### 2.1 Concept of physical fitness

In 1971, the concept of physical fitness was put forward, which means "perform energetically every day without being too tired; enjoy all kinds of leisure time, get enough rest, and be able to cope with emergencies” [6]. With the progress of society with people’s emphasis on sports, the concept of physical fitness has become more and more important. It did not appear in Chinese literature until the 1990s and was translated by experts from Hong Kong and Taiwan. However, in mainland China, the term began to appear in the twenty-first century [7]. Physical fitness means proper and healthy in English, which is why some scientists regard it as “healthy,” that is, physical function is in the most suitable state [8]. There are also German scientists who translated as work ability, French scientists translate it as physical fitness, Japanese scientists translate it as physical strength, and some Hong Kong and Taiwan scientists believe that it is translated as “physical fitness” [9]. In physical fitness, in terms of reasonable meanings and definitions, this research refers to several current editions around the world: “Physical Education and Prospects” defines physical fitness as a person chooses the correct exercise method and amount of exercise under different conditions to improve his physical fitness and maintain health condition, different people should have different levels of exercise due to different physical fitness [10]. The definition of physical fitness in the book “Exploring Modern College Sports” is: physical fitness refers to the need for speed, endurance, and energy exercise and sensitivity. It helps to improve work ability, and the content of exercise includes healthy fitness and technology [11]. The book “Sports and Health” describes physical fitness as: having the spirit of daily activities and good a strong body with a sense of relaxation and emergency response, ordinary exercise will not feel extreme fatigue, but there is no specific description of physical fitness [12]. The World Health Organization describes the concept of physical fitness as: except for daily work, the body will not feel too much tired, while having the power to use for daily entertainment and emergency situations, its content includes healthy physical fitness and technical physical fitness [13]. Hong Kong experts in China define physical fitness as: physical fitness refers to not only suitable for daily work, it is also strong enough to enjoy the joy of life, and the sensitivity and sensitivity of a person who can cope with stress and sudden changes [14]. Physical fitness is a part of the adaptability of the whole body, and it is the spirit and body of people in modern life. The definition of fitness by experts in Taiwan is: First, the body’s ability to adapt to health, activities and the environment (such as temperature, climate change, and bacteria). The second is the body’s ability to cope with life and adapt to nature. It includes healthy body fitness and competitive fitness. Based on the above six points, the definition, content, and essential description of the term physical fitness are very close to the World Health Organization's definition of physical fitness.

### 2.2 Healthy physical fitness and its evaluation index

In the middle of the twentieth century, the international education system put forward the concept of healthy physical fitness for the first time. Subsequently, some researchers in the USA conducted studies on the differences between exercises related to healthy physical fitness, including explosive power, speed, agility, Sensitivity and other fitness related to healthy physical fitness, and concluded that health physical fitness can prevent diseases, promote health, improve daily life, and enhance learning and efficiency [15]. After consulting-related literature, healthy physical fitness includes four main index components, namely cardiopulmonary fitness, muscle fitness, sensitivity and body composition [16]. Cardiopulmonary capacity: the ability of the lungs, heart, and blood to transport oxygen. Each tissue effectively transports life-sustaining oxygen to various parts of the body, and muscles and cell tissues can effectively use this oxygen for metabolism and energy production [17]. Muscle capacity: Muscle strength and muscular endurance are the basic elements of healthy physical fitness. Muscle strength refers to the maximum strength that a muscle can produce when resisting a certain resistance [18]; muscle endurance refers to the number of repetitions and the length of time for continuous muscle exertion in the process of continuous exertion [19]. Sensitivity refers to the range of movement of the limbs and the angle of joint movement. Body composition (appropriate percentage of body fat): Stored fat is more accumulated in the subcutaneous tissue, too much fat causes obesity, and excess fat produced by obesity is a serious health risk factor [20]. At the end of the twentieth century, the American Sports Medicine Association published the American Sports Medicine Monograph in 1992. This book establishes medical tests as a way to check physical fitness. Experimental indicators include 1.6 km (cardiorespiratory endurance) and push-ups (muscle strength and muscle strength). Healthy physical fitness can keep the body active for a long time, quickly eliminate fatigue and promote physical recovery. Maintaining healthy physical fitness can make people active in sports and recreational activities, and can also allow people to work long hours without excessive fatigue and allows people to exercise in all directions during work and leisure. Healthy physical fitness also has requirements for body composition. Body composition mainly includes fat, muscle, bone, and other relevant parts of the body in an appropriate percentage. Among them, body fat is a key factor in determining body composition, and a healthy body should maintain a certain proportion of body fat. Commonly used diagnostic methods include bioelectrical impedance analysis, two-way X-ray input method, double-labeled water method, ventilation method, skin tightening method, etc. [21]. In view of the above, whether it is in the field of sports science research or the field of medicine, there are several schemes for measuring specific indicators of health and fitness. Also, due to regional and ethnic differences, the selected indicator systems have substantial differences. In the actual situation, even if there are many test items, it is impossible to comprehensively, objectively and scientifically evaluate the individual’s physical fitness [22]. Based on the selection of traditional healthy physical fitness evaluation indicators, this study combined with novel and effective cardiopulmonary track and field sensors to conduct related research to observe the changes in the limbs and heart function reserve of different subjects during exercise, with a view to healthy physical fitness Evaluation provides novel, comprehensive and effective evaluation indicators, and provides a more comprehensive, scientific and efficient method and guidance.

### 2.3 Research optimal configuration of physical fitness cardiopulmonary track and field sensors based on intelligent algorithms

With the development of sensor technology, low-energy electronics, and radio frequency technology, low-energy wireless microelectronic sensors are gradually being used on a large scale, and a responsive wireless sensor network is born. Due to the characteristics of intelligent perception, small size, light weight, accurate data, good real-time performance, and no errors in the motion sensor monitoring technology in track and field events, the test results can be objectively fed back in time when the athlete’s proprioception has not disappeared. The purpose of improving exercise technology and monitoring exercise effects, thereby improving the effectiveness and pertinence of training, reducing blindness, excessive fatigue and injury during exercise, and improving athletic performance.

Based on the health perception of the Internet of Things and the flexible resources of intelligent algorithms, it realizes the collection and management of sports personnel health information, community physical examination, community diagnosis and other information, and integrates personal health perception equipment data, medical data, hospital diagnosis and treatment information, and various types of information. Health-related data, so as to establish residents’ sports health files, provide residents with personal-centered sports health services, and realize remote diagnosis, consultation, and corresponding remote medical services of sports personnel’s health information, and realize cloud-based sports personnel health information management and services [23]. The data flow diagram of the system is shown in Fig. 1.

In the sensor subsystem, various sensors are installed to sense the loads and effects of moving people in various environments, and they are stored in the computer in a certain way [24]. The sensor is a certain Wu Lilian measuring device that converts the measurement to a certain degree with a certain degree of correspondence, and is convenient to use. It usually consists of a sensitive element and a conversion element to form a conversion circuit. The conversion element takes the input of the sensitive element as the output, and converts the input into circuit parameters. The sensitive element can directly sense the measured and output a certain physical quantity element that has a certain relationship with the measured. The data processing and control subsystem is used to comprehensively control data collection, transmission, processing, storage and display, and can assist in the process of calibration, processing, transmission and reliability testing of the data acquired by the data acquisition and transmission subsystem key data for subsequent status assessment. The data management and analysis evaluation subsystem mainly includes functions such as monitoring data management, structural state early warning, reliability evaluation, fatigue evaluation, and comprehensive structural state evaluation. The relationship between the various subsystems is shown in Fig. 2.

How to make the information of the measured person measured by the sensor can most truly reflect the current person's health status, and realize the evaluation of the person's status is a key research issue of sensor optimization configuration [25]. Before constructing the optimal sensor configuration model, we must first establish a finite element model of human health, perform modal analysis, and obtain the modal vibration matrix *Ψ* according to the modal data obtained from the modal analysis [26, 27]. According to the characteristics of the sensor optimal configuration problem, construct the objective function for:

$$\min \max \left\{ {{\text{MAC}}_{mn} } \right\}$$

(1)

$${\text{MAC}}_{mn} = \frac{{(\psi_{m} \psi_{n} )^{2} }}{{\left( {\psi_{m} \psi_{m} } \right)(\psi_{n} \psi_{n} )}}$$

(2)

*Ψ*_{m} is the mode vector of the *m*th order; *Ψ*_{n} is the mode vector of the *n*th mode. If the non-diagonal element MAC_{mn} of the MAC matrix approaches 0, it indicates that the *m*th and *n*th modes have better resolvability, and the linear independence is good; on the contrary, the resolution is not good. As a typical combinatorial optimization problem, the optimal configuration of healthy physical fitness cardiopulmonary track and field sensors has high computational complexity. The currently developed sensor configuration methods can be roughly divided into traditional optimization algorithms and intelligent optimization algorithms [28, 29]. The traditional optimization algorithm assumes that the modal vectors in the modal matrix *Ψ* of the theoretical model are independent and orthogonal, and the output of initially selecting × candidate measuring points is:

The estimated simulation coordinates are:

$$p = \left[ {\psi_{{\text{x}}} \psi_{x} } \right]\psi S$$

(4)

Among them, *S* is the output of initially selected candidate measuring points; *Ψx* is the part of the modal matrix that is less on the candidate measuring points; *p* is the modal coordinate vector. If the actual number of selected measuring points is *i*, then the problem can be expressed as how to find *i* measuring points from the selected measuring points of *x*, and the modal linear independence measured by these *i* points is modal space Best estimate. Here, the covariance of the error is taken as the best estimate. Considering the influence of noise, the output equation is rewritten as:

$$S = \psi_{x} p + {\text{i}}$$

(5)

where *S* is the output of the initially selected candidate measurement points, *ψ*_{x} is the lesser part of the candidate measurement points in the modal matrix; *p* is the modal coordinate vector, and the number of measurement points is *i*.

Then, the covariance of the estimation error is:

$$Q = \left[ {(p - \mathop {p)}\limits^{ \wedge } } \right] = \psi_{s} \psi_{z} = P$$

(6)

Among them is the information matrix. Assuming that the noise is Gaussian white noise, then:

$$P = \frac{{\psi_{m} \psi_{n} }}{{\varphi_{0} }} = \frac{A}{{\varphi_{0}^{2} }}$$

(7)

It can be seen from formula 6 that the minimum of the covariance *Q* of the estimation error is equivalent to the maximum of the Fisher information matrix *P*, that is, the estimation of the trace of matrix *A* or the maximum value of its determinant in formula 7 is an unbiased estimation. Matrix *A* can be written as:

$$A = \sum\limits_{i = 1}^{z} {\left[ {\psi_{m} } \right]} \left[ {\psi_{n} } \right] = \sum\limits_{i = 1}^{z} {A^{{_{i} }} }$$

(8)

Among them, *A*^{i} represents the contribution of the first degree of freedom to the matrix. The characteristic equation of solution matrix *A* is:

$$\left( {A - \lambda {\text{k}}} \right)\psi = 0$$

(9)

$$\psi_{{\text{n}}} A\psi = \lambda \psi_{{\text{n}}} \psi = k$$

(10)

$$\psi_{n} \lambda \psi = A^{ - 1}$$

(11)

The construction matrix *E* is:

$$E = \psi \varphi \lambda \left( {\psi_{m} \varphi } \right)^{{_{n} }}$$

(12)

$$E = \psi_{n} \left( {\psi_{{_{m} }} \psi } \right)^{ - 1} \psi^{{_{n} }}$$

(13)

Obviously in Eq. 12, *E* is an idempotent matrix, its eigenvalue is 1 or 0, and the trace is equal to the rank, that is:

$${\text{tr}}(A) = {\text{rank}}(A)$$

(14)

The *m*th element on the diagonal represents the contribution of the *m*th degree of freedom or measurement point to the rank of the matrix *Ψ*, that is, the contribution to the matrix *A*. Write the diagonal elements of *E* as a column vector as:

$$E_{k} = \left[ {E_{11} ,E_{22} , \ldots ,E_{xx} } \right]$$

(15)

Among them, the size of each element represents the relative size of the contribution of each degree of freedom or measurement point to the rank of the matrix *Ψ*. According to the effective independence method, when the Fisher information matrix *P* takes the maximum value. The covariance *Q* of the estimation error is minimum, the norm selected here is:

$$\left\| P \right\| = (\psi^{{\text{T}}} \psi )_{2}$$

(16)

The requirement of *P* can be met by *Ψ*. According to the related matrix theory, QR decomposition of column principal elements is a simple and effective method when selecting a subset of matrix column vectors with the largest norm. Perform QR decomposition of column principal elements of *Ψ*, and select a subset of the column vector group as:

$$\psi E = QR = \left[ {\begin{array}{*{20}c} {R_{11} } & {R_{1M} } & {R_{1N} } \\ . & . & . \\ 0 & {R_{MM} } & {R_{NN} } \\ \end{array} } \right]$$

(17)

Among them, *E* is the permutation matrix, and the first *M* columns of the matrix *ΨE* correspond to a set of row vectors with a larger norm in the matrix *Ψ*. This *M* measurable degree of freedom is a set of measurable degrees of freedom that makes the information matrix have a larger norm. Assuming a mode matrix *Ψ* with *i*th mode shape, the modal kinetic energy corresponding to the *k*th mode of *i*th test degree of freedom is defined as:

$$MKE = \psi \sum\limits_{{{\text{j}} = 1}}^{{}} {M\psi }$$

(18)

For a kinematic structure, which has n degrees of freedom, the strain energy matrix *E* of each degree of freedom on the structure is defined as:

$$E = \frac{1}{2}uKu = \frac{1}{2}(\psi p)K\psi p$$

(19)

Among them, *Ψ* is the normalized mode matrix; *u* is the displacement matrix; *p* is the normalized coordinate matrix; *K* is the stiffness matrix, which is a symmetric matrix. The modal strain matrix is defined as:

$$E_{mse} = \left[ {\begin{array}{*{20}c} {\sum\limits_{{}} {\psi_{i1} k_{ij} \psi_{j1}^{{}} } } & {\sum\limits_{{}} {\psi_{i2} k_{ij} \psi_{j2}^{{}} } } & {\sum\limits_{{}} {\psi_{in} k_{ij} \psi_{jn}^{{}} } } \\ {\sum\limits_{{}} {\psi_{i2} k_{ij} \psi_{j1}^{{}} } } & {\sum\limits_{{}} {\psi_{i2} k_{ij} \psi_{j2}^{{}} } } & {\sum\limits_{{}} {\psi_{i2} k_{ij} \psi_{jn}^{{}} } } \\ {\sum\limits_{{}} {\psi_{in} k_{ij} \psi_{j1}^{{}} } } & {\sum\limits_{{}} {\psi_{in} k_{ij} \psi_{jn}^{{}} } } & {\sum\limits_{{}} {\psi_{in} k_{ij} \psi_{jn}^{{}} } } \\ \end{array} } \right]$$

(20)

Among them, *k*_{ij} is the connection coefficient between node *i* and node *j*; *Ψ*_{ij} is the component of the *j*th order matrix on the *i*th degree of freedom, and the matrix *E* is a symmetric matrix. The element in the *i*th row and the *j* column of the matrix represents the strain energy related to *i*th and *j*th modes; the sum of all the elements in *i*th row represents the total modal strain energy related to *i*th mode. Select *m* from the *n* degrees of freedom of the dynamic structure. The set of *m* measuring points with the largest modal kinetic energy is used as the sensor configuration point.

Because the single intelligent optimization algorithm has different performance defects, the traditional optimization bit algorithm based on the single intelligent optimization algorithm also has defects, and the algorithm based on the single intelligent optimization algorithm also has shortcomings. The traditional optimization algorithm has fast convergence speed and high optimization accuracy, but it is easy to fall into the local optimum in the later stage, resulting in poor optimization results at individual times; the intelligent optimization algorithm has good stability and strong global optimization ability, and it is not easy to fall into the local optimum. However, its convergence speed is slower than traditional optimization algorithms, and the optimization accuracy is slightly lower than that of intelligent optimization algorithms.