# The Value of Wearable Sensors in Swimming Flexibility Training under the Background of the Internet of Things

Authors: Kai Bao; Jie Gao; Xiaomin Zhang; Wen Qi; Xurui Liu; Hao Tian
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

Flexibility training in swimming is a key to improving the flexibility index of athletes. In this era of rapid development of IoT technology, it is necessary to combine the Internet of Things technology with the application of wearable sensors in swimming flexibility training. This article is to study the value of wearable sensors in swimming flexibility training under the background of the Internet of Things. In this paper, by combining the interconnected nature of the Internet of Things technology, choosing Apache MINA and the XStream library platform to construct the Internet of Things system, combined with the data measurement characteristics of wearable sensors, an improved strategy is analyzed by measuring various indicators in the flexibility training of swimmers and through the movement interference removal combined with the adaptive algorithm to reduce the energy consumption in flexibility training. In this paper, two sets of flexibility training experiments of static stretching and dynamic stretching are designed. In the experiment, the flexibility index and energy consumption of athletes are received through the wearable sensor of the Internet of Things, and finally, the new improved strategy is analyzed through the received data. And this article also designed a set of control experiments. The experiment shows that wearing IoT wearable sensors can improve the flexibility index of swimmers up to 20.41, while the highest is 15.53 without wearing them.


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## Body

## 1. Introduction

Swimming course is one of the main courses of sports training majors in general higher physical education universities. It focuses on posture education and has the characteristics of water sports. The standards of the Internet of Things are the highest peak of the international Internet of Things technology competition. Therefore, it is essential to study the main technologies related to the Internet of Things in practical applications. How to combine the Internet of Things and wearable sensors in swimming is a focus of this article.In the process of swimming instruction and training, the traditional static stretching method and dynamic stretching method have some shortcomings when training athletes. At the same time, swimming is a sport that requires overall high physical strength. While attaching importance to flexibility training, if you want to quickly improve your swimming level, muscle training cannot be ignored. Therefore, this article studies the application of wearable sensors based on the Internet of Things technology in swimming flexibility training. Wearable IoT wearable sensors can improve the flexibility index of swimmers in flexibility training.As coal mine safety production has received increasingly attention, coal mine informatization has also been developed by leaps and bounds. To study the safety of mine equipment, Dong et al. established a predictive maintenance system, which, based on the Internet of Things technology, changed the existing coal mine equipment maintenance mode [1]. Although its research is related to the Internet of Things technology, this article studies sensors based on the Internet of Things technology. People’s lifestyles and working methods may be changed, and a large number of new services can be seamlessly exchanged based on the IoT paradigm. Palattella et al. analyzed in detail the potential of 5G technology for the Internet of Things from two aspects of technology and standardization [2]. It combines 5G technology to study the development of the Internet of Things and does not specifically involve the application of the Internet of Things, which has little relevance to this article. The Internet of Things (IoT) can achieve innovations that improve the quality of life, but it will generate unprecedented amounts of data that are difficult to process with traditional systems, clouds, and even edge computing. Dastjerdi and Buyya believe that fog computing can overcome these limitations [3]. To gain widespread adoption of its solutions, it must satisfy the IoT system including application developers, equipment providers, and users. Mineraud et al. evaluate representative samples of these platforms based on their ability to meet the expectations of different IoT users, including proprietary and open source platforms [4]. Wearable sensors can measure the frequency and amplitude of football players’ head impacts. The goal of Siegmund et al. is to quantify the collision detection rate and effectiveness of the orientation and peak kinematics of two wearable sensors: the helmet system (HITS) and the mouthguard system (X2) [5]. His research is to use wearable sensors to study the frequency and amplitude of an athlete’s head impact. However, this article mainly studies the value of flexibility training in swimming. Gait analysis is an important medical diagnosis process, which has a wide range of applications in medical treatment, rehabilitation, treatment, and sports training. Lin et al. proposed a new type of sensor device, namely, smart insoles, to meet the challenge of effective gait monitoring in real life [6]. It uses sensing devices in the insole, but this article studies flexibility training in swimming. If he can apply the Internet of Things to the sensor equipment, then its reference value will increase accordingly. To study the relationship between flexibility and pain during swimming, Eiichi et al. investigated the relationship between shoulder pain and shoulder flexibility of Japanese elite male water polo players [7]. The content of its research on the flexible relationship of athletes can be referred to, but the reference value is not great. Most of the above documents are based on the Internet of Things technology and wearable sensors. Although some of them are about flexibility training, they are not relevant. This paper needs to strengthen research on the improvement of flexibility index of wearable sensors based on Internet of Things technology in improving the flexibility training of swimmers [8].The innovation of this article lies in the analysis of the energy consumed by flexibility training in swimming through the Internet of Things technology to build an Internet of Things system, through Apache MINA combined with XStream library, combined with wearable sensors. Then, combined with the motion interference removal of the adaptive algorithm, a scientific and effective training strategy is designed to reduce energy consumption and improve efficiency, and the wearing process of the wearable sensor of the Internet of Things can improve the flexibility index of the flexibility training of swimmers.


## 2. Design Method of Wearable Sensors Based on the Internet of Things

### 2.1. Internet of Things

The Internet of Things [9] is the “Internet connection of things,” which is for data exchange and communication based on the Internet, and extends the user side of the network to the physical world, one of the most well-known applications is smart home. Its application field is shown in Figure 1.Figure 1
Application area of IoT technology.


#### 2.1.1. Technical Architecture of the Internet of Things

The Internet of Things system is generally divided into 3 levels; they are the perception layer, the network layer, and the intelligence layer. The detection layer is composed of various detection terminals such as temperature, humidity, concentration, pH value, and GPS [10]. The key technologies based on the IoT system are explained as follows.(1) Key Technologies of the Perception Layer. The perception layer is the most basic layer in the Internet of Things architecture, which mainly completes object recognition and data collection. Radio frequency identification technology, positioning technology, sensor technology [11], and laser technology are the main technologies.RFID [12] is a noncontact automatic identification technology based on electromagnetic theory. It realizes noncontact two-way communication through radio frequency, automatically recognizes the communication object, has strong anti-interference ability, can adapt to various complex environments, and has high recognition accuracy and operability.WSN [13] is composed of multiple inexpensive micro wireless sensor nodes scattered in the monitoring area. These sensors can form a multihop wireless network system by detecting information such as pressure, temperature, and humidity. Communicating with each other wirelessly and continuously sends the information of the target object in the surveillance area to the observer.GIS (Geographic Information System) is sometimes called “Geographic Information System.” It is a specific and essential spatial information system. It is a technical system that collects, stores, manages, calculates, analyzes, displays, and describes related geographic distribution data in the entire part of the earth’s surface (including the atmosphere) space under the support of computer hardware and software systems.GPS is an omnidirectional, all-weather, all-time, high-precision satellite navigation system developed by the US Department of Defense. It can provide global users with low-cost, high-precision three-dimensional position, speed, and precise timing navigation information.The difference between GIS and GPS is that GPS can provide global users with low-cost, high-precision navigation information such as three-dimensional position, speed, and precise timing. It is a model application of satellite communication technology in the navigation field. It has greatly improved the informatization level of the earth society and strongly promoted the development of the digital economy. GIS is mainly used in the analysis of urban planning and infrastructure design and can input, manage, analyze, and express geospatial data.(2) Key Technologies at the Network Layer. The network layer [14] is built on the basis of the existing mobile communication network, the Internet, and radio and television networks. To connect the information obtained by the perception layer and the transmission equipment, a variety of access equipment is used to achieve barrier-free, reliable, and safe information transmission.(3) Key Technologies of the Intelligent Layer. The main technology of the intelligent layer [15] is cloud computing technology. Cloud computing shares and connects multiple computing resources distributed on the network and performs integrated management and intelligent scheduling through a software system which is a completely new application computing method. It needs to be used and has high scalability, high reliability, high resource utilization, and on-demand services.


#### 2.1.2. Related Technologies of IoT Sensor Data Processing Platform

(1) Maven. Maven [16] is a project management tool for all Java applications. Project developers can use Maven to understand the framework of the entire project in the shortest time. The Maven Project Object Model (POM) is a software project management tool that can manage the construction, reporting, and documentation of a project through a short description of information.(2) SSH. SSH [17] (Struts2+Spring+Hibernate) is the three frameworks of J2EE, which implements the construction of Web applications from the presentation layer, business logic layer, and data persistence layer. The execution process is shown in Figure 2.Figure 2
Struts2 workflow.(3) MINA. Apache MINA [17] is a network application framework that helps users develop high-performance and high-stability applications; it is a relatively new project organized by Apache, which provides a very convenient application framework for the development of high-performance and high-availability network applications, as shown in Figure 3.Figure 3
MINA network hierarchy.As shown in Figure4, MINA is mainly divided into three levels: I/O Service, I/O Filter Chain, and I/O Handler.Figure 4
MINA frame structure and flowchart.(4) XStream. XStream [18] is a simple library that can serialize objects into XML (JSON) or deserialize XML (JSON) into objects. At runtime, the Java reflection mechanism is used to investigate the structure of the serialized object tree. XStream can serialize internal fields containing private fields and final fields and supports nonpublic classes and internal classes. The design platform used in this article is Apache MINA combined with XStream library.


### 2.2. Wearable Sensors

With the continuous development of sensor technology [19], wearable devices have gradually integrated into people’s lives. At present, wearable products on the market include head-supported glasses, wrist-supported watches, and foot-supported shoes. The collection of walking information and the collected data are processed on mobile phones. The situation of mobile phones occupies a part of the market. General wearable devices are shown in Figure 5.Figure 5
Common wearable devices.To realize the tracking, reconstruction, and analysis of human motion, this article needs to construct a human kinematics model that conforms to the basic motion characteristics of the human body. According to the theory of human anatomy, the human motion system is a large system composed of 204 bones, 78 joints, and more than 600 muscles, with a total of more than 200 degrees of freedom [20]. If this article constructs an accurate human kinematics model completely according to the constraint relationship of bones and joints, it will be an extremely complicated process, which will increase the difficulty of analysis and application. Therefore, this article needs the necessary abstraction and simplification of the human body structure. As long as the movement of the key limbs and joints is grasped, the human body movement process can be restored as realistically as possible [21].Bones and joints are the lowest part of the human body structure, which can represent the movement process of the human body. Therefore, this paper ignores the tissues such as muscles and skin and simplifies the complex human movement process into a combination of each bone rotating around the corresponding joints. For human bones, this article ignores those tiny bones and merges some bones according to the body’s main limb composition. For example, the forearm is composed of an ulna and radius. For the convenience of research, this article merges the ulna and radius into forearm bones. Each bone is regarded as a rigid body link, and its motion characteristics strictly conform to rigid body kinematics and dynamics [22]. The joint structure of the human body is more complicated. This article ignores the tiny translational freedom of the joints, only retains the rotational freedom of the joints, and simplifies it into a hinge-like joint. The bones are connected by joints and are constrained by the joints at the same time.


### 2.3. Motion Interference Removal Design of Adaptive Algorithm

The principle structure diagram of the adaptive filter is shown in Figure6.Figure 6
Schematic diagram of adaptive filter principle.Adaptive filtering technology is a filtering method that can automatically adjust the filter parameters through the feedback of the results at all times and achieve the filtering method that can change with the changes of the signal and noise. The adaptive filter is generally composed of a structure with a feedback function and an algorithm that can iterate coefficients according to the results. Among them,dn represents the collected signal, which includes the original signal sn and the noise signal kn; there is no connection between the two. The rn output by the noise source signal is related to the background noise kn in a certain relationship; vn is the current simulation of the background noise signal kn, which can be output from the noise source signal rn after being weighted by the adaptive filter weight coefficient wn, that is, as shown in
(1)vn=∑l=0Mwlrn−l=WTnRn.Among them,Wn represents the filter weight coefficient vector at n time and represents the adjacent vector from n times to the past M+1 noise sources.
(2)Rn=rn,rn−1,⋯,rn−mT.Therefore, the output signalen, that is, the error is
(3)en=dn−vn=sn+kn−vn.en is the desired denoising signal, and its expected mean square value is
(4)Qe2n=Qd2n+Qkn−vn2+2Qdnkn−vn.Since the original signalsn is not related to the background noise kn and the estimated noise vn, there is
(5)2Qsnkn−vn=0.Therefore, formula (6) can be transformed into
(6)Qe2n=Qd2n+Qkn−vn2.In order to makeQe2n the minimum value, Qkn−vn2 is the minimum value. There are two algorithms to achieve the calculation purpose: one is the least mean square error algorithm (LMS), and the other is the recursive least squares algorithm (RLS). For the least squares algorithm, there are
(7)Qd2n+Qkn−vn2=Qd2n+Qkn−WTnRn2.And to speed up the filter’s response to interference changes, a forgetting factorγ can be introduced, and its error weight can be reduced according to the exponential law:
(8)Qe2n=Qd2nγM−n+QγM−nkn−WTnRn2.And the error at timen based on time n−1 is
(9)xn=dn−RTnWn−1−dn−∑l=0Mwn−1lrn−l.The recursive formula of the filter coefficients of the adaptive filter is derived from the least squares algorithm:(10)Wn=Wn−1+Nnxn.Formulas (9) and (10) can be combined to get
(11)Nn=Wn−Wn−1dn−∑l=0Mwn−1lrn−l.To achieve the best effect of the filter,(12)Qkn−vn2=0.We can get the formula(13)Nn=∑rn−lWnγn+WTn∑rn−lWn.Among them,δ is between 0 and 1, usually around 1, such as 0.99.ForQe2n, the most ideal situation is to perfectly filter the noise signal in the signal, that is, when kn=vn, it is expected that Qe2n reaches the minimum value, that is to say
(14)kn=∑l=0Mwlrn−l.This needs to adjust the weight coefficientWn of the adaptive filter to achieve the purpose of adjusting vn to kn, making Qen2 the minimum value. Therefore, substituting formula (1), assuming that there is a certain Wn at a certain time, the mean square error at this time is
(15)an=Qe2n=Qd2n−2QdnRTnWn+WTnQRnRTnWn.Then, the gradient vector ofan relative to Wn can be obtained as
(16)∇n=−2QdnRn+RnRTnWn.Let∇n=0, then
(17)Wn=RnRTn−1QdnRn.Substituting formula (17) into (16), we have
(18)an=Qe2n=Qd2n−QdnRnWn.Andan is the expectation of the square of the output signal, which is a nonnegative quadratic function, so there must be a minimum value aminn, and according to the behavior of adaptive filtering, there is
(19)Wn=RnRTn−1QdnRn.When the above formula is satisfied, the minimum value ofan can be obtained. Assuming that the gradient ∇n of an to Wn is known, there is a recursive formula:
(20)Wn+1=Wn+μ−∇n.Among them,μ is a normal number. The actual meaning of this formula is that the value of the weighting coefficient W of the adaptive filter at time n+1 is the value at time n plus a correction amount, and the correction amount is proportional to the inverse of the gradient value. Then, when μ selects a suitable value, an can be made to obtain the minimum value.The adaptive algorithm itself is a set of algorithms for estimating unknown signals.∇n is usually unknown, so you can set Δn to the estimated value of ∇n and make Δn approach ∇n through iteration, from formula (20),
(21)Wn+1=Wn+μ−Δn.The mathematical meaning of the gradient value is(22)Δn=∂e2n∂Wn=2en∂en∂Wn.Then, for a fixedWn, Δn is ∇n unbiased likelihood estimation, so
(23)Wn+1=Wn+μ−Δn=Wn+2μen∂en∂Wn.Therefore, this system adopts an improved variable step size LMS filtering algorithm after combining previous research results and actual experimental verification so that(24)μn+1=μmax,μn+1>μmax,μmin,μn+1<μmin,μn+1,else,(25)μn+1=aμn+e2n.Among them,0<a<1; μmax generally select the unstable step size point near the standard LMS, and after a large number of experiments in this system, μmax=0.85/λmax,μmax=0.1/λmax is selected, and a generally selects a parameter close to 1 to speed up the convergence. In this system, choose a=1. The advantage of this algorithm is that, at the beginning of the algorithm, the error signal en is larger, and the calculated μn is larger, so that the algorithm can converge at a faster speed. When the program runs for a certain period of time, the system algorithm tends to a steady state, and the error signal en is small, μn is calculated to be small, and a small error can be generated near the optimal weight coefficient.


## 2.1. Internet of Things

The Internet of Things [9] is the “Internet connection of things,” which is for data exchange and communication based on the Internet, and extends the user side of the network to the physical world, one of the most well-known applications is smart home. Its application field is shown in Figure 1.Figure 1
Application area of IoT technology.


### 2.1.1. Technical Architecture of the Internet of Things

The Internet of Things system is generally divided into 3 levels; they are the perception layer, the network layer, and the intelligence layer. The detection layer is composed of various detection terminals such as temperature, humidity, concentration, pH value, and GPS [10]. The key technologies based on the IoT system are explained as follows.(1) Key Technologies of the Perception Layer. The perception layer is the most basic layer in the Internet of Things architecture, which mainly completes object recognition and data collection. Radio frequency identification technology, positioning technology, sensor technology [11], and laser technology are the main technologies.RFID [12] is a noncontact automatic identification technology based on electromagnetic theory. It realizes noncontact two-way communication through radio frequency, automatically recognizes the communication object, has strong anti-interference ability, can adapt to various complex environments, and has high recognition accuracy and operability.WSN [13] is composed of multiple inexpensive micro wireless sensor nodes scattered in the monitoring area. These sensors can form a multihop wireless network system by detecting information such as pressure, temperature, and humidity. Communicating with each other wirelessly and continuously sends the information of the target object in the surveillance area to the observer.GIS (Geographic Information System) is sometimes called “Geographic Information System.” It is a specific and essential spatial information system. It is a technical system that collects, stores, manages, calculates, analyzes, displays, and describes related geographic distribution data in the entire part of the earth’s surface (including the atmosphere) space under the support of computer hardware and software systems.GPS is an omnidirectional, all-weather, all-time, high-precision satellite navigation system developed by the US Department of Defense. It can provide global users with low-cost, high-precision three-dimensional position, speed, and precise timing navigation information.The difference between GIS and GPS is that GPS can provide global users with low-cost, high-precision navigation information such as three-dimensional position, speed, and precise timing. It is a model application of satellite communication technology in the navigation field. It has greatly improved the informatization level of the earth society and strongly promoted the development of the digital economy. GIS is mainly used in the analysis of urban planning and infrastructure design and can input, manage, analyze, and express geospatial data.(2) Key Technologies at the Network Layer. The network layer [14] is built on the basis of the existing mobile communication network, the Internet, and radio and television networks. To connect the information obtained by the perception layer and the transmission equipment, a variety of access equipment is used to achieve barrier-free, reliable, and safe information transmission.(3) Key Technologies of the Intelligent Layer. The main technology of the intelligent layer [15] is cloud computing technology. Cloud computing shares and connects multiple computing resources distributed on the network and performs integrated management and intelligent scheduling through a software system which is a completely new application computing method. It needs to be used and has high scalability, high reliability, high resource utilization, and on-demand services.


### 2.1.2. Related Technologies of IoT Sensor Data Processing Platform

(1) Maven. Maven [16] is a project management tool for all Java applications. Project developers can use Maven to understand the framework of the entire project in the shortest time. The Maven Project Object Model (POM) is a software project management tool that can manage the construction, reporting, and documentation of a project through a short description of information.(2) SSH. SSH [17] (Struts2+Spring+Hibernate) is the three frameworks of J2EE, which implements the construction of Web applications from the presentation layer, business logic layer, and data persistence layer. The execution process is shown in Figure 2.Figure 2
Struts2 workflow.(3) MINA. Apache MINA [17] is a network application framework that helps users develop high-performance and high-stability applications; it is a relatively new project organized by Apache, which provides a very convenient application framework for the development of high-performance and high-availability network applications, as shown in Figure 3.Figure 3
MINA network hierarchy.As shown in Figure4, MINA is mainly divided into three levels: I/O Service, I/O Filter Chain, and I/O Handler.Figure 4
MINA frame structure and flowchart.(4) XStream. XStream [18] is a simple library that can serialize objects into XML (JSON) or deserialize XML (JSON) into objects. At runtime, the Java reflection mechanism is used to investigate the structure of the serialized object tree. XStream can serialize internal fields containing private fields and final fields and supports nonpublic classes and internal classes. The design platform used in this article is Apache MINA combined with XStream library.


## 2.1.1. Technical Architecture of the Internet of Things

The Internet of Things system is generally divided into 3 levels; they are the perception layer, the network layer, and the intelligence layer. The detection layer is composed of various detection terminals such as temperature, humidity, concentration, pH value, and GPS [10]. The key technologies based on the IoT system are explained as follows.(1) Key Technologies of the Perception Layer. The perception layer is the most basic layer in the Internet of Things architecture, which mainly completes object recognition and data collection. Radio frequency identification technology, positioning technology, sensor technology [11], and laser technology are the main technologies.RFID [12] is a noncontact automatic identification technology based on electromagnetic theory. It realizes noncontact two-way communication through radio frequency, automatically recognizes the communication object, has strong anti-interference ability, can adapt to various complex environments, and has high recognition accuracy and operability.WSN [13] is composed of multiple inexpensive micro wireless sensor nodes scattered in the monitoring area. These sensors can form a multihop wireless network system by detecting information such as pressure, temperature, and humidity. Communicating with each other wirelessly and continuously sends the information of the target object in the surveillance area to the observer.GIS (Geographic Information System) is sometimes called “Geographic Information System.” It is a specific and essential spatial information system. It is a technical system that collects, stores, manages, calculates, analyzes, displays, and describes related geographic distribution data in the entire part of the earth’s surface (including the atmosphere) space under the support of computer hardware and software systems.GPS is an omnidirectional, all-weather, all-time, high-precision satellite navigation system developed by the US Department of Defense. It can provide global users with low-cost, high-precision three-dimensional position, speed, and precise timing navigation information.The difference between GIS and GPS is that GPS can provide global users with low-cost, high-precision navigation information such as three-dimensional position, speed, and precise timing. It is a model application of satellite communication technology in the navigation field. It has greatly improved the informatization level of the earth society and strongly promoted the development of the digital economy. GIS is mainly used in the analysis of urban planning and infrastructure design and can input, manage, analyze, and express geospatial data.(2) Key Technologies at the Network Layer. The network layer [14] is built on the basis of the existing mobile communication network, the Internet, and radio and television networks. To connect the information obtained by the perception layer and the transmission equipment, a variety of access equipment is used to achieve barrier-free, reliable, and safe information transmission.(3) Key Technologies of the Intelligent Layer. The main technology of the intelligent layer [15] is cloud computing technology. Cloud computing shares and connects multiple computing resources distributed on the network and performs integrated management and intelligent scheduling through a software system which is a completely new application computing method. It needs to be used and has high scalability, high reliability, high resource utilization, and on-demand services.


## 2.1.2. Related Technologies of IoT Sensor Data Processing Platform

(1) Maven. Maven [16] is a project management tool for all Java applications. Project developers can use Maven to understand the framework of the entire project in the shortest time. The Maven Project Object Model (POM) is a software project management tool that can manage the construction, reporting, and documentation of a project through a short description of information.(2) SSH. SSH [17] (Struts2+Spring+Hibernate) is the three frameworks of J2EE, which implements the construction of Web applications from the presentation layer, business logic layer, and data persistence layer. The execution process is shown in Figure 2.Figure 2
Struts2 workflow.(3) MINA. Apache MINA [17] is a network application framework that helps users develop high-performance and high-stability applications; it is a relatively new project organized by Apache, which provides a very convenient application framework for the development of high-performance and high-availability network applications, as shown in Figure 3.Figure 3
MINA network hierarchy.As shown in Figure4, MINA is mainly divided into three levels: I/O Service, I/O Filter Chain, and I/O Handler.Figure 4
MINA frame structure and flowchart.(4) XStream. XStream [18] is a simple library that can serialize objects into XML (JSON) or deserialize XML (JSON) into objects. At runtime, the Java reflection mechanism is used to investigate the structure of the serialized object tree. XStream can serialize internal fields containing private fields and final fields and supports nonpublic classes and internal classes. The design platform used in this article is Apache MINA combined with XStream library.


## 2.2. Wearable Sensors

With the continuous development of sensor technology [19], wearable devices have gradually integrated into people’s lives. At present, wearable products on the market include head-supported glasses, wrist-supported watches, and foot-supported shoes. The collection of walking information and the collected data are processed on mobile phones. The situation of mobile phones occupies a part of the market. General wearable devices are shown in Figure 5.Figure 5
Common wearable devices.To realize the tracking, reconstruction, and analysis of human motion, this article needs to construct a human kinematics model that conforms to the basic motion characteristics of the human body. According to the theory of human anatomy, the human motion system is a large system composed of 204 bones, 78 joints, and more than 600 muscles, with a total of more than 200 degrees of freedom [20]. If this article constructs an accurate human kinematics model completely according to the constraint relationship of bones and joints, it will be an extremely complicated process, which will increase the difficulty of analysis and application. Therefore, this article needs the necessary abstraction and simplification of the human body structure. As long as the movement of the key limbs and joints is grasped, the human body movement process can be restored as realistically as possible [21].Bones and joints are the lowest part of the human body structure, which can represent the movement process of the human body. Therefore, this paper ignores the tissues such as muscles and skin and simplifies the complex human movement process into a combination of each bone rotating around the corresponding joints. For human bones, this article ignores those tiny bones and merges some bones according to the body’s main limb composition. For example, the forearm is composed of an ulna and radius. For the convenience of research, this article merges the ulna and radius into forearm bones. Each bone is regarded as a rigid body link, and its motion characteristics strictly conform to rigid body kinematics and dynamics [22]. The joint structure of the human body is more complicated. This article ignores the tiny translational freedom of the joints, only retains the rotational freedom of the joints, and simplifies it into a hinge-like joint. The bones are connected by joints and are constrained by the joints at the same time.


## 2.3. Motion Interference Removal Design of Adaptive Algorithm

The principle structure diagram of the adaptive filter is shown in Figure6.Figure 6
Schematic diagram of adaptive filter principle.Adaptive filtering technology is a filtering method that can automatically adjust the filter parameters through the feedback of the results at all times and achieve the filtering method that can change with the changes of the signal and noise. The adaptive filter is generally composed of a structure with a feedback function and an algorithm that can iterate coefficients according to the results. Among them,dn represents the collected signal, which includes the original signal sn and the noise signal kn; there is no connection between the two. The rn output by the noise source signal is related to the background noise kn in a certain relationship; vn is the current simulation of the background noise signal kn, which can be output from the noise source signal rn after being weighted by the adaptive filter weight coefficient wn, that is, as shown in
(1)vn=∑l=0Mwlrn−l=WTnRn.Among them,Wn represents the filter weight coefficient vector at n time and represents the adjacent vector from n times to the past M+1 noise sources.
(2)Rn=rn,rn−1,⋯,rn−mT.Therefore, the output signalen, that is, the error is
(3)en=dn−vn=sn+kn−vn.en is the desired denoising signal, and its expected mean square value is
(4)Qe2n=Qd2n+Qkn−vn2+2Qdnkn−vn.Since the original signalsn is not related to the background noise kn and the estimated noise vn, there is
(5)2Qsnkn−vn=0.Therefore, formula (6) can be transformed into
(6)Qe2n=Qd2n+Qkn−vn2.In order to makeQe2n the minimum value, Qkn−vn2 is the minimum value. There are two algorithms to achieve the calculation purpose: one is the least mean square error algorithm (LMS), and the other is the recursive least squares algorithm (RLS). For the least squares algorithm, there are
(7)Qd2n+Qkn−vn2=Qd2n+Qkn−WTnRn2.And to speed up the filter’s response to interference changes, a forgetting factorγ can be introduced, and its error weight can be reduced according to the exponential law:
(8)Qe2n=Qd2nγM−n+QγM−nkn−WTnRn2.And the error at timen based on time n−1 is
(9)xn=dn−RTnWn−1−dn−∑l=0Mwn−1lrn−l.The recursive formula of the filter coefficients of the adaptive filter is derived from the least squares algorithm:(10)Wn=Wn−1+Nnxn.Formulas (9) and (10) can be combined to get
(11)Nn=Wn−Wn−1dn−∑l=0Mwn−1lrn−l.To achieve the best effect of the filter,(12)Qkn−vn2=0.We can get the formula(13)Nn=∑rn−lWnγn+WTn∑rn−lWn.Among them,δ is between 0 and 1, usually around 1, such as 0.99.ForQe2n, the most ideal situation is to perfectly filter the noise signal in the signal, that is, when kn=vn, it is expected that Qe2n reaches the minimum value, that is to say
(14)kn=∑l=0Mwlrn−l.This needs to adjust the weight coefficientWn of the adaptive filter to achieve the purpose of adjusting vn to kn, making Qen2 the minimum value. Therefore, substituting formula (1), assuming that there is a certain Wn at a certain time, the mean square error at this time is
(15)an=Qe2n=Qd2n−2QdnRTnWn+WTnQRnRTnWn.Then, the gradient vector ofan relative to Wn can be obtained as
(16)∇n=−2QdnRn+RnRTnWn.Let∇n=0, then
(17)Wn=RnRTn−1QdnRn.Substituting formula (17) into (16), we have
(18)an=Qe2n=Qd2n−QdnRnWn.Andan is the expectation of the square of the output signal, which is a nonnegative quadratic function, so there must be a minimum value aminn, and according to the behavior of adaptive filtering, there is
(19)Wn=RnRTn−1QdnRn.When the above formula is satisfied, the minimum value ofan can be obtained. Assuming that the gradient ∇n of an to Wn is known, there is a recursive formula:
(20)Wn+1=Wn+μ−∇n.Among them,μ is a normal number. The actual meaning of this formula is that the value of the weighting coefficient W of the adaptive filter at time n+1 is the value at time n plus a correction amount, and the correction amount is proportional to the inverse of the gradient value. Then, when μ selects a suitable value, an can be made to obtain the minimum value.The adaptive algorithm itself is a set of algorithms for estimating unknown signals.∇n is usually unknown, so you can set Δn to the estimated value of ∇n and make Δn approach ∇n through iteration, from formula (20),
(21)Wn+1=Wn+μ−Δn.The mathematical meaning of the gradient value is(22)Δn=∂e2n∂Wn=2en∂en∂Wn.Then, for a fixedWn, Δn is ∇n unbiased likelihood estimation, so
(23)Wn+1=Wn+μ−Δn=Wn+2μen∂en∂Wn.Therefore, this system adopts an improved variable step size LMS filtering algorithm after combining previous research results and actual experimental verification so that(24)μn+1=μmax,μn+1>μmax,μmin,μn+1<μmin,μn+1,else,(25)μn+1=aμn+e2n.Among them,0<a<1; μmax generally select the unstable step size point near the standard LMS, and after a large number of experiments in this system, μmax=0.85/λmax,μmax=0.1/λmax is selected, and a generally selects a parameter close to 1 to speed up the convergence. In this system, choose a=1. The advantage of this algorithm is that, at the beginning of the algorithm, the error signal en is larger, and the calculated μn is larger, so that the algorithm can converge at a faster speed. When the program runs for a certain period of time, the system algorithm tends to a steady state, and the error signal en is small, μn is calculated to be small, and a small error can be generated near the optimal weight coefficient.


## 3. Energy Consumption Experiment of Wearable Sensors Based on IoT Technology in Flexibility Training

This article integrates the Internet of Things technology into a wearable sensor, and the sensor can collect the energy consumption of swimmers during flexibility training. By collecting swimmers doing static stretching and dynamic stretching, respectively, this article gets the acceleration comparison chart as shown in Figure7.Figure 7
Static and dynamic acceleration signal diagram.It can be seen from Figure7 that the acceleration amplitude and frequency are significantly different in the static and dynamic flexibility training situations. The amplitude and frequency of the acceleration signal under dynamic conditions are clearly greater than those under static conditions. According to its acceleration signal, this article can get the energy consumption diagram of two kinds of flexibility training, as shown in Figure 8.Figure 8
Static and dynamic plus energy consumption diagram.It can be seen from Figure8 that dynamic stretching clearly consumes much more energy than static stretching. The data obtained through the wearable sensors of the Internet of Things can be analyzed, and a more scientific and effective method of flexibility training can be found through the analysis.


## 4. Test of Improving Flexibility Training with Wearable Sensors Based on IoT Technology

### 4.1. Based on IoT Wearable Sensors to Test the Flexibility of the Shoulder Joint in Swimming

This article selects 30 students from the swimming specialty of sports training as the experimental subjects, randomly divided into three groups (Table1 for basic information), of which 10 people were in the static stretching swimming group, 10 people were in the dynamic stretching swimming group, and 10 people were in the IoT sensor stretching swimming group. Ask before the test to rule out shoulder joint disease.Table 1
Basic situation of the three groups of students.
Group (n=10 people)Age (years) (M±SD)Height (cm) (M±SD)Weight (kg) (M±SD)Static stretching swimming group21.2±0.88172.3±7.1168.5±9.13Dynamic stretch swimming group21.1±1.23172.8±9.1167.1±11.42IoT sensor stretch swimming group20.6±1.23172.9±6.8166.7±10.63Before the experiment, the shoulder flexibility, muscle strength, and sports performance of the three swimming student groups were measured. The measurement is carried out in accordance with the measurement rules introduced in the textbook “Sports Measurement and Evaluation” edited by the National Sports University. The content of shoulder flexibility measurement is an index of shoulder rotation. The content of the sports performance test is the 100-meter freestyle stroke score (the test tools are tape measurement, scale, and stopwatch), the total power, power, relative power, and other muscle function indicators around the shoulder joint (the test instrument is Cybex6000 isokinetic meter), as well as statistical analysis of the data. (Note: except for the flexibility training in the training class, students in each experimental group cannot perform special flexibility training after the class.) After 8 weeks of the experiment, students in the 3 groups will be checked again, about the flexibility of the shoulder joint, muscle strength, and special activities. Regarding the performance measurement, a doublet-test was carried out before and after the experiment, and the uniformity of dispersion and unidirectional dispersion analysis was carried out between the groups. Before the experiment, the results of the dispersion analysis of the flexibility quality indexes of each group of shoulder joints are shown in Table 2.Table 2
The results of variance analysis of the first three groups of shoulder joint flexibility quality indicators.
Group (n=10 people)Levene statisticSig.Static stretching swimming group0.0870.915Dynamic stretch swimming group0.0880.913IoT sensor stretch swimming group0.0860.916From the test results of the homogeneity of variance in Table2, it can be seen that sig=0.916>0.05 in this figure, so it is believed that there is no difference in the overall variance of each group, and one-way analysis of variance can be further carried out. The multiple comparison results of the LSD method are shown in Table 3.Table 3
Multiple comparison results of the LSD method.
(I) Group(J) GroupMean difference between groups (I−J)P95% confidence intervalLower limitUpper limitStatic stretching swimming groupStatic stretching swimming group0.180.972-10.8211.16Dynamic stretch swimming group0.210.969-10.8311.22Dynamic stretch swimming groupIoT sensor stretch swimming group-0.050.969-10.8010.83Static stretching swimming group-0.130.994-10.9211.02IoT sensor stretch swimming groupDynamic stretch swimming group-0.230.967-11.2810.67IoT sensor stretch swimming group0.040.935-11.0310.89It can be seen from Table3 that the probability of shoulder joint flexibility indexes between the first three groups after the LSD method is more than 0.05 after multiple comparisons, so there is no significant difference between the groups, which meets the experimental conditions and can be further analyzed and studied. After the experiment, the results of the variance analysis of the shoulder joint flexibility quality indexes between the groups are shown in Table 4.Table 4
The results of variance analysis of the three groups of shoulder joint flexibility quality indicators after the experiment.
Group (n=10 people)Levene statisticSig.Static stretching swimming group0.2070.811Dynamic stretch swimming group0.2130.824IoT sensor stretch swimming group0.2080.813It can be seen from Table4 that the result of the homogeneity of variance test shows that sig=0.813>0.05, so it is considered that there is no difference in the overall variance of each group, and one-way analysis of variance can be further performed, as shown in Table 5.Table 5
Multiple comparison results of the LSD method.
(I) Group(J) GroupMean difference between groups (I−J)P95% confidence intervalLower limitUpper limitStatic stretching swimming groupStatic stretching swimming group-11.650.031∗-22.13-1.25Dynamic stretch swimming group-10.740.044∗-21.23-0.34Dynamic stretch swimming groupIoT sensor stretch swimming group11.670.035∗-11.1322.35Static stretching swimming group0.810.863-10.9311.43IoT sensor stretch swimming groupDynamic stretch swimming group10.720.042∗-11.2621.23IoT sensor stretch swimming group-0.810.867-11.039.59Figure9 shows the changes in the flexibility quality indexes of the shoulder joints in each group before and after the experiment.Figure 9
Changes in the flexibility of the shoulder joints in each group before and after the experiment.
(a)
Before the experiment(b)
After the testIt can be seen from Figure9 that after the corresponding t-test, the probabilities of the three groups of students before and after the experiment are less than 0.01, and great changes have occurred. This shows that the students in the three groups have changed a lot after different flexibility training methods.


### 4.2. Test of New Wearable Sensors

The wearable sensor designed based on the Internet of Things technology can improve the flexibility index of swimmers. To explore how much it can be improved, a set of control experiments is designed in this article. The experiment divided 20 swimming professional athletes into two groups. One group did not use wearable sensors for flexibility training, which was the control group; the other group used wearable sensors for flexibility training, which was the experimental group. The degree of improvement is judged by the flexibility indexes before and after the flexibility training of the two groups of members, as shown in Figure10.Figure 10
Changes in flexibility indexes of the two groups of athletes before and after the experiment in flexibility training.
(a)
Before training(b)
After trainingIt can be seen from Figure10 that wearing the new IoT wearable sensor can significantly improve the flexibility index of the athlete’s flexibility training. Among them, the flexibility index has the highest increase of 20.41 after wearing the new IoT wearable sensor for flexibility training. However, the highest improvement in flexibility index after flexibility training without wearing the new IoT wearable sensor was only 15.53. This shows that the new IoT wearable sensor can significantly improve the effectiveness of flexibility training for swimmers.


## 4.1. Based on IoT Wearable Sensors to Test the Flexibility of the Shoulder Joint in Swimming

This article selects 30 students from the swimming specialty of sports training as the experimental subjects, randomly divided into three groups (Table1 for basic information), of which 10 people were in the static stretching swimming group, 10 people were in the dynamic stretching swimming group, and 10 people were in the IoT sensor stretching swimming group. Ask before the test to rule out shoulder joint disease.Table 1
Basic situation of the three groups of students.
Group (n=10 people)Age (years) (M±SD)Height (cm) (M±SD)Weight (kg) (M±SD)Static stretching swimming group21.2±0.88172.3±7.1168.5±9.13Dynamic stretch swimming group21.1±1.23172.8±9.1167.1±11.42IoT sensor stretch swimming group20.6±1.23172.9±6.8166.7±10.63Before the experiment, the shoulder flexibility, muscle strength, and sports performance of the three swimming student groups were measured. The measurement is carried out in accordance with the measurement rules introduced in the textbook “Sports Measurement and Evaluation” edited by the National Sports University. The content of shoulder flexibility measurement is an index of shoulder rotation. The content of the sports performance test is the 100-meter freestyle stroke score (the test tools are tape measurement, scale, and stopwatch), the total power, power, relative power, and other muscle function indicators around the shoulder joint (the test instrument is Cybex6000 isokinetic meter), as well as statistical analysis of the data. (Note: except for the flexibility training in the training class, students in each experimental group cannot perform special flexibility training after the class.) After 8 weeks of the experiment, students in the 3 groups will be checked again, about the flexibility of the shoulder joint, muscle strength, and special activities. Regarding the performance measurement, a doublet-test was carried out before and after the experiment, and the uniformity of dispersion and unidirectional dispersion analysis was carried out between the groups. Before the experiment, the results of the dispersion analysis of the flexibility quality indexes of each group of shoulder joints are shown in Table 2.Table 2
The results of variance analysis of the first three groups of shoulder joint flexibility quality indicators.
Group (n=10 people)Levene statisticSig.Static stretching swimming group0.0870.915Dynamic stretch swimming group0.0880.913IoT sensor stretch swimming group0.0860.916From the test results of the homogeneity of variance in Table2, it can be seen that sig=0.916>0.05 in this figure, so it is believed that there is no difference in the overall variance of each group, and one-way analysis of variance can be further carried out. The multiple comparison results of the LSD method are shown in Table 3.Table 3
Multiple comparison results of the LSD method.
(I) Group(J) GroupMean difference between groups (I−J)P95% confidence intervalLower limitUpper limitStatic stretching swimming groupStatic stretching swimming group0.180.972-10.8211.16Dynamic stretch swimming group0.210.969-10.8311.22Dynamic stretch swimming groupIoT sensor stretch swimming group-0.050.969-10.8010.83Static stretching swimming group-0.130.994-10.9211.02IoT sensor stretch swimming groupDynamic stretch swimming group-0.230.967-11.2810.67IoT sensor stretch swimming group0.040.935-11.0310.89It can be seen from Table3 that the probability of shoulder joint flexibility indexes between the first three groups after the LSD method is more than 0.05 after multiple comparisons, so there is no significant difference between the groups, which meets the experimental conditions and can be further analyzed and studied. After the experiment, the results of the variance analysis of the shoulder joint flexibility quality indexes between the groups are shown in Table 4.Table 4
The results of variance analysis of the three groups of shoulder joint flexibility quality indicators after the experiment.
Group (n=10 people)Levene statisticSig.Static stretching swimming group0.2070.811Dynamic stretch swimming group0.2130.824IoT sensor stretch swimming group0.2080.813It can be seen from Table4 that the result of the homogeneity of variance test shows that sig=0.813>0.05, so it is considered that there is no difference in the overall variance of each group, and one-way analysis of variance can be further performed, as shown in Table 5.Table 5
Multiple comparison results of the LSD method.
(I) Group(J) GroupMean difference between groups (I−J)P95% confidence intervalLower limitUpper limitStatic stretching swimming groupStatic stretching swimming group-11.650.031∗-22.13-1.25Dynamic stretch swimming group-10.740.044∗-21.23-0.34Dynamic stretch swimming groupIoT sensor stretch swimming group11.670.035∗-11.1322.35Static stretching swimming group0.810.863-10.9311.43IoT sensor stretch swimming groupDynamic stretch swimming group10.720.042∗-11.2621.23IoT sensor stretch swimming group-0.810.867-11.039.59Figure9 shows the changes in the flexibility quality indexes of the shoulder joints in each group before and after the experiment.Figure 9
Changes in the flexibility of the shoulder joints in each group before and after the experiment.
(a)
Before the experiment(b)
After the testIt can be seen from Figure9 that after the corresponding t-test, the probabilities of the three groups of students before and after the experiment are less than 0.01, and great changes have occurred. This shows that the students in the three groups have changed a lot after different flexibility training methods.


## 4.2. Test of New Wearable Sensors

The wearable sensor designed based on the Internet of Things technology can improve the flexibility index of swimmers. To explore how much it can be improved, a set of control experiments is designed in this article. The experiment divided 20 swimming professional athletes into two groups. One group did not use wearable sensors for flexibility training, which was the control group; the other group used wearable sensors for flexibility training, which was the experimental group. The degree of improvement is judged by the flexibility indexes before and after the flexibility training of the two groups of members, as shown in Figure10.Figure 10
Changes in flexibility indexes of the two groups of athletes before and after the experiment in flexibility training.
(a)
Before training(b)
After trainingIt can be seen from Figure10 that wearing the new IoT wearable sensor can significantly improve the flexibility index of the athlete’s flexibility training. Among them, the flexibility index has the highest increase of 20.41 after wearing the new IoT wearable sensor for flexibility training. However, the highest improvement in flexibility index after flexibility training without wearing the new IoT wearable sensor was only 15.53. This shows that the new IoT wearable sensor can significantly improve the effectiveness of flexibility training for swimmers.


## 5. Conclusions

This article mainly studies the value of wearable sensors in swimming flexibility training under the background of the Internet of Things. In this paper, by studying the relevant background of the Internet of Things technology, design an IoT system based on the build platform to receive information, based on the Internet of Things technology combined with wearable sensors to measure the various indicators of flexibility training, and design a new type of flexibility training strategy through the use of various indicators combined with the movement interference removal of the adaptive algorithm. This paper designs two flexible training methods, static stretching and dynamic stretching. The wearable sensors of the Internet of Things are used to obtain energy consumption information, and the energy consumption information is combined to improve the training methods of athletes. Finally, a control experiment is used to verify the degree of improvement in swimming flexibility training. The experimental results show that wearing the wearable sensor of the Internet of Things can effectively improve the flexibility index of the swimmer’s flexibility training, and the wearable sensor can increase flexibility index up to 20.41, while without the wearable sensor flexibility index can only increase up to 15.53.



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*Source: 3035001-2022-03-07.xml*