A parachute ladder system modeling optimization method and system based on mechanics and parameter optimization

Abstract

The present invention discloses a parachute ladder system modeling and optimization method and system based on mechanics and parameter optimization, which relates to the technical field of wind power generation modeling. The present invention proposes an efficient parachute ladder system modeling and optimization method by combining mechanical analysis with parameter optimization algorithm, which significantly improves the performance and reliability of the high-altitude wind energy capture system; the CPO optimization algorithm is used to perform dynamic parameter optimization of the floating system and the working system under multiple constraints, ensuring that the output power is maximized under the premise of meeting the buoyancy balance, rope speed limit and parachute area constraints. Through the adaptive learning rate adjustment mechanism and the dynamic update of the trust region radius, the algorithm can quickly converge to the optimal solution, avoid the local optimality or constraint violation problems commonly found in traditional optimization methods, can adapt to changes in wind conditions at different heights, and can effectively prevent the system from overturning, ensuring long-term stable operation.

Description

Technical Field

[0001] The present invention relates to the technical field of wind power generation modeling, and in particular to a parachute ladder system modeling optimization method and system based on mechanics and parameter optimization. Background Art

[0002] High-altitude wind power generation technology has attracted considerable attention in recent years due to its stable wind speeds and high energy density. However, existing technologies still face significant challenges in practical application. Traditional high-altitude wind energy capture devices (such as kite-based power generation systems or airship-mounted turbines) have limitations: First, system stability is insufficient. The devices are susceptible to turbulence and wind shear in complex aerodynamic environments, leading to structural vibration or the risk of overturning. This is especially true when the floating system is dynamically coupled with the working components, making it difficult to accurately maintain mechanical equilibrium. Second, energy conversion efficiency is low. Existing aerodynamic models often rely on simplified assumptions, such as ignoring wake attenuation effects or nonlinear variations in the vertical wind speed distribution. This leads to large power prediction errors, and optimization methods (such as genetic algorithms) are prone to local optimality under multiple constraints, failing to fully tap the potential of high-altitude wind energy. Third, engineering feasibility is limited. Parameter design fails to fully consider the coordination of multiple objectives (such as buoyancy balance, rope speed limits, and parachute area constraints), resulting in a disconnect between optimization results and actual operating conditions and a lack of dynamic adjustment mechanisms to address environmental changes. Summary of the Invention

[0003] The purpose of the present invention is to provide a parachute ladder system modeling optimization method and system based on mechanics and parameter optimization to improve the above technical problems.

[0004] In order to achieve the above-mentioned object of the invention, the embodiment of the present invention provides the following technical solutions:

[0005] A parachute ladder system modeling and optimization method based on mechanics and parameter optimization includes:

[0006] S1. Obtaining the design parameters and environmental parameters of the parachute ladder system;

[0007] S2. Based on the design parameters and environmental parameters, perform force analysis on the floating system and the working system to obtain floating analysis results and working analysis results;

[0008] S3. Based on the results of the floating analysis and the work analysis, the parachute ladder system is modeled to obtain an initial parachute ladder model;

[0009] S4. Set system constraints and modeling objectives, use the improved CPO algorithm to optimize the initial model of the parachute ladder, and obtain the parachute ladder optimization model.

[0010] Furthermore, the design parameters include the parachute opening height, the number of active parachutes, the active parachute projection radius, the helium balloon radius, the cable running speed, the angle between the cable and the ground, the helium balloon weight, the helium weight, the active parachute weight and the cable weight; the environmental parameters include the wind speed and atmospheric density corresponding to the active parachute rising height.

[0011] Furthermore, the S2 includes:

[0012] S2-1. Setting a motion coordinate system for a power parachute; setting a corresponding tension coefficient for each power parachute based on a tension coefficient attenuation relationship between the power parachutes; the tension coefficient includes a first tension coefficient and a second tension coefficient for each power parachute;

[0013] S2-2. Based on the design parameters, calculate the total weight of the floating system, the weight of the cable and the weight of the power parachute;

[0014] S2-3. Construct and solve the buoyancy balance system of the helium balloon to obtain the floating analysis result, that is, the cable tension pulling the helium balloon;

[0015] S2-4. Calculate the power of each parachute in the power system based on the results of the floating analysis, design parameters, and environmental parameters;

[0016] S2-5. Based on the power of each working parachute, calculate the total power of the working system, that is, the sum of the power of each working parachute, and obtain the work analysis result.

[0017] Furthermore, the S2-4 includes:

[0018] S2-4-1. Calculate the gravity of each parachute and the corresponding parachute-cable gravity based on the design parameters;

[0019] S2-4-2. Calculate the relative vector wind speed based on the wind speed and cable running speed;

[0020] S2-4-3. Calculate the axial drag and vertical lift corresponding to each power parachute based on the respective drag coefficients and relative vector wind speeds;

[0021] S2-4-4, according to the formula:

[0022] ;

[0023] Calculate the supplementary gravity angle ;in, represents the integral direction of the cable along the axial direction, represents the integral function, represents the torque about the ground due to the weight acting on the cable, Indicates the number of parachutes doing work, Indicates the weight of the working parachute, It represents the projected force area of ​​the work parachute, Indicates the cable running speed, Indicates the angle between the cable and the ground corresponding to the last working parachute, Indicates wind speed, represents the atmospheric density, Indicates the first tension coefficient corresponding to the last working parachute, represents the lift-to-drag coefficient ratio, 、 、 denote the cosine function, sine function and tangent function respectively, Indicates the mass of the cable per meter, Indicates the total weight of the cable, represents the integral function;

[0024] S2-4-5. Calculate the power of each powered parachute based on the results of the float analysis, the supplementary gravity angle, the relative vector wind speed, the drag along each axis, and the lift along each vertical axis.

[0025] Furthermore, the initial model of the parachute ladder in S3 is the power model of the parachute ladder system, and the corresponding formula is:

[0026] ;

[0027] in, Indicates the power of the parachute ladder system, Indicates the number of parachutes doing work, Indicates the The first tension coefficient corresponding to the working parachute is, Indicates the The wind speed of a power parachute, represents the cosine function, represents the cable speed, represents the air density, Indicates the The angle between the cable and the ground plane corresponding to the parachute, Indicates the power of the last working parachute, represents the buoyancy of a helium balloon, It represents the projected force area of ​​the working parachute.

[0028] Furthermore, the system constraints include range constraints and buoyancy balance constraints; and the modeling objective is to lose minimum working power.

[0029] Furthermore, the improved CPO algorithm is used to optimize the initial model of the parachute ladder, and the corresponding process is:

[0030] S4-1. Set the trust region radius for the current round, randomly generate an initial parameter combination and use it as the strategy vector for the current round; determine whether the initial parameter combination meets the range constraint of the system constraint conditions; if so, proceed to S4-2; otherwise, regenerate the initial parameter combination;

[0031] S4-2, the power model of the parachute ladder system is used as the objective function, and the system constraints are used as the constraint function;

[0032] S4-3. Calculate the target gradient of the objective function and the constraint gradient of the constraint function corresponding to the current round's policy vector using Monte Carlo sampling or automatic differentiation methods;

[0033] S4-4, according to the formula:

[0034] ;

[0035] Constructing the optimization objective function ;in, represents the Lagrange multiplier, represents the penalty coefficient, represents the maximum function, represents the objective function, represents the constraint function, represents the total number of constraints;

[0036] S4-5. Update the current round’s strategy vector based on the optimization objective function.

[0037] S4-6, update the Lagrange multiplier and trust region radius;

[0038] S4-7. Calculate whether the updated strategy vector and its objective function satisfy the system constraints and modeling objectives. If so, use the strategy vector of the current round as the optimized parameter combination. Otherwise, return to S4-3.

[0039] S4-8. Apply the optimized parameter combination to the initial model of the parachute ladder to complete the optimization of the initial model of the parachute ladder.

[0040] Furthermore, the S4-6 includes:

[0041] S4-6-1. According to the formula:

[0042] ;

[0043] Update the Lagrange multiplier and get the updated Lagrange multiplier ;

[0044] S4-6-2, according to the formula:

[0045] ;

[0046] Dynamically update the learning rate to get the updated learning rate ;in, represents the norm, represents the gradient of the current round, represents the gradient of the previous round, represents the learning rate of the previous round, 、 Represent the trust region radius and the updated trust region radius respectively;

[0047] S4-6-3, according to the formula:

[0048] ;

[0049] Based on the updated learning rate, update the trust region radius to obtain the updated trust region radius .

[0050] A parachute ladder system modeling and optimization system based on mechanics and parameter optimization includes:

[0051] System parameter acquisition module, used to obtain the design parameters and environmental parameters of the parachute ladder system;

[0052] The force analysis module is used to perform force analysis on the floating system and the working system based on design parameters and environmental parameters, and obtain the floating analysis results and the working analysis results;

[0053] The parachute ladder modeling module is used to model the parachute ladder system based on the results of the floating analysis and the work analysis to obtain the initial model of the parachute ladder;

[0054] The parachute ladder optimization module is used to set system constraints and modeling objectives, and uses the improved CPO algorithm to optimize the initial parachute ladder model to obtain the parachute ladder optimization model.

[0055] The beneficial effects of the present invention are:

[0056] This paper combines mechanical analysis with parameter optimization algorithms to propose an efficient parachute-ladder system modeling and optimization method, significantly improving the performance and reliability of high-altitude wind energy capture systems. The CPO optimization algorithm is used to dynamically optimize the parameters of the floating and power systems under multiple constraints, ensuring maximum output power while satisfying buoyancy balance, rope speed limits, and parachute area constraints. Through an adaptive learning rate adjustment mechanism and dynamic updates of the trust region radius, the algorithm rapidly converges to the optimal solution, avoiding the local optimality or constraint violation issues common in traditional optimization methods. It can adapt to changing wind conditions at different altitudes while effectively preventing system overturning and ensuring long-term stable operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without making any creative efforts.

[0058] Figure 1 is a flow chart of a method in an embodiment of the present invention;

[0059] Figure 2 Schematic diagram of a parachute ladder system in an embodiment of the present invention;

[0060] Figure 3 This is a force analysis diagram of the floating system in an embodiment of the present invention;

[0061] Figure 4 Schematic diagrams of different stages of the floating system in an embodiment of the present invention; wherein (a) is a schematic diagram of the floating system in the initial stage, and (b) is a schematic diagram of the floating system in the working stage;

[0062] Figure 5 For the embodiment of the present invention Force analysis diagram of a working parachute;

[0063] Figure 6 This is a force analysis diagram of the last power-performing parachute in an embodiment of the present invention;

[0064] Figure 7 is a graph showing the relationship between power and radius of a working parachute in an embodiment of the present invention;

[0065] Figure 8 is a relationship diagram between power and the number of working parachutes under the first working condition in an embodiment of the present invention;

[0066] Figure 9 is a relationship diagram between power and the number of working parachutes under the second working condition in an embodiment of the present invention;

[0067] Figure 10 is a relationship diagram between power and the number of working parachutes under the third working condition in an embodiment of the present invention;

[0068] Figure 11 is a relationship diagram between power and cable speed (rope speed) under the first working condition in an embodiment of the present invention;

[0069] Figure 12 is a relationship diagram between power and cable speed (rope speed) under the second working condition in an embodiment of the present invention;

[0070] Figure 134 is a relationship diagram between power and cable speed (rope speed) under the third working condition in an embodiment of the present invention. DETAILED DESCRIPTION

[0071] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. The components of the embodiments of the present invention generally described and represented in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0072] See also Figure 1 This embodiment provides a parachute ladder system modeling optimization method based on mechanics and parameter optimization, which includes:

[0073] S1. Obtain the design parameters and environmental parameters of the parachute ladder system; the parachute ladder system includes a floating system and a working system. In this embodiment, the parachute ladder system is a wind energy conversion and utilization device, and its aerial part is mainly composed of a helium balloon, a working parachute and a cable. The power of capturing wind energy is crucial to the force of the aerial system. Therefore, the floating system is a helium balloon, which provides tension for the working system; the working system includes multiple working parachutes and cables. Parachute ladder combined wind capture device such as Figure 2 As shown, a cable suspended from a helium balloon connects to a ground-based power generation device. Several parachutes are deployed on the cable, capturing high-altitude wind energy through the parachute's aerodynamic effect. This generates a significant tension on the cable near the ground, driving the cable upward to generate work, which in turn drives the tethered aircraft to generate electricity. Each power-generating parachute in the parachute ladder system has identical structure and parameters.

[0074] The design parameters include the parachute opening height 、Number of working parachutes , Projected force area of ​​the working parachute , helium balloon radius , Cable running speed , Angle between cable and ground , helium balloon weight , helium weight , weight of working parachute and cable weight ;in, , Indicates the projection radius of the umbrella surface projection circle of the power umbrella, The environmental parameters include the wind speed corresponding to the height of the parachute. and atmospheric density .

[0075] S2. Based on the design parameters and environmental parameters, perform force analysis on the floating system and the working system to obtain floating analysis results and working analysis results;

[0076] A helium balloon is mounted at the top of the ladder and, when the ladder is not in operation, is restrained to the ground by a tether. Since the power parachute can only deploy successfully at the rated deployment wind speed, it provides greater operational pull. The rated wind speed can only be achieved at a certain altitude above the ground. Therefore, during the initial flotation phase, before the ladder system reaches the deployment altitude for the power parachute, the helium balloon provides the required lift to guide the system into the air. Once the power parachute reaches the deployment altitude, the power parachute deploys, and the ladder system enters the power phase, where the helium balloon provides additional lift to assist the system in its work. During the power phase, the helium balloon's buoyancy exerts a strong force perpendicular to the tether, preventing the system from tipping over. After the power phase, the power parachute retracts, and the ladder system enters the recovery phase. The power system begins descending under its own weight. The lift provided by the helium balloon slows the system's descent, preventing tipping and ensuring safe operation. When the power parachute reaches the deployment position, the power parachute assembly is promptly controlled to reopen, entering the next power phase. It can be seen that helium balloons play an important role in the entire wind power generation process.

[0077] Thus, the S2 includes:

[0078] S2-1, set the pressure center of the power parachute as the origin, and the running direction of the power parachute (i.e. the running direction of the cable or along the cable) as axis, and The direction perpendicular to the axis (the direction of the vertical rope) is set to The axis sets the motion coordinate system for the powered parachute. Based on the drag coefficient attenuation relationship between the powered parachutes, the drag coefficients for each powered parachute are set. The pressure center of the powered parachute is the center of the parachute's canopy projection circle. The drag coefficients include the first and second drag coefficients for each powered parachute, both of which follow the drag coefficient attenuation relationship. The first drag coefficient is the aerodynamic coefficient along the axial direction of the powered parachute; the second drag coefficient is the aerodynamic coefficient perpendicular to the axial direction of the powered parachute.

[0079] The force of a single power parachute basically follows the force characteristics of a traditional parachute. However, since multiple power parachutes are connected in series on the same cable, the aerodynamic characteristics of the power system are more complicated. To ensure the reliability of the model, the formula corresponding to the tension coefficient attenuation relationship is:

[0080] ;

[0081] in, Indicates the moment, Indicates the The tension coefficient corresponding to the working parachute is 、 They represent the tension coefficients corresponding to the first and last power parachute, Represents a natural constant.

[0082] S2-2. Calculate the total weight of the floating system based on the design parameters (weight of helium balloon + helium), weight of cable and the weight of the power parachute , the corresponding formulas include:

[0083] ;

[0084] ;

[0085] ;

[0086] S2-3. Construct the buoyancy balance system of the helium balloon and solve it to obtain the floating analysis results, that is, the cable tension pulling the helium balloon ;

[0087] like Figure 3 and Figure 4 As shown, the buoyancy system is used to provide sufficient lift for the parachute ladder system so that the parachute ladder system reaches the minimum parachute opening height. It is required that in the vertical direction, the buoyancy provided by the helium balloon can at least overcome the weight of the parachute rope, the balance device, and the weight of the helium balloon and the helium gas inside it. When the helium balloon drives the first working parachute to reach the parachute opening height, the entire system is in a balanced state. In the vertical direction, the sum of the weight of the parachute rope pulled by the helium balloon, the weight of the first working parachute, the weight of the balance device, and the weight of the helium balloon and the helium gas inside it is equal to the buoyancy it experiences. The equation corresponding to the buoyancy balance system is:

[0088] ;

[0089] ;

[0090] ;

[0091] ;

[0092] in, Indicates the length of the cable corresponding to the height of the helium balloon. represents the volume of the helium balloon calculated from the radius of the helium balloon, represents the tension of the cable pulling the helium balloon, represents the density of the helium balloon, represents the acceleration due to gravity, Indicates the weight of all working parachutes, represents the acceleration due to gravity, represents the buoyancy of a helium balloon, represents the resistance provided by the wind to the helium balloon, represents the relative speed of the wind relative to the helium balloon, represents the air resistance coefficient of the helium balloon, represents the frontal area of ​​the helium balloon, 、 represent the cosine and sine functions respectively.

[0093] exist Figure 3 middle, Indicates the speed of the helium balloon. 、 They represent the horizontal resistance and vertical resistance provided by the wind to the helium balloon, Indicates resistance The angle with the ground, Indicates the gravity acting on the parachute. Figure 4 In the equation, h represents the height of the helium balloon's ascent.

[0094] S2-4. Calculate the power of each parachute in the power system based on the results of the floating analysis, design parameters, and environmental parameters;

[0095] The appearance of the power parachute is basically the same as that of the common drag parachute, and it is mainly composed of a canopy, parachute ropes, main cables, etc. The canopy is connected to the parachute ropes; the parachute ropes are of uniform length, pass through the rope buckles evenly arranged on the bottom edge of the canopy, and converge at a point on the main cable below the canopy. In the initial floating stage, the power parachute remains closed and does not provide lift; after reaching the power parachute opening height and wind speed, the power parachute opens in turn and enters the power generation stage; after opening, the power parachute is affected by aerodynamic force, and the rope component of the aerodynamic force it receives is transmitted to the ground in the form of rope force through the cable to drive the generator to generate electricity. Thus, if Figure 5 As shown, the process corresponding to S2-4 is:

[0096] S2-4-1. Calculate the gravity of each parachute and the corresponding parachute-cable gravity based on the design parameters. The formula corresponding to S2-4-1 is:

[0097] ;

[0098] ;

[0099] ;

[0100] in, Indicates the The gravity corresponding to the work parachute, Indicates the The power parachute-cable gravity corresponding to the power parachute, Indicates the The cable length corresponding to the power parachute is Indicates the mass of the cable per meter, Indicates the total weight of the cable.

[0101] S2-4-2. Calculate the relative vector wind speed based on the wind speed and the cable running speed; the formula corresponding to S2-4-2 is:

[0102] ;

[0103] ;

[0104] ;

[0105] in, represents the relative vector wind speed, represents the relative vector wind speed along the axis, Indicates the relative vector wind speed along the vertical axis.

[0106] S2-4-3. Based on each pull coefficient and relative vector wind speed, calculate the axial drag and vertical axis lift corresponding to each power parachute; the formula corresponding to S2-4-3 is:

[0107] ;

[0108] ;

[0109] in, Indicates the The vertical axis lift corresponding to the power parachute is Indicates the The second tension coefficient corresponding to the working parachute is, Indicates the The first tension coefficient corresponding to the working parachute is, Indicates the The axial resistance corresponding to each working parachute.

[0110] S2-4-4, according to the formula:

[0111] ;

[0112] Calculate the supplementary gravity angle ;in, represents the integral direction of the cable along the axial direction, represents the integral function, represents the torque about the ground due to the weight acting on the cable, represents the tangent function, Indicates the first tension coefficient corresponding to the last working parachute, represents the lift-to-drag coefficient ratio, Indicates the angle between the cable corresponding to the last working parachute and the ground.

[0113] like Figure 6 As shown in the figure, due to the long rope, the force acting on the cable corresponding to the last working parachute is partially tilted compared to the ground direction. This angle is the supplementary gravity angle. To ensure the accuracy of the model, the supplementary gravity angle is introduced into the equilibrium equation of the last working parachute. The corresponding formula for this equilibrium equation is:

[0114] ;

[0115] in, Indicates the power corresponding to the last working parachute, Indicates aerodynamic force, It represents the sum of the weight of the power parachute and the equivalent cable mass of the cable corresponding to the last power parachute.

[0116] The equivalent tether mass is determined by calculating the torque around the ground station due to gravity. Since the equivalent cable mass is located at the end of the parachute, the torque around the ground station generated by the tether distributed mass and the equivalent tether mass is equal. Therefore, the formula for the equivalent tether mass is:

[0117] ;

[0118] thereby, The corresponding formula is:

[0119] ;

[0120] From this, the supplementary gravity angle can be obtained The formula. Figure 5 middle, Indicates the speed of the power parachute. Indicates wind force. Figure 6 middle, Indicates the ground, represents the force exerted by the ground on the last parachute doing work, Indicates aerodynamic force.

[0121] S2-4-5. Calculate the power of each powered parachute based on the results of the float analysis, the supplementary gravity angle, the relative vector wind speed, the drag forces along each axis, and the lift forces along each vertical axis;

[0122] The first parachute to The formulas corresponding to the power of each power parachute are: ;

[0123] ;

[0124] The formula corresponding to the power of the last working parachute is:

[0125] ;

[0126] ;

[0127] in, When 1, for , which is the cable tension that pulls the helium balloon (floating analysis result).

[0128] S2-5. Calculate the total power of the power system based on the power of each power parachute , that is, the sum of the power of each work-doing parachute, and the work analysis result is obtained.

[0129] S3. Based on the work analysis results, the parachute ladder system is modeled to obtain an initial parachute ladder model;

[0130] The initial model of the parachute ladder in S3 is the power model of the parachute ladder system, and the corresponding formula is:

[0131] ;

[0132] ;

[0133] in, Indicates the power of the parachute ladder system, Indicates the The first tension coefficient corresponding to the working parachute is, Indicates the The wind speed of a power parachute, represents the cosine function, represents the cable speed, represents the air density, Indicates the The angle between the cable and the ground plane corresponding to the power parachute, = represents the power of the last power parachute. Since the power parachutes are connected in series on the cable, the angles between each power parachute and the ground plane are similar to the angles between the cable and the ground plane, both of which are .

[0134] The modeling process is an existing technology, so I will not describe it in detail.

[0135] S4. Set system constraints and modeling objectives, use the improved CPO algorithm to optimize the initial model of the parachute ladder, and obtain the parachute ladder optimization model.

[0136] The system constraints include range constraints and buoyancy balance constraints; range constraints include 、 、 、 、 、 :in, 、 Respectively represent the minimum helium balloon radius threshold and the maximum helium balloon radius threshold, 、 They represent the maximum working parachute projected force area threshold and the minimum working parachute projected force area threshold, respectively. 、 Respectively represent the minimum cable speed threshold and the maximum cable speed threshold, 、 They represent the minimum and maximum thresholds for the number of active parachutes, 、 They represent the minimum parachute opening height threshold and the maximum parachute opening height threshold respectively. 、 They represent the minimum angle threshold and the maximum angle threshold respectively. The buoyancy balance constraint is the buoyancy balance constraint of the existing parachute ladder model.

[0137] The modeling target is the minimum working power loss of each parachute. In this embodiment, the minimum working power loss is 5MW.

[0138] The CPO algorithm is a CPO optimizer (Crowned Porcupine Optimizer). CPO algorithms typically use a fixed learning rate and trust region radius, or have a relatively simple update mechanism. The optimization objective and constraint handling mechanism are unclear, and this can lead to suboptimal performance when dealing with complex constraints. Therefore, the present invention introduces an augmented Lagrangian function and a dynamic update mechanism. The improved CPO algorithm is used to optimize the initial umbrella ladder model. The corresponding process is as follows:

[0139] S4-1. Set the trust region radius of the current round , the initial parameter combination will be randomly generated, namely the radius of the helium balloon, the radius of the power parachute, the speed of the cable, the number of power parachutes, the parachute opening height, and the angle between the cable and the ground, and used as the strategy vector for the current round ; Determine whether the initial parameter combination meets the range constraint of the system constraint condition. If so, proceed to S4-2; otherwise, regenerate the initial parameter combination;

[0140] S4-2. Using the power model of the parachute ladder system as the objective function , taking the system constraints as constraint functions ;

[0141] S4-3. Calculate the current policy vector using Monte Carlo sampling or automatic differentiation methods The corresponding objective function The target gradient and constraint functions The constrained gradient ; When i is 1, the constraint function is the range of the radius of the helium balloon. Similarly, when i is 7, the constraint function is , that is, the range of values ​​for minimum working power loss.

[0142] S4-4, based on the objective function and constraint function, construct the optimization objective function. The corresponding formula is:

[0143] ;

[0144] in, represents the Lagrange multiplier, represents the penalty coefficient, represents the maximum function, Represents the total number of constraints.

[0145] S4-5. Based on the optimization objective function, update the strategy vector of the current round. The corresponding formula is:

[0146] ;

[0147] in, represents the updated policy vector, Represents the transposed matrix of the gradient vector corresponding to the optimization objective function at the current round’s policy vector, Represents new parameters to be optimized (candidate parameters).

[0148] S4-6, update the Lagrange multiplier and trust region radius, the corresponding process is:

[0149] S4-6-1. According to the formula:

[0150] ;

[0151] Update the Lagrange multiplier and get the updated Lagrange multiplier The updated Lagrange multiplier is used to optimize the objective function in the next round.

[0152] S4-6-2. Use the adaptive learning rate adjustment mechanism to dynamically update the learning rate and obtain the updated learning rate , the corresponding formula is:

[0153] ;

[0154] in, represents the norm, represents the gradient of the current round, represents the gradient of the previous round, Represents the learning rate of the previous round.

[0155] S4-6-3. Based on the updated learning rate, update the trust region radius, i.e. The updated trust region radius is used to update the strategy vector in the next round.

[0156] S4-7. Calculate whether the updated strategy vector and its objective function satisfy the system constraints and modeling objectives. If so, use the strategy vector of the current round as the optimized parameter combination. Otherwise, return to S4-3.

[0157] S4-8. Apply the optimized parameter combination to the initial model of the parachute ladder to complete the optimization of the initial model of the parachute ladder.

[0158] A parachute ladder system modeling and optimization system based on mechanics and parameter optimization includes:

[0159] System parameter acquisition module, used to obtain the design parameters and environmental parameters of the parachute ladder system;

[0160] The force analysis module is used to perform force analysis on the floating system and the working system based on design parameters and environmental parameters, and obtain the floating analysis results and the working analysis results;

[0161] The parachute ladder modeling module is used to model the parachute ladder system based on the results of the floating analysis and the work analysis to obtain the initial model of the parachute ladder;

[0162] The parachute ladder optimization module is used to set system constraints and modeling objectives, and uses the improved CPO algorithm to optimize the initial parachute ladder model to obtain the parachute ladder optimization model.

[0163] In this embodiment, a parachute ladder system is modeled to simulate the energy conversion process of the parachute ladder system. The corresponding experimental parameters are shown in Tables 1 and 2.

[0164] Table 1 Floating system parameters

[0165] name quantity parameter inclination - 40°-45° Parachute opening height - 200m Cable mass per unit length - 4.9kg / Number of parachutes 1 - Quality of working umbrella 1 400kg Number of balancing devices 2 Balancing device mass 1 40kg Helium balloon fabric quality - 50kg Air density - <![CDATA[1.225kg / m 3 ]]> Helium density - 0.1785 Helium balloon radius - 8m

[0166] Table 2

[0167] Air density First parachute tension coefficient CT1 Tail parachute tension coefficient CTN 0.805kg / m³-0.875kg / m³ 0.8 1.6

[0168] Based on system efficiency standards and typical energy conversion losses, the ground-based power generation system is expected to experience a 20% power loss. Due to the potential for fluid-structure interaction to impact system performance and the potential for the dual-parachute ladder's coordinated operation to not be fully realized, a 20% power design margin is added to the ground-based power generation system's losses. Taking these factors into account, to ensure the desired power generation target is achieved, the parachute ladder's direct output power (excluding losses and margin) must reach at least 7.5MW, assuming a single parachute group power generation capacity of 5MW. This design not only meets the project's total power generation requirements but also provides sufficient margin for the system to cope with actual operational challenges, ensuring the power generation target is achieved or exceeded.

[0169] Regarding the determination of wind speed, this measurement selected the wind speed data under the P10 wind condition of the Alxa League test site, and selected the wind speeds corresponding to the three altitude ranges of 1500-2000 meters, 2000-2500 meters and 2500-3000 meters as estimated data for comparison, as shown in Table 3.

[0170] Table 3

[0171] Height range (m) 1500-2000 2000-2500 2500-3000 Wind speed (m / s) 15.5-18.1 18.1-21.3 21.3-23

[0172] The present invention models the parachute-ladder system with the parameters set in Tables 1 to 3, and selects a linear relationship between the radius of the working parachute, the cable speed, the number of working parachutes and the power under different working conditions.

[0173] like Figure 7 As shown, under different wind speeds, the power P increases with the increase of the radius of the power parachute. Under the condition of wind speed of 15.5m / s to 18.1m / s, the power parachute radius needs to reach about 60 meters to achieve the target power, but the production technology of the parachute is relatively high; when the wind speed reaches above 18.1m / s, the radius of the power parachute that meets the 5MW condition only needs to be greater than 45m; when the wind speed continues to increase to above 21.3m / s, the radius of the power parachute that meets the conditions continues to decrease to about 40m. It can be seen from this that when considering the wind speed of the parachute ladder operating environment, that is, the operating range, it is necessary to comprehensively consider the local wind resource conditions and other conditions. Figure 7 In the figure, the horizontal straight line is the 5MW power line.

[0174] Set three working conditions, namely:

[0175] Working condition 1: wind speed 15.5 m / s to 18.1 m / s, parachute radius R = 58 meters.

[0176] Working condition 2: wind speed 18.1 m / s to 21.3 m / s, parachute radius R = 46 meters.

[0177] Working condition three: wind speed 21.3 m / s to 23 m / s, parachute radius R = 40 meters.

[0178] like Figure 8 、 Figure 9 and Figure 10 As shown in the figure, power P increases with the number of parachutes. Under all three operating conditions, the minimum number of parachutes required to achieve a 5MW output power is five. Therefore, when the wind speed is between 15.5 m / s and 18.1 m / s, five parachutes with a radius of 58 meters are required to achieve the target output power; when the wind speed is between 18.1 m / s and 21.3 m / s, five parachutes with a radius of 46 meters are required to achieve the target output power; and when the wind speed is between 21.3 m / s and 23 m / s, five parachutes with a radius of 40 meters are required to achieve the target output power.

[0179] like Figure 11 、 Figure 12 and Figure 13 As shown, the power increases first and then decreases with the increase of rope speed (cable speed). Three working conditions were analyzed respectively. Under working condition 1, the power requirement can be met when the rope speed is around 4m / s; under working condition 2, the power reaches its maximum when the rope speed is around 5m / s, and the output power is met at most speeds within the rope speed range of 4m / s to 5m / s; under working condition 3, the power reaches its maximum when the rope speed is between 5m / s and 6m / s, and the output power can be met within the speed range of 4m / s to 7m / s.

[0180] This indicates that the output power of a parachute ladder is related to the ambient wind speed during operation. Under the three operating conditions selected, the output power is positively correlated with the radius of the parachute. Furthermore, the radius required to meet the output power requirement decreases as the wind speed range increases. Since the actual operating altitude range of the parachute ladder is still unknown, we matched appropriate parachute radii within the three speed ranges and then analyzed the relationship between power, the number of parachutes, and rope speed.

[0181] In summary, this invention combines mechanical analysis with parameter optimization algorithms to propose an efficient parachute-ladder system modeling and optimization method, significantly improving the performance and reliability of high-altitude wind energy capture systems. The CPO optimization algorithm is used to dynamically optimize the parameters of the floating and power systems under multiple constraints, ensuring maximum output power while satisfying buoyancy balance, rope speed limits, and parachute area constraints. Through an adaptive learning rate adjustment mechanism and dynamic updates of the trust region radius, the algorithm rapidly converges to the optimal solution, avoiding the local optimality or constraint violation issues common in traditional optimization methods. It can adapt to changing wind conditions at different altitudes, effectively prevent system overturning, and ensure long-term stable operation.

[0182] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A parachute ladder system modeling and optimization method based on mechanics and parameter optimization, characterized in that: include: S1. Obtaining the design parameters and environmental parameters of the parachute ladder system; S2. Based on the design parameters and environmental parameters, perform force analysis on the floating system and the working system to obtain floating analysis results and working analysis results; S3. Based on the results of the floating analysis and the work analysis, the parachute ladder system is modeled to obtain an initial parachute ladder model; S4. Set system constraints and modeling objectives, and use the improved CPO algorithm to optimize the initial model of the parachute ladder to obtain the parachute ladder optimization model; The improved CPO algorithm is used to optimize the initial model of the parachute ladder, and the corresponding process is: S4-1. Set the trust region radius for the current round, randomly generate an initial parameter combination and use it as the strategy vector for the current round; determine whether the initial parameter combination meets the range constraint of the system constraint conditions; if so, proceed to S4-2; otherwise, regenerate the initial parameter combination; S4-2, the power model of the parachute ladder system is used as the objective function, and the system constraints are used as the constraint function; S4-3. Calculate the target gradient of the objective function and the constraint gradient of the constraint function corresponding to the current round's policy vector using Monte Carlo sampling or automatic differentiation methods; S4-4, according to the formula: ； Constructing the optimization objective function ;in, represents the Lagrange multiplier, represents the penalty coefficient, represents the maximum function, represents the objective function, represents the constraint function, represents the total number of constraints; S4-5. Update the current round’s strategy vector based on the optimization objective function. S4-6, update the Lagrange multiplier and trust region radius; S4-7. Calculate whether the updated strategy vector and its objective function satisfy the system constraints and modeling objectives. If so, use the strategy vector of the current round as the optimized parameter combination. Otherwise, return to S4-3. S4-8. Apply the optimized parameter combination to the initial model of the parachute ladder to complete the optimization of the initial model of the parachute ladder.

2. The parachute ladder system modeling and optimization method based on mechanics and parameter optimization according to claim 1 is characterized in that: The design parameters include the parachute opening height, the number of active parachutes, the projected radius of the active parachutes, the radius of the helium balloon, the cable running speed, the angle between the cable and the ground, the weight of the helium balloon, the weight of the helium, the weight of the active parachutes and the weight of the cable; the environmental parameters include the wind speed and atmospheric density corresponding to the active parachute's ascent height.

3. The parachute ladder system modeling and optimization method based on mechanics and parameter optimization according to claim 2 is characterized in that: The S2 includes: S2-1, set the working parachute motion coordinate system; based on the tension coefficient attenuation relationship between the working parachute, set the tension coefficient corresponding to each working parachute; the tension coefficient includes a first tension coefficient and a second tension coefficient of each working parachute; S2-2. Based on the design parameters, calculate the total weight of the floating system, the weight of the cable and the weight of the power parachute; S2-3. Construct and solve the buoyancy balance system of the helium balloon to obtain the floating analysis result, that is, the cable tension pulling the helium balloon; S2-4. Calculate the power of each parachute in the power system based on the cable tension, design parameters, and environmental parameters of the helium balloon. S2-5. Based on the power of each working parachute, calculate the total power of the working system, that is, the sum of the power of each working parachute, and obtain the work analysis result.

4. The parachute ladder system modeling and optimization method based on mechanics and parameter optimization according to claim 3 is characterized in that: The S2-4 includes: S2-4-1. Calculate the gravity of each parachute and the corresponding parachute-cable gravity based on the design parameters; S2-4-2. Calculate the relative vector wind speed based on the wind speed and cable running speed; S2-4-3. Calculate the axial drag and vertical lift corresponding to each power parachute based on the respective drag coefficients and relative vector wind speeds; S2-4-4, according to the formula: ； Calculate the supplementary gravity angle ;in, represents the integral direction of the cable along the axial direction, represents the integral function, represents the torque about the ground due to the weight acting on the cable, Indicates the number of parachutes doing work, Indicates the weight of the working parachute, It represents the projected force area of ​​the work parachute, Indicates the cable running speed, Indicates the angle between the cable and the ground corresponding to the last working parachute, Indicates wind speed, represents the atmospheric density, Indicates the first tension coefficient corresponding to the last working parachute, represents the lift-to-drag coefficient ratio, 、 、 denote the cosine function, sine function and tangent function respectively, Indicates the mass of the cable per meter, Indicates the total weight of the cable, represents the integral function, represents the acceleration due to gravity; S2-4-5. Calculate the power of each powered parachute based on the cable tension pulling the helium balloon, the angle of supplementary gravity, the relative vector wind speed, the drag along each axis, and the lift along each vertical axis.

5. The parachute ladder system modeling and optimization method based on mechanics and parameter optimization according to claim 2 is characterized in that: The initial model of the parachute ladder in S3 is the power model of the parachute ladder system, and the corresponding formula is: ； in, Indicates the power of the parachute ladder system, Indicates the number of parachutes doing work, Indicates the The first tension coefficient corresponding to the working parachute is, Indicates the The wind speed of a power parachute, represents the cosine function, represents the cable speed, represents the air density, Indicates the The angle between the cable and the ground plane corresponding to the power parachute, Indicates the power of the last working parachute, represents the buoyancy of a helium balloon, It represents the projected force area of ​​the working parachute.

6. The parachute ladder system modeling and optimization method based on mechanics and parameter optimization according to claim 2 is characterized in that: The system constraints include range constraints and buoyancy balance constraints; the modeling goal is to lose minimum working power.

7. The parachute ladder system modeling and optimization method based on mechanics and parameter optimization according to claim 5 is characterized in that: The S4-6 includes: S4-6-1. According to the formula: ； Update the Lagrange multiplier and get the updated Lagrange multiplier ; S4-6-2, according to the formula: ； Dynamically update the learning rate to get the updated learning rate ;in, represents the norm, represents the gradient of the current round, represents the gradient of the previous round, Indicates the learning rate of the previous round; S4-6-3, according to the formula: ； Based on the updated learning rate, update the trust region radius to obtain the updated trust region radius ; 、 represent the trust region radius and the updated trust region radius respectively.

8. A parachute ladder system modeling and optimization system based on mechanics and parameter optimization, used to implement the parachute ladder system modeling and optimization method based on mechanics and parameter optimization according to any one of claims 1 to 7, characterized in that: include: System parameter acquisition module, used to obtain the design parameters and environmental parameters of the parachute ladder system; The force analysis module is used to perform force analysis on the floating system and the working system based on design parameters and environmental parameters, and obtain the floating analysis results and the working analysis results; The parachute ladder modeling module is used to model the parachute ladder system based on the results of the floating analysis and the work analysis to obtain the initial model of the parachute ladder; The parachute ladder optimization module is used to set system constraints and modeling objectives, and uses the improved CPO algorithm to optimize the initial parachute ladder model to obtain the parachute ladder optimization model.

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