Research on quantitative assessment model and application strategy of volleyball players’ physical training effect

As a competitive and confrontational sport, the development of volleyball is closely linked to physical training. In modern volleyball games, high-intensity confrontation, fast rhythm and frequent jumping, moving and hitting actions put forward extremely high requirements on athletes’ physical fitness [1-4].

High-level volleyball players in colleges and universities are also an important talent pool of the country, and an important path to select and cultivate the new generation of talents. As one of the “three major balls” in China, the cultivation and training of high level volleyball players in colleges and universities is particularly important [5-6]. Volleyball not only requires strength, endurance, speed, but also coordination, flexibility and agility, and athletes need to be able to play their own specialized skills and techniques stably in high-intensity sports [7-8]. Some studies have pointed out that the confrontation of high-level volleyball is actually the confrontation of players’ specialized physical fitness, so the specialized physical fitness training is crucial to whether players can win in the game [9-10].

However, the physical training of Chinese volleyball players has long existed the phenomenon of lagging behind in specialized physical training, serious disconnection with the development of technical and tactical level, and only focusing on the technical aspects of training without paying attention to physical training [11-12]. It can be seen that the research in the field of physical training of volleyball players can not only improve the training theory and training method system of Chinese volleyball, but also promote the scientific training of high-level women’s volleyball teams in colleges and universities [13-14]. The research on the scope of volleyball physical training has become an urgent task and has important practical significance. In the current context, improving the special physical fitness quality of Chinese women’s volleyball players is particularly important for improving the overall competitive level of the whole team [15-16]. As an important reserve force for the integration of sports and education in schools, the improvement of the special physical fitness quality of college high-level female volleyball players also has an important role and value for future development, and it is also of great practical significance to take college high-level female volleyball players as research samples [17-18].

At present, there are relatively few theoretical studies on the physical training of high-level athletes in Chinese colleges and universities, and at present, most of them are studies on the analysis of the current situation of physical fitness and physical training, while there are few studies on the analysis of the training results [19]. In practice, the managers and coaches of domestic university sports teams also rarely pay special attention to the physical training of athletes, and always put most of the time and energy on the technical and tactical training, but seldom with reference to the results of a variety of tests to carry out targeted physical training, so I think that this kind of neglect of targeted physical training leads to volleyball competitive level is difficult to improve [20-23]. Therefore, the research on the issue of physical training of high level athletes in colleges and universities has positive significance both in theory and reality [24].

Literature [25] based on a variety of physical training methods to carry out differentiated physical training for volleyball players to improve the efficiency of athletes’ physical preparation, and based on a comparative analysis of 20 physical preparation indexes, pointed out that differentiated physical training effectively improves the physical preparation of volleyball players. Literature [26] systematically reviewed the process stages of volleyball training and the role played by coaches in it, and concluded that coaches need to arrange training in conjunction with training objectives, playing field scenarios, and determined base sequences, base efforts, and base injury levels. Literature [27] constructed a model of general and special preparation of volleyball players dependent on the characteristics of the preparation, as well as clarifying the dynamic characteristics of the indicators of the special physical training of volleyball players, and carried out a research and analysis, pointing out that the construction of the training process program is beneficial for volleyball players to maintain a high level of the indicators of the special physical fitness in the competition. Literature [28] used the method of literature review and controlled experimental methods to explore how enhanced jump training affects the physical fitness of volleyball players, and based on the results of the study, it was learned that the strong jump training (PJT) improved the physical fitness of volleyball players to a certain extent. Literature [29] introduced the sports staging theory and the concept of residual training, and examined the staging of volleyball and how to improve the physical fitness level of volleyball players through residual training, pointing out that the volleyball special analysis theory is in the dynamic process of continuous improvement, and more and more can scientifically solve the problems related to the training of volleyball players. Literature [30] emphasized that the physical quality and tactical skills of the athletes are more and more important in the 2-2.5-hour volleyball competitive matches, so it is necessary to pay great attention to the physical training of the volleyball players, and the physical quality of the volleyball players is the basis for mastering volleyball skills. The above researchers focus on the physical training of volleyball from the perspective of sports staging, differentiation, special training and coaching training planning, aiming to improve the effect of volleyball physical training from a multi-dimensional perspective.

Literature [31] conceptualized a physical training assessment strategy with grey Markov model as the core logic, which helps to optimize and improve the physical training effect, and promotes the physical fitness level of volleyball players. Literature [32] combined the scale tools such as the score of perceived physical fitness (sRPE) and the well-being questionnaire to assess and quantify the training load, physical performance of athletes, revealing the relationship between the quantification of athletes’ training loads, the assessment of physical performance, and the mall time, and the study provided a certain reference for the personalized training of athletes. Literature [33] used the heart rate index as the core of the quantitative method to measure the changes in the distribution of high intensity of sports training how to affect the physical performance of athletes and training loads, as well as based on the whole-body indexes generated by the exercise-induced physiological stress, the study pointed out that the changes in the distribution of high intensity of sports training measured by the proposed method appeared to be contradictory to the impact on the physical performance and quantification of the training loads, and when setting high intensity, the proposed method to measure the training loads had a certain impact on the physical performance and training loads. The study pointed out that the proposed method to measure the changes in the distribution of high intensity of exercise training had contradictory effects on physical performance and quantification of training load, and that the proposed quantification method had some limitations in measuring training load when setting high intensity. Literature [34] empirically evaluated the relationship between training load (TL) and volleyball players’ physical performance, biochemical indicators and psychological stress during the short preparatory period (SPP). Based on the results of the analyzed experiments, it was learned that volleyball matches in the short preparatory period prompted a steep rise in the training load, CK, and psychological stress of the athletes, with an increase in the training load leading to an increase in the level of CK, which did not affect the physical performance. . Literature [35] reviewed the research on wearable devices to assess athletes’ performance in volleyball game tables and volleyball training, and also wanted to think that the assessment focus of the related literature mainly focuses on the key variable of volleyball, i.e., the vertical jumping ability, and pointed out that coaches as well as the related researchers can consider using wearable devices to realize volleyball monitoring as well as the assessment of training effects on volleyball players. Literature [36] in a nineteen-week volleyball training observation, based on the known exercise intensity (RPE) method to achieve the quantification of the training load, and the use of Total Quality Recovery (TQR) scale assessed the training recovery status of the athletes, the quantitative analysis of the data compared with the actual performance, confirming the feasibility of the proposed program. In summary, the main strategies used nowadays for the quantitative assessment of physical training are the Gray Markov Model, the Perceived Physical Performance (PPP) Scale, the Heart Rate Indicator (HRI), the Wearable Devices (WDs), and the Exercise Intensity Scale (EIS) tool.

In this paper, to improve the accuracy of the comprehensive assessment of athletes’ training effects, a physical training effect assessment model based on the Markov model is proposed. Mechanical parameters are combined with big data sampling methods to analyze parametric constraints, correlation, and fuzzy characterization of the physical training effects of athletes. Mechanical information fusion methods for feature extraction and moment of inertia distribution modeling are applied to carry out distributed reconstruction of mechanical features in order to improve the accuracy of physical training assessment. The Markov model is applied to assess the effects of volleyball doubles explosive strength and lower limb strength training, with the goal of exploring the reliability and accuracy of the methods presented in this paper.

2

Current status of research on training assessment models for volleyball players

The current common way of evaluating physical training is mainly through manual assessment, which is still based on paper records. With the arrival of the informationization era, modern physical training forms are moving towards intelligence. Numerous researchers have combined embedded, artificial intelligence and other technologies with physical training assessment to meet the need for informationization changes in physical training assessment system, and intelligent training assessment system has a broad application prospect.

Key youth volleyball is the strong reserve force of Chinese volleyball, and the quality of their training will directly affect whether Chinese volleyball can flourish and maintain the leading position in the world volleyball arena. At present, the evaluation method implemented in the winter training of key youth volleyball is generally to take people by the temporary results, focus on the summative evaluation, and ignore the formative evaluation of the training effect, therefore, the evaluation often does not take into account the training foundation factors of the athletes of each team, and it is not to discriminatively analyze the magnitude of the improvement of the quality of the teams before and after the winter training and the development trend of the whole process of the athlete’s training, but rather, it isolates the one-time quality test result after winter training as the basis of evaluation. Instead, it isolates the one-time quality test results after winter training as the basis for evaluation, and ranks the sequence of winter training effect of each team and measures the training quality of each team accordingly. Obviously, the current evaluation method is not scientific, accurate and objective enough, and it cannot truly reflect the objective status quo of the training effect of each team on the basis of excluding the differences in the training basis of each team, which is not conducive to mobilizing and stimulating the training enthusiasm of the coaches, and is not conducive to encouraging the first to burst out and spurring on the latter to advance, and at the same time, it is not convenient for the coaches to understand and obtain the various kinds of feedback information that truly reflect the status quo of the training, and to carry out the optimal training control and corrective action. At the same time, it is also not convenient for coaches to understand and obtain all kinds of feedback information that truly reflect the current training situation and implement optimal training control and correction.

In recent years, research on athlete training in China has focused on improving training effect or safety protection. For example, the simulation training system for athletes is based on virtual reality technology, while the simulation simulation system for athletes’ training is based on artificial intelligence technology. The scientific training of Chinese athletes has been fully launched late, and at this stage, there is no basic assessment system that accurately and in detail records the training content and comprehensive results, which cannot realize in-depth analysis, resulting in a low assessment accuracy rate. For example, the improved fuzzy hierarchical analysis method is used, combining quantitative and qualitative analysis, but the determination of indicator weight vectors is more subjective. Combining the characteristics of the dataset of athletes’ training and assessing the comprehensive effect of their training can increase the reference base of the assessment, and the method of assessing the training effect of athletes based on the Markov model is proposed to construct an empirical analysis model for the evaluation of the effect of athletes’ physical training. In view of this, this paper introduces the Markov chain principle and assessment analysis method into the assessment of the physical training effect of key youth volleyball, in order to make the assessment of the physical training level of key youth volleyball more scientific and more in line with the objective reality, which can provide feedback information reflecting the status of the training process to the coaches of each team.

3

Markov-based model for assessing the effectiveness of physical training

3.1

Markov model

The main research objectives and tasks of this paper are to establish a key youth volleyball physical training effect evaluation and prediction analysis model by invoking the principle of Mars’ chain, and to provide a feasible and effective method of quantitative checking, evaluation and prediction of training effect for training. Develop a training effect evaluation and analysis software that integrates the information input of training effect indicators, quantitative checking, evaluation and prediction, so as to make the evaluation work gradually move towards scientification, modernization, electronization, informatization and standardization. Experimental validation of the implementation effect of the Markov chain assessment model is carried out to examine the correctness and effectiveness of its application.

According to the composition of a Markov chain, its process has the following characteristics: 1)

Randomness of the process. The transfer from one state to another within the system is random, and the possibility of transformation is represented by the probability value of the original historical situation within the system, which is still of practical significance if the system has stability.

2)

Discrete nature of the process. The development of the system can be discretized in time into a finite or listable number of states, and this discrete characteristic provides an operational level for the use of the Mars model.

3)

The non-sequitur nature of the process. The probability of transfer within a system is related only to the current state and not to previous states. That is, the n+1st outcome of some factor in the transfer of a given system is affected only by the nth outcome and is independent of other outcomes.

3.1.1

Markov chains

Let a random sequence ${X_{n}, n \geq 0}$ $$\left\{ {{X_n},n \ge 0} \right\}$$, for any i₀, i₁, …i_n ∈ S, S be the state space: (1) $P {X_{0} = i_{0}, ... X_{n}} > 0$ $$P\{ {X_0} = {i_0},...{X_n}\} > 0$$

And: (2) $P {X_{n + 1} = i_{n + 1} | X_{0} = i_{0}, X_{1} = i_{1}, ... X_{n} = i_{n}}} = P {X_{n + 1} = i_{n + 1} | X_{n} = i_{n}}$ $$P\{ {X_{n + 1}} = {i_{n + 1}}|{X_0} = {i_0},{X_1} = {i_1},...{X_n} = {i_n}\} \} = P\{ {X_{n + 1}} = {i_{n + 1}}|{X_n} = {i_n}\}$$

Then the random sequence ${X_{n}, n \geq 0}$ $$\left\{ {{X_n},n \ge 0} \right\}$$ is said to be a Mahalanobis chain.

One-step transfer probability matrix:

∀i, j ∈ S, call P{X_n + 1 = j|X_n = i} = P_ij(n) the one-step transfer probability at the moment of n. If ∀i, j ∈ S, P_ij(n) = P_ij, i.e., P_i is independent of n, call ${X_{n}, n \geq 0}$ $$\left\{ {{X_n},n \ge 0} \right\}$$ a chi-square Markov chain. Call P the one-step transfer matrix for ${X_{n}, n \geq 0}$ $$\left\{ {{X_n},n \ge 0} \right\}$$.

State classification:

Definition 1(i up to j): state i is said to be up to j if there exists n > = 0 such that P_ij⁽ⁿ⁾ > 0, denoted i → j, i and j are said to be interoperable if i → j and j → i, denoted i ↔ j, a subset A of state set ζ is said to be closed if ∀i ∈ A there is $\sum_{j \in A} P_{i j} = 1$ $$\sum\limits_{j \in A} {{P_{ij}} = 1}$$, and a martenschain is said to be irreducible if ζ does not contain a true closed subset.

Define 2 state as always returning, if P (w; ∃1 ≤ n < + ∞, makes ε_n = i|ε₀ = i) = 1. Otherwise, i is called not always returning (or transient state).

i A constant return means that from i, a finite number of steps must return to i, such that: (3) $\begin{array}{l} f_{i j} (n) \overset{Δ}{=} P_{i} (ε reaches j at time n) (n \geq 1) \\ = P_{i} (ε_{n} = j, ε_{k} \neq j; 0 < k < n) \end{array}$ $$\begin{array}{l} {f_{ij}}(n)\mathop = \limits^\Delta {P_i}(\varepsilon {\text{ reaches }}j{\text{ at time }}n)(n \ge 1) \\ = {P_i}({\varepsilon _n} = j,{\varepsilon _k} \ne j;0 < k < n) \\ \end{array}$$

and: (4) $\begin{array}{l} f_{i j}^{*} \overset{Δ}{=} P_{i} (ε reaches j in finite time) \\ = \sum_{n = 1}^{\infty} P_{i} (ε reaches j at n) = \sum_{n = 1}^{\infty} f_{i j} (n) \end{array}$ $$\begin{array}{l} f_{ij}^*\mathop = \limits^\Delta {P_i}(\varepsilon {\text{ reaches }}j{\text{ in finite time}}) \\ = \sum\limits_{n = 1}^\infty {{P_i}} (\varepsilon {\text{ reaches }}j{\text{ at }}n) = \sum\limits_{n = 1}^\infty {{f_{ij}}} (n) \\ \end{array}$$

Easy to see: (5) $\begin{array}{rcl} P_{i j} (n) & = & P_{i} (ε_{n} = j) \\ = & \sum_{k - 1}^{n} P_{i} (ε_{n} = j, ε reaches j at k) \\ = & \sum_{k = 1}^{n} P_{i} (ε reaches j at k) P (ε_{n} = j | ε_{k} = j) \\ = & \sum_{k = 1}^{n} f_{i j} (k) P_{i j} (n - k) \end{array}$ $$\begin{array}{rcl} {P_{ij}}(n) &=& {P_i}({\varepsilon _n} = j) \\ &=& \sum\limits_{k - 1}^n {{P_i}} ({\varepsilon _n} = j,\varepsilon {\text{ reaches }}j{\text{ at }}k) \\ &=& \sum\limits_{k = 1}^n {{P_i}} (\varepsilon {\text{ reaches }}j{\text{ at }}k)P({\varepsilon _n} = j|{\varepsilon _k} = j) \\ &=& \sum\limits_{k = 1}^n {{f_{ij}}} (k){P_{ij}}(n - k) \\ \end{array}$$

Definition 3 State i is said to be periodic with d if P_i(m) = 0 when m is not an integer multiple of d and there exists k₀ such that P_ii(kd) > 0 when k > k₀ and again non-periodic when d = 1.

Definition 4 Let π= (π₁, π₂, …π_k…) be such that $\sum_{i} π_{i} P_{\ddot{v}} = π_{j}, π_{j} \geq 0 (\forall j)$ $$\sum\limits_i {{\pi _i}} {P_{\ddot v}} = {\pi _j},{\pi _j} \ge 0(\forall j)$$, π_j are not all zero, then π is said to be an invariant measure of P. Also if $\sum_{i} π_{i} = 1$ $$\sum\limits_i {{\pi _i}} = 1$$, then it is called an invariant probability measure.

Definition 5 Let there be a non-degenerate σ − algebraic family ${F_{t}, t \in T}$ $$\left\{ {{F_t},t \in T} \right\}$$ on (Ω, F, P), and a “random variable” τ(w) taking the value of ${T \cup {+ \infty}}$ $$\left\{ {T \cup \left\{ { + \infty } \right\}} \right\}$$ is called a stopping time with respect to {F_t} if, intuitively, for ∀t ∈ T, {w:τ(w) ≤ t} ∈ F_t the stopping time is a random time that does not depend on the future.

Theorem 1 If i is constant return, then $\sum f_{\ddot{n}} (n) = 1, \sum P_{\ddot{n}} (n) = + \infty$ $$\sum {{f_{\ddot n}}} (n) = 1,\sum {{P_{\ddot n}}} (n) = + \infty$$, and when i is not constant return, then there is: (6) $\forall j, \sum_{n} P_{j i} (n) < + \infty$ $$\forall j,\sum\limits_n {{P_{ji}}} (n) < + \infty$$

Theorem 2 If H is an equivalence class obtained by the reciprocity relation, i₀ ∈ H, i₀ are always returnable, all states in H = {i ∈ ζ|i ↔ i₀} are always returnable, and a finite time must elapse from a state in H to reach i₀ and never to a state outside H.

Theorem 3 All states in the same class of constant returns have the same period.

Theorem 4 Let ξ be an irreducible martensitic chain with constant returns and a transfer array of P. Then: 1)

L = 1π.

2)

π_i(i = 1, 2, 3, …) is all zeroes, or all non-zeroes.

3)

An invariant probability measure for P exists if and only if π is not 0. This is when π is the only invariant probability measure for P. Definition 6 State i is called normal return if L_ii > 0. It is called zero return if i return and L_ii = 0.

Theorem 5 Let P be incommensurable normal return nonperiodic, then: (7) $\lim_{n \to \infty} P^{n} = L$ $$\mathop {\lim }\limits_{n \to \infty } {P^n} = L$$

Theorem 6 Let P be zero-constant return, incommensurable, and nonperiodic, then $\lim_{n} \to \infty P^{n} = 0$ $$\mathop{\lim}\limits_{n} \to \infty {P^n} = 0$$.

Theorem 7 The states of an irreducible finite Markov chain are all positive constant return states.

Theorem 8 The irreducible nonperiodic Markov chain of finite states must have a unique smooth distribution.

3.1.2

Markov model definition and application

A Markov model is a doubly stochastic process containing two sequences of random variables: one is an unobservable Markov chain that describes the transfer of states, expressed in terms of transfer probabilities. The other is an observable random sequence that describes the relationship between the state and the observations, expressed in terms of observation probabilities. The complete Hidden Markov Model is represented by a quintuple λ = (S, V, A, B, π), where: 1)

S is the set of hidden states, S = {s₁, s₂, ⋯, s_N}, |S| = N and remember that the state at moment t is q_t, q_t ∈ S.

2)

V is the set of observed symbols, V = {v₁, v₂, ⋯, v_M}, |V| = M and note that the symbol observed at moment t is o_t, o_t ∈ V.

3)

A is the state transfer probability matrix, and A = (a_ij), a_ij denotes the probability of transferring to state s_j at moment t + 1 if the state is s_i at moment t − 1, i.e., a_ij = P(q_t+1 = s_j|q_t = s_i)1 ≤ i, j ≤ N.

4)

B is the observed symbol probability distribution for the state, B = {b_j(k)}, b_j(k) denotes the probability of observing symbol v_k in state s_j, i.e. b_j(k) = P(o_t = v_k|q_t = s_j)1 ≤ k ≤ M, 1 ≤ j ≤ N.

5)

π is the probability distribution of the initial state, π= {π_i}, π_i denote the probability of being in state s_i at moment t = 1, i.e. π_i = P(q_i = s_i)1 ≤ i ≤ N.

The properties of the Markov model are fully defined by A, B, π, which for convenience is abbreviated as λ = (A, B, π). Unless otherwise stated, this refers to a first-order Hidden Markov Model (HMM).

Knowing the observation sequence O = (o₁, o₂, ⋯, o_T) and the model λ = (A, B, π), the HMM solves the following three problems in practical applications: 1)

Evaluation problem: find the conditional probability P(O|λ) that model λ produces observation sequence O, which can be solved using the forward algorithm.

2)

Decoding problem: find the most probable sequence of states for model λ to produce observation sequence O, which can be solved using the Viterbi algorithm.

3)

Learning problem: using observation sequence O, adjust the parameters of model λ to maximize conditional probability P(O|λ), which can be solved using the Baum-Welch algorithm.

3.2

Steps in assessing the effectiveness of Markovian physical training

3.2.1

Sampling of Statistical Information for Assessing the Effectiveness of Athletes’ Physical Training

In order to realize the optimization design of athletes’ physical training effect assessment model based on Markov model, adopt big data feature analysis method to carry out the adaptive optimization search of athletes’ physical training effect, establish the adaptive fusion parameter analysis model of athletes’ physical training effect assessment, adopt big data analysis and feature scheduling method to carry out the big data information sampling for the athletes’ physical training effect assessment, combine with the statistical information Mining method for athletes’ physical training effect assessment, dividing the grade x⁽⁰⁾ of athletes’ physical training effect assessment into N grades for x^(l), x⁽²⁾, ⋯, x^(N), i.e., $x^{(0)} = \cup_{i = 1}^{N} x^{(6)}$ $${x^{(0)}} = \bigcup\limits_{i = 1}^N {{x^{(6)}}}$$, adopting the similarity feature analysis method for the statistical analysis and optimization assessment of athletes’ physical training effect assessment, adopting the analysis method of multiple regression test to establish the fuzzy constraint parameter analysis model for training effect assessment, adopting the fuzzy statistical analysis and quantitative gaming method, to carry out adaptive learning of athletes’ physical training effect assessment, to establish the quantitative analysis model of athletes’ physical training effect assessment, and to obtain the statistical function of athletes’ physical training effect assessment as: (8) $\begin{array}{l} \min F = R^{2} + A \sum_{i} ξ_{i} \\ s . t : | | ϕ (x_{i}) - o | |^{2} \leq R^{2} + ξ_{i} a n d ξ_{i} \geq 0, i = 1, 2, \dots \end{array}$ $$\begin{array}{l} \min F = {R^2} + A\sum\limits_i {{\xi _i}} \\ s.t:||\phi ({x_i}) - o|{|^2} \le {R^2} + {\xi _i}and{\xi _i} \ge 0,i = 1,2, \cdots \\ \end{array}$$ (9) $\begin{array}{l} \max \sum_{i} α_{i} K (x_{i}, x_{i}) - \sum_{i} \sum_{j} α_{i} α_{j} K (x_{i}, x_{j}) \\ s . t : \sum_{i} α_{i} \leq 1 a n d 0 \leq α_{i} \leq A, i = 1, 2, \dots \end{array}$ $$\begin{array}{l} \max \sum\limits_i {{\alpha _i}} K({x_i},{x_i}) - \sum\limits_i {\sum\limits_j {{\alpha _i}} } {\alpha _j}\;K({x_i},{x_j}) \\ s.t:\sum\limits_i {{\alpha _i}} \le 1and0 \le {\alpha _i} \le A,i = 1,2, \cdots \\ \end{array}$$

The above equation represents the adaptive parameter distribution set of the assessment of athletes’ physical training effect, and the correlation fusion cluster analysis method is used to establish the standard normal distribution function of the assessment of athletes’ physical training effect, and ω is the inertia weight of the distribution of statistical features of the assessment of athletes’ physical training effect, and the homogeneous information fusion method is used to carry out the quantitative analysis of the assessment of athletes’ physical training effect, and the quantitative analysis of the assessment of athletes’ physical training effect is established. The associative distribution relationship between the constraint parameter set R^N and X^N of the physical training effect assessment is: (10) $p (R^{N} = r_{i}) = p | \begin{matrix} X^{N} = x_{i} | | x_{i} | = | r_{i} |, a n g l e (x_{i}) \\ = (a n g l e (r_{i}) - φ_{g}) \mod (2 π) \end{matrix} |$ $$p({R^N} = {r_i}) = p\left| {\begin{array}{*{20}{c}} {{X^N} = {x_i}||{x_i}| = |{r_i}|,angle({x_i})} \\ { = (angle({r_i}) - {\varphi _g})\bmod (2\pi )} \end{array}} \right|$$

Combining autocorrelation feature matching methods for convergent processing of athletes’ physical training. Improving the adaptive nature of the assessment of athletes’ physical training effects.

3.2.2

Information fusion for training effectiveness evaluation

Combining the statistical analysis of mechanical parameters and the method of big data sampling, the mechanical parameters of athletes’ physical training big data fusion processing, the descriptive statistical sequence of athletes’ physical training effect {x(t₀ + iΔt)}, i = 0, 1, …, N − 1, the optimized characteristic parameters of athletes’ physical training optimization search for optimal quantization set is: (11) $X = {[s_{1}, s_{2}, \dots, s_{K}]}_{n} = (x_{n}, x_{n - r}, \dots, x_{n - (m - l)} π)$ $$X = {[{s_1},{s_2}, \cdots ,{s_K}]_n} = ({x_n},{x_{n - r}}, \cdots ,{x_{n - (m - l)}}\pi )$$

Construct a model for assessing the effect of physical training of athletes based on the joint analysis of muscular endurance and explosive force characteristics. And combine the statistical data to carry out and the method of big data sampling. To carry out the analysis of the effect evaluation parameters of athletes’ physical training, and to establish the fuzzy parameter fusion model of athletes’ physical training effect evaluation. The expression for constructing the statistical analysis model for the assessment of the effect of physical training of large athletes is: (12) $\frac{d z (t)}{d t} = F (z)$ $$\frac{{dz(t)}}{{dt}} = F(z)$$

Order f(si) = (f(x₁), f(x₂), ⋯, f(x_n)), using mechanical sensors, physical data acquisition of athletes’ physical training explosive force is carried out, and the parameters are obtained.

Distribution model is P(n_i) = {p_k|pr_kj = 1, k = 1, 2, ⋯, m}, the correlation scheduling and fuzzy degree characterization of the assessment of the effect of athletes’ physical training, the establishment of the distribution model of the moment of inertia of the explosive force of athletes’ physical training, combined with the fuzzy information fusion feature extraction method for the reconstruction of the distribution of the mechanical features of athletes’ physical training, and the distribution of the mechanical features of the athletes’ physical training is in the following equation: (13) $\begin{array}{l} λ = \frac{1}{1 + α {(\frac{\partial S}{\partial t})}^{2}} \\ {\hat{k}}_{μ} (t + 1) = {\hat{k}}_{μ} (t) + Q (t + 1) \times [\frac{\partial {\hat{F}}_{μ} / M g}{\partial t} - \frac{\partial S}{\partial t} {\hat{k}}_{μ} (t)] \end{array}$ $$\begin{array}{l} \lambda = \frac{1}{{1 + \alpha {{(\frac{{\partial S}}{{\partial t}})}^2}}} \\ {\widehat k_\mu }(t + 1) = {\widehat k_\mu }(t) + Q(t + 1) \times \left[ {\frac{{\partial {{\widehat F}_\mu }/Mg}}{{\partial t}} - \frac{{\partial S}}{{\partial t}}{{\widehat k}_\mu }(t)} \right] \\ \end{array}$$

Among them: (14) $Q (t + 1) = P (t + 1) \frac{\partial S}{\partial t}$ $$Q(t + 1) = P(t + 1)\frac{{\partial S}}{{\partial t}}$$ (15) $P (t + 1) = \frac{1}{λ} [P (t) - \frac{P^{2} (t) {(\frac{\partial S}{\partial t})}^{2}}{λ + P (t) {(\frac{\partial S}{\partial t})}^{2}}]$ $$P(t + 1) = \frac{1}{\lambda }\left[ {P(t) - \frac{{{P^2}(t){{(\frac{{\partial S}}{{\partial t}})}^2}}}{{\lambda + P(t){{(\frac{{\partial S}}{{\partial t}})}^2}}}} \right]$$ (16) $\frac{\partial S}{\partial t} = \frac{r}{v_{c}} \frac{\partial ω_{w}}{\partial t}$ $$\frac{{\partial S}}{{\partial t}} = \frac{r}{{{v_c}}}\frac{{\partial {\omega _w}}}{{\partial t}}$$

In the formula, λ represents the large number of athletes’ physical training effect assessment.

Data fuzzy degree distribution factor, ${\hat{F}}_{μ}$ $${\hat F_\mu }$$ is the statistical characteristic component of athletes’ physical training effect assessment ω_w is the adaptive weighting coefficient, constructing the information optimization fusion model of athletes’ physical training effect assessment, combining with the mechanical parameter analysis method, and carrying out the optimization of athletes’ physical training effect assessment.

3.3

Mathematical and statistical methods

Markov chain analysis was used to establish a mathematical model for assessing and predicting the effectiveness of key youth volleyball physical training. Adopt “sS law” and normality test method to test the abnormal data, and test the normality of the test data. The data standardization method and the “deviation method” were used to standardize the dimensionless data information of the test indexes, and then the grading model was developed. The validity of this rating method was examined using the grade correlation analysis method. Software preparation method adopts high-level software language to prepare computer-aided assessment and analysis software integrating indicator data input and storage, quantitative inspection, assessment and prediction, etc., so as to achieve the purpose of “indicator information storage archiving, quantitative assessment and analysis, standardized and rapid information output”. The experimental verification method uses mathematical statistics and logic to test the validity and applicability of the assessment method through experimental control and comparison.

4

Research on the application of training assessment models for volleyball players

4.1

Reliability testing

Taking University H in a province as the background condition for method testing, the proposed Markov model-based physical training effect assessment model method, and the traditional type-graded assessment method are respectively utilized to carry out the teaching effect assessment of physical education courses, and the test conclusions are drawn based on the obtained assessment results.

In this paper, a sports college is used as the experimental background, and athletes from two volleyball major classes are selected as experimental subjects to ensure the persuasiveness of the test results. The students selected for this evaluation are freshmen and sophomores, and a random sampling method is used to randomly select 10 college students, of which 5 are male and 5 are female, which in turn randomly selects 1,000 students in this sports institution as the experimental subjects, and the specific information of the experimental subjects is shown in Table 1. In order to ensure the scientificity and rigor of the test results, using content validity and reliability with data analysis software, to measure whether the physical training effect of this test is in line with the test evaluation requirements, in which the test results of validity are shown in Table 1. KMO is one of the validity test indicators, usually when the value of KMO is above 0.9, this indicator proves that the test content is very suitable for test analysis. Meanwhile, the internal consistency coefficient of Cronbach is utilized to test the reliability of the test content, and when the result of this test is above 0.7, then it indicates that the consistency of the test content is better.The attendance rate and average grade of the 10 students are all above 90.

Table 1.

Basic information of the experimental object

Majors	Student selection	Attendance rate	Average performance
1	Volleyball	97.52%	92.8
2	Volleyball	94.09%	95.84
3	Volleyball	95.36%	93.27
4	Volleyball	96.97%	92.82
5	Volleyball	94.82%	94.1
6	Volleyball	98.58%	95.73
7	Volleyball	99.20%	94.66
8	Volleyball	98.6%	96.0
9	Volleyball	97.84%	97.84
10	Volleyball	96.84%	95.47

In this test, the proposed method was used as experimental group A, while the traditional method was used as experimental group B. The test results obtained are shown in Fig. 1. Analyzing the above two groups of pictures, it can be seen that the assessment value of the training effect of the proposed assessment method is more similar to the actual test results of the students, and the average similarity level is calculated to be 98.83%. While in the traditional method, the average similarity level is 84.34%, which is 14.49% lower than the assessment results of the proposed assessment method. It can be seen that the assessment performance based on Markov’s physical training effectiveness assessment model is superior.

In order to verify the accuracy of the training assessment model proposed in this paper for volleyball players in practical application and whether it has higher reliability, one of the classes evaluates its training process using the assessment model proposed in this paper, and the other class evaluates its training process using the traditional assessment model to validate the assessment model designed in this paper. In order to realize the comparability of the two assessment models, this paper chooses the reliability evaluation scale as the evaluation index of the two models. Before the experiment, firstly, grade Ⅰ is defined as the model with very good evaluation results, and its value is taken in (0.85,0.95]. Grade Ⅱ is the model with fairly good evaluation results, which takes the value of (0.75,0.85]. Grade III is the model with acceptable but not too good results, and its value is (0.65,0.75). Grade Ⅳ is the model with the best evaluation result to be discarded, which takes the value of (0.60,0.65]. Based on the above specified criteria, the assessment results of the two assessment models are examined. For the convenience of the test, the reliability statistics of the final results obtained from the two assessment models were recorded and plotted in a table.

The total correlation and reliability coefficients are shown in Table 2. As can be seen from the data results, the total correlation and reliability coefficients of the assessment model of this paper are significantly higher than those of the traditional assessment model, which belongs to the Ⅰ grade evaluation sub-district as stipulated above in this paper, while the traditional assessment model belongs to the Ⅲ and Ⅳ grade evaluation sub-districts only as stipulated above in this paper. The training assessment model of volleyball players proposed in this paper has higher reliability and credibility in practical application, which is conducive to the development of training planning contents for volleyball players that are more in line with their training needs.

Table 2.

Two evaluation model reliability statistics

	Training quantity and density		Training contents and forms		The athlete’s heart rate changes
	This article evaluates the model	Traditional assessment model	This article evaluates the model	Traditional assessment model	This article evaluates the model	Traditional assessment model
Total correlation	0.864	0.643	0.867	0.658	0.964	0.655
Coefficient of alpha (reliability coefficient)	0.961	0.643	0.962	0.660	0.902	0.640

4.2

Assessment of the effectiveness of lower limb strength training for volleyball players

A city volleyball team was used as the experimental subject. It was divided into control and experimental groups according to age, with 14 members in each group. The volleyball players were tested for half-squat jump and squat jump performance, which was taken as the initial performance, and the detailed parameters are shown in Table 3. There was no significant difference in the initial performance of the volleyball players in the two groups before training.

Table 3.

The control group and the experimental group were half squat

Age	The experimental group was half squatting/cm	Control group half squat jump/cm
12	33.21±0.67	33.57±0.36
13	33.8±0.32	36.14±0.58
14	34.17±0.97	34.36±0.98
15	35.2±0.65	36.02±0.38
16	36.35±0.68	37.15±0.22
17	37.14±0.98	37.89±0.96
18	38.17±0.75	39.25±0.98

Taking the experimental group as the experimental object, using the model of this paper to evaluate the lower limb strength semi-squat jump training effect of the experimental group of volleyball players, the results are shown in Table 4, the experimental group of volleyball players after the strict implementation of the lower limb training program, its different age groups of volleyball players semi-squat jump performance are improved, from the perspective of its lower limb strength training evaluation results, the 17 and 18 years old volleyball players semi-squat jump performance to improve their performance by the largest, the average value of 4.09, 5.47 respectively. From the evaluation results of their lower limb strength training, 17 and 18 years old volleyball players improved their semi-squat jump performance the most, and the average value improved by 4.09 and 5.47 respectively, so their evaluation grade was V. The semi-squat jump performance of volleyball players with relatively small age in terms of their lower limb strength improved a little bit. To summarize the results, the model of this paper can effectively evaluate the effect of semi-squat jump training on the lower limb strength training of volleyball players, and it has good applicability.

Table 4.

The results of the training effect of the athletes’ lower limb strength

Age	The experimental group was half squatting/cm	Evaluation grade
12	35.24±0.23	Ⅲ
13	37.11±0.62	Ⅵ
14	36.28±0.22	Ⅵ
15	37.35±0.98	Ⅲ
16	38.04±0.16	Ⅵ
17	41.23±0.58	V
18	43.64±0.65	V

To further validate the model of this paper to evaluate the performance of volleyball players, the experimental group and the control group were taken as the experimental subjects to assess the lower limb strength training effect of their volleyball players when they were in different time periods, and the results are shown in Figure 2. The experimental group completed the lower limb strength training program for a total of 12 weeks, and from the assessment results, the volleyball players showed a trend of phased increase in their lower limb strength training effect during the period of performing lower limb strength training. While the control group for the implementation of the lower limb strength training program, only daily routine training, its lower limb strength training effect, although also shows a phased increase trend, but its lower limb strength training effect increased by a smaller magnitude, indicating that the contribution of its routine training to increase its lower limb strength is small. To summarize the results, using the model in this paper to assess the lower limb strength training effect of volleyball players can present the lower limb strength training results of volleyball players at different stages, provide stage-by-stage guidance for volleyball players’ training, and have strong applicability.

4.3

Distribution of movement characteristics of volleyball doubles explosiveness

In order to test the performance of the application of the above method to realize the evaluation of the training effect of volleyball doubles explosive force, simulation test is conducted, the algorithm design of the experiment is implemented using Matlab, and the distribution of the action characteristics of volleyball doubles explosive force is shown in Table 5.

Table 5.

The movement characteristics of the double punch

i	q_i/radian	a_i/radian	a_i/mm	d_i/mm	Explosive moment
1	m₁	−π/4	1_s	2	[−π/6, π/6]
2	m₂ − π/2	−π/4	2	2	[−π/6, π/6]
3	m₃ − π/2	π/4	2	1_u	[−63π/18, π/6]
4	m₄	−π/4	2	2	[0,69π/36]
5	m₅	π/4	2	1_f	[0,35π/18]
6	m₆ − π/2	−π/4	2	2	[−π/8, π/8]
7	m₇	π/4	1_h	2	[−π/8, π/8]

According to the explosive force output parameter settings in the table. The evaluation of the explosive force training effect for volleyball doubles was carried out, and the sampling model of force generation characteristic parameters was obtained as shown in Fig. 3.

According to the parameter sampling distribution in the above figure, the parameter testing and evaluation of volleyball doubles explosive power was carried out, and the dynamic evaluation results were obtained as shown in Fig. 4.

According to the results of parameter optimization search for convergence control in the process of volleyball doubles explosive force training effect assessment, the assessment output is obtained as shown in Figure 5. Analysis has shown that the method of this paper can effectively realize the volleyball doubles explosive force training effect assessment, test the accuracy of the assessment, and the accuracy of the physical training effect assessment model based on Markov model for volleyball doubles explosive force training effect assessment is high, reaching more than 90%.

5

Conclusion

This paper mainly proposes an assessment model based on Markov physical training. Facing the volleyball physical training, taking volleyball players as the research object, collecting all kinds of training data, through the sub-assessment of the training data, thus providing timely and effective information for training, and scientifically formulating and adjusting the training program according to the assessment results. Applied in volleyball lower limb strength and explosive force training, the experiment proved that the model can effectively improve the relevance and reliability of the assessment results, and can accurately reflect the actual training situation of volleyball players, so as to make a more accurate assessment. From the assessment results, the volleyball players applying the assessment model of this paper showed a continuous improvement in the training effect during the lower limb strength training, compared with the traditional method, the model of this paper can provide stage-by-stage guidance for the athletes. The accuracy and adaptability of the model used in this paper for assessing the effect of volleyball doubles explosive strength training are high. Therefore, in the future, it is planned to extend the physical training assessment model of this paper to various sports training to promote the intelligent development of physical training.

Język:: Angielski

Częstotliwość wydawania:: 1 razy w roku
Dziedziny czasopisma:: Nauki biologiczne, Nauki biologiczne, inne, Matematyka, Matematyka stosowana, Matematyka ogólna, Fizyka, Fizyka, inne

Kanał RSS czasopisma

Research on quantitative assessment model and application strategy of volleyball players’ physical training effect

Dan Lv

Jiale Qu

Data publikacji: 21 mar 2025

Otrzymano: 25 paź 2024

Przyjęty: 17 lut 2025

DOI: https://doi.org/10.2478/amns-2025-0680

Słowa kluczowe<kwd>Markov model</kwd>, <kwd>Physical training</kwd>, <kwd>Mechanical parameters</kwd>, <kwd>Big data sampling</kwd>

© 2025 Dan Lv et al., published by Sciendo

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

Słowa kluczowe
<kwd>Markov model</kwd>, <kwd>Physical training</kwd>, <kwd>Mechanical parameters</kwd>, <kwd>Big data sampling</kwd>