# Construction and Analysis of Urban Cultural Plane Space Mode considering Particle Swarm Cultural Scientific Computing Algorithm

Authors: Jiayong Yu; Qi Li
Journal: Security and Communication Networks
 (2022)

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## Abstract

In the tide of economic and social internationalization and high-speed urbanization, urban culture has increasingly attracted widespread attention from all walks of life and has a very critical strategic significance in the construction of urban space. This paper aims to construct and analyze the plane space mode of urban culture based on the particle swarm cultural scientific computing algorithm. This article first explains the concept of urban cultural space. Urban cultural space uses urban spatial structure as a media carrier and uses urban cultural time for vertical extension and development; then we proposed the particle swarm cultural scientific calculation algorithm and gave the particle swarm algorithm flowchart; then based on the particle swarm optimization algorithm, the evaluation of the configuration performance of urban cultural facilities is researched and discussed, and at the same time, the evolution law of urban spatial morphology is explored based on the particle swarm optimization algorithm. The particle swarm algorithm is a random search algorithm based on group cooperation developed by simulating the foraging behavior of birds. Urban cultural space is the development of urban space based on urban culture. It plays a special and important role in urban cultural development and urban space planning. According to the statistics of the survey and research results, the utilization rate of city-level cultural facilities in City A is 77, the utilization rate of district-level cultural facilities is 72, the utilization rate of street-community cultural facilities is 69, and the overall evaluation score is 70. It shows that there are significant differences in the actual use of cultural facilities, so it is particularly important to eliminate the differences in the use of cultural facilities between urban and rural areas. In the exploration of the law of urban spatial morphology evolution, it is found that the number of college students, total real estate investment, urban population, and total commercial housing sales have a significant impact on urban spatial expansion and evolution.


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## Body

## 1. Introduction

The strong transmission of world history and culture has brought a great impact on cultural industries all over the world, and consumer art culture and entertainment art culture have gradually penetrated into society. The existence of ethnic minorities and regional economic status and social culture of various countries have been severely affected, and the cultural traditions of ethnic minorities of various countries have also been threatened. And various art and cultural spaces are a kind of container to deal with this crisis. At the beginning of the economic era of the last century, the functions of cultural elements have gradually become clear, and various excellent cultural innovation products have gradually appeared. They are regarded as the cultural attraction of one of the three major soft powers of society, which has created benefits for the entire economic and social development. A new type of social structure was created, namely, cultural development space design, cultural entertainment space design, cultural consumption space design, and social and cultural gathering areas. How to organize and integrate this structure to promote the common development of society is a brand-new topic that must be faced in particular.Observing the problems of cultural space planning in today’s social cities, some have separated the urban cultural space planning from the overall urban space planning and separated it from regional development; there are also cities that overconstruct and develop culture, so that they ignore the urban living space and other important consumption spaces. Therefore, it is self-evident to analyze and study the importance of urban cultural space. Only by comprehensively analyzing the social conditions of urbanization development and attaching importance to the function of urban cultural construction can we propose a rational strategy for urban cultural space planning and at the same time, it is the rationality of the two to look at its positive and negative aspects. This paper first expounds the concept of urban cultural space, then proposes a particle swarm cultural scientific computing algorithm, and gives a flowchart of the particle swarm algorithm. Finally, based on the particle swarm optimization algorithm, the evaluation of the configuration performance of urban cultural facilities is studied and discussed, and the evolution law of urban space morphology based on the particle swarm optimization algorithm is also explored. This paper aims to construct and analyze the plane space mode of urban culture based on the particle swarm cultural scientific calculation algorithm, hoping to provide a practical effect on the promotion of urban culture.According to the research progress at home and abroad, different scholars also have a certain degree of cooperation in the construction of particle swarm cultural scientific calculation algorithm and the construction of urban cultural plane space mode: Yang H proposed a new cooperative control method based on loop tracking algorithm and fuzzy control idea to realize the reconstruction of multiagent formation in 3D space. His idea is to use nonlinear loop tracking control in the longitudinal movement of the formation and use a piecewise proportional derivative (PD) controller based on fuzzy control for the cooperative control of the normal movement. The results show that this method improves the performance and accuracy of formation reconfiguration control, avoids collisions between members, and enhances the stability of the system [1]. The methodology used by M’Hammedi is an evaluation of the main methods used in the creation of the bare new city of Rabat. He experimented with urban landscape based on spatial functionalism, landscape treatment, urban composition, and architectural planning, emphasizing architectural design influenced by different forms of decorative art [2]. The purpose of Kherbouche and Djedid’s research is to test the ever-changing cognition of the city’s image, evaluate its persistence, and determine its relationship with the development of sustainable cultural tourism. It is tested by empirical research combining qualitative and quantitative methods. The qualitative research is based on semidirect interviews, and the quantitative research is based on statistics from the Wilaya Tourism Bureau. The results of this study show that residents’ perception of the city’s image is not static. It follows the same evolution process as tourists’ perception of the image. To achieve the sustainable development of cultural tourism, the sustainability of the image must be verified internally and externally [3]. The research of Amen MA aims to find the internal symbol system in the urban space organization, explore the hidden space organization, and find the inner power as the aesthetic symbol of the urban space organization. The results show that, without considering the existing sign system, the results of introducing new concepts into urban spatial organization are different. This difference may be the source of misunderstanding and confusion in the spatial organization system, which needs to be understood and reorganized through the development of procedures [4]. Lee S research analyzed the urban microspatial structure by considering the complex use of the interior of the building. The significance of the research lies in taking into account the complex uses of buildings, constructing a more refined and microurban spatial structure, clarifying the structural differences in retail office land prices and price formation factors; through the analysis of the hierarchical linear model, it is found that the land price formation structure of commercial real estate may vary depending on the use of the region [5]. Naseri and Jafari Navimipour proposed a new hybrid approach to achieve efficient service composition in cloud computing. Agent-based methods are also used to combine services by identifying QoS parameters and use particle swarm optimization (PSO) algorithms to select the best services based on fitness functions. The simulation results show the performance of this method in reducing combined resources and waiting time [6]. Wang introduced the origin and background of PSO and conducted a theoretical analysis of PSO. Then he analyzed its research and application status in algorithm structure, parameter selection, topology structure, discrete PSO algorithm, and parallel PSO algorithm, multiobjective optimization PSO, and its engineering application. Finally, the existing problems are analyzed, and future research directions are proposed [7]. Wu and Song first introduced the development history and related research work of swarm intelligence algorithms at home and abroad. Secondly, the importance of particle swarm optimization algorithm in power system network reconstruction is proposed, and the basic principle, essential characteristics, and basic model of particle swarm optimization algorithm are expounded. The improved particle swarm optimization algorithm proposed by Wu and Song provides a good solution for power system network reconstruction and has important research significance for the subsequent optimization of power system and the improvement of particle swarm optimization algorithm [8]. However, these scholars did not combine the particle swarm cultural scientific calculation algorithm with the construction of urban cultural plane space mode to explain the problem but unilaterally explored their meaning. The purpose of this study is to make up for the research gap in the construction of urban cultural plane space model, in order to provide practical effects on the promotion of urban culture.The innovations of this article are mainly reflected in the following: (1) firstly, it explained the concept of urban cultural space. Urban cultural space uses urban spatial structure as a media carrier and uses urban cultural time for vertical extension and development; (2) it proposed the particle swarm cultural scientific computing algorithm and gave the particle swarm algorithm flowchart; (3) at the same time, based on the particle swarm optimization algorithm, the evaluation of the configuration performance of urban cultural facilities is researched and discussed, and at the same time, based on the particle swarm optimization algorithm, the evolution of urban spatial morphology is explored.


## 2. The Construction and Analysis Method of Urban Cultural Plane Space Mode Taking Into Account the Particle Swarm Cultural Scientific Computing Algorithm

### 2.1. Urban Cultural Space

City cultural space is the development of urban space based on urban culture. It plays a special and important role in urban cultural development and urban space planning [8]. The formation of urban cultural space is an organic synthesis of urban development, cultural development, and industrial development. The implementation of urban cultural space development strategy is an important path for urban cultural development and an effective way for urban economic development. It is also a trend and successful experience of urban cultural development and urban space planning at home and abroad [9]. A city’s cultural image is the appearance of a city’s culture. It is a city form and feature that can inspire people’s thoughts and emotions. It is the specific perception, overall view, and comprehensive evaluation of the city’s internal and external public on the city’s inherent strength, apparent vitality, and development prospects. In the process of its formation and development, the city has created its own urban culture, becoming an important part of human culture and the most active, brilliant, creative element and the crystallization of wisdom. It is the high-level expression or highest form of culture created by mankind on the Earth. The development of urban culture, especially the protection and utilization of historical and cultural heritage, the protection and utilization of scenic spots, urban ecological environment protection, urban cultural construction and activities, etc., has made great progress and development.Regarding the definition of urban social and cultural public space, people first proposed that the city is a cultural place that occupies the corresponding material public space and at the same time has been widely recognized by the citizens and reflects the characteristics of urban public civilization [10]. It is formed by organically fusing the three basic elements of human beings as the main body of the spatial structure of social, historical, and cultural activities, activities that constitute nodes of time, and cultural places of spatial structure nodes, interacting and coexisting. It is divided according to the differentiation of the spatial structure of people’s concentrated living, the difference in the intensity of collective social, historical, and cultural activities, and the spatial structure of locations. The spatial structure of urban social, historical, and cultural activities is divided into the overall urban social, historical, and cultural image space, the large-scale historical and cultural divisions of the urban internal structure, the microsized cultural areas in the urban internal structure, and the microsized cultural facilities of the urban internal structure. In terms of demand, the design of urban cultural space is divided into basic cultural space design that allows residents to survive normally, allows the city to run smoothly, and highlights the background of urban civilization; it is known as the iconic cultural space of the iconic blocks, facilities, and venues of the city’s “image project” [11]. The spatial structure of urban culture is also regarded as the cultural spiritual dimension of urban spatial structure, the highest form of urban spatial structure, and an important way of expressing the interaction between material and spiritual activities of urban people. It is mainly composed of three dimensions: the rich historical and cultural spatial structure of urban traditional historical culture, the diverse real spatial structure of urban reality and culture, and the extended spatial structure of urban social culture in the future [12]. At the same time, the urban cultural space is regarded as the existence form expressed by the material-social cultural form created by people, and it has the six characteristics of location, economy, humanity, symbolism, citizenship, and modernity [13]. Figure 1 shows the urban cultural landscape.Figure 1
Urban cultural landscape.It can be seen that the urban cultural space takes the urban space structure as the medium carrier and uses urban cultural time to carry out vertical extension and development [14]. According to the broad and narrow categories of urban culture, we can define the category of urban cultural space as broad urban cultural space and narrow urban cultural space [15]. That is, the broad sense of urban cultural space refers to the composition and combination of living space constituted by the life energy and spiritual wealth provided by the urban subject in the historical development of the city, while the narrow urban cultural space refers to the long time in the city by the urban subject. The historical development of the city has cultivated and produced a social and cultural space organization composed of unique urban common thinking, values, basic beliefs, urban spirit, behavioral norms, and other valuable spiritual wealth [16].


### 2.2. Particle Swarm Cultural Scientific Computing Algorithm

This paper aims to construct and analyze the plane space pattern of urban culture based on particle swarm algorithm. As a system composed of various types and levels, the urban cultural facility system should first consider the integrity of its functional structure in each area of the city when evaluating the fairness of its facilities. In order to judge whether it can meet the multilevel cultural needs of urban residents, based on the particle swarm algorithm, the cultural space users are simulated as a flock of birds, the urban cultural space is simulated as food, and the behavior of searching for cultural facilities is simulated as birds searching for food.The particle swarm optimization algorithm is an intelligent algorithm based on an iterative model. Its basic idea is to randomly initialize each particle that has memory but lacks volume and mass. Each particle represents a possible solution in the swarm optimization problem, and a fitness distribution value is defined for it by the fitness function. The fineness of the particles is also judged according to the size of the fitness distribution value [17]. Each particle has the ability to remember and can adjust its trajectory according to its current position, information sharing between companions, and the best position it has experienced in memory. After iteration, it keeps getting closer to the best position and finally reaches the best position [18]. The so-called optimal position is a point in the solution space that corresponds to the smallest or largest value of the fitness function. Figure 2 shows the energy-efficient power distribution method based on particle swarm algorithm.Figure 2
Energy-efficient power allocation method based on particle swarm algorithm.Among them, genetic algorithm is a computational model that simulates the biological evolution process of natural selection and genetic mechanism of Darwin’s biological evolution theory and is a method to search for the optimal solution by simulating the natural evolution process. Among them, the shortcomings of genetic algorithm include coding irregularities and inaccuracy of the representation of the code: a single genetic algorithm code cannot fully express the constraints of the optimization problem; being easy to prematurely converge, the accuracy and feasibility of the algorithm, computational complexity, etc.: there is no effective quantitative analysis method yet. Among them, the advantage of evolutionary computing of particle swarm optimization algorithm is that it can deal with some problems that traditional methods cannot handle. For PSO to simulate the predation behavior of a flock of birds, it means that a flock of birds is searching for food at random, and there is only one piece of food in this area. All the birds do not know where the food is. But they know how far they are from the food. So what is the optimal strategy for finding food? The easiest and most effective way is to search the area around the bird closest to the food.For example, nondifferentiable node transfer function or no gradient information exists. But the disadvantages are as follows: the performance is not particularly good on some problems; the coding of network weights and the selection of genetic operators are sometimes troublesome.The mathematical description of the basic particle swarm algorithm is as follows:Assuming that the population size of the particle isM, the position information of the nth particle in the D-dimensional space is used to represent an:(1)an=an1,an2,…,and,…,anD.The velocity of thenth particle is used to represent kn:(2)kn=kn1,kn2,…,knd,…,knD.Therefore, at the timeh + 1, the flight speed of the nth particle in the d-dimensional subspace knD is adjusted according to the following formula:(3)knDh+1=knDh+e1w1hQndh−anDh+e2w2hQjdh−anDh.(4)knDh+1=kmax,ifknDh+1>kmax,knDh+1=−kmax,ifknDh+1<−kmax.w1, w2 are a random number distributed between [0, 1].During the search process, the particles integrate their own previous flight experience and the experience of their companions. Finally, determine your own flight speed according to formula [19]. Figure 3 is a schematic diagram of particle position update. The particle position update formula is as follows:(5)andh+1=andh+kndh.Figure 3
Schematic diagram of particle position update.The particle motion is coordinated by (3)–(5), and the optimal solution of various optimization problems is finally obtained by the iterative mode [20].From the velocity update formula and position update formula, it can be seen that each dimension in the search range is independent of each other, so the convergence analysis of the algorithm can be simplified to one dimension [21]. And supposing that, in the population except for the nth one, the rest of the individuals remain motionless, then the behavior of a single individual can be studied, so the subscript n can be omitted. In order to simplify the calculation, suppose that the historical optimal position of the individual itself and the historical optimal position of the group remain unchanged, denoted as qs and js; let μ1=e1w1, μ2=e2w2. Then formula (3) and formula (5) can be simplified as(6)kh+1=lkh+μ1Qs−ah+μ2Qs−ah,ah+1=ah+kh+1.It can be obtained from the above formula:(7)kh+2=lkh+1+μ1Qs−ah+1+μ2Qs−ah+1,ah+2=ah+1+kh+2,Substituting (7) and (8) into (9) we get(8)ah+2=ah+1+kh+2=ah+1+lkh+1+μ1Qs−ah+1+μ2Qs−ah+1=ah+1+lah+1−ah+μ1Qs−ah+1+μ2Qs−ah+1=l−μ1−μ2+1ah+1−lah+μ1Qs+μ2Qs.Converting formula (10) into a standard form is(9)ah+2+l−μ1−μ2+1ah+1+lah=μ1Qs+μ2Q.The above formula is a second-order nonhomogeneous difference equation with constant coefficients, so its characteristic equation can be analyzed [22].Solve the characteristic equation of (9): γ2+−l+μ1+μ2−1γ+l=0. According to the solution of the quadratic equation in one variable, we can get(10)γ1=l−μ1−μ2+1+1Δ2,γ1=l−μ1−μ2+1−1Δ2.Among themΔ=−l+μ1+μ2−12−4l; if Δ≥0 , then γ1 and γ2 are real numbers; if Δ≤0, then γ1 and γ2 are complex numbers. At this time formula (9) can be written as(11)ah=m0+m1γ1h+m2γ2h.The same can be obtained:(12)kh=n1γ1h+n2γ2h.For the convenience of description, ifγ1 and γ2 are real numbers, γ1 and γ2 represent the absolute values of γ1 and γ2, respectively; if γ1 and γ2 are complex numbers, γ1 and γ2 represent the modulus of γ1 and γ2, respectively.If and only if(13)maxγ1,γ2≤1,the particle swarm optimization algorithm converges.Proof.
Find the limit of the following equation:(14)limh⟶∞ah=limh⟶∞m0+m1γ1h+m2γ2h=m0+m1limh⟶∞γ1h+m2limh⟶∞γ2h.
Whenmaxγ1,γ2>1, the limit value of (13) does not exist, so the trajectory of the particle diverges.
Whenmaxγ1,γ2=1, we can get limh⟶∞ah=m0+m1+m2, or limh⟶∞ah=m0+m1, or limh⟶∞ah=m0+m2, so the trajectory of the particle converges.
Whenmaxγ1,γ2<1, we get limh⟶∞ah=m0, and the trajectory of the particle also converges [23].
In the particle swarm optimization algorithm, the position of the particle represents the solution searched by the algorithm in the search space, so the proposition is established.
The convergence area is(15)l<1,μ1+μ2>0,2l−μ1−μ2+2>0.
The above convergence range is also the main parameter selection range of the algorithm [24]. The key issue that affects the calculation performance and effect is the selection of parameters. The above analysis methods of convergence provide a basis for the selection of parameters [25]. The position of the current optimal predicted solution obtained by the particle itself and the position of the current optimal predicted solution of the entire population are dynamically changing. Although there are differences between the two, the selection of parameters can still be guided in the convergence area.
If the particle swarm optimization algorithm converges, the particle speed will either gradually decrease from the initial value to 0 or iterate at the initial speed until the end of the algorithm.Proof.
Find the limit of formula (15):(16)limh⟶∞kh=limh⟶∞n1γ1h+n2γ2h=n1limh⟶∞γ1h+n2limh⟶∞γ2h.
If the algorithm converges, then(17)maxγ1,γ2≤1.
Whenmaxγ1,γ2<1, the limit value of formula (13) is 0; that is, the particle velocity gradually decreases from the initial value to 0.
Whenmaxγ1,γ2<1 is used, limh⟶∞kh=n1+n2, limh⟶∞kh=n1, or limh⟶∞kh=n2 can be obtained. From the initialization condition of (12), it can be known that the particle has been iterated at the initialization speed until the end of the algorithm.
If an individual’s current position, the individual’s historical best predicted position, and the group’s historical best predicted position are all the same, the individual will leave the best historical area because its previous speed and inertia weight are not zero. So the algorithm does not converge; if the individual’s previous velocity is very close to zero, once the number of particles catches up with the highest particle of the current population, the diversity of the population will gradually decrease, all particles will be concentrated in the same place and stagnant, and the overall optimization process will appear. The situation is stopped, and the global optimal predictive value cannot be found. In this case, most of the premature phenomenon will be caused; and if the individual speed iterates at the initialization rate until the end of the particle swarm optimization algorithm, it is equivalent to no longer affecting the individual’s own cognitive part and the social part. It is not conducive to the search of the global optimal prediction value, and the adaptability of the algorithm will also be greatly reduced [26].
Based on the above analysis, it can be known that the particle swarm optimization algorithm cannot guarantee the convergence to the global optimal value. It can only show that the algorithm will eventually converge to the current population optimal solution; that is, if the algorithm does not search for the global optimum before converging, premature convergence will occur. Figure4 shows the flowchart of the particle swarm algorithm.Figure 4
Flowchart of particle swarm algorithm.


## 2.1. Urban Cultural Space

City cultural space is the development of urban space based on urban culture. It plays a special and important role in urban cultural development and urban space planning [8]. The formation of urban cultural space is an organic synthesis of urban development, cultural development, and industrial development. The implementation of urban cultural space development strategy is an important path for urban cultural development and an effective way for urban economic development. It is also a trend and successful experience of urban cultural development and urban space planning at home and abroad [9]. A city’s cultural image is the appearance of a city’s culture. It is a city form and feature that can inspire people’s thoughts and emotions. It is the specific perception, overall view, and comprehensive evaluation of the city’s internal and external public on the city’s inherent strength, apparent vitality, and development prospects. In the process of its formation and development, the city has created its own urban culture, becoming an important part of human culture and the most active, brilliant, creative element and the crystallization of wisdom. It is the high-level expression or highest form of culture created by mankind on the Earth. The development of urban culture, especially the protection and utilization of historical and cultural heritage, the protection and utilization of scenic spots, urban ecological environment protection, urban cultural construction and activities, etc., has made great progress and development.Regarding the definition of urban social and cultural public space, people first proposed that the city is a cultural place that occupies the corresponding material public space and at the same time has been widely recognized by the citizens and reflects the characteristics of urban public civilization [10]. It is formed by organically fusing the three basic elements of human beings as the main body of the spatial structure of social, historical, and cultural activities, activities that constitute nodes of time, and cultural places of spatial structure nodes, interacting and coexisting. It is divided according to the differentiation of the spatial structure of people’s concentrated living, the difference in the intensity of collective social, historical, and cultural activities, and the spatial structure of locations. The spatial structure of urban social, historical, and cultural activities is divided into the overall urban social, historical, and cultural image space, the large-scale historical and cultural divisions of the urban internal structure, the microsized cultural areas in the urban internal structure, and the microsized cultural facilities of the urban internal structure. In terms of demand, the design of urban cultural space is divided into basic cultural space design that allows residents to survive normally, allows the city to run smoothly, and highlights the background of urban civilization; it is known as the iconic cultural space of the iconic blocks, facilities, and venues of the city’s “image project” [11]. The spatial structure of urban culture is also regarded as the cultural spiritual dimension of urban spatial structure, the highest form of urban spatial structure, and an important way of expressing the interaction between material and spiritual activities of urban people. It is mainly composed of three dimensions: the rich historical and cultural spatial structure of urban traditional historical culture, the diverse real spatial structure of urban reality and culture, and the extended spatial structure of urban social culture in the future [12]. At the same time, the urban cultural space is regarded as the existence form expressed by the material-social cultural form created by people, and it has the six characteristics of location, economy, humanity, symbolism, citizenship, and modernity [13]. Figure 1 shows the urban cultural landscape.Figure 1
Urban cultural landscape.It can be seen that the urban cultural space takes the urban space structure as the medium carrier and uses urban cultural time to carry out vertical extension and development [14]. According to the broad and narrow categories of urban culture, we can define the category of urban cultural space as broad urban cultural space and narrow urban cultural space [15]. That is, the broad sense of urban cultural space refers to the composition and combination of living space constituted by the life energy and spiritual wealth provided by the urban subject in the historical development of the city, while the narrow urban cultural space refers to the long time in the city by the urban subject. The historical development of the city has cultivated and produced a social and cultural space organization composed of unique urban common thinking, values, basic beliefs, urban spirit, behavioral norms, and other valuable spiritual wealth [16].


## 2.2. Particle Swarm Cultural Scientific Computing Algorithm

This paper aims to construct and analyze the plane space pattern of urban culture based on particle swarm algorithm. As a system composed of various types and levels, the urban cultural facility system should first consider the integrity of its functional structure in each area of the city when evaluating the fairness of its facilities. In order to judge whether it can meet the multilevel cultural needs of urban residents, based on the particle swarm algorithm, the cultural space users are simulated as a flock of birds, the urban cultural space is simulated as food, and the behavior of searching for cultural facilities is simulated as birds searching for food.The particle swarm optimization algorithm is an intelligent algorithm based on an iterative model. Its basic idea is to randomly initialize each particle that has memory but lacks volume and mass. Each particle represents a possible solution in the swarm optimization problem, and a fitness distribution value is defined for it by the fitness function. The fineness of the particles is also judged according to the size of the fitness distribution value [17]. Each particle has the ability to remember and can adjust its trajectory according to its current position, information sharing between companions, and the best position it has experienced in memory. After iteration, it keeps getting closer to the best position and finally reaches the best position [18]. The so-called optimal position is a point in the solution space that corresponds to the smallest or largest value of the fitness function. Figure 2 shows the energy-efficient power distribution method based on particle swarm algorithm.Figure 2
Energy-efficient power allocation method based on particle swarm algorithm.Among them, genetic algorithm is a computational model that simulates the biological evolution process of natural selection and genetic mechanism of Darwin’s biological evolution theory and is a method to search for the optimal solution by simulating the natural evolution process. Among them, the shortcomings of genetic algorithm include coding irregularities and inaccuracy of the representation of the code: a single genetic algorithm code cannot fully express the constraints of the optimization problem; being easy to prematurely converge, the accuracy and feasibility of the algorithm, computational complexity, etc.: there is no effective quantitative analysis method yet. Among them, the advantage of evolutionary computing of particle swarm optimization algorithm is that it can deal with some problems that traditional methods cannot handle. For PSO to simulate the predation behavior of a flock of birds, it means that a flock of birds is searching for food at random, and there is only one piece of food in this area. All the birds do not know where the food is. But they know how far they are from the food. So what is the optimal strategy for finding food? The easiest and most effective way is to search the area around the bird closest to the food.For example, nondifferentiable node transfer function or no gradient information exists. But the disadvantages are as follows: the performance is not particularly good on some problems; the coding of network weights and the selection of genetic operators are sometimes troublesome.The mathematical description of the basic particle swarm algorithm is as follows:Assuming that the population size of the particle isM, the position information of the nth particle in the D-dimensional space is used to represent an:(1)an=an1,an2,…,and,…,anD.The velocity of thenth particle is used to represent kn:(2)kn=kn1,kn2,…,knd,…,knD.Therefore, at the timeh + 1, the flight speed of the nth particle in the d-dimensional subspace knD is adjusted according to the following formula:(3)knDh+1=knDh+e1w1hQndh−anDh+e2w2hQjdh−anDh.(4)knDh+1=kmax,ifknDh+1>kmax,knDh+1=−kmax,ifknDh+1<−kmax.w1, w2 are a random number distributed between [0, 1].During the search process, the particles integrate their own previous flight experience and the experience of their companions. Finally, determine your own flight speed according to formula [19]. Figure 3 is a schematic diagram of particle position update. The particle position update formula is as follows:(5)andh+1=andh+kndh.Figure 3
Schematic diagram of particle position update.The particle motion is coordinated by (3)–(5), and the optimal solution of various optimization problems is finally obtained by the iterative mode [20].From the velocity update formula and position update formula, it can be seen that each dimension in the search range is independent of each other, so the convergence analysis of the algorithm can be simplified to one dimension [21]. And supposing that, in the population except for the nth one, the rest of the individuals remain motionless, then the behavior of a single individual can be studied, so the subscript n can be omitted. In order to simplify the calculation, suppose that the historical optimal position of the individual itself and the historical optimal position of the group remain unchanged, denoted as qs and js; let μ1=e1w1, μ2=e2w2. Then formula (3) and formula (5) can be simplified as(6)kh+1=lkh+μ1Qs−ah+μ2Qs−ah,ah+1=ah+kh+1.It can be obtained from the above formula:(7)kh+2=lkh+1+μ1Qs−ah+1+μ2Qs−ah+1,ah+2=ah+1+kh+2,Substituting (7) and (8) into (9) we get(8)ah+2=ah+1+kh+2=ah+1+lkh+1+μ1Qs−ah+1+μ2Qs−ah+1=ah+1+lah+1−ah+μ1Qs−ah+1+μ2Qs−ah+1=l−μ1−μ2+1ah+1−lah+μ1Qs+μ2Qs.Converting formula (10) into a standard form is(9)ah+2+l−μ1−μ2+1ah+1+lah=μ1Qs+μ2Q.The above formula is a second-order nonhomogeneous difference equation with constant coefficients, so its characteristic equation can be analyzed [22].Solve the characteristic equation of (9): γ2+−l+μ1+μ2−1γ+l=0. According to the solution of the quadratic equation in one variable, we can get(10)γ1=l−μ1−μ2+1+1Δ2,γ1=l−μ1−μ2+1−1Δ2.Among themΔ=−l+μ1+μ2−12−4l; if Δ≥0 , then γ1 and γ2 are real numbers; if Δ≤0, then γ1 and γ2 are complex numbers. At this time formula (9) can be written as(11)ah=m0+m1γ1h+m2γ2h.The same can be obtained:(12)kh=n1γ1h+n2γ2h.For the convenience of description, ifγ1 and γ2 are real numbers, γ1 and γ2 represent the absolute values of γ1 and γ2, respectively; if γ1 and γ2 are complex numbers, γ1 and γ2 represent the modulus of γ1 and γ2, respectively.If and only if(13)maxγ1,γ2≤1,the particle swarm optimization algorithm converges.Proof.
Find the limit of the following equation:(14)limh⟶∞ah=limh⟶∞m0+m1γ1h+m2γ2h=m0+m1limh⟶∞γ1h+m2limh⟶∞γ2h.
Whenmaxγ1,γ2>1, the limit value of (13) does not exist, so the trajectory of the particle diverges.
Whenmaxγ1,γ2=1, we can get limh⟶∞ah=m0+m1+m2, or limh⟶∞ah=m0+m1, or limh⟶∞ah=m0+m2, so the trajectory of the particle converges.
Whenmaxγ1,γ2<1, we get limh⟶∞ah=m0, and the trajectory of the particle also converges [23].
In the particle swarm optimization algorithm, the position of the particle represents the solution searched by the algorithm in the search space, so the proposition is established.
The convergence area is(15)l<1,μ1+μ2>0,2l−μ1−μ2+2>0.
The above convergence range is also the main parameter selection range of the algorithm [24]. The key issue that affects the calculation performance and effect is the selection of parameters. The above analysis methods of convergence provide a basis for the selection of parameters [25]. The position of the current optimal predicted solution obtained by the particle itself and the position of the current optimal predicted solution of the entire population are dynamically changing. Although there are differences between the two, the selection of parameters can still be guided in the convergence area.
If the particle swarm optimization algorithm converges, the particle speed will either gradually decrease from the initial value to 0 or iterate at the initial speed until the end of the algorithm.Proof.
Find the limit of formula (15):(16)limh⟶∞kh=limh⟶∞n1γ1h+n2γ2h=n1limh⟶∞γ1h+n2limh⟶∞γ2h.
If the algorithm converges, then(17)maxγ1,γ2≤1.
Whenmaxγ1,γ2<1, the limit value of formula (13) is 0; that is, the particle velocity gradually decreases from the initial value to 0.
Whenmaxγ1,γ2<1 is used, limh⟶∞kh=n1+n2, limh⟶∞kh=n1, or limh⟶∞kh=n2 can be obtained. From the initialization condition of (12), it can be known that the particle has been iterated at the initialization speed until the end of the algorithm.
If an individual’s current position, the individual’s historical best predicted position, and the group’s historical best predicted position are all the same, the individual will leave the best historical area because its previous speed and inertia weight are not zero. So the algorithm does not converge; if the individual’s previous velocity is very close to zero, once the number of particles catches up with the highest particle of the current population, the diversity of the population will gradually decrease, all particles will be concentrated in the same place and stagnant, and the overall optimization process will appear. The situation is stopped, and the global optimal predictive value cannot be found. In this case, most of the premature phenomenon will be caused; and if the individual speed iterates at the initialization rate until the end of the particle swarm optimization algorithm, it is equivalent to no longer affecting the individual’s own cognitive part and the social part. It is not conducive to the search of the global optimal prediction value, and the adaptability of the algorithm will also be greatly reduced [26].
Based on the above analysis, it can be known that the particle swarm optimization algorithm cannot guarantee the convergence to the global optimal value. It can only show that the algorithm will eventually converge to the current population optimal solution; that is, if the algorithm does not search for the global optimum before converging, premature convergence will occur. Figure4 shows the flowchart of the particle swarm algorithm.Figure 4
Flowchart of particle swarm algorithm.


## 3. The Construction of the Urban Cultural Plane Space Model and the Analysis of the Experimental Results Taking Into Account the Particle Swarm Cultural Scientific Computing Algorithm

### 3.1. Evaluation of the Performance of Urban Cultural Facilities Allocation Based on Particle Swarm Optimization Algorithm

This paper aims to construct and analyze the plane space pattern of urban culture based on the particle swarm cultural scientific computing algorithm. Particle swarm intelligence algorithm generally has good versatility. Due to the variety of practical application problems, the mathematical properties of many of them are difficult to determine. The optimization process of particle swarm intelligence algorithm does not depend on the strict mathematical properties of the problem itself, such as continuity and derivability. It also does not need precise mathematical description of objective function and constraints, which makes the particle swarm intelligence algorithm have better generality.The urban cultural facility system is a system composed of multiple types and multiple levels. The evaluation of the fairness of its facilities must first consider the integrity of its functional structure in each area of the city. It is used to judge whether it can meet the multilevel cultural needs of urban residents. The functional settings of cultural facilities mainly include reading and reading, cultural performances, knowledge lectures, cultural exhibitions, leisure and entertainment, and cultivating sentiments. Urban residents of different backgrounds have different preferences for cultural functions. The evaluation of the rationality of cultural facilities functions is mainly judged from the perspective of residents’ needs.This paper takes the results of the questionnaire as the basis for the evaluation of the index and divides the evaluation of the functional rationality of cultural facilities in the questionnaire into five levels: very reasonable, relatively reasonable, general, unreasonable, and very unreasonable. Figure5 is a statistical chart of the rationality evaluation of cultural facilities in City A.Figure 5
Evaluation of functional rationality of cultural facilities in City A.The quality of cultural facilities mainly refers to the quality of physical buildings. Evaluation factors include building appearance, internal environment, lighting and ventilation, and fire safety. The evaluation of this indicator is based on the perception of users of cultural facilities. In the questionnaire, five levels of quality, good, good, fair, poor, and very poor are set. Figure6 shows the physical quality evaluation of cultural facilities in City A.Figure 6
Physical quality evaluation of cultural facilities in City A.Through field investigations, it was found that the physical quality of large-scale cultural facilities in City A is better, and the environment comfort is higher. Among them, the newly built venues such as the City A Library, the Cathay Pacific Art Center, and the Natural History Museum have a grand appearance, spacious and comfortable interior space, full lighting, ventilation, and lighting facilities, and the fire exits comply with the architectural markings and are highly safe; although the facades of old venues such as Children’s Palace and the Mass Art Center are somewhat obsolete, the internal use space is repaired in real time and can perform better functions. Figure7 shows the physical map of cultural facilities in City A.Figure 7
Physical map of cultural facilities in City A.The quality of district-level cultural facilities is quite different, and the construction of district-level cultural centers and libraries has been paid more attention. In addition, the construction of the district-level elderly activity center is relatively lagging, and the update status is not good, resulting in the breakdown of the building entity and the problems of hardware facilities such as air conditioning and lighting. Among the basic cultural facilities, the construction quality of the sublibraries of the district-level cultural facilities belonging to the street level is better. The flow of people is attracted by the newly built cultural facilities with high environmental quality, and the dilapidated old community has become a settlement for the elderly with low economic conditions and low education level. This has led to the decline of cultural spaces in traditional communities.Environmental comfort mainly describes the creation of cultural atmosphere. It evaluates the quality of cultural facilities based on higher-level human psychological cognition to measure whether the activity space, environment construction, and software equipment of cultural facilities can be used comfortably by residents. The evaluation of this indicator is based on the experience of users of cultural facilities. Five levels are set in the questionnaire: very comfortable, relatively comfortable, average, not very comfortable, and very uncomfortable. Corresponding the evaluation results to the scores of each level in the questionnaire, calculate the quantifiable scores. Figure8 shows a statistical diagram of the environmental comfort evaluation of cultural facilities in the main urban area of City A.Figure 8
Evaluation of the environmental comfort of cultural facilities in the main urban area of City A.The five factors influencing the configuration of cultural facilities mentioned above include cultural activities. The development of cultural activities is of great significance to the improvement of residents’ utilization rate and the creation of cultural atmosphere. In addition, the development of cultural activities is closely related to the measurement of the service level of cultural facilities, describing from the side whether the hardware and software of cultural facilities can support the development of cultural activities. The evaluation of this indicator is based on the participation of users and the cultural activity data provided by the staff. The research set up five levels in the questionnaire: good, good, fair, not very good, and very bad. Corresponding the evaluation results to the scores of each level in the questionnaire, calculate a quantifiable score.The activities of cultural facilities in City A mainly include knowledge lecture activities carried out by book-reading facilities, calligraphy and painting exhibitions and publicity activities carried out in cultural and cultural exhibition facilities, festivals, cultural performances, and cultural competitions carried out in cultural activities facilities. Figure9 is a statistical chart of the evaluation of the development of cultural activities in the main urban area of City A.Figure 9
Evaluation of the development of cultural activities in the main urban area of City A.Residents’ cultural activities are generally organized by cultural departments and spontaneously formed. Activities in large-scale cultural venues are mostly in the form of lectures and exhibitions, and activities organized by grassroots cultural venues are mostly carried out in the activity venues of streets and communities or open spaces in the community. In the in-depth interviews at various research sites, it was found that residents have a strong demand for cultural activities, but at this stage, many cultural facilities are not equipped to hold large-scale cultural activities. Among them, the municipal and district-level cultural facilities have the equipment and conditions to hold rich cultural activities, but the publicity of cultural activities is not good, and ordinary citizens have a weak sense of participation. Activities such as art competitions are mostly participated in through cultural groups; the form of knowledge lecture activities is single and the types are insufficient. The cultural activities held in the grassroots cultural facilities are closer to the community residents, such as traditional festival celebrations and performing arts activities, but the activities carried out have a greater relationship with the management level of the community, and the situation of different communities is quite different.Among them, the users of cultural facilities in the main urban area of City A include urban residents and tourists from outside the city. The cultural facilities participated in by tourists from outside the city are mainly cultural and museum facilities supported by historical and natural cultural resources and landmark large-scale cultural exhibition venues. Their main purpose is to visit mainly, is a one-time use behavior, and has greater mobility. Although the number of users of cultural venues has been greatly increased, it is not considered in this paper. This article mainly considers the use of cultural facilities by urban residents.City-level cultural facilities have rich functions, comfortable environment, and strong attractiveness, so the residents use the composition that is relatively rich and residents of all ages have. At the district level and below, the majority of users of cultural facilities are old men and young people. Young people are more willing to engage in consumer cultural and entertainment activities, and middle-aged people use it less frequently during working days. Within 20 minutes of travel distance, residents are more willing to go to higher-level cultural facilities for cultural activities. Figure10 shows the evaluation of the utilization rate of cultural facilities in the main urban area of City A, where 1 represents very good, 2 represents good, 3 represents fair, 4 represents not good, and 5 represents very bad.Figure 10
Evaluation of the utilization rate of cultural facilities in the main urban area of City A.In actual research, it was found that the actual use of cultural facilities differed significantly. Among them, the utilization rate of city-level cultural facilities scored 77, the utilization rate of district-level cultural facilities scored 72, the utilization rate of street-community cultural facilities scored 69, and the overall evaluation score was 70. Among them, municipal-level cultural facilities are generally more efficient due to their relatively complete functions, and municipal-level cultural facilities can attract residents who are far away. The use efficiency of district-level cultural facilities is closely related to its own hardware configuration, and the use efficiency varies greatly, and the use efficiency gap of street-community-level cultural facilities is relatively obvious. Among them, the use efficiency of street-level cultural facilities is higher than that of community cultural sites, and the use rate of cultural facilities in high-end residential areas is higher than that in residential areas with lower construction levels.


### 3.2. The Evolution Law of Urban Spatial Morphology Based on Particle Swarm Optimization Algorithm

The spatial expansion and evolution of City A are the result of the mutual influence of many factors. According to relevant data, the topography, location, transportation, economy, policy, and other factors of the city have jointly affected the spatial expansion of the city. Economic development will inevitably lead to urban expansion. At the same time, economic development also needs the support of urban land. According to the regression analysis of the total fixed asset investment, GDP, gross industrial production value, tertiary industry gross production value, and construction land of City A in the urban area of City A, it is found that the total fixed asset investment, GDP, industrial production value, tertiary industry production value of the whole society, and the construction land area of City A all show a certain positive correlation, as shown in Table1. This means that there is a close connection between economic development and urban spatial expansion.Table 1
The relationship between the economic development and construction area of City A.
Total investment in fixed assets of the whole society (10 million yuan)Construction land area (km2)GDP (ten million yuan)Construction land area (km2)Industrial production value (10 million yuan)Construction land area (km2)GDP of the tertiary industry (10 million yuan)Construction land area (km2)01000001000100100003502000034020000400100003402000042040000530400004902000044030000500600007006000052030000520Selecting the social and economic conditions of City A in recent years for data statistics and using multiple stepwise regression modeling to study the degree of influence of economic and social factors on urban spatial expansion and evolution, the dependent variable is the area of the urban built-up area.The explanatory variables include 13 indicators: urban population, GDP, GDP per capita, total investment in fixed assets, total retail sales of consumer goods, industrial production, secondary industry production, urban road construction length, road construction area, and real estate investment total, the total sales of commercial housing, the number of students in colleges and universities, and the GDP of the tertiary industry.It can be seen from Table2 that since the value of the R2 coefficient increases with the increase in the number of independent variables in the regression equation, the value of the R2 coefficient cannot be used as an indicator to reflect the accuracy of the model. However, the modified R2 value is not directly related to the number of variables, so it can be used as an index to judge the fitness. Combining R2 and modified R2, it can be seen that the regression equation has a relatively good fit.Table 2
Summary of the fitting process.
ModelRR-squareAdjustR-squaredError in standard deviation estimate10.9910.9820.98117.000120.9990.9990.9994.4574310.9990.9993.9863410.9990.9993.4967Table3 shows the results of the analysis of variance at each step in the regression fitting process. It can be seen from the table that when the regression equation contains different independent variables, the significance probability values are all less than 0.001, so the regression equation should include these 4 variables.Table 3
Analysis of variance.
ModelSum of squaresdfMean squareF1Regress360236.2131360785.3611256.734Residual error6602.50123291.326—2Regress367089.7362179368.9868796.501Residual error449.9672219.986—3Regress369782.1523119867.9617308.496Residual error349.1372117.062—4Regress359876.787489978.8677362.612Residual error251.412011.698—Table4 shows the results of each step of the regression equation process. The significance levels of the constant term, the number of college students, and the total real estate investment are less than 0.001, and the significance levels of the urban population and the total sales of commercial housing are 0.005 and 0.009, respectively. The fitted equation satisfies the requirements of linearity and homogeneity of variance and has a good fitting effect, which can be used to explain the internal driving mechanism of urban spatial expansion and evolution.Table 4
Regression coefficient table.
ModelNonstandardized coefficientStandard coefficientTBStandard errorBetaConstant89.86535.936—15.023Number of students in institutions of higher learning0.00301200.90940.002Total real estate investment0.0501210.0040.29113.061Urban population−0.0863120.031−0.079−3.098Total sales of commercial housing−0.0132710.004−0.078−3.012This section analyzes the internal mechanism of urban spatial expansion from the aspects of economy, population, and transportation development and selects 13 influencing factors to analyze the influence mechanism of urban spatial expansion and evolution. Taking the area of urban construction area as the dependent variable and 13 influencing factors as variables, the stepwise regression fitting calculation is carried out. From the equation obtained, it can be seen that the expansion of urban space is mainly linearly related to factors such as the number of students in colleges and universities, the total real estate investment, the urban population, and the total sales of commercial housing. This shows that the number of college students, total real estate investment, urban population, and total commercial housing sales have a significant impact on the expansion and evolution of urban space.


## 3.1. Evaluation of the Performance of Urban Cultural Facilities Allocation Based on Particle Swarm Optimization Algorithm

This paper aims to construct and analyze the plane space pattern of urban culture based on the particle swarm cultural scientific computing algorithm. Particle swarm intelligence algorithm generally has good versatility. Due to the variety of practical application problems, the mathematical properties of many of them are difficult to determine. The optimization process of particle swarm intelligence algorithm does not depend on the strict mathematical properties of the problem itself, such as continuity and derivability. It also does not need precise mathematical description of objective function and constraints, which makes the particle swarm intelligence algorithm have better generality.The urban cultural facility system is a system composed of multiple types and multiple levels. The evaluation of the fairness of its facilities must first consider the integrity of its functional structure in each area of the city. It is used to judge whether it can meet the multilevel cultural needs of urban residents. The functional settings of cultural facilities mainly include reading and reading, cultural performances, knowledge lectures, cultural exhibitions, leisure and entertainment, and cultivating sentiments. Urban residents of different backgrounds have different preferences for cultural functions. The evaluation of the rationality of cultural facilities functions is mainly judged from the perspective of residents’ needs.This paper takes the results of the questionnaire as the basis for the evaluation of the index and divides the evaluation of the functional rationality of cultural facilities in the questionnaire into five levels: very reasonable, relatively reasonable, general, unreasonable, and very unreasonable. Figure5 is a statistical chart of the rationality evaluation of cultural facilities in City A.Figure 5
Evaluation of functional rationality of cultural facilities in City A.The quality of cultural facilities mainly refers to the quality of physical buildings. Evaluation factors include building appearance, internal environment, lighting and ventilation, and fire safety. The evaluation of this indicator is based on the perception of users of cultural facilities. In the questionnaire, five levels of quality, good, good, fair, poor, and very poor are set. Figure6 shows the physical quality evaluation of cultural facilities in City A.Figure 6
Physical quality evaluation of cultural facilities in City A.Through field investigations, it was found that the physical quality of large-scale cultural facilities in City A is better, and the environment comfort is higher. Among them, the newly built venues such as the City A Library, the Cathay Pacific Art Center, and the Natural History Museum have a grand appearance, spacious and comfortable interior space, full lighting, ventilation, and lighting facilities, and the fire exits comply with the architectural markings and are highly safe; although the facades of old venues such as Children’s Palace and the Mass Art Center are somewhat obsolete, the internal use space is repaired in real time and can perform better functions. Figure7 shows the physical map of cultural facilities in City A.Figure 7
Physical map of cultural facilities in City A.The quality of district-level cultural facilities is quite different, and the construction of district-level cultural centers and libraries has been paid more attention. In addition, the construction of the district-level elderly activity center is relatively lagging, and the update status is not good, resulting in the breakdown of the building entity and the problems of hardware facilities such as air conditioning and lighting. Among the basic cultural facilities, the construction quality of the sublibraries of the district-level cultural facilities belonging to the street level is better. The flow of people is attracted by the newly built cultural facilities with high environmental quality, and the dilapidated old community has become a settlement for the elderly with low economic conditions and low education level. This has led to the decline of cultural spaces in traditional communities.Environmental comfort mainly describes the creation of cultural atmosphere. It evaluates the quality of cultural facilities based on higher-level human psychological cognition to measure whether the activity space, environment construction, and software equipment of cultural facilities can be used comfortably by residents. The evaluation of this indicator is based on the experience of users of cultural facilities. Five levels are set in the questionnaire: very comfortable, relatively comfortable, average, not very comfortable, and very uncomfortable. Corresponding the evaluation results to the scores of each level in the questionnaire, calculate the quantifiable scores. Figure8 shows a statistical diagram of the environmental comfort evaluation of cultural facilities in the main urban area of City A.Figure 8
Evaluation of the environmental comfort of cultural facilities in the main urban area of City A.The five factors influencing the configuration of cultural facilities mentioned above include cultural activities. The development of cultural activities is of great significance to the improvement of residents’ utilization rate and the creation of cultural atmosphere. In addition, the development of cultural activities is closely related to the measurement of the service level of cultural facilities, describing from the side whether the hardware and software of cultural facilities can support the development of cultural activities. The evaluation of this indicator is based on the participation of users and the cultural activity data provided by the staff. The research set up five levels in the questionnaire: good, good, fair, not very good, and very bad. Corresponding the evaluation results to the scores of each level in the questionnaire, calculate a quantifiable score.The activities of cultural facilities in City A mainly include knowledge lecture activities carried out by book-reading facilities, calligraphy and painting exhibitions and publicity activities carried out in cultural and cultural exhibition facilities, festivals, cultural performances, and cultural competitions carried out in cultural activities facilities. Figure9 is a statistical chart of the evaluation of the development of cultural activities in the main urban area of City A.Figure 9
Evaluation of the development of cultural activities in the main urban area of City A.Residents’ cultural activities are generally organized by cultural departments and spontaneously formed. Activities in large-scale cultural venues are mostly in the form of lectures and exhibitions, and activities organized by grassroots cultural venues are mostly carried out in the activity venues of streets and communities or open spaces in the community. In the in-depth interviews at various research sites, it was found that residents have a strong demand for cultural activities, but at this stage, many cultural facilities are not equipped to hold large-scale cultural activities. Among them, the municipal and district-level cultural facilities have the equipment and conditions to hold rich cultural activities, but the publicity of cultural activities is not good, and ordinary citizens have a weak sense of participation. Activities such as art competitions are mostly participated in through cultural groups; the form of knowledge lecture activities is single and the types are insufficient. The cultural activities held in the grassroots cultural facilities are closer to the community residents, such as traditional festival celebrations and performing arts activities, but the activities carried out have a greater relationship with the management level of the community, and the situation of different communities is quite different.Among them, the users of cultural facilities in the main urban area of City A include urban residents and tourists from outside the city. The cultural facilities participated in by tourists from outside the city are mainly cultural and museum facilities supported by historical and natural cultural resources and landmark large-scale cultural exhibition venues. Their main purpose is to visit mainly, is a one-time use behavior, and has greater mobility. Although the number of users of cultural venues has been greatly increased, it is not considered in this paper. This article mainly considers the use of cultural facilities by urban residents.City-level cultural facilities have rich functions, comfortable environment, and strong attractiveness, so the residents use the composition that is relatively rich and residents of all ages have. At the district level and below, the majority of users of cultural facilities are old men and young people. Young people are more willing to engage in consumer cultural and entertainment activities, and middle-aged people use it less frequently during working days. Within 20 minutes of travel distance, residents are more willing to go to higher-level cultural facilities for cultural activities. Figure10 shows the evaluation of the utilization rate of cultural facilities in the main urban area of City A, where 1 represents very good, 2 represents good, 3 represents fair, 4 represents not good, and 5 represents very bad.Figure 10
Evaluation of the utilization rate of cultural facilities in the main urban area of City A.In actual research, it was found that the actual use of cultural facilities differed significantly. Among them, the utilization rate of city-level cultural facilities scored 77, the utilization rate of district-level cultural facilities scored 72, the utilization rate of street-community cultural facilities scored 69, and the overall evaluation score was 70. Among them, municipal-level cultural facilities are generally more efficient due to their relatively complete functions, and municipal-level cultural facilities can attract residents who are far away. The use efficiency of district-level cultural facilities is closely related to its own hardware configuration, and the use efficiency varies greatly, and the use efficiency gap of street-community-level cultural facilities is relatively obvious. Among them, the use efficiency of street-level cultural facilities is higher than that of community cultural sites, and the use rate of cultural facilities in high-end residential areas is higher than that in residential areas with lower construction levels.


## 3.2. The Evolution Law of Urban Spatial Morphology Based on Particle Swarm Optimization Algorithm

The spatial expansion and evolution of City A are the result of the mutual influence of many factors. According to relevant data, the topography, location, transportation, economy, policy, and other factors of the city have jointly affected the spatial expansion of the city. Economic development will inevitably lead to urban expansion. At the same time, economic development also needs the support of urban land. According to the regression analysis of the total fixed asset investment, GDP, gross industrial production value, tertiary industry gross production value, and construction land of City A in the urban area of City A, it is found that the total fixed asset investment, GDP, industrial production value, tertiary industry production value of the whole society, and the construction land area of City A all show a certain positive correlation, as shown in Table1. This means that there is a close connection between economic development and urban spatial expansion.Table 1
The relationship between the economic development and construction area of City A.
Total investment in fixed assets of the whole society (10 million yuan)Construction land area (km2)GDP (ten million yuan)Construction land area (km2)Industrial production value (10 million yuan)Construction land area (km2)GDP of the tertiary industry (10 million yuan)Construction land area (km2)01000001000100100003502000034020000400100003402000042040000530400004902000044030000500600007006000052030000520Selecting the social and economic conditions of City A in recent years for data statistics and using multiple stepwise regression modeling to study the degree of influence of economic and social factors on urban spatial expansion and evolution, the dependent variable is the area of the urban built-up area.The explanatory variables include 13 indicators: urban population, GDP, GDP per capita, total investment in fixed assets, total retail sales of consumer goods, industrial production, secondary industry production, urban road construction length, road construction area, and real estate investment total, the total sales of commercial housing, the number of students in colleges and universities, and the GDP of the tertiary industry.It can be seen from Table2 that since the value of the R2 coefficient increases with the increase in the number of independent variables in the regression equation, the value of the R2 coefficient cannot be used as an indicator to reflect the accuracy of the model. However, the modified R2 value is not directly related to the number of variables, so it can be used as an index to judge the fitness. Combining R2 and modified R2, it can be seen that the regression equation has a relatively good fit.Table 2
Summary of the fitting process.
ModelRR-squareAdjustR-squaredError in standard deviation estimate10.9910.9820.98117.000120.9990.9990.9994.4574310.9990.9993.9863410.9990.9993.4967Table3 shows the results of the analysis of variance at each step in the regression fitting process. It can be seen from the table that when the regression equation contains different independent variables, the significance probability values are all less than 0.001, so the regression equation should include these 4 variables.Table 3
Analysis of variance.
ModelSum of squaresdfMean squareF1Regress360236.2131360785.3611256.734Residual error6602.50123291.326—2Regress367089.7362179368.9868796.501Residual error449.9672219.986—3Regress369782.1523119867.9617308.496Residual error349.1372117.062—4Regress359876.787489978.8677362.612Residual error251.412011.698—Table4 shows the results of each step of the regression equation process. The significance levels of the constant term, the number of college students, and the total real estate investment are less than 0.001, and the significance levels of the urban population and the total sales of commercial housing are 0.005 and 0.009, respectively. The fitted equation satisfies the requirements of linearity and homogeneity of variance and has a good fitting effect, which can be used to explain the internal driving mechanism of urban spatial expansion and evolution.Table 4
Regression coefficient table.
ModelNonstandardized coefficientStandard coefficientTBStandard errorBetaConstant89.86535.936—15.023Number of students in institutions of higher learning0.00301200.90940.002Total real estate investment0.0501210.0040.29113.061Urban population−0.0863120.031−0.079−3.098Total sales of commercial housing−0.0132710.004−0.078−3.012This section analyzes the internal mechanism of urban spatial expansion from the aspects of economy, population, and transportation development and selects 13 influencing factors to analyze the influence mechanism of urban spatial expansion and evolution. Taking the area of urban construction area as the dependent variable and 13 influencing factors as variables, the stepwise regression fitting calculation is carried out. From the equation obtained, it can be seen that the expansion of urban space is mainly linearly related to factors such as the number of students in colleges and universities, the total real estate investment, the urban population, and the total sales of commercial housing. This shows that the number of college students, total real estate investment, urban population, and total commercial housing sales have a significant impact on the expansion and evolution of urban space.


## 4. Discussion

There is a close relationship between urban cultural strategy and space construction, because urban cultural strategy often must have a load on the medium to be effectively expressed, and one of the main manifestations of space load is the urban cultural landscape space. In fact, the spatial change of the urban cultural landscape is also the most intuitive effect in the urban cultural strategy. According to the scale classification of urban space, the spatial effect is mainly manifested in the emergence of historical and cultural gathering areas, the renewal of historical and cultural spaces, and the increase of historical and cultural spaces in isolation and historical and cultural landmark systems. Urban spatial structure refers to the interrelationship of important components such as the material environment, social function activities, and human values in the city. The expansion and evolution of City A’s morphological structure are affected by natural conditions, traffic factors, economic development, population growth, government regulation, and other factors. This paper selects 13 variable indicators such as urban population, GDP, and GDP per capita from the aspects of transportation, population, and economy and uses the stepwise regression analysis method for in-depth study and analysis of the impact mechanism of 13 factors on urban expansion and evolution. From the results of multiple regression analysis, the number of students in urban colleges and universities, the total real estate investment, the urban population, and the total sales of commercial housing have a significant impact on the expansion and evolution of the urban spatial structure. Among them, the number of students in urban institutions of higher learning is the most important factor driving the spatial expansion and evolution, followed by the total real estate investment, urban population, and total commercial housing sales.


## 5. Conclusions

In the context of the global economic and cultural globalization of the world, cultural soft power has become a concentrated expression of the overall strength of the economy and cities.At the same time, in order to respond to the development needs of the cultural industry and establish a public service-oriented government, public and benefit-oriented urban cultural infrastructure planning will be adopted to fill the gaps in the contradiction between supply and demand in the construction of cultural industries. At the same time, in order to achieve the fairness and efficiency of the urban cultural infrastructure planning and construction process, research and analysis have been carried out on the evaluation of the urban cultural infrastructure configuration performance. It is found that the actual use of cultural facilities is significantly different, and the municipal cultural facilities are generally more efficient due to their relatively complete functions. In addition, municipal cultural facilities can attract the use of residents who are far away. The use efficiency of district-level cultural facilities is more related to its own hardware configuration, and the use efficiency varies greatly. In this regard, it is particularly important to eliminate the difference in the use of cultural facilities between urban and rural areas. Carrying out the evaluation of the configuration performance of urban cultural infrastructure is of great significance for understanding the current situation and determining the direction of urban planning. Based on the particle swarm algorithm, this paper simulates the cultural space users as a flock of birds and the urban cultural space as food and simulates the behavior of seeking cultural facilities as birds searching for food. Based on the results of this survey and research, the utilization rate of public cultural facilities in City A is 77, the utilization rate of district-level cultural facilities is 72, the utilization rate of street-community cultural facilities is 69, and the overall evaluation score is 70. The actual use of cultural facilities varies significantly, so it is particularly important to eliminate the differences in the use of cultural facilities between urban and rural areas. Among them, this article is limited by graphic data and does not make further detailed research on the administrative office, scientific research design, culture and entertainment, sports and health, and other urban functional lands in the municipal facility land. This part will be studied in the future work and study.



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*Source: 9838782-2022-03-14.xml*