject’s forearm were used as wavelet bases to perform 3-layer wavelet packet decomposition on the SEMG signal. The processed data is shown in Figs. 3 and 4.

Fig. 3

SEMG waveform of the brachioadialis.

Fig. 4

SEMG waveform of radiocarpus.

It can be seen from Figs. 3 –10 that each of the original SEMG signals of each path has 8 scale coefficients after the 3-layer wavelet packet transform, which are coefficient 0, coefficient 1, coefficient 2, coefficient 3, coefficient 4, coefficient 5, coefficient 6, coefficient 7, and each coefficient has 10,000 sampling points; Comparing the eight coefficients of an action category under a single muscle, it can be seen that the wavelet packet coefficient 0 and the coefficient 1 amplitude of each action are relatively large, while the other coefficients 2 to 7 are relatively small; Comparing the four movements of the radial flexor and iliac muscles, it can be seen that the wavelet-scale coefficient of the fist movement in the diaphragm and the radial wrist muscles is relatively large at the same wavelet packet scale, while the wavelet-scale coefficient of the boxing muscle in the diaphragm and the radial wrist is relatively small. When the wrist is turned inward, the amplitude of the SMG wavelet packet coefficient of the radial wrist muscle is larger than that of the diaphragm. However, when the wrist is everted, the magnitude of the SEMG wavelet packet coefficient of the radial wrist muscle is smaller than that of the diaphragm. Therefore, there are significant differences in the coefficients of the wavelet packet obtained by different muscles in different motions after wavelet packet transform, which lays a good theoretical and experimental basis for the subsequent motion recognition. We assume that after the acquired SEMG signals X₁, X₂ pass WPT, the wavelet packet coefficients matrix S₁, S₂ are obtained. Wavelet packet number matrix $S_{i} = {[S_{0}^{i}, S_{1}^{i}, S_{2}^{i}, S_{3}^{i}, S_{4}^{i}, S_{5}^{i}, S_{6}^{i}, S_{7}^{i}]}^{T}$ .

Fig. 5

SEMG waveform of the brachioradial during the exhibition boxing.

Fig. 6

SEMG waveform of the radiocarpus during the exhibition boxing.

Fig. 7

SEMG waveform of the brachioradial during wrist inversion.

Fig. 8

SEMG waveform of the radiocarpus during wrist inversion.

Fig. 9

SEMG waveform of the brachioradial during wrist valgus.

Fig. 10

SEMG waveform of the radiocarpus during wrist valgus.

$S_{j}^{i} = [S_{j, 1}^{1}, S_{j, 2}^{1}, . . ., S_{j, 40000}^{1}]$ is the data of the j-th scale after the wavelet packet transform of the four kinds of action SEMG signals collected by the i-th path, i = 1, 2, j = 0, 1, . . . , 7. In the 40000 data of each wavelet packet scale, 1-10000 is the punch fist data, 10001-20000 is the exhibition fist data, 20001-30000 is the wrist inversion data, 30001-40000 is the wrist flip data. According to the sampling point order and the unit of 100 data without overlap, 400 data segments of four actions can obtain 400 data segments. Then, the root mean square of the wavelet packet coefficients of each data segment is calculated by the equation (13) and is taken as a feature parameter to constitute a wavelet coefficient feature matrix. However, in theory, the dimension of the wavelet packet coefficients in the wavelet packet transform grows very fast, and the wavelet coefficients of the single-channel signal are decomposed by 8 layers, and the wavelet coefficients of the two signals are as high as 16 dimensions, and the data redundancy is large, which increases the calculation amount and storage space of the algorithm. After analyzing the relationship between the wavelet packet coefficients and the influence on the recognition results, it is found that not all wavelet packet coefficients play a leading role, and the principal elements in the wavelet coefficient matrix have the greatest influence on the experimental results. Therefore, the principal component analysis method can be used to reduce the dimension of the wavelet coefficient matrix to remove data redundancy, reduce the calculation amount of the classifier, and improve the signal recognition efficiency.

5 Principal component analysis

Principal component analysis is an analytical method that reduces the number of dimensions by eliminating the strict linear correlation or strong correlation of independent variable information. Moreover, principal component analysis is a commonly used data compression method in the field of statistics. By processing the data information by principal component analysis, it is possible to characterize the data samples with fewer feature quantities, thereby reducing the sample data dimension. In addition, the main data in the original data can be retained by the principal component analysis method, so that the data after the principal component analysis is more convenient to process.

The total number of features of the SEMG wavelet coefficient feature matrix yi is 2^L, L = 3, and the number of sampling points is N, N = 400. Sample space is $y_{i} = {[y_{0}^{i}, y_{0}^{i}, . . ., y_{2^{L} - 1}^{i}]}^{T}$ , $y_{j}^{i} = [y_{j, 1}^{i}, y_{j, 2}^{i}, . . ., y_{j, N}^{i}], j = 0, 1, . . ., 2^{L} - 1, i = 1, 2$ represents the SEMG signal collected by the i-th path. T represents the transpose of the matrix, and the matrix processed by PCA is Y_i.

The principal component analysis algorithm is as follows:

Step 1: The empirical mean of each dimension SEMG wavelet packet coefficient input data $y_{j, d}^{i}, d = 1, 2, . . ., N$ is calculated. Then, the mean u_j calculated by equation (16) is taken as the element of the (2^L) × 1-dimensional empirical mean vector u: $u_{j} = \frac{1}{N} \sum_{d = 1}^{N} y_{j}^{i}$ (16)

Step 2: The difference vector B of the SEMG wavelet coefficient feature matrix and the empirical mean vector is obtained. $B = y_{i} - uh$ (17)

Among them, h is an 1 × N dimensional row vector with an element of 1.

Step 3: The covariance matrix C is calculated. $C = \frac{1}{N} \sum B^{T} B$ (18)

Step 4: The eigenvectors and eigenvalues of the covariance matrix are calculated, and the eigenvectors are arranged according to the eigenvalues from large to small. In the 2^L dimensional sample space, there are 2^L number values. Then, the cumulative contribution rate Z_i of each eigenvalue λ_j is calculated according to equation (19). Then, according to the threshold Z_i> 97 %, the first P_i (P_i < 2^L) principal elements are selected to constitute a feature vector D. $Z_{i} = (\sum_{j = 1}^{P_{i}} λ_{j} / \sum_{j = 1}^{2^{L}} λ_{j}) \times 100 %$ (19)

Step 5: The SEMG signal characteristic matrix Y_i after orthogonal transformation is calculated.

The two-packet SEMG packet coefficient feature matrices y₁ and y₂ are transformed by PCA to obtain the SEMG signal characteristic matrix Y₁, Y₂. $Y^{i} = {[Y_{1}^{i}, Y_{2}^{i}, . . ., Y_{P_{i}}^{i}]}^{T}$ , T represents the transpose of the matrix, and $Y_{t}^{i} = [Y_{t, 1}^{i}, Y_{t, 1}^{i}, . . ., Y_{t, N}^{i}]$ . Y₁, Y₂ combined into a motion feature matrix $Y = {[Y_{1}^{1}, Y_{2}^{1}, . . ., Y_{P 1}^{1}, Y_{1}^{2}, Y_{2}^{2}, . . ., Y_{P_{2}}^{1}]}^{T}$ . Then, Y is entered into the LDA classification. The contribution rates of the eight eigenvalues of the two SEMG signals processed by WPPCA are shown in Table 1.

Table 1

Contribution rate of two SEMG signal eigenvalues after WPPCA processing (%)

Eigenvalues	Lateral wrist muscle	Diaphragm
Feature 1	93.3973	94.7795
Feature 2	5.0186	4.4792
Feature 3	1.1147	0.3806
Feature 4	0.3407	0.2847
Feature 5	0.0753	0.0424
Feature 6	0.0362	0.0158
Feature 7	0.0131	0.0133
Feature 8	0.0039	0.0043

It can be seen from Table 1 and Fig. 11 that in the temporal matrix of the wrist and the iliac muscles obtained by the WPGCA after the WPGCA, t the cumulative contribution rates obtained by adding the contribution rates of the first two features 1, 2 are 98.42% and 99.26%, respectively, which satisfy the threshold conditions Z_i≥ 97%. However, the cumulative contribution rate obtained after the addition of the last six feature contribution rates is less than 2%. Therefore, according to the principal component analysis method, the last six features can be ignored. Then, the 16-dimensional wavelet coefficient matrix is reduced to a 4-dimensional principal to obtain a motion mode feature matrix $Y = [Y_{1}^{1}, Y_{2}^{1}, Y_{1}^{2}, Y_{2}^{2}], P_{1} = P_{2} = 2$ .

Fig. 11

Statistical chart of contribution rate.

After extracting features from the EMG signal, which classifier is selected to discriminate the motion pattern to which the signal belongs is one of the key issues in the EMG signal to discriminate upper limb motion. Considering the problem of computation time and classification accuracy, this paper chooses a simple and practical linear discriminant analysis method as the classifier for forearm motion recognition.

The differential SEMG signal acquisition electrode is placed on the ulnar wrist flexor and the diaphragm of the human body, and the skin surface at the wrist joint is selected as a reference point to eliminate the common mode signal.

6 Analysis of results

Accurate classification of SEMG signals with different actions is a key issue to improve athletes’ training efficiency and reliability. At present, there are many methods for classifying SEMG waveforms in action mode, but there are fewer reliable and practical methods. The reason is that the surface EMG signal has a low signal-to-noise ratio, and the actual data is interfered by many factors, such as spatial electromagnetic waves, power frequency interference, electrode position sliding, muscle fatigue and skin surface state. These factors will have different degrees of impact on the accuracy of motion recognition. Therefore, the reliability of preprocessing, feature extraction, and classification methods have an important impact on the accuracy of motion recognition classification results. This topic is based on a large number of literatures on the research of EMG signal processing, wavelet packet theory analysis, principal component analysis and SEMG signal pattern recognition, and a large number of theoretical analysis and experiments.

In this paper, a new method for extracting the characteristics of surface electromyography signals from wavelet packet principal component analysis is proposed. The wavelet packet principal component analysis method can overcome the problem of high dimensionality in the wavelet packet transform process, and the characteristic parameters extracted from the original SEMG data can effectively characterize the SEMG signal. In addition, this paper uses wavelet packet transform to analyze the SEMG signal and uses the sub-band arms of each frequency band as the feature vector of each action mode and establishes the principal component analysis (PCA) model. Wavelet packet principal component analysis (WPPCA) has good feature expression ability when using time domain analysis, wavelet packet analysis and wavelet packet principal to analyze four different SEMG signal feature extraction methods. Experiments show that in the case of fixed linear discriminant classifier, the signal features extracted by WPCCA method are better than other two feature extraction methods for motion recognition, and the classification accuracy is higher.

The linear discriminant analysis (LDA) method was used to discriminate the four motion categories of the upper limb forearm of the SEMG signal motion pattern feature matrix. After that, the LDA classifier is used to classify and identify the moving feature matrix of the obtained SEMG signal after wavelet packet principal component analysis, and compare it with BP network, RBF network and support vector machine. It can be seen that the LDA classifier has the highest recognition rate, and the algorithm is simple, fast, and robust.

7 Conclusion

The surface EMG signal has important practical application significance for athletes’ muscle rehabilitation engineering and muscle training project application. Therefore, this study analyzes the surface EMG signals of athletes. By performing mathematical operations and statistics on the time domain signal data, the SEMG features that can be obtained mainly include the mean absolute value, the root mean square, the standard deviation, and the mean square error. Moreover, analysis of SEMG signals using frequency analysis can be used to study the rate of EMG signaling and muscle fatigue. However, the frequency domain analysis method can only be used to process stationary signals, and it still has limitations in the research and application of SEMG signals. Wavelet packet principal component analysis is a method for feature extraction of principal component analysis model based on wavelet packet analysis. It uses the wavelet packet principal component analysis to extract the two SEMG signal feature matrices and obtains the motion feature matrix for subsequent motion recognition. Moreover, wavelet packet transform is a more detailed signal analysis method developed on the principle of wavelet analysis. In addition, experimental research shows that the principal component analysis method can be used to reduce the dimension of the wavelet coefficient matrix to remove data redundancy, reduce the computational complexity of the classifier, and improve the signal recognition efficiency.

References

Ben Messaoud

M.A.

, Bouzid

and Ellouze

, Speech enhancement based on wavelet packet of an improved principal component analysis, Computer Speech & Language 35 (2016), 58–72.

, Chen

and Tan

, An efficient method of P2P traffic identification based on wavelet packet decomposition and kernel principal component analysis, International Journal of Communication Systems 27(10) (2015), 1476–1490.

Shao

, Hu

, Wang

, et al., The fault feature extraction and classification of gear using principal component analysis and kernel principal component analysis based on the wavelet packet transform, Measurement 54 (2014), 118–132.

Sahu

, Apley

D.W.

and Runger

G.C.

, Feature selection for noisy variation patterns using kernel principal component analysis, Knowledge-Based Systems 72(11) (2014), 37–47.

Shuihua

, Xiaojun

, Yudong

, et al., Identification of green, oolong and black teas in China via wavelet packet entropy and fuzzy support vector machine, Entropy 17(12) (2015), 6663–6682.

You

, Gao

and Katayama

, WPD-PCA-based laser welding process monitoring and defects diagnosis by using FNN and SVM, IEEE Transactions on Industrial Electronics 62(1) (2015), 628–636.

Zhu

, Poostchi

, Vernon

S.A.

, et al., Detecting abnormality in optic nerve head images using a feature extraction analysis, Biomedical Optics Express 5(7) (2014), 2215.

Bobovská

Adela

, Tvaro?Ka

and Juraj

Kóňa

, A theoretical study on the catalytic mechanism of the retaining α-1,2-mannosyltransferase Kre2p/Mnt1p: the impact of different metal ions on catalysis, Organic & Biomolecular Chemistry 12(24) (2014), 4201.

Yanyan

, Gang

, Chaolin

, et al., The analysis of hand movement distinction based on relative frequency band energy method, BioMed Research International 20(4) (2014), 1–8.

10.

Wong

P.K.

, Yang

, Vong

C.M.

, et al., Real-time fault diagnosis for gas turbine generator systems using extreme learning machine, Neurocomputing 128(8) (2014), 249–257.

11.

Almaadeed

, Aggoun

and Amira

, Speaker identification using multimodal neural networks and wavelet analysis, Iet Biometrics 4(1) (2015), 18–28.

12.

Majidnezhad

Vahid

, A novel hybrid of genetic algorithm and ANN for developing a high efficient method for vocal fold pathology diagnosis, EURASIP Journal on Audio, Speech, and Music Processing 20(1) (2015), 34–42.

13.

Yang

, Deng

, Choi

K.S.

, et al., Transductive domain adaptive learning for epileptic electroencephalogram recognition, Artificial Intelligence in Medicine 62(3) (2014), 165–177.

14.

Wang

Shuihua

, Yang , et al., Entropy identification of green, oolong and black teas in China via wavelet packet entropy and fuzzy support vector machine, Entropy 17(10) (2015), 6663–6682.

15.

Saeedi

, Faez

and Moradi

M.H.

, Hybrid fractal-wavelet method for multi-channel EEG signal compression, Circuits, Systems, and Signal Processing 33(8) (2014), 2583–2604.

16.

Weiguo

, Xiaodong

, Fenwei

, et al., Feature extraction and early warning of agglomeration in fluidized bed reactors based on an acoustic approach, Powder Technology 279(11) (2015), 185–195.

17.

Xie

, Huang

, Zhao

, et al., Inspection of magnetic tile internal cracks based on impact acoustics, Nondestructive Testing and Evaluation 30(2) (2015), 147–164.

18.

Xueqin

, Qin

, Yi

, et al., Inverting study on soil water content based on harmonic analysis and hyperspectral remote sensing, Acta Optica Sinica 37(10) (2017), 1028001.

19.

Chatterjee

and Roy

, Application of non-decimated wavelet packet transfer function in web error prediction, International Journal of System Assurance Engineering & Management 6(4) (2014), 1–27.

20.

Kevric

and Subasi

, Comparison of signal decomposition methods in classification of EEG signals for motor-imagery BCI system, Biomedical Signal Processing and Control 31 (2017), 398–406.

21.

Xin

L.I.

, Xiaoqi

, Xin

, et al., Research on electroencephalogram emotion recognition based on the feature fusion algorithm of auto regressive model and wavelet packet entropy, Journal of Biomedical Engineering 34(6) (2017), 831–836.

22.

Roy

and Barman

, Improved gene prediction by principal component analysis based autoregressive Yule–Walker method, Gene 575(2) (2016), 488–497.

23.

Tayyaba

Shahzadi

, et al., Skin insertion analysis of microneedle using ANSYS and fuzzy logic, Journal of Intelligent & Fuzzy Systems 38(5) (2020), 5885–5895.

24.

Liang

Q.Z.

, Guo

X.M.

, Zhang

W.Y.

, et al., Identification of heart sounds with arrhythmia based on recurrence quantification analysis and kolmogorov entropy, Journal of Medical & Biological Engineering 35(2) (2015), 209–217.

25.

Bhardwaj , Shubham , et al., A new parallel galactic swarm optimization algorithm for training artificial neural networks, Journal of Intelligent & Fuzzy Systems 38(5) (2020), 6691–6701.

26.

Shan

, Zhibiao

and Yan

, Identification method of tool wear based on multi-feature fusion, Journal of Vibration Measurement & Diagnosis 34(3) (2014), 576–584.

27.

Wan

, Wang

, Tse

P.W.

, et al., A critical study of different dimensionality reduction methods for gear crack degradation assessment under different operating conditions, Measurement 78(12) (2016), 138–150.