A Spatial Spectrum Estimation Method for Optimization and Improvement of Resource Allocation and Management of Public Sport and Health Facilities.

With the improvement of people's health awareness, the state increases the construction of public sport facilities, which complicates the allocation and management of resources. The existing spatial spectrum estimation method cannot eliminate the relevant interference data, resulting in duplicate data in the results of resource allocation and management, reducing the accuracy of resource allocation and management. In order to optimize the allocation and management of public sport facilities resources, this study proposes a spatial spectrum estimation method, which is used to deeply tap the potential information in public sport facilities resources and optimize the allocation and management. First, analyze the resources of public sport facilities and put forward the feature vector of allocation and management optimization. Then, use the spatial spectrum estimation method to learn the test samples, get the optimal threshold and weight, and build the resource allocation and management model of public sport facilities. Finally, the accuracy of spatial spectrum estimation method is 98% and the variation range is (0, 10), which is better than the accuracy of the original algorithm is 80% and the variation range is (0, 20). Moreover, change of the spatial spectrum estimation method is smoother, and the correlation between various analyses is better. In unit time, the amount of configuration and management data of spatial spectrum estimation method is higher than that of existing algorithms, which indirectly indicate that the configuration and management time of the spatial spectrum estimation method is short. At the same time, unstructured data account for a large proportion of the data tested this time. Therefore, the accuracy and variation range of the spatial spectrum estimation method is good, which is suitable for the construction of public sport facilities and realizes the optimization of resource allocation and management.

1. Introduction

By the end of 2021, as reported by Zhao et al. [1], China's provinces and cities will increase public sport facilities, with a facility coverage rate of 23.4%, which can serve 478 million urban and rural residents [2], indicating that the allocation and management of public sport facilities resources is the key issue of public health. When the local government manages the resources of public sport facilities, it will produce a large amount of management information data and consume a lot of human, material, and financial resources. Spectrum estimation, spatial allocation, and management of public sport facilities resources can delete duplicate management information [3] and not only save resource allocation and management costs but also improve the utilization rate of public sport facilities resources and improve the management accuracy of users. Therefore, it has a certain theoretical significance and practical value to optimize the allocation and management of public sport facilities resources of government and health institutions [4]. Domestic literature on resource allocation and management optimization of public sport facilities has increased year by year, and the results are given in Table 1.

Table 1

Research on resource allocation and management of public sport facilities.

Time	Number of documents	Growth ratio
2013	595.56	—
2014	630.00	5.78
2015	654.44	3.88
2016	676.67	3.40
2017	733.33	8.37
2018	746.67	1.82
2019	913.33	22.32
2020	964.44	5.60
2021	990.00	2.65
2022	1094.44	10.55

The data come from well-known databases such as HowNet, SCI, and CSCI.

In recent years, some scholars have analyzed the allocation and management of public sport facilities resources, combined with the characteristics of public sport facilities resources, mined the data characteristics of customers by Python and the spatial spectrum estimation method, and put forward the optimization algorithm for the allocation and management of public sport facilities resources [5]. Scholars also use the clustering method to estimate the spatial distribution and management of public facilities and reduce the dispersion of sport resources [6]. However, when monitoring the resources of public sport facilities, it is found that the calculation accuracy of the spatial spectrum estimation method is negatively correlated with the amount of information and data, which cannot meet the accuracy requirements of public sport facilities resource management and increase the occupation rate of public resources [7]. Some scholars combined the k-clustering method with the spatial spectrum estimation method to analyze the allocation and management factors and found that this method can improve the resource allocation and management level of public sport facilities [8]. Some scholars also integrated Fourier series and discrete function into allocation and management [9] and found that classifying public sport facility resources can improve the accuracy of allocation and management and shorten the processing time of public sport facility resources. In short, domestic scholars have integrated the spatial spectrum estimation method, Fourier series [10], spatial spectrum estimation method, and other comprehensive analysis methods into the analysis process [11], which can reduce the data dispersion and improve the accuracy of resource allocation and management results of public sport facilities [12]. Therefore, using the spatial spectrum estimation method to manage public sport facilities resources can not only realize the comprehensive allocation of resources but also improve the management level and realize multifactor analysis. The spatial spectrum estimation method first carries out spatial classification and then carries out a detailed analysis, which can realize comprehensive analysis of data and reduce the error analysis rate of data.

Based on the above background, based on the existing research, this study integrates the spatial spectrum estimation method with the original spatial spectrum estimation method and analyzes its allocation and management effect on the resources of public sport facilities. First, based on the existing research, this study constructs a theoretical model analysis to describe the allocation and management parameters of public sport facilities resources [13]. Second, deeply excavate the data in the resource allocation and management of public sport facilities and identify the eigenvalues [14]. Finally, the resource allocation and management algorithm of public sport facilities based on the spatial spectrum estimation method is compared with the existing spatial spectrum estimation method to verify the analysis time and accuracy of different algorithms [15]. Therefore, the spatial spectrum estimation method is applied to the management of public sport facilities, and different sport facilities are divided into different space. According to the distribution characteristics of the spatial spectrum estimation method, comprehensive analysis is carried out. At the same time, spatial division can better find local solutions and comprehensive analysis of sport facilities, facilities management, facilities management, and other aspects. The spatial spectrum estimation method can realize massive data processing and reduce the initial data processing capacity.

2. Description of Resource Allocation and Management of Public Sport Facilities

In the process of public sport facility resource management, it is assumed that the configuration and management set G=(n, e), N represents the node set of any public sport facility resource, and E represents the association number set in the public sport facility resource. Any public sport facility resource N is composed of n node spaces, which can also be expressed N=set(n1,…, n) as belonging to any natural number [16]. E is composed of m associations, which can be expressed E=set{e1,…, e} and n ∈ M belongs to any natural number. If the government and health institutions want to allocate and manage the resources of public sport facilities [17], they need to judge the relationship between the resources of public sport facilities and the management unit. The judgment contents are node management and association management. Suppose the management unit G=(NE), where N represents the set of nodes configured with the management unit in the server and E represents the set of association numbers in the server management unit [18]. Therefore, the relationship between management unit and public sport facility resources is

Among them, the constrained Jaro algorithm is to calculate the similarity of any facility resources, ω is the correlation coefficient between public sport facility resources and public health, and σ is the correlation management coefficient [19], which represents the requirements of public health. In order to better allocate and manage the resources of public sport facilities, it is necessary to construct the resource matrix H of public sport facilities and calculate its eigenvalue, which represents the best value of resource allocation and management [20]. Among them, public sport facilities resource matrix H is a multiorder matrix of spatial spectrum estimation, as shown in the following formula.

In formula (2), θ represents the relationship between sport infrastructure and uncertain factors in various regions, and p is the result of the Jaro algorithm to judge the similarity between n public sport facility resources and NJ public sport facility resources [22]. The higher the similarity, the lower the level of resource allocation and management, and corresponding optimization is needed. According to formula (2), there are n fields between two sport facilities, P is the eigenvalue between p and p, and the similarity space of all fields is F, as shown in the following formula.

3. Resource Allocation and Management Algorithm Analysis of Public Sport Facilities

The spatial spectrum estimation method first classifies the data, removes irrelevant data, then gives the data permit, and analyzes the data according to the permission, so as to improve the data processing efficiency. In order to better analyze the allocation and management of public sport facilities resources of government and health institutions, improve the allocation and management effect of public sport facilities resources [23]. The solution of this study is as follows: determine the number of correlation paths EI between the allocation and management node NQ and public sport facilities resources; according to the number of associated roads e, the space of public sport facilities resources is divided into GK; divide the resource occupancy rate of the resource node Ni of public sport facilities [24]. The higher the number of resource occupancy, the higher the weight of the sport facilities on the configuration and management unit NQ and the higher the configuration of NQ node; and sort the analysis results. The specific steps are described as follows.

3.1. Spatial Spectrum Estimation Method

The spatial spectrum estimation methods mainly assume the number of configuration and management unit modes and the quality of public sport facility resources. It is assumed that the input of the ith node of public sport facility resources is represented by II. It is necessary to calculate the relationship between the associated sport facility nodes and the relationship between configuration and management unit nodes [25]. The calculation results are shown in the following formula.where α and β is the adjustment coefficient of node configuration and relevance, f() is the projection function, c0 is the maximum number of public sport facility resource nodes, b0 is the maximum value of public sport facility resource nodes, (N · α · n/(q+n)) represents the relevance of the in-sport facility, and (E · β · n/(q+n)) represents the configuration of the ith sport facility. Since there is a certain error between the resources and allocation of public sport facilities and the nodes of the management unit, the error adjustment function () should be constructed to make it closer to the real. The calculation is shown in the following formula.where (∀(N · α · n/(q+n))), are the change values of (N · α · n/(q+n)) and (E · β · n/(q+n)), which changes with the continuous iteration of sport facilities space until it is less than the preset error value of spatial distribution. If in formula (4), ∀(N · α · n/(q+n)) > c0 and , α is the representative weight, 0∼I sport facilities are included in g, and then repeat the calculation in steps (4) and (5) until i = n.

3.2. Spatial Spectrum Estimation Methods

The spatial spectrum estimation method finds the public sport facility resources with double heights of N and E, sets them as the initial point, and then configures the management association number E and the association number E of public sport facility resources to search, so as to obtain the maximum value of g. In order to reduce the space of public sport facilities resources and realize the optimization of allocation and management. The spatial spectrum estimation method is used to analyze the resources of public sport facilities, assuming that the adjacent sport facilities are , , , corresponding allocation and management. Therefore, the relationship between the three is n⟶n⟶n, n⟶e, n⟶e, n⟶e.where ch(·) is the quantity function, and ∑∃ch(n) is the sum of the association between the configuration and the snap in node. As can be seen from formula (1), ω is the ratio of the spectral estimation of public sport facilities resources gin the total number of allocation and management nodes, representing the minimum correlation of g. ∑ch(n) represents the sum of relevant data. The greater the value, the less the correlation of g. The calculation formula of σ is

The importance of public sport facilities resources is the sum of the importance of all sport facilities. ∡θ∑S(n) is the ratio of GK in the allocation and management of public sport facilities resource spectrum estimation, andσ represents the best division position of g spectrum estimation. The greater the value, the higher the importance of g. The final spectrum estimation g of public sport facilities resources is determined by σ and ω. According to the resource allocation and management data of sport facilities of the government and health institutions, set the initial value of σ and ω to 1. Through continuous calculation, the best spectral evaluation score of g is determined. Then, output σ andω values.

3.3. Poor Management of Public Sport Facilities and Resources

Bad management will reduce the allocation and management effect of public sport facilities resources. Bad data should be identified in time, optimized and improved. Through the analysis of E and E in g space, judge the bad management of public sport facilities resources and redistribute the corresponding sport facilities. It is assumed that the bad management of sport facilities is expressed in R(n∑P) and the occurrence rate of bad management is expressed in P(n∑P). Then, formulas (8) and (9) can be obtained [26].

Among them, n is any sport facility and Q is the maximum tolerance of the government and health institutions for the allocation and management of public sport facility resources. According to formulas (8) and (9), the greater the R(n∑P) value, the worse the poor management of sport facilities. In formula (9), P(n∑P) and P(n∑n) are obtained through the spatial spectrum estimation of sport facilities. is the probability that sport facilities have no bad management record.

3.4. Implementation Steps of Resource Allocation and Management Algorithm of Public Sport Facilities

According to the spatial spectrum estimation method, the following steps are required:

Step 1: the government and health institutions analyze the table of sport facilities in allocation and management, form a collection N=set{n1,…, n} and E=set{e1,…, e}, and determine the relationship between sport facilities in different spaces n⟶n⟶n.

Step 2: using formulas (5) and (6), obtain ω andσ. ω < ω and σ < σ and meet the allocation and management conditions of sport facilities; otherwise, the sport facilities shall be eliminated. At the same time, the management units of configuration and management points are divided into multiple independent sets.

Step 3: use formulas (8) and (9) to judge the bad management records of public sport facilities and resources and sort the space where the sport facilities are located to get the final configuration and management results. If the judgment process does not reach the expected iteration value, repeat steps P2 and 3; otherwise, proceed to step 4.

Step 4: output the resource allocation and management results of public sport facilities based on the spatial spectrum estimation method. The flowchart is shown in Figure 1.

Figure 1

Calculation steps.

4. Case Studies on Resource Allocation and Management of Actual Public Sport Facilities

4.1. Case Introductions

The topological map of public sport facilities resources is generated by spatial layout software in the laboratory, and there are 821 sport facilities in total, with 13 spaces. The dispersion of sport facilities in each space is 0.97, which is basically in a completely discrete state. According to the standardized management measures for the allocation and management of public sport facilities and the requirements for the allocation and management of public sport facilities resources maxω and maxσ, the space of sport facilities is divided into 0.77 and 0.73 respectively. In order to reduce the processing capacity of public sport facility resource data, the statistical method of random sampling is adopted y=sin  ς∑2πy, and the number of simulation iterations is set to 50 to analyze the degree, accuracy, configuration, and management time of configuration and management. The specific simulation model construction is shown in Figure 2.

Figure 2

Simulation model of public sport facilities resources.

4.2. Analysis of Configuration and Management Degree

The configuration and management degree of the spatial spectrum estimation method and existing algorithms are compared, and the results are shown in Figure 3.

Figure 3

Resource allocation and management degree of public sport facilities.

It can be seen from Figure 3 that the configuration and management degree of the spatial spectrum estimation method is concentrated in −20–100%, while the configuration and management degree of the dynamic programming algorithm is concentrated in 0–100%. Moreover, the curve is convex in the middle and descending around, which meets the requirements of normal distribution. Therefore, the configuration and management range of the spatial spectrum estimation method is better than that of the dynamic programming algorithm. Moreover, the configuration and management range of the spatial spectrum estimation method is smaller than that of the existing algorithms, which indicate that there are many “redundant” sport facilities in the existing algorithms, and there are a large number of abnormal user values. It also repeatedly explains the phenomenon of “value hopping,” which is consistent with the relevant domestic research [9].

4.3. The Accuracy

Accuracy is the key indicator of resource allocation and management of public sport facilities, as shown in Figure 4.

Figure 4

Comparison of accuracy of different methods.

It can be seen from Figure 4 that the accuracy of the spatial spectrum estimation method is 98%, the variation range is (0, 10), and the accuracy better than the original algorithm is 80%, the variation range is (0, 20). At the same time, the curves show the trend of gradually concentrating, which shows that the solution effect is more obvious. Moreover, the change of the spatial spectrum estimation method is smoother, and the correlation between various analyses is better. Previous studies believe that the accuracy of the dynamic programming algorithm is high, but the influence of amplitude variation of accuracy is ignored. This shows that the main reason for the poor accuracy of the dynamic programming algorithm is not the low accuracy, but the large range of accuracy change, which is basically consistent with the relevant domestic research conclusions [10].

4.4. Configuring and Managing Data Volume

Configuring and managing the amount of data is an important index of public sport facility resource management, which reflects the data processing ability of the algorithm in unit time. Generally speaking, the resource allocation and management time of public sport facilities is 25 seconds; otherwise, it cannot meet the future development needs of the government and health institutions, nor can it carry out the allocation and management of massive sport facilities. The calculation results are given in Table 2.

Table 2

Resource allocation analysis of multispace public sport facilities.

Different algorithms	Optimal spatial spectrum estimation point	Data output in a single time (MB)	Spatial correlation coefficient (none)	Error variation (%)
Dynamic time method	41112	121112	0.620.710.63	161514
Dynamic throughput method	41210	121312	0.320.380.29	121311
Spatial spectrum estimation method	3109	141516	0.620.600.56	296
Dynamic parameter method	498	131211	0.520.560.58	151413

It can be seen from Figure 5 that in unit time, the amount of configuration and management data of the spatial spectrum estimation method is higher than that of existing algorithms, which also indirectly indicates that the configuration and management time of the spatial spectrum estimation method is short. At the same time, unstructured data accounts for a large proportion of the data in this test, so most of the data in the figure are unstructured data. Through the comparison of unstructured data, the advantages of the spatial spectrum estimation method are further verified. The main reason is the poor management of sport facilities P(n) and R(n). Through the corresponding probability calculation, the preliminary data standardization processing is carried out to reduce the complexity of public sport facilities and resources.

Figure 5

Configuration and management time of different methods. Positive numbers represent structured data and negative numbers represent unstructured data.

5. Conclusion

The resource allocation and management of public sport facilities is a process in which the government and health institutions use the comprehensive analysis method to optimize in response to the adjustment of the expansion of power grid and the soaring number of sport facilities [27]. The higher the level of resource allocation and management of public sport facilities, the less the amount of data processed by the servers of governments and health institutions and the lower the difficulty of calculation. The spatial spectrum estimation method of public sport facilities resources has the problem of subjective bias, which will reduce the accuracy of analysis under a large amount of sport facilities information. This not only increases the management cost of the government and health institutions but also wastes a lot of power resources. The spatial spectrum estimation method is a comprehensive analysis method to judge from the two aspects of quantity and quality. It analyzes the unit management in the government and health institutions, judges the resources of public sport facilities in the chain, and estimates, judges, allocates, and manages them. MATLAB simulation results show that the degree of configuration and management of the spatial spectrum estimation method focuses on 69–83%, the accuracy is 98%, the variation range is (97, 98), and the amount of configuration and management data is 234 mb, which is significantly better than the existing algorithms. Therefore, the spatial spectrum estimation algorithm for the public sport facilities optimization effect is very obvious, with the distribution of resources in different space, more accurate calculation results. The spatial spectrum estimation method can meet the requirements of the existing government and health institutions for the allocation and management of public sport facilities resources and realize the comprehensive improvement of the management level of public sport facilities resources.