Swivel bridge spherical hinge structure optimization design method based on Bayesian algorithm

Abstract

The invention discloses a Bayesian algorithm-based swivel bridge spherical hinge structure optimization design method, which is characterized in that a parameterized model of a swivel bridge spherical hinge structure is constructed, and a finite element simulation technology and a Bayesian optimization algorithm are combined, so that multi-target global optimization design is realized. The method specifically comprises the following steps: establishing a refined finite element model of the swivel bridge spherical hinge; defining input design variables (spherical radius, supporting radius, pin roll radius and the like) and output optimization targets (maximum contact stress, horizontal and vertical friction moment); adopting Latin hypercube sampling (LHS) to generate a plurality of groups of initial parameter combinations; dynamically selecting a high-value parameter combination through a Bayesian optimization framework to carry out finite element simulation; training a Gaussian process agent model and carrying out iterative optimization; and quantizing the parameter sensitivity and outputting a Pareto optimal solution set. According to the method, the simulation frequency can be remarkably reduced, the design efficiency is effectively improved, and the problem that traditional experience design is prone to falling into local optimum is solved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of bridge structure optimization design, and particularly relates to a swivel bridge spherical hinge structure optimization design method based on a Bayesian algorithm, which is suitable for global optimization of the geometric parameters and material parameters of a swivel bridge spherical hinge under complex stress conditions. BACKGROUND

[0002] The swivel bridge spherical hinge is a core load-bearing and rotating component in swivel construction, and its stress characteristics are influenced by multiple factors such as geometric parameters (such as spherical radius and supporting radius), material characteristics (elastic modulus and friction coefficient) and external load (swivel weight), and present highly nonlinear characteristics. The traditional design method relies on empirical formula or limited number of orthogonal tests, and it is difficult to efficiently balance the multi-objective conflict (such as minimizing stress and friction torque), and it is easy to fall into local optimization.

[0003] In the prior art, the method of combining finite element simulation with a meta-model (such as Kriging, SVR, etc.) can reduce the calculation cost, but still requires a large number of initial samples, and lacks dynamic optimization capability. The Bayesian optimization algorithm can realize global optimization in a small number of simulation times by fusing a probabilistic proxy model and an active learning strategy, and is particularly suitable for high-dimensional, multi-objective and high-cost engineering optimization problems.

[0004] Using the Bayesian algorithm to analyze the structural rationality of the swivel bridge spherical hinge is an efficient and innovative technical path, which realizes global optimization design of the spherical hinge under the coupling action of multiple parameters by constructing a Gaussian process proxy model and a dynamic acquisition function in combination with finite element simulation data. The method uses the active learning strategy of Bayesian optimization to accurately explore the design space in a small number of simulation times, and reveals the complex nonlinear relationship between the geometric parameters (such as spherical radius and supporting radius) and the mechanical objectives (maximum contact stress and friction torque). The deep integration of Bayesian algorithm and finite element technology provides theoretical support for the multi-objective trade-off and robust design of the spherical hinge structure, is a frontier exploration in the field of intelligent design of bridge engineering, and has significant engineering application value. SUMMARY

[0005] In order to overcome the problems of low efficiency and lack of globality in the traditional swivel bridge spherical hinge design method in the related art, the application provides a swivel bridge spherical hinge structure optimization design method based on a Bayesian algorithm.

[0006] The technical scheme adopted by the application to solve the above problems is as follows: a swivel bridge spherical hinge structure optimization design method based on a Bayesian algorithm, comprising the following steps:

[0007] S1: establishing a three-dimensional nonlinear contact model of the swivel bridge spherical hinge, and performing grid encryption processing on the spherical hinge contact surface;

[0008] S2: Construct an index system to characterize the force characteristics of the spherical hinge contact surface of the rotating body, mainly including input indicators (factors affecting the force characteristics) and output indicators (indicators representing the force characteristics);

[0009] S3: Initial sample generation and finite element simulation. Latin hypercube sampling (LHS) is used to generate multiple sets of initial parameter combinations, and the finite element model established in step S1 is used for simulation calculation to obtain target values. The data is normalized to obtain a data set;

[0010] S4: Construct a Bayesian optimization framework, use Gaussian process (GP) modeling, combine expected improvement (EI) and confidence boundary (UCB), based on the Pareto frontier, use NSGA-II algorithm to screen the non-dominated solution set, and use the improved hyper volume (EHVI) to select the optimal solution set;

[0011] S5: Iterative optimization and convergence determination. In each iteration, the top-5 candidate points are selected for simulation, and the GP model is updated;

[0012] S6: Robustness and parameter sensitivity analysis. Simulate the manufacturing tolerance by Monte Carlo sampling to evaluate the stability of the design solution, and perform global sensitivity analysis on the force characteristics of the spherical hinge contact surface of the rotating bridge based on the Sobol index method.

[0013] Further, in step S1, a numerical model of the rotating structure is established using finite element software, and the upper and lower spherical hinges and their contact surfaces are finely processed to improve the accuracy of the model calculation.

[0014] Further, in step S2, the input indicators (factors affecting the force characteristics) representing the force characteristics of the spherical hinge contact surface of the rotating body include indicators representing the geometric characteristics of the spherical hinge, indicators representing the material characteristics of the spherical hinge, and the weight of the rotating body (X7) representing the external load characteristics. The indicators representing the geometric characteristics of the spherical hinge include the spherical hinge curvature radius (X1), the spherical hinge support radius (X2), and the spherical hinge thickness (X3). The indicators representing the material characteristics of the spherical hinge include the spherical hinge elastic modulus (X4), the spherical hinge Poisson's ratio (X5), and the spherical hinge friction coefficient (X6).

[0015] Further, in step 2, the output indicators (indicators representing the force characteristics) representing the force characteristics of the spherical hinge contact surface of the rotating body include three indicators: maximum contact stress (σ max ), horizontal friction torque (M H ), and vertical friction torque (M V );

[0016] In step 2, to construct an index system to characterize the force characteristics of the spherical hinge contact surface of the rotating body, first determine the upper and lower limits of each input indicator, i.e., determine X i ∈[X imin ,Ximax ](i=1,2,…,7),where X imin and X imax represent the minimum and maximum values of the index X i , respectively.

[0017] Further, in step 3, the working conditions for numerical simulation are designed, three indexes X1, X2, X3 are used to represent the geometric characteristics of the spherical hinge, and four indexes X4, X5, X6, X7 are used to represent the factors affecting the stress characteristics. The LHS method is used to generate multiple sets of initial samples, ensuring that each parameter is uniformly distributed within its range and the sample points are not overlapped.

[0018] Further, in step 3, the results under each working condition are obtained by analyzing and calculating, and the contact stress distribution function σ(r) is obtained. The maximum contact stress σ max , the horizontal frictional torque M H , and the vertical frictional torque M V are calculated as follows:

[0019]

[0020]

[0021] where a is the maximum support radius of the contact surface, r is the bearing radius of the spherical hinge, R is the curvature radius of the spherical hinge, μ is the friction coefficient of the contact surface, and θ is the angle between the line passing through any point on the spherical surface and the center line of the spherical hinge.

[0022] In step 3, the data results of each working condition are summarized to further eliminate the scale difference of each variable data in the index system, increase the generalization ability of the meta-model, and speed up the convergence speed of the model. The data is normalized, including the normalization of X1-X7 input indexes and the standardization of three output indexes (maximum contact stress σ max , horizontal frictional torque M H , and vertical frictional torque M V ), which is the data set for constructing the meta-model.

[0023] Further, in step 4, the Gaussian (GP) model is trained using the mixed kernel function and the maximum likelihood estimation (MLE). The general form of the mixed kernel function is: k(x,x′)=RBF+Matern52

[0024] The general form of the maximum likelihood estimation (MLE) is: f(x)~GP(m(x),k(x,x′))

[0025] where m(x) is the mean function and k(x,x′) is the covariance function.

[0026] The hybrid acquisition function combining expected improvement (EI) and upper confidence bound (UCB) is adopted to dynamically adjust the exploration and exploitation weights, and the expected hypervolume improvement (EHVI) is used to calculate the contribution of candidate points to the Pareto front hypervolume.

[0027] The general form of the hybrid acquisition function is: α(x)=λ·EI(x)+(1-λ)·UCB(x)

[0028] where λ exponentially decays with the iteration number (e.g., λ=e -0.1t , and the exploration is emphasized in the early stage (λ≈1) and the exploitation is emphasized in the later stage (λ≈0).

[0029] Further, in step 4, the NSGA-II algorithm is used to screen the non-dominated solution set, the reference point in the objective space is defined by using the hypervolume calculation, the hypervolume occupied by the solution set is calculated to quantify the optimization progress, and a variance penalty term is introduced into the objective function to suppress the design sensitive to noise.

[0030] The general form of the penalty term is: F robust (x)=F(x)+γ·Var(F∣x)

[0031] where γ is the penalty coefficient.

[0032] Further, in step 5, the Top-5 parameter combinations with the highest acquisition function values are selected in each iteration, and finite element simulation is submitted; the new data is added to the training set, the GP model is retrained, and the hyperparameters are updated.

[0033] In step 5, for each candidate point, an input file is dynamically generated, and the parameters are adjusted. Multiple simulation tasks are submitted simultaneously using the HPC cluster to shorten the single iteration time.

[0034] In step 5, the maximum contact stress σ max , the horizontal frictional torque M H and the vertical frictional torque M V are extracted from the simulation output file, and the input data is normalized and the output data is standardized.

[0035] In step 5, based on the new data set, the kernel function parameters are updated by maximum likelihood estimation (MLE); the determination coefficient R 2 of the model on the validation set is calculated to ensure that R 2 >0.9, otherwise the kernel function combination or sampling strategy is adjusted.

[0036] In step 5, the relative change of the weighted sum of the objective function of the current round and the previous three rounds is calculated:

[0037] The general form of the relative change is:

[0038] If ΔF < 1% for 3 consecutive rounds, the convergence is determined; if the maximum iteration number is reached, the current optimal solution set is output.

[0039] Further, in step 6, random perturbation is applied to the optimized key parameters to simulate the actual manufacturing tolerance. n groups of perturbed samples are generated for each optimal solution in the optimal solution set to generate parameter combinations;

[0040] The general form of simulating the actual manufacturing tolerance is: X i ′ = X i · (1 + δ)

[0041] Where δ is a uniformly distributed random perturbation;

[0042] In step 6, batch simulation is performed on the perturbed samples to extract the maximum contact stress σ max , horizontal frictional torque M H and vertical frictional torque M V ; the perturbed parameters and target values are stored in the database;

[0043] In step 6, the standard deviation of the target value of each optimal solution under perturbation is calculated, and the optimal solution set is filtered

[0044] The general form of the target value standard deviation is:

[0045] Where N is the number of perturbed samples, is the target mean value;

[0046] In step 6, Sobol model is used for global sensitivity analysis of the contact surface stress characteristics; the evaluation indexes of Sobol model include main effect sensitivity index S i and total effect sensitivity index ST i :

[0047]

[0048] Where Y is the output variable; X ～i is a vector composed of all other input parameters except the i-th parameter; E X～i (Y|X i ) is the conditional expectation value of Y under the change of other parameters X i when the parameter X ～i is fixed; is the conditional expectation value of Y caused only by the change of X ～i when other parameters X i are fixed; Var(Y), is the variance of each order.

[0049] With the technical scheme, the force characteristics of the ball hinge structure of the rotating bridge are globally optimized and robustly designed by combining the Bayesian optimization algorithm and the finite element simulation technology. The nonlinear mapping relationship between the geometric parameters and the mechanical targets is accurately fitted in a small number of simulation times by the efficient sampling strategy of the Bayesian algorithm and the Gaussian process proxy model, and the calculation cost is significantly reduced. The stability of the design solution is evaluated by simulating the manufacturing tolerance by Monte Carlo sampling, and the global sensitivity of the contact surface force characteristics is analyzed by using the Sobol model method. The force characteristics of the contact surface of the rotating ball hinge under the joint action of multiple factors are explored by sensitivity analysis, and the influence degree of different parameters on the force characteristics of the ball hinge structure is analyzed, and then the key influencing factors of the force characteristics of the ball hinge are determined, which has important reference significance for the design of the rotating ball hinge structure and the stability analysis of the rotating structure. Through global sensitivity analysis and Monte Carlo perturbation verification, the sensitivity of key parameters such as spherical radius and friction coefficient on contact stress and friction torque can be determined, thereby guiding the manufacturing tolerance control and process optimization. The method provides data-driven decision support for high-precision design of the rotating ball hinge of the rotating bridge, and has important engineering significance for improving the safety and reliability of the rotating bridge construction. BRIEF DESCRIPTION OF DRAWINGS

[0050] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0051] Figure 1 A specific flowchart of the ball hinge structure optimization design method based on the Bayesian algorithm provided by the present application is provided.

[0052] Figure 2 A finite element model diagram of the bridge rotating structure and the ball hinge provided by the embodiment of the present application is provided.

[0053] Figure 3 The ball hinge contact surface stress distribution fitting condition under a certain working condition provided by the embodiment of the present application is provided.

[0054] Figure 4 The frequency distribution characteristics of the input index provided by the embodiment of the present application are provided.

[0055] Figure 5 The frequency distribution characteristics of the output index provided by the embodiment of the present application are provided.

[0056] Figure 6 The step 4 key part flowchart provided by the embodiment of the present application is provided.

[0057] Figure 7 Sobol model index sensitivity analysis results provided for embodiments of the application. DETAILED DESCRIPTION

[0058] To make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the protection scope of the present application.

[0059] In the embodiments of the present application, the present application provides a ball hinge structure optimization design method for a swivel bridge based on a Bayesian algorithm, as shown in Figure 1 The method specifically includes the following steps:

[0060] S1: A three-dimensional nonlinear contact model of the swivel bridge ball hinge is established, and the grid encryption processing is performed on the ball hinge contact surface.

[0061] S2: An index system representing the force characteristics of the swivel ball hinge contact surface is constructed, mainly including input indexes (factors affecting the force characteristics) and output indexes (indexes representing the force characteristics).

[0062] S3: Initial sample generation and finite element simulation, a plurality of initial parameter combinations are generated by using Latin hypercube sampling (LHS), and the finite element model established in step 1 is used for simulation calculation in parallel to obtain target values, and the data is normalized to obtain a data set.

[0063] S4: A Bayesian optimization framework is constructed, a Gaussian process (GP) model is built, EI and UCB are fused, based on the Pareto front, the NSGA-II algorithm is used to screen the non-dominated solution set, and the EHVI is used to select the optimal solution set.

[0064] S5: Iterative optimization and convergence determination, Top-5 candidate points are selected for simulation in each iteration, and the GP model is updated.

[0065] S6: Robustness and parameter sensitivity analysis, manufacturing tolerances are simulated by Monte Carlo sampling, the stability of the design solution is evaluated, and the global sensitivity of the contact surface force characteristics is analyzed based on Sobol index.

[0066] The specific working principle of the present application will be described in detail below in combination with embodiments:

[0067] For S1, the finite element software ABAQUS is used to establish a numerical model of the bridge rotation structure, and the upper and lower spherical hinges and their contact surfaces are finely processed to improve the accuracy of the model calculation, as shown in Figure 2

[0068] For S2, the curvature radius of the spherical hinge (X1), the spherical hinge support radius (X2), the spherical hinge thickness (X3), and the like are selected as three indexes representing the geometric characteristics of the spherical hinge, and the spherical hinge elastic modulus (X4), the spherical hinge Poisson's ratio (X5), the spherical hinge friction coefficient (X6), and the like are selected as three indexes representing the material characteristics of the spherical hinge, and the rotation weight (X7) representing the external load characteristics and the like are selected as seven indexes (factors affecting the stress characteristics) as input indexes representing the stress characteristics of the contact surface of the rotation spherical hinge.

[0069] For S2, three indexes (indexes representing stress characteristics) such as the maximum contact stress (S1), the horizontal frictional moment (S2), and the vertical frictional moment (S3) are selected as output indexes representing the stress characteristics of the contact surface of the rotation spherical hinge.

[0070] For S2, the index system is constructed. First, the upper and lower limit ranges of each input index are determined, that is, it is determined that:

[0071] X i ∈[X imin ,X imax ](i=1,2,…,7)

[0072] Wherein, X imin and X imax represent the minimum and maximum values of the index X i .

[0073] Further, the input index system of the stress characteristics of the contact surface of the rotation spherical hinge constructed in this embodiment is shown in Table 1.

[0074] Table 1. Input index system

[0075]

[0076] Note: U represents uniform distribution.

[0077] For S3, the LHS method is used to generate 50 groups of initial samples to ensure that each parameter is uniformly distributed within its range and the sample points are not overlapped. As shown in Table 2

[0078] Table 2. LHS initial sample

[0079]

[0080]

[0081] ​Further, the contact stress distribution value along the spherical hinge support radius direction from the spherical hinge center to the contact edge is extracted, and then the stress distribution function σ(r) is obtained by fitting, as shown in Figure 3 for the stress distribution fitting under certain working conditions.

[0082] Further, the maximum contact stress σ max :

[0083]

[0084] Further, the horizontal frictional resistance moment M H :

[0085]

[0086] Further, the vertical frictional resistance moment M V :

[0087]

[0088] wherein a is the maximum support radius of the contact surface; r is the spherical hinge plane support radius; R is the spherical hinge curvature radius; μ is the contact surface friction coefficient; and θ is the angle between the line passing through any point on the spherical surface and the spherical hinge center line and the spherical hinge center line.

[0089] For S3, the data results of each working condition are summarized to further eliminate the scale difference of each variable data in the index system, increase the generalization ability of the meta-model, and speed up the convergence speed of the model. The data is normalized.

[0090] Further, the seven input indicators X1-X7 are normalized, as shown in Figure 4 ; the three output indicators S1-S3 are standardized, as shown in Figure 5 The data obtained by the above processing is summarized to obtain the data set for constructing the meta-model.

[0091] For S4, the Gaussian (GP) model is trained based on the data set in S3 using the mixed kernel function and maximum likelihood estimation (MLE).

[0092] Further, the general form of the mixed kernel function is: k(x,x') = RBF + Matern52

[0093] Further, the general form of the maximum likelihood estimation (MLE) is: f(x) ~ GP(m(x), k(x,x'))

[0094] wherein m(x) is the mean function and k(x,x') is the covariance function.

[0095] For S4, a hybrid acquisition function combining expected improvement (EI) and upper confidence bound (UCB) is adopted to dynamically adjust the exploration-exploitation weight. The expected hypervolume improvement (EHVI) is used to calculate the contribution of candidate points to the Pareto front. The process is as follows Figure 6 .

[0096] Further, the general form of the hybrid acquisition function is: α(x) = λ·EI(x) + (1-λ)·UCB(x)

[0097] where λ decays exponentially with the iteration number (e.g., λ = e -0.1t , and focuses on exploration in the early stage (λ ≈ 1) and exploitation in the later stage (λ ≈ 0).

[0098] For S4, the non-dominated solution set is filtered by the NSGA-II algorithm, and the reference point in the objective space is defined by the hypervolume calculation. The hypervolume occupied by the solution set is calculated to quantify the optimization progress. A variance penalty term is introduced in the objective function to suppress designs sensitive to noise.

[0099] Further, the general form of the variance penalty term is: robust F(x) = F(x) + γ·Var(F | x)

[0100] where γ is the penalty coefficient.

[0101] For S5, the Top-5 parameter combinations with the highest acquisition function values are selected for each iteration, and finite element simulations are submitted. The new data is added to the training set, and the GP model is retrained to update the hyperparameters.

[0102] Further, for each candidate point, an input file is dynamically generated to adjust the parameters. Multiple simulation tasks are submitted simultaneously using the HPC cluster to shorten the single iteration time.

[0103] Further, the maximum contact stress S1, friction torque S2 and S3 are extracted from the simulation output file, and the input data is normalized and the output data is standardized.

[0104] Further, based on the new data set, the kernel function parameters are updated by maximum likelihood estimation (MLE). The determination coefficient R 2 of the model on the validation set is calculated to ensure R 2 > 0.9, otherwise adjust the kernel function combination or sampling strategy.

[0105] For S5, the relative change of the weighted sum of the objective function of the current round and the previous three rounds is calculated:

[0106] Further, the general form of the relative change is:

[0107] If ΔF < 1% for three consecutive iterations, the system is considered to have converged. If the maximum number of iterations is reached, the system is forcibly terminated and the current optimal solution set is output.

[0108] For S6, random perturbations are applied to the optimized key parameters to simulate actual manufacturing tolerances.

[0109] Furthermore, the general form of simulating actual manufacturing tolerances is: X i ′=X i ·(1+δ)

[0110] Wherein, δ is a uniformly distributed random perturbation (±0.5%), and 100 sets of perturbation samples are generated for each optimal solution, resulting in a total of 50×100=5000 sets of parameter combinations.

[0111] Furthermore, batch simulations are performed on the perturbed samples to extract the target values ​​S1, S2, and S3. The perturbed parameters and target values ​​are then stored in a database.

[0112] For S6, calculate the standard deviation of the target value under the perturbation for each optimal solution, and then filter.

[0113] Furthermore, the general form of the target value standard deviation is:

[0114] Where N = 100 is the number of perturbation samples. The target mean.

[0115] For S6, the Sobol model was used to perform a global sensitivity analysis of the force characteristics of the contact surface. The evaluation metrics for the Sobol model include the main effect sensitivity index S. i And the overall effect sensitivity index ST i .

[0116] Furthermore, the main effect sensitivity index S i The general form is:

[0117] Furthermore, the total effect sensitivity index ST i The general form is:

[0118] Where Y is the output variable; X ～i E is a vector consisting of all input parameters except the i-th parameter; X～i (Y|X i ) is for a fixed parameter X i At that time, other parameters X ～i The conditional expected value of Y under the change; To keep other parameters X fixed ～i At that time, only X ithe conditional expectation of Y due to the change; Var(Y), for each order variance.

[0119] Further, the sensitivity analysis results of Sobol model for each output variable are shown in Table 3. Figure 7 .

[0120] Further, the global sensitivity analysis results for each output index are shown in Table 4.

[0121] Table 4. Global sensitivity analysis results

[0122]

[0123] Further, the sensitivity analysis results for the output index maximum contact stress (S1) are shown in Table 5.

[0124] Table 5. Sensitivity analysis results of maximum contact stress (S1)

[0125]

[0126] Further, the sensitivity analysis results for the output index horizontal frictional resistance moment (S2) are shown in Table 6.

[0127] Table 5. Sensitivity analysis results of horizontal frictional resistance moment (S2)

[0128]

[0129] Further, the sensitivity analysis results for the output index vertical frictional resistance moment (S3) are shown in Table 6.

[0130] Table 6. Sensitivity analysis results of vertical frictional resistance moment (S3)

[0131]

[0132] Further, it is considered that in the structure of the swivel spherical hinge, the curvature radius X1 and the friction coefficient X6 have the most significant influence on the target (ST i >0.6), and the manufacturing tolerance needs to be optimized and controlled in priority.

[0133] Further, the swivel weight X7 has a high contribution to the vertical frictional resistance moment S3 (ST i =0.35), which needs to be focused on in the design of construction load.

[0134] Further, the interaction contribution of X1 and X6 (0.15-0.16) is significant, indicating that the coupling effect of spherical geometry and friction characteristics cannot be ignored. The interaction of X7 and other parameters (such as ST i -Si = 0.13), indicating that the uncertainty of geometric parameters will be amplified by the weight change of the rotating body.

[0135] In the above embodiment, the present application explores the mechanical response characteristics of the spherical hinge of the rotating bridge under the coupling effect of multiple parameters through the Bayesian optimization algorithm and global sensitivity analysis, and reveals the sensitivity law of key parameters such as curvature radius and friction coefficient on the contact stress and friction torque. Combined with the Monte Carlo perturbation verification and the Pareto frontier trade-off, the parameter tolerance control requirements of the high robustness design solution are determined, which provides a data-driven theoretical basis for the optimization of the spherical hinge geometry, material selection and manufacturing process improvement. The method breaks through the limitations of traditional empirical design, significantly improves the safety and economy of the rotating bridge construction, and has important popularization value for the intelligent design and performance prediction of complex bridge structures.

[0136] Although the present application has been disclosed as above with the preferred embodiments, this is only part of the embodiments of the present application, and cannot be used to limit the present application. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present application by using the disclosed methods and technical contents without departing from the spirit and scope of the present application. Any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application, which does not deviate from the technical solutions of the present application, belongs to the protection scope of the technical solutions of the present application.

Claims

1. A method for optimizing the design of a spherical hinge structure for a rotating bridge based on Bayesian algorithm, characterized in that: Includes the following steps: S1: Establish a three-dimensional nonlinear contact model of the ball joint of the rotating bridge, and refine the mesh of the ball joint contact surface; S2: Construct an index system to characterize the force characteristics of the contact surface of the rotating ball joint, mainly including input indexes (factors affecting force characteristics) and output indexes (indicators characterizing force characteristics); S3: Initial sample generation and finite element simulation. Multiple sets of initial parameter combinations are generated using Latin hypercube sampling (LHS). The finite element model established in step S1 is used in parallel to perform simulation calculations to obtain target values. The data is then normalized to obtain a dataset. S4: Construct a Bayesian optimization framework, use Gaussian process (GP) modeling, integrate expected improvement (EI) and confidence boundary (UCB), based on Pareto front, use NSGA-II algorithm to screen non-dominated solution set, and use hypervolume improvement (EHVI) to select optimal solution set; S5: Iterative optimization and convergence determination. In each iteration, the Top-5 candidate points are selected for simulation, and the GP model is updated. S6: Robustness and parameter sensitivity analysis: Manufacturing tolerances are simulated using Monte Carlo sampling to evaluate the stability of the design solution, and global sensitivity analysis of the force characteristics of the ball joint contact surface of the swivel bridge is performed based on the Sobol exponent method.

2. The method for optimizing the design of a spherical hinge structure of a rotating bridge based on Bayesian algorithm according to claim 1, characterized in that: In step S1, a numerical model of the rotating structure is established using finite element software, and the upper and lower ball joints and their contact surfaces are refined to improve the accuracy of the model calculation.

3. The method for optimizing the design of a spherical hinge structure of a rotating bridge based on Bayesian algorithm according to claim 1, characterized in that: In step S2, the input indicators (factors affecting the force characteristics) characterizing the contact surface of the rotating ball joint include indicators characterizing the geometric characteristics of the ball joint, indicators characterizing the material characteristics of the ball joint, and the rotating weight (X7) characterizing the external load characteristics. The indicators characterizing the geometric characteristics of the ball joint include the ball joint radius of curvature (X1), the ball joint support radius (X2), and the ball joint thickness (X3). The indicators characterizing the material characteristics of the ball joint include the ball joint elastic modulus (X4), the ball joint Poisson's ratio (X5), and the ball joint friction coefficient (X6).

4. The method for optimizing the design of a spherical hinge structure of a rotating bridge based on Bayesian algorithm according to claim 1, characterized in that: In step 2, the output index (indicator characterizing the force characteristics) representing the contact surface of the rotating ball joint includes the maximum contact stress (σ). max ), horizontal frictional torque (M) H ) and vertical frictional torque (M V Three indicators; In step 2, constructing an index system characterizing the force characteristics of the contact surface of the rotating ball joint first requires determining the upper and lower limits of each input index, i.e., determining X. i ∈[X imin ,X imax (i = 1, 2, ..., 7), where X imin and X imax They represent the indicators X respectively i The minimum and maximum values.

5. The method for optimizing the design of a spherical joint structure of a rotating bridge based on Bayesian algorithm according to claim 4, characterized in that: In step 3, the working conditions for numerical simulation are designed. X1, X2, and X3 are three indicators that characterize the geometric characteristics of the ball joint, and X4, X5, X6, and X7 are four indicators that characterize the factors affecting the force characteristics. The LHS method is used to generate multiple sets of initial samples to ensure that each parameter is evenly distributed within its range and that the sample points do not overlap.

6. The method for optimizing the design of a spherical joint structure of a rotating bridge based on Bayesian algorithm according to claim 5, characterized in that: In step 3, the stress distribution function σ(r) of the contact surface is obtained by analyzing and calculating the results under various working conditions, and the maximum contact stress σ is calculated as the output index. max Horizontal frictional torque M H Vertical frictional torque M V They are respectively: Where a is the maximum support radius of the contact surface; r is the support radius of the ball joint plane; R is the radius of curvature of the ball joint; μ is the friction coefficient of the contact surface; θ is the angle between the line connecting any point on the sphere and the center of the sphere and the center line of the ball joint; In step 3, the data results for each working condition are summarized. To further eliminate scale differences in the data of each variable in the indicator system, increase the generalization ability of the meta-model, and accelerate the convergence speed of the model, the data is standardized, including normalizing the input indicators X1 to X77 and the three output indicators (maximum contact stress σ). max Horizontal frictional torque M H Vertical frictional torque M V The dataset is then standardized to obtain the dataset for constructing the meta-model.

7. The method for optimizing the design of a spherical hinge structure of a rotating bridge based on Bayesian algorithm according to claim 1, characterized in that: In step 4, a Gaussian (GP) model is trained using a mixture kernel function and maximum likelihood estimation (MLE). The general form of the hybrid kernel function is: k(x,x′)=RBF+Matern52 The general form of maximum likelihood estimation (MLE) is: f(x) ~ GP(m(x), k(x, x′)). Where m(x) is the mean function and k(x,x′) is the covariance function; A hybrid acquisition function combining expected improvement (EI) and confidence boundary (UCB) is adopted to dynamically adjust the exploration and development weights. The contribution of candidate points to the Pareto front hypervolume is calculated through hypervolume improvement (EHVI). The general form of the hybrid acquisition function is: α(x)=λ·EI(x)+(1-λ)·UCB(x) Wherein, λ decays exponentially with the number of iterations (e.g., λ = e^(-λ / t)). -0.1t The initial focus is on exploration (λ≈1), and the later focus is on development (λ≈0).

8. The method for optimizing the design of a spherical hinge structure of a rotating bridge based on Bayesian algorithm according to claim 7, characterized in that: In step 4, the NSGA-II algorithm is used to screen the non-dominated solution set, the hypervolume calculation is used to define the reference point in the target space, the hypervolume occupied by the solution set is calculated, the optimization progress is quantified, and a variance penalty term is introduced into the objective function to suppress noise-sensitive designs. The general form of a penalty item is: F robust (x)=F(x)+γ·Var(F∣x) Where γ is the penalty coefficient.

9. The method for optimizing the design of a spherical joint structure of a rotating bridge based on Bayesian algorithm according to claim 1, characterized in that: In step 5, the top-5 parameter combinations with the highest acquisition function values ​​are selected in each iteration and submitted for finite element simulation. Add new data to the training set, retrain the GP model, and update the hyperparameters; In step 5, an input file is dynamically generated and parameters are adjusted for each candidate point. Multiple simulation tasks are submitted simultaneously using an HPC cluster, shortening the iteration time per round. In step 5, the maximum contact stress σ is extracted from the simulation output file. max Horizontal frictional torque M H and vertical frictional torque M V The input data is normalized, and the output data is standardized. In step 5, based on the new dataset, the kernel function parameters are updated using maximum marginal likelihood estimation (MLE); the coefficient of determination R of the model on the validation set is calculated. 2 Ensure R 2 If the value is greater than 0.9, otherwise adjust the kernel function combination or sampling strategy; In step 5, calculate the relative change between the current round and the weighted sum of the objective functions of the previous three rounds: The general form of relative change is: If ΔF < 1% for 3 consecutive rounds, then convergence is determined; if the maximum number of iterations is reached, the process is forcibly terminated and the current optimal solution set is output.

10. The method for optimizing the design of a spherical joint structure of a rotating bridge based on Bayesian algorithm according to claim 1, characterized in that: In step 6, random perturbations are applied to the optimized key parameters to simulate actual manufacturing tolerances. For each optimal solution in the optimal solution set, n sets of perturbation samples are generated to produce parameter combinations. The general form of simulating actual manufacturing tolerances is: X i ′=X i ·(1+δ) Where δ represents a uniformly distributed random disturbance; In step 6, batch simulations are performed on the disturbed samples to extract the target value of maximum contact stress σ. max Horizontal frictional torque M H and vertical frictional torque M V Store the perturbed parameters and target values ​​in the database; In step 6, the standard deviation of the target value under the perturbation for each optimal solution is calculated, and the optimal solution is selected. The general form of the standard deviation of the target value is: Where N is the number of perturbation samples, The target mean; In step 6, the Sobol model is used to perform a global sensitivity analysis of the force characteristics of the contact surface; the evaluation index of the Sobol model includes the main effect sensitivity index S. i And the overall effect sensitivity index ST i : Where Y is the output variable; X ～i E is a vector consisting of all input parameters except the i-th parameter; X～i (Y|X i ) is for a fixed parameter X i At that time, other parameters X ～i The conditional expected value of Y under the change; To keep other parameters X fixed ～i At that time, only X i The conditional expected value of Y caused by the change; Var(Y), Let be the variance of each order.

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