Cable force optimization method and device for stay cable of cable-stayed bridge, medium and product

Abstract

The invention discloses a cable-stayed bridge inhaul cable force optimization method and device, a medium and a product, and relates to the technical field of bridge engineering and intelligent optimizing.The method comprises the steps that a simplified cable-stayed bridge model is built based on a target cable-stayed bridge; based on the HiDeNN and a finite element method, a HiDeNN-FEM proxy model is constructed; the HiDeNN-FEM proxy model is a model which is established based on a HiDeNN network and is used for calculating the vertical displacement of a control point of the target stayed-cable bridge, and the vertical displacement of the control point is used for representing the structural load response of the target stayed-cable bridge, the control points are points where tension truss units corresponding to inhaul cables of the target stayed-cable bridge are connected with parallel chord plane truss structures corresponding to beams; and according to the HiDeNN-FEM proxy model, a genetic algorithm is adopted to carry out optimal cable force solution on the target cable-stayed bridge, and an optimal cable force value is obtained. According to the method, the cable force optimization efficiency can be effectively improved.

Description

Technical Field

[0001] The present application relates to the field 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 light appearance. The ideal state of a cable-stayed bridge requires "flat beams and straight towers", uniform cable force and no negative reaction force from supports. The key to its design lies in the layout and force setting of the cables. Traditional cable force optimization methods, such as the finite element method (FEM), although taking into account factors such as nonlinearity, concrete creep shrinkage, and temperature effects, are prone to local convergence and long calculation time when dealing with complex structures such as large-span, dense-cable cable-stayed bridges, resulting in low efficiency in cable force optimization and failure 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 model of the cable-stayed bridge is constructed; the simplified model of the cable-stayed bridge 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 with the parallel chord plane truss structures corresponding to the beams.

[0008] According to 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.

[0009] Optionally, based on the target cable-stayed bridge, a simplified model of the cable-stayed bridge 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 by tension truss units, and the beams and towers are simulated by parallel-chord plane trusses. The internal force and deformation of the plane truss units are used to simulate the force and deformation of the beams and towers.

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

[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, in the local coordinate system, the shape function of its corresponding parent unit 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 N 1 and N 2 represents the shape function of the i-th parent element at 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, S 1 and S 2 represents the displacement at two nodes;

[0018] The interpolation displacement of the i-th parent 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 1 Indicates the position coordinate of one of the two nodes of the ith subunit in the global coordinate system, x 2 and 2 Represents the position coordinates of the other node of the two nodes of the i-th subunit in the global coordinate system;

[0024]

[0025] in, Represents the interpolated displacement of the ith 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 mode 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 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, specifically including:

[0028] The HiDeNN-FEM proxy model is optimized by 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 which time the vertical displacement of the control point output by the HiDeNN-FEM proxy 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-described methods for optimizing the cable force of a cable-stayed bridge.

[0041] In a fourth aspect, the present application provides a computer program product, including 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, device, 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, under the premise of the HiDeNN-FEM proxy model, the optimal cable force of the target cable-stayed bridge is solved by a genetic algorithm, so that the optimal cable force value is solved efficiently and conveniently. While ensuring accuracy, repeated calculation of finite elements is avoided, and the efficiency of cable force optimization is effectively improved. 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 drawings required for use in the embodiments will be briefly introduced below. 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 paying 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 A schematic diagram of a method for optimizing the cable force of 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 unit provided in an embodiment of the present application.

[0050] Figure 6 A schematic diagram of a DNN representation of a parent 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 cable-stayed bridge with parameters provided in one embodiment of the present application.

[0053] Fig. 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] Fig.10 A schematic diagram of the deformation of an optimized cable-stayed bridge provided in one embodiment of the present application.

[0055] Fig.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 the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0057] In order to make the purpose, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below in conjunction with 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. The method is applicable to a cable-stayed bridge 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 FIG. 1 , 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 cable force optimization design of a cable-stayed bridge. Specifically, the following steps are included:

[0059] Step S1: constructing a simplified model of a cable-stayed bridge based on a target cable-stayed bridge, wherein the simplified model of the cable-stayed bridge 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 cable 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 and only subjected to node loads. It is an abstract simplification of some engineering structures where the rod axes intersect at one point, such as Figure 4As shown. The cables are simulated by tension truss elements, and the beams and towers are simulated by 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. The loads only involve the situations acting on the nodes, and the node loads can be input to the network in the form of vectors. The boundary conditions of the cable-stayed bridge are converted into the displacements of the nodes in the truss structure, and the displacements of the locked degrees of freedom are set to zero. By simplifying the cable-stayed bridge to a truss structure, the computational complexity is reduced, and the main mechanical characteristics of the cable-stayed bridge are retained.

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

[0064] In order to avoid the need to consider multiple units when building the network, which increases the complexity of the optimization method, this embodiment chooses to retain only one unit, namely the truss unit, to represent the cable-stayed bridge. Therefore, in the process of converting the research object of the cable-stayed bridge into a mathematical model, the entire cable-stayed bridge is represented in the form of a plane truss structure to ensure that the research object does not change. As a result, the cable-stayed bridge can be digitized into a series of one-dimensional bar units, which are fully and clearly input into HiDeNN (Hierarchical Deep Learning Neural Network, hierarchical deep neural network), while retaining as much physical information as possible, reducing the complexity of program writing and improving calculation efficiency. Since the cable-stayed bridge is converted into a truss structure, the load can only act on the node, so the load can also be input into the HiDeNN network in the form of a vector, and its number is the same as the total degree of freedom of the structure (number of nodes × dimension). Therefore, when considering the working conditions such as the self-weight, external load and cable pre-tensioning force of the bridge, it is necessary to reasonably convert them 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 quantity 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, according to the simplified model of the cable-stayed bridge, based on HiDeNN and finite element method, construct a HiDeNN-FEM proxy model. Wherein, the HiDeNN-FEM proxy model is a model established based on HiDeNN for calculating the vertical displacement of the control point of the target cable-stayed bridge, and the vertical displacement of the control point is used to characterize the structural load response of the target cable-stayed bridge, wherein the control point is 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.

[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 adopted to map each sub-unit 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, 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, and N 1 and N 2 represents the shape function of the i-th parent unit at two nodes in the local coordinate system, where the two nodes refer to the two endpoints 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, S 1 and S 2 represents the displacements at two nodes.

[0073] The interpolation displacement of the i-th parent 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 a specific meaning: s represents the node displacement vector of the parent unit, h represents the interpolated displacement, that is, the result of the shape function N(ξ) interpolating the node displacement s, and e represents the interpolated displacement. 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] 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, x 1 and 1 Indicates the position coordinate of one of the two nodes of the ith subunit in the global coordinate system, x 2 and 2 Represents the position coordinates of the other node 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 ith 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 mode 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 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. 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 mode of each subunit 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 the result is obtained, the displacement u of each node in the global coordinate system is solved by the above formula h .

[0083] Step S3: According to 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 to find the optimal solution in this embodiment is to make the vertical displacement of all control points smaller than the preset threshold.

[0084] In this embodiment, step S3 uses a genetic algorithm to solve the optimal cable force of the target cable-stayed bridge according to 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 to optimize the HiDeNN-FEM proxy model, and calculating the vertical displacement of the control point.

[0086] Step S32, determine whether the vertical displacement of the control point is less than the preset threshold. If so, the cable force value corresponding to the vertical displacement of the control point is used as the optimal cable force value; otherwise, jump to step S31 "using a genetic algorithm to optimize the HiDeNN-FEM proxy model and 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, which represents the structural load response of the target cable-stayed bridge, and reflects the displacement of a certain 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 requirement of "beam flat and tower straight", that is, the beam of the cable-stayed bridge is horizontal and the tower of the cable-stayed bridge is vertical. For the judgment of "beam flat and tower straight", it is usually to enlarge the picture of the cable-stayed bridge and visually inspect whether the bridge deck is horizontal. This is the most basic requirement for the design of the 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 at this time.

[0089] When judging whether the cable-stayed bridge has a flat beam and a straight tower, this embodiment sets a preset threshold and compares the vertical displacement of the control point with the preset threshold to quantify the judgment of "flat beam and straight tower". 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 cable-stayed 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 rope force vector.

[0092] Step S312: Generate the initial cable force value corresponding to each individual in a random average distribution 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, crossover operation, mutation operation and 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 which time the vertical displacement of the control point output by the HiDeNN-FEM proxy model is obtained.

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

[0097] (1) Individual coding

[0098] The traditional standard genetic algorithm expresses the optimization variable as a binary string, which is more suitable for discretized search space. For continuous variables such as cable force, encoding and decoding will incur additional computational costs, resulting in reduced efficiency. Therefore, this embodiment adopts a method based on direct operation of real numbers, that is, each individual is directly represented by the corresponding cable force vector.

[0099] (2) Generating 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, minimize the optimization. In the genetic algorithm, individuals with higher fitness will have more inheritance opportunities. Therefore, in this embodiment, the fitness F is taken as the inverse of the objective function, 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 is to exchange the genetic elements between two individuals with a certain probability. First, the crossover parameter β is set between 0 and 1. During the operation, the two individuals selected for pairing are multiplied by β and (1-β) respectively, and then cross-summed to obtain new offspring. The crossover operation can transfer excellent genes between individuals in the population. By continuously generating new individuals around the known optimal solution and searching the variable space around the known optimal solution, the accuracy of the local optimal solution can be further improved.

[0107] (5) Mutation operation

[0108] The mutation operation is to change the gene value of an individual with a small probability. When a mutation occurs, a random value is directly added to a variable in the chromosome, and the final value is guaranteed not to exceed the specified upper and lower bounds. The mutation operation is an important step to prevent the genetic algorithm search from falling into the local optimal solution, which can enhance the global search ability of the algorithm and avoid the phenomenon of premature convergence.

[0109] (6) Generate offspring

[0110] Through crossover, mutation, and selection, the genetic algorithm generates a population of offspring that is different from its parents and has better fitness.

[0111] (7) Select operation

[0112] By imitating the natural law of survival of the fittest, the genetic algorithm eliminates the population according to its fitness. In this embodiment, the parent population and the child population are merged before elimination, and the individuals with the highest fitness are retained. This operation can retain excellent individuals and avoid the loss of excellent genes due to crossover or mutation. The population size can be gradually reduced as the number of iterations increases, while ensuring convergence. It can effectively reduce the amount of calculation, thereby improving the 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, which 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 can no longer be updated or the maximum number of iterations is reached.

[0116] In order to make the technical solution of the present application clearer, this embodiment is described in the form of examples. Figure 3 The cable force optimization of the target cable-stayed bridge is carried out 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 whole bridge has 70 nodes and 171 bar 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 bar elements. The 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 embodiment, a fixed end constraint is added to the tower base of the target cable-stayed bridge, and the tower beam is fixedly connected. The equivalent node load method can be used to convert the working load of the target cable-stayed bridge into the vertical displacement of the control point to characterize its structural load response. In this embodiment, a 200 kN vertical downward force is applied to each node (nodes 51-70) representing the bridge deck.

[0121] In order to reflect the deformation of the target cable-stayed bridge under working conditions, the nodes connecting the bridge deck and the cables (nodes 52-69) are selected as control points. The nodes include control points and non-control points. The control points refer to 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, while the non-control points are ordinary nodes other than the above control points. And because the bridge tower will deform axially when it is compressed, in order to better represent the smoothness of the bridge, the control point displacement is set to the relative displacement △y between the vertical displacement of the node and the vertical deformation of the bridge tower base (vertical displacement of nodes 7 and 8).

[0122] In this embodiment, the HiDeNN proxy model is first used to perform a calculation without the bridge cable force (the initial cable force is 0), and the result is compared with the solution of the traditional finite element method. The deformation is shown in the figure. Fig. 9 As shown, Fig. 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 of 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. Fig.10 , Fig.10 It 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] It can be seen from Table 3 that 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 optimal cable force results are shown in Table 4.

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

[0131] Cable No. 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] Since the existing cable force optimization method of cable-stayed bridges often relies on the experience and judgment of experts, this embodiment aims to propose a new cable force optimization method that does not rely on the experience and judgment of experts. The framework of the HiDeNN-FEM proxy model has significant advantages. DNN is used instead of shape functions, which can improve the computational efficiency while ensuring accuracy. The efficiency can be further improved by solving partial differential equations through the back-propagation solver.

[0133] This embodiment proposes a cable force optimization method for a cable-stayed bridge based on a HiDeNN network and a genetic algorithm, which is applicable to cable-stayed bridge structures. The method optimizes the cable force by combining a HiDeNN proxy model with a genetic algorithm, establishes a HiDeNN-FEM proxy model based on HiDeNN and the finite element method, quickly and accurately calculates the structural response, and the genetic algorithm is used to optimize the cable force distribution and improve the overall performance and stability of the cable-stayed bridge. Specifically, a HiDeNN-FEM proxy model is first constructed to calculate the stress and deformation of the cable-stayed bridge, and the shape function and its derivative are used to calculate the structural response through automatic differentiation technology to establish a fast mapping between the cable force and the structural response. Then, a genetic algorithm is used to minimize the variance of the control displacement to obtain an optimized design result that meets the "beam flat tower straight" goal. This method can efficiently and conveniently solve the cable force of the cable-stayed bridge, and optimize the cable force distribution, reducing the need for expert experience in adjusting the cable when designing the cable-stayed bridge, while avoiding repeated calculations of finite elements as much as possible, 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: Fig.11 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. The processor, the memory and the 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 the computer program in the non-volatile storage medium. The database of the computer device is used to store relevant data for optimizing the cable force of a cable-stayed bridge. 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 force optimization method of the cable-stayed bridge is implemented.

[0135] Those skilled in the art will understand that Fig.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 those shown in the figure, or combine certain components, or have a different arrangement of components.

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

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

[0138] In an exemplary embodiment, a computer program product is provided, including a computer program, and 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 of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed 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 the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can 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 can 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 database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0142] The technical features of the above embodiments may 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 article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will 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 method for optimizing the cable force of a cable-stayed bridge, characterized in that: The cable force optimization method of the cable-stayed bridge comprises: Based on the target cable-stayed bridge, a simplified model of the cable-stayed bridge is constructed; the simplified model of the cable-stayed bridge 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 point of the target cable-stayed bridge, and the vertical displacement of the control point is used to characterize the structural load response of the target cable-stayed bridge, wherein the control point is 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; According to 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.

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 model of the cable-stayed bridge 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 by tension truss units, and the beams and towers are simulated by parallel-chord plane trusses. The internal force and deformation of the plane truss units are used to simulate the force and deformation of the beams and towers.

3. The cable force optimization method for a cable-stayed bridge according to claim 1, characterized in that: 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, 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, in the local coordinate system, the shape function of its corresponding parent unit 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 two nodes in the local coordinate system; The displacement of the two nodes of the i-th parent unit is expressed as: Among them, s represents the displacement of the two nodes of the i-th parent unit, S1 and S2 represent the displacement at the two nodes; The interpolation displacement of the i-th parent 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: 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; in, Represents the interpolated displacement of the ith subunit in the global coordinate system.

4. The cable force optimization method for a cable-stayed bridge according to claim 3, characterized in that: 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 mode of each sub-unit 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 residual as the loss function for optimization, and determines the displacement of each sub-unit in the overall coordinate system by continuously adjusting the weights.

5. The cable force optimization method for a cable-stayed bridge according to claim 1, characterized in that: According to 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, which specifically includes: The HiDeNN-FEM proxy model is optimized by 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.

6. The cable force optimization method for a cable-stayed bridge according to claim 5, characterized in that: The HiDeNN-FEM proxy model is optimized by 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; According to the initial cable force value corresponding to each individual, calculate the fitness value of 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 which time the vertical displacement of the control point output by the HiDeNN-FEM proxy model is obtained.

7. The cable force optimization method for a cable-stayed bridge according to claim 6, 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.

8. 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 7.

9. 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 7 is implemented.

10. 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 7 is implemented.

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