Research on sustainable design of sports centre based on algorithm verification

Cluster analysis is to establish a classification method to automatically classify a batch of sample data (or variables) according to their affinity in nature without prior knowledge [4]. In the design of sustainable sports centre, the strategy of venue merger design is often adopted to make efficient use of resources. Among them, the size and functional efficiency of venues are important parameters for the merger of venues. Therefore, this paper attempts to judge whether it is suitable for the combined design by cluster analysis of the two elements of venue scale and functional efficiency of the sports centre. According to the distance-based cluster analysis algorithm, the venues of the sports centre are numbered respectively, and the size of the venues is set as the x-value parameter and the function efficiency is set as the y-value parameter. In terms of size parameters, if 100 seats are assigned as 1 point, 10000 seats will be 100 points. In terms of function parameters, the high frequency of function use is 100-80 points, generally frequency is 80-60 points and the low frequency is less than 60 points. After assignment, cluster calculation is carried out according to the square educated distance equation:

That is, SEUCLID(x,y)=∑i=1k(xi−yi)2 {\rm{SEUCLID}}\left( {{\rm{x}},{\rm{y}}} \right) = \sum\nolimits_{i = 1}^k {\left( {{x_i} - {y_i}} \right)^2}

The distance between two samples (x, y) is the sum of squares (k variables) of the difference between each variable value of each sample. Through calculation, it is concluded whether there is obvious clustering effect between the venues of the sports centre, which is suitable for combined design.

The main theory of spatial analysis using spatial syntax is called ‘spatial syntax theory’. This theory was proposed by Bill Hillier and others. Taking spatial ontology as the research object, it makes quantitative analysis and visual expression of spatial form through indicators such as integration, traversal and intelligence. It is a method that attempts to explain and quantitatively express space from the behaviour of people in space and the topology structure of spatial ontology [5]. Years of empirical studies have shown that space syntax as an algorithm for the quantitative description of street space topology has a good correlation with the distribution of various traffic movements and active functions in the city [6].

SDNA is a spatial syntax calculation software embedded in GIS developed by the research team of Cardiff University. It improves the traditional spatial syntax graph theory, emphasising the dual topological relationship between ‘points’ and ‘lines’ in spatial networks, and when calculating, the road network deflection angle and Euclidean distance can be weighted at the same time, so that the calculation method is conceptually closer to the urban road network analysis with a certain scale and complexity. Combined with the analysis ability of GIS, it has a wide range of application prospect in the field of urban planning [7]. Among them, the key evaluation indexes are closeness degree and betweeness degree, and the evaluation index related to space is Moran index. Combined with yolo-v3 and DeepSnRh algorithms of deep learning, spatial syntax can also provide a broader perspective for environmental space research [8].

Closeness degree represents the difficulty of a road network to the rest of the road network within the search radius. The road network with high integration usually has a high integration ability in the region and has greater attraction to the crowd. In SDNA, the closeness degree is expressed by NQPDAn (n represents the calculated road network radius), and its calculation equation is as follows: NQPDA(x)=∑y∈Rxp(y)d(x,y) NQPDA(x) = \sum\limits_{y \in Rx} {{p(y)} \over {d(x,y)}} Where: P (y) is the weight of node y in search radius R. in continuous space analysis, P (y) ∈ [0,1], and in discrete space analysis, P (y) is 0 or 1; d (x, y) is the shortest topological distance from node x to node y; NQPDA (x) is the degree of integration.

Betweeness degree is also an important parameter (hPBt) provided by SDNA. It is usually used to measure the probability that the road network has been through the traffic flow within the search radius. The higher the betweeness degree, the greater the probability that the road network has been selected to pass through, bearing the role of rapid traffic rather than stay aggregation. Different from the integration degree, the former emphasises the arrival, while the betweeness degree represents trafficability. Its calculation equation is: OD(y,z,x)={1,x is on the shortest path from y to Z12,x≡y≢z12,x≢y≡z13,x≡y≡z0,other situations OD(y,z,x) = \left\{ {\matrix{ {1,} \hfill & {x\;{\rm{is}}\;{\rm{on}}\;{\rm{the}}\;{\rm{shortest}}\;{\rm{path}}\;{\rm{from}}\;y\;{\rm{to}}\;Z} \hfill \cr {{1 \over 2},} \hfill & {x \equiv y \nequiv z} \hfill \cr {{1 \over 2},} \hfill & {x \nequiv y \equiv z} \hfill \cr {{1 \over 3},} \hfill & {x \equiv y \equiv z} \hfill \cr {0,} \hfill & {{\rm{other}}\;{\rm{situations}}} \hfill \cr } } \right. TPBt(x)=∑y∈N∑z∈RyOD(y,z,x)P(z)Links(y) TPBt(x) = \sum\limits_{y \in N} \sum\limits_{z \in Ry} OD(y,z,x){{P(z)} \over {Links(y)}} where OD (y, Z, x) is the total number of nodes passing through node X within the search radius r, Links (y) is the total number of nodes within the search radius r of each node y, and P (z) is the weight of node Z.

Moran's I coefficient is an important means to measure spatial correlation, and its operation equation is: I=nS0∑i=1n∑j=1nwi,jzizj∑i=1nzi2 I = {n \over {{S_0}}}{{\sum\limits_{i = 1}^n \sum\limits_{j = 1}^n {w_{i,j}}{z_i}{z_j}} \over {\sum\limits_{i = 1}^n z_i^2}} where Z_i is the deviation between the attribute of element i and its average value (xi−X¯) \left( {{x_i} - \overline X } \right) , W_i,j is the spatial weight between elements i and j, n is equal to the total number of elements, and S0 is the aggregation of all spatial weights.

With the analysis of spatial syntax, we can verify the relationship between the urban spatial closeness degree and betweeness degree of sports centre and its contribution to the sustainable development of urban public space, so as to provide reference for the design of Sports Centre in the future.

Urban stadiums and gymnasiums often need a large volume to meet their needs as urban landmarks; However, too large volume and scale will cause waste of construction cost and future operation cost. Therefore, how to coordinate the contradiction between them is a problem that needs to be solved in design.

In recent years, the scale setting of new sports centres in China has been blindly greedy. Taking the seat size of stadiums as an example, this paper analyses the case data of 13 new town sports centres newly built in recent years. More than half of the stadiums have more than 50,000 seats, 1/3 have between 40,000 and 50,000 seats, and only about 15% have less than 40,000 seats. This is particularly evident in the construction of the Sports Centre Gymnasium in the new city. These large-scale sports centres are difficult to hold events matching their scale and specifications in practical use. On the contrary, they are vacant for a long time, affecting urban development. Therefore, the venue scale of the Sports Centre shall be reasonably formulated according to the needs of urban development.

The Kunming Mingxing Sports Centre is an earlier case of adopting the design idea of ‘all-in-one venues’ to solve this contradiction. In addition, there is also the Shenyang Olympic Sports Centre. The former includes a stadium and a gymnasium. In view of the high use of gymnasium and the low utilisation rate of stadiums, the seat size of the easier-to-operate gymnasium was adjusted to 10,000, and the seat size of the stadium was reduced to 10,000. On this basis, the stadium and the gymnasium were combined. The Shenyang Olympic Sports Centre combined a natatorium with a tennis stadium because of a similar scale and low utilisation rate.

Number and assign virtual values to the four types of venues with high frequency set in the sports centre. Among them, No. 01 is the stadium, No. 02 is the stadium, No. 03 is the natatorium and No. 04 is the tennis stadium. With reference to the venues of Kunming Xingyao sports centre and Shenyang Olympic Sports Centre, and combined with the scale and universal functional use of four types of venues, the clustering elements (x, y) of venues are assigned. Based on years of research experience, the utilisation rate of gymnasiums in sports centres is generally higher than that of stadiums and tennis courts; The utilisation rate of natatoriums is related to the regional characteristics of the South and the north. Generally, the utilisation rate of natatoriums in the south is high while in the north it is low. As Shenyang is located in the north and the sports centre is located in the suburbs, the accessibility is low, so the functional parameters of the natatorium need to be assigned a lower value. Finally, 01 (100, 60), 02 (100, 90), 03 (20, 60), 04 (40, 50) are assigned. After clustering calculation, it is concluded that the clustering effect between natatorium and tennis hall is the most obvious, only 500; The clustering distance between small stadiums and large stadiums is 900, which are obvious and suitable for combined setting (Table 1).

The design starting point of Kunming Xingyao sports centre is ensuring the ability to hold large-scale activities by improving the scale of the gymnasium with high utilisation rate; Reduce the construction scale of stadiums with low utilisation rate to reduce the construction cost and daily operation consumption; The combined design of large gymnasium and small stadium further ensures the landmark of the sports centre needed by the city. Shenyang Sports Centre also combines the natatorium and tennis hall with low utilisation rate in order to improve the overall utilisation efficiency. Through the cluster analysis in calculations, it can be concluded that the two designs are quite reasonable. It has been proved by practice; the reasonable venue scale control and the combination of venues enable Kunming Xingyao sports and Shenyang Olympic Sports Centre to maintain their sustainable development with lower daily operating expenses and higher operating income under a small land scale [9]. However, if the venue integration design is not appropriate, the expected purpose may not be achieved. Therefore, the use of cluster analysis in the integrated design and planning of stadiums and gymnasiums will help to provide effective judgement support on how to merge stadiums and gymnasiums, and ensure the feasibility of merging stadiums and gymnasiums and the sustainability of the development of sports centres in the future.

Verifying the accessibility of sports centres that promote urban development through spatial syntax, it can be found that high accessibility is an important feature of these sports centres. Take Tianhe Sports Centre as an example. Tianhe Sports Centre is an important case that has a positive effect on urban development in China, making the area around the sports centre in Tianhe District of Guangzhou from farmland in the 1980s to the current urban core area. Through the spatial algorithm calculation of different metric radius (800m, 1500m, 2000m and 3000m) of Tianhe Sports Centre and surrounding street network, the results show that the sports centre is located in the high accessibility area of the area under different scales of walking radius, public transport travel radius and vehicle travel radius (Figure 1). Taking the global closeness degree and global betweeness degree as indicators, the standard deviation ellipse is created to summarise the spatial characteristics of geographical elements (central trend, dispersion and direction characteristics, including 68% of the calculation results). It is found that Tianhe Sports Centre is located in the centre of the two indicators and is completely included, indicating that the sports centre is the centre point of arrival traffic in the region, and it dominates the surrounding street network (Figure 2).

Fig. 1

Fig. 2

Based on the algorithm and combined with the surrounding traffic conditions, it is found that there are 4 rail transit passing by and 6 subway stations; the ground public transportation is also convenient. There are 22 urban bus stops around, including 10 BRh stops on Tianhe Road, the main urban transportation road in the south. The accessibility is improved through convenient public transport distribution, which strengthens the convenience and willingness of citizens to reach the area.

It can be said that high accessibility is a necessary means to ensure the effective role of sports centres. Due to the large area of the sports centre, with the development of the city, the high land price in the old urban area is obviously difficult to support the construction of the new sports centre. Therefore, new sports centres are often located at the periphery of the city or in the start-up area or core area of the new city. However, regardless of the site selection, the sports centre is often far away from the existing mature urban areas, and the development degree of the surrounding plots is often not high when it is put into use. Therefore, accessibility is an important problem that must be solved to realise the sustainable coupling between sports centre and city. During the planning of the new sports centre in the future, it is necessary not only to ensure accessibility through urban space design and road network design, but also to introduce large or medium volume public transport through the improvement of transportation supporting facilities, so as to improve accessibility and meet the needs of daily operation when the sports centre undertakes large-scale competitions and after competitions.

Urban function combination refers to the compatible state of multiple urban functions in a certain space and time range. It is the result of the mixing of different land use modes, functional layout, business forms and spatial forms. Its significance lies in the provision of supportive services between functions [10]. The city is an organism, and each plot will be related to the surrounding plots. Compound function and symbiosis are a basic concept followed by modern cities. In the planning stage, the residential, commercial and office facilities around the Sports Centre shall be provided, and other supporting facilities shall be improved. On the one hand, the users of the surrounding facilities are the potential users of the sports centre, on the other hand, these facilities can attract flow of people from other places together with the sports centre. The compound plot design strategy is conducive to the exertion of the sports function of the sports centre. For example, when Guangzhou built Tianhe Sports Centre, a large number of surrounding commercial and financial functional plots were designed. These plots also brought people flow to Tianhe Sports Centre, making Tianhe Sports Centre become the regional centre and development core of Tianhe District, driving the development of the whole urban area.

On the other hand, in addition to the composite function setting of sports, commerce, residence and other functions, from the perspective of spatial layout, the grid like spatial vitality pattern is conducive to the role of public services and can play an important role in promoting regional development. Using spatial syntax, this paper analyses the Moran index of Tianhe Sports Centre and its surrounding urban space. First, through the spatial autocorrelation analysis of the closeness degree operation value, the p value is 0, indicating that the result has statistical significance, and it can be considered that the regional network is clustered in the concept of closeness degree (Figure 3). Based on this, through the analysis of local Moran's index (local Moran's I, which is measured to identify statistically significant hot spots, cold spots and spatial outliers), it can be found that the sports centre is the core of gathering in the region, but the road network with high characteristics in the region is not completely attached to the sports centre, but also has a high degree of correlation with the surrounding grid plots, indicating that the surrounding areas have high vitality (Figure 4). Therefore, when there is no way to form a finer plot division within the sports centre, the efficient grid plot division of surrounding plots can make up for this deficiency.

Fig. 3

Fig. 4