(1) Theoretical basis of integrated technology acceptance and use model.
Unified Theory of Acceptance and Use of Technology (UTAUT) model is developed on the basis of Technology Acceptance Model (TAM), which is a unity. This includes seven models: technology acceptance model, theoretical behavior theory, planned behavior theory, incentive model, innovation diffusion theory, social cognition theory and computer use theory. It is mainly composed of influencing factors of use intention and use behavior: performance expectation, effort expectation, social influence and promotion conditions. It also points out that gender, age, experience and voluntariness as control variables significantly affect key factors, as shown in Fig. 6. Performance expectation is the perceived usefulness of users using the system. It involves five key model variables, namely perceived usefulness, external motivation, work consistency, comparative advantage and outcome expectation. Effort expectation is how much effort users need to make when using the system. It consists of three key model variables, namely perceived ease of use, complexity and ease of use. Social impact refers to the extent to which individuals think they are affected by the surrounding environment. It consists of three key model variables: subjective norms, social factors and social image. The promotion condition emphasizes the individual’s perception behavior control of relevant technology and equipment, objective reinforcement condition and compatibility.
Fig. 6
Integrated technology acceptance and use model.
Aiming at the sustainable development of skating sports training, this study discusses how to provide professional and personalized training services for teenagers while protecting the environment. The research shows that participation in skating training can not only improve the skill and level of sports, but also increase the theoretical knowledge of sports, which has important educational value. The pleasurable level of the training experience is closely related to the trainees’ attention to the training process, and also affects their participation expectations and confidence. The trainees’ trust in the ability of coaches and the system of training institutions directly affects their understanding and mastery of the training content, and then affects the training effect and the willingness to continue to participate. As shown in Fig. 7, the conceptual model proposed in this study shows that adolescents’ cognitive interest in skating sports training has a positive impact on their effort expectations and willingness to continue to participate. At the same time, the actual situation of skating training also affects the students’ expectations and willingness to participate. Contextuality plays a mediating role between these expectations and wishes, regulating students’ performance and participation in decision-making. The perceived degree of training pleasure mediates the expectation of effort and the willingness to continue to participate. Finally, on the basis of the trainees’ trust in the training institutions, the effort expectation and performance expectation have a positive impact on their willingness to continue to participate in the training, so as to promote the youth’s continuous participation in the skating training behavior.
Fig. 7
Conceptual model of continuous participation behavior of young skating students.
(2) Structural formula model.
The variables of the sustainable development structure formula model of youth skating training are composed of implicit variables and explicit variables. Implicit variable (also known as structural variable) is composed of exogenous implicit variable ξ in youth skating training and endogenous implicit variable η in youth skating training. The implicit variables of youth skating training cannot be directly observed, but can only be measured by the corresponding set of explicit variables of youth skating training. Dominant variables (also known as observation variables) are represented by x and y. Each recessive variable of juvenile skating training corresponds to a group of dominant variables, and each recessive variable of juvenile skating training and its dominant variable group constitute a block group. The inter-group relationship is in the external position, and the intra-group relationship is in the internal position. The structural formula model of sustainable development of youth skating training is as follows:
$$\:\eta\:=B\eta\:+\varGamma\:\xi\:+\xi\:$$
(1)
For sample i, it can be transformed into form:
$$\:B{\eta\:}_{i}+\varGamma\:{\xi\:}_{i}+{\xi\:}_{i}$$
(2)
By using the partial least squares model, the implicit variable scores \({\eta\:}_{i}\) and \({\xi\:}_{i}\) of adolescent skating training are calculated. After obtaining the estimated value, the partial least squares model is used to subdivide the calculation results.
It is assumed that the i-th sample of the k-th class obeys Gaussian conditional distribution:
$$\:{f}_{i}{|}_{k}\left({\eta\:}_{i}|{\xi\:}_{i},{B}_{k},{\varGamma\:}_{k},{\varPsi\:}_{k}\right)$$
(3)
According to Gaussian conditional distribution Formula (3), it can be deduced that:
$$\:{f}_{i}{|}_{k}({\eta\:}_{i}\left|{\xi\:}_{i},{B}_{k},{\varGamma\:}_{k},{\varPsi\:}_{k}\right)=\left(-\frac{1}{2}\right)\left({B}_{k}{\eta\:}_{i}+{\varGamma\:}_{k}{\xi\:}_{i}\right){\varPsi\:}_{k}^{-1}\left({B}_{k}{\eta\:}_{i}+{\varGamma\:}_{k}{\xi\:}_{i}\right)$$
(4)
The matrix of \({B}_{k}={\beta\:}_{mrk}\) and M*M refers to the path coefficient between the endogenous implicit variables of adolescent skating training in category k. Among them, r = 1,…, M.
The matrix of \({\varGamma\:}_{k}={\gamma\:}_{mjk}\) and M*J refers to the path coefficient between the endogenous and exogenous implicit variables of adolescent physical training in category k.
The diagonal matrix of \({\varPsi\:}_{k}\) and M*M refers to the variance of the regression residuals of the endogenous implicit variables of each adolescent skating training in category k.
For any \({\eta\:}_{i}\) , it follows the Gaussian conditional distribution of the finite mixture model:
$$\:{\eta\:}_{i}\sim\:\sum\:_{k=1}^{k}{\rho\:}_{k}{f}_{i}{|}_{k}({\eta\:}_{i}\left|{\xi\:}_{i},{B}_{k},{\varGamma\:}_{k},{\varPsi\:}_{k}\right)$$
(5)
Among them, \({\rho\:}_{k}\) is the weight of implicit variables of youth sports training.
The incomplete data is represented by\({z}_{ik}\) , and the distribution density of the complete data of adolescent skating training is:
$$\:{\eta\:}_{i}\sim\:\prod\:_{k=1}^{k}{\rho\:}_{k}^{{z}_{ik}}{f}_{{}_{i}{|}_{k}}\left({\eta\:}_{i}|{\xi\:}_{i},{B}_{k},{\varGamma\:}_{k},{\varPsi\:}_{k}\right)$$
(6)
The likelihood function is:
$$\:L=\prod\:_{i=1}^{i}\prod\:_{k=1}^{k}{\rho\:}_{{}_{k}}^{{z}_{ik}}{f}_{{}_{i}{|}_{k}}\left({\eta\:}_{i}|{\xi\:}_{i},{B}_{k},{\varGamma\:}_{k},{\varPsi\:}_{k}\right)$$
(7)
The log likelihood function is:
$$\:InL=\sum\:_{i}\sum\:_{k}{z}_{ik}In{\left({f}_{i}\right)}_{k}\left({\eta\:}_{i}|{\xi\:}_{i},{B}_{k},{\varGamma\:}_{k},{\varPsi\:}_{k}\right))$$
(8)
The posterior probability of class k is:
$$\:P\left({z}_{ik}=1\right)={\rho\:}_{k}{f}_{{}_{i}{|}_{k}}\left({\eta\:}_{i}|{\xi\:}_{i},{B}_{k},{\varGamma\:}_{k},{\varPsi\:}_{k}\right)$$
(9)
Let the formula be:
$$\:{P}_{ik}=E\left({z}_{ik}\right)=P\left({z}_{ik}=1\right)$$
(10)
For the m-term formula in the structural model, the dependent variable is the endogenous implicit variable of m-term adolescent skating training, and the independent variable is the endogenous implicit variable of predicting all the adolescent skating training and the exogenous implicit variable of adolescent skating training.
The sustainable dependent variables of youth sports training are:
$$\:{y}_{mi}={\eta\:}_{mi}$$
(11)
The independent variable of youth sports training sustainability is:
$$\:{x}_{mi}=\left({\xi\:}_{mi},{\eta\:}_{mi}\right)$$
(12)
According to the least square method, the path coefficient is:
$$\:{x}_{mi}=\left({\beta\:}_{mr},{\gamma\:}_{mj}\right)={\left({x}_{m}^{{\prime\:}}{x}_{m}\right)}^{-1}\left({x}_{m}^{{\prime\:}}{y}_{m}\right)$$
(13)
Multiplication by block matrix is:
$$\:{\tau\:}_{m}=\left({\beta\:}_{mr},{\gamma\:}_{mj}\right)=\sum\:_{i}{\left({x}_{m}^{{\prime\:}}{x}_{m}\right)}^{-1}\sum\:_{i}{x}_{m}^{{\prime\:}}{y}_{m}$$
(14)
By considering the k-th class in subdivision, the path coefficient is:
$$\:{\tau\:}_{mk}=\left({\beta\:}_{mrk},{\gamma\:}_{mjk}\right)=\sum\:_{i}{\left({p}_{ik}{x}_{m}^{{\prime\:}}{x}_{m}\right)}^{-1}\sum\:_{i}{p}_{ik}{x}_{mi}^{{\prime\:}}{y}_{mi}$$
(15)
The diagonal elements of the variance matrix \({\varPhi\:}_{k}\) of the regression formula is:
$$\:{\omega\:}_{mk}=\sum\:_{i}{p}_{ik}\left({y}_{mi}-{x}_{mi}{\tau\:}_{mk}^{{\prime\:}}\right)$$
(16)
In the n-th iteration, the weight estimation of youth sports training sustainability is:
$$\:{\rho\:}_{k}^{\left(n\right)}=\sum\:_{i=1}^{I}{p}_{ik}^{\left(n-1\right)}$$
(17)
Among them, \({p}_{ik}^{\left(n-1\right)}\) is the \(\:{p}_{ik}\) value of the n-1 iteration, and the information entropy of youth sports training is:
$$\:EN=1-\sum\:_{i}\sum\:_{k}-{p}_{ik}In{p}_{ik}$$
(18)
The EN value is between 0 and 1. The larger the EN, the better the effect of fuzzy clustering. By considering two extreme cases, when EN is zero, the posterior probability is:
$$\:{p}_{ik}=\sum\:\left({\xi\:}_{i},k\right)$$
(19)
The cluster regression analysis of adolescent skating training directly calculates the maximum likelihood function of Formula (19):
$$\:L=\prod\:_{i=1}^{i}\left(\prod\:_{k=1}^{k}{\rho\:}_{k}{f}_{i{|}_{k}}\left({\eta\:}_{i}|{\xi\:}_{i},{B}_{k},{\varGamma\:}_{k},{\varPsi\:}_{k}\right)\right)$$
(20)
Results and evaluation of the experimental data of the new ecology of sports training and environmental protection measures
The sustainable development of youth skating training involves many aspects. The quality of training institutions, the quality of training coaches, the purpose of youth training, the content of training programs, and training difficulties may all affect the sustainable willingness of youth skating training. In order to further explore the deep influencing factors of the sustainable development of youth skating training, this study selects the sustainability of youth skating training as the dependent variable q; the quality of training institutions is an independent variable q1; the quality of training coaches is an independent variable q2; the purpose of adolescent training is independent variable q3; the training content is q4; the training difficulty factor q5 is an independent variable. The multiple regression model is constructed. The discrete variables q1, q2, q3, q4 and q5 are further logarithmically processed and then added to the regression formula for analysis.
(1) Data correlation.
Table 5 shows the results of correlation analysis among various variables. It can be concluded that the correlation between variable q and q1, q2, q3, q4, q5 is large and each variable has a strong correlation, so the next step of multiple regression analysis can be carried out.
Table 5 Test on the correlation of variables related to the sustainable development of adolescent skating training.
(2) Standard deviation.
The standard deviation is the deviation of each data from the average value. The larger the standard deviation, the greater the distance between each data point and the average value of data distribution. It can be seen from Fig. 8 that youth training purpose q3, training project content q4 and training difficulty factor q5 have standard deviations greater than 0.8.
Fig. 8
Youth skating training sustainability standard deviation score.
(3) Skewness.
The skewness test aims to measure whether the data are asymmetric or evenly distributed. When the deviation exceeds 0, the data distribution is left biased and characterized by the right long tail. When the skewness is below 0, the data distribution is right skewed and shows a long left tail. It can be seen from Fig. 9 that the skewness analysis results of youth training purpose, training project content and training difficulty factors are larger and more directional.
Fig. 9
Analysis on the skewness of sustainable development of adolescent skating training.
(4) Kurtosis.
The kurtosis specifically describes the data distribution, and the peak value of the standard normal distribution is at 0. In the case of scattered data distribution, the kurtosis below 0 is a low peak. When the data distribution is relatively centralized, the peak is when the kurtosis is above 0. It can be seen from Fig. 10 that the peak values of youth training purpose and training project content are greater than 1, which indicates that these data values are relatively concentrated in a certain range.
Fig. 10
Statistics of sustainable development peak of youth skating training.
The regression model analysis shows that the independent variables such as the purpose of youth training, the content of training programs, the factors of training difficulties, the quality of training institutions, and the quality of training coaches have a significant impact on the sustainable intention of youth skating training. In other words, the more active the purpose of youth training and the more diversified the content of training programs, the more sustainable participation behavior of youth skating training can be improved. In general, the construction of the model not only improves the sustainable participation willingness of youth skating training by 3.66%, but also creates a good policy environment for the development of youth skating training.
In order to test the generalization ability of the model, five sports such as basketball, swimming, track and field, football and tennis are selected for corresponding experiments. Multiple regression analysis is used to assess the sustainability of youth training in different sports and to compare the key influencing factors in these sports. Data is collected for each variable (q1, q2, q3, q4, q5), and the regression coefficient of each independent variable is calculated to evaluate its impact on training sustainability (q). The results of the evaluation are shown in Table 6.
Table 6 Results of multiple exercise tests.
Table 6 shows the impact of key factors in five sports on the sustainability of youth training. The results show that q2 plays an important role in several sports, especially in football, swimming and basketball, indicating that good coaching can significantly increase youth’s willingness to participate in the long-term. q3 is evident in athletics and tennis, demonstrating that clear personal goals are crucial to maintaining motivation to participate. q5 has a large impact in basketball and track and field, and appropriate challenges can help improve participation. Overall, the emphasis of the influencing factors in each sport is different, reflecting the unique needs of each sport.
