A method, device, medium and product for optimizing cable force of a cable-stayed bridge

Abstract

This application discloses a cable-stayed bridge cable force optimization method, equipment, medium, and product, relating to the fields of bridge engineering and intelligent optimization technology. The method comprises constructing a simplified cable-stayed bridge model based on a target cable-stayed bridge; constructing a HiDeNN-FEM proxy model based on the HiDeNN network and the finite element method; the HiDeNN-FEM proxy model is a model established based on the HiDeNN network for calculating the vertical displacement of the control points of the target cable-stayed bridge. The vertical displacement of the control points is used to characterize the structural load response of the target cable-stayed bridge, wherein the control points are the points where the tension truss elements corresponding to the cables of the target cable-stayed bridge connect with the parallel-chord plane truss structures corresponding to the beams; and using the HiDeNN-FEM proxy model, a genetic algorithm is used to solve the optimal cable force of the target cable-stayed bridge to obtain the optimal cable force value. This application can effectively improve the efficiency of cable force optimization.

Description

Technical Field

[0001] The present application relates to the fields of bridge engineering and intelligent optimization technology, and in particular to a method, equipment, medium and product for optimizing the cable force of a cable-stayed bridge. Background Art

[0002] Cable-stayed bridges are widely used in modern bridge engineering due to their strong spanning capacity, flexible layout, and lightweight appearance. The ideal completed cable-stayed bridge requires a flat beam and straight tower, uniform cable tension, and no negative support reactions. The key to its design lies in the layout and tension setting of the cables. Traditional cable-stayed optimization methods, such as the Finite Element Method (FEM), take into account factors such as nonlinearity, concrete creep shrinkage, and temperature effects. However, when dealing with complex structures such as large-span, densely cabled cable-stayed bridges, they are prone to local convergence and time-consuming calculations, resulting in low cable-stayed optimization efficiency and an inability to meet engineering requirements. Summary of the Invention

[0003] The purpose of this application is to provide a method, equipment, medium and product for optimizing the cable force of a cable-stayed bridge, which can effectively improve the efficiency of cable force optimization.

[0004] To achieve the above objectives, this application provides the following solutions:

[0005] In a first aspect, the present application provides a method for optimizing the cable force of a cable-stayed bridge, the method comprising:

[0006] Based on the target cable-stayed bridge, a simplified cable-stayed bridge model is constructed; the simplified cable-stayed bridge model is a model of the truss structure of the target cable-stayed bridge.

[0007] According to the simplified model of the cable-stayed bridge, a HiDeNN-FEM proxy model is constructed based on HiDeNN and the finite element method; the HiDeNN-FEM proxy model is a model established based on the HiDeNN network for calculating the vertical displacement of the control points of the target cable-stayed bridge, and the vertical displacement of the control points is used to characterize the structural load response of the target cable-stayed bridge, wherein the control points are the points where the tension truss units corresponding to the cables of the target cable-stayed bridge are connected to the parallel chord plane truss structures corresponding to the beams.

[0008] According to the HiDeNN-FEM agent model, a genetic algorithm is used to solve the optimal cable force of the target cable-stayed bridge to obtain the optimal cable force value.

[0009] Optionally, based on the target cable-stayed bridge, a simplified cable-stayed bridge model is constructed, specifically including:

[0010] According to the actual size of the target cable-stayed bridge, the truss structure corresponding to the target cable-stayed bridge is constructed by converting the three-dimensional structure into a plane truss. The cables are simulated using tension truss units, and the beams and towers are simulated using parallel-chord plane trusses. The internal forces and deformations of the plane truss units are used to simulate the forces and deformations of the beams and towers.

[0011] Optionally, according to the simplified cable-stayed bridge model, a HiDeNN-FEM proxy model is constructed based on HiDeNN and the finite element method, specifically including:

[0012] According to the simplified model of the cable-stayed bridge, coordinate transformation is adopted to use the parent unit in the one-dimensional local coordinate system to map each sub-unit in the actual two-dimensional global coordinate system. For the i-th sub-unit, the shape function of its corresponding parent unit in the local coordinate system is expressed as:

[0013]

[0014] Where N(ξ) represents the shape function of the parent unit corresponding to the i-th child unit in the local coordinate system, ξ represents the local coordinate axis, and N1 and N2 represent the shape functions of the i-th parent unit at the two nodes in the local coordinate system;

[0015] The displacement of the two nodes of the i-th parent unit is expressed as:

[0016]

[0017] Where s represents the displacement of the two nodes of the i-th parent unit, S1 and S2 represent the displacements at the two nodes;

[0018] The interpolation displacement of the i-th mother unit in the local coordinate system is expressed as:

[0019]

[0020] in, represents the interpolated displacement of the i-th parent unit in the local coordinate system, s represents the node displacement vector of the parent unit, h represents the displacement after interpolation, and e i represents the i-th parent unit;

[0021] The Jacob matrix representing the transformation between global coordinates and local coordinates is introduced. The expression of the Jacob matrix is:

[0022]

[0023] Where J represents the Jacob matrix, X represents the abscissa of the global coordinate system, and X = [XY], X = [XY] represents the global coordinate system, x1 and y1 represent the position coordinates of one of the two nodes of the i-th subunit in the global coordinate system, and x2 and y2 represent the position coordinates of the other of the two nodes of the i-th subunit in the global coordinate system;

[0024]

[0025] in, Represents the interpolated displacement of the i-th subunit in the global coordinate system.

[0026] Optionally, the HiDeNN-FEM proxy model includes a DNN network layer, a solution layer and an operation layer, wherein the DNN network layer is used to represent the shape function of the parent unit in the finite element method; the solution layer is used to solve the interpolation displacement of each sub-unit in the overall coordinate system to obtain the displacement pattern of each sub-unit in the global coordinate system; the operation layer is used to fit the unit stiffness matrix, and the HiDeNN-FEM proxy model is optimized with the sum of squares of the total potential energy residuals as the loss function, and the displacement of each sub-unit in the overall coordinate system is determined by continuously adjusting the weights.

[0027] Optionally, according to the HiDeNN-FEM agent model, a genetic algorithm is used to solve the optimal cable force of the target cable-stayed bridge to obtain the optimal cable force value, specifically including:

[0028] The HiDeNN-FEM proxy model is optimized using a genetic algorithm to calculate the vertical displacement of the control point.

[0029] Determine whether the vertical displacement of the control point is less than a preset threshold. If so, use the cable force value corresponding to the vertical displacement of the control point as the optimal cable force value; otherwise, jump to the step of "optimizing the HiDeNN-FEM proxy model using a genetic algorithm to calculate the vertical displacement of the control point" until the vertical displacement of the control point is less than the preset threshold.

[0030] Optionally, a genetic algorithm is used to optimize the HiDeNN-FEM proxy model to calculate the vertical displacement of the control point, specifically including:

[0031] The real number direct operation method is used to encode each individual, and each individual is represented as a corresponding cable force vector.

[0032] According to the cable force vector corresponding to each individual, the initial cable force value corresponding to each individual is generated in an average distribution random manner.

[0033] According to the initial cable force value corresponding to each individual, the fitness value of each individual is calculated.

[0034] Based on the fitness value of each individual, crossover operation, mutation operation and selection operation are performed on all individuals to obtain an individual population including multiple new individuals.

[0035] Based on the individual population, jump to the step of "calculating the fitness value of each individual according to the initial cable force value corresponding to each individual" until the individual population can no longer be updated or the maximum number of iterations is reached. At this time, the vertical displacement of the control point output by the HiDeNN-FEM agent model is obtained.

[0036] Optionally, the calculation formula of the fitness value is:

[0037]

[0038] Among them, F represents fitness, Δu i Indicates the vertical displacement of the control point.

[0039] In a second aspect, the present application provides a computer device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement any of the above-described methods for optimizing the cable force of a cable-stayed bridge.

[0040] In a third aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the above-mentioned methods for optimizing the cable force of a cable-stayed bridge.

[0041] In a fourth aspect, the present application provides a computer program product, comprising a computer program, which, when executed by a processor, implements any of the above-mentioned methods for optimizing the cable force of a cable-stayed bridge.

[0042] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0043] The present application provides a method, equipment, medium and product for optimizing the cable force of a cable-stayed bridge, which combines HiDeNN network technology, finite element method and genetic algorithm. By simplifying the target cable-stayed bridge into a simplified model of a cable-stayed bridge in the form of a truss structure, the HiDeNN network and the finite element method are combined to construct a HiDeNN-FEM proxy model. Then, based on the HiDeNN-FEM proxy model, the optimal cable force of the target cable-stayed bridge is solved by a genetic algorithm, thereby efficiently and conveniently solving the optimal cable force value. While ensuring accuracy, repeated calculations of the finite element method are avoided, effectively improving the efficiency of cable force optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0045] Figure 1 A schematic flow chart of a method for optimizing cable forces in a cable-stayed bridge provided in one embodiment of the present application.

[0046] Figure 2 This is a schematic diagram of a cable force optimization method for a cable-stayed bridge provided in one embodiment of the present application.

[0047] Figure 3 A schematic diagram of a target cable-stayed bridge provided in one embodiment of the present application.

[0048] Figure 4 A schematic diagram of a simplified model of a cable-stayed bridge provided in one embodiment of the present application.

[0049] Figure 5 A schematic diagram of mapping a one-dimensional rod element provided in one embodiment of the present application.

[0050] Figure 6 A schematic diagram of the DNN representation of the mother unit shape function provided in one embodiment of the present application.

[0051] Figure 7 A schematic diagram of the hierarchical network structure of HiDeNN in the form of a plane truss provided in one embodiment of the present application.

[0052] Figure 8 A schematic diagram of a simplified model of a parameterized cable-stayed bridge provided in one embodiment of the present application.

[0053] Figure 9 A schematic diagram of the deformation of a cable-stayed bridge under a no-cable tension condition provided in one embodiment of the present application.

[0054] Figure 10 Schematic diagram of the deformation of the optimized cable-stayed bridge provided in one embodiment of the present application.

[0055] Figure 11 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0056] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0057] In order to make the purpose, features and advantages of this application more obvious and easy to understand, this application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0058] like Figure 1 As shown, this embodiment proposes a cable force optimization method for a cable-stayed bridge. This method is applicable to cable-stayed bridges and is mainly used to optimize the cable force of the cable-stayed bridge and determine the optimal cable force. Figure 2 As shown in the figure, the method mainly includes the steps of constructing a simplified model of a cable-stayed bridge, constructing a HiDeNN-FEM (Hierarchical Deep Learning NeuralNetwor-Finite Element Method) proxy model, genetic algorithm optimization, and optimizing the cable force design of the cable-stayed bridge. Specifically, the following steps are included:

[0059] Step S1: constructing a simplified cable-stayed bridge model based on a target cable-stayed bridge, wherein the simplified cable-stayed bridge model is a model of a truss structure of the target cable-stayed bridge.

[0060] In this embodiment, step S1 mainly includes the following contents:

[0061] According to the actual size of the target cable-stayed bridge, a truss structure corresponding to the target cable-stayed bridge is constructed in the form of a plane truss. Each rod in the truss structure corresponds to a truss unit, and the truss unit is used to simulate the axial deformation of the cables of the target cable-stayed bridge.

[0062] In this embodiment, a certain cable-stayed bridge is selected as the research object, and the cable-stayed bridge is called the target cable-stayed bridge. Figure 3 As shown in the figure, the target three-dimensional cable-stayed bridge is simplified into a two-dimensional plane truss structure, an ideal hinged symmetrical truss structure with equal straight rods subjected only to nodal loads. It is an abstract simplification of some engineering structures where the rod axes intersect at one point, such as Figure 4As shown in the figure. Cables are modeled using tension truss elements, while beams and towers are modeled using parallel-chord plane trusses. The internal forces and deformations of the plane truss elements are used to simulate the forces and deformations of the beams and towers. Loads are applied only to nodes, and nodal loads can be input to the network as vectors. The boundary conditions of the cable-stayed bridge are converted to displacements of the nodes in the truss structure, setting the displacements of locked degrees of freedom to zero. By simplifying the cable-stayed bridge to a truss structure, the computational complexity is reduced while retaining its key mechanical properties.

[0063] In traditional bridge finite element analysis methods, elements are mainly divided into beam elements and truss elements. These two elements represent different force transmission systems. Among them, beam elements can simulate the deformation forms such as bending, shear and torsion of beams and towers, while truss elements are used to simulate the axial deformation of cables.

[0064] To avoid the increased complexity of the optimization method due to the need to consider multiple units when constructing the network, this embodiment chooses to retain only one unit, the truss unit, to represent the cable-stayed bridge. Therefore, when converting the cable-stayed bridge research object into a mathematical model, the entire cable-stayed bridge is represented as a planar truss structure to ensure that the research object does not change. This allows the cable-stayed bridge to be digitized as a series of one-dimensional bar units and fully and clearly input into the HiDeNN (Hierarchical Deep Learning Neural Network), preserving as much physical information as possible while reducing programming complexity and improving computational efficiency. Since the cable-stayed bridge is converted into a truss structure, loads can only act on nodes. Therefore, loads can also be input into the HiDeNN network in the form of vectors, with a number equal to the total degrees of freedom of the structure (number of nodes × dimension). Therefore, when considering working conditions such as the bridge's deadweight, external loads, and cable pretension, they need to be properly converted into vertical or horizontal forces acting on the nodes of the truss structure. The displacement boundary condition of the truss structure is the displacement of the node, which is also input in the form of a vector with the same number as the total degree of freedom. The locking method is to set the displacement of the locked degree of freedom to zero after each training, thereby ensuring that the boundary node does not displace.

[0065] Step S2: Based on the simplified cable-stayed bridge model, a HiDeNN-FEM proxy model is constructed using HiDeNN and the finite element method. The HiDeNN-FEM proxy model is a model established based on HiDeNN for calculating the vertical displacements of the control points of the target cable-stayed bridge. The vertical displacements of the control points are used to characterize the structural load response of the target cable-stayed bridge. The control points are the points where the tension truss elements corresponding to the cables of the target cable-stayed bridge connect with the parallel-chord plane truss structures corresponding to the beams.

[0066] In this embodiment, step S2 specifically includes the following steps:

[0067] According to the simplified model of the cable-stayed bridge, coordinate transformation is used to map the sub-units in the actual two-dimensional global coordinate system using the parent unit in the one-dimensional local coordinate system, such as Figure 5 As shown, X and Y are used to represent the global coordinate axes, and ξ is used to represent the local coordinate axis. Figure 5 The left part of the figure is the global coordinate system, and the right part is the local coordinate system. The displacement of the parent unit is represented by s, the displacement of the child unit is represented by u and v, and the coordinates are represented by (x, y). For the i-th child unit, in the local coordinate system, the shape function of the corresponding parent unit is expressed as:

[0068]

[0069] Where N(ξ) represents the shape function of the parent unit corresponding to the i-th child unit in the local coordinate system, ξ represents the local coordinate axis, N1 and N2 represent the shape functions of the i-th parent unit at two nodes in the local coordinate system, where the two nodes refer to the two end points of the parent unit. The DNN representation of this shape function is as follows Figure 6 As shown, in this embodiment, the shape function of the traditional finite element is represented by a DNN network, and a DNN network is used to replace the original shape function.

[0070] The displacement of the two nodes of the i-th parent unit is expressed as:

[0071]

[0072] Where s represents the displacement of the two nodes of the i-th parent unit, and S1 and S2 represent the displacements at the two nodes.

[0073] The interpolation displacement of the i-th mother unit in the local coordinate system is expressed as:

[0074]

[0075] in, represents the interpolation displacement of the i-th parent unit in the local coordinate system, Each letter in has its own specific meaning: s represents the node displacement vector of the parent element, h represents the displacement after interpolation, that is, the result of the shape function N(ξ) interpolating the node displacement s, and e i represents the i-th parent unit.

[0076] In this embodiment, in order to obtain the displacement mode in the global coordinate system The Jacob matrix representing the transformation between global coordinates and local coordinates is introduced. The expression of the Jacob matrix is:

[0077]

[0078] Wherein, J represents the Jacob matrix, X represents the abscissa of the global coordinate system, and X=[XY], X=[XY] represents the global coordinate system, x1 and y1 represent the position coordinates of one of the two nodes of the i-th subunit in the global coordinate system, and x2 and y2 represent the position coordinates of the other of the two nodes of the i-th subunit in the global coordinate system.

[0079] Then we have:

[0080]

[0081] in, Represents the interpolated displacement of the i-th subunit in the global coordinate system.

[0082] In this embodiment, the combination of the above formulas is the HiDeNN-FEM proxy model. The HiDeNN-FEM proxy model mainly includes a DNN network layer, a solution layer, and an operation layer, wherein the DNN network layer is used to represent the shape function of the parent unit in the finite element method; the solution layer is used to solve the interpolation displacement of each sub-unit in the overall coordinate system to obtain the displacement pattern of each sub-unit in the global coordinate system; the operation layer is used to fit the unit stiffness matrix, and the HiDeNN-FEM proxy model uses the sum of the squares of the total potential energy residuals as the loss function for optimization, and determines the displacement of each sub-unit in the overall coordinate system by continuously adjusting the weights. Due to The layer where it is located is the solution layer, which is equivalent to adding a hidden layer to the hierarchical deep learning network, while the node coordinates and displacement are still the parameters in the hierarchical deep learning network, such as Figure 7 As shown. The displacement pattern of each sub-unit in the global coordinate system is obtained, and then the unit stiffness matrix is fitted through the operation layer. Finally, the square sum of the total potential energy residual is used as the loss function for optimization, and the weight of the S part is continuously adjusted. After obtaining the result, the displacement u of each node in the global coordinate system is solved by the above formula. h .

[0083] Step S3: Based on the HiDeNN-FEM proxy model, a genetic algorithm is used to solve the optimal cable force of the target cable-stayed bridge to obtain the optimal cable force value. The ultimate goal of using the genetic algorithm for optimization in this embodiment is to make the vertical displacement of all control points less than a preset threshold.

[0084] In this embodiment, step S3 uses a genetic algorithm to solve the optimal cable force of the target cable-stayed bridge based on the HiDeNN-FEM proxy model to obtain the optimal cable force value, which specifically includes the following steps:

[0085] Step S31: Using a genetic algorithm, the HiDeNN-FEM proxy model is optimized to calculate the vertical displacement of the control point.

[0086] Step S32: Determine whether the vertical displacement of the control point is less than a preset threshold. If so, use the cable force corresponding to the vertical displacement of the control point as the optimal cable force. Otherwise, proceed to step S31, "Optimize the HiDeNN-FEM proxy model using a genetic algorithm to calculate the vertical displacement of the control point," until the vertical displacement of the control point is less than the preset threshold.

[0087] In this embodiment, the preset threshold may be set to 0.5, or may be set to other values.

[0088] In this embodiment, the output of the HiDeNN-FEM proxy model is the vertical displacement of the control point. The vertical displacement of the control point represents the structural load response of the target cable-stayed bridge and reflects the displacement of a control point on the cable-stayed bridge in the vertical direction under the load of the cable-stayed bridge. The control point refers to the point where the tension truss unit corresponding to the cable of the target cable-stayed bridge is connected to the parallel chord plane truss structure corresponding to the beam. For cable-stayed bridges, there is usually a "beam flat and tower straight" requirement, that is, the beam of the cable-stayed bridge is horizontal and the tower of the cable-stayed bridge is vertical. To judge whether the "beam flat and tower straight" is usually done by enlarging the picture of the cable-stayed bridge and visually inspecting whether the bridge deck is horizontal. This is the most basic requirement for the design of a cable-stayed bridge. After applying the optimal cable force, the cable-stayed bridge as a whole achieves "beam flat and tower straight", and the vertical displacement value is basically 0.

[0089] When judging whether a cable-stayed bridge has a flat beam and a straight tower, this embodiment quantifies the judgment of whether the bridge has a flat beam and a straight tower by setting a preset threshold and comparing the vertical displacement of the control point with the preset threshold. As long as the vertical displacement of the control point is less than the preset threshold, for example, 0.5 mm, it means that the bridge has a flat beam and a straight tower. In this case, the cable force value corresponding to the vertical displacement of the control point at this time will be used as the optimal cable force value after the final cable force optimization.

[0090] In this embodiment, step S31 uses a genetic algorithm to optimize the HiDeNN-FEM proxy model and calculate the vertical displacement of the control point, which specifically includes the following steps:

[0091] Step S311: Use the real number direct operation method to encode each individual, and represent each individual as a corresponding force vector.

[0092] Step S312: Generate the initial cable force value corresponding to each individual in a random and averagely distributed manner according to the cable force vector corresponding to each individual.

[0093] Step S313: Calculate the fitness value of each individual according to the initial cable force value corresponding to each individual.

[0094] Step S314: Based on the fitness value of each individual, a crossover operation, a mutation operation, and a selection operation are performed on all individuals to obtain an individual population including multiple new individuals.

[0095] Step S315: Based on the individual population, jump to the step of "calculating the fitness value of each individual according to the initial cable force value corresponding to each individual" until the individual population can no longer be updated or the maximum number of iterations is reached. At this time, the vertical displacement of the control point output by the HiDeNN-FEM agent model is obtained.

[0096] In this embodiment, the cable force optimization problem of a cable-stayed bridge is described as a problem of minimizing an objective function with the cable force as the problem parameter. The specific implementation steps and optimization methods are as follows:

[0097] (1) Individual coding

[0098] Traditional standard genetic algorithms express optimization variables as binary strings, a design more suitable for discretized search spaces. However, for continuous variables like cable forces, encoding and decoding incurs additional computational overhead, resulting in reduced efficiency. Therefore, this embodiment employs a method based on direct manipulation of real numbers, where each individual is directly represented by its corresponding cable force vector.

[0099] (2) Generate the initial population

[0100] The initial population is the starting search point of all individuals. This embodiment adopts a method of randomly generating initial cable forces based on average distribution.

[0101] (3) Fitness calculation

[0102] In this embodiment, in order to reflect the deformation of the cable-stayed bridge under load conditions, the square sum of the vertical displacements of the control points ∑(Δu i ) 2 As the objective function, the minimization optimization is performed. Since individuals with higher fitness will have more inheritance opportunities in the genetic algorithm, the fitness F is taken as the inverse of the objective function in this embodiment, that is:

[0103]

[0104] Among them, F represents fitness, Δu i Indicates the vertical displacement of the control point.

[0105] (4) Crossover operation

[0106] The crossover operation exchanges genetic elements between two individuals with a certain probability. The crossover parameter β is set between 0 and 1. The two individuals selected for pairing are multiplied by β and (1-β), respectively, and then the crossover sum is calculated to produce a new offspring. The crossover operation can transfer excellent genes between individuals in a population. By continuously generating new individuals around a known optimal solution and searching the variable space surrounding the known optimal solution, the accuracy of the local optimal solution can be further improved.

[0107] (5) Mutation operation

[0108] Mutation operations modify the genetic values of an individual with a small probability. When a mutation occurs, a random value is added to a variable within the chromosome, ensuring that the final value does not exceed specified upper and lower bounds. Mutation operations are crucial for preventing genetic algorithms from finding local optimal solutions. They enhance the algorithm's global search capabilities and avoid premature convergence.

[0109] (6) Generate offspring

[0110] Through crossover, mutation, and selection, the genetic algorithm generates offspring populations that are different from their parents and have stronger fitness.

[0111] (7) Select operation

[0112] Mimicking the natural law of survival of the fittest, the genetic algorithm eliminates individuals from the population based on their fitness. This embodiment merges the parent and child populations before eliminating them, retaining individuals with the highest fitness. This approach preserves high-performing individuals and prevents the loss of excellent genes due to crossover or mutation. It also allows the population size to be gradually reduced as the number of iterations increases, while ensuring convergence. This effectively reduces computational effort and improves optimization efficiency.

[0113] The selection operation is the core of the genetic algorithm, which enables certain individuals in the current population to be inherited to the next generation population according to certain rules. The discovery of this rule is the optimization process and is the basis for the algorithm to find the optimal solution.

[0114] (8) Reproduction

[0115] In this embodiment, the optimal solution can be obtained by repeatedly executing operations (3)-(7) until the population cannot be updated further or the maximum number of iterations is reached.

[0116] In order to make the technical solution of this application clearer, this embodiment is described in the form of examples. Figure 3 The cable-stayed bridge of the medium-target cable-stayed bridge is optimized for cable force as follows:

[0117] In this embodiment, for Figure 3 The specific load and material parameters of the target cable-stayed bridge are as follows: Figure 8 The target cable-stayed bridge has a beam length of 84m and a tower height of 32m. The bridge consists of 70 nodes and 171 member elements, including 18 cables numbered S1-S18 from left to right. The towers, beams, and cables of the target cable-stayed bridge use different types of member elements. Detailed mechanical properties are shown in Table 1.

[0118] Table 1 Mechanical properties of each unit of the truss structure of the cable-stayed bridge

[0119]

[0120] In this example, fixed-end constraints are added to the tower base of the target cable-stayed bridge, creating a fixed tower-to-beam connection. Using the equivalent nodal load method, the target cable-stayed bridge's operating loads are converted into vertical displacements of control points to characterize its structural load response. In this example, a 200 kN vertical downward force is applied to each node representing the bridge deck (nodes 51-70).

[0121] To reflect the deformation of the target cable-stayed bridge under operating conditions, the nodes connecting the bridge deck and the cables (nodes 52-69) were selected as control points. Nodes include control points and non-control points. Control points are the points where the tension truss elements corresponding to the cables of the target cable-stayed bridge connect with the parallel-chord plane truss structures corresponding to the beams, while non-control points are ordinary nodes other than these control points. Furthermore, since bridge towers undergo axial deformation under compression, to better represent the smoothness of the bridge, the displacement of the control points is set as the relative displacement Δy between the vertical displacement of the node and the vertical deformation of the tower base (vertical displacement of nodes 7 and 8).

[0122] In this embodiment, a calculation is first performed using the HiDeNN proxy model without the bridge cable tension (initial cable tension is 0), and the result is compared with the solution of the traditional finite element method. The deformation is shown in the figure below. Figure 9 As shown, Figure 9 This is the effect diagram after the deformation is magnified 10 times. The specific data are shown in Table 2.

[0123] Table 2 Displacement values of control points of cable-stayed bridge under no cable tension condition

[0124]

[0125] It can be seen intuitively from Table 2 that the HiDeNN-FEM proxy model established in this embodiment has sufficient accuracy.

[0126] In this embodiment, a genetic algorithm combined with the HiDeNN-FEM agent model is used to solve the optimal cable force for the target cable-stayed bridge. In this embodiment, the population size of the genetic algorithm is 200, the mutation probability is 0.1, the number of iterations is 100, and the objective function is the sum of the squares of the control point displacements. The deformation after optimization is shown in the figure below. Figure 10 , Figure 10 This is the effect diagram after the deformation is magnified 10 times. The comparison of data before and after optimization is shown in Table 3.

[0127] Table 3 Comparison of relative displacements of control points of cable-stayed bridge before and after optimization

[0128] Node number Relative displacement before optimization (mm) Relative displacement after optimization (mm) 52、69 -256.95 -0.26 53、68 -210.99 0.45 54、67 -170.32 -0.26 55、66 -134.36 0.09 56、65 -102.32 0.00 57、64 -73.59 -0.13 58、63 -48.01 0.11 59、62 -26.14 0.10 60、61 -9.26 -0.03

[0129] As can be seen from Table 3, this embodiment achieves the overall design requirement of "flat beam and straight tower", the displacement of the specific control point is almost 0, the optimization effect is good, and the obtained optimal cable tension results are shown in Table 4.

[0130] Table 4 Optimal cable force values obtained by cable force optimization method

[0131] Cable number Optimal cable force (kN) S1, S18 879.931 S2, S17 546.357 S3, S16 417.655 S4, S15 552.871 S5, S14 535.808 S6, S13 494.973 S7, S12 503.528 S8, S11 437.303 S9, S10 402.364

[0132] Because existing cable-stayed bridge cable force optimization methods often rely heavily on expert judgment, this embodiment aims to propose a new cable force optimization method that does not rely on expert judgment. The HiDeNN-FEM proxy model framework offers significant advantages. Replacing shape functions with a DNN improves computational efficiency while maintaining accuracy. Efficiency can be further improved by solving partial differential equations using a backpropagation solver.

[0133] This embodiment proposes a cable force optimization method for cable-stayed bridges based on a HiDeNN network and a genetic algorithm. This method is applicable to cable-stayed bridge structures. This method uses a HiDeNN proxy model combined with a genetic algorithm to optimize cable forces. A HiDeNN-FEM proxy model is established based on HiDeNN and the finite element method to quickly and accurately calculate the structural response. The genetic algorithm is used to optimize the cable force distribution, improving the overall performance and stability of the cable-stayed bridge. Specifically, a HiDeNN-FEM proxy model is first constructed to calculate the forces and deformations of the cable-stayed bridge. The structural response is calculated using shape functions and their derivatives through automatic differentiation techniques, establishing a rapid mapping between cable forces and structural responses. A genetic algorithm is then employed to minimize the variance of the control displacements, resulting in an optimized design that meets the "straight tower and flat beam" objective. This method can efficiently and conveniently solve the cable forces and optimize the cable force distribution of cable-stayed bridges. This reduces the need for expert experience in cable adjustment during cable-stayed bridge design while minimizing repeated finite element calculations and improving the efficiency of cable force optimization.

[0134] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 11 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O) and a communication interface. The processor, memory and input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device is used to store relevant data for cable-stayed bridge cable force optimization. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, the cable-stayed bridge cable force optimization method is implemented.

[0135] Those skilled in the art will understand that Figure 11 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0136] In an exemplary embodiment, a computer device is further provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiments when executing the computer program.

[0137] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0138] In an exemplary embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0139] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0140] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0141] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0142] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0143] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A cable force optimization method for a cable-stayed bridge, characterized in that: The cable force optimization method for a cable-stayed bridge comprises: Based on the target cable-stayed bridge, a simplified cable-stayed bridge model is constructed; the simplified cable-stayed bridge model is a model of the truss structure of the target cable-stayed bridge; According to the simplified model of the cable-stayed bridge, a HiDeNN-FEM proxy model is constructed based on HiDeNN and the finite element method. The HiDeNN-FEM proxy model is a model established based on the HiDeNN network for calculating the vertical displacement of the control points of the target cable-stayed bridge. The vertical displacement of the control points is used to characterize the structural load response of the target cable-stayed bridge. The control points are the points where the tension truss elements corresponding to the cables of the target cable-stayed bridge are connected to the parallel-chord plane truss structures corresponding to the beams. According to the simplified cable-stayed bridge model, a HiDeNN-FEM proxy model is constructed based on HiDeNN and the finite element method, which specifically includes: According to the simplified model of the cable-stayed bridge, coordinate transformation is adopted to use the parent unit in the one-dimensional local coordinate system to map each sub-unit in the actual two-dimensional global coordinate system. For the i-th sub-unit, the shape function of its corresponding parent unit in the local coordinate system is expressed as: Where N(ξ) represents the shape function of the parent unit corresponding to the i-th child unit in the local coordinate system, ξ represents the local coordinate axis, and N1 and N2 represent the shape functions of the i-th parent unit at the two nodes in the local coordinate system; The displacement of the two nodes of the i-th parent unit is expressed as: Where s represents the displacement of the two nodes of the i-th parent unit, S1 and S2 represent the displacements at the two nodes; The interpolation displacement of the i-th mother unit in the local coordinate system is expressed as: in, represents the interpolated displacement of the i-th parent unit in the local coordinate system, s represents the node displacement vector of the parent unit, h represents the displacement after interpolation, and e i represents the i-th parent unit; The Jacob matrix representing the transformation between global coordinates and local coordinates is introduced. The expression of the Jacob matrix is: Where J represents the Jacob matrix, X represents the abscissa of the global coordinate system, and X = [XY], X = [XY] represents the global coordinate system, x1 and y1 represent the position coordinates of one of the two nodes of the i-th subunit in the global coordinate system, and x2 and y2 represent the position coordinates of the other of the two nodes of the i-th subunit in the global coordinate system; in, represents the interpolated displacement of the i-th subunit in the global coordinate system; The HiDeNN-FEM proxy model includes a DNN network layer, a solution layer, and an operation layer. The DNN network layer is used to represent the shape function of the parent unit in the finite element method; the solution layer is used to solve the interpolated displacement of each subunit in the global coordinate system to obtain the displacement pattern of each subunit in the global coordinate system; the operation layer is used to fit the unit stiffness matrix. The HiDeNN-FEM proxy model uses the sum of squares of the total potential energy residuals as the loss function for optimization, and determines the displacement of each subunit in the global coordinate system by continuously adjusting the weights. According to the HiDeNN-FEM agent model, a genetic algorithm is used to solve the optimal cable force of the target cable-stayed bridge to obtain the optimal cable force value.

2. The cable force optimization method for a cable-stayed bridge according to claim 1, characterized in that: Based on the target cable-stayed bridge, a simplified cable-stayed bridge model is constructed, including: According to the actual size of the target cable-stayed bridge, the truss structure corresponding to the target cable-stayed bridge is constructed by converting the three-dimensional structure into a plane truss. The cables are simulated using tension truss units, and the beams and towers are simulated using parallel-chord plane trusses. The internal forces and deformations of the plane truss units are used to simulate the forces and deformations of the beams and towers.

3. The cable force optimization method for a cable-stayed bridge according to claim 1, characterized in that: Based on the HiDeNN-FEM agent model, a genetic algorithm is used to solve the optimal cable force of the target cable-stayed bridge to obtain the optimal cable force value, specifically including: The HiDeNN-FEM proxy model is optimized using a genetic algorithm to calculate the vertical displacement of the control point; Determine whether the vertical displacement of the control point is less than a preset threshold. If so, use the cable force value corresponding to the vertical displacement of the control point as the optimal cable force value. Otherwise, jump to the step of "optimizing the HiDeNN-FEM proxy model using a genetic algorithm to calculate the vertical displacement of the control point" until the vertical displacement of the control point is less than the preset threshold.

4. The cable force optimization method for a cable-stayed bridge according to claim 3, characterized in that: The HiDeNN-FEM proxy model is optimized using a genetic algorithm to calculate the vertical displacement of the control point, specifically including: The real number direct operation method is used to encode each individual, and each individual is represented as a corresponding cable force vector; According to the cable force vector corresponding to each individual, the initial cable force value corresponding to each individual is generated by using an average distribution random method; Calculate the fitness value of each individual according to the initial cable force value corresponding to each individual; Based on the fitness value of each individual, crossover operation, mutation operation and selection operation are performed on all individuals to obtain an individual population including multiple new individuals; Based on the individual population, jump to the step of "calculating the fitness value of each individual according to the initial cable force value corresponding to each individual" until the individual population can no longer be updated or the maximum number of iterations is reached. At this time, the vertical displacement of the control point output by the HiDeNN-FEM proxy model is obtained.

5. The cable force optimization method for a cable-stayed bridge according to claim 4, characterized in that: The calculation formula of the fitness value is: Among them, F represents fitness, Δu i Indicates the vertical displacement of the control point.

6. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the cable force optimization method for a cable-stayed bridge according to any one of claims 1 to 5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for optimizing the cable force of a cable-stayed bridge according to any one of claims 1 to 5 is implemented.

8. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the method for optimizing the cable force of a cable-stayed bridge according to any one of claims 1 to 5 is implemented.

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