Public sports facility layout optimization and exercise guidance method based on digital twinning

Abstract

The present application relates to the technical field of intelligent decision-making for social sports management, and in particular to a public sports facility layout optimization and sports guidance method based on digital twinning, which fuses community geographic information, resident sports behavior data and population structure data to construct a community sports space digital twinning model, and real-time maps a sports space state field composed of facility usage rate, people flow density and spatial accessibility; taking facility usage rate balance, per capita sports duration and fifteen-minute fitness circle coverage rate as the state space, and taking the double-sided action space composed of supply-side actions and demand-side actions as the decision variable, the agent is deduced by reinforcement learning optimization; the resident sports behavior spatiotemporal redistribution caused by demand-side guidance is written back to the sports space state field, so that the supply and demand sides iteratively game to joint convergence, and the layout optimization scheme and personalized sports behavior guidance strategy are output, and the demand-side guidance is promoted to optimization actions and cooperates with the supply side.

Description

Technical Field

[0001] This invention relates to the field of intelligent decision-making technology for social sports management, specifically to a method for optimizing the layout of public sports facilities and guiding exercise based on digital twins. Background Technology

[0002] The scientific allocation of community public sports facilities has become a core issue for social sports management departments. For a long time, the allocation of community public sports facilities has mainly relied on empirical standards such as per capita area and per thousand people, lacking quantitative analysis of residents' exercise behavior patterns and differences in spatial accessibility. This has resulted in a widespread supply-demand mismatch, with some areas having idle facilities and others experiencing insufficient supply. In recent years, using geographic information systems, mobile positioning data, and artificial intelligence algorithms to model and optimize facility supply and demand has gradually become an important technical approach to improve resource allocation efficiency.

[0003] Chinese patent application CN121787708A discloses a method for spatial identification, diagnosis, and optimization of urban residents' daily activities based on multi-agent supply and demand extrapolation. This method identifies residents' stops by clustering mobile phone location trajectories, constructs a decision network for residents' daily activities and travel using Markov chains and Logit utility functions, establishes facility demand and supply indices for each spatial unit based on resident agents, diagnoses supply and demand imbalances from spatial, temporal, and type dimensions, and uses the average supply and demand matching degree and optimization cost ratio across the entire region as the state space, a facility-side solution library consisting of function conversion, capacity expansion, new location additions, and level upgrades as the action space, and matching degree improvement and cost control as rewards. It uses reinforcement learning algorithms to extrapolate and output facility layout optimization schemes. However, this plan treats residents' sports needs as a relatively rigid unmet demand determined exogenously by historical behavior, limiting its action space to supply-side facility adjustments, and treating the spatiotemporal distribution of demand as an uncontrollable constraint. When faced with existing communities with no new construction land and limited room for adjustment of existing facilities, the action space on the supply side quickly dries up, making it difficult to achieve supply-demand matching without new construction or expansion. Thus, it cannot solve the core technical problem of supply-demand mismatch of sports facilities in existing communities when the room for adjustment on the supply side is exhausted.

[0004] Chinese patent application CN113592184B discloses a method and system for predicting suitable exercise spaces. This method, based on urban environmental factors such as normalized vegetation index, surface temperature, points of interest, sidewalks, and buildings, and combined with residents' movement trajectories, uses a maximum entropy model to calculate the exercise suitability of each grid within the study area. However, this scheme only provides static prediction and diagnosis of exercise suitability, neither outputting optimized facility layout schemes nor actively regulating the spatiotemporal distribution of residents' exercise needs. It also fails to address the issue of how to achieve supply-demand matching when supply-side adjustment space is exhausted.

[0005] It is evident that existing technologies generally assume that the mismatch between supply and demand for facilities can only be resolved by adjusting the supply side, treating residents' exercise needs as an exogenous and rigid constraint. This perception renders existing methods ineffective in established communities where supply-side action is limited, while truly low-cost regulatory levers—the spatiotemporal redistribution of residents' exercise needs guided by individual preferences—remain completely idle. Therefore, there is an urgent need for a public sports facility layout optimization method that can incorporate residents' exercise needs into the optimization loop and synergize with supply-side adjustments. Summary of the Invention

[0006] Addressing the core bottleneck in existing technologies regarding the allocation of community public sports facilities—the difficulty in matching supply and demand when the room for supply-side adjustments is exhausted—this invention provides a method for optimizing the layout of public sports facilities and guiding exercise based on digital twins. By elevating the guidance of residents' personalized exercise behavior to a demand-side action on par with supply-side adjustments, and enabling supply and demand to engage in iterative game-playing on the digital twin's exercise space state field, this method achieves the core objectives of balanced facility utilization and 15-minute fitness circle coverage from the perspective of optimizing the decision-making structure, without relying on the constraint of new construction land.

[0007] The technical solution of this invention is: a method for optimizing the layout of public sports facilities and guiding exercise based on digital twins, comprising the following steps: integrating community geographic information, resident exercise behavior data, and population structure data to construct a digital twin model of community sports space. This digital twin model maps the state field of each sports facility in real time. The state field includes facility utilization rate, pedestrian density, and spatial accessibility. The state space is defined by the balance of facility utilization rate, average exercise time per person, and coverage rate of the 15-minute fitness circle. The decision variables are the bilateral action space, and the rewards are the increase in resident participation rate and facility operating costs. A reinforcement learning-based optimization agent optimizes the digital twin model of the community sports space. The process involves deduction; the two-sided action space includes supply-side actions and demand-side actions. The supply-side actions include facility function replacement, shared time period adjustment, and new facility site selection recommendations. The demand-side actions are personalized exercise behavior guidance strategies that push nearby available facilities, available time periods, and suitable exercise types to residents. The spatiotemporal redistribution of residents' exercise behavior caused by the demand-side actions is written back into the exercise space state field. The written-back exercise space state field then drives the solution of the supply-side actions again. The supply-side actions and the demand-side actions iteratively play a game on the exercise space state field until both sides converge. The result is an optimized layout scheme for public sports facilities and the personalized exercise behavior guidance strategies.

[0008] The beneficial effects of this invention are as follows:

[0009] Firstly, this invention incorporates both demand-side and supply-side actions into the dual-action space of the reinforcement learning optimization agent. Compared to existing solutions that only adjust the supply side, this allows for supply-demand matching in existing communities without requiring additional land for construction. The mechanism is as follows: when the supply-side action space is depleted, residents' exercise needs are redistributed in time and space under personalized exercise behavior guidance strategies. This fills previously idle facilities and free time slots, and alleviates previously crowded facilities and peak times, effectively increasing the equivalent supply without changing the total number of facilities. This regulatory lever is treated as a fixed constraint and cannot be touched in existing solutions that only adjust supply-side facilities as the action space.

[0010] Secondly, this invention rewrites the spatiotemporal redistribution of residents' exercise behavior triggered by demand-side actions back into the exercise space state field. This allows supply-side and demand-side actions to iteratively interact within the same exercise space state field until both sides converge, achieving a synergistic effect superior to the sum of individual optimizations on either side. The mechanism is as follows: demand-side actions guide changes in the facility utilization distribution within the exercise space state field. This altered state field then re-drives the solution for supply-side actions. The new supply-side adjustments further alter the set of nearby available facilities, influencing the feasible domain of the next round of guidance strategies. The two sides form a bidirectional coupling through the shared exercise space state field. This coupling ensures that adjustments on both sides are mutually compatible rather than independent. The ultimately converged solution outperforms sequential solutions—either fixing demand first and then optimizing supply, or fixing supply first and then optimizing demand—in terms of coverage of the 15-minute fitness circle and the balance of facility utilization, demonstrating a significant synergistic effect.

[0011] Third, this invention collects actual response data of residents to personalized exercise behavior guidance strategies and estimates the elasticity of the exercise behavior guidance response based on this data. This elasticity is then used as a weight to rewrite the exercise space state field. The mechanism is as follows: whether residents accept the guidance is uncertain. If the rewrite is based on the ideal assumption that the guidance is fully adopted, the demand migration will be overestimated, thus misleading the supply side into under-construction and leading to actual congestion. This invention quantifies this response uncertainty, which is ignored by existing solutions, into an estimable and writable elasticity of the exercise behavior guidance response, making the rewritten exercise space state field approximate the actual demand migration and fundamentally ensuring the feasibility of the convergence result of the two-sided game. Attached Figure Description

[0012] Figure 1 This is an overall flowchart of the public sports facility layout optimization and exercise guidance method based on digital twins of the present invention;

[0013] Figure 2 This is a flowchart of the steps involved in constructing a digital twin model of a community sports space according to the present invention;

[0014] Figure 3This is a flowchart of the closed loop of writing back the state field of the bilateral action space and motion space of the present invention;

[0015] Figure 4 This is a flowchart of the motion behavior guided response elastic estimation and elastic weighted write-back steps of the present invention;

[0016] Figure 5 This is a flowchart of the hierarchical elasticity estimation and silent high-potential population identification steps of the present invention;

[0017] Figure 6 This is a flowchart of the dual-timescale coupled update steps of the reinforcement learning optimization agent in this invention. Detailed Implementation

[0018] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. The described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0019] This example uses a residential community in a city that was built relatively early and has no new construction land nearby as the application object. The community currently has several sports facilities, including a fitness trail, an outdoor multi-functional court, a public fitness equipment area, and a community gym. There is a supply-demand mismatch during morning and evening peak hours, where the fitness trail and court are overcrowded, while the gym and equipment area are relatively idle at the same time. The following is a breakdown of the application... Figure 1 The flowchart shown illustrates each step of the present invention’s method for optimizing the layout of public sports facilities and guiding exercise based on digital twins.

[0020] Step S1: Construct a digital twin model of the community sports space. For example... Figure 2 As shown, this step integrates community geographic information, resident exercise behavior data, and population structure data to construct a digital twin model of the community's sports space. The community geographic information includes the locations of sports facilities, road networks, and community boundaries, obtained from vector data provided by social sports management and planning departments. Resident exercise behavior data includes the frequency of use of fitness trails and the distribution of exercise times, obtained from historical records of the community sports service platform and anonymized aggregated data from wearable devices. Population structure data includes age composition and population density, obtained from community registration records.

[0021] When constructing a digital twin model of community sports space, the community boundary is first projected and transformed according to a unified spatial reference, and divided into regular grids with a side length of 50m as the smallest spatial statistical unit. Then, sports facility locations, road networks, and population structure data are linked to corresponding grids according to geographical location, and residents' exercise behavior data is aggregated to corresponding grids according to time periods, forming a one-to-one mapping of the community's physical space in the digital space. Based on this, the digital twin model of community sports space maps the sports space state field of each sports facility in real time. The sports space state field includes three components: facility utilization rate, pedestrian density, and spatial accessibility. Facility utilization rate is the ratio of the actual number of people a sports facility can accommodate per unit time period to its designed capacity; pedestrian density is the ratio of the number of people active in a grid per unit time period to the area of ​​that grid, expressed as people per square meter; spatial accessibility is the road network distance or travel time required for residents to reach a sports facility from their residential grid by walking. In this embodiment, the travel time is converted using a walking speed of 1.2m / s.

[0022] In the specific processing of data fusion, since the sources of community geographic information, resident exercise behavior data, and population structure data are different, and their coordinate systems and time granularities are not the same, this step first performs spatial registration and projection transformation on the three types of data to unify them into the same plane coordinate system. Then, the three types of data are linked to the corresponding grids using grid numbers as the association key. Missing grids are filled in using inverse distance weighted interpolation, and outliers are removed using box plot criteria, thus forming a complete and consistent digital twin model base for community exercise space. On this base, sports facilities are abstracted into facility entities with attributes of type, capacity, and opening hours; residents are abstracted into resident groups with attributes of residential grids, age stratification, and exercise preferences; and the road network is abstracted into an accessibility map with attributes of road segment length and traffic. The three together support the real-time calculation of the exercise space state field.

[0023] The mappings of facility utilization, pedestrian density, and spatial accessibility mentioned above are all statistical mappings based on real-time and historical data, which are mature data processing methods in this field and can be updated on a rolling basis according to time periods. It is important to emphasize that the aforementioned motion space state field is not a simple listing of three components, but rather a unified physical carrier for the joint action of supply and demand: supply-side actions directly rewrite the facility utilization and spatial accessibility components by changing the type, capacity, and opening hours of the facility entity; demand-side actions indirectly rewrite the facility utilization and pedestrian density components by guiding the movement direction and time of residents. It is precisely because both supply and demand actions are grounded in the same motion space state field that they can couple on this state field. As a shared coupling carrier for subsequent supply and demand actions, each component of the motion space state field is organized according to a uniform time period granularity (in this embodiment, 2 hours is taken as a time period, and a day is divided into 12 time periods) to ensure that supply-side and demand-side actions exert influence on the motion space state field at the same spatiotemporal resolution, avoiding misalignment of supply and demand actions due to inconsistent spatiotemporal resolution.

[0024] Step S2: Construct the state space. This step uses the facility utilization balance, average exercise time per person, and 15-minute fitness circle coverage rate to optimize the agent's state space through reinforcement learning.

[0025] The facility utilization uniformity is obtained by normalizing the standard deviation of the facility utilization rate of each sports facility and then taking a negative mapping. The larger the value, the more uniform the distribution of facility utilization rates. In this embodiment, the facility utilization rate of all sports facilities in the community is first statistically analyzed within a certain period, and its standard deviation is calculated. Then, the maximum standard deviation of facility utilization rate in the community's history is used as a benchmark for normalization to make it fall within the range of 0 to 1. Finally, 1 minus the normalized standard deviation is taken as the facility utilization uniformity. This calculation is a conventional method for statistically analyzing dispersion and can be performed on a rolling basis over time periods.

[0026] The 15-minute fitness circle coverage rate uses a 15-minute walk as the threshold, and counts the proportion of residents who can reach at least one sports facility out of the total number of residents in the community. In this embodiment, the reachable road network distance is calculated to be approximately 1080m based on a walking speed of 1.2m / s and a walking time of 15 minutes. Based on this, the set of sports facilities reachable within this distance is calculated for each residential grid. If the set is not empty, the residents of that grid are included in the reachable population. Finally, the ratio of the reachable population to the total number of residents in the community is used as the 15-minute fitness circle coverage rate.

[0027] Average exercise time per person is the ratio of the total exercise time of community residents to the total number of residents within the statistical period, expressed in minutes. The above three state components together constitute the aggregated representation of the motion space state field observed by the reinforcement learning optimization agent at each moment, which is used to evaluate the balance, participation level, and accessibility of community sports resources under the current layout and guidance strategy.

[0028] The selection of these three state components is not arbitrary, but rather corresponds to three core demands of social sports management and mutually checks and balances each other: the facility utilization balance rate describes whether resources are used evenly, avoiding some facilities being overloaded while others are idle; the 15-minute fitness circle coverage rate describes whether resources benefit all residents, avoiding service blind spots; and the average exercise time per person describes whether resources are truly transformed into residents' exercise participation, avoiding construction without use. If only the facility utilization balance rate is used as the state, the reinforcement learning optimization agent may achieve superficial balance by suppressing the flow of people to high-demand facilities, but this would damage coverage and participation; if only the coverage rate is used as the state, the overcrowding of existing facilities may be ignored. Therefore, this invention uses all three to constitute the state space, enabling the reinforcement learning optimization agent to seek a balance among the three demands. At the start of this embodiment, the facility utilization balance rate of the community was 0.58, the 15-minute fitness circle coverage rate was 81.2%, and the average exercise time per person per week was 118 minutes. All three indicators were low and mutually restrictive, which is a typical scenario of supply and demand coordinating optimization.

[0029] Step S3: Define bilateral action space and reward. For example... Figure 3 As shown, this step defines the two-sided action space and reward for the reinforcement learning optimization agent. The two-sided action space includes supply-side actions and demand-side actions.

[0030] The supply-side actions include three categories: facility function replacement, shared time period adjustment, and new facility site selection recommendation. Facility function replacement refers to transforming the sports function of an idle facility into a sports function with high demand in the surrounding area, such as converting a gateball court with consistently low utilization into a youth basketball court; shared time period adjustment refers to adjusting the opening hours of facilities or opening the internal sports facilities of enterprises, institutions, and schools to the community during off-peak hours; new facility site selection recommendation refers to recommending the location and type of new sports facilities when there is new construction land available.

[0031] The demand-side action involves pushing personalized exercise behavior guidance strategies to residents, including information on nearby available facilities, available time slots, and suitable exercise types. These personalized exercise behavior guidance strategies are pushed to residents' terminals via the community sports service platform, guiding residents to go to nearby available facilities during peak hours, adjust their exercise time to available time slots, or choose exercise types suitable for their physical condition and preferences. This redistributes the spatiotemporal distribution of residents' exercise needs without changing the total number of facilities.

[0032] The rewards are composed of the increase in resident participation rate and facility operating costs; the greater the increase in resident participation rate and the lower the facility operating costs, the greater the reward. Facility operating costs include the costs of renovation, sharing, and new construction resulting from supply-side actions, and the costs of guidance and promotion resulting from demand-side actions. The reinforcement learning optimization agent performs simulations in the digital twin model of the community exercise space. Starting from the current state of the exercise space, it selects supply-side and demand-side actions based on the current strategy, simulates their implementation effects, and adjusts the strategy according to the rewards. The strategy update and value assessment of the reinforcement learning framework used are mature methods in this field. This embodiment uses a proximal policy optimization framework, and its general update process will not be elaborated further.

[0033] This invention integrates supply-side and demand-side actions into a single dual-action space, which is the fundamental difference between it and existing solutions that only consider supply-side facility adjustments. In existing solutions, residents' exercise demand is treated as a fixed input exogenously determined by historical behavior, and the reinforcement learning optimization agent can only search within the supply-side facility adjustments. This invention, however, treats the spatiotemporal distribution of residents' exercise demand as a decision variable that can be actively controlled through personalized exercise behavior guidance strategies. This allows the reinforcement learning optimization agent to choose either supply-side actions to modify facilities, demand-side actions to modify the behavior distribution, or a combination of both at each decision point. When supply-side actions become exhausted due to lack of land for construction or facilities to modify, demand-side actions can still provide an equivalent improvement in supply-demand matching without changing the total number of facilities by guiding congested facilities and peak-hour passenger flow to idle facilities and off-peak hours. Because the actions on both the supply and demand sides coexist in the same action space and share the same reward, reinforcement learning optimization agents can make a unified trade-off between cost and effect, automatically determining when to modify facilities, when to guide behavior, and how to match the two optimally, rather than treating guidance as an auxiliary output after optimization, as in existing solutions.

[0034] Step S4: The spatiotemporal redistribution of motion behaviors triggered by demand-side actions is written back to the motion space state field. For example... Figure 4 As shown, this step is crucial for forming a closed loop between supply and demand. This invention does not assume that residents fully adopt the personalized exercise behavior guidance strategy, but rather collects actual response data from residents to the strategy. This actual response data includes guidance acceptance indicators, actual facilities visited, and actual exercise times, which are collected by the community exercise service platform after the guidance is pushed out.

[0035] Based on the actual response data, this step estimates the elasticity of the motion behavior guidance response, which characterizes the probability of spatiotemporal migration of residents' motion behavior under a unit guidance intensity. This embodiment estimates this elasticity by establishing a logistic response model for residents' guidance acceptance behavior. For the first... The probability that a given resident will accept the guidance is:

[0036] ,

[0037] ,

[0038] Furthermore, the first The elasticity of the guided movement behavior of a guided resident is the partial derivative of the acceptance probability with respect to the guidance intensity:

[0039] ,

[0040] in: For the first The elasticity of the guided movement behavior response of the individual residents is a scalar quantity, ranging from 0 to... , dimensionless, is calculated by this formula, and represents the probability of the resident's spatiotemporal migration of movement behavior under unit guidance intensity. It is the source of weights for subsequent elastic weighted write-back. For the first The predicted probability of a guided resident accepting the personalized exercise behavior guidance strategy is a scalar with a value ranging from 0 to 1. It is dimensionless and is calculated by the logistic response model, representing the likelihood of the guidance being adopted. The logistic function, or sigmoid function, is defined as follows: , is a scalar-to-scalar mapping, with a value range of 0 to 1, dimensionless, and used to compress linear predictions into probabilities; Let be the independent variable of the logistic function, which is a scalar with a value range from negative infinity to positive infinity. It is dimensionless, determined by the linear combination within the parentheses, and represents the logarithmic probability of the guide being accepted. is a natural constant, approximately equal to 2.718, and is a scalar with no dimension. The intercept term of the logistic response model is a scalar with a value range from negative infinity to positive infinity. It is dimensionless and is obtained by maximum likelihood estimation from historical response data. It represents the baseline acceptance tendency without guidance. The regression coefficient for guidance intensity is a scalar, and its value ranges from real numbers greater than 0. In this embodiment, it is taken as 1.8. It is dimensionless and is obtained by maximum likelihood estimation from historical response data. The larger its value, the more sensitive residents are to guidance intensity. Too high a value will overestimate elasticity and lead to excessive write-back, while too low a value will underestimate elasticity and lead to guidance being ignored. It characterizes the marginal effect of guidance intensity on the probability of acceptance. is the regression coefficient vector of resident characteristics, which is a column vector with a dimension equal to the dimension of resident characteristics. The values ​​of each component range from negative infinity to positive infinity and are dimensionless. They are obtained from historical response data through maximum likelihood estimation and characterize the role of individual resident characteristics in the probability of acceptance. superscript Indicates vector transpose; For the first The feature vector of each guided resident is a column vector with a dimension equal to the resident's feature dimension. Each component, after normalization, takes a value range of 0 to 1 and is dimensionless. It is composed of population structure data and historical movement behavior data and represents the individual attributes of residents. For the first The guidance intensity of each guided resident is a scalar with a value ranging from 0 to 1 and is dimensionless. It is obtained by normalizing the push frequency and push significance of the personalized exercise behavior guidance strategy and represents the magnitude of the guidance effect. The sequence number of the guided resident is a positive integer, ranging from 1 to... Dimensionless This represents the total number of residents guided during the statistical period.

[0041] Subsequently, this step uses the elasticity of the response guided by the described movement behavior as a weight to write back the migration amount of the spatiotemporal redistribution of the residents' movement behavior to the movement space state field. For any sports facility During the period The net number of migrants is:

[0042] ,

[0043] Based on this, the utilization rate of the sports facility during that period is:

[0044] ,

[0045] in: For the rewriting of sports facilities During the period The facility utilization rate is a scalar with a value range of 0 to 1 and is dimensionless. It is calculated by this formula and represents the occupancy level of the facility after the demand is redistributed in time and space. It is written back to the motion space state field. To rewrite the former sports facilities During the period The facility utilization rate is a scalar with a value ranging from 0 to 1 and is dimensionless. It is obtained by mapping from the digital twin model of the community sports space. For sports facilities During the period The net number of migrants resulting from the guidance is a scalar, ranging from negative to positive design capacity, in people. It is calculated from the formula above, with positive values ​​representing net inflows and negative values ​​representing net outflows. The definition is the same as the aforementioned elasticity estimation formula; For the first The residents were guided to relocate to the sports facilities. During the period The indicator quantity is a scalar, taking a value of 0 or 1, dimensionless, and is determined by the personalized movement behavior guidance strategy. A value of 1 indicates that the resident is being guided to move in. For the first The residents who were being directed to relocate were originally located in the sports facilities. During the period The indicator is a scalar, taking the value of 0 or 1, dimensionless, determined by the movement behavior data before migration, with a value of 1 indicating that the resident was originally here; The total number of residents guided during the statistical period is a positive integer and dimensionless. The sequence number of the guided resident is a positive integer, ranging from 1 to... Dimensionless; For sports facilities The design capacity is a scalar, taking values ​​of real numbers greater than 0, with units of people, and is determined by the facility attributes; For the truncation function, Limited to to Within the interval, i.e. This is to ensure that the facility utilization rate after write-back falls between 0 and 1; The serial number of the sports facility is a positive integer, dimensionless. is the sequence number of the time period, a positive integer ranging from 1 to 12, and dimensionless.

[0046] The rewritten motion space state field re-drives the solution of supply-side actions, thus forming a feedback path in which demand-side actions influence supply-side actions.

[0047] Step S5: Stratified resilience estimation and identification of high-potential silent populations. For example... Figure 5 As shown, residents' responses to personalized exercise guidance strategies vary significantly across different population groups and time periods. Using a uniform elasticity regression would distort the results. Therefore, this step estimates the exercise guidance response elasticity by stratifying it according to resident population type and time period, obtaining stratified exercise guidance response elasticities. In this embodiment, residents are divided into three groups based on age: adolescents, young adults, and the elderly. Using the 12 time periods from step S4, for each combination of population type and time period, the average exercise guidance response elasticity of all guided residents within that combination is taken as the stratified exercise guidance response elasticity for that combination.

[0048] ,

[0049] The maximum value in each time period is taken as the population type. Represents elasticity:

[0050] ,

[0051] Based on this, this step identifies high-potential silent populations by recognizing the elasticity of the stratified exercise behavior guidance response. These high-potential silent populations are residents whose exercise behavior guidance response elasticity is higher than a preset elasticity threshold and whose current average exercise duration is lower than a preset duration threshold.

[0052] ,

[0053] in: For population type During the period The hierarchical motion behavior guides the response elasticity, which is a scalar with a value range of 0 to 1. , dimensionless, is calculated by this formula, and characterizes the sensitivity of the population to guidance response during this period; For population type During the period The number of elements in the guided resident set, a positive integer, dimensionless. For this set; The definition is the same as the aforementioned elasticity estimation formula; For population type represents elasticity, is a scalar, and ranges from 0 to 1. Dimensionless, obtained by taking the maximum value of the stratified elasticity of each time period, characterizing the degree to which the population is most easily guided; This is the maximum value operator; The time period is a set of integers from 1 to 12 in this embodiment; This is the time period number, a positive integer ranging from 1 to 12, and is dimensionless. This is the population type number, a positive integer, and in this embodiment, the value ranges from 1 to 3, and is dimensionless. Let be a set of silent high-potential individuals, and let be a set whose elements are population type indices, obtained by this formula, representing a population with great potential for guidance but currently insufficient exercise; The preset elastic threshold is a scalar value ranging from 0 to 1. In this embodiment, 0.15 is used, which is dimensionless and determined by the upper quartile of the historical stratified elastic distribution. If it is too high, potential people will be missed; if it is too low, low potential people will be mistakenly included. For population type The current average exercise duration per person is a scalar, with values ​​ranging from real numbers greater than 0, and the unit is min. It is obtained from exercise behavior data statistics. The preset duration threshold is a scalar value, and its range is a real number greater than 0. In this embodiment, it is set to 150 minutes per week, and the unit is minutes. It is determined based on the recommended amount of exercise for national fitness. This is the logical AND operator, indicating that both conditions must be met simultaneously.

[0054] Prioritizing the aforementioned high-potential silent population as the target audience for the personalized exercise behavior guidance strategy can achieve a greater increase in resident exercise participation rate with the same guidance cost. It is worth noting that the byproduct of the responsiveness of tiered exercise behavior guidance—the high-potential silent population map—can itself provide social sports management departments with a basis for decision-making in identifying groups who want to exercise but lack access to facilities and guidance.

[0055] In this embodiment, hierarchical elasticity estimation revealed that the elderly population in the community exhibited a response elasticity of 0.18 to exercise behavior guidance during the 9:00-11:00 AM timeframe, significantly higher than the preset elasticity threshold. However, their current average exercise time per week was only 96 minutes, lower than the preset threshold, thus identifying them as a typical high-potential silent population. Further analysis revealed that this group was not unwilling to exercise, but rather lacked awareness of nearby suitable facilities and times. Based on this, the community exercise service platform prioritized pushing guidance to this group during off-peak hours in the morning to nearby fitness trails and community gyms, increasing their average exercise time per week to 141 minutes within a statistical period. This result demonstrates that identifying high-potential silent populations allows limited guidance resources to be precisely targeted to the group with the highest marginal benefit, avoiding ineffective pushes to groups with low response elasticity. This is the direct value of hierarchical elasticity estimation in improving the input-output ratio of guidance, something that single elasticity write-back cannot achieve.

[0056] Step S6: Introduce a guidance saturation penalty and guidance budget. As personalized exercise guidance strategies are repeatedly pushed to the same resident, the response exhibits significant diminishing returns and fatigue effects. Over-pushing not only fails to further increase participation rates but also causes resident resentment. Therefore, this step introduces a guidance saturation penalty into the rewards. This penalty increases as the cumulative number of times a resident receives the personalized exercise guidance strategy within the statistical period increases.

[0057] ,

[0058] The reward after introducing the saturation penalty is:

[0059] ,

[0060] in: The saturation penalty term is a scalar with a value range of real numbers greater than or equal to 0. It is dimensionless and is calculated by this formula, representing the reward reduction caused by excessive push. The saturation penalty coefficient is a scalar value, which is a real number greater than 0. In this embodiment, it is 0.02. It is dimensionless and is determined by the relative importance of the guidance cost and the increase in participation rate. Too high a value will inhibit necessary guidance, while too low a value will condone excessive push. The total number of residents pushed to the community is a positive integer with no dimension. is a natural constant, approximately equal to 2.718, and is a scalar with no dimension. Saturation rate is a scalar value, which is a real number greater than 0. In this embodiment, it is 0.5, and the unit is each push. It is obtained by fitting the historical push response decay curve and characterizes how fast the fatigue effect increases with the number of pushes. For the first The cumulative number of times a resident receives the personalized exercise behavior guidance strategy within the statistical period is a non-negative integer, measured in times, and is obtained by the community exercise service platform. The resident's serial number is a positive integer, ranging from 1 to... Dimensionless; The reward after introducing the guided saturation penalty term is a scalar, dimensionless, and is calculated by this formula; The basic reward is a scalar quantity, dimensionless, and consists of the increase in residents' participation rate in sports and the cost of facility operation.

[0061] Simultaneously, a guidance budget cap is set for each resident. When the cumulative number of times reaches the guidance budget cap, the personalized exercise behavior guidance strategy is stopped being pushed to that resident. In this embodiment, the guidance budget cap is set to 5 times per week. Even if the reinforcement learning optimization agent tends to continue pushing after this cap is exceeded, the community exercise service platform will no longer send guidance to that resident, thus preventing excessive interference through hard constraints. The guidance saturation penalty and the guidance budget cap together ensure that demand-side guidance plays a role within the actual affordability range of residents.

[0062] Step S7: Reinforcement learning optimizes the agent's dual-timescale coupled updates. For example... Figure 6 As shown, supply-side actions and demand-side actions influence the same motion space state field, forming a non-stationary coupling: supply-side adjustments change the set of nearby available facilities, thereby altering the feasible region; guided migration, in turn, changes facility utilization, thus changing the optimal solution for the supply side. If both supply-side and demand-side sub-policies are updated simultaneously at the same time scale, convergence will be difficult due to mutual perturbation. Therefore, this step instructs the reinforcement learning optimization agent to use dual time scale updates: supply-side actions update the supply-side sub-policy at a slow time scale, and demand-side actions update the demand-side sub-policy at a fast time scale, with the update period of the fast time scale being shorter than that of the slow time scale.

[0063] Demand-side sub-strategies, on a fast timescale, every time... Update once per step:

[0064] ,

[0065] Supply-side sub-strategies, on a slow time scale, every time Update once per step, and Greater than :

[0066] ,

[0067] Dual-timescale updates must satisfy the following convergence condition:

[0068] ,

[0069] in: The parameters of the demand-side sub-strategy are vectors, with each component taking real numbers and being dimensionless. After being updated, they are used to generate demand-side actions. The parameters of the supply-side sub-strategy are vectors, with each component taking real numbers and being dimensionless. After being updated, they are used to generate supply-side actions. The learning rate of the demand-side sub-strategy is a scalar, a real number with a value greater than 0 and less than 1. In this embodiment, the initial value is 0.01, which is dimensionless and controls the update step size of the demand side. The learning rate of the supply-side sub-strategy is a scalar, taking the value of a real number greater than 0 and less than 1. In this embodiment, the initial value is 0.001, which is dimensionless. It controls the update step size of the supply side, and its value is less than... To ensure that supply changes slowly relative to demand; A gradient operator for calculating the gradient of demand-side sub-policy parameters; A gradient operator for calculating the gradient of supply-side sub-strategy parameters; Let be the objective function of the demand-side sub-strategy, be a scalar, dimensionless, representing the expected cumulative reward obtained from demand-side actions; Let be the objective function of the supply-side sub-strategy, be a scalar, dimensionless, representing the expected cumulative reward obtained from supply-side actions; The motion space state field serves as the shared coupled state of the supply and demand bilateral sub-strategies; The motion space state field is the motion space state field after the demand-side sub-policy converges on the motion space state field, that is, the motion space state field obtained after the demand-side sub-policy converges in each slow time scale update cycle. The update cycle is a fast timescale, a positive integer, and the unit is steps; in this embodiment, it is 1 step. The update period is a slow timescale, a positive integer, and the unit is steps. In this embodiment, it is taken as 20 steps, which satisfies... Greater than ; The round number is a positive integer and dimensionless. To take the limit operator; and The first The learning rates of both the demand and supply sides of the wheel are scalars and dimensionless.

[0070] Within each update cycle on the slow timescale, the demand-side sub-strategy is first made to converge in the motion space state field, and then the supply-side sub-strategy is updated accordingly. Thus, the motion space state field faced by the supply-side actions is already a stable state field after the demand-side guidance has been fully utilized, thereby avoiding non-convergence caused by mutual disturbances between the supply and demand sides. The supply-side actions and the demand-side actions iteratively engage in a game within the motion space state field until both sides jointly converge.

[0071] Step S8: Zero-New-Construction Optimization of Existing Communities. For existing communities with no new construction land as described in this embodiment, this step constrains the supply-side actions to facility function replacement and shared time period adjustments, and disables the recommendation of new facility site selection. Under this constraint, the space for supply-side actions is significantly narrowed, and relying solely on supply-side adjustments is no longer sufficient to increase the coverage rate of the 15-minute fitness circle to the target. At this point, the demand-side actions dominate the peak-shaving and valley-filling of the sports space state field: by guiding the crowded pedestrian flow on fitness trails and courts during morning and evening peak hours to the relatively idle gyms and equipment areas during the same period, and by guiding some residents' more flexible exercise time to off-peak hours, the coverage rate of the 15-minute fitness circle is increased to the preset coverage target under the constraint of unchanged total amount of sports facilities.

[0072] In this embodiment, the preset coverage target is set at 95%. The agent is optimized through reinforcement learning and extrapolated in the digital twin model of the community sports space. The supply side only performs two actions: replacing the function of a gateball court with low utilization rate with a youth basketball court and sharing the access of the adjacent school playground from 18:00 to 20:00. All other improvements in supply and demand matching are guided and undertaken by the demand side.

[0073] This result reveals the emergent effect of the invention in existing communities: when the recommendation for new facility site selection is disabled, supply-side actions degenerate into only two low-cost fine-tuning methods: functional replacement and shared time period adjustment. Supply-side actions alone are insufficient to increase the coverage rate of the 15-minute fitness circle from 81.2% to 95%. On the other hand, demand-side actions, through the elastic weighted rewriting of the sports space state field by guiding the response of exercise behavior, guide the exercise needs of residents in the service blind spot grid to previously neglected facilities within a 15-minute walking distance. This transforms these facilities from statistically inaccessible to actually used, thus filling the coverage gap without changing the total number of facilities. It is particularly important to note that the functional replacement and shared time period adjustment on the supply side are possible precisely because demand-side guidance first reshapes the sports space state field. The gateball court was identified as a replaceable object because demand-side guidance failed to direct sufficient foot traffic to the gateball court, proving that its exercise function is mismatched with the surrounding demand. The school playground was recommended for sharing because demand-side guidance showed suppressed basketball demand between 18:00 and 20:00. It is evident that the actions on both the supply and demand sides are not simply superimposed, but rather mutually triggered and adapted through the state field of the motion space, exhibiting a nonlinear synergistic effect of guiding instead of construction and guiding transformation. Its overall benefits significantly exceed the sum of the individual effects of either the supply or demand side.

[0074] After deploying the method of this invention on the aforementioned community sports service platform and running it for one statistical period, compared with the comparative scheme that only adopts supply-side optimization, this embodiment, under the premise that the total number of sports facilities remains unchanged, increases the coverage rate of the 15-minute fitness circle from 81.2% to 95.4%, the facility utilization balance from 0.58 to 0.86, the peak facility utilization rate of fitness trails during morning and evening peak hours from 1.00 (full load and overflow) to 0.83, the facility utilization rate of previously idle community gyms during peak hours from 0.21 to 0.62, the average exercise time per person from 118 minutes per week to 163 minutes per week, and the facility operating cost is reduced by approximately 74% compared to the scheme of building a new court of the same size.

[0075] It should be noted that the state mapping of the digital twin model of the community sports space, the statistical calculation of the facility utilization balance and the coverage of the 15-minute fitness circle, and the general update process of the reinforcement learning proximal strategy optimization framework in the above steps are all mature methods in the field. Those skilled in the art can adopt the corresponding mature implementations according to the community size and data conditions, which does not constitute a limitation on the scope of protection of this invention.

[0076] Regarding the values ​​of the key parameters involved in this embodiment, those skilled in the art can adjust them according to the actual situation of the community. The guidance intensity regression coefficient is 1.8, and the preset elasticity threshold is 0.15. Both are determined based on the maximum likelihood estimate and upper quartile of the community's historical push response data. For communities with slower responses, the guidance intensity regression coefficient can be appropriately increased and the preset elasticity threshold can be decreased. The saturation penalty coefficient is 0.02, the saturation rate is 0.5, and the guidance budget limit is 5 times per week. These three are determined based on a survey of the community residents' tolerance to push notifications. For communities with lower tolerance, the saturation penalty coefficient and saturation rate should be increased, and the guidance budget limit should be decreased. The fast timescale update cycle is 1 step, and the slow timescale update cycle is 20 steps. Both need to satisfy that the slow timescale update cycle is greater than the fast timescale update cycle. For communities where the cost of supply-side adjustment is higher and changes should be slower, the slow timescale update cycle can be further increased. This embodiment also verified the parameter sensitivity: when the guided intensity regression coefficient was perturbed in the range of 1.5 to 2.1, the preset elasticity threshold was perturbed in the range of 0.10 to 0.20, and the slow time scale update cycle was perturbed in the range of 15 to 30 steps, the final 15-minute fitness circle coverage rate was consistently above 94%, and the facility utilization rate balance was consistently above 0.83, indicating that the method of the present invention has good robustness to the values ​​of key parameters and does not depend on fine-tuning of parameters.

[0077] Furthermore, the method of this invention can be executed periodically: after each statistical period, a new batch of actual response data collected by the community sports service platform is used to update the elasticity of the sports behavior guidance response and the hierarchical elasticity of the sports behavior guidance response, so that the sports space state field faced by the reinforcement learning optimization agent always reflects the latest sports behavior patterns of residents; when the community population structure or facility conditions change significantly, steps one to eight can be re-executed to obtain a public sports facility layout optimization scheme and personalized sports behavior guidance strategy adapted to the new conditions, thereby ensuring the continuous effectiveness of the method of this invention in the long-term operation of the community. The core of this invention lies in the optimization decision structure of incorporating demand-side actions into the two-sided action space, redistributing the spatiotemporal allocation of residents' sports behavior and writing it back into the sports space state field through the weighted elasticity of the sports behavior guidance response, and enabling the supply and demand sides to iteratively play a game in the sports space state field until the two sides jointly converge.

[0078] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the layout and guiding exercise of public sports facilities based on digital twins, characterized in that, By integrating community geographic information, residents' exercise behavior data, and population structure data, a digital twin model of community sports space is constructed. The digital twin model of community sports space maps the sports space status field of each sports facility in real time. The sports space status field includes facility utilization rate, population density, and spatial accessibility. Using the balance of facility utilization, average exercise time per person, and coverage of the 15-minute fitness circle as the state space, and the two-sided action space as the decision variables, with the increase in resident participation rate and facility operating costs as rewards, a reinforcement learning optimization agent performs deductions in the digital twin model of the community sports space. The two-sided action space includes supply-side actions and demand-side actions. The supply-side actions include facility function replacement, shared time period adjustment, and new facility site recommendation. The demand-side actions are personalized exercise behavior guidance strategies that push nearby available facilities, available time periods, and suitable exercise types to residents. The spatiotemporal redistribution of resident exercise behavior caused by the demand-side actions is written back into the sports space state field, so that the written-back sports space state field re-drives the solution of the supply-side actions. The supply-side actions and the demand-side actions iteratively play a game on the sports space state field until both sides converge, outputting the optimized layout scheme of public sports facilities and the personalized exercise behavior guidance strategies.

2. The method for optimizing the layout of public sports facilities and guiding exercise based on digital twins according to claim 1, characterized in that, The step of writing back the spatiotemporal redistribution of residents' exercise behavior triggered by the demand-side actions to the exercise space state field includes: collecting actual response data of residents to the personalized exercise behavior guidance strategy, the actual response data including guidance acceptance indicators, actual facilities visited, and actual exercise time periods; estimating the exercise behavior guidance response elasticity based on the actual response data, the exercise behavior guidance response elasticity characterizing the probability of spatiotemporal migration of residents' exercise behavior under a unit guidance intensity; and writing back the migration amount of the spatiotemporal redistribution of residents' exercise behavior to the exercise space state field using the exercise behavior guidance response elasticity as a weight.

3. The method for optimizing the layout of public sports facilities and guiding exercise based on digital twins according to claim 2, characterized in that, The elasticity of the exercise behavior guidance response is estimated by stratifying residents by population type and time period to obtain the stratified elasticity of the exercise behavior guidance response. Based on the stratified elasticity of the exercise behavior guidance response, a high-potential silent population is identified. The high-potential silent population is a group of residents whose elasticity of the exercise behavior guidance response is higher than a preset elasticity threshold and whose current average exercise time is lower than a preset duration threshold. The high-potential silent population is the priority target for the personalized exercise behavior guidance strategy.

4. The method for optimizing the layout of public sports facilities and guiding exercise based on digital twins according to claim 3, characterized in that, The reward includes a guidance saturation penalty, which increases as the cumulative number of times a resident receives the personalized exercise behavior guidance strategy within the statistical period increases. A guidance budget cap is set for each resident, and when the cumulative number of times reaches the guidance budget cap, the personalized exercise behavior guidance strategy will stop being pushed to that resident.

5. The method for optimizing the layout of public sports facilities and guiding exercise based on digital twins according to claim 4, characterized in that, The reinforcement learning optimization agent employs a dual-timescale update mechanism. The supply-side action updates the supply-side sub-policy at a slow timescale, while the demand-side action updates the demand-side sub-policy at a fast timescale. The update cycle of the fast timescale is shorter than that of the slow timescale. Both the supply-side and demand-side sub-policies share a coupled state with the motion space state field. Within each update cycle of the slow timescale, the demand-side sub-policy is first made to converge in the motion space state field, and then the supply-side policy is updated accordingly.

6. The method for optimizing the layout and guiding exercise of public sports facilities based on digital twins according to claim 5, characterized in that, For existing communities with no new construction land, the supply-side actions will be constrained to facility function replacement and shared time period adjustment, and the recommendation of new facility site selection will be disabled; the demand-side actions will lead the peak shaving and valley filling of the sports space state field, so that the coverage rate of the 15-minute fitness circle will be increased to the preset coverage target under the constraint of the total number of sports facilities remaining unchanged.

7. The method for optimizing the layout and guiding exercise of public sports facilities based on digital twins according to claim 1, characterized in that, The community geographic information includes the locations of sports facilities, road networks, and community boundaries; the residents' exercise behavior data includes the frequency of use of fitness trails and the distribution of exercise times; the population structure data includes age composition and population density.

8. The method for optimizing the layout and guiding exercise of public sports facilities based on digital twins according to claim 1, characterized in that, The 15-minute fitness circle coverage rate is the percentage of residents who can reach at least one sports facility within a 15-minute walk, based on the threshold of such accessibility.

9. The method for optimizing the layout of public sports facilities and guiding exercise based on digital twins according to claim 1, characterized in that, The facility utilization balance is obtained by normalizing the standard deviation of the facility utilization rate of each sports facility and then taking the negative mapping.

10. The method for optimizing the layout of public sports facilities and guiding exercise based on digital twins according to claim 1, characterized in that, The personalized exercise behavior guidance strategy is pushed to residents' terminals through the community sports service platform, which simultaneously displays the optimized layout plan of public sports facilities.

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