A cable-stayed bridge completion cable force multi-objective intelligent optimization method

Abstract

The present application relates to the technical field of bridge engineering, and provides a cable-stayed bridge completion cable force multi-objective intelligent optimization method: a finite element model of the cable-stayed bridge is established, the minimum bending energy method is adopted, and the cable force is initially uniform according to the principle of "long cable force is large, and short cable force is small"; a small sample support vector machine regression proxy model based on a radial basis kernel function is constructed, grid search and leave-one-out cross-validation are adopted to optimize the super parameters, and the mapping relationship between the cable force and the bending moment, displacement and other structural responses is represented; a multi-objective optimization model with bending strain energy and combined displacement as optimization objectives is established; and a multi-objective intelligent optimization method based on a double optimization strategy is used to guide the general cable force to approach the two types of excellent cable forces, the iteration optimization is adjusted through a direction factor and a strength factor, the Pareto optimal cable force candidate set is updated through a non-dominated sorting, a hypercube grid and a crowding degree strategy, and finally a comprehensive optimal cable force is obtained as the cable-stayed bridge completion cable force.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering technology, and more specifically, to a multi-objective intelligent optimization method for cable forces in a cable-stayed bridge. Background Technology

[0002] Cable-stayed bridges mainly consist of bridge towers, main girders, and stay cables. The upper ends of the stay cables are anchored to the bridge towers, and the lower ends are connected to the main girders. It is a cable-stayed bridge structure that utilizes the stay cables to provide elastic support to the main girders, thereby increasing the bridge's span. Cable-stayed bridges have a large span capacity and good structural stability, making them a highly competitive bridge type among kilometer-class long-span bridges. Cable-stayed bridges are highly statically indeterminate structures, and the cable forces directly affect the stress state of the main girders and bridge towers. Different cable forces result in different stress states for the main girders and bridge towers. Therefore, optimizing the cable forces to achieve rational and even optimal stress distribution in cable-stayed bridges is a crucial task in the design process.

[0003] Methods for optimizing cable forces in cable-stayed bridges include traditional empirical methods for determining cable forces, classical cable force optimization methods, and modern intelligent cable force optimization methods. Traditional empirical cable force methods used before the 1980s, such as the zero-displacement method, the rigid-supported continuous beam method, and the moment distribution method, are essentially structural analysis methods. These methods do not establish an objective function or perform mathematical optimization; they rely mainly on engineers' experience, iteratively adjusting cable forces and performing structural analysis. This method cannot guarantee optimal structural stress. Classical cable force optimization methods, which emerged after the 1980s, such as the minimum bending energy method, the displacement control method, and the influence matrix method, have explicit objective functions and systematic mathematical optimization processes, enabling the attainment of the optimal structural stress state. These are currently the mainstream cable force optimization methods in engineering. However, for nonlinear, multi-objective, complex-constrained, and complex bridge types, classical cable force optimization methods often suffer from high computational complexity and large computational loads, and may even be unsolvable. Modern intelligent optimization methods developed after 2000, such as genetic algorithms, particle swarm optimization, and simulated annealing, have shown good applicability to nonlinear, complex constraints, and complex bridge types. However, the iterative calculation process using intelligent optimization algorithms still suffers from the problem of repeatedly calling the bridge finite element model or dealing with large cable force influence matrices, which still affects the calculation speed. Multi-objective intelligent algorithms such as MOGA, NSGA-II / III, and MOPSO, developed based on genetic algorithms and particle swarm optimization, employ a process of intelligent optimization followed by manual decision-making. The algorithms do not obtain a single optimal solution, but rather a solution set containing multiple Pareto optimal solutions. Multi-objective intelligent optimization algorithms do not consider decision-making requirements during the optimization process. In engineering practice, a Pareto optimal solution needs to be selected from the solution set based on subjective decision-making needs. Therefore, there are problems with insufficient automation and quantification of decision-making, requiring further efficiency improvements.

[0004] In conclusion, it is necessary to improve the method for establishing proxy models for cable-stayed bridges and develop multi-objective intelligent optimization algorithms that take into account decision-making needs, so as to improve work efficiency and ensure the reliability of results. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides a multi-objective intelligent optimization method for cable forces in cable-stayed bridges.

[0006] This invention is achieved through the following technical solution: a multi-objective intelligent optimization method for cable forces in a cable-stayed bridge, specifically including the following steps:

[0007] Step S1: Establish a finite element model of the cable-stayed bridge and perform preliminary optimization of the cable forces. The minimum bending energy method is used for preliminary optimization of the cable forces, and the cable forces are initially uniformized according to the principle of "longer cables have larger cable forces and shorter cables have smaller cable forces".

[0008] Step S2: Construct a small-sample surrogate model of the cable-stayed bridge to characterize the mapping relationship between cable forces and structural responses including bending moments and displacements;

[0009] Step S3: Establish a multi-objective optimization model for the cable forces of the cable-stayed bridge to define the functional relationship between the optimization objectives, including bending strain energy, resultant displacement, and structural response.

[0010] Step S4: The cable force is optimized using a multi-objective intelligent optimization method based on the dual-optimization strategy for cable-stayed bridges. The Pareto optimal cable force set is obtained, and a comprehensive optimal cable force is selected as the final cable force of the bridge.

[0011] As a preferred option, the small-sample surrogate model for cable-stayed bridges adopts the support vector machine regression RBF-SVR surrogate model based on radial basis function kernel function. The model hyperparameters are tuned using grid search and leave-one-out cross-validation suitable for small samples.

[0012] Furthermore, the specific construction process of the small-sample surrogate model for cable-stayed bridges is as follows:

[0013] Step S2-1: Use the finite element model of a cable-stayed bridge to collect a training dataset of cable force-structure response;

[0014] Step S2-2: Data preparation; Load cable force-structure response training data, verify data validity, and standardize training data.

[0015] Step S2-3: Construct the proxy model and define the leave-one-out evaluation function;

[0016] Step S2-4: Proxy model hyperparameter tuning. Grid search and leave-one-out cross-validation are used for tuning to select the optimal penalty coefficient C and kernel width γ for each output model.

[0017] As a preferred option, the multi-objective intelligent optimization method for cable-stayed bridge cable forces based on the dual-optimization strategy is to iteratively optimize the general cable force set and select non-dominated cable forces to enter the optimal cable force candidate set. The iterative optimization mechanism is guided by the comprehensive optimal cable force and the partial optimal cable force, which guides the general cable force to approach the two types of excellent cable forces and gradually improves the performance of the cable force set.

[0018] Furthermore, the specific optimization method of the multi-objective intelligent optimization method for cable-stayed bridge cable forces based on the dual-optimization strategy is as follows:

[0019] Step S4-1: Initialize general cable forces and multi-objective fitness :

[0020] General cable tension The values ​​are taken within the range of 0.9 to 1.1 times the initial uniform cable force; the general cable force is calculated using a small-sample surrogate model for cable-stayed bridges. Based on the corresponding structural response, and using the multi-objective optimization model of cable-stayed bridge cable forces, the general cable forces are calculated. Multi-objective fitness corresponding to structural response ;

[0021] Step S4-2: Initialize the Pareto optimal cable force candidate set:

[0022] Non-dominated forces are sorted according to multi-objective fitness, and non-dominated forces are added to the Pareto optimal force candidate set.

[0023] Step S4-3: Normalize the multi-objective fitness of non-dominated cable forces;

[0024] Step S4-4: Define the ideal fitness of cable force :

[0025] The ideal fitness is composed of the best single-objective fitness normalized by all non-dominated forces. ;

[0026] Step S4-5: Define the overall optimal cable force and the partial optimal cable force:

[0027] Calculate the fitness non-ideal bias of cable forces in the Pareto optimal cable force candidate set. , Pick and Euclidean distance; according to fitness non-ideal deviation Sort by fitness from smallest to largest, select the best overall fitness and the least favorable fitness; consider the deviation from ideal fitness. For equal cable forces, one is randomly selected as the optimal cable force or the slightly optimal cable force.

[0028] Step S4-6, Cable Iteration:

[0029] Generally, the cable force is iteratively optimized towards both the overall optimal cable force and the partially optimal cable force. The value of the general cable force after the (k+1)th iteration optimization is calculated according to the following formula, which sets the direction factor and the intensity factor.

[0030]

[0031] In the above formula, Let i be the force after the k-th iteration optimization. Let i be the force after the (k+1)th iteration. For comprehensive and superior cable force, For a slightly preferred force; and This is called the direction factor, which is randomly selected as 1 or -1 to adjust the direction of iterative optimization. and It is called the intensity factor, which is a uniformly random number within [0,2] and is used to adjust the magnitude of the iterative optimization. By combining the direction factor and the intensity factor in two directions, multi-directional iterative optimization can be achieved.

[0032] Step S4-7, Cable tension selection:

[0033] according to Calculate the fitness of cable forces for multiple targets, if Dominate ,but Pick ,otherwise Maintain the status quo ;

[0034] Step S4-8: Update the Pareto optimal skeletal candidate set:

[0035] The non-dominated sorting is performed again, and the non-dominated forces are selected to update the Pareto optimal force candidate set. To maintain the diversity of solutions, the hypercube grid and roulette wheel selection strategy are used during the update. To ensure capacity, the crowding removal strategy is used to maintain the upper limit of the number of forces in the Pareto optimal force candidate set.

[0036] Step S4-9: Repeat steps S4-3 to S4-8 for iteration.

[0037] Step S4-10: Stop iterating after reaching the required number of iterations or meeting the accuracy requirements, output the final Pareto optimal cable force set, and select a comprehensive optimal cable force as the cable force for the completed bridge.

[0038] The present invention, by adopting the above technical solutions, has the following beneficial effects compared with the prior art: the small sample proxy model of cable-stayed bridge described in the present invention has a faster calculation speed during the iteration process.

[0039] This invention sorts the candidates for optimal Pareto forces according to their fitness deviation. In each iteration, the force with the smallest fitness deviation is selected as the overall optimal force, and finally, the force with the smallest fitness deviation, i.e., the overall optimal force, is directly given, thus improving decision-making efficiency. In each iteration, the force with the largest fitness deviation, i.e., the partially optimal force, is selected and retained to avoid premature convergence of the algorithm, thereby improving optimization accuracy.

[0040] Additional aspects and advantages of the invention will become apparent in the following description or may be learned by practice of the invention. Attached Figure Description

[0041] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0042] Figure 1 This is a flowchart illustrating a multi-objective intelligent optimization method for cable-stayed bridge cable forces based on a dual-optimization strategy.

[0043] Figure 2 A schematic diagram illustrating the process of constructing a small-sample surrogate model for cable-stayed bridges based on RBF-SVR;

[0044] Figure 3 For ideal fitness and fitness deviation Schematic diagram;

[0045] Figure 4 This is a schematic diagram illustrating the cable force iteration guided by the overall optimal cable force and the partial optimal cable force. Detailed Implementation

[0046] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0047] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0048] The following is combined with Figures 1 to 4 The multi-objective intelligent optimization method for cable-stayed bridge cable forces according to an embodiment of the present invention will be described in detail.

[0049] This invention proposes a multi-objective intelligent optimization method for cable forces in cable-stayed bridges, which specifically includes the following steps:

[0050] Step S1: Establish a finite element model of the cable-stayed bridge and perform preliminary optimization of the cable forces. The minimum bending energy method is used for preliminary optimization of the cable forces, and the cable forces are initially uniformized according to the principle of "longer cables have larger cable forces and shorter cables have smaller cable forces".

[0051] The finite element model consists of 28 cable-stayed elements, 30 main girder elements, 16 bridge tower elements, and 31 main girder nodes and 16 bridge tower nodes. The unconstrained minimum bending energy method is used for initial optimization of cable forces, and initial uniform cable forces are then applied. The initial uniform cable forces are listed as vectors, i.e.: [11027.0;10880.2;10620.4;10258.9;9958.2;9735.0;9271.5;8788.4;8374.3;8044.4;7623.3;7110.8;6581.9;6068.8;6054.4;6574.8;7051.4;7535.7;7988.8;8184.4;8361.5;9422.0;11468.1;11601.3;11732.6;11835.5;11938.4;12133.4].

[0052] Step S2: Construct a small-sample surrogate model for the cable-stayed bridge to characterize the mapping relationship between cable forces and structural responses, including bending moments and displacements. The small-sample surrogate model for the cable-stayed bridge is constructed using a support vector machine regression (RBF-SVR) model based on radial basis function kernel functions, referred to as the RBF-SVR surrogate model. The model hyperparameters are optimized using grid search and leave-one-out cross-validation methods suitable for small samples. The specific construction process is as follows:

[0053] Step S2-1: Using the finite element model of the cable-stayed bridge, collect a cable force-structure response training dataset. The training dataset consists of 30 sets of data, representing a small sample size. Each set includes 28 cable force values, 30 left bending moment values ​​for beam elements, 30 right bending moment values ​​for beam elements, 16 left bending moment values ​​for tower elements, 16 right bending moment values ​​for tower elements, 31 beam node displacement values, 16 tower node displacement values, and 3 node reaction force values. That is, each set of data has 28 dimensions of input and 142 dimensions of output.

[0054] This embodiment uses Matlab software to construct a proxy model for cable-stayed bridges and perform multi-objective intelligent optimization of cable forces in completed cable-stayed bridges. The following steps are implemented using Matlab programming language.

[0055] Step S2-2: Data preparation; Load the cable force-structure response training data, verify the data validity, and then use the Z-score method to standardize the training data into a normal distribution with a mean of 0 and a variance of 1, and save the mean and standard deviation of the original data for later destandardization.

[0056] Step S2-3: Construct the proxy model and define the leave-one-out evaluation function;

[0057] A support vector machine regression (RBF-SVR) model based on radial basis function kernel function was used to construct a small-sample surrogate model for cable-stayed bridges. The surrogate model was defined as a function named rbfSvrloocv.

[0058] One set of training data is repeatedly extracted as a reserved validation set. The remaining data and the RBF-SVR model are used to train and predict the validation set. The mean squared error of the predicted validation set and the reserved validation set is compared with the currently set best mean squared error to complete the model evaluation. This process is defined in Matlab as the leave-one-out evaluation function, named loocv_evaluate.

[0059] Step S2-4: Proxy model hyperparameter tuning; use grid search and call the leave-one-out evaluation function loocv_evaluate for cross-validation tuning to select the optimal penalty coefficient C and kernel width γ for each output model, and use these optimal parameters to train the optimal model for all samples, and save the optimal model parameters and the corresponding mean squared error.

[0060] Step S3: Establish a multi-objective optimization model for the cable forces of the cable-stayed bridge to define the functional relationship between the optimization objectives, including bending strain energy, resultant displacement, and structural response.

[0061] This embodiment selects two objective functions: minimizing the bending strain energy U and minimizing the resultant displacement D. The bending strain energy U is a quadratic function of the bending moment M at the control section, and the resultant displacement D is a nonlinear function of the nodal displacement δ. Both the bending moment M at the control section and the nodal displacement δ are functions of the cable force t, calculated from the cable force t using a small-sample surrogate model for cable-stayed bridges.

[0062] The constraints include: maximum and minimum bending moments of the main girder are ±35000kNm; maximum and minimum bending moments of the bridge tower are ±25000kNm; maximum and minimum displacements of the main girder are ±20mm; maximum displacement of the main tower is 0mm and minimum displacement is -20mm; maximum cable force is 13000kN and minimum cable force is 6000kN; minimum support reaction force is 1000kN.

[0063] The support reaction force is also a function of the cable force t, and is calculated based on the cable force t using a small-sample surrogate model of cable-stayed bridges.

[0064] The initial value of the cable force is taken as the initial uniform cable force.

[0065] Step S4: The cable force is optimized using a multi-objective intelligent optimization method based on a dual-optimization strategy for the cable force of the completed cable-stayed bridge, and the Pareto optimal solution for the cable force of the completed cable-stayed bridge is obtained.

[0066] The multi-objective intelligent optimization method for cable-stayed bridge cable forces based on a dual-optimization strategy is a swarm intelligence optimization method. The approach involves iteratively optimizing a general set of cable forces, selecting non-dominated cable forces to enter the optimal candidate set. The iterative optimization mechanism guides the general cable forces towards these two types of excellent forces, guided by overall optimal and partially optimal cable forces, thereby gradually improving the performance of the cable force set. The specific optimization method is as follows:

[0067] Step S4-1: Initialize general cable forces and multi-objective fitness :

[0068] Initialize the population size to 200.

[0069] General cable tension The initial uniform force is taken in the range of 0.9 to 1.1 times, and 200 row vectors are randomly generated.

[0070] Use a small-sample surrogate model of a cable-stayed bridge to calculate general cable forces. Based on the corresponding structural response, and using the multi-objective optimization model of cable-stayed bridge cable forces, the general cable forces are calculated. Multi-objective fitness corresponding to structural response Multi-objective fitness That is, to minimize the bending strain energy and minimize resultant displacement The resulting row vectors consist of 200 cable force row vectors, calculated from the bending moments of 200 control sections using a small-sample surrogate model for cable-stayed bridges. Row vectors, nodal displacements Row vectors are then used to calculate 200 bending strain energies using the objective function. Combined displacement The row vectors formed by these vectors.

[0071] Step S4-2: Initialize the Pareto optimal cable force candidate set, with a capacity of 200 candidates.

[0072] Fitness for 200+ objectives Perform non-dominated ranking and select several non-dominated multi-objective fitnesss. and the corresponding cable force Enter the Pareto optimal force candidate set.

[0073] Step S4-3, Non-dominated cable force multi-objective fitness Normalization. This example uses the min-max normalization method.

[0074] Step S4-4: Define the ideal fitness of cable force :

[0075] The ideal fitness is composed of the best single-objective fitness normalized from all non-dominated individuals. For the minimum optimization problem, (0,0,...,0).

[0076] Step S4-5: Define the overall optimal cable force and the partial optimal cable force:

[0077] Calculate the fitness non-ideal bias of cable forces in the Pareto optimal cable force candidate set. , Pick and Euclidean distance; according to fitness non-ideal deviation Sort by fitness from smallest to largest, select the best overall fitness and the least favorable fitness; consider the deviation from ideal fitness. For equal cable forces, randomly select one as the optimal or slightly optimal cable force; select the cable force with the smallest deviation in fitness as the optimal cable force. The cable force with the largest deviation in fitness is the biased cable force. .

[0078] Step S4-6, Cable Iteration:

[0079] Generally, the cable force is iteratively optimized towards both the overall optimal cable force and the partially optimal cable force. The value of the general cable force after the (k+1)th iteration optimization is calculated according to the following formula, which sets the direction factor and the intensity factor.

[0080]

[0081] In the above formula, Let i be the force after the k-th iteration optimization. Let i be the force after the (k+1)th iteration. For comprehensive and superior cable force, For a slightly preferred force; and This is called the direction factor, which is randomly selected as 1 or -1 to adjust the direction of iterative optimization. and It is called the intensity factor, which is a uniformly random number within [0,2] and is used to adjust the magnitude of the iterative optimization. By combining the direction factor and the intensity factor in two directions, multi-directional iterative optimization can be achieved.

[0082] The cable force is iterated according to formula (1) of this invention. and Randomly select 1 or -1. and Take uniformly random numbers within [0,2] to obtain the cable force after iteration. .

[0083] Step S4-7, Cable tension selection:

[0084] according to Calculate the fitness of the cable force for multiple targets. If the cable force is improved after iteration... Dominate ,but Pick ,otherwise Maintain the status quo .

[0085] Step S4-8: Update the Pareto optimal skeletal candidate set:

[0086] The Pareto optimal force candidate set is updated according to the non-dominated principle. Non-dominated forces are selected using a hypercube grid and roulette wheel selection strategy to ensure the diversity of the Pareto optimal force candidate set. When applying the hypercube grid strategy, the number of grids in each dimension is set to 20. Forces are filtered according to the crowding strategy to ensure the capacity of the Pareto optimal force candidate set.

[0087] Step S4-9: Repeat steps S4-3 to S4-8 for iteration.

[0088] Step S4-10: Stop iteration after reaching the required number of iterations or meeting the accuracy requirements. Output the final Pareto optimal cable force set and select the best cable force as the final bridge cable force. The maximum number of iterations is 100. The final bridge cable force in this example is: =[10514.8;10514.6;10514.8;10514.8;10335.6;10335.0;9817.6;9388.4;8948.4;8644.0;8061.6;7710.8;6527.2;6527.2;6654.4;7127.9;7168.6;7312.5;7388.8;7706.0;8961.5;9684.6;11435.2;11435.2;11864.9;11958.0;12371.5;12427.6].

[0089] In the description of this specification, the terms "one embodiment," "some embodiments," "specific embodiment," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the present invention. In this specification, the 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.

[0090] The above are merely preferred embodiments of the present invention and are not intended to limit the present 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.

Claims

1. A multi-objective intelligent optimization method for cable forces in a cable-stayed bridge, characterized in that... Specifically, it includes the following steps: Step S1: Establish a finite element model of the cable-stayed bridge and perform preliminary optimization of the cable forces. The minimum bending energy method is used for preliminary optimization of the cable forces, and the cable forces are initially uniformized according to the principle of "longer cables have larger cable forces and shorter cables have smaller cable forces". Step S2: Construct a small-sample surrogate model of the cable-stayed bridge to characterize the mapping relationship between cable forces and structural responses including bending moments and displacements; Step S3: Establish a multi-objective optimization model for the cable forces of the cable-stayed bridge to define the functional relationship between the optimization objectives, including bending strain energy, resultant displacement, and structural response. Step S4: The cable force is optimized using a multi-objective intelligent optimization method for cable-stayed bridge cable forces based on a dual-optimization strategy. This yields the Pareto optimal cable force set, and a comprehensive optimal cable force is selected as the final bridge cable force. The specific optimization method of the multi-objective intelligent optimization method for cable forces in cable-stayed bridges based on a dual-optimization strategy is as follows: Step S4-1: Initialize general cable forces and multi-objective fitness : General cable tension The values ​​are taken within the range of 0.9 to 1.1 times the initial uniform cable force; the general cable force is calculated using a small-sample surrogate model for cable-stayed bridges. Based on the corresponding structural response, and using the multi-objective optimization model of cable-stayed bridge cable forces, the general cable forces are calculated. Multi-objective fitness corresponding to structural response ; Step S4-2: Initialize the Pareto optimal cable force candidate set: Non-dominated forces are sorted according to multi-objective fitness, and non-dominated forces are added to the Pareto optimal force candidate set. Step S4-3: Normalize the multi-objective fitness of non-dominated cable forces; Step S4-4: Define the ideal fitness of cable force : The ideal fitness is composed of the best single-objective fitness normalized by all non-dominated forces. ; Step S4-5: Define the overall optimal cable force and the partial optimal cable force: Calculate the fitness non-ideal bias of cable forces in the Pareto optimal cable force candidate set. , Pick and Euclidean distance; according to fitness non-ideal deviation Sort by fitness from smallest to largest, select the best overall fitness and the least favorable fitness; consider the deviation from ideal fitness. For equal cable forces, one is randomly selected as the optimal cable force or the slightly optimal cable force. Step S4-6, Cable Iteration: Generally, the cable force is iteratively optimized towards both the overall optimal cable force and the partially optimal cable force. The value of the general cable force after the (k+1)th iteration optimization is calculated according to the following formula, which sets the direction factor and the intensity factor. ， In the above formula, Let i be the force after the k-th iteration optimization. Let i be the force after the (k+1)th iteration. For comprehensive and superior cable force, For a slightly preferred force; and This is called the direction factor, which is randomly selected as 1 or -1 to adjust the direction of iterative optimization. and It is called the intensity factor, which is a uniformly random number within [0,2] and is used to adjust the magnitude of the iterative optimization. By combining the direction factor and the intensity factor in two directions, multi-directional iterative optimization can be achieved. Step S4-7, Cable tension selection: according to Calculate the fitness of cable forces for multiple targets, if Dominate ,but Pick ,otherwise Maintain the status quo ; Step S4-8: Update the Pareto optimal skeletal candidate set: The non-dominated sorting is performed again, and the non-dominated forces are selected to update the Pareto optimal force candidate set. To maintain the diversity of solutions, the hypercube grid and roulette wheel selection strategy are used during the update. To ensure capacity, the crowding removal strategy is used to maintain the upper limit of the number of forces in the Pareto optimal force candidate set. Step S4-9: Repeat steps S4-3 to S4-8 for iteration; Step S4-10: Stop iterating after reaching the required number of iterations or meeting the accuracy requirements, output the final Pareto optimal cable force set, and select a comprehensive optimal cable force as the cable force for the completed bridge.

2. The multi-objective intelligent optimization method for cable forces in a cable-stayed bridge as described in claim 1, characterized in that... The cable-stayed bridge small-sample surrogate model adopts the support vector machine regression RBF-SVR surrogate model based on radial basis function kernel function. The model hyperparameters are tuned using grid search and leave-one-out cross-validation suitable for small samples.

3. The multi-objective intelligent optimization method for cable forces in a cable-stayed bridge as described in claim 2, characterized in that... The specific construction process of the small sample surrogate model for cable-stayed bridges is as follows: Step S2-1: Use the finite element model of a cable-stayed bridge to collect a training dataset of cable force-structure response; Step S2-2: Data preparation; Load cable force-structure response training data, verify data validity, and standardize training data. Step S2-3: Construct the proxy model and define the leave-one-out evaluation function; Step S2-4: Optimize the hyperparameters of the surrogate model; use grid search and leave-one-out cross-validation to optimize and select the optimal penalty coefficient C and kernel width γ for each output model.

4. The multi-objective intelligent optimization method for cable forces in a cable-stayed bridge as described in claim 1, characterized in that... The multi-objective intelligent optimization method for cable-stayed bridge cable forces based on the dual-optimization strategy involves iteratively optimizing a general set of cable forces and selecting non-dominated cable forces from it to enter the Pareto optimal cable force candidate set. The iterative optimization mechanism is guided by the overall optimal cable force and the partial optimal cable force, leading the general cable force to approach the two types of excellent cable forces, and gradually improving the performance of the cable force set.

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