A Sensitivity Analysis Method and System for the Force Characteristics of the Contact Surface of a Rotating Ball Joint Based on a Meta-model

Abstract

This invention discloses a sensitivity analysis method and system for the force characteristics of the contact surface of a rotating ball joint based on a meta-model. The method includes the following steps: establishing a finite element model of the rotating structure and refining the model of the ball joint; constructing an index system characterizing the force characteristics of the contact surface of the rotating ball joint; designing and using the finite element model to perform numerical simulation calculations for various working conditions; summarizing the calculation results, standardizing the data, and establishing a meta-model of the force characteristics of the ball joint contact surface; obtaining the optimal meta-model through comparison and expanding the dataset; sampling the dataset using an optimized Latin hypercube sampling method and performing a global sensitivity analysis of the contact surface force characteristics. Through sensitivity analysis, the force characteristics of the contact surface of the rotating ball joint under the combined action of multiple factors can be explored, and the influence of different parameters on the force characteristics of the ball joint structure can be analyzed, thereby determining the key influencing factors of the ball joint force characteristics.

Description

Technical Field

[0001] This invention relates to the field of structural parameter sensitivity analysis technology, specifically to a sensitivity analysis method and system for the force characteristics of the contact surface of a rotating ball joint based on a meta-model. Background Technology

[0002] As a key load-bearing and force-transmitting component of bridges undergoing rotation, the spherical hinge is subjected to the interaction of pressure transmitted from the entire weight of the bridge and frictional torque at the hinge contact surfaces during rotation. Furthermore, since the contact surfaces are mostly curved, the stress performance of the spherical hinge structure is highly complex and exhibits significant nonlinear characteristics. Therefore, exploring the contact friction mechanism between the hinge surfaces and analyzing the stress characteristics of the hinge contact surfaces is of paramount importance for the design of spherical hinge structures.

[0003] Current research on the stress characteristics of ball joint contact surfaces mainly focuses on theoretical analysis of the stress characteristics of ball joint structures based on models such as elasticity and contact mechanics, as well as the improvement and correction of these models. Examples include models of elastic half-space bodies under uniformly distributed pressure, elastic half-plane bodies under normal concentrated force, non-Hertz contact, and GW contact. However, most of these models are based on certain basic assumptions, and the established model formulas ignore the influence of some parameters, resulting in some differences from actual engineering conditions.

[0004] Finite element method (FEM) simulation is an efficient and convenient method for calculating and analyzing the stress characteristics of the contact surface of a bridge spherical hinge. By simulating the structural stress under different working conditions, the stress characteristics of the contact surface can be explored and the reliability of the structure can be evaluated. By training and testing the data results from the FEM calculations, a meta-model can be established that reveals the implicit nonlinear mapping relationship between the stress characteristics of the contact surface and its influencing factors. This is a relatively novel method that combines the FEM method with meta-modeling technology for structural stress characteristic analysis and sensitivity analysis, and it warrants further investigation. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a sensitivity analysis method and system for the force characteristics of the contact surface of a rotating ball joint based on a meta-model. By combining meta-model technology and the finite element method, the method performs sensitivity analysis on the influencing factors of the force characteristics of the contact surface of the rotating ball joint, thus solving the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a sensitivity analysis method for the force characteristics of the contact surface of a rotating ball joint based on a meta-model, comprising the following steps:

[0007] S1. Establishing a finite element model: Establishing a finite element numerical model of the bridge rotation structure and performing refined modeling of the ball joint contact surface;

[0008] S2. Construct an index system: Construct an index system to characterize the force characteristics of the contact surface of the rotating ball joint, including input indicators of factors affecting the force characteristics and output indicators characterizing the force characteristics;

[0009] S3. Working condition simulation calculation: Design numerical simulation working conditions and use the finite element model established in step S1 to perform simulation calculations.

[0010] S4. Establish a meta-model: Summarize the data results of each working condition, and standardize the data to obtain the dataset of the meta-model. Then, establish a meta-model of the force characteristics of the contact surface of the rotating ball joint.

[0011] S5. Expand the dataset using the optimal meta-model: Obtain the optimal meta-model by comparing the fitting effects of each meta-model, and then expand the dataset.

[0012] S6. Global Sensitivity Analysis: The optimized Latin hypercube sampling method is used to sample the dataset, and a global sensitivity analysis of the parameters affecting the force characteristics of the contact surface is performed.

[0013] Preferably, in step S2, the input indicators include three indicators characterizing the geometric properties of the ball joint: ball joint curvature radius X1, ball joint support radius X2, and ball joint thickness X3; three indicators characterizing the material properties of the ball joint: ball joint elastic modulus X4, ball joint Poisson's ratio X5, and ball joint friction coefficient X6; and an indicator characterizing the external load characteristics: rotational weight X7; the output indicators include three indicators: maximum contact stress S1, horizontal frictional torque S2, and vertical frictional torque S3.

[0014] Preferably, in step S2, when constructing the index system characterizing the force characteristics of the contact surface of the rotating ball joint, the upper and lower limits of each input index must first be determined, i.e., the X value must be determined. i ∈[X imin ,X imax (i = 1, 2, ..., 7), where X imin and X imax Indicator X i The minimum and maximum values; secondly, the number of level levels n for each input indicator needs to be set. i First, divide the range of values ​​into equal parts, and then determine the level values ​​for each indicator, that is: Where j = 1, 2, ..., n i Number the level value of the indicator, X ij is the j-th level value of the i-th input indicator.

[0015] Preferably, step S3 specifically includes the following:

[0016] S31. Design the working conditions for numerical simulation. Construct n1n2n3 basic numerical models by combining the three indices X1 to X3 that characterize the geometric properties of the ball joint. Use the four indices X4 to X7 as adjustable parameters. Based on the orthogonal design principle, construct an orthogonal experimental scheme. Combine Python with the command flow method to quickly and efficiently calculate the working conditions under each basic numerical model.

[0017] S32. By analyzing and calculating the results under various working conditions, the stress distribution function σ(r) of the contact surface is obtained, and the maximum contact stress, horizontal friction torque and vertical friction torque are calculated and output.

[0018] The maximum contact stress S1 is σ max Horizontal frictional torque S2, i.e., M H Vertical frictional torque S3, i.e., M V Expressed as formulas respectively:

[0019] σ max =max{σ i |i=0,...,r}

[0020]

[0021] Where r is the radius of the ball joint plane support; R is the radius of curvature of the ball joint; μ is the coefficient of friction 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; and β is the integral angle between any point on the sphere within the ball joint support plane.

[0022] Preferably, in step S4, the data results of each working condition are summarized. In order to further eliminate the scale difference of each variable data in the indicator system, increase the generalization ability of the meta-model, and accelerate the convergence speed of the model, the data is normalized, including normalizing the input indicators X1 to X77 and standardizing the output indicators S1 to S33, thus obtaining the dataset for constructing the meta-model.

[0023] Preferably, in step S4, the meta-model for establishing the force characteristics of the contact surface of the rotating ball joint is established using three methods: polynomial chaotic expansion (PCE), Gaussian process regression (Kriging), and support vector regression (SVR).

[0024] The general form of PCE is:

[0025]

[0026] Among them, M PCE (x) represents the model output for input parameter x; Θ i (x) is an orthogonal polynomial basis; β iwhere are the coefficients corresponding to the polynomial basis.

[0027] The general form of Kriging is:

[0028] M K (x)=β T f(x)+σ 2 Z(x,ω)

[0029] Where x is the model input parameter; M K (x) represents the model output for input parameter x; β T f(x) is the trend function, composed of the basis function vector f(x) and the regression coefficient vector β; σ 2 ω and ω represent the model variance and probability space, respectively.

[0030] The general form of SVR is:

[0031]

[0032] Where, α i and α i * For Lagrange multipliers, k(x) i ,x) is the kernel function.

[0033] Preferably, in step S5, R is used. 2 adjusted The accuracy and precision of each meta-model are compared and analyzed, and the formula is expressed as follows:

[0034]

[0035] In the formula, p represents the number of input variables in the model; n represents the number of validation samples; y i Indicates the output variable, y i * y is the meta-model's prediction of the input variables, and y is the mean of the dependent variable; if R 2 adjusted The closer a value is to 1, the stronger the meta-model's ability to interpret the data and the better its fit.

[0036] By comparing the R values ​​of each metamodel 2 adjusted It is worthwhile to obtain the optimal meta-model and use the optimal meta-model to expand the original dataset into a full permutation dataset of each factor and each level.

[0037] Preferably, in step S6, the maximum-minimum distance method is used to improve Latin hypercube sampling in order to increase the dispersion and uniformity between sample points, thereby obtaining an optimized Latin hypercube sampling method.

[0038] Preferably, in step S6, the Morris basic effect index and the Sobol sensitivity model are used to perform a global sensitivity analysis on the force characteristics of the contact surface.

[0039] The Morris basic effect index, expressed by the formula:

[0040]

[0041] in, The basic effect index; Δ represents the variable x. i The change in; x represents the input variables of the model; x1, x2, ..., x i ,x i+1 ,…,x M M(x1,x2,…,x) represents the components of the input variable x; i +Δ,x i+1 ,…,x M M(x) represents the objective function after parameter changes; M(x) represents the initial objective function.

[0042] Using d i * The sensitivity of the parameters is evaluated by the mean μ* and standard deviation σ of the absolute values ​​of (x). μ* represents the importance of the input variables to the model output and is positively correlated; σ is used to measure the nonlinearity of the input variables to the model and the interaction between variables, and is also positively correlated.

[0043] Evaluation metrics for the Sobol model include the main effect sensitivity index (MSI). i And the total effect sensitivity index TSI i The formula is expressed as:

[0044]

[0045] Among them, MSI i and TSI i D represents the main effect sensitivity index and the total effect sensitivity index, respectively; i D ij D 1,2,…,k D represents the variances of order 1, order 2, and order k, respectively; ～i Indicates the division variable x i The variance is the variance resulting from the combined effects of other variables besides the variable k; k is the number of variables.

[0046] On the other hand, to achieve the above objectives, the present invention also provides the following technical solution: a sensitivity analysis system for the force characteristics of the contact surface of a rotating ball joint based on a meta-model, the system comprising the following modules:

[0047] Finite element model building module: Builds a finite element numerical model of the bridge rotation structure and performs fine modeling processing on the ball joint contact surface;

[0048] Indicator System Construction Module: Construct an indicator system to characterize the force characteristics of the contact surface of the rotating ball joint, including input indicators of factors affecting force characteristics and output indicators characterizing force characteristics;

[0049] Working condition simulation calculation module: Design numerical simulation working conditions and use the finite element model established by the finite element model building module to perform simulation calculations;

[0050] Meta-model building module: Summarizes the data results of various working conditions, performs data standardization processing to obtain the dataset of the meta-model, and then establishes a meta-model of the force characteristics of the contact surface of the rotating ball joint;

[0051] Dataset expansion module: The optimal meta-model is obtained by comparing the fitting effects of various meta-models, and the dataset is expanded.

[0052] Global Sensitivity Analysis Module: The optimized Latin hypercube sampling method is used to sample the dataset and perform global sensitivity analysis on the parameters affecting the force characteristics of the contact surface.

[0053] The beneficial effects of this invention are as follows: This invention combines meta-modeling technology and the finite element method to perform sensitivity analysis on the influencing factors of the stress characteristics of the contact surface of a rotating ball joint. Using the meta-modeling method improves computational efficiency and reduces the computation time and cost of numerical simulation. Sensitivity analysis allows for the investigation of the stress characteristics of the contact surface of the rotating ball joint under the combined action of multiple factors, and analyzes the degree of influence of different parameters on the stress characteristics of the ball joint structure. This helps to determine the key influencing factors of the ball joint's stress characteristics, providing valuable insights for the design of rotating ball joint structures and the stability analysis of rotating structures. Attached Figure Description

[0054] Figure 1 A flowchart illustrating the steps of a sensitivity analysis method for the force characteristics of a rotating ball joint contact surface based on a meta-model, provided by the present invention.

[0055] Figure 2 A schematic diagram of the finite element model of the bridge rotation structure and ball joint provided in an embodiment of the present invention;

[0056] Figure 3 A schematic diagram of the stress distribution fitting of the ball joint contact surface under a certain working condition provided in an embodiment of the present invention;

[0057] Figure 4 A schematic diagram of the calculation model for the horizontal frictional torque of a ball joint provided in an embodiment of the present invention;

[0058] Figure 5A schematic diagram of the calculation model for the vertical frictional torque of a ball joint provided in an embodiment of the present invention;

[0059] Figure 6 Box plots showing the fitting effect of the meta-model provided in this embodiment of the invention, (a) is output index S1, (b) is output index S2, and (c) is output index S3;

[0060] Figure 7 The diagram shows the sensitivity analysis results of the Morris basic effect index provided in the embodiments of the present invention. (a) is the output index S1, (b) is the output index S2, and (c) is the output index S3.

[0061] Figure 8 The diagram shows the results of the Sobol model exponential sensitivity analysis provided in the embodiments of the present invention. (a) is the output index S1, (b) is the output index S2, and (c) is the output index S3.

[0062] Figure 9 This is a schematic diagram of a sensitivity analysis system module for the force characteristics of the contact surface of a rotating ball joint based on a meta-model in an embodiment of the present invention.

[0063] In the diagram, 110 is the finite element model establishment module; 120 is the index system construction module; 130 is the working condition simulation calculation module; 140 is the meta-model establishment module; 150 is the dataset expansion module; and 160 is the global sensitivity analysis module. Detailed Implementation

[0064] 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 embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] Please see Figure 1-5 This invention provides a technical solution: a sensitivity analysis method for the force characteristics of the contact surface of a rotating ball joint based on a meta-model, such as... Figure 1 As shown, the method specifically includes the following steps:

[0066] Step S1: Establish a finite element model of the bridge rotation structure and perform detailed modeling of the ball joint contact surface.

[0067] Step 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).

[0068] Step S3: Design numerical simulation conditions and use the finite element model established in step S1 to perform simulation calculations.

[0069] Step S4: Summarize the data results of each working condition obtained in Step S3, and standardize the data to obtain the dataset of the meta-model. Then, establish a meta-model of the force characteristics of the contact surface of the rotating ball joint.

[0070] Step S5: Obtain the optimal meta-model by comparing the fitting effects of each meta-model, and expand the dataset.

[0071] Step S6: The dataset is sampled using the optimized Latin hypercube sampling method, and a global sensitivity analysis of the parameters affecting the force characteristics of the contact surface is performed.

[0072] The specific working principle of the present invention will be described in detail below with reference to embodiments:

[0073] For step S1, a numerical model of the bridge rotation structure was established using the finite element software ABAQUS, and the upper and lower ball joints and their contact surfaces were refined to improve the accuracy of the model calculations, such as... Figure 2 As shown.

[0074] For step S2, three indicators characterizing the geometric properties of the ball joint are selected: the ball joint curvature radius (X1), the ball joint support radius (X2), and the ball joint thickness (X3). These, along with three indicators characterizing the material properties of the ball joint (X4), the ball joint elastic modulus (X4), the ball joint Poisson's ratio (X5), and the ball joint friction coefficient (X6), and seven other indicators (factors affecting the force characteristics), including the rotation weight (X7) characterizing the external load characteristics, are used as input indicators characterizing the force characteristics of the contact surface of the rotating ball joint.

[0075] For step S2, three indicators (indicators characterizing the force characteristics) are selected as output indicators characterizing the force characteristics of the contact surface of the rotating ball joint: maximum contact stress (S1), horizontal frictional torque (S2), and vertical frictional torque (S3).

[0076] For step S2, construct the indicator system. First, determine the upper and lower limits of each input indicator, i.e., determine:

[0077] X i ∈[X imin ,X imax (i = 1, 2, ..., 7)

[0078] Among them, X imin and X imax Indicator X i The minimum and maximum values.

[0079] Furthermore, the number of level levels n for each input indicator is set. iGenerally, the range of values ​​is divided equally to determine the level values ​​for each indicator, that is:

[0080]

[0081] Where j = 1, 2, ..., n i Number the level value of the indicator, X ij This represents the j-th level value of the i-th input indicator.

[0082] Furthermore, the input index system for the force characteristics of the contact surface of the rotating ball joint constructed in this embodiment is shown in Table 1.

[0083] Table 1 Input Indicator System

[0084]

[0085] Note: U indicates uniform distribution.

[0086] For step S3, the working conditions for numerical simulation are designed. A total of 3×3×3=27 basic working conditions for numerical models are constructed by the mutual permutation and combination of three indicators representing the geometric characteristics of the ball joint, such as X1~X3, as shown in Table 2.

[0087] Table 2. Basic working conditions of the numerical model (X1~X3)

[0088]

[0089] Furthermore, using four adjustable parameters, X4 to X7, and based on the orthogonal design principle, an L-shaped design is constructed. 25 (5 4 The orthogonal experimental schemes are shown in Table 3.

[0090] Table 3L 25 (5 4 Orthogonal experimental design

[0091]

[0092]

[0093] Furthermore, under the basic working conditions of each numerical model (composed of X1 to X3), orthogonal experimental schemes (composed of X4 to X7) were used respectively, and the calculation results of all (25×27=675 groups) design working conditions were quickly and efficiently calculated using the command flow method in Python.

[0094] Furthermore, the contact stress distribution values ​​along the radius direction of the ball joint support from the center of the ball joint to the contact edge are extracted, and then the stress distribution function σ(r) is obtained by fitting, such as... Figure 3 The figure shows the stress distribution fitting under a certain working condition.

[0095] Furthermore, the maximum contact stress σ can be calculated as an output index. max :

[0096] σ max =max{σ i |i=0,...,r}

[0097] Furthermore, based on Figure 4 As shown, the horizontal frictional torque M can be calculated. H :

[0098]

[0099] Furthermore, based on Figure 5 As shown, the vertical frictional torque M can be calculated. V :

[0100]

[0101] Where r is the radius of the ball joint plane support; R is the radius of curvature of the ball joint; μ is the coefficient of friction 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; and β is the integral angle between any point on the sphere within the ball joint support plane.

[0102] For step S4, the data results of each working condition are summarized. In order to further eliminate the scale difference of 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.

[0103] Furthermore, the seven input indicators X1 to X7 are normalized, and the three output indicators S1 to S3 are standardized. The data obtained from the above processing are then summarized to obtain the dataset for constructing the meta-model.

[0104] Furthermore, a meta-model of the force characteristics of the contact surface of the rotating ball joint is established using three methods: polynomial chaotic expansion (PCE), Gaussian process regression (Kriging), and support vector regression (SVR).

[0105] Furthermore, the general form of PCE is:

[0106]

[0107] Among them, M PCE (x) represents the model output for input parameter x; Θ i (x) is an orthogonal polynomial basis; β i where are the coefficients corresponding to the polynomial basis.

[0108] Furthermore, the general form of Kriging is:

[0109] M K (x)=β T f(x)+σ 2 Z(x,ω)

[0110] Where x is the model input parameter; M K (x) represents the model output for input parameter x; β T f(x) is the trend function, composed of the basis function vector f(x) and the regression coefficient vector β; σ 2 Let ω and ω be the model variance and probability space, respectively.

[0111] Furthermore, the general form of SVR is:

[0112]

[0113] Where, α i and α i * For Lagrange multipliers, k(x) i ,x) is the kernel function.

[0114] For step S5, R is used. 2 adjusted The accuracy and precision of each meta-model were compared and analyzed, and the calculation formula is as follows:

[0115]

[0116]

[0117] Where p represents the number of input variables in the model; n represents the number of validation samples; y i Indicates the output variable, y i * y is the meta-model's prediction of the input variables, and y is the mean of the dependent variable. If R 2 adjusted The closer a value is to 1, the stronger the meta-model's ability to interpret the data and the better its fit.

[0118] Furthermore, the 675 sets of data obtained from the simulation were divided into 9 sample sets: 75, 150, 225, 300, 375, 450, 525, 600, and 675, for training and testing of the meta-model.

[0119] Furthermore, to obtain reliable and reasonable results and to find the optimal sample set and the optimal meta-model, each sample set was resampled 50 times, and the R-values ​​of different meta-models under the 50 sampling conditions were summarized. 2 adjusted The values ​​are calculated, and box plots of the fit of the meta-model for each output metric are drawn, such as... Figure 6 As shown.

[0120] Furthermore, comparing the R values ​​of each meta-model 2 adjusted It is worthwhile to identify SVR as the optimal meta-model. Using this trained SVR model, the original dataset is expanded to include all permutations of each factor and level (total 3). 3 ×5 4 =16875 sets) dataset.

[0121] For step S6, the maximum-minimum distance method is used to improve the Latin hypercube sampling in order to increase the dispersion and uniformity between sample points, thus obtaining the optimized Latin hypercube sampling method.

[0122] Furthermore, the Morris basic effect index and Sobol model were used to conduct a global sensitivity analysis of the force characteristics of the contact surface.

[0123] Furthermore, the general form of the Morris basic effects index is:

[0124]

[0125] in, The basic effect index; Δ represents the variable x. i The change in; x represents the input variables of the model; x1, x2, ..., x i ,x i+1 ,…,x M M(x1,x2,…,x) represents the components of the input variable x; i +Δ,x i+1 ,...,x M ) represents the objective function after parameter changes; M(x) represents the initial objective function.

[0126] Furthermore, using d i * The sensitivity of the parameters is evaluated by the mean μ* and standard deviation σ of the absolute values ​​of (x). μ* represents the importance of the input variables to the model output and is positively correlated. σ is used to measure the nonlinearity of the input variables on the model and the interaction between variables, and is also positively correlated.

[0127] Furthermore, the sensitivity analysis results of the Morris basic effect index for each output index were obtained, such as... Figure 7 As shown.

[0128] Furthermore, the evaluation metrics for the Sobol model include the main effect sensitivity index (MSI). i And the total effect sensitivity index TSI i :

[0129]

[0130] Among them, MSI i and TSI i D represents the main effect sensitivity index and the total effect sensitivity index, respectively; i D ij D 1,2,…,k D represents the variances of order 1, order 2, and order k, respectively; ～i Indicates the division variable x i The variance is the variance resulting from the combined effects of other variables besides the variable k; k is the number of variables.

[0131] Furthermore, the sensitivity analysis results of the Sobol model for each output index were obtained, such as... Figure 8 As shown.

[0132] Furthermore, the sensitivity analysis results for the output index, maximum contact stress (S1), are shown in Table 4.

[0133] Table 4. Sensitivity analysis results of maximum contact stress (S1)

[0134]

[0135] Furthermore, the sensitivity analysis results for the output index horizontal friction torque (S2) are shown in Table 5.

[0136] Table 5. Sensitivity analysis results of horizontal frictional torque (S2)

[0137]

[0138] Furthermore, the sensitivity analysis results for the output index vertical friction torque (S3) are shown in Table 6.

[0139] Table 6. Sensitivity analysis results of vertical frictional torque (S3)

[0140]

[0141] Furthermore, based on the above sensitivity analysis results, it is believed that the Morris basic effect index and the Sobol model have good consistency in the global sensitivity analysis of the parameters of the three output indicators, namely maximum contact stress (S1), horizontal frictional torque (S2), and vertical frictional torque (S3), and thus the sensitivity of each output indicator to its influencing factors can be determined.

[0142] Furthermore, in the swivel ball joint structure, there are four main factors affecting the maximum contact stress on the contact surface, which are ranked from largest to smallest sensitivity as follows: radius of curvature (X1), elastic modulus (X4), support radius (X2), and swivel weight (X7). The remaining factors have a relatively small impact on this index.

[0143] Furthermore, in a spherical hinge structure, there are three main factors affecting the horizontal frictional torque, which are ranked from largest to smallest sensitivity as follows: radius of curvature (X1), coefficient of friction (X6), and weight of the rotating body (X7). Other factors have a relatively small impact on this indicator.

[0144] Furthermore, in the spherical hinge structure, there are four main factors affecting the vertical frictional torque, which are listed in descending order of sensitivity: friction coefficient (X6), spherical weight (X7), radius of curvature (X1), and support radius (X2). The remaining factors have a relatively small impact on this indicator.

[0145] Based on the same inventive concept as the above-described method embodiments, this application also provides a sensitivity analysis system for the force characteristics of the contact surface of a rotating ball joint based on a meta-model. This system can achieve the functions provided by the above-described method embodiments, such as... Figure 9 As shown, the system includes the following modules:

[0146] Finite element model establishment module 110: Establishes a finite element numerical model of the bridge rotation structure and performs fine modeling processing on the ball joint contact surface;

[0147] Indicator System Construction Module 120: Construct an indicator system to characterize the force characteristics of the contact surface of the rotating ball joint, including input indicators of factors affecting force characteristics and output indicators characterizing force characteristics;

[0148] Working condition simulation calculation module 130: Designs numerical simulation working conditions and uses the finite element model established by finite element model building module 110 to perform simulation calculations;

[0149] Meta-model building module 140: Summarizes the data results of each working condition, performs data standardization processing to obtain the dataset of the meta-model, and then establishes a meta-model of the force characteristics of the contact surface of the rotating ball joint.

[0150] Dataset expansion module 150: Obtains the optimal meta-model by comparing the fitting effects of various meta-models, and expands the dataset;

[0151] Global Sensitivity Analysis Module 160: The dataset is sampled using an optimized Latin hypercube sampling method, and a global sensitivity analysis of the parameters affecting the force characteristics of the contact surface is performed.

[0152] Based on the same inventive concept as the above method embodiments, this application also provides an electronic device, the device including: a processor; and a memory for storing one or more programs;

[0153] When the one or more programs are executed by the processor, the processor performs the sensitivity analysis method for the force characteristics of the contact surface of the rotating ball joint based on the meta-model.

[0154] Based on the same inventive concept as the above-described method embodiments, this application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the aforementioned sensitivity analysis method for the force characteristics of the contact surface of a rotating ball joint based on a meta-model.

[0155] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A sensitivity analysis method for the force characteristics of the contact surface of a rotating ball joint based on a meta-model, characterized in that, Includes the following steps: S1. Establishing a finite element model: Establishing a finite element numerical model of the bridge rotation structure and performing refined modeling of the ball joint contact surface; S2. Constructing an Index System: Construct an index system to characterize the force characteristics of the contact surface of the rotating ball joint, including input indicators of factors affecting force characteristics and output indicators characterizing force characteristics; the input indicators include three indicators characterizing the geometric characteristics of the ball joint: ball joint curvature radius X1, ball joint support radius X2, and ball joint thickness X3; three indicators characterizing the material properties of the ball joint: ball joint elastic modulus X4, ball joint Poisson's ratio X5, and ball joint friction coefficient X6; and an indicator characterizing the external load characteristics: rotating weight X7; the output indicators include three indicators: maximum contact stress S1, horizontal frictional torque S2, and vertical frictional torque S3; S3. Working condition simulation calculation: Design numerical simulation working conditions and use the finite element model established in step S1 to perform simulation calculations. S4. Establish a meta-model: Summarize the data results of each working condition and normalize the data to obtain the dataset of the meta-model. Then, establish a meta-model of the force characteristics of the contact surface of the rotating ball joint. The establishment of the meta-model of the force characteristics of the contact surface of the rotating ball joint is achieved by using three methods: polynomial chaotic expansion (PCE), Gaussian process regression (Kriging), and support vector regression (SVR). S5. Expand the dataset using the optimal meta-model: Obtain the optimal meta-model by comparing the fitting effects of various meta-models, and then expand the dataset; specifically including: using R... 2 adjusted The accuracy and precision of each meta-model are compared and analyzed, and the formula is expressed as follows: In the formula, p represents the number of input variables in the model; n represents the number of validation samples; y i Indicates the output variable, y i * It is the meta-model's prediction of the input variables. It is the mean of the dependent variable; if R 2 adjusted The closer a value is to 1, the stronger the meta-model's ability to interpret the data and the better its fit. By comparing the R values ​​of each metamodel 2 adjusted It is worthwhile to obtain the optimal meta-model and use the optimal meta-model to expand the original dataset into a full permutation dataset of each factor and each level; S6. Global Sensitivity Analysis: The optimized Latin hypercube sampling method is used to sample the dataset, and a global sensitivity analysis of the parameters affecting the force characteristics of the contact surface is performed.

2. The sensitivity analysis method for the force characteristics of the contact surface of a rotating ball joint based on a meta-model according to claim 1, characterized in that: In step S2, when constructing the index system characterizing the force characteristics of the contact surface of the rotating ball joint, the upper and lower limits of each input index must first be determined, i.e., X must be determined. i ∈[X imin ,X imax (i = 1, 2, ..., 7), where X imin and X imax Indicator X i The minimum and maximum values; secondly, the number of level levels n for each input indicator needs to be set. i First, divide the range of values ​​into equal parts, and then determine the level values ​​for each indicator, that is: Where j = 1, 2, ..., n i Number the level value of the indicator, X ij This represents the j-th level value of the i-th input indicator.

3. The sensitivity analysis method for the force characteristics of the contact surface of a rotating ball joint based on a meta-model according to claim 1, characterized in that: Step S3 specifically includes the following: S31. Design the working conditions for numerical simulation. Construct n1n2n3 basic numerical models by combining the three indices X1 to X3 that characterize the geometric properties of the ball joint. Use the four indices X4 to X7 as adjustable parameters. Based on the orthogonal design principle, construct an orthogonal experimental scheme. Combine Python with the command flow method to quickly and efficiently calculate the working conditions under each basic numerical model. S32. By analyzing and calculating the results under various working conditions, the stress distribution function σ(r) of the contact surface is obtained, and the maximum contact stress, horizontal friction torque and vertical friction torque are calculated and output.

4. The sensitivity analysis method for the force characteristics of the contact surface of a rotating ball joint based on a meta-model according to claim 1, characterized in that: In step S4, the data is normalized, including normalizing the input indicators X1 to X77 and standardizing the output indicators S1 to S33, thus obtaining the dataset for constructing the meta-model.

5. The sensitivity analysis method for the force characteristics of the contact surface of a rotating ball joint based on a meta-model according to claim 1, characterized in that: In step S6, the maximum-minimum distance method is used to improve Latin hypercube sampling in order to increase the dispersion and uniformity between sample points, thus obtaining the optimized Latin hypercube sampling method.

6. The sensitivity analysis method for the force characteristics of the contact surface of a rotating ball joint based on a meta-model according to claim 1, characterized in that: In step S6, the Morris basic effect index and the Sobol sensitivity model are used to perform a global sensitivity analysis on the force characteristics of the contact surface. The Morris basic effect index, expressed by the formula: in, The basic effect index; Δ represents the variable x. i The change in; x represents the input variables of the model; x1, x2, ..., x i ,x i+1 ,…,x M M(x1,x2,…,x) represents the components of the input variable x; i +Δ,x i+1 ,…,x M M(x) represents the objective function after parameter changes; M(x) represents the initial objective function. use The sensitivity of the parameters is evaluated by the mean μ* and standard deviation σ of the absolute values ​​of the input variables. μ* represents the importance of the input variables to the model output and is positively correlated; σ is used to measure the nonlinearity of the input variables to the model and the interaction between variables, and is also positively correlated. Evaluation metrics for the Sobol model include the main effect sensitivity index (MSI). i And the total effect sensitivity index TSI i The formula is expressed as: Among them, D i D ij D 1,2,…,k D represents the variances of order 1, order 2, and order k, respectively; ～i Indicates the division variable x i The variance is the variance resulting from the combined effects of other variables besides the variable k; k is the number of variables.

7. A sensitivity analysis system for the force characteristics of a rotating ball joint contact surface based on a meta-model, according to any one of claims 1-6, characterized in that: The system includes the following modules: Finite element model establishment module (110): Establishes a finite element numerical model of the bridge rotation structure and performs fine modeling processing on the ball joint contact surface; Indicator system construction module (120): Construct an indicator system to characterize the force characteristics of the contact surface of the rotating ball joint, including input indicators of factors affecting the force characteristics and output indicators characterizing the force characteristics; Working condition simulation calculation module (130): Design numerical simulation working conditions and use the finite element model established by the finite element model establishment module (110) to perform simulation calculations; Meta-model building module (140): Summarize the data results of each working condition, and standardize the data to obtain the dataset of the meta-model, and then build a meta-model of the force characteristics of the contact surface of the rotating ball joint; Dataset expansion module (150): The optimal meta-model is obtained by comparing the fitting effects of each meta-model, and the dataset is expanded. Global Sensitivity Analysis Module (160): The optimized Latin hypercube sampling method is used to sample the dataset and to perform global sensitivity analysis on the parameters affecting the force characteristics of the contact surface.

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