Cable-stayed bridge power optimization method based on response surface method-genetic algorithm

Abstract

The invention discloses a response surface method-genetic algorithm-based cable-stayed bridge dynamic optimization method, which comprises the following steps of: 1, establishing a finite element model of a cable-stayed bridge, and generating a sample based on a Box-Behnken design method by taking three factors influencing the inclination angle of a cable of the cable-stayed bridge as design variables; 2, determining factor levels and test index values, modifying the finite element model according to the factor levels of different test samples, and loading seismic waves to obtain response values; and 3, obtaining response surface functions of different index values by adopting a response surface method, constructing an objective function, then carrying out iterative optimization by adopting a genetic algorithm, obtaining a Pareto optimal solution set, modifying the finite element model by using the factor combination of the optimal solution, and then applying seismic waves to compare with the seismic response of the original finite element model. The method can effectively solve the problems that the number of test groups needed in bridge power optimization is too large, interaction of different factors cannot be considered, and the weight of selected indexes needs to be known.

Description

Technical Field

[0001] The present invention belongs to the field of bridge seismic technology, specifically a cable-stayed bridge dynamic optimization method based on response surface method-genetic algorithm Background Art

[0002] my country's complex topography, influenced by the Eurasian and Pacific tectonic plates, results in a high frequency and widespread distribution of earthquakes. Bridges, a crucial component of transportation systems, can cripple highway transport systems if damaged. To ensure the proper functioning of bridges and minimize earthquake damage, research on bridge dynamics optimization is necessary.

[0003] Dynamic optimization design, without the need for additional substructures, improves the bridge's seismic resistance by adjusting its local shape and structure. However, dynamic optimization design for complex bridge systems requires numerous repeated structural dynamic response analyses. Several design methods can reduce the number of dynamic response analyses. Common optimization methods include orthogonal experimental design, Latin hypercube sampling, and response surface methodology. Orthogonal design can significantly reduce the number of experiments, but it cannot explore factor interactions and has a fixed number of factor levels, limiting flexibility. Latin hypercube sampling relies on randomness in sample generation, making it difficult to dynamically expand the sample size once it is fixed. Response surface methodology can analyze interactions and main utilities, and the number of factor levels is an interval rather than a fixed value. It supports gradient optimization and multi-objective optimization. However, when using response surface methodology for design optimization, the weights corresponding to each indicator value must be known, and calculating weights for unconventional indicator values ​​can be difficult. Summary of the Invention

[0004] In order to overcome the shortcomings of the existing technology, the present invention provides a cable-stayed bridge dynamic optimization method based on response surface methodology-genetic algorithm, so as to achieve dynamic optimization of the cable-stayed bridge and reduce the dynamic response of the cable-stayed bridge, thereby overcoming many problems in the optimization design, such as the large number of test groups required, the inability to analyze the interaction of factors, and the need to know the weights of various indicators for optimization.

[0005] In order to achieve the above-mentioned object, the present invention adopts the following technical solutions: The present invention provides a cable-stayed bridge dynamic optimization method based on response surface methodology-genetic algorithm, which comprises the following steps: Step 1: Use finite element software to model the cable-stayed bridge and obtain a finite element model of the cable-stayed bridge; Step 2: Take the cable-free area at the tower base of the cable-stayed bridge as the height h t , the main beam tower root without cable area a , Length of the cable-free area in the middle of the main beam span a1 is the design variable of the cable inclination angle; according to the design rules of cable-stayed bridges, the value range of the design variable and the horizontal division value of the design variable are determined, so that different test group data are obtained by using the Box-Behnken design method. The data are then substituted into the finite element model of the cable-stayed bridge to obtain the finite element model corresponding to each test group data; Step 3: According to the site and structural dynamic characteristics of the cable-stayed bridge, select the seismic wave and apply it to the finite element model corresponding to each test group data to obtain the seismic response time history diagram of the cable-stayed bridge. Take the maximum value of the seismic response time history diagram as the dynamic response index value to obtain the dynamic response index group corresponding to each test group data, including: the bending moment at the bottom of the main pier of the bridge W 1. Curvature of the bottom of the main pier W 2. Bending moment in the span of the main beam W 3; The least squares method is used to fit the response surface equation of each dynamic response index under all test group data, and variance analysis is used to test whether each response surface equation meets the accuracy requirements. If so, step 4 is executed; otherwise, step 2 is returned to re-determine the value range of the design variable and the level division value of the design variable; Step 4: Construct three response surface equations that meet the accuracy requirements, and use the three response surface equations as the dynamic optimization objective function of the cable-stayed bridge. Using the boundary values ​​of the three design variables as constraints, establish an equation relationship model between the objective function and the design variables. Then, use the genetic algorithm to solve the equation relationship model and obtain the Pareto optimal solution set. From the Pareto optimal solution set, obtain the three design variable values ​​corresponding to the optimal dynamic response index group of the cable-stayed bridge; Step 5: Based on the three design variable values ​​corresponding to the optimal dynamic response index group of the cable-stayed bridge obtained in Step 4, the finite element model of the cable-stayed bridge is optimized. After applying the same seismic wave as in Step 3 to the optimized finite element model of the cable-stayed bridge, the seismic response time history diagram of the cable-stayed bridge is obtained.

[0006] The electronic device of the present invention includes a memory and a processor, and is characterized in that the memory is used to store a program that supports the processor to execute the cable-stayed bridge dynamic optimization method, and the processor is configured to execute the program stored in the memory.

[0007] The present invention provides a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium. The computer program executes the steps of the cable-stayed bridge dynamic optimization method when the computer program is executed by a processor.

[0008] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention achieves the optimal design of the dynamics of a cable-stayed bridge by adjusting the local shape and structure of the bridge with a smaller number of tests. Compared with traditional dynamic optimization methods, this method does not require a large number of repeated bridge structure dynamic response analyses and requires less computer memory, thereby significantly reducing the amount of calculation and time.

[0009] 2. The finite element model of the cable-stayed bridge proposed in this invention is universal. By changing the height of the cable-free area at the tower root of the cable-stayed bridge, h t , the main beam tower root without cable area a , Length of the cable-free area in the middle of the main beam span a 1. It overcomes the problem of different types of cable-stayed bridges and can be applied to the dynamic optimization problems of various types of cable-stayed bridges.

[0010] 3. Compared to traditional orthogonal experimental designs and Latin hypercube sampling, the proposed method can generate a response surface for each indicator value through function fitting, allowing for a clearer and more intuitive observation of the impact of each design factor on the indicator value and their interactions. Using a genetic algorithm for iterative optimization, it eliminates the need to define weights for each indicator value. The algorithm iteratively analyzes the relationship between each indicator value, plotting a Pareto optimal frontier diagram to determine the optimal factor combination. This combination was used to modify the finite element model, reducing the bridge's dynamic response while only slightly adjusting the bridge structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 Schematic diagram of the specific process of the method of the present invention; Figure 2 This is a front view of the bridge model of the present invention; Figure 2 a This is a schematic diagram of fiber division in the cross section of the main pier of the bridge according to the present invention; Figure 2 b Schematic diagram of fiber division in the cross section of a bridge tower according to the present invention; Figure 2 c This is a schematic diagram of fiber division of the bridge cable cross section of the present invention; Figure 3 a Response surface plot of indicator 1 selected for the present invention; Figure 3 b Response surface plot of indicator 2 selected for the present invention; Figure 3 c Response surface plot of indicator 3 selected for the present invention; Figure 4 is the Pareto optimal solution set graph of the present invention; Figure 5 This is the bending moment diagram of the main pier bottom before and after optimization under earthquake action according to the present invention. DETAILED DESCRIPTION

[0012] In this embodiment, a cable-stayed bridge dynamic optimization method based on response surface methodology-genetic algorithm is used to solve the dynamic optimization problem of cable-stayed bridges. This method solves the problems of too many test groups required, the inability to consider the interaction of factors, and the need to know the weights of the index values ​​selected for dynamic optimization. Specifically, Figure 1 Shown is a flow chart of the method of the present invention, which is carried out according to the following steps: Step 1: Use finite element software to model the cable-stayed bridge and obtain a finite element model of the cable-stayed bridge; In this embodiment, the bridge background is a low-tower cable-stayed bridge, such as Figure 2 The figure shows the front view of the bridge model. The finite element model of the low-tower cable-stayed bridge was established using finite element software; the fiber cross-section division of the pier is referenced Figure 2 a , the fiber section division of the bridge tower refers to Figure 2 b , the fiber cross section of the cable is divided according to Figure 2 c Because the main beam rarely undergoes plastic deformation under earthquakes, no cross-sectioning is performed. The low-tower cable-stayed bridge features a main pier height of 128 meters and a side pier height of 92 meters. The span is 500 meters, with a main span of 130 meters and side spans of 120 meters each. The main bridge piers are rectangular hollow piers. The prestressed concrete sections of the cable-stayed bridge are 10 meters longitudinally and 17 meters transversely, with a longitudinal wall thickness of 1.2 meters and a transverse wall thickness of 0.9 meters. The cable towers are constructed of C55 reinforced concrete and stand 32 meters tall. The main towers are divided into two sections. The lower tower, 19 meters above the main beam, features a split-limb design, while the upper tower has a dumbbell-shaped cross-section. The cables are arranged in parallel, with 18 groups of cables per tower. The bridge comprises 72 cable-stayed cables.

[0013] Step 2: Take the cable-free area at the tower base of the cable-stayed bridge as the height h t , the main beam tower root without cable area a , Length of the cable-free area in the middle of the main beam span a 1 is the design variable of the cable inclination angle; according to the design rules of cable-stayed bridges, the value range of the design variable and the horizontal division value of the design variable are determined, so that different test group data are obtained by using the Box-Behnken design method. The data are then substituted into the finite element model of the cable-stayed bridge to obtain the finite element model corresponding to each test group data; Since the cable inclination angle of the low-tower cable-stayed bridge is affected by the height of the cable-free area at the tower base, h t , the main beam tower root without cable area a , Length of the cable-free area in the middle of the main beam span a1, and the cable inclination angle of the low-tower cable-stayed bridge will affect the mechanical performance of the low-tower cable-stayed bridge. Therefore, these three factors are used as design variables for the dynamic optimization design of the low-tower cable-stayed bridge. In this embodiment, according to the parameter value rule of the low-tower cable-stayed bridge, the tower height of the low-tower cable-stayed bridge is about 0.08 to 0.125 times the main span, the length of the cable-free area of ​​the main beam is about 0.15 to 0.2 times the main span, and the length of the cable-free area in the middle of the main beam is about 0.2 to 0.35 times the main span. The three design variables are set to three levels, where h 1 is between 20m and 24.3m. a The value ranges from 28.25m to 34.25m. a The value of 1 is 39m~51m. By adjusting the values ​​of the three design variables, the inclination angle of the cable can be adjusted to improve the mechanical performance of the bridge.

[0014] The Box-Behnken experimental design method generates different numbers of experimental groups based on the number of factors and factor levels. Based on the above-mentioned factor values ​​and factor levels, the Box-Behnken design method is used to generate experimental groups. The data of different experimental groups are substituted into the finite element model of the cable-stayed bridge to obtain the finite element model corresponding to each experimental group.

[0015] In this embodiment, there are 3 factors, and the factor levels are divided into 3 levels. The Box-Behnken design method generates 17 experimental groups, of which 5 groups are central experimental groups, indicating the existence of experimental errors caused by human factors. Since there is no experimental error caused by human factors in numerical simulation, only one central experimental group is set; the factor combination table is shown in Table 1. The finite element model is modified by the factor combination in Table 1, and 13 finite element models are obtained.

[0016] Table 1 Factor combination table Step 3: According to the site and structural dynamic characteristics of the cable-stayed bridge, select the seismic wave and apply it to the finite element model corresponding to each test group data to obtain the seismic response time history diagram of the cable-stayed bridge. Take the maximum value of the seismic response time history diagram as the dynamic response index value to obtain the dynamic response index group corresponding to each test group data, including: the bending moment at the bottom of the main pier of the bridge W 1. Curvature of the bottom of the main pier W 2. Bending moment in the span of the main beam W 3; The least squares method is used to fit the response surface equation of each dynamic response index under all test group data, and variance analysis is used to test whether each response surface equation meets the accuracy requirements. If so, step 4 is executed; otherwise, step 2 is returned to re-determine the value range of the design variable and the level division value of the design variable; In order to obtain accurate structural seismic response, the selection of seismic waves should match the bridge site characteristics (including site type, design seismic parameters, etc.) and the structural dynamic characteristics (such as fundamental period, mass distribution, etc.). In this embodiment, the basic seismic peak acceleration of the bridge site is 0.20g, and the corresponding seismic fortification intensity is 8 degrees, which is a strong earthquake zone. The Pacific Earthquake Engineering Research Center (PEER) selected a near-fault pulse earthquake as the seismic input. W 1. W 2 and W 3 The corresponding bridge earthquake response value is the optimization target, and the definition of W 1. W 2 and W 3 with interactive quadratic polynomial as the response surface function. In this embodiment, the design variables are h t 、 a 、 a 1, its function expression is: (1) In formula (1), For the i The dynamic response value of the index value, Indicates the i The reference value of the dynamic response of the index value, Respectively represent h t 、 a 、 a 1 pair i The linear influence of the dynamic response of each index value; Respectively represent h t and a , h t and a 1, a and a 1 pair i The interactive effect of the dynamic response of the index values; Respectively represent h t 、 a 、 a 1st i The nonlinear influence of the dynamic response of each index value.

[0017] After obtaining the response surface equation, the response surface graph can be drawn, as shown in Figure 3 a To Figure 3 c，The response surface graph can intuitively observe the interaction between two factors. The flatter the surface, the worse the interaction and the smaller the impact on the index value. Perform variance analysis on the response surface function obtained in the above steps; obtain the complex correlation coefficient of the response surface function .

[0018] and The expression is as follows: (2) (3) In formula (2), Represents the arithmetic mean of the test values; represents the predicted value of the i-th response; stands for the regression sum of squares; it represents the h t 、 a 、 a 1 changes caused by W changes; In formula (3), is the sum of squares of the residuals, which represents the random error, For the i Dynamic response value of each index value; In getting and Then divide the two equations to get the complex correlation coefficient commonly used to evaluate the model fitting accuracy of multivariate fitting. , The expression is as follows: (4) Comparative multiple correlation coefficients Whether the accuracy requirements are met, if If the accuracy requirement is met, the response surface model is reasonable and step 4 can be performed. If the accuracy requirements are not met, repeat step 2, redefine the value range of the design variables and the horizontal division value of the design variables, and proceed to subsequent steps until the response surface model meets the accuracy requirements.

[0019] In this embodiment, W The complex correlation coefficient of the response surface equation corresponding to 1 is equal to 0.9911. W The complex correlation coefficient of the response surface equation corresponding to 2 is equal to 0.9937. W The complex correlation coefficient of the response surface equation corresponding to 3 is equal to 0.9902, and all three are greater than 0.95, meeting the accuracy requirements of the response surface model.

[0020] Step 4: three response surface equations are constructed to meet the accuracy requirements, and the three response surface equations are combined into an equation set as the cable-stayed bridge dynamic optimization objective function, with the boundary values of the three design variables as the constraint conditions, an equation relationship model of the objective function and the design variables is established, and then the genetic algorithm is used to solve the equation relationship model to obtain a Pareto optimal solution set, and the three design variable values corresponding to the optimal dynamic response index group of the cable-stayed bridge can be obtained from the Pareto optimal solution set; The solving of multiple index values to obtain the optimal index group belongs to a minimization problem, and the mathematical form is as follows: (5) In formula (5): h t 、 a 、 a 1 is a variable; is h t 、 a 、 a 1 is a variable; W is the objective function; is the target to be optimized. h t 、 a 、 a 1 is denoted as x , h t 、 a 、 a 1 is denoted as 。 Suppose is the solution of the objective function, when there is no other solution in the decision space to dominate , that is , then is the Pareto optimal solution of the objective function. The set composed of all the Pareto optimal solutions is called the Pareto optimal solution set, denoted as : (6) The mapping of the Pareto optimal solution set in the objective space constitutes the Pareto optimal front, denoted as : (7) The population size of the genetic algorithm is set to 100, the maximum number of iterations is 300, the algorithm optimization is independently run multiple times, and the Pareto optimal solution set is obtained. Refer to Figure 4 .

[0021] Step 5: Optimize the finite element model of the cable-stayed bridge according to the three design variable values ​​corresponding to the optimal dynamic response index group of the cable-stayed bridge obtained in step 4, and apply the same seismic wave as in step 3 to the optimized finite element model of the cable-stayed bridge to obtain a seismic response time history diagram of the cable-stayed bridge.

[0022] In this embodiment, the bridge is a low-tower cable-stayed bridge. The height of the cable-free area at the tower root obtained by the Pareto optimal solution set is h t , the main beam tower root without cable area a , Length of the cable-free area in the middle of the main beam span a 1 is introduced into the finite element model of the low-tower cable-stayed bridge to obtain a new finite element model of the low-tower cable-stayed bridge. The seismic motion selected in step 4 is applied, and the bending moment value at the bottom of the main pier of the low-tower cable-stayed bridge is recorded as the dynamic response value after optimization. The seismic motion selected in step 4 is applied to the finite element model of the low-tower cable-stayed bridge obtained in step 1, and the bending moment value at the bottom of the main pier of the low-tower cable-stayed bridge is recorded as the dynamic response value before optimization. The bending moment diagrams of the main piers of the cable-stayed bridge before and after optimization are referred to Figure 5 .

[0023] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0024] In this embodiment, a computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method are executed.

Claims

1. A dynamic optimization method for cable-stayed bridges based on response surface methodology-genetic algorithm, characterized in that: The steps include: Step 1: Use finite element software to model the cable-stayed bridge and obtain a finite element model of the cable-stayed bridge; Step 2: Take the cable-free area at the tower base of the cable-stayed bridge as the height h t , the main beam tower root without cable area a , Length of the cable-free area in the middle of the main beam span a 1 is the design variable of the cable inclination angle; according to the design rules of cable-stayed bridges, the value range of the design variable and the horizontal division value of the design variable are determined, so that different test group data are obtained by using the Box-Behnken design method. The data are then substituted into the finite element model of the cable-stayed bridge to obtain the finite element model corresponding to each test group data; Step 3: According to the site and structural dynamic characteristics of the cable-stayed bridge, select the seismic wave and apply it to the finite element model corresponding to each test group data to obtain the seismic response time history diagram of the cable-stayed bridge. Take the maximum value of the seismic response time history diagram as the dynamic response index value to obtain the dynamic response index group corresponding to each test group data, including: the bending moment at the bottom of the main pier of the bridge W 1. Curvature of the bottom of the main pier W 2. Bending moment in the span of the main beam W 3; The least squares method is used to fit the response surface equation of each dynamic response index under all test group data, and variance analysis is used to test whether each response surface equation meets the accuracy requirements. If so, step 4 is executed; otherwise, step 2 is returned to re-determine the value range of the design variable and the level division value of the design variable; Step 4: Construct three response surface equations that meet the accuracy requirements, and use the three response surface equations as the dynamic optimization objective function of the cable-stayed bridge. Using the boundary values ​​of the three design variables as constraints, establish an equation relationship model between the objective function and the design variables. Then, use the genetic algorithm to solve the equation relationship model and obtain the Pareto optimal solution set. From the Pareto optimal solution set, obtain the three design variable values ​​corresponding to the optimal dynamic response index group of the cable-stayed bridge; Step 5: Based on the three design variable values ​​corresponding to the optimal dynamic response index group of the cable-stayed bridge obtained in Step 4, the finite element model of the cable-stayed bridge is optimized. After applying the same seismic wave as in Step 3 to the optimized finite element model of the cable-stayed bridge, the seismic response time history diagram of the cable-stayed bridge is obtained.

2. An electronic device comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the cable-stayed bridge dynamic optimization method according to claim 1, and the processor is configured to execute the program stored in the memory.

3. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the cable-stayed bridge dynamic optimization method according to claim 1 are executed.

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