A cable force optimization method for cable-stayed bridge based on agent model assisted evolutionary algorithm

Abstract

The application discloses a cable-stayed bridge completion cable force optimization method and device and a medium, wherein the method comprises the following steps: establishing a cable-stayed bridge model; determining the upper and lower bounds of the solution space of an optimization problem, and calculating an initial data set DB; obtaining a training set according to the data set DB, and training a radial basis neural network as a surrogate model; based on the surrogate model, using a social learning particle swarm optimization algorithm as an optimizer to optimize the prediction function g(x) in the solution space; after the optimizer reaches a convergence threshold, selecting multiple individuals in the last population for real solution evaluation, and adding the evaluated solutions to the data set DB; and outputting the data set DB. By adopting the radial basis neural network assisted particle swarm optimization algorithm, the application can achieve good optimization effect within a limited number of solution evaluations, and obtain an excellent feasible solution in the cable-stayed bridge completion cable force optimization problem at a lower cost. The application can be widely applied to the fields of bridge design and intelligent optimization algorithms.

Description

Technical Field

[0001] This invention relates to the field of bridge design and intelligent optimization algorithms, and in particular to a method, device and storage medium for optimizing cable forces in a cable-stayed bridge based on a surrogate model-assisted evolutionary algorithm. Background Technology

[0002] In modern bridges, cable-stayed bridges possess high overall stiffness, excellent wind resistance, strong spanning capacity, and beautiful appearance, making them one of the fastest-growing and most competitive bridge types. A cable-stayed bridge consists of three parts: towers, main girder, and cables. A reasonable completed bridge generally requires low structural bending moments, uniform cable stress, and excellent overall structural performance. Given a specific cable-stayed bridge structural system, the cable forces can be adjusted within a certain range to achieve a reasonable completed bridge state. Existing methods for optimizing cable forces in cable-stayed bridges include the zero-displacement method, the rigid support continuity method, the zero-support reaction method, and the bending energy minimization method. These classic optimization methods provide problem modeling and optimization objectives, and can be combined with influence matrix methods, linear programming, least squares methods, Newton's method, and other mathematical optimization methods to iteratively optimize cable forces and obtain feasible solutions. However, as cable-stayed bridges become increasingly densely cabled, design variables increase, and problem scale expands, traditional mathematical optimization methods consume more computational power and suffer from reduced global convergence. Therefore, intelligent optimization algorithms, such as particle swarm optimization and genetic algorithms, are gradually emerging in this field. These algorithms have good stability, versatility and global convergence ability, and are also well adapted to handling constraints and multi-objectives. They have been gradually and widely applied to the optimization of cable forces in cable-stayed bridges.

[0003] The bending energy method is a cable force optimization method that uses the bending strain energy of the main girder and tower elements of a cable-stayed bridge as the objective function. This method models the cable force optimization problem of a completed cable-stayed bridge as a single-objective optimization problem with cable force vectors as variables. It also incorporates indices such as bending moment, stress, displacement, and cable force uniformity as constraints. The functional relationship between these indices and cable forces is highly nonlinear, and traditional search algorithms based on derivative information are prone to getting trapped in local optima. Therefore, intelligent optimization algorithms are a better choice. However, traditional intelligent optimization algorithms, such as particle swarm optimization, rely on a large number of solution evaluations to find feasible solutions. In this problem scenario, solution evaluation involves modeling and analyzing using finite element analysis software to obtain the required indices. When the bridge is large and there are many cable force variables, the required computational power and time costs become considerable. This optimization scenario is also known as an expensive optimization problem in the field of optimization. Summary of the Invention

[0004] In order to at least partially solve one of the technical problems existing in the prior art, the present invention aims to provide a method, device and storage medium for optimizing the cable force of a cable-stayed bridge based on a surrogate model-assisted evolutionary algorithm.

[0005] The technical solution adopted in this invention is:

[0006] A method for optimizing cable forces in a cable-stayed bridge based on a surrogate model-assisted evolutionary algorithm includes the following steps:

[0007] S1. Establish a cable-stayed bridge model, determine the objective function, and optimize the cable-stayed bridge model using the objective function; substitute candidate cable force settings into the cable-stayed bridge model, perform solution analysis, and update the objective function based on the analysis results;

[0008] S2. Determine the upper and lower bounds of the solution space for the optimization problem based on the cable stress constraints. Sample the solution space to obtain an initial set of solutions. Analyze the cable-stayed bridge model to solve the objective function and obtain the initial dataset. DB ;

[0009] S3, Based on the dataset DB Obtain a training set and train a radial basis function neural network as a surrogate model; the surrogate model is used to provide solution predictions for subsequent optimizer optimization, and the prediction function of the surrogate model is denoted as... g (x) is a fit to the objective function f(x);

[0010] S4. Based on the surrogate model, using the social learning particle swarm optimization algorithm as the optimizer, the prediction function is evaluated in the solution space. g (x) is used to find the optimal value;

[0011] S5. After the optimizer reaches the convergence threshold, select multiple individuals from the final population to evaluate the actual solutions, and add the evaluated solutions to the dataset. DB middle;

[0012] S6. Determine whether the number of solution evaluations has reached the preset threshold. max_FEs If so, output the dataset. DB Otherwise, return to step S3.

[0013] Furthermore, the establishment of the cable-stayed bridge model includes:

[0014] Determine the bridge structural and material parameters other than cable forces, sequentially label each stay cable, and denote the cable force vector as x = ( x 1, x 2,… x D ),in D This represents the total number of stay cables. x i Indicates the first i The tension in the cable;

[0015] The objective function fThe objective of (x) is to minimize the bending strain energy, by giving the objective function... f (x) Adding a penalty term to ensure uniform cable tension.

[0016] Furthermore, the objective function f The calculation method for (x) is as follows:

[0017] Calculate the sum of bending strain energies of beam-tower elements U The formula is as follows:

[0018]

[0019] In the formula, N t and N g These represent the number of finite element samples for the bridge tower and the main girder, respectively. L t and L g These are the lengths of the bridge tower and the main beam unit, respectively. E t I t and E g I g These are the bending stiffnesses of the bridge tower and the main beam unit, respectively. M ti and M tj These are the bending moments at both ends of the bridge tower unit; M gi and M gj These are the bending moments at the left and right ends of the main beam element, respectively.

[0020] Based on the sum of the bending strain energies of the beam-tower elements U Calculate the objective function f The formula for (x) is as follows:

[0021]

[0022]

[0023] In the formula, U ( x ) represents the sum of bending strain energies of the beam-tower elements when the cable force setting is x; Δ(x) represents the index for measuring the uniformity of cable force. m Indicates the penalty coefficient; m Δ(x) is the penalty term.

[0024] Furthermore, the prediction function g The expression for (x) is:

[0025]

[0026]

[0027] in, (.) denotes the radial basis function, and the coefficients are... l i It is a real number, ||.|| represents R. D Euclidean norm on, p (x) represents the polynomial; x is the candidate cable force vector, x i This represents the evaluated cable force vector. r To solve for the cable force distance between two points in space.

[0028] Furthermore, the optimization process of the social learning particle swarm optimization algorithm is as follows:

[0029] A1. Initialize the position and velocity of individuals in the population: Randomly sample Np solutions in the solution space as the initial positions of individuals in the population, and randomly assign them initial velocities; the individual positions and velocities are represented by x and v, respectively. D dimensional vector; substitute the solution into the prediction function g (x) is used to calculate and obtain the fitness value;

[0030] A2. Sort the individuals in the population in descending order based on their fitness values, and update some of the individuals;

[0031] A3. After the population is updated, determine whether the stopping condition is met based on the updated population. If it is met, output the final population and the corresponding fitness value; otherwise, return to step A2 to continue updating the population.

[0032] Furthermore, the updating of some individuals includes:

[0033] For individuals i The probability of updating in this iteration is:

[0034]

[0035] The better an individual's fitness value, the higher the probability that its position will be preserved in the current iteration, and the higher the probability that its position will be preserved in the next iteration. t In a population, the update formulas for individual velocity and position are as follows:

[0036]

[0037]

[0038] in, v id and x idRepresenting the population number i The speed and position of each individual d dimensional variables, x kd Individuals with better fitness values k ( k ≠ i The position of the first d dimensional variables, Indicates the position of all individuals in the population at the th position. d The average value of the dimensional variable. r 1. r 2. r 3 is a random number within the interval [0,1]. β It is the proportional coefficient that controls the influence of the third item.

[0039] Furthermore, the step of determining whether the stopping condition is met based on the updated population includes:

[0040] Determine whether the degree of convergence has reached the preset convergence threshold;

[0041] The convergence indices are shown below:

[0042]

[0043] In the formula, It represents the average Euclidean distance between any two individuals in a population, and is used to measure the degree of convergence of the population. , Represents two individuals;

[0044] The convergence thresholds are as follows:

[0045]

[0046] In the formula, Ub and Lb represent the upper and lower bounds of the solution space, respectively. i yes pmd In [0,1] D The expected value of a random population in space. e It is the proportional coefficient for controlling the threshold;

[0047] e These are control parameters; let's assume the current position is the [number]. i The first time the optimizer is used, its calculation is as follows:

[0048]

[0049] In the formula, cur_FEs This indicates the number of times the true solution is evaluated in the current overall method. c It is the coefficient that controls the decline of the index.

[0050] Furthermore, in step S2, the cable stress limit is designed according to the cable breaking force in the specification; if the bridge already has an initial cable force design value, the solution space is determined with the initial design value as the center.

[0051] Another technical solution adopted in this invention is:

[0052] A cable-stayed bridge cable force optimization device based on surrogate model-assisted evolutionary algorithm, comprising:

[0053] At least one processor;

[0054] At least one memory for storing at least one program;

[0055] When the at least one program is executed by the at least one processor, the at least one processor implements the method described above.

[0056] Another technical solution adopted in this invention is:

[0057] A computer-readable storage medium storing a processor-executable program, which, when executed by a processor, performs the method described above.

[0058] The beneficial effects of this invention are: by employing a radial basis function neural network-assisted particle swarm optimization algorithm, this invention can achieve good optimization results within a limited number of solution evaluations, thereby obtaining excellent feasible solutions in complex, large-scale cable-stayed bridge cable force optimization problems with less time cost and lower computational expenditure. Attached Figure Description

[0059] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following description is provided with accompanying drawings of the relevant technical solutions in the embodiments of the present invention or the prior art. It should be understood that the accompanying drawings described below are only for the purpose of clearly illustrating some embodiments of the technical solutions of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0060] Figure 1 This is a flowchart of a cable-stayed bridge cable force optimization method based on surrogate model-assisted evolutionary algorithm in an embodiment of the present invention;

[0061] Figure 2 This is an Ansys model diagram of the north branch of the Pearl River Huangpu Bridge in an embodiment of the present invention. Detailed Implementation

[0062] The embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. The step numbers in the following embodiments are set only for ease of explanation, and there is no limitation on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0063] In the description of this invention, it should be understood that the orientation descriptions, such as up, down, front, back, left, right, etc., are based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0064] In the description of this invention, "several" means one or more, "more than" means two or more, "greater than," "less than," and "exceeding" are understood to exclude the stated number, while "above," "below," and "within" are understood to include the stated number. The use of "first" and "second" in the description is merely for distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0065] Furthermore, in the description of this invention, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. The character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0066] In the description of this invention, unless otherwise explicitly defined, terms such as "set up," "install," and "connect" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0067] For costly optimization problems, the field of intelligent optimization algorithms has seen relevant research, with Surrogate Assisted Evolutionary Algorithm (SAEA) being one of the more widely studied methods. SAEA is characterized by collecting data evaluated using real solutions as a dataset, training a Kriging model or radial basis function neural network as a surrogate model, and replacing part of the real solution evaluation to provide reliable fitness predictions for candidate solutions, thereby reducing the cost of real evaluation. SAEA can integrate particle swarm optimization algorithms as optimizers and has good adaptability to cable-stayed bridge optimization algorithms modeled by the bending energy method. However, it still needs to consider indices such as cable force uniformity and how to collect data and fully utilize the surrogate model. Therefore, it is urgent to improve the traditional particle swarm optimization algorithm by combining it with the inherent characteristics of bridge design through a surrogate model-assisted approach to fully leverage the algorithm's optimization capabilities in cable force optimization problems of cable-stayed bridges.

[0068] like Figure 1 As shown, this embodiment provides a method for optimizing cable forces in a cable-stayed bridge based on a surrogate model-assisted evolutionary algorithm. This method uses model data from finite element analysis (FEM) software as the dataset to train a radial basis function neural network (RBFNN) to replace the FEM software's evaluation. It also proposes a progressive strategy to control the use of particle swarm optimization (PSO) and real-world evaluation, preventing the algorithm from getting trapped in local optima. Furthermore, this method employs a penalty term when handling constraints to ensure the uniformity of cable forces. The method specifically includes the following steps:

[0069] S1. Establish a cable-stayed bridge model, determine the objective function, and optimize the cable-stayed bridge model using the objective function; substitute candidate cable force settings into the cable-stayed bridge model, perform solution analysis, and update the objective function based on the analysis results.

[0070] The cable-stayed bridge model was constructed using finite element analysis software. In this modeling process, we first determined the bridge's structural and material parameters, excluding cable forces. We then sequentially labeled each cable, denoting the cable force vector as x = ( x 1, x 2,… x D ),in D This represents the total number of stay cables. x i Indicates the first i The tension in the cable.

[0071] This method aims to minimize bending strain energy, and defines the objective function as follows: f (x) represents the bending strain energy. The ultimate goal of this optimization problem is to find a feasible solution x such that... f(x) should be as small as possible. Meanwhile, to satisfy a reasonable bridge formation condition, this method uses... f (x) Adding a penalty term ensures uniform cable force. The established bridge model, substituted with candidate cable force settings, can be solved and analyzed in finite element software. Further calculations yield... f (x), this process is called a solution evaluation, which takes a long time. We denote the solution evaluation budget for the entire process as . max_FEs Second-rate.

[0072] objective function f (x) is calculated in the following way:

[0073] First, calculate the sum of the bending strain energies of the beam-tower elements. U The formula is as follows:

[0074] (1)

[0075] in N t and N g These represent the number of finite element samples for the bridge tower and the main girder, respectively. L t and L g These are the lengths of the bridge tower and the main beam unit, respectively. E t I t and E g I g These are the bending stiffnesses of the bridge tower and the main beam unit, respectively. M ti and M tj These are the bending moments at both ends of the bridge tower unit; M gi and M gj These represent the bending moments at the left and right ends of the main beam element, respectively; given the bridge model, these parameters can all be provided by finite element analysis software. Furthermore, f The specific calculation of (x) is as follows:

[0076] (2)

[0077] (3)

[0078] in U ( x) represents the sum of bending strain energies of beam-tower elements calculated by collecting finite element analysis data and formula (1) when the cable force setting is x; Δ(x) represents the index defined in this method for measuring the uniformity of cable force. m This represents the penalty coefficient, which is typically set to 0.01. m The Δ(x) term is the penalty term mentioned in step (1) of this method, which incorporates the uniformity index into the consideration; the calculation of Δ(x) is shown in formula (3). D -1 is an indicator of uniformity, representing the maximum percentage difference between the tensions of adjacent cables.

[0079] S2. Determine the upper and lower bounds of the solution space for the optimization problem based on the cable stress constraints. Sample the solution space to obtain an initial set of solutions. Analyze the cable-stayed bridge model to solve the objective function and obtain the initial dataset. DB .

[0080] Initial sampling of the solution space is performed. First, the upper and lower bounds of the solution space for this optimization problem are determined according to the cable stress constraints in the design specifications. Then, the solution space is sampled using the Latin hypercube sampling method to obtain a set of initial solutions. Through the modeling and analysis in step S1, the objective function is solved to obtain the initial dataset, denoted as . DB .

[0081] Specifically, according to the specifications, the tension in the stay cables must be ≤0.32. x pd , x pd This represents the breaking force of the stay cables. In practice, the upper limit of the cable force is designed based on this, and it is important to ensure that the cable force is not zero or too low to avoid waste. Additionally, if the bridge already has initial cable force design values, the solution space can be determined centered on these initial design values. Besides cable force limitations, general specifications also limit indicators such as the maximum displacement and maximum bending moment of beam-tower elements. However, these indicators have a strong positive correlation with bending strain energy, and from an algorithmic perspective, it is unnecessary to explicitly design optimization methods for them.

[0082] S3, Based on the dataset DB Obtain a training set and train a radial basis function neural network as a surrogate model; the surrogate model is used to provide solution predictions for subsequent optimizer optimization, and the prediction function of the surrogate model is denoted as... g (x) represents the objective function. f Fitting (x).

[0083] Prediction function g The specific calculation of (x) is shown below:

[0084] (4)

[0085] (5)

[0086] in, (.) denotes the radial basis function, and the coefficients are... l i It is a real number, ||.|| represents R. D Euclidean norm on, p (x) represents a polynomial, x is a candidate cable force vector, and x i This represents the evaluated cable force vector. r To solve for the cable force distance between two points in the solution space, the radial basis function used here is the Cubic radial basis function, whose form is shown in equation (5). The coefficients in equation (4) l i as well as p (x) is learned by least squares during the training process.

[0087] S4. Based on the surrogate model, using the social learning particle swarm optimization algorithm as the optimizer, the prediction function is evaluated in the solution space. g (x) is used for optimization.

[0088] The social learning particle swarm optimization algorithm is used as the optimizer for optimization. Based on the surrogate model obtained in step S3, this method uses the social learning particle swarm optimization algorithm to optimize the solution space defined in step S2. g (x) is used for optimization. It should be noted that... g (x) cannot be equivalent to f (x), because any model's predictions have errors. Therefore, this method sets a population convergence threshold for the optimizer and adopts a gradual strategy to avoid the optimizer converging too early or getting trapped in local optima, thus avoiding waste.

[0089] Specifically, the optimization process of social learning particle swarm optimization is as follows:

[0090] S41. Initialize the position and velocity of individuals in the population. Randomly sample within the solution space. N p Each solution represents the position of an individual in the initial population, and each individual is randomly assigned an initial velocity. The individual's position and velocity are represented by x and v, respectively. D Dimensional vector. N p Usually set to The fitness value is calculated for the solution, which in this method is achieved by substituting the solution into... g (x) is used for calculation.

[0091] S42. Sort the individuals in the population in descending order based on their fitness values, and then update some of the individuals. i The probability that it will be updated in this iteration is:

[0092] (6)

[0093] The better an individual's fitness value, the higher the probability that its position will be preserved in the current iteration, and the higher the probability that its position will be preserved in the next iteration. t In a population, the update formulas for individual velocity and position are as follows:

[0094] (7)

[0095] (8)

[0096] in v id and x id Representing the population number i The speed and position of each individual d dimensional variables, x kd Individuals with better fitness values k ( k ≠ i The position of the first d dimensional variables, Indicates the position of all individuals in the population at the th position. d The average value of the dimensional variable. r 1. r 2. r 3 is a random number within the interval [0,1]. β It is the proportionality coefficient that controls the influence of the third term, and is usually set to 1. D *10 -4 After the individual velocity is updated, the position is updated according to formula (8).

[0097] S43. After the population is updated, determine whether it meets the stopping condition, that is, whether the convergence degree reaches the convergence threshold designed in this method. If the population convergence degree reaches the threshold, the final population and the corresponding fitness value can be output. Otherwise, return to step S42 to continue updating the population.

[0098] The convergence metric defined in this embodiment is as follows:

[0099] (9)

[0100] This formula represents the average Euclidean distance between any two individuals in the population, used to measure the degree of convergence. The convergence threshold designed in this method is shown below:

[0101] (10)

[0102] Where Ub and Lb represent the upper and lower bounds of the solution space, respectively. i yes pmd In [0,1] D The expected value of a random population in space. e This is the proportional coefficient for controlling the threshold, and it is the control parameter of the progressive strategy proposed in this method. Assuming the current value is the [number]th [th value]... i The first time the optimizer is used, its calculation is as follows:

[0103] (11)

[0104] in cur_FEs This indicates the evaluation of the true solution used in the current overall method (i.e., computation). f The number of times (x) is given when cur_FEs Not exceeding 0.9* max_FEs hour, e It initially showed a linear downward trend, followed by an exponential decline. c This is the coefficient that controls the decline of the index. The recommended range is [0.4, 0.8], and it is usually set to 0.6.

[0105] S5. After the optimizer reaches the convergence threshold, select multiple individuals from the final population to evaluate the actual solutions, and add the evaluated solutions to the dataset. DB middle.

[0106] Based on the optimizer results, a subset of candidate solutions are selected for evaluation of the true solution. After the optimizer reaches the convergence threshold in step S4, we select the final solution from the population. N s Each individual solution is evaluated using real solutions. These evaluated solutions are then added to... DB Among them.

[0107] in, N s The size can be designed based on the budget of the actual solution evaluation, and can usually be set to 10. When selecting individuals, consider prioritizing the individual with the best fitness value in the population output by step S4, and the rest can be randomly selected from the population.

[0108] S6. Determine whether the number of solution evaluations has reached the preset threshold. max_FEs If so, output the dataset. DB Otherwise, return to step S3.

[0109] If the number of evaluations does not exceed [a certain number] at this time max_FEs If the condition is met, return to step S3 and continue iterating; otherwise, output all candidate solutions for the cable force that have been evaluated by the true solution (i.e., ...). DB These parameters, along with their corresponding bending strain energy, cable force uniformity, and beam-tower element displacement, are selected and the final scheme is determined by professional designers.

[0110] The above method will be explained in detail below with reference to the accompanying drawings and specific embodiments.

[0111] See Figure 1 This embodiment provides a method for optimizing the cable force of a cable-stayed bridge based on a surrogate model-assisted evolutionary algorithm. The operation steps are as follows:

[0112] Step 1: Use the finite element analysis software Ansys to model the entire Huangpu Pearl River Bridge North Branch Cable-Stayed Bridge. The model is as follows: Figure 2 As shown, its span arrangement is 383 m + 197 m + 63 m + 62 m, with a total of 88 stay cables, which can be divided into 44 pairs. In modeling this problem, we first determine the bridge structure and material parameters other than the cable forces, and then sequentially label each stay cable, denoting the cable force vector as x = ( x 1, x 2,… x D ),in D This represents the total number of cable force parameters for the stay cables, which is 44. x i Indicates the first i The cable force at the tension point. This method aims to minimize the bending strain energy, and its calculation is shown below:

[0113] (1)

[0114] in N t and N g These represent the number of finite element samples for the bridge tower and the main girder, respectively. L t and L g These are the lengths of the bridge tower and the main beam unit, respectively. E t I t and E g I g These are the bending stiffnesses of the bridge tower and the main beam unit, respectively. M ti and M tj These are the bending moments at both ends of the bridge tower unit; M gi and M gj These represent the bending moments at the left and right ends of the main beam element, respectively; given the bridge model, these parameters can all be provided by finite element analysis software. Further, the objective function is defined. f The specific calculation of (x) is as follows:

[0115] (2)

[0116] (3)

[0117] in U ( x ) represents the sum of bending strain energies of beam-tower elements calculated according to formula (1) when the cable force is set to x; Δ(x) represents the index for measuring the uniformity of cable force. m This represents the penalty coefficient, which is 0.01. m The Δ(x) term is the penalty term, which incorporates the uniformity index into the consideration; the calculation of Δ(x) is shown in formula (3). D -1 is an indicator of uniformity, representing the maximum percentage difference between the tensions of adjacent cables.

[0118] Once the bridge model is established, the candidate cable force settings can be substituted into it for solution analysis in the finite element software Ansys. Further calculations will yield... f Let (x) be the solution evaluation budget for the entire process. max_FEs The value is set to 1000 times.

[0119] Step 2: Perform initial sampling of the solution space. We perform sampling according to the design specifications (i.e., the cable breaking force is...). x pd ), and based on the existing preliminary design values ​​(denoted as x init The solution space of the cable forces is determined by the center, satisfying... x ≤ 0.32 x pd 0.75 x init ≤ x ≤1.25 x init Besides cable tension constraints, general specifications also limit the maximum displacement and maximum bending moment of beam-tower elements. However, these parameters have a strong positive correlation with bending strain energy, and from an algorithmic perspective, it is unnecessary to explicitly design optimization methods for them. Then, the solution space is sampled using the Latin hypercube sampling method to obtain an initial set of solutions. Through the modeling and analysis in step 1, the objective function is solved to obtain the initial dataset, denoted as . DB .

[0120] Step 3: Train the agent model. DB The radial basis function neural network is trained as a surrogate model using the training dataset, and its prediction function is denoted as . g (x) represents the objective function. fThe fitting of (x) is specifically calculated as follows:

[0121] (4)

[0122] (5)

[0123] in, (.) denotes the radial basis function, and the coefficients are... l i It is a real number, ||.|| represents R. D Euclidean norm on, p (x) represents a polynomial, and the radial basis function used here is the Cubic radial basis function, which has the form shown in formula (5). The coefficients in formula (4) l i as well as p (x) is learned by least squares during the training process.

[0124] Step 4: Use the social learning particle swarm optimization algorithm as the optimizer for optimization. Based on the surrogate model obtained in Step 3, this method uses the social learning particle swarm optimization algorithm to optimize the solution space defined in Step 2. g (x) performs optimization. The optimization process of the social learning particle swarm optimization algorithm is shown below:

[0125] B1. Initialize the position and velocity of individuals in the population. Randomly sample within the solution space. N p Each solution represents the position of an individual in the initial population, and each individual is randomly assigned an initial velocity. The individual's position and velocity are represented by x and v, respectively. D Dimensional vector. N p Usually set to Substitute the solution into g (x) Calculate the fitness value.

[0126] B2. Sort the individuals in the population in descending order based on their fitness values, and then update some of the individuals. i The probability that it will be updated in this iteration is:

[0127] (6)

[0128] In the t In a population, the update formulas for individual velocity and position are as follows:

[0129] (7)

[0130] (8)

[0131] in vid and x id Representing the population number i The speed and position of each individual d dimensional variables, x kd Individuals with better fitness values k ( k ≠ i The position of the first d dimensional variables, Indicates the position of all individuals in the population at the th position. d The average value of the dimensional variable. r 1. r 2. r 3 is a random number within the interval [0,1]. β It is the proportionality coefficient that controls the influence of the third term, and is usually set to 1. D *10 -4 After the individual velocity is updated, the position is updated according to formula (8).

[0132] B3. After the population update, determine whether the stopping condition is met, i.e., whether the convergence degree reaches the convergence threshold designed in this method. The convergence index defined in this method is as follows:

[0133] (9)

[0134] This formula represents the average Euclidean distance between any two individuals in the population, used to measure the degree of convergence. The convergence threshold designed in this method is shown below:

[0135] (10)

[0136] Where Ub and Lb represent the upper and lower bounds of the solution space, respectively. i yes pmd In [0,1] D The expected value of a random population in space. e This is the proportional coefficient for controlling the threshold, and it is the control parameter of the progressive strategy proposed in this method. Assuming the current value is the [number]th [th value]... i The first time the optimizer is used, its calculation is as follows:

[0137] (11)

[0138] in cur_FEs This indicates the evaluation of the true solution used in the current overall method (i.e., computation). f The number of times (x) is given when cur_FEs Not exceeding 0.9* max_FEs hour, e It initially showed a linear downward trend, followed by an exponential decline. cIt is the coefficient that controls the decrease of the index, and in this embodiment it is set to 0.6.

[0139] If the population convergence reaches the threshold, the final population and corresponding fitness values ​​can be output; otherwise, return to B2 to continue updating the population.

[0140] Step 5: Select a subset of candidate solutions for evaluation based on the optimizer results. After the optimizer reaches the convergence threshold in Step 4, we select from the final population. N s Each individual will be evaluated using real solutions. In this embodiment, we will... N s Set the fitness value to 10. When selecting individuals, prioritize choosing the individual with the best fitness value from the population output in step 4, and then select the remaining individuals. N s -1 individual can be randomly selected from the population. The selected candidate solution is then added to the population after true evaluation. DB Among them.

[0141] Step 6: If the number of evaluations at this point does not exceed max_FEs If the condition is met, return to step 3 and continue iterating; otherwise, output all candidate solutions for the cable force that have been evaluated by the true solution (i.e., ...). DB These parameters, along with their corresponding bending strain energy, cable force uniformity, and beam-tower element displacement, are selected and the final scheme is determined by professional designers.

[0142] In summary, the method of this embodiment has at least the following advantages and beneficial effects compared to the prior art:

[0143] (1) This embodiment uses radial basis neural network to assist particle swarm optimization algorithm and uses a progressive strategy to control the population search. It can reasonably and effectively play the role of the surrogate model and achieve good optimization effect within a limited number of solution evaluations. Thus, it can obtain excellent feasible solution in the complex large-scale cable-stayed bridge cable force optimization problem with less time cost and less computational cost.

[0144] (2) In this embodiment, the method of adding a penalty term is adopted to incorporate the uniformity index of cable force into the objective function, so that the final solution can better meet the reasonable bridge state, that is, the structural bending moment is small, the cable is uniformly stressed, and the overall structural performance is excellent.

[0145] This embodiment also provides a cable force optimization device for cable-stayed bridges based on a surrogate model-assisted evolutionary algorithm, including:

[0146] At least one processor;

[0147] At least one memory for storing at least one program;

[0148] When the at least one program is executed by the at least one processor, the at least one processor implements Figure 1 The method shown.

[0149] This embodiment of the cable-stayed bridge cable force optimization device based on surrogate model-assisted evolutionary algorithm can execute the cable force optimization method based on surrogate model-assisted evolutionary algorithm provided in the method embodiment of the present invention. It can execute any combination of implementation steps of the method embodiment and has the corresponding functions and beneficial effects of the method.

[0150] This application also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform... Figure 1 The method shown.

[0151] This embodiment also provides a storage medium storing instructions or programs that can execute the cable force optimization method for cable-stayed bridges based on a surrogate model-assisted evolutionary algorithm provided in the method embodiment of the present invention. When the instructions or programs are run, any combination of implementation steps of the method embodiment can be executed, and the method has the corresponding functions and beneficial effects.

[0152] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this invention are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is altered and sub-operations described as part of a larger operation are executed independently.

[0153] Furthermore, although the invention has been described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the described functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the invention. Rather, given the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed herein, the actual implementation of the module will be understood within the scope of conventional skill of an engineer. Therefore, those skilled in the art can implement the invention as set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and not intended to limit the scope of the invention, which is determined by the full scope of the appended claims and their equivalents.

[0154] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0155] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0156] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0157] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0158] In the foregoing description of this specification, references to terms such as "one embodiment," "another embodiment," or "some embodiments" indicate that a specific feature, structure, material, or characteristic described in connection with an embodiment or example is included in at least one embodiment or example of the present invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0159] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0160] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A method for optimizing cable forces in a cable-stayed bridge based on a surrogate model-assisted evolutionary algorithm, characterized in that, Includes the following steps: S1. Establish a cable-stayed bridge model, determine the objective function, and optimize the cable-stayed bridge model using the objective function; The candidate cable force settings are substituted into the cable-stayed bridge model, and the solution analysis is performed. The objective function is updated based on the analysis results. S2. Determine the upper and lower bounds of the solution space for the optimization problem based on the cable stress constraints. Sample the solution space to obtain an initial set of solutions. Analyze the cable-stayed bridge model to solve the objective function and obtain the initial dataset. DB ; S3, Based on the dataset DB Obtain a training set and train a radial basis function neural network as a surrogate model; the surrogate model is used to provide solution predictions for subsequent optimizer optimization, and the prediction function of the surrogate model is denoted as... g (x); S4. Based on the surrogate model, using the social learning particle swarm optimization algorithm as the optimizer, the prediction function is evaluated in the solution space. g (x) is used to find the optimal value; S5. After the optimizer reaches the convergence threshold, select multiple individuals from the final population to evaluate the actual solutions, and add the evaluated solutions to the dataset. DB middle; S6. Determine whether the number of solution evaluations has reached the preset threshold. max_FEs If so, output the dataset. DB ; Otherwise, return to step S3; The establishment of the cable-stayed bridge model includes: Determine the bridge structural and material parameters other than cable forces, sequentially label each stay cable, and denote the cable force vector as x = ( x 1, x 2,… x D ),in D This represents the total number of stay cables. x i Indicates the first i The tension in the cable; The objective function f The objective of (x) is to minimize the bending strain energy, by giving the objective function... f (x) Adding a penalty term to ensure uniform cable tension; The objective function f The calculation method for (x) is as follows: Calculate the sum of bending strain energies of beam-tower elements U The formula is as follows: In the formula, N t and N g These represent the number of finite element samples for the bridge tower and the main girder, respectively. L t and L g These are the lengths of the bridge tower and the main beam unit, respectively. E t I t and E g I g These are the bending stiffnesses of the bridge tower and main beam units, respectively. M ti and M tj These are the bending moments at both ends of the bridge tower unit; M gi and M gj These are the bending moments at the left and right ends of the main beam element, respectively. Based on the sum of the bending strain energies of the beam-tower elements U Calculate the objective function f The formula for (x) is as follows: In the formula, U ( x ) represents the sum of bending strain energies of the beam-tower elements when the cable force setting is x; Δ(x) represents the index for measuring the uniformity of cable force. μ Indicates the penalty coefficient; μ Δ(x) is the penalty term.

2. The method for optimizing cable forces in a cable-stayed bridge based on a surrogate model-assisted evolutionary algorithm according to claim 1, characterized in that, The prediction function g The expression for (x) is: in, (.) denotes radial basis functions, with coefficients... λ i It is a real number, ||.|| represents R. D Euclidean norm on, p (x) represents a polynomial, where x is a candidate cable force vector. i This represents the evaluated cable force vector. r To solve for the cable force distance between two points in space.

3. The method for optimizing cable forces in a cable-stayed bridge based on a surrogate model-assisted evolutionary algorithm according to claim 1, characterized in that, The optimization process of the social learning particle swarm optimization algorithm is as follows: A1. Initialize the position and velocity of individuals in the population: Randomly sample Np solutions in the solution space as the initial positions of individuals in the population, and randomly assign them initial velocities; the individual positions and velocities are represented by x and v, respectively. D dimensional vector; substitute the solution into the prediction function g (x) is used to calculate and obtain the fitness value; A2. Sort the individuals in the population in descending order based on their fitness values, and update some of the individuals; A3. After the population is updated, determine whether the stopping condition is met based on the updated population. If it is met, output the final population and the corresponding fitness value. Otherwise, return to step A2 to continue updating the population.

4. The method for optimizing cable forces in a cable-stayed bridge based on a surrogate model-assisted evolutionary algorithm according to claim 3, characterized in that, The updating of some individuals includes: For individuals i The probability of updating in this iteration is: The better an individual's fitness value, the higher the probability that its position will be preserved in the current iteration, and the higher the probability that its position will be preserved in the next iteration. t In a population, the update formulas for individual velocity and position are as follows: in, v id and x id Representing the population number i The speed and position of each individual d dimensional variables, x kd Individuals with better fitness values k ( k ≠ i The position of the first d dimensional variables, Indicates the position of all individuals in the population at the th position. d The average value of the dimensional variable. r 1. r 2. r 3 is a random number within the interval [0,1]. β It is the proportional coefficient that controls the influence of the third item.

5. The method for optimizing cable forces in a cable-stayed bridge based on a surrogate model-assisted evolutionary algorithm according to claim 3, characterized in that, The step of determining whether the stopping condition is met based on the updated population includes: Determine whether the degree of convergence has reached the preset convergence threshold; The convergence indices are shown below: In the formula, It represents the average Euclidean distance between any two individuals in a population, and is used to measure the degree of convergence of the population. , Represents two individuals; The convergence thresholds are as follows: In the formula, Ub and Lb represent the upper and lower bounds of the solution space, respectively. θ yes pmd In [0,1] D The expected value of a random population in space. ε It is the proportional coefficient for controlling the threshold; ε These are control parameters; let's assume the current position is the [number]. i The first time the optimizer is used, its calculation is as follows: In the formula, cur_FEs This indicates the number of times the true solution is evaluated in the current overall method. γ It is the coefficient that controls the decline of the index.

6. The method for optimizing cable forces in a cable-stayed bridge based on a surrogate model-assisted evolutionary algorithm according to claim 1, characterized in that, In step S2, the cable stress limit is designed according to the cable breaking force in the specification; if the bridge already has an initial cable force design value, the solution space is determined with the initial design value as the center.

7. A cable-stayed bridge cable force optimization device based on surrogate model-assisted evolutionary algorithm, characterized in that, include: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the method according to any one of claims 1-6.

8. A computer-readable storage medium storing a processor-executable program, characterized in that, The processor-executable program, when executed by the processor, is used to perform the method as described in any one of claims 1-6.

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