Method and system for predicting flight distance of diving platform skiing project based on self-adaptive pneumatic coupling integral, and storage medium

Abstract

The invention relates to a method and a system for predicting the flight distance of a diving platform skiing project based on self-adaptive pneumatic coupling integral, and a storage medium, and belongs to the field of diving platform skiing sports engineering. Comprises: establishing a diving platform skiing human body model; performing computational fluid mechanics simulation on the human body model based on the relative airflow velocity at the current moment and the human body total attack angle to obtain lift force and resistance at the current moment; obtaining the acceleration at the current moment based on the lift force and the resistance; updating the centroid speed and position of the human body by using the acceleration at the current moment based on the self-adaptive pneumatic coupling integral; and judging whether the human body falls to the ground according to the updated position, if so, obtaining a flight distance, otherwise, continuously iterating until the flight distance is obtained. According to the method, the lift force and the resistance are dynamically calculated at each time step through real-time calculation fluid mechanics simulation, and the mass center speed and the position of the human body are updated by utilizing the acceleration based on the self-adaptive pneumatic coupling integral, so that the flight distance is obtained, and the prediction precision of the flight distance is improved.

Description

Technical Field

[0001] This invention relates to the field of ski jumping engineering technology, and in particular to a method, system and storage medium for predicting the flight distance of ski jumping events based on adaptive aerodynamic coupling integral. Background Technology

[0002] The flight distance in ski jumping is a key indicator for measuring the performance of athletes in this event. The flight distance depends on a variety of factors, such as takeoff speed, body weight, and the terrain of the ski jump. How to accurately predict the flight distance and landing point of athletes has become a research hotspot in this field.

[0003] In existing technologies, traditional empirical models are mainly built based on simplified physical assumptions or historical experimental results to approximate flight trajectories. These models rely on experience and existing athlete data, which leads to significant errors.

[0004] In recent years, with the development of artificial intelligence, data-driven methods for predicting flight distance have emerged. For example, data from thousands of jumps across multiple ski jumping sites is collected and used to train a deep learning model to predict an athlete's flight distance and landing point. However, this method requires accumulating a large amount of high-precision jump data for model training, resulting in high data acquisition costs, long processing times, and reliance on the historical records of specific sites and athletes. Furthermore, for new ski jumps, different wind conditions, or new athletes, the model's accuracy is significantly reduced due to a lack of corresponding training data, leading to poor adaptability. Summary of the Invention

[0005] In view of the above analysis, the present invention aims to provide a method, system and storage medium for predicting the flight distance of ski jumping events based on adaptive aerodynamic coupling integral, so as to solve the problems of poor adaptability and low accuracy of current ski jumping flight distance prediction.

[0006] This invention provides a method for predicting flight distance in ski jumping events based on adaptive aerodynamic coupling integral, the method comprising the following steps: Step S1: Establish a ski jumping human model and set the flight posture parameters and environmental parameters of the human model; Step S2: Calculate the relative airflow velocity and the total angle of attack of the human body at the current moment based on the flight attitude parameters and environmental parameters; Step S3: Perform computational fluid dynamics simulation on the human body model based on the relative airflow velocity and the total angle of attack of the human body at the current moment to obtain the lift and drag acting on the human body at the current moment; obtain the acceleration of the human body at the current moment based on the lift and drag. Step S4: Based on the adaptive aerodynamic coupling integral, update the velocity and position of the human body's center of mass using the acceleration corresponding to the human body at the current moment; determine whether the human body has landed based on the updated position. If so, obtain the flight distance of the human body; otherwise, return to step S2 and continue execution until the flight distance of the human body is obtained.

[0007] Furthermore, the relative airflow velocity at the current moment is calculated using the following formula: , in, This represents the relative horizontal airflow velocity at the current moment. This indicates the speed of the human body's center of mass in the horizontal direction at the current moment. This indicates the wind speed in the horizontal direction. This indicates the vertical relative airflow velocity at the current moment. This indicates the current velocity of the human body's center of mass in the vertical direction. t represents the vertical wind speed, and t represents the current time.

[0008] Furthermore, the trajectory angle is calculated using the following formula: , in, Indicates the trajectory angle; The total angle of attack of the human body at the current moment is calculated using the following formula: , in, Indicates the total angle of attack of the human body. Indicates the pitch angle of the flight attitude.

[0009] Furthermore, the computational fluid dynamics simulation of the human body model based on the current relative airflow velocity and the total angle of attack of the human body to obtain the lift and drag acting on the human body at the current moment includes: The computational domain is set according to the human body model; The computational domain and the human body model are meshed; Set the calculation parameters, input the relative airflow velocity and the total angle of attack of the human body at the current moment, and perform computational fluid dynamics simulation on the human body model after meshing in the computational domain to obtain the lift and drag acting on the human body at the current moment.

[0010] Furthermore, obtaining the acceleration of the human body at the current moment based on the lift and drag includes: decomposing the lift and drag into a Cartesian coordinate system according to the trajectory angle to obtain the resultant force in the horizontal direction and the resultant force in the vertical direction; and obtaining the acceleration of the human body at the current moment based on the resultant force in the horizontal direction and the resultant force in the vertical direction.

[0011] Furthermore, the step of updating the velocity and position of the human body's center of mass based on the adaptive aerodynamic coupling integral using the acceleration corresponding to the human body at the current moment includes: defining an initial time step and defining a state vector based on the acceleration corresponding to the human body at the current moment; in each time step: calculating an intermediate slope vector, obtaining the corresponding fourth-order and fifth-order solutions based on the intermediate slope vector, obtaining the local error based on the fourth-order and fifth-order solutions, and if the local error is less than or equal to the error threshold, updating the velocity and position of the human body's center of mass using the fifth-order solution, updating the next time step, and entering the next time step; otherwise, adjusting the current time step and recalculating the intermediate slope vector until the local error is less than or equal to the error threshold.

[0012] Furthermore, if the local error is less than or equal to the error threshold, the velocity and position of the human body's center of mass are updated using the following formula: , in, This represents the updated velocity of the human body's center of mass in the horizontal direction. This represents the updated velocity of the human body's center of mass in the vertical direction. Indicates the current time step. This represents the updated horizontal displacement relative to the initial position of the human body. This represents the updated vertical displacement relative to the initial position of the human body. This represents the first element of the fifth-order solution. This represents the second element of the fifth-order solution. This represents the third element of the fifth-order solution. This represents the fourth element of the fifth-order solution; and the next time step is updated using the following formula: , in, This represents the minimum step size ratio. This indicates the maximum step size ratio. Indicates the error threshold. Indicates local error. Indicates the safety factor; Otherwise, adjust the current time step using the formula described above.

[0013] Furthermore, after each update of the human body's center of mass position, the following expression is used to determine whether the human body has landed: , in, This indicates the vertical position of the human body's center of mass after the update. This indicates the vertical height of the corresponding ski jump slope, i.e., the corresponding ground height.

[0014] Furthermore, the system includes: The initialization module is used to establish a ski jumping human body model, set the flight attitude parameters and environmental parameters of the human body model, and send the flight attitude parameters and environmental parameters to the calculation module and the human body model to the simulation module. The calculation module is used to calculate the relative airflow velocity and the total angle of attack of the human body at the current moment based on the flight attitude parameters and environmental parameters, and send the relative airflow velocity and the total angle of attack of the human body at the current moment to the simulation module; The simulation module is used to perform computational fluid dynamics simulation on the human body model based on the relative airflow velocity and the total angle of attack of the human body at the current moment to obtain the lift and drag acting on the human body at the current moment; based on the lift and drag, the acceleration corresponding to the human body at the current moment is obtained, and the acceleration corresponding to the human body at the current moment is sent to the integration module; The integration module is used to update the velocity and position of the human body's center of mass based on the current acceleration of the human body using adaptive aerodynamic coupling integration, and then send the updated position to the flight distance acquisition module. The flight distance acquisition module is used to determine whether the human body has landed based on the updated position. If so, the flight distance of the human body is obtained; otherwise, the calculation module is called until the flight distance of the human body is obtained.

[0015] Furthermore, the computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method for predicting the flight distance of a ski jumping event based on adaptive aerodynamic coupling integral.

[0016] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. This invention dynamically calculates the lift and drag acting on the human body at each time step through real-time computational fluid dynamics simulation based on relative airflow velocity and the total angle of attack of the human body, taking into account the influence of flight attitude pitch angle and wind speed; based on adaptive aerodynamic coupling integral, the acceleration corresponding to the human body is used to update the velocity and position of the human body's center of mass, thereby obtaining the flight distance of the human body, without relying on historical data or empirical fitting curves, thus improving the prediction accuracy of flight distance.

[0017] 2. This invention can input environmental parameters such as ski jump terrain function, flight attitude pitch angle, and wind speed according to actual conditions, and combine them with the individual characteristics of athletes (such as weight, take-off speed, etc.) to make high-precision predictions of ski jump flight distance. It can be adapted to different ski jumps, action techniques, and wind conditions, and can also make personalized predictions for different athletes, with high generalization ability and versatility.

[0018] 3. This invention obtains the landing point through interpolation, which improves the prediction accuracy of the landing point and makes the landing point continuous and differentiable, making it suitable for use in engineering optimization algorithms.

[0019] 4. This invention reduces traditional experiments and tests, lowers costs, and improves efficiency through computational fluid dynamics simulation.

[0020] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0021] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. Figure 1 This is a flowchart of a method for predicting flight distance in ski jumping events based on adaptive aerodynamic coupling integral, according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the flight posture of a ski jumping human model according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the computational domain according to an embodiment of the present invention; Figure 4 This is a block diagram of a ski jumping distance prediction system based on adaptive aerodynamic coupling integral, according to an embodiment of the present invention. Detailed Implementation

[0022] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0023] Example 1: One specific embodiment of the present invention discloses a method for predicting flight distance in ski jumping events based on adaptive aerodynamic coupling integral. For example... Figure 1 As shown, the method includes the following steps: Step S1: Establish a ski jumping human model and set the flight posture parameters and environmental parameters of the human model; Step S2: Calculate the relative airflow velocity and the total angle of attack of the human body at the current moment based on the flight attitude parameters and environmental parameters; Step S3: Perform computational fluid dynamics simulation on the human body model based on the relative airflow velocity and the total angle of attack of the human body at the current moment to obtain the lift and drag acting on the human body at the current moment; obtain the acceleration of the human body at the current moment based on the lift and drag. Step S4: Based on the adaptive aerodynamic coupling integral, update the velocity and position of the human body's center of mass using the acceleration corresponding to the human body at the current moment; determine whether the human body has landed based on the updated position. If so, obtain the flight distance of the human body; otherwise, return to step S2 and continue execution until the flight distance of the human body is obtained.

[0024] Specifically, in step S1, establishing the ski jumping human model includes: obtaining a human model of the ski jumping flight posture through human body scanning.

[0025] Specifically, a scanning imaging device is used to scan the posture of ski jumpers in their ski equipment during the flight phase to obtain a human model of their ski jump flight posture. The ski equipment includes ski jump suits, skis, helmets, goggles, etc.

[0026] Preferably, a professional athlete is dressed in a ski jumping suit and poses in a ski jumping flight posture. The athlete is scanned using an F6 SMART handheld 3D scanning imager, and then other ski equipment is scanned separately. The original scanned files are input into ECHO model processing software to generate digital models of the human body and ski equipment respectively. The digital models of ski equipment and human body are precisely aligned and integrated to achieve virtual wearing of ski equipment, thereby obtaining a human body model of the ski jumping flight posture.

[0027] Furthermore, the flight attitude parameters of the human model include the initial velocity of the human body, the mass of the human model, the pitch angle of the flight attitude, and the initial position of the human body. The environmental parameters include wind speed and the terrain curve of the jumping platform.

[0028] Specifically, the initial velocity of the human body refers to the velocity of the body's center of mass at the instant of takeoff in ski jumping, including both horizontal and vertical initial velocities. The horizontal initial velocity is denoted as v. x,0 The initial vertical velocity, obtained through actual measurement or by taking historical averages, is expressed as v. y,0 Set to 0 or as needed. The mass of the human model refers to the total mass of the human body and the ski equipment worn by the body, denoted as m. For example... Figure 2 As shown, the pitch angle refers to the angle between the skis and the horizontal plane, set as a fixed value, denoted as β. The trajectory angle refers to the angle between the relative airflow direction and the horizontal axis, denoted as θ. The total angle of attack of the human body is the sum of the trajectory angle and the pitch angle, denoted as α, and can be set in radians or degrees. The initial position of the human body refers to the starting point of the ski jump, set as the origin of the coordinate system, denoted as x0=0, y0=H(0). The wind speed refers to the average wind speed in the surrounding environment during ski jumping, including horizontal and vertical wind speeds, denoted as v. wind,h v wind,vThe terrain curve of the ski jump refers to a function representing the profile of the ski jump slope, denoted as H(x). This function is a differentiable real function, where x represents the horizontal position and H(x) represents the ground height corresponding to x.

[0029] Specifically, in step S2, the relative airflow velocity at the current moment is calculated using the following formula: , in, This represents the relative horizontal airflow velocity at the current moment. This indicates the speed of the human body's center of mass in the horizontal direction at the current moment. This indicates the wind speed in the horizontal direction. This indicates the vertical relative airflow velocity at the current moment. This indicates the current velocity of the human body's center of mass in the vertical direction. t represents the vertical wind speed, and t represents the current time.

[0030] It should be noted that relative airflow speed refers to the instantaneous speed of an athlete relative to still air.

[0031] Furthermore, the trajectory angle is calculated using the following formula: , in, This represents the trajectory angle.

[0032] Specifically, the total angle of attack of the human body at the current moment is calculated using the following formula: , in, Indicates the total angle of attack of the human body. Indicates the pitch angle of the flight attitude.

[0033] Specifically, in step S3, the computational fluid dynamics simulation of the human body model based on the current relative airflow velocity and the total angle of attack of the human body at the current moment to obtain the lift and drag acting on the human body at the current moment includes: The computational domain is set according to the human body model; The computational domain and the human body model are meshed; Set the calculation parameters, input the relative airflow velocity and the total angle of attack of the human body at the current moment, and perform computational fluid dynamics simulation on the human body model after meshing in the computational domain to obtain the lift and drag acting on the human body at the current moment.

[0034] Specifically, setting the computational domain based on the human body model includes: setting the geometric model size of the computational domain, the distances from the human body model to the upstream, downstream, upper, lower, left, and right boundaries of the computational domain, and the entrance boundary conditions, exit boundary conditions, and wall boundary conditions of the computational domain; wherein, the computational domain is a cube, the geometric model size of the computational domain includes the length, width, and height of the computational domain, and the human body model is located inside the computational domain.

[0035] Preferred, such as Figure 3 As shown, the vertical plane of the fluid domain is symmetrically divided along the centerline of the human body, with the left and right computational domains being completely symmetrical. The computational domain is set as the right-side region after the division, with a length, width, and height of 48.3m, 9.9m, and 16m, respectively. The distances from the human body model to the upstream, downstream, upper, lower, left, and right boundaries of the computational domain are set to 11.5m, 34.5m, 7.3m, 7.3m, 9m, and 9m, respectively. The inlet boundary condition of the fluid domain is set to a velocity inlet with a velocity of 26m / s, and the flow Reynolds number Re is approximately 2.7 × 10⁻⁶. 6 The outlet boundary condition is set to a pressure outlet, and an ambient static pressure of 1 atmosphere is applied at the outlet. The wall boundary conditions of the four surfaces of the fluid domain (upper, lower, left, and right) are all set to symmetry plane boundary conditions. The model surface is set to a no-slip wall condition, and the fluid is air.

[0036] It's important to note that Computational Fluid Dynamics (CFD) is a field that uses numerical simulation methods and computer technology to study fluid motion and interactions. CFD discretizes the fluid dynamics equations into a series of mathematical equations, then uses a computer to numerically solve them to simulate and analyze the fluid's motion, pressure, temperature, and other characteristics. The computational domain refers to the entire spatial region used to calculate fluid flow and related physical phenomena in a CFD simulation. The boundary of the computational domain defines the range of fluid flow and includes inlet boundary conditions, outlet boundary conditions, and wall boundary conditions. The fluid domain refers to the region within the computational domain that actually contains the fluid. Inlet boundary conditions are the physical conditions applied at the inlet of the fluid domain, outlet boundary conditions are the physical conditions applied at the outlet of the fluid domain, and wall boundary conditions are the physical conditions applied at the boundary where the fluid domain contacts the wall. The upstream boundary is the boundary where the fluid enters the computational domain in the direction of fluid flow; the downstream boundary is the boundary where the fluid exits the computational domain in the direction of fluid flow. The upstream boundary is usually set as the fluid inlet boundary condition, the downstream boundary is usually set as the fluid outlet boundary condition, and the left and right boundaries as well as the top and bottom boundaries are usually set as the fluid wall boundary conditions.

[0037] Specifically, the meshing of the computational domain and the human body model includes: Set the maximum and minimum size of the surface mesh; Set the type of volume mesh and its maximum and minimum sizes; Set the size of several locally encrypted influence bodies; Set the thickness of the first layer of the expansion layer mesh, the growth factor, and the number of expansion layers; The computational domain and the human body model are meshed according to the above settings.

[0038] Preferably, the computational domain and the human body model are meshed using the pre-processing software ANSYS Fluent Meshing. The maximum and minimum dimensions of the surface mesh are set to 16 mm and 8 mm, respectively; the volume mesh type is set to unstructured tetrahedral mesh, with maximum and minimum dimensions of 400 mm and 2 mm, respectively; the dimensions of the three local refinement influence volumes are set to 5 mm, 10 mm, and 20 mm, respectively; the thickness of the first layer of the expansion layer mesh is set to 0.05 mm, the growth factor to 1.2, and the number of expansion layers to 15. Meshing the computational domain and each human body model according to the above settings yields approximately 3.8 million mesh elements for each human body model.

[0039] It should be noted that the localized mesh refinement effect is used to refine the mesh in a specific region without additionally dividing the computational domain, thereby improving the accuracy of the simulation. The expanded layer mesh is used to generate a high-resolution mesh near the wall boundary of the fluid domain to better capture the flow characteristics within the boundary layer. The thickness of the first layer of the expanded layer mesh refers to the thickness of the first layer of mesh cells generated near the wall boundary; the expansion factor of the expanded layer mesh refers to the ratio of the thicknesses of two adjacent layers of mesh cells in the expanded layer; and the number of expanded layers refers to the number of expanded layer mesh layers generated near the wall boundary.

[0040] Furthermore, the calculation parameters are set, and the relative airflow velocity and the total angle of attack of the human body at the current moment are input. Computational fluid dynamics simulation is then performed on the meshed human body model within the computational domain to obtain the lift and drag acting on the human body at the current moment, including: Select the solver and numerical solution method, set the corresponding calculation parameters, and input the current relative airflow velocity and the total angle of attack of the human body into the simulation software; Based on the solver and numerical solution method, computational fluid dynamics simulation is performed on the meshed human body model in the computational domain using simulation software to obtain the lift and drag acting on the human body at the current moment.

[0041] Specifically, the selection of the solver and numerical solution method, setting of corresponding calculation parameters, and inputting the current relative airflow velocity and the total angle of attack of the human body into the simulation software include: selecting a turbulence model solver based on the characteristics of the air surrounding the person skiing on a ski jump, wherein the SST k-ω turbulence model is used to close the Reynolds-averaged equations to obtain the governing equations; using the finite volume method to discretize the governing equations, wherein a second-order scheme is used to spatially discretize the spatial derivatives to reduce numerical discretization errors caused by mesh misalignment; selecting a pressure-velocity coupled solution method and using the SIMPLE algorithm to solve the problem to achieve better convergence performance; monitoring the lift and drag of the human body, while keeping the other settings at default.

[0042] It should be noted that the air surrounding a person during ski jumping is an incompressible fluid. The flow of the fluid around the person and skiing equipment is described by solving the Reynolds-Averaged Navier-Stokes equation (RANS). The RANS includes a continuity equation and a momentum equation. The expression for the continuity equation is shown below: Continuity equation: , The expression for the momentum equation is shown below: , in, The time-averaged velocity component of the fluid. For fluid density, This refers to fluid pressure. For fluid volume force components, Let be the dynamic viscosity coefficient of the fluid. The turbulent pulsating velocity component is relative to the time-averaged flow velocity. This represents the Reynolds stress.

[0043] Turbulence is an irregular flow phenomenon that occurs at high Reynolds numbers. Turbulence is often simulated numerically, with turbulence models serving as mathematical relationships for calculating Reynolds stress, forming a closed system of equations together with the Reynolds-averaged Navier-Stokes equations. The standard SST (shear-stress transport) k-ω turbulence model is a widely used two-equation hybrid model. It uses the Wilcox k-ω model in the near-wall boundary region and the k-ε model at the boundary layer edge and free shear layer, with a mixing function facilitating the transition. It belongs to the two-equation eddy viscosity mode of incompressible / compressible turbulence integrated to the wall, thus providing a more accurate analysis of the flow field around the human body and the distribution of drag and lift. Therefore, the SST k-ω turbulence model was used to numerically calculate the flow field of a ski jump human model.

[0044] Specifically, based on the aforementioned solver and numerical solution method, the human body model after mesh generation is simulated within the computational domain in the simulation software. The simulation time step and total time are set as needed. During the simulation, the changes in drag and lift experienced by the human body are monitored to ensure simulation convergence. The average lift and average drag after convergence are obtained as the applied lift and drag. Here, lift is represented by L. t The resistance is represented by D. t .

[0045] Furthermore, obtaining the acceleration of the human body at the current moment based on the lift and drag includes: decomposing the lift and drag into a Cartesian coordinate system according to the trajectory angle to obtain the resultant force in the horizontal direction and the resultant force in the vertical direction; and obtaining the acceleration of the human body at the current moment based on the resultant force in the horizontal direction and the resultant force in the vertical direction.

[0046] Specifically, the resultant force in the horizontal direction and the resultant force in the vertical direction can be obtained using the following formulas: , in, This represents the resultant force in the horizontal direction. This represents the resultant force in the vertical direction. Indicates the quality of the human body model. This represents the gravitational constant.

[0047] It should be noted that the lift and drag obtained from computational fluid dynamics simulations are aerodynamic forces defined along the relative airflow direction, and need to be decomposed into a Cartesian coordinate system according to the trajectory angle for subsequent dynamic integration.

[0048] Specifically, the acceleration of the human body at the current moment can be obtained using the following formula: , in, This represents the horizontal acceleration of the human body at the current moment. This represents the vertical acceleration of the human body at the current moment.

[0049] It should be noted that the above mechanical decomposition process takes into account the effects of wind speed and the total angle of attack of the human body on the lift and drag of the human body, providing a physical basis for subsequent adaptive aerodynamic coupling integration.

[0050] Specifically, in step S4, updating the velocity and position of the human body's center of mass using the acceleration corresponding to the human body at the current moment based on adaptive aerodynamic coupling integral includes: defining an initial time step and defining a state vector based on the acceleration corresponding to the human body at the current moment; in each time step: calculating an intermediate slope vector, obtaining the corresponding fourth-order and fifth-order solutions based on the intermediate slope vector, obtaining the local error based on the fourth-order and fifth-order solutions, and if the local error is less than or equal to the error threshold, updating the velocity and position of the human body's center of mass using the fifth-order solution, updating the next time step, and entering the next time step; otherwise, adjusting the current time step and recalculating the intermediate slope vector until the local error is less than or equal to the error threshold.

[0051] Specifically, the state vector is represented as: , in, Indicates to Differentiate, This indicates the current position of the human body's center of mass in the horizontal direction. This indicates the current position of the human body's center of mass in the vertical direction.

[0052] It should be noted that, This represents the horizontal displacement relative to the initial position of the human body, i.e., x0. This represents the vertical displacement relative to the initial position of the human body, i.e., y0.

[0053] Specifically, the intermediate slope vector consists of 7 slopes, represented as [k1, k2, ..., k6, k7]; k1 to k7 are calculated using the following formula: , in, Indicates the current time step; For fixed coefficients, ; For fixed coefficients, , .

[0054] It should be noted that, In specific implementation, for Each element in the text, through The intermediate slope vector is obtained by finding the corresponding elements. Specifically, based on the current state, the velocity and displacement of the human body's center of mass at the current moment can be obtained. According to the flight attitude parameters and environmental parameters, the relative airflow velocity and the total angle of attack of the human body at the current moment are calculated. By performing computational fluid dynamics simulation, the lift and drag acting on the human body at the current moment are obtained. Based on the lift and drag, the acceleration corresponding to the human body at the current moment is obtained. The acceleration and the velocity of the human body's center of mass are substituted into the expression of the intermediate slope vector to calculate k1 to k7.

[0055] Specifically, the corresponding fourth-order and fifth-order solutions are obtained using the following formulas: , in, This represents the corresponding fourth-order solution. This represents the corresponding fifth-order solution; , This represents the weighting coefficient, which is a constant. .

[0056] Specifically, the local error is obtained using the following formula: .

[0057] Specifically, if the local error is less than or equal to the error threshold, the velocity and position of the human body's center of mass are updated using the following formula: , in, This represents the updated velocity of the human body's center of mass in the horizontal direction. This represents the updated velocity of the human body's center of mass in the vertical direction. Indicates the current time step. This represents the updated horizontal displacement relative to the initial position of the human body. This represents the updated vertical displacement relative to the initial position of the human body. This represents the first element of the fifth-order solution. This represents the second element of the fifth-order solution. This represents the third element of the fifth-order solution. This represents the fourth element of the fifth-order solution; and the next time step is updated using the following formula: , in, This represents the minimum step size ratio. This indicates the maximum step size ratio. Indicates the error threshold. Indicates local error. Indicates the safety factor; Otherwise, adjust the current time step using the formula described above.

[0058] It should be noted that the above formula can adaptively adjust the current time step and the next time step according to the magnitude of the local error.

[0059] Understandably, the adaptive aerodynamic coupling integral algorithm has a nested fourth- and fifth-order structure, enabling error estimation and adaptive adjustment of the time step. This invention obtains the local error by comparing the difference between the fourth- and fifth-order solutions, and employs an adaptive step-size adjustment strategy with upper and lower limit control based on the local error. This not only improves the accuracy requirements for updating the center of mass velocity and position of the human body but also ensures computational efficiency.

[0060] Furthermore, after each update of the human body's center of mass position, the following expression is used to determine whether the human body has landed: , in, This indicates the vertical position of the human body's center of mass after the update. This indicates the vertical height of the corresponding ski jump slope, i.e., the corresponding ground height.

[0061] It should be noted that when the above expression is satisfied, it means the human body has landed. If ,but The human body lands at the exact moment, and the horizontal position of the landing point is... .like ,but The human body had already landed before the specified time, and the horizontal position of the landing point was determined by interpolation.

[0062] Specifically, assuming , The horizontal position of the landing point can be obtained using the following formula: , in, This indicates the horizontal position of the landing point, where 0 < λ < 1.

[0063] Furthermore, if the above expression is not satisfied, the process proceeds to the next time step iteration and returns to step S2 to continue execution until it is determined that the human body has landed.

[0064] Understandably, this invention simulates the entire flight process of a human ski jumper through numerical integration iteration and accurately predicts the horizontal position of the landing point of the human body through interpolation.

[0065] Preferably, after obtaining the flight distance of the human body, the following results data are output for subsequent analysis and visualization: The distance a person can fly is represented by x. land , refers to the horizontal displacement of the human body from the point of takeoff to the point of landing; Flight trajectory data, represented as (x t ,y t ( ), refers to the trajectory of the human body's center of mass during flight; The velocity time series is represented as (v x,t ,v y,t This represents the change in human flight speed over time. Aerodynamic data, expressed as (L t D t ), representing the lift and drag forces acting on the human body as obtained from computational fluid dynamics simulation at each time step; The total flight time of a human body, denoted as T, refers to the total time from takeoff to landing, reflecting the human body's ability to remain airborne.

[0066] Understandably, the above output can not only be used to predict the flight distance of athletes in ski jumping, but also to provide a reference for optimizing athletes' aerial posture and analyzing competition tactics.

[0067] Example 2: Another specific embodiment of the present invention discloses a prediction system for flight distance in ski jumping events based on adaptive aerodynamic coupling integral, such as... Figure 4 As shown, the system includes: The initialization module is used to establish a ski jumping human body model, set the flight attitude parameters and environmental parameters of the human body model, and send the flight attitude parameters and environmental parameters to the calculation module and the human body model to the simulation module. The calculation module is used to calculate the relative airflow velocity and the total angle of attack of the human body at the current moment based on the flight attitude parameters and environmental parameters, and send the relative airflow velocity and the total angle of attack of the human body at the current moment to the simulation module; The simulation module is used to perform computational fluid dynamics simulation on the human body model based on the relative airflow velocity and the total angle of attack of the human body at the current moment to obtain the lift and drag acting on the human body at the current moment; based on the lift and drag, the acceleration corresponding to the human body at the current moment is obtained, and the acceleration corresponding to the human body at the current moment is sent to the integration module; The integration module is used to update the velocity and position of the human body's center of mass based on the current acceleration of the human body using adaptive aerodynamic coupling integration, and then send the updated position to the flight distance acquisition module. The flight distance acquisition module is used to determine whether the human body has landed based on the updated position. If so, the flight distance of the human body is obtained; otherwise, the calculation module is called until the flight distance of the human body is obtained.

[0068] Preferably, the system further includes an output module for outputting result data, which includes the human body's flight distance, flight trajectory data, speed time series, aerodynamic data, and total flight time. The human body's flight distance is represented by x. land , refers to the horizontal displacement of the human body from the takeoff point to the landing point; flight trajectory data, represented as (x t ,y t (v) refers to the trajectory of the human body's center of mass during flight; the velocity time series is represented as (v... x,t ,v y,t (), representing the change in human flight speed over time; aerodynamic data, expressed as (L t D t ), representing the lift and drag forces experienced by the human body as obtained from computational fluid dynamics simulation at each time step; the total flight time of the human body, denoted as T, refers to the total time from takeoff to landing, reflecting the human body's ability to remain airborne.

[0069] Example 3: Another specific embodiment of the present invention discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the method for predicting the flight distance of a ski jumping event based on adaptive aerodynamic coupling integral as described above.

[0070] Compared with existing technologies, the beneficial effects of the ski jumping flight distance prediction method based on adaptive aerodynamic coupling integral provided by this invention are as follows: 1. This invention dynamically calculates the lift and drag acting on the human body at each time step through real-time computational fluid dynamics simulation based on relative airflow velocity and the total angle of attack of the human body, taking into account the influence of flight attitude pitch angle and wind speed; based on adaptive aerodynamic coupling integral, the acceleration corresponding to the human body is used to update the velocity and position of the human body's center of mass, thereby obtaining the flight distance of the human body, without relying on historical data or empirical fitting curves, thus improving the prediction accuracy of flight distance.

[0071] 2. This invention can input environmental parameters such as ski jump terrain function, flight attitude pitch angle, and wind speed according to actual conditions, and combine them with the individual characteristics of athletes (such as weight, take-off speed, etc.) to make high-precision predictions of ski jump flight distance. It can be adapted to different ski jumps, action techniques, and wind conditions, and can also make personalized predictions for different athletes, with high generalization ability and versatility.

[0072] 3. This invention obtains the landing point through interpolation, which improves the prediction accuracy of the landing point and makes the landing point continuous and differentiable, making it suitable for use in engineering optimization algorithms.

[0073] 4. This invention reduces traditional experiments and tests, lowers costs, and improves efficiency through computational fluid dynamics simulation.

[0074] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0075] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting flight distance in ski jumping events based on adaptive aerodynamic coupling integral, characterized in that, The method includes the following steps: Step S1: Establish a ski jumping human model and set the flight posture parameters and environmental parameters of the human model; Step S2: Calculate the relative airflow velocity and the total angle of attack of the human body at the current moment based on the flight attitude parameters and environmental parameters; Step S3: Perform computational fluid dynamics simulation on the human body model based on the relative airflow velocity and the total angle of attack of the human body at the current moment to obtain the lift and drag acting on the human body at the current moment; obtain the acceleration of the human body at the current moment based on the lift and drag. Step S4: Based on the adaptive aerodynamic coupling integral, update the velocity and position of the human body's center of mass using the acceleration corresponding to the human body at the current moment; determine whether the human body has landed based on the updated position. If so, obtain the flight distance of the human body; otherwise, return to step S2 and continue execution until the flight distance of the human body is obtained.

2. The method for predicting flight distance in ski jumping events based on adaptive aerodynamic coupling integral as described in claim 1, characterized in that, The relative airflow velocity at the current moment can be calculated using the following formula: ， in, This represents the relative horizontal airflow velocity at the current moment. This indicates the speed of the human body's center of mass in the horizontal direction at the current moment. This indicates the wind speed in the horizontal direction. This indicates the vertical relative airflow velocity at the current moment. This indicates the current velocity of the human body's center of mass in the vertical direction. t represents the vertical wind speed, and t represents the current time.

3. The method for predicting flight distance in ski jumping events based on adaptive aerodynamic coupling integral as described in claim 1, characterized in that, The trajectory angle is calculated using the following formula: , in, Indicates the trajectory angle; The total angle of attack of the human body at the current moment is calculated using the following formula: ， in, Indicates the total angle of attack of the human body. Indicates the pitch angle of the flight attitude.

4. The method for predicting flight distance in ski jumping events based on adaptive aerodynamic coupling integral as described in claim 1, characterized in that, The lift and drag forces acting on the human body at the current moment, obtained by computational fluid dynamics simulation of the human body model based on the current relative airflow velocity and the total angle of attack of the human body, include: The computational domain is set according to the human body model; The computational domain and the human body model are meshed; Set the calculation parameters, input the relative airflow velocity and the total angle of attack of the human body at the current moment, and perform computational fluid dynamics simulation on the human body model after meshing in the computational domain to obtain the lift and drag acting on the human body at the current moment.

5. The method for predicting flight distance in ski jumping events based on adaptive aerodynamic coupling integral as described in claim 1, characterized in that, The process of obtaining the acceleration of the human body at the current moment based on the lift and drag includes: decomposing the lift and drag into a Cartesian coordinate system according to the trajectory angle to obtain the resultant force in the horizontal direction and the resultant force in the vertical direction; and obtaining the acceleration of the human body at the current moment based on the resultant force in the horizontal direction and the resultant force in the vertical direction.

6. The method for predicting flight distance in ski jumping events based on adaptive aerodynamic coupling integral as described in claim 1, characterized in that, The method of updating the velocity and position of the human body's center of mass based on the adaptive aerodynamic coupling integral using the acceleration corresponding to the human body at the current moment includes: defining an initial time step and defining a state vector based on the acceleration corresponding to the human body at the current moment; in each time step: calculating an intermediate slope vector, obtaining the corresponding fourth-order and fifth-order solutions based on the intermediate slope vector, obtaining the local error based on the fourth-order and fifth-order solutions, and if the local error is less than or equal to the error threshold, updating the velocity and position of the human body's center of mass using the fifth-order solution, updating the next time step, and entering the next time step; otherwise, adjusting the current time step and recalculating the intermediate slope vector until the local error is less than or equal to the error threshold.

7. The method for predicting flight distance in ski jumping events based on adaptive aerodynamic coupling integral as described in claim 6, characterized in that, If the local error is less than or equal to the error threshold, the velocity and position of the human body's center of mass are updated using the following formula: ， in, This represents the updated velocity of the human body's center of mass in the horizontal direction. This represents the updated velocity of the human body's center of mass in the vertical direction. Indicates the current time step. This represents the updated horizontal displacement relative to the initial position of the human body. This represents the updated vertical displacement relative to the initial position of the human body. This represents the first element of the fifth-order solution. This represents the second element of the fifth-order solution. This represents the third element of the fifth-order solution. This represents the fourth element of the fifth-order solution; and the next time step is updated using the following formula: ， in, This represents the minimum step size ratio. This indicates the maximum step size ratio. Indicates the error threshold. Indicates local error. Indicates the safety factor; Otherwise, adjust the current time step using the formula described above.

8. The method for predicting flight distance in ski jumping events based on adaptive aerodynamic coupling integral as described in claim 6, characterized in that, After each update of the human body's center of mass position, determine whether the human body has landed using the following expression: ， in, This indicates the vertical position of the human body's center of mass after the update. This indicates the vertical height of the corresponding ski jump slope, i.e., the corresponding ground height.

9. A prediction system for flight distance in ski jumping events based on adaptive aerodynamic coupling integral, characterized in that, The system includes: The initialization module is used to establish a ski jumping human body model, set the flight attitude parameters and environmental parameters of the human body model, and send the flight attitude parameters and environmental parameters to the calculation module and the human body model to the simulation module. The calculation module is used to calculate the relative airflow velocity and the total angle of attack of the human body at the current moment based on the flight attitude parameters and environmental parameters, and send the relative airflow velocity and the total angle of attack of the human body at the current moment to the simulation module; The simulation module is used to perform computational fluid dynamics simulation on the human body model based on the relative airflow velocity and the total angle of attack of the human body at the current moment to obtain the lift and drag acting on the human body at the current moment; based on the lift and drag, the acceleration corresponding to the human body at the current moment is obtained, and the acceleration corresponding to the human body at the current moment is sent to the integration module; The integration module is used to update the velocity and position of the human body's center of mass based on the current acceleration of the human body using adaptive aerodynamic coupling integration, and then send the updated position to the flight distance acquisition module. The flight distance acquisition module is used to determine whether the human body has landed based on the updated position. If so, the flight distance of the human body is obtained; otherwise, the calculation module is called until the flight distance of the human body is obtained.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method for predicting the flight distance of a ski jumping event based on adaptive aerodynamic coupling integral as described in claims 1-8.

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