Research on the Accurate Measurement Method of Athletes’ Physical Consumption Using Intelligent Wearable Devices in Table Tennis Training

In recent years, with the continuous progress of science and technology and people’s pursuit of healthy life, wearable device technology has been widely used in table tennis training. These small devices can monitor the physiological indicators of athletes, provide real-time feedback and personalized training plans to help athletes optimize the training effect, prevent sports injuries, and improve competitive performance [1-4].

First of all, wearable device technology provides athletes with comprehensive and accurate physiological indicator monitoring. For example, heart rate monitors can monitor athletes’ heart rate in real time, provide data on heart rate zones, and provide real-time warnings to athletes through the alarm function to help them control their training intensity [5-8]. In addition, the exercise tracker can measure the number of steps, mileage, calorie consumption and other data to help athletes understand their own exercise situation, so as to better adjust the training program [9-11]. The accuracy and timeliness of these data enable athletes to better understand their physical responses, make targeted training adjustments, and improve training effects [12-14].

Second, wearable device technology provides athletes with real-time feedback and personalized training plans. By connecting with devices such as smartphones or computers, athletes can obtain real-time training data and sports analysis reports [15-17]. These reports can analyze the athlete’s posture, movement, strength and other aspects of the problem, and provide personalized recommendations for improvement according to individual circumstances. For example, in strength training, wearable device technology can detect whether an athlete’s movements are standardized and remind the athlete to maintain the correct posture to avoid injuries [18-21]. This kind of real-time feedback and personalized guidance can help athletes better adjust their exercise techniques and improve their training methods, thus improving their competitive level faster [22-23].

In this paper, Actigraph GT9X was applied to collect the acceleration data of table tennis players, and through the acceleration composite vector, correlation analysis was performed to determine the explanatory and explanatory variables of the regression analysis, determine the regression model, establish the regression equations, and after various tests on the regression equations, the Bland-Altman plot statistical method was used for validation, and the predicted values were compared with the measured values. Averages were subjected to a t-test to verify the validity of the two equations in predicting the physical exertion data of table tennis players.

2

Method

2.1

Experimental design of Actigraph-based table tennis physical exertion measurement

2.1.1

Subject of the study

The experimental subjects of this paper are college table tennis beginners and college table tennis skilled players in a city sports institute. Sixty (30 male, 30 female) college table tennis players with the foundation of table tennis (college students majoring in table tennis training or studying for one year or more) were selected as the skilled group, and another 60 (30 male, 301 female) college students with preliminary study of table tennis or less than one year’s study were selected as the beginner group for the study, and the two of them were tested in a comparative manner. Among them, the error rate of each stage more than 10% was invalid data, and the relevant test was re-conducted. After the test, 50 skilled players (30 males and 30 females) with better performance and 50 beginners (30 males and 30 females) were selected as valid samples. The study protocol was signed with informed consent with the consent of the subjects. Before the official start of the test, the participants received relevant training to understand the precautions and procedures throughout the test. Their physical condition was also assessed. No contraindications to exercise and no abnormal physical or psychological symptoms were required. Prior to the start of the test, each participant completed a table tennis skill level questionnaire based on the table tennis rating scale to confirm their appropriate skill level. After the energy consumption prediction model was completed, 10 skilled players (5 males and 5 females) were selected to conduct a comparative test to validate the prediction model of table tennis energy consumption equation.

The informed consent form was signed by all subjects, who understood the subject’s research program. Before proceeding with the research program, the subjects were properly trained and informed about the precautions and working procedures throughout the experiment. They were also prepared and assessed for their physical health. Physical health includes physical health, mental health, and social adaptation.

2.1.2

Research methodology

1)

Literature method

479 papers in Chinese and English were reviewed in various databases with the keywords of acceleration sensor, exercise energy expenditure, physical education major (table tennis specialization), structural equation modeling, college students, etc., and books on sports psychology, table tennis teaching and training, sports research methods, structural equation modeling, etc. were also read.

2)

Expert interview method

A number of experts and scholars specialized in table tennis, statistics, and sports engineering were interviewed about the method of detecting sports data, table tennis training methods, etc., to listen to the experts’ and scholars’ opinions on the content of this study.

3)

Experimental research method

All subjects wore ActigraphGT9X acceleration sensors for four table tennis tests, and subjects in the skilled group wore ActigraphGT9X and CosmedK4b2 for table tennis singles tests. The Actigraph heart rate monitor was worn to monitor heart rate during all tests. The four basic table tennis athletic ability tests were right side forehand stroke, left side backhand stroke, right front forehand stroke, and left front backhand stroke in four test protocols, and the VM values (composite vector values) calculated by three axes were used to perform the analysis of variance between the skilled group and the beginner group, and between males and females, and to understand the athletic differences of the different groups [24].

4)

Mathematical statistical method

The raw data collected by Cosmedk4b2 was saved as *.xpo format through the Cosmedk4b2’s own software’s after the completion of each test, and then converted to every 60s at a later stage and saved on Excel. Input the relevant data collected by the ActiGraphGT9X accelerometer into the computer. The relevant data were exported and organized through ActiLife 6.0 software, and statistics were performed using GraphPad Prism software. At the end of the test, the Cosmedk4b2 data were imported into the computer to obtain the indicators of EE (Energy Expenditure), MET (Metabolic Equivalent of Energy) and other metabolites through the self-contained data analysis software CosmedK4b2 7.0, and the GT9X data were imported into the computer through the The GT9X data were imported into the computer and analyzed by the self-owned data analysis software Actilife6 to obtain the coronal axis (ACx), vertical axis (ACy), sagittal axis (ACz) and other body indicators, and the statistical data were analyzed by the SPSS 20 statistical software after the data collection was completed.

2.1.3

Definition of terms

1)

Energy Expenditure (EE): is the process of consuming energy in the body during human activity. That is, the process of energy metabolism. In this experiment, energy expenditure was measured by gas metabolism analyzer, and the detection principle of gas metabolism analyzer is to use gas metabolism analyzer to measure oxygen-related indexes, and calculate the total energy consumption of human body through these indexes.

2)

Metabolic Equivalent (MET): Metabolic Equivalent is a commonly used indicator to express the relative level of energy metabolism of different activities according to the energy consumption during sitting.

3)

Acceleration Sensor: The GT9X can be worn to obtain the values of the three axes of different wearing parts, namely, the lost axis (ACx), the coronal axis (ACy) and the vertical axis (ACz). Also can be obtained by the formula of the integrated vector axis VM value. VM can illustrate the magnitude of the acceleration in the integrated direction while performing the movement, as well as the magnitude of the movement. The greater the acceleration, the greater the magnitude of motion, and the greater the energy expenditure.

2.2

Multiple linear regression models

Linear regression modeling:

Regression algorithms are relative to categorical algorithms and are related to the type of value of the target variable Y that you want to predict. If the target variable Y is a categorical variable, such as predicting the gender of the user, predicting the color of the flowers, etc., a classification algorithm is needed to fit the data and make a prediction; if Y is a continuous variable, such as predicting the revenue of the product, predicting the performance of the sales, etc., a regression model is needed [25]. Linear regression is a simple, versatile and easy to understand model. The equation is obtained by using Y as the dependent variable and X as the independent variable: (1) $Y = α + β X$ $$Y = \alpha + \beta X$$

When parameters α and β are given, a straight line is displayed within the coordinate plot. When only one value of X is used to predict the value of Y, it is called a one-way regression. Univariate linear regression is a calculation to find the most appropriate a straight line to fit the data. Suppose there is a scatter plot based on a set of data, one-way linear regression is to find a straight line that fits the data points in the scatter plot as closely as possible, and the difference between the calculated theoretical data and the actual value is the error, which is denoted by μ in statistics. Thus the equation is obtained: Y = α + βX + μ. The point of linear regression analysis is to find the best straight line that fits the actual data. Here it is necessary to introduce the concept of residuals, the residuals are the difference between the true value and the predicted value, which can be understood as the distance or gap between the two, as shown in the following equation: (2) $e = y - \hat{y}$ $$e = y - \hat y$$

For the dependent variable x₁, there is a corresponding independent variable y₁, and the prediction of the resulting ${\hat{y}}_{i}$ $${\hat y_i}$$, after calculating the value of $e_{i} = y_{i} - {\hat{y}}_{i}$ $${e_i} = {y_i} - {\hat y_i}$$, and then square it, and then calculate each point in the data, and finally add up all the $e_{i}^{2}$ $$e_i^2$$ can be calculated to fit a straight line and the actual value of the error between. The so-called best-fitting straight line is the smaller the value of the calculated sum of squares of the residuals, i.e. the smaller the error the better the fit. In order to calculate the minimum sum of squares of the residuals, you can make $Q = \sum_{i = 1}^{n} {[y_{i} - (α + β x_{i})]}^{2}$ $$Q = \sum\limits_{i = 1}^n {{{\left[ {{y_i} - \left( {\alpha + \beta {x_i}} \right)} \right]}^2}}$$, the use of calculus for the principle of the extreme value of the α and β partial derivatives, and make its first-order derivatives equal to 0 to solve α and β, that is, the least squares estimation method: (3) $\frac{\partial Q}{\partial α} = 2 Σ (y_{i} - α - β x_{i}) (- 1) = 0$ $$\frac{{\partial Q}}{{\partial \alpha }} = 2\Sigma \left( {{y_i} - \alpha - \beta {x_i}} \right)( - 1) = 0$$ (4) $\frac{\partial Q}{\partial β} = 2 Σ (y_{i} - α - β x_{i}) (- x_{i}) = 0$ $$\frac{{\partial Q}}{{\partial \beta }} = 2\Sigma \left( {{y_i} - \alpha - \beta {x_i}} \right)\left( { - {x_i}} \right) = 0$$

When there are two or more independent variables, a computational analysis of multiple linear regression is required. Multiple linear regression analysis addresses the following problems: (1) Determining whether there is a correlation between several specific variables. (2) Predicting or controlling the value of another variable based on the value of one or more variables, with the possibility of knowing its accuracy. (3) Factor analysis, which factors are significant and which are minor with respect to the common effects among several independent variables of a variable.

In multiple linear regression, a dependent variable begins to be influenced by more than one independent variable, so its equation takes the form: (5) $y = β_{0} + β_{1} x_{1} + \dots β_{n} x_{n} + ε$ $$y = {\beta _0} + {\beta _1}{x_1} + \cdots {\beta _n}{x_n} + \varepsilon$$ (6) $E (y) = β_{0} + β_{1} x_{1} + \dots β_{n} x_{n}$ $$E(y) = {\beta _0} + {\beta _1}{x_1} + \cdots {\beta _n}{x_n}$$

Since an observation in multiple linear regression is no longer a scalar but a vector, the observations of the independent variables become $(1, x_{11}, \dots, x_{1 n})$ $$\left( {1,{x_{11}}, \cdots ,{x_{1n}}} \right)$$, $(1, x_{21}, \dots, x_{2 p})$ $$\left( {1,{x_{21}}, \ldots ,{x_{2p}}} \right)$$, while the observations of the corresponding dependent variables remain unchanged, so that each row of these observations is superimposed to become a vector or matrix. (7) $y = [\begin{matrix} y_{1} \\ y_{2} \\ ⋮ \\ y_{n} \end{matrix}] X = [\begin{matrix} 1 & x_{11} & \dots & x_{1 p} \\ 1 & x_{21} & x_{2 p} \\ ⋮ & ⋮ \\ 1 & x_{n 1} & \dots & x_{n p} \end{matrix}]$ $$y = \left[ {\begin{array}{*{20}{c}} {{y_1}} \\ {{y_2}} \\ \vdots \\ {{y_n}} \end{array}} \right]X = \left[ {\begin{array}{*{20}{c}} 1&{{x_{11}}}& \ldots &{{x_{1p}}} \\ 1&{{x_{21}}}&{}&{{x_{2p}}} \\ \vdots &{}&{}& \vdots \\ 1&{{x_{n1}}}& \cdots &{{x_{np}}} \end{array}} \right]$$ (8) $\in = [\begin{matrix} \in_{1} \\ \in_{2} \\ ⋮ \\ \in_{n} \end{matrix}] β = [\begin{matrix} β_{0} \\ β_{1} \\ ⋮ \\ β_{n} \end{matrix}]$ $$ \in = \left[ {\begin{array}{*{20}{c}} {{ \in _1}} \\ {{ \in _2}} \\ \vdots \\ {{ \in _n}} \end{array}} \right]\beta = \left[ {\begin{array}{*{20}{c}} {{\beta _0}} \\ {{\beta _1}} \\ \vdots \\ {{\beta _n}} \end{array}} \right]$$

After determining the multiple regression equation, the coefficient of determination r² and the standard error of estimate can be used to determine the goodness of fit of the equation. The coefficient of determination is used to explain how much of the change in Y is explained by the change in the selected independent variable, and if the value of r² is too large, the presence of multicollinearity between the variables needs to be considered; the standard error of estimation is used to explain the average deviation between the actual value of Y and the estimated value of Y_i when the independent variable is given.

Multiple linear regression equations and univariate linear models are tested in the same way by using t to test each partial regression coefficient and F to test the significance of the entire multiple regression model. The significance test of the equation is used to test whether the equation is valid or not, if the test shows that it is not significant, then the equation is not valid. F test: used for all the independent variables $(x_{1}, \dots, x_{n})$ $$\left( {{x_1}, \cdots ,{x_n}} \right)$$ in the whole for the y linear significance, F test need to look at the Significant F value. P-value and Significant F value is generally required to be less than 0.05, and the smaller the result the more significant.

After determining the multiple regression equation, it is also necessary to calculate the variance inflation factor (VIF) of each independent variable to determine whether there is a correlation between the independent variables. If there is a high degree of correlation or complete correlation between the independent variables, then there is multicollinearity among the independent variables, and the effects of each variable on the dependent variable cannot be accurately distinguished. Based on the variance inflation factor, it is possible to determine whether there is multicollinearity between each independent variable. It is determined whether the VIF of each independent variable is greater than 5, if so, this variable needs to be eliminated and if the VIF is less than 5, then it can be assumed that the multiple regression equation that has been determined does not suffer from severe multicollinearity.

Residual analysis is used to evaluate the fit of the linear regression model to the actual data. [26]. When testing a multiple linear regression model, the residual plots of the simple linear regression equation between each independent and dependent variable can be analyzed separately. Such a multiple linear regression model can be considered valid if the scatter in the residual plots is shown to be relatively random and when it is not obvious that there is a certain pattern in the scatter.

3

Results and Discussion

3.1

MET Values and K4b² Values for Different Wearing Sites

In this study, different hitting styles were tested at low ball speed, high ball speed and simulated free singles situations. Table 1 shows the predicted MET values for GT3X and the measured MET values for K4b². The average K4b² measured MET values for all phases of combined and free singles were 9.2 and 9.4, which were not significantly different from each other, while there was a significant difference between the predicted MET values of the GT3X for different parts of the body. The predicted values of the waist, thigh and ankle joints in both modes were significantly lower than the predicted values of the wrist and handle sites, which were smaller than the measured values; while the predicted values of the wrist and handle were significantly larger than the measured values.

Table 1.

List of met measurements

GT3X wearing parts	Free singles		Phase integration
GT3X wearing parts	GTSX	K4b²	GTSX	K4b²
Waist	6.4±1.3	9.4±1.2	6.3±1.5	9.2+1.5
Thigh	6.7±1.2		6.2±1.3
Ankle joint	8.5±1.2		8.3±1.6
Wrist	13.8±3.3		14.6±6.8
Handle	27.5±11.6		28.8±15.7

The degree of error in the MET prediction of the ankle was significantly lower than that of the other sites, while the degree of error in the clapper handle and wrist (overestimation) was significantly greater than that of the waist, thigh, and ankle (underestimation); the variability between the predicted values of the waist, thigh, and ankle was small, whereas the variability between the wrist and the clapper handle was large, with the clapper handle predicted values being significantly greater than those predicted for the wrist in terms of the degree of overestimation.

The results of the paired t-tests are shown in Table 2, with highly significant differences between MET predictions and K4b2 measurements for different sites of GT3X in all phases and free singles mode.

Table 2.

Matching t test analysis results

GT3X wearing parts	Phase integration		Free singles
GT3X wearing parts	T	P	T	P
Waist	16.3	0.000	55.4	0.000
Thigh	13.5	0.000	53.1	0.000
Ankle joint	11.7	0.000	47.6	0.000
Wrist	-6.3	0.000	-21.6	0.000
Handle	-2.8	0.000	-22.7	0.000

3.2

EE and K4b² Values for Different Wearing Sites

The statistical analysis of the predicted EE values and the measured EE values of K4b² is shown in Table 3, the average measured EE values of K4b² in free singles and in all stages of synthesis were 10.7 kccals/min and 10.5 kccals/min, which were not significantly different from each other, while there was a significant difference between the predicted values of EE in different parts of the GT3X. The predicted values of waist, thigh and ankle joints in both modes were significantly lower than the predicted values of wrist and handle sites and smaller than the measured values; while the predicted values of wrist and handle sites were significantly larger than the measured values.

Table 3.

A list of predicted and measured values

GT3X wearing parts	Free singles		Phase integration
GT3X wearing parts	GTSX	K4b²	GTSX	K4b²
Waist	7.2±2.1	10.7±1.7	6.8±1.6	10.5+1.6
Thigh	7.4±1.6		7.7±1.4
Ankle joint	8.3±1.5		8.6±1.5
Wrist	23.7±7.5		21.5±6.9
Handle	32.8±8.9		28.4±7.6

The degree of error in EE prediction was significantly lower for the ankle than for the other sites, while the degree of error was significantly greater for the clapper handle and wrist (overestimation) than for the waist, thigh, and ankle (underestimation); the variability between the predicted values for the waist, thigh, and ankle was small, while the variability between the wrist and the clapper handle was large, with the clapper handle predicted values being significantly more overestimated than the wrist predicted values.

The results of the paired t-tests are shown in Table 4, with highly significant differences between the predicted values of EE and the K4b² measurements for the different wearing parts of the GT3X in all phases and in free singles mode.

Table 4.

Matching t test analysis results

GT3X wearing parts	Phase integration		Free singles
GT3X wearing parts	T	P	T	P
Waist	16.4	0	60.5	0
Thigh	10.4	0	44.2	0
Ankle joint	3.8	0	-5.8	0
Wrist	-21.2	0	-69.4	0
Handle	-29.3	0	-99.3	0

3.3

Consistency Analysis of Measurements at Different Wearing Sites

The consistency of the predicted values of EE and MET for GT3X at different wearing sites was further compared with the measured values of K4b², with K4b² and GT3X and the mean as the horizontal coordinate and the difference between K4b² and GT3X as the vertical coordinate, where the scatter falls closer to the 0-difference-mean line in the confidence interval, the better the consistency is.

Figures 1 and 2 show the results of the free singles EE, MET analysis, and Figures 3 and 4 show the results of the combined exercise EE, MET analysis.

The results show that, both in free singles and integrated sports mode, the scatters of EE and MET predicted values of GT3X in waist, ankle and thigh areas fall significantly in the region above the 0 value within the 95% confidence interval, which indicates that the consistency with K4b² is low, and that there is a significant underestimation of all the three; the scatters of the predicted values of EE and MET of GT3X in racket handle and wrist areas fall significantly in the region below the 0 value within the 95% confidence interval, and are significantly higher than those of the K4b². The scatter of EE and MET predicted values of GT3X in the handle and wrist area fell in the region below the value of 0 within the 95% confidence interval, and was obviously farther away than the upper region, indicating that it was in lower consistency with K4b², and there was obvious overestimation in both, and the degree of overestimation of the predicted values of the handle was even higher; meanwhile, the degree of error of the predicted values of the handle and the wrist was obviously greater than that of the predicted values of the waist, ankle, and thigh areas.

3.4

Analysis of physical exertion in table tennis

3.4.1

Modeling of energy expenditure equations for table tennis sports

1)

Actigraph and K4b²

Correlation analysis was performed using the VM values, ACy, ACx, and ACz of the Actigraph of each wearing part with the measured EEm of K4b², in which the correlation indexes were higher for the shoulder VM, (R=0.727, P<0.01), the VM of the chest fossa (R=0.704, P<0.01), and the VM of the thigh (R=0.660, P<0.01); the accelerometer ACy and K4b² measured EEm correlation coefficients in the chest fossa is the largest; accelerometer ACx and K4b² measured EEm correlation coefficients in the shoulder correlation coefficient is the largest, accelerometer ACz and K4b² measured EEm correlation coefficients in the chest fossa correlation coefficient is the largest; the results show that the accelerometer wearing parts with higher Eem correlation coefficients are close to the center of the human body, the The correlation coefficients are higher at the chest socket and shoulder, while the correlation coefficients are lower at the wrist, beat handle, and ankle, which are far away from the center of the body. Table 5 shows the correlation between each count value of Actigrap and calibration EEm.

Table 5.

The Actigrap count value is associated with the EEm

Pearson correlation	Wrist	Elbow	Shoulder	Handle	Thorax	Iliac crest	Thigh	Ankle
Vm and EEM	0.527**	0.617**	0.725**	0.521**	0.715**	0.643**	0.666**	0.562**
Acy and EEM	0.558**	0.624**	0.616**	0.469**	0.696**	0.668**	0.653**	0.483**
Acx and EEM	0.423**	0.573**	0.648**	0.482**	0.547**	0.495**	0.519**	0.516**
Acz and EEM	0.456**	0.544**	0.585**	0.493**	0.642**	0.517**	0.594**	0.537**

Actigraph can calculate individual energy consumption based on age, gender, height, weight, and other information using its self-contained software. The energy consumption measured by Actigraph at each site was analyzed by mean comparison analysis and paired-sample t-test with the calibration value (K4b²) to analyze the accuracy of the accelerometer energy consumption measurement at each site. The results are shown in Table 6.

Table 6.

The difference between the Actigrap and the calibration value EEm

Match sample t test	X+SD	T	P
EEm	6.16±2.37	/	/
Wrist	20.42±11.36	34.871	0**
Elbow	11.28±5.96	30.436	0**
Shoulder	6.49±3.75	4.185	0**
Handle	23.17±12.59	37.193	0**
Thorax	4.98±3.08	-14.928	0**
Iliac crest	4.38±2.64	-24.306	0**
Thigh	4.61±2.87	-20.443	0**
Ankle	3.92±2.95	-22.285	0**

The results showed that there was a strong significant difference between the energy consumption calculated by Actigraph and the calibration value at each site (P < 0.01); and the accelerometers worn at the wrist, elbow, and racket handle overestimated the energy consumption; the accelerometers at the thoracic fossa, iliac crest, thigh, and ankle underestimated the energy consumption; and the energy consumption value of the accelerometers at the shoulder was closer to the calibration value.

2)

Correlation between basic information and EEm

The highest correlation coefficient between basic information and EEm in Table 7 is the weight variable, with a correlation coefficient of 0.365 (P < 0.01). Age and body fat percentage were negatively correlated with EEm, with a correlation of P > 0.05 for age, and height, weight, and BMI were positively correlated with EEm.

3)

Correlation of Actigraph VM values for each site with measured MET values of K4b²

For metabolic equivalents, the Pearson correlation analysis of each count value of Actigraph at each wearing site with the MET values measured by calibration K4b² was performed, and the results are shown in Table 8. The VM values at the sternal fossa, iliac crest, and thighs were highly correlated with K4b², and the average correlations were at the handle of the clapper, ankle, and wrist.

4)

Correlation results between basic information and K4b² measured MET values

Table 9 shows the results of correlation analysis between basic information and calibration MET. Table 9 shows that the correlation with MET is P<0.01 for age and body fat percentage, and P>0.05 for height, weight and BMI with K4b² measured MET values.

Table 7.

The basic information is associated with the eem

Correlation	Age	Height	Weight	BMI	Body fat rate
Pearson correlation	-0.037	0.345**	0.3625**	0.278**	-0.278**

Table 8.

The accelerometer vm value is associated with the met value

Correlation	VM
Correlation	Wrist	Elbow	Shoulder	Handle	Thorax	Iliac crest	Thigh	Ankle
Pearson correlation	0.576**	0.638**	0.621**	0.483**	0.647**	0.675**	0.668**	0.472**

Table 9.

The basic information is associated with the school standard met

Correlation	Age	Height	Weight	BMI	Body fat rate
Pearson correlation	-0.165**	0.032**	-0.029	0.0054	-0.292**

3.4.2

Stepwise Regression Screening Equation Independent Variables

In this part, each VM value of accelerometers worn by subjects in the test group was taken as the independent variable, and the EEm value measured by calibration K4b² was taken as the dependent variable, and the stepwise regression method was used to screen out the two parts of the accelerometers that had higher regression coefficients of the accelerometers. Then the basic information such as height, weight, age, body fat percentage and BMI were brought into the regression equation, and the stepwise regression method was used to finally obtain the equation 1 for table tennis energy consumption and the equation 2 for table tennis MET value.

When establishing the regression equation, the residual plot analysis was utilized for the judgment and deletion of the strong shadow strong points, and the data outside the ±3 (double line labeled) residuals were deleted to make the data’s more reasonable and effective, and the specific residuals are shown in Figure 5.

3.4.3

Selection of Regression Model Variables and Model Building

The study finalized the independent variables for equation 1 as shoulder VM, ankle VM, and weight; and for equation 2 as shoulder VM, ankle VM, age, and body fat percentage.

Table 10 shows the EEm and MET value prediction regression models, and Table 11 summarizes the EEm and MET value prediction models (coefficients of determination).

Table 10.

EE MET value prediction regression model

Equation	Equation model
1	EEm=-1.939+0.000407 ShoulderVM+0.000246 AnkleVM+0.074 Weight
2	METs=4.908+0.000377 ShoulderVM+0.000239 AnkleVM -0.0855 Age-0.025 Body fat rate

Table 11.

EE MET value prediction model summary (determinant coefficient)

Equation model	R	R²	Adjust R²
1	0.855**	0.723	0.722
2	0.836**	0.706	0.708

EE predicted energy consumption regression equation 1, with an adjusted R² of 0.722, and MET value prediction regression equation 2, with an adjusted R² of 0.708, and the constructed equations 1 and 2 were valid equations.

3.4.4

Tests of regression equations

1)

Paired-sample t-test to verify the validity of the regression equation

The validation group data were brought into Equation 1 and Equation 2, and the resulting predicted values, which were compared with the actual K4b² calibration values, were subjected to paired samples t-test and correlation analysis. The test results are shown in Table 12.

To verify the consistency of equation 1 for assessing table tennis energy expenditure and equation 2 for estimating MET values, the prior correlation between equation 1 (table tennis energy expenditure projection equation) and the calibration values was 0.937 (correlation P < 0.01) and the paired-sample t-test with the calibration values yielded a P > 0.05, which is not significantly different; the prior correlation between equation 2 (table tennis metabolic equivalent projection equation) and the calibration values was 0.876 (correlation P<0.01), and the paired-sample t-test with the calibration values yielded P>0.05, indicating that there was no significant difference between the predicted values of equations 1 and 2 and the calibration values, and the correlation with the calibration values was high, so they were effective in predicting the energy expenditure of table tennis.

2)

Bland-Altman Plot statistical method to verify the validity of regression equations

The Bland-Altman Plot statistical method was used to verify the consistency between the predicted values of the two equations and the calibrated values.The Bland-Altman Plot statistical method was mainly based on the measurements of the calibration instrument (K4b2) and the Actigraph, and the consistency bounds were calculated and presented in conjunction with the BA plot.The vertical coordinate of the BA plot is the difference between the calibrated values of energy consumption and the predicted values of the equations. The difference between the calibration values and the predicted values of the equations is presented as the difference between the calibration values and the predicted values of the equations, and the horizontal coordinate is (calibration values + predicted values)/2. The Bland-Altman Plot statistical method was used to calculate the limits of agreement intervals between calibration values and predicted values, and to determine the systematic bias, with a confidence interval of 95%. The scatter points of the table tennis ball energy consumption projection equations (Equation 1 and Equation 2) basically fell between ±1.97 SD, which further proved that Equation 1 and Equation 2 had good predictive ability.

Table 12.

Correlation and matching t test results

Equation	Correlation r	Predictive value/calibration value	t	Pair t check (p)
Equation 1(EEm)	0.937**	(6.09±1.94)/(6.17±2.02)	-1.808	0.075
Equation 2(MET)	0.876**	(5.91±1.58)/(6.03±1.71)	-1.833	0.069

4

Conclusion

In this paper, multiple linear regression equations were constructed to investigate the accurate measurement of physical exertion in table tennis players. It was found that the average K4b² measured MET values of integrated and free singles at all stages were 9.2 and 9.4, which were not significantly different; while there were significant differences between the predicted MET values of GT3X at different sites. The predicted values of the waist, thigh and ankle joints in both modes were significantly lower than the predicted values of the wrist and handle sites, which were smaller than the measured values; while the predicted values of the wrist and handle were significantly larger than the measured values. There is no significant difference between the predicted values of the constructed equations 1 and 2 and the calibration values, and the correlation with the calibration values is high, so they can effectively measure the energy expenditure of table tennis sports.

Language:: English

Publication timeframe:: 1 times per year
Journal Subjects:: Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other

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Research on the Accurate Measurement Method of Athletes’ Physical Consumption Using Intelligent Wearable Devices in Table Tennis Training

Wenjing Nian

Dongyan Cheng

Ye Gao

Xing Liu

Guorong Huang

Published Online: Mar 21, 2025

Received: Nov 08, 2024

Accepted: Feb 07, 2025

DOI: https://doi.org/10.2478/amns-2025-0589

KeywordsActiGraph, Multiple linear regression, Metabolic equivalent, Physical energy consumption

© 2025 Wenjing Nian et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
ActiGraph, Multiple linear regression, Metabolic equivalent, Physical energy consumption