Research on reliability of sports intelligent training system based on hybrid wolf pack algorithm and IoT

To expand the application scope of the WCA algorithm in the actual process, this research has optimized the problems in the algorithm in two aspects: The first aspect further improves the operating mechanism of the WCA algorithm and improves the performance of optimization problem. In the second aspect, other optimization strategy mechanisms of the WCA algorithm are introduced to enable the algorithm to optimize multi-objective and multidimensional problems. This paper studies a physical test system and sports intelligent based on hybrid wolf pack algorithm and IoT. The system collects and sends data from the data collection terminal of the Web server, receives the data through the wireless module, and sends it to the Web server through the network. The Web server processes and stores the data information to generate a database, and users can view their own sports information by logging in to the Web service program with the account password. In addition, the teacher and administrator accounts have the ability to view all users' exercise information. The system adds three sports items, pull-ups, squats, and standing long jumps. At the same time, the system uses a general motion recognition algorithm, which can effectively reuse and add new sports items. According to the actual needs of intelligent sports training, this paper combines somatosensory technology, bone tracking technology, and motion recognition algorithm to realize a high-precision, low-latency intelligent sports training system.


Introduction
Optimization is an important concept in the scientific field (Zhu et al. 2011). Generally speaking, it is to find the optimal solution or solution set that people need in a complex and insoluble problem. Optimization includes many types, such as linear, nonlinear, discrete, and continuous. In our daily life and production, we often encounter such as how to arrange production resources and marketing plans, how the company deploys personnel in product development to maximize the benefits of the company, and how to make the indicators of the corresponding products achieve the most reasonable use of resources. These problems can all be referred to as optimization problems (Stein 2012;Kessentini et al. 2008;Sangaiah et al. 2023). With the continuous progress of society, the development of various industries is inseparable from the establishment of optimization models to find the optimal solution to save costs (Caunhye et al. 2012). In short, optimization exists in all aspects of the development process of human society. At the same time, optimization methods are flourishing with the richness of model descriptions. The emergence and use of optimization methods greatly promoted the development of society at that time. With the continuous development of engineering optimization problems, optimization models are no longer continuous and derivable, but tend to be largescale, discretized, and even without a clear functional form (Amaldi et al. 2003;Capone et al. 2010). These problems are difficult to solve with classical optimization methods and cannot meet actual needs in terms of convergence and solution time.

Related work
In terms of algorithm research, the literature proposed an algorithm for wolf pack strategy based on leader strategy. Experiments have shown that the algorithm is more accurate and converges faster (Chi 2019). The literature proposed the cultural wolf optimization algorithm and found that the cultural wolf optimization algorithm has faster convergence speed and higher accuracy than other algorithms in the actual use process (Xu et al. 2022). The literature adds new random survival rules on the basis of WPA and ensures the diversity of algorithms by adding new rules (Li et al. 2015). Experimental results show that the increased update rules make the convergence speed and accuracy of the algorithm significantly improved. The literature uses the WSA algorithm as the framework and then uses the nonlinear simplex method to improve the local search ability of the WSA algorithm (Baykasoglu and Akpinar 2015). In the process of actual experiments, it is found that the algorithm can obtain higher solution accuracy when solving the problem. The literature proposed the CWCA algorithm. In the process of practical application, the CWCA algorithm forms new points through methods such as mapping, expansion, and contraction, and replaces the original old points with newly generated new points. It calculates to improve the accuracy of the algorithm (Caragata et al. 2015). It pointed out the application of WCA algorithm in the field of smart grid, the use of WCA algorithm can achieve high-precision control of smart grid time synchronization, and the algorithm has achieved good application effects in the field of smart grid. The literature pointed out that the WPA algorithm can be applied to the medical field (Velusamy and Pugalendhi 2020). For example, the WPA algorithm can be used for the medical diagnosis of diabetes. With the continuous development of modern technology, the superiority of the WPA algorithm is gradually manifested. In the literature, the DE algorithm and the WPA algorithm are fused together to realize the complementary advantages of the DE algorithm and the WPA algorithm, and the mixed algorithm is applied to the deception and jamming recognition of satellite navigation (Bisoi et al. 2020). The literature Hierarchy-Wolfs algorithm adopts the dual coding method and applies the HWA algorithm in the field of optimal placement of three-dimensional sensors (Mathematics 2021). It established a UVA trajectory model and used the WPA algorithm to solve the UVA problem. The literature uses the WPA algorithm to optimize the initial weights and thresholds of the BP neural network algorithm, which improves the convergence speed and accuracy of the algorithm (Han et al. 2016;Sangaiah et al. 2020a, b;Javadpour et al. 2023). It applied the LWCA algorithm to the photovoltaic array MPPT, effectively tracking the global maximum power point, and verified the feasibility of the algorithm. The literature proposed the IWPS algorithm and applied it to the optimal dispatching of hydropower stations and reservoirs. It proved through experiments that the self-organizing neural network spectrum sensing algorithm based on wolf group optimization has better spectrum sensing capabilities.
3 Overview of wolf pack algorithm

The basic principle of the wolf pack algorithm
The wolf pack algorithm is designed to simulate the optimization problem of wolf pack hunting behavior processing function. The basic idea of the algorithm is to start from an initial prey group in the space to be optimized, and take the wolf with the best fitness value as the first wolf. This operation is called the first wolf generation criterion. Then, the best M wolves except the first wolf are selected as the scouts, and the optimal search is performed in the predetermined direction. Adopt new and old predation rules to keep better prey. Once a prey that is better than the current first wolf is found, the scout with the prey becomes the first wolf. This process is called wandering behavior. The first wolf began to howl, telling the ferocious wolves around to quickly approach the first wolf, looking for quality prey. If the high-quality prey found is better than the first wolf, the wolf will replace the first wolf and start howling again until the wolf stops at a certain distance from the prey. This process is called running behavior. It eliminates R wolves with the worst fitness value and randomly generates R wolves in the optimal space to supplement. This process is called the strongest surviving wolf pack update mechanism. The key steps in the WPA algorithm are described in detail below: The first step is to initialize the prey group. The formula for prey production is as follows: The artificial wolf with the optimal fitness value is used as the first wolf in this iteration.
The position of Tanlang i in the d-dimensional space is as follows: When the wolf i evolves for the k = 1 time, the position in the d-dimensional variable space is as follows: The judgment distance need is as follows: The siege behavior of the wolves is as follows: The following relationships exist:

Features of wolf pack algorithm
Combined with the research of relevant literature, we can conclude that the wolf pack algorithm has six characteristics: systemicity, adaptability, distribution, diversity, freedom, and feedback. In order to have a deeper understanding of the characteristics of the wolf pack algorithm, we select four different algorithms to compare with the WPA algorithm, including ABC algorithm, GA algorithm, FSA algorithm, and DE algorithm. The advantages, disadvantages, and applicable scope of each algorithm are shown in Table 1.
After comparison, we can see that each algorithm has its advantages and disadvantages. Although the development process of WPA algorithm is relatively short, it also has many advantages. Therefore, in the future development process, WPA algorithm will be widely used.

Proof of convergence of wolf pack algorithm
The transition matrix of the Markov chain is defined as follows: Create a non-empty collection, Group transition probability matrix: Combining with the group transition probability matrix, recalculate the non-empty set: 4 Sports intelligent training system based on the Internet of Things

Definition of the Internet of Things
The Internet of Things is actually an ''Internet of Everything'' network, which connects all the things around with the network through sensors and other electronic devices, and exchanges data at the same time. They believe that the Internet of Things must be a network in addition to its previous characteristics. The network must be composed of

Overview of IoT technology
The Internet of Things technology can be divided into three levels: perception layer, network layer, and application layer. The technology of the perception layer includes RFID technology, sensor technology, and so on. This article focuses on the key technologies of the perception layer. The composition of the sensor is shown in Fig. 1.

Overall scheme design
The system is mainly used in communities and schools, and is oriented to people of all ages. Therefore, before system design, the system architecture must be planned in detail to meet the needs of people of all ages as much as possible.
During the operation, not only the stability and safety of the operation, but also the upgrade and maintenance of the system must be considered. In order to achieve these goals, the following four basic principles must be followed in the system design process: (1) The principle of stability and safety, as an intelligent system serving the public, must ensure stable and safe operation during the user's use, and does not appear technical loopholes. At the same time, it is necessary to improve the system and software upgrade and maintenance system, so that when the system has problems, it can be solved quickly.
(2) The principle of simplicity and practicality is a very important principle. Because the service target of the system we designed also includes some elderly people, too complicated and cumbersome operating procedures will often bring great inconvenience to them. Therefore, it pays attention to this detail in the system design process and simplifies the operation process as much as possible. (3)The low price principle, the price of a system often determines its competitiveness in the market. People usually choose products with high performance and low price. Therefore, in the system design process, some cost-effective electronic devices should be selected to meet product performance and reduce costs. (4) The principle of scalability, scalability is an important factor to be considered when designing a system. After fully considering the above four basic principles, we designed a qualified sports testing department. The system consists of three parts: data collection terminal, data base station, and WEB website. Overall flowchart of the system is shown in Fig. 2.
The design goal of the data collection terminal of this system is: When the user puts the campus card in the card reader, the reader reads the campus card message and displays it on the LCD screen. At the same time, the wireless module sends the data to the base station. The appearance design of the data collection terminal is shown in Fig. 3.
In this paper, according to the actual needs and the summary of relevant algorithms, the relevant data base station is designed, and its structure design is shown in Fig. 4.
After the data base station is designed, how to use it is the next key problem. Therefore, this paper constructs the specific process as shown in Fig. 5 to facilitate data collection and transmission.
The function of the upper computer software is to calculate and process the data information stored in the data base station, and then obtain the user's long-distance running speed, distance, and other information, and store it in the PC hard disk file for query.
The subject of this paper is an intelligent sports training system based on somatosensory technology. That is to say, the system can recognize that the user completes the preset types of exercises within the effective range of motion, so it needs to meet the body's whole body recognition. While ensuring the accuracy of motion recognition, it is necessary to minimize the required support costs and optimize them through algorithm and software design. After market research, I finally selected two optical sensing device options: KinectV2 launched by Microsoft in 2014, and RealSenseSR300 launched by Intel in 2016. After a more detailed comparison and analysis, somatosensory equipment selection comparison is shown in Table 2.
Finally, this article selects KinectV2 as the somatosensory acquisition device of this system. First, a wider tracking range allows the human body to move more freely under the premise of full-body motion recognition. The detection range of Kinect is 4.5 m far greater than the 1.5 m of SR300; secondly, although RealSenseSR300 has higher accuracy, it has advantages in the field of face recognition and gesture recognition. The accuracy of Kinect for the whole body motion of human limbs is enough to provide basic data for motion recognition algorithms; finally, it is also Microsoft under the Windows

Motion recognition algorithm and implementation
The first chapter briefly introduces the classification of motion recognition algorithms. Each algorithm has more suitable application scenarios. In different application environments, no algorithm is effective and universal. This requires detailed analysis of the characteristic parameters and purpose of the human body movement in the application scenario. According to the application purpose and quantification standard of these extracted features, the logic design and system design of the motion recognition algorithm are completed. The purpose of this system research is to develop a set of sports training equipment for non-professional sports and fitness personnel. Therefore, this article combines the ''National Physical Exercise Standards'' to better understand the daily activities of campus students Research on reliability of sports intelligent training system based on hybrid wolf pack algorithm and… 10193 for college students. This is conducive to the early testing and application of the system. Finally, the goal of choosing traction exercises to exercise upper limb strength and lower limb strength is clear. Plus a more reasonable humancomputer interaction process, this article analyzes the requirements of the motion recognition algorithm as follows and obtains the corresponding functional requirements: (1) The motion recognition algorithm must use the same motion recognition algorithm process for different motions, which can not only realize the multiple use of a set of equipment, but also improve the scalability and higher reusability of the system, which is a fast new motion. Be prepared for expansion and addition. It is a general motion recognition algorithm.
(2) This system is used for daily exercise training, so the user's action standards should be higher in the process of exercise and use, so the motion recognition algorithm should fully consider the standard degree of each decomposition action, with higher the recognition accuracy.
(3) As a real-time motion recognition system, it is different from a motion recognition system based on video images. It needs to consider the user's experience during use and can provide timely feedback and content interaction on the action process. Therefore, there are higher requirements for the efficiency and speed of motion recognition, lower delay, but higher system efficiency. (4) The human body is the target of motion recognition, but the difference in body shape and exercise habits of each person must be considered. For different body shapes, the motion recognition algorithm is  Available platforms XBOX, Windows, Linux, and mac Windows and Linux required to have good robustness, which can handle the motion recognition of different body shapes without losing the standard requirements for each decomposition action during the movement. For different exercise habits, a reasonable and natural exercise ending action for different exercises helps the system cope with individual differences.
The characteristics of measurement error are usually composed of the accuracy and precision of the system. The accuracy of the system is well understood, that is, how close the system measurement value is to the actual value measurement. Precision refers to the degree of concentration of ownership measured at one point repeatedly. As shown in the figure, four systems are used to repeatedly measure the position of the hand to illustrate the concept of accuracy and precision. The four measuring systems measure the position of the hand as shown in Fig. 6.
The black X in the figure represents the position of the hand in the real world, and the red dots represent the position of the hand measured by several measurement systems. The first figure represents an inaccurate and inaccurate measurement system; the second figure represents an inaccurate but accurate measurement system; the third figure represents an accurate and precise measurement system; and the fourth figure represents an accurate and more precise measurement system. The first two have large deviations and errors and cannot be used, while the third system does not exist in real life. The fourth is already a very good measurement system, and it does exist, such as KinectV2, but the data can be further reduced by filtering. Deviation is to achieve close to the real measurement system. This system uses a filter that combines jitter removal and double exponential smoothing. Jitter cleaning attempts to limit the allowable range of variation in the output of each frame to suppress the peak of the input.
In median filtering, the output of the filter is the median of the last N inputs. The median filter helps eliminate impulse peak noise, as shown in the figure. Ideally, the filter size N should be chosen to be greater than the duration of the peak noise. However, the delay of the filter directly depends on N, so a larger N increases the delay. Ideally, the order of the filter should be greater than the duration of the peak noise, but considering the original intention that the delay cannot exceed 100 ms, we can choose N = 5 at most, which can effectively eliminate the impulse peak noise.
The double exponential smoothing filter has different formulas, and there are subtle differences between them. The mainstream is described by the following two formulas, where T represents the trend, F represents the filter output, and a and c represent the parameters.
The trend bn is calculated as an exponential filter that is the difference between the last two outputs of the filter, and Xðn À 1Þ þ bðn À 1Þ is used to calculate the output of the filter. Including this trend helps reduce latency because the filter fits a line of locally input data, and bn is the slope of the fitted line. c controls the weight of input data and is used for trend calculation. Therefore, c controls the sensitivity of the trend to recent input changes.
Generally speaking, this filtering method has excellent performance in prediction. However, the signal overshoot is obvious in the prediction output. A simple but useful improvement is to adjust the a and c parameters based on the adaptation of the joint speed, so that when the joints are not moving fast, by using smaller a and c parameters more accurate filtering. When a joint does not move fast, the result of this adaptation will smooth the output. When the joint is moving fast, use larger a and c parameters, which will have a better response to input changes, thereby reducing delay. This article uses two preset a and c parameters: one for alow and clow at low speed, and the other for ahigh and chigh at high speed. Based on the above analysis, the a parameter is applied at time N in the following algorithm design. a n ¼ No one filtering solution can be applied to all situations. Taking into account the application scenarios of the Fig. 6 The four measuring systems measure the position of the hand Research on reliability of sports intelligent training system based on hybrid wolf pack algorithm and… 10195 system, the output delay and smoothness are balanced. The output data in KinectV2 are filtered by a joint filtering method combining jitter removal and double exponential smoothing. It provides stable data input for motion recognition to ensure smooth application and good user experience. Normally, the Euclidean distance is used as formula (16): The regular path needs to meet the following monotonicity constraints: The model of a finite number of states and the switching and actions between these states is called a finite state machine. The main function is to describe the state sequence of the target in its cycle and how to respond to the influence of various external events on the state. Finite state machines have two main characteristics: discrete state and finite state. It consists of states, transitions, detectors, and events. Event refers to an important thing defined by the system, which will be triggered when it reaches a certain state. A state transition triggers an event to switch from one state to another state. The state directly reflects the change of the system input from the beginning to the present, and the transition indication will only change when the condition description for the state transition occurs. A limited number of state transitions will only be triggered when the relevant conditions are touched, so it is discrete and limited. The description of the operation to be performed at a given time is called an operation. There are many types of operations: input, transfer, input, and exit.

Application of smart sports training system
Smart sports venues and modern sports venues attach great importance to intelligence. Modern information technology can connect the software and hardware of the building to enable efficient operation of building functions and improve the economic benefits of the building. The ''smart'' stadium has also greatly improved the comfort and convenience on the original basis. Sensors and intelligent air-conditioning systems are used to detect the temperature and humidity of the stadium, thereby making adjustments to improve the comfort of the audience. With the athlete's intelligent management system, the managers can understand the athletes' conventional physiological indicators, analyze the athletes' strengths and weaknesses. The system can combine the training plan of physical education with the local environment. For example, the needs of the sports training on the plateau and the plain are different, so that the sports state of the athletes is more in line with the local climate environment. In many practices, the venue will provide relevant manuals, which can help the athlete to know the status of the game and his physical indicators at any time. Smart hardware products are not only limited to bracelets or watches, but also smart scales, smart headphones, smart glasses, etc.; sports monitoring equipment equipped with sensors mainly includes running shoes, insoles, socks, underwear, and other necessary sports equipment. The intelligence of sports equipment is simply that the relevant equipment can obtain the user's sports information and constitute a machine learning process. When the athlete has movement deviation or is not in good condition, it will make timely adjustment and provide relevant personalized services according to the actual needs of the user.

Conclusion
At present, the development of smart sports is a mainstream of the combination of the field of big data and sports. Various intelligent equipment, intelligent sports software, and intelligent sports venues are emerging in an endless stream. The system combines intelligent technology with physical education, applies the basic skills of hybrid wolf pack algorithm and Internet of Things, and builds the relevant training platform. According to the actual needs of intelligent sports training, this paper combines somatosensory technology, bone tracking technology, and motion recognition algorithm to realize a highprecision, low-latency intelligent sports training system. The system provides scientific physical training for the non-professional sports fitness public and students. The multi-functional and networked design can break through the limitations, can really check the progress of the exercise, make a training plan, and at the same time, users can log in to the system in real time to view themselves training status and exercise data.
Funding The authors have not disclosed any funding.
Data availability Data will be made available on request.

Declarations
Conflict of interest The authors declare that they have no conflict of interest.
Ethical approval This article does not contain any studies with human participants performed by any of the authors.