Acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II

Abstract

This invention provides an acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II, relating to the field of vibration reduction and noise reduction technology for rail transit bridges. The method includes: establishing a structural acoustic numerical model of the steel-concrete composite bridge; setting a uniform design table for the steel-concrete composite bridge; conducting simulation experiments based on the uniform design table and the structural acoustic numerical model to obtain multiple sets of acoustic response data; training a pre-set RBF neural network based on the multiple sets of acoustic results data to obtain a surrogate model; performing multi-objective optimization of the design variables of the steel-concrete composite bridge using the NSGA-II optimization algorithm and the surrogate model to obtain an optimal solution set for the design variables; evaluating each solution in the optimal solution set to obtain the optimal solution for the design variables; and using the design variables in the optimal solution set as the optimization result for the steel-concrete composite bridge. This invention solves the problem that existing technologies cannot simultaneously meet the requirements of optimizing structural acoustic response, structural mechanics, and economic efficiency.

Description

Technical Field

[0001] This invention relates to the field of vibration reduction and noise reduction technology for rail transit bridges, and more specifically, to an acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II. Background Art

[0002] Steel-concrete composite girder bridges play a vital role in modern transportation infrastructure, becoming an indispensable component of railway networks due to their superior span capacity and excellent mechanical properties. Compared to traditional bridge structures, steel-concrete composite bridge structures excel in load-bearing capacity, seismic performance, and durability, making them widely used in critical projects such as long-span bridges and high-speed railway bridges.

[0003] However, the noise problem of steel-concrete composite bridges cannot be ignored. Existing noise control methods for steel-concrete composite bridges often rely on external means such as constrained damping layers and vibration-damping tracks, while the impact of various cross-sectional parameters of steel-concrete composite bridges on noise characteristics remains at the level of single-parameter analysis. How to adjust the cross-sectional parameters of steel-concrete composite bridges to optimize structural acoustic characteristics while meeting structural mechanics and economic requirements is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] The purpose of this invention is to provide an acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II to improve the aforementioned problems. To achieve this objective, the technical solution adopted by this invention is as follows:

[0005] This application provides an acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II, including:

[0006] Obtain the parameter information of the steel-concrete composite bridge, and establish a structural acoustic numerical model of the steel-concrete composite bridge based on the parameter information;

[0007] A uniform design table for steel-concrete composite bridges is set up, wherein the design variables of the uniform design table include concrete slab thickness, steel web thickness, steel web height, steel flange thickness, and steel flange width.

[0008] Multiple sets of design variables from the uniform design table are input into the structural acoustic numerical model for simulation experiments to obtain multiple sets of acoustic response data.

[0009] A pre-set RBF neural network is trained based on the multiple sets of acoustic result data to obtain a surrogate model;

[0010] The design variables of the steel-concrete composite bridge are optimized using the NSGA-II optimization algorithm and the surrogate model to obtain the optimal solution set of the design variables. The objective function of the multi-objective optimization consists of the acoustic response and total material cost of the steel-concrete composite bridge.

[0011] Each solution in the optimal solution set of the design variables is evaluated to obtain the optimal solution of the design variables. The design variables in the optimal solution of the design variables are used as the optimization result of the steel-concrete composite bridge.

[0012] The beneficial effects of this invention are as follows:

[0013] This invention designs a structural acoustic numerical model for steel-concrete composite bridges, accurately simulating the bridge's acoustic response. Simultaneously, it combines a surrogate model and the NSGA-II optimization algorithm to perform multi-objective optimization of the bridge's acoustic characteristics and total material cost, achieving a balance between acoustic response and material cost. Finally, each solution is evaluated, and the parameter combination with the highest score is selected. This combination can be directly applied in practical engineering, improving the design quality and construction efficiency of steel-concrete composite bridges. Furthermore, the optimized design variables meet the actual needs of steel-concrete composite bridges, ensuring not only structural acoustic performance but also reducing material costs. Therefore, this invention provides technical support for the acoustic optimization design of steel-concrete composite bridges.

[0014] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. Attached Figure Description

[0015] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic diagram of the acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II as described in an embodiment of the present invention.

[0017] Figure 2 This is a side view of the steel-concrete composite bridge to be optimized in an embodiment of the present invention;

[0018] Figure 3 This is a cross-sectional view of the steel-concrete composite bridge to be optimized in an embodiment of the present invention;

[0019] Figure 4 This is a schematic diagram of the structural acoustic numerical model in an embodiment of the present invention;

[0020] Figure 5 This is a comparison chart of the prediction results of the surrogate model and the calculation results of the structural acoustic numerical model in an embodiment of the present invention;

[0021] Figure 6 This is a schematic diagram illustrating the iterative convergence of the NSGA-II optimization algorithm in an embodiment of the present invention;

[0022] Figure 7 This is a schematic diagram illustrating the optimal solution set of design variables in an embodiment of the present invention;

[0023] Figure 8 This is a comparison diagram of the acoustic response of the design variables before and after optimization in an embodiment of the present invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0025] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0026] Example 1:

[0027] This embodiment provides an acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II.

[0028] See Figure 1 The figure shows that the method includes steps S100, S200, S300, S400, S500 and S600.

[0029] Step S100: Obtain the parameter information of the steel-concrete composite bridge, and establish a structural acoustic numerical model of the steel-concrete composite bridge based on the parameter information;

[0030] Step S100 includes:

[0031] Step S101: Obtain parameter information of the steel-concrete composite bridge, the parameter information including excitation parameters and material parameters of the steel-concrete composite bridge;

[0032] In this embodiment, the material parameters include density, elastic modulus, Poisson's ratio, and damping loss factor.

[0033] Step S102: Establish the finite element model and statistical energy analysis model of the steel-concrete composite bridge based on the parameter information;

[0034] Step S102 includes:

[0035] Step A100: Perform modal density analysis on the steel-concrete composite bridge to obtain the modal density of each component of the steel-concrete composite bridge;

[0036] Step A200: Based on the modal density, all components of the steel-concrete composite bridge are divided into a first component and a second component, wherein the modal density of the first component is less than that of the second component;

[0037] Step A300: Based on the material parameters, perform finite element modeling on the first component to obtain a finite element model;

[0038] Step A400: Based on the material parameters, perform statistical energy analysis modeling on the second component to obtain the statistical energy analysis model.

[0039] Step S103: Couple the finite element modeling and the statistical energy analysis model to obtain the numerical model of the steel-concrete composite bridge;

[0040] Step S104: Assign the excitation parameters to the numerical model to obtain the structural acoustic numerical model of the steel-concrete composite bridge.

[0041] In this embodiment, the structural acoustic numerical model can directly calculate the sound pressure level at a certain point in the steel-concrete composite bridge, as well as the sound radiation efficiency and energy of each component. Through the sound pressure level, sound radiation efficiency, and energy, the total sound power level of the steel-concrete composite bridge structure can be calculated. In this embodiment, the total sound power level of the steel-concrete composite bridge is taken as the acoustic response, that is, the acoustic characteristics of the steel-concrete composite bridge.

[0042] Step S200: Set up a uniform design table for the steel-concrete composite bridge. The design variables in the uniform design table include the thickness of the concrete slab, the thickness of the steel web, the height of the steel web, the thickness of the steel flange, and the width of the steel flange.

[0043] In this embodiment, the cross-sectional parameters of the steel-concrete composite bridge are designed. First, design variables for the cross-sectional parameters are set. The design variables actually represent a combination of multiple cross-sectional optimization parameters. The optimization range and learning range of the design variables are set, and the learning range is made larger than the optimization range to reduce boundary errors.

[0044] A uniform design table is set up for the design variables. In this embodiment, there are 5 parameters, and the uniform design table U can be selected. 16* (16 12 Meanwhile, designing a uniform design table to reasonably distribute design variables not only avoids experimental redundancy but also reduces the number of simulation runs and lowers computational costs.

[0045] Step S300: Input multiple sets of design variables from the uniform design table into the structural acoustic numerical model for simulation experiments to obtain multiple sets of acoustic response data;

[0046] Step S400: Train a preset RBF neural network based on the multiple sets of acoustic result data to obtain a surrogate model;

[0047] In this embodiment, the RBF neural network includes an input layer, hidden layers, and an output layer. The transformation from the input layer to the hidden layer is non-linear, while the transformation from the hidden layer to the output layer is linear. To achieve the non-linear transformation, the hidden layer typically chooses a Gaussian function as its radial basis function, and the output of the output layer can be represented as a linear superposition of the hidden layers.

[0048] In this embodiment, within the learning range of the design variables, the Adam optimizer is selected to train the RBF neural network to obtain a surrogate model. The surrogate model greatly reduces the computational load of subsequent optimization solutions and significantly improves optimization efficiency.

[0049] Step S500: Perform multi-objective optimization on the design variables of the steel-concrete composite bridge using the NSGA-II optimization algorithm and surrogate model to obtain the optimal solution set of the design variables. The objective function of the multi-objective optimization consists of the acoustic response and total material cost of the steel-concrete composite bridge.

[0050] In this embodiment, the NSGA-II optimization algorithm is used for multi-objective optimization, which combines fast non-dominated sorting and crowding degree. It has low computational complexity, more uniform distribution of solutions in the optimal solution set of design variables, and better robustness.

[0051] Step S500 includes:

[0052] Step S501: Randomly generate an initial population, the initial population including multiple individuals, the individuals including design variables of the steel-concrete composite bridge;

[0053] In this embodiment, each individual represents a set of design variables and the total material cost of the steel-concrete composite bridge, where the total material cost is calculated using these design variables. An initial population is randomly generated, i.e., multiple individuals are initialized. Within the optimization range, optimization parameters for each section of the design variables are randomly generated.

[0054] Step S502: Input each individual into the agent model to calculate the individual's acoustic response;

[0055] Step S503: Perform fast non-dominated sorting on the population, calculate the violation value of each individual, and divide all individuals according to the size of the violation value to obtain the Pareto optimal solution set;

[0056] Step S503 specifically includes:

[0057] Step B100: Calculate the individual's violation value;

[0058] Step B200: Based on the violation value, divide all individuals into feasible and infeasible solutions;

[0059] Step B300: Perform fast non-dominated sorting on the feasible solutions to divide the feasible solutions into multiple Pareto front layers;

[0060] Step B400: Select the first Pareto front layer as the Pareto optimal solution set.

[0061] In this embodiment, the violation value of each individual is first calculated. Based on the violation value, all individuals are divided into feasible and infeasible solutions. The feasible solutions are then sorted by fast non-dominated ordering. The feasible solutions are divided into multiple Pareto front layers. The first Pareto front layer containing multiple optimal individuals is selected as the Pareto optimal solution set.

[0062] Step S504: Based on the objective function, the individual's rank, and the individual's acoustic response, calculate the crowding degree of each individual in the Pareto optimal solution set;

[0063] Step S504 includes:

[0064] Step C100: Calculate the objective function value for each individual in the Pareto optimal solution set based on the objective function;

[0065] Step C200: Sort all individuals in ascending order of the objective function value;

[0066] Step C300: Obtain the objective function values ​​of the two adjacent individuals for each individual, and calculate the crowding degree of each individual based on the objective function values ​​of the two adjacent individuals.

[0067] In this embodiment, the formula for calculating congestion is:

[0068]

[0069] In the formula, d i f represents the crowding level of the i-th individual. k (i+1) represents the objective function value of the k-th objective function for the (i+1)-th individual, f k (i-1) represents the objective function value of the k-th objective function for the (i-1)-th individual. This represents the maximum value of the k-th objective function in the Pareto optimal solution set. The minimum value of the k-th objective function in the Pareto optimal solution set, where m represents the number of objective functions.

[0070] Step S505: Based on the crowding degree and the violation value, perform selection, crossover and mutation operations on the individuals in the Pareto optimal solution set in sequence to obtain a new population;

[0071] Step S505 includes:

[0072] Step D100: Calculate the selection probability based on the crowding level and the violation value;

[0073] Step D200: Select individuals from the Pareto optimal solution set using the selection probability to obtain the first group;

[0074] Step D300: Select some design variables of each individual in the first population and perform crossover operation to obtain the second population;

[0075] Step D400: Calculate the mutation probability based on the crowding degree and the violation value;

[0076] Step D500: Perform mutation operations on the individuals in the second population based on the mutation probability to obtain a new population.

[0077] Step S506: Determine whether the number of iterations has reached the preset threshold. If so, stop the iteration and use the Pareto optimal solution as the optimal solution set for the design variables. Otherwise, use the new population as the initial population for the next iteration and proceed with the next iteration.

[0078] In this embodiment, the steps for constructing the objective function are as follows:

[0079] Step E100: Calculate the acoustic response under the design variables using a surrogate model, and calculate the total material cost corresponding to the design variables.

[0080] Step E200: Minimize both the acoustic response and the total material cost as the objective function;

[0081] Step E300: Define the constraints of the objective function, including the optimization range of the design variables, the maximum tensile stress constraint function, and the bridge fundamental frequency constraint function.

[0082] This embodiment includes multiple objective functions, namely minimizing the acoustic response and the total material cost. The formulas for the objective functions are as follows:

[0083] min{W(x), C(x)}x=(tc , t w , l w , t f , l f )

[0084] In the formula, W(x) represents the total sound power level when design variable x, C(x) represents the total material cost when design variable x, min{·} represents taking the minimum value, and t c The thickness of the concrete slab is represented by t. w Indicates the thickness of the steel web, l w Indicates the height of the steel web, t f Indicates the thickness of the steel flange, l f This indicates the width of the steel flange.

[0085] Simultaneously, the optimization range, maximum tensile stress constraint function, and bridge fundamental frequency constraint function are set for each design variable. The expression for the maximum tensile stress constraint function is:

[0086] σ(x)-σ(x0)≤0

[0087] In the formula, σ(·) represents the maximum tensile stress in the span of the steel-concrete composite bridge under uniformly distributed static load, x represents the design variable, and x0 represents the original design variable.

[0088] The expression for the bridge fundamental frequency constraint function is:

[0089] f(x0)-f(x)≤0

[0090] In the formula, f(·) represents the fundamental frequency of the bridge, x represents the design variable, and x0 represents the original design variable.

[0091] In this embodiment, the maximum tensile stress is conveniently calculated using structural mechanics equations, the bridge fundamental frequency can be calculated using calculation formulas from relevant specifications, and the original design variables are the initial cross-sectional parameters of the steel-concrete composite bridge to be optimized.

[0092] Step S600: Evaluate each solution in the optimal solution set of design variables to obtain the optimal solution of design variables, and use the design variables in the optimal solution of design variables as the optimization result of the steel-concrete composite bridge.

[0093] Step S600 includes:

[0094] Step S601: Calculate the indices of each solution in the optimal solution set of design variables, including acoustic response and total material cost;

[0095] Step S602: Calculate the distance between each solution and the ideal optimal solution and the ideal worst solution based on the aforementioned index;

[0096] Step S602 includes:

[0097] Step F100: Negatively process and standardize all indices to obtain the standard indices corresponding to each solution;

[0098] In this embodiment, the indicators are negativeized to obtain negative indicators. Negative indicators are those with smaller values, and acoustic response and total material cost are both negative indicators.

[0099] The standardized formula is as follows:

[0100]

[0101] In the formula, z ab′ z represents the b-th negative index of the a-th solution. ab Let M represent the b-th standard index of the a-th solution, M represent the number of solutions in the optimal solution set of the design variables, and N represent the number of indices.

[0102] Step F200: Calculate the distance between each solution and the ideal optimal solution and the ideal worst solution based on the standard index.

[0103] In this embodiment, for each standard index, the ideal optimal solution is the minimum value of the standard index, and the ideal worst solution is the maximum value of the standard index.

[0104] The formula for calculating the distance to the ideal optimal solution is:

[0105]

[0106] In the formula, d a,+ z represents the distance between the a-th solution and the ideal optimal solution. ab This represents the b-th standard index of the a-th solution. Let N represent the ideal optimal solution for the b-th standard indicator, and N represent the number of indicators.

[0107] The formula for calculating the distance from the ideal worst solution is:

[0108]

[0109] In the formula, d a，- z represents the distance between the a-th solution and the ideal optimal solution. ab This represents the b-th standard index of the a-th solution. Let b represent the ideal worst-case solution for the b-th standard indicator, and N represent the number of indicators.

[0110] Step S603: Based on the distance between each solution and the ideal optimal solution and the ideal worst solution, calculate the relative proximity of each solution, and select the solution with the largest relative proximity as the optimal solution for the design variables;

[0111] In this embodiment, it is necessary to determine how close each solution is to the ideal solution of the design variables. Therefore, the relative closeness is calculated to measure the closeness, and the solution with the largest relative closeness is selected as the optimal solution of the design variables. The formula for calculating the relative closeness is as follows:

[0112]

[0113] In the formula, S a d represents relative proximity. a，+ d represents the distance between the a-th solution and the ideal optimal solution. a,- This represents the distance between the a-th solution and the ideal optimal solution.

[0114] Step S604: Use the design variables in the optimal solution of the design variables as the optimization result of the steel-concrete composite bridge.

[0115] Example 2:

[0116] In this embodiment, Figure 2 and Figure 3 Taking the steel-concrete composite bridge to be optimized as an example, Table 1 shows the material parameters designed in this embodiment.

[0117] Table 1

[0118]

[0119] Table 2 shows the excitation parameter table designed in this embodiment.

[0120] Table 2

[0121]

[0122]

[0123] In this embodiment, a structural acoustic numerical model is established as follows: Figure 4 As shown, the concrete slab is modeled using the finite element method (FE), while the steel web and steel flanges are modeled using statistical energy analysis (SEA). The forces transmitted to the bridge can be calculated using a frequency domain wheel-rail force program, a vehicle-bridge coupling program, or obtained through actual measurement.

[0124] After establishing the structural acoustic numerical model, the design variables, optimization range, and learning range are determined based on the actual situation. In this embodiment, the design variables include the concrete slab thickness, steel web thickness, steel web height, steel flange thickness, and steel flange width. Table 3 shows the optimization range of the design variables.

[0125] Table 3

[0126]

[0127] Select a suitable uniform design table to design multiple sets of design variables and calculate the acoustic response of each set of design variables. In this embodiment, the total sound power level is used as the acoustic response.

[0128] In this embodiment, the acoustic response results are used to train a preset REF neural network to obtain a surrogate model. The surrogate model is then used to obtain the acoustic response of a steel-concrete composite bridge that can accurately predict different combinations of design variables.

[0129] exist Figure 5 The paper presents a comparison between the prediction of the total sound power level of a set of design variables in the 20-2000Hz frequency band and the calculation of the structural acoustic numerical model. The small deviation indicates that the surrogate model can predict the acoustic response of the steel-concrete composite bridge well.

[0130] In this embodiment, the NSGA-II optimization algorithm was used for 200 iterations, meaning the population had 200 generations. The convergence results and the optimal solution set for the design variables are as follows: Figure 6 and Figure 7 As shown, the material cost change rate represents the change rate of the total material cost.

[0131] In this embodiment, as Figure 7 As shown, a cutoff limit is set, and solutions with a total sound power less than 137.4 dB are taken as the optimal solution set for design variables. These are all design variables that further reduce structural noise compared to the original design. Theoretically, these solutions can all be selected according to the actual situation. However, in order to obtain the optimal solution that balances noise and total material cost, this embodiment evaluates all solutions in the optimal solution set for design variables and obtains the optimal solution X for design variables, where X∈x, x=(t c ,t w ,l w ,t f ,l f X = (0.5328, 0.0200, 2.9719, 0.03002, 0.9562)m, where x represents the design variable.

[0132] The optimal solution for this design variable is compared with the sound power level of the original design variable, for example... Figure 8 As shown, the sound power level drops by 5 dB, and the total material cost decreases by 21% at this point.

[0133] In summary, the method of this invention achieves noise reduction by altering the cross-sectional design parameters of steel-concrete composite bridges. Simultaneously, this design meets stiffness and strength requirements while maintaining low cost. Therefore, this invention, considering various constraints, achieves acoustic optimization for steel-concrete composite bridges and can provide assistance in their design.

[0134] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0135] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. An acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II, characterized in that, include: Obtain the parameter information of the steel-concrete composite bridge, and establish a structural acoustic numerical model of the steel-concrete composite bridge based on the parameter information; A uniform design table for steel-concrete composite bridges is set up, wherein the design variables of the uniform design table include concrete slab thickness, steel web thickness, steel web height, steel flange thickness, and steel flange width. Multiple sets of design variables from the uniform design table are input into the structural acoustic numerical model for simulation experiments to obtain multiple sets of acoustic response data. A pre-set RBF neural network is trained based on the multiple sets of acoustic result data to obtain a surrogate model; The design variables of the steel-concrete composite bridge are optimized using the NSGA-II optimization algorithm and the surrogate model to obtain the optimal solution set of the design variables. The objective function of the multi-objective optimization consists of the acoustic response and total material cost of the steel-concrete composite bridge. Each solution in the optimal solution set of the design variables is evaluated to obtain the optimal solution of the design variables. The design variables in the optimal solution of the design variables are used as the optimization result of the steel-concrete composite bridge. The process of obtaining parameter information for the steel-concrete composite bridge and establishing a structural acoustic numerical model of the steel-concrete composite bridge based on the parameter information includes: Obtain parameter information of the steel-concrete composite bridge, including excitation parameters and material parameters of the steel-concrete composite bridge; Based on the parameter information, a finite element model and a statistical energy analysis model of the steel-concrete composite bridge were established. The finite element model and the statistical energy analysis model are coupled to obtain the numerical model of the steel-concrete composite bridge. The excitation parameters are assigned to the numerical model to obtain the structural acoustic numerical model of the steel-concrete composite bridge. The establishment of the finite element model and statistical energy analysis model of the steel-concrete composite bridge based on parameter information includes: Modal density analysis was performed on the steel-concrete composite bridge to obtain the modal density of each component of the steel-concrete composite bridge. Based on the modal density, all components of the steel-concrete composite bridge are divided into a first component and a second component, wherein the modal density of the first component is less than that of the second component. Based on the material parameters, a finite element model is performed on the first component to obtain a finite element model; Based on the material parameters, statistical energy analysis modeling is performed on the second component to obtain the statistical energy analysis model.

2. The acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II according to claim 1, characterized in that... The multi-objective optimization of the steel-concrete composite bridge using the NSGA-II optimization algorithm and surrogate model yields the optimal solution set for the design variables, including: An initial population is randomly generated, which includes multiple individuals, and the individuals include the design variables of the steel-concrete composite bridge. Each individual is input into the proxy model to calculate the individual's acoustic response; Perform a fast non-dominated sort on the population, calculate the violation value of each individual, and divide all individuals according to the size of the violation value to obtain the Pareto optimal solution set; Based on the objective function, the individual's rank, and the individual's acoustic response, the crowding degree of each individual in the Pareto optimal solution set is calculated; Based on the crowding degree and the violation value, the individuals in the Pareto optimal solution set are selected, crossed over, and mutated in sequence to obtain a new population; Determine if the number of iterations has reached a preset threshold. If so, stop the iteration and use the Pareto optimal solution as the optimal solution set for the design variables. Otherwise, use the new population as the initial population for the next iteration and proceed with the next iteration.

3. The acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II according to claim 2, characterized in that... The process of performing fast non-dominated sorting on the population, calculating the violation value of each individual, and partitioning all individuals based on the magnitude of the violation value to obtain the Pareto optimal solution set includes: Calculate the individual's violation value; Based on the aforementioned violation values, all individuals are divided into feasible and infeasible solutions; The feasible solutions are sorted by fast nondominated sorting, and the feasible solutions are divided into multiple Pareto front layers; The first Pareto front layer is selected as the Pareto optimal solution set.

4. The acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II according to claim 2, characterized in that... The calculation of the crowding degree of each individual in the Pareto optimal solution set includes: Calculate the objective function value for each individual in the Pareto optimal solution set based on the objective function; Sort all individuals in ascending order of their objective function values; Obtain the objective function values ​​of the two adjacent individuals for each individual, and calculate the crowding degree of each individual based on the objective function values ​​of the two adjacent individuals.

5. The acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II according to claim 2, characterized in that... Based on the crowding level and the violation value, selection, crossover, and mutation operations are sequentially performed on individuals in the Pareto optimal solution set to obtain a new population, including: The selection probability is calculated based on the crowding level and the violation value; The first group is obtained by selecting individuals in the Pareto optimal solution set using the selection probability. Select some design variables of each individual in the first population and perform crossover operations to obtain the second population; The mutation probability is calculated based on the crowding level and the violation value; Based on the mutation probability, mutation operations are performed on individuals in the second population to obtain a new population.

6. The acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II according to claim 1, characterized in that... The steps for constructing the objective function are as follows: The acoustic response under the design variables is calculated using a proxy model, and the total material cost corresponding to the design variables is calculated using the design variables. Minimizing both acoustic response and total material cost is used as the objective function; Define the constraints of the objective function, including the optimization range of the design variables, the maximum tensile stress constraint function, and the bridge fundamental frequency constraint function.

7. The acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II according to claim 1, characterized in that... Each solution in the optimal solution set of the design variables is evaluated to obtain the optimal solution of the design variables. The design variables in the optimal solution of the design variables are used as the optimization result of the steel-concrete composite bridge, including: Calculate the indices for each solution in the optimal solution set of design variables, including acoustic response and total material cost; Calculate the distance between each solution and the ideal optimal solution and the ideal worst solution based on the aforementioned indicators; Based on the distance between each solution and the ideal optimal solution and the ideal worst solution, calculate the relative proximity of each solution, and select the solution with the largest relative proximity as the optimal solution for the design variables; The design variables in the optimal solution are used as the optimization result for the steel-concrete composite bridge.

8. The acoustic optimization method for steel-concrete composite bridges based on RBF-NSGA-II according to claim 7, characterized in that... The step of calculating the distance between each solution and the ideal optimal solution and the ideal worst solution based on the aforementioned index further includes: All indicators are negativeized and standardized to obtain the standard indicator corresponding to each solution; Based on the aforementioned standard indicators, the distance between each solution and the ideal optimal solution and the ideal worst solution are calculated respectively.

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