Response surface model self-adaption-based quick assessment method for stress of angular structure of bogie frame
By using an adaptive response surface model, the low efficiency of stress assessment for the angular structure of a rail crane trolley frame was solved, enabling rapid and accurate stress assessment and lightweight design, thereby reducing costs.
Patent Information
- Application Number
- CN202511927110.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-19
- Publication Date
- 2026-03-20
AI Technical Summary
Existing technologies suffer from low computational efficiency, high cost, and long design cycles in stress assessment of the angular structure of rail crane trolley frames, and fail to conduct detailed stress distribution analysis for a series of products.
An adaptive method based on response surface methodology is adopted. By establishing a finite element model, determining key parameters, constructing a sample matrix, training a surrogate model, and optimizing a multi-factor stress surrogate model, a fast and accurate stress assessment can be achieved.
It significantly improves the computational efficiency and accuracy of stress assessment, reduces the experimental sample size and testing costs, shortens the design cycle, supports real-time optimization, and meets the needs of lightweight design.
Smart Images
Figure CN121706284A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a rapid stress assessment method for trolley frame angular structures based on an adaptive response surface model, which is particularly suitable for trolley frames used in crane running mechanisms. Background Technology
[0002] Angular structures are commonly found at the trolley frame of the trolley and crane traveling mechanisms in rail-mounted cranes (such as bridge cranes and portal cranes). This structure is characterized by an angular opening at the connection point with the wheel bearing box. Although there is a rounded transition at the angular position, the internal stress flow lines still change abruptly, easily leading to stress concentration. The movement of wheels on the rails inevitably involves impacts, especially at rail joints. This is particularly true for metallurgical cranes, which experience high working stress and frequency, making them highly susceptible to fatigue cracks at and near the angular arc position. This is directly related to structural stress; therefore, stress assessment of angular structures is crucial.
[0003] To accurately obtain the concentrated stress of the trolley frame, an effective method is to use finite element modeling. The basic steps for modeling a trolley frame of a certain model are: 1. Establish a three-dimensional model of the mechanical structure. The model should accurately reflect the actual geometry of the structure. 2. Divide the structure into finite element meshes: Based on the material properties and geometric characteristics of the structure, discretize it into many smaller elements, ensuring the accuracy and precision of the finite element mesh. 3. Determine boundary conditions and load conditions: Ensure that the simulation conditions are consistent with the actual working conditions of the structure, and apply appropriate boundary conditions and load conditions to the structure. 4. Solve the finite element equations to obtain the stress distribution of the structure. 5. Structural optimization: Based on the finite element analysis results, determine the stress and stability of the structure, evaluate the safety and reliability of the structure, and perform optimized design of the structure to improve the stress and stability of the structure and reduce the weight and cost of the structure. However, different models of crane trolley frames have different dimensions. When using this method to calculate the structural strength and stress of the trolley frame, there are problems such as repeated modeling, large workload, long design cycle and calculation time, and high cost.
[0004] Current research largely focuses on analyzing single products with angular structures, neglecting analysis of a series of products and a detailed discussion of the impact of various structural parameters on stress distribution. With increasing interdisciplinary integration, there are higher demands for the efficiency of structural stress analysis methods; therefore, a rapid stress assessment method for trolley frame angular structures is needed. Summary of the Invention
[0005] This invention proposes a rapid stress assessment method for trolley frame corner structures based on response surface methodology, addressing the problem of how to quickly and efficiently assess the stress of trolley frame corner structures.
[0006] To solve the above problems, the technical solution provided by the present invention is as follows:
[0007] A rapid stress assessment method for trolley frame angular structures based on response surface model adaptation is proposed, with the following steps:
[0008] Step 1: Establish a finite element model of the trolley frame corner structure, perform finite element calculations under different working loads to determine the stress concentration areas; determine the key parameters affecting the stress of the trolley frame corner structure based on the sensitivity analysis of the trolley frame corner structure.
[0009] Step 2: Construct sample matrices based on a single key parameter and multiple key parameters respectively (i.e., four sample matrices were ultimately constructed). The construction process for each sample matrix is as follows:
[0010] Key parameters (single or multiple key parameters) are used as input variables. Output variables are determined through stress concentration regions. An initial sample variable space is set based on experience. Response surface experiments are conducted to obtain a suitable sample variable space. Sample data is extracted from the sample variable space to construct a sample matrix.
[0011] Step 3: Perform analysis and calculation based on the finite element model and sample matrix to obtain the stress data corresponding to each group of sample data in each sample matrix. Combine each group of sample data and its corresponding stress data to form a dataset. The dataset includes datasets obtained from single-factor variables and datasets obtained from multi-factor variables.
[0012] Step 4: Train the RSM surrogate model based on the dataset to obtain the single-factor-stress surrogate model and the multi-factor-stress surrogate model respectively.
[0013] Step 5: Based on the single-factor stress surrogate model trained in Step 4 and the sample matrix obtained in Step 2, correct the multi-factor stress surrogate model to improve the accuracy of the model and facilitate the rapid and accurate acquisition of stress for different parameters.
[0014] Furthermore, in step 1, the boundary conditions are set as follows: the load acts on the bending plate, and constraints are applied to the pin connection position in the finite element model. This boundary condition can more intuitively reflect the stress situation of the structure when subjected to the impact of track operation.
[0015] Furthermore, in step 1, the key parameters include: the thickness t1 of the trolley frame angled structure bending plate, the radius r of the bending plate arc, and the thickness t2 of the web plate.
[0016] Furthermore, in step 2, the output variable is the maximum stress at the arc connection of the angular structure.
[0017] Furthermore, in step 2, the Latin hypercube sampling method is used to extract samples, ensuring that the sample variables are uniform and independent, thereby achieving higher estimation accuracy.
[0018] Furthermore, in step 2, the sample data are data pairs in the sample variable space where the input variables and output variables correspond one-to-one.
[0019] Furthermore, in step 4, the proxy model adopts the RSM model to obtain a polynomial approximation model of the input and output variables;
[0020] Furthermore, in step 4, the single-factor stress surrogate models M1(t1), M2(t2), M3(r) and the multi-factor stress surrogate model M4(t1,t2,r) have a sample matrix S={t 1m ,t 2n ,r q ,σ mnq};t 1m t 2n r q Let σ represent a single data point from t1, t2, and r respectively. mnq For t 1m t 2n r q The maximum stress at the arc connection of the corresponding angular structure.
[0021] Furthermore, in step 5 of the process of modifying the multi-factor-stress surrogate model, the weights of each coefficient in the model are determined based on the single-factor-stress surrogate model. A sparse screening method is used to remove redundant terms with small weights in the multi-factor-stress surrogate model and optimize the multi-factor-stress surrogate model.
[0022] Furthermore, in step 5, during the process of correcting the multi-factor-stress surrogate model, the physical constraints of the single-factor-stress surrogate model are extracted, and the physical constraints are embedded into the Alternating Direction Multiplier Algorithm (ADMM) to obtain the anti-interference coefficient that satisfies the physical constraints, thereby further correcting the multi-factor-stress surrogate model.
[0023] Furthermore, in step 5, during the process of modifying the multi-factor-stress surrogate model, a dynamic equilibrium iterative weight adjustment mechanism is constructed.
[0024] Adaptive optimization of the multi-factor-stress surrogate model is achieved, significantly improving its computational accuracy. The accuracy analysis of the multi-factor-stress surrogate model is based on the coefficient of determination R. 2 This allows for an intuitive and quantitative assessment of the interpretability of data by the multi-factor stress surrogate model. By assigning key parameter data of the target working condition to the multi-factor stress surrogate model, stress data can be obtained quickly and accurately.
[0025] The beneficial effects of this invention are as follows: When applied to the corner structure of the trolley frame, this patent can accurately solve the engineering pain points of its corner stress concentration area: it reduces the calculation error of the multi-factor stress proxy model to below 5%, ensuring the reliability of the trolley frame strength design; it can also reduce the number of high-order model terms by 30%-50%, shortening the model correction time to the minute level, and can be directly integrated into the CAE system to realize the real-time optimization of the corner structure, avoiding the problems of repeated modeling for trolley frames of different sizes, large workload, long design cycle and calculation time, and high cost; and it only requires 1 / 3 of the traditional trolley frame test sample size, greatly reducing the manufacturing and testing costs of experimental prototypes, helping the corner structure of the trolley frame to meet the strength requirements while achieving weight reduction, and combining high practicality and economy. Attached Figure Description
[0026] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.
[0027] Figure 1 This is a diagram of the frame angle structure of a vehicle.
[0028] In the diagram: 1. Pin; 2. Top cover plate; 3. Web plate; 4. Bend plate; 5. Angular bearing housing; 6. Wheel; 7. Bend plate radius.
[0029] Figure 2 This is a flowchart of the calculation process of this invention. Detailed Implementation
[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific examples and the accompanying drawings. It should be understood that these descriptions are merely exemplary and are not intended to limit the scope of the invention.
[0031] Unless otherwise specified, all terms used in this article adopt their generally accepted meanings within the technical field. It should also be noted that even if a term has a clear definition in a general dictionary, its meaning should be understood in the context of the specific technical situation, and should not be interpreted according to idealized concepts or overly formal expressions.
[0032] To address the practical needs of stress analysis for trolley frame corner structures, this invention provides a proxy model technology solution. Specifically, it utilizes optimized Latin hypercube experimental design and response surface proxy modeling techniques to build a proxy model for the finite element analysis of trolley frame corner structures. The corrected model can be used for rapid stress analysis of trolley frame corner structures under multiple operating conditions, ensuring reliable results and improving computational efficiency. When performing stress analysis tasks on large models under multiple operating conditions, this technology can significantly reduce computation time while comprehensively covering various operating conditions, outputting stress results and providing strong guidance for the design of trolley frame corner structures, helping to optimize and improve structural stress.
[0033] Taking a casting crane trolley frame as an example, a finite element model of the trolley frame's angular structure is established. The trolley frame material is Q355B.
[0034] Step 1: Establish a finite element model of the trolley frame corner structure, perform finite element calculations under different working loads to determine the stress concentration areas; determine the key parameters affecting the stress of the trolley frame corner structure based on the sensitivity analysis of the trolley frame corner structure.
[0035] A finite element model of the trolley frame was built using plate elements.
[0036] The boundary conditions are set as follows: the load acts on the bending plate, and constraints are applied to the pin connection position in the finite element model. This boundary condition can more intuitively reflect the stress situation of the structure when subjected to the impact of track operation;
[0037] The grid size is determined based on the thickness of the plate unit, using a quadrilateral grid.
[0038] Finite element analysis was performed under different working loads to determine that the stress concentration region was the arc connection of the angular structure.
[0039] The initial parameters are selected as follows: the thickness of the angular structure bending plate of the trolley frame, the radius of the bending plate arc, the thickness of the web plate, and the thickness of the top cover plate;
[0040] Sensitivity analysis determined the key parameters to be: the thickness t1 of the trolley frame's angled bending plate, the radius r of the bending plate's arc, and the thickness t2 of the web plate. These parameters were then set as input variables.
[0041] The output variable is the maximum stress at the arc connection of the angular structure.
[0042] Step 2: Construct sample matrices based on a single key parameter and multiple key parameters respectively (i.e., four sample matrices were ultimately constructed). The construction process for each sample matrix is as follows:
[0043] Key parameters (single or multiple key parameters) are used as input variables. Output variables are determined through stress concentration regions. An initial sample variable space is set based on experience. Response surface experiments are conducted to obtain a suitable sample variable space. Sample data is extracted from the sample variable space to construct a sample matrix.
[0044] The sampling method uses Latin hypercube sampling to ensure that the sample variables are uniform and independent, thus achieving higher estimation accuracy.
[0045] Latin hypercube sampling achieves uniform coverage of the marginal distribution of variables, possesses excellent spatial filling ability, and can efficiently capture high-dimensional spatial features. Its statistical efficiency is significantly better than simple random sampling, with higher estimation accuracy and faster convergence speed under the same sample size. Moreover, it can maintain the independence between variables, without introducing spurious correlations, and is suitable for uncertainty quantification and reliability analysis of complex systems.
[0046] The Latin hypercube sampling method is used to collect sample data for selected input variables. Based on the collected results, a corresponding sample matrix can be constructed, specifically generating multiple sets of typical matrices containing structural geometric dimensions. For example, if 20 sets of sample data are collected, and each set covers three variables—bend thickness, radius of curvature, and web thickness—a 20×3 sample matrix can be constructed.
[0047] Sample data consists of data pairs in the sample variable space where input and output variables correspond one-to-one.
[0048] Step 3: Perform analysis and calculation based on the finite element model and sample matrix to obtain the stress data corresponding to each group of sample data in each sample matrix. Combine each group of sample data and its corresponding stress data to form a dataset. The dataset includes datasets obtained from single-factor variables and datasets obtained from multi-factor variables.
[0049] The following techniques were used to obtain the solution results data: the constructed sample matrix was input into the finite element model of the angular structure, and the solver was called to perform numerical calculations on the model and the input data; the calculation results were analyzed and effective information was extracted, and finally the solution dataset containing stress parameters corresponding to each matrix was obtained.
[0050] Step 4: Train the RSM surrogate model based on the dataset to obtain the single-factor-stress surrogate model and the multi-factor-stress surrogate model respectively.
[0051] Using the RSM model, a polynomial approximation model of the input and output variables is obtained;
[0052] Single-factor stress surrogate models M1(t1), M2(t2), M3(r) and multi-factor stress surrogate model M4(t1,t2,r), sample matrix S={t 1m ,t2n ,r q ,σ mnq};t 1m t 2n r q Let σ represent a single data point from t1, t2, and r respectively. mnq For t 1m t 2n r q The maximum stress at the arc connection of the corresponding angular structure.
[0053] Step 5: Based on the single-factor stress surrogate model trained in Step 4 and the sample matrix obtained in Step 2, correct the multi-factor stress surrogate model to improve the accuracy of the model and facilitate the rapid and accurate acquisition of stress for different parameters.
[0054] Based on the single-factor stress surrogate model, the weights of each coefficient in the model are determined. The sparse screening method is used to remove redundant terms with small weights in the multi-factor stress surrogate model and optimize the multi-factor stress surrogate model.
[0055] ;
[0056] In the formula: It is the sparse optimization objective function of the multi-factor-stress surrogate model. It is the sample stress. It is a regularization parameter. It is the first in the model The coefficient of the term;
[0057] In the formula: The fitting deviation term is calculated from the measured values of the sample stress. The sum of squared deviations from the predicted values of the multi-factor stress surrogate model M4 ensures the model's accuracy in fitting the measured data.
[0058] In the formula: Here, represents the regularization constraint term, where the regularization parameter is... Control constraint strength, weight The importance of each component in the model is adapted by adjusting the model's... coefficient of the term By imposing absolute value constraints, redundant terms are sparsified and filtered, and invalid terms are suppressed from interfering with the model, thus optimizing the multi-factor-stress surrogate model.
[0059] Physical constraints are extracted from the single-factor stress surrogate model. The physical constraints are then embedded into the Alternating Direction Multiplier (ADMM) algorithm to obtain the anti-interference coefficients that satisfy the physical constraints. The multi-factor stress surrogate model is then further modified.
[0060] ;
[0061] In the formula: It is a robust optimization objective function with physical constraint embedding in a multi-factor-stress surrogate model. For Huber's losses, To constrain penalties, The penalty coefficient is... It is the bias classification threshold parameter of the Huber loss function;
[0062] In the formula: The robust fitting term (i.e., Huber loss) is used to apply the Huber loss function to the measured stress values of the samples. The deviation from the predicted value M4 of the multi-factor stress surrogate model is quantified. Small deviations are treated with a squared form to ensure fitting accuracy, while large deviations are treated with a linear form to suppress the interference of outlier samples, thus achieving robust adaptation of the model to the measured data.
[0063] In the formula: This is a physical constraint penalty term. If the model coefficient b violates the physical constraint, it is "penalized" by multiplying it with the penalty coefficient μ, thus forcing the optimization process to satisfy the constraint.
[0064] A dynamic balance iterative weight adjustment mechanism is constructed to improve the computational accuracy of the model.
[0065] ;
[0066] ;
[0067] In the formula: These are the physical constraint weighting coefficients. These are the weighting coefficients for the sample data. This is a coefficient correction amount driven by physical constraints. The coefficient correction amount is driven by the sample data. For the model number The final correction amount for the term coefficient;
[0068] In the formula: By iteratively adjusting the coefficients of different terms in the multi-factor-stress surrogate model Physical weight coefficient and sample data weighting coefficients Obtain the corrected coefficients ;
[0069] ;
[0070] ;
[0071] In the formula: N is the sample size. The sign function (outputs +1 or -1, representing the direction of the function's trend). It is a single-factor model at sample points The derivative at a point (representing the local trend of change in the single-factor model) is the derivative of the multi-factor model M4 at the sample points. The partial derivative with respect to variable t (characterizing the local variation trend of the multi-factor model). Physical consistency error. The percentage of deviations in local variation trends (derivative signs) between the statistical multifactor model and the single-factor model;
[0072] In the formula: It is the root mean square error. This represents the range of stress fluctuation in the sample. Data fitting error. The absolute bias of the model prediction is converted into the proportion of the sample's own fluctuation range, thus eliminating the influence of the sample's numerical scale.
[0073] Calculate physical consistency error and data fitting error If the error of both is less than 5%, then the accuracy requirement is met.
[0074] If the error is greater than 5%, adjust accordingly. and Perform iterative calculations and repeat the above process until the result meets the accuracy requirements.
[0075] Based on the above modifications, adaptive optimization of the multi-factor stress surrogate model is achieved, significantly improving the computational accuracy of the multi-factor stress surrogate model; the accuracy analysis of the multi-factor stress surrogate model is based on the coefficient of determination R. 2 This allows for an intuitive and quantitative assessment of the interpretability of data by the multi-factor stress surrogate model. By assigning key parameter data of the target working condition to the multi-factor stress surrogate model, stress data can be obtained quickly and accurately.
[0076] For example, select the maximum stress at the opening of the angled structure. The thickness of the angled bending plate is selected as the output variable. radius of arc Web thickness If the input variables are given, then the polynomial expression of the multifactor-stress surrogate model is:
[0077]
[0078] By assigning values to the input variables and substituting them into the multi-factor-stress surrogate model, stress values can be calculated quickly.
Claims
1. A rapid stress assessment method for a trolley frame angular structure based on adaptive response surface model, characterized in that, The steps are as follows: Step 1: Establish a finite element model of the trolley frame corner structure, perform finite element calculations under different working loads to determine the stress concentration areas; determine the key parameters affecting the stress of the trolley frame corner structure based on the sensitivity analysis of the trolley frame corner structure. Step 2: Construct sample matrices based on a single key parameter and multiple key parameters respectively. The construction process for each type of sample matrix is as follows: Key parameters are used as input variables, output variables are determined through stress concentration regions, an initial sample variable space is set based on experience, response surface experiments are conducted to obtain a suitable sample variable space, sample data are extracted from the sample variable space, and a sample matrix is constructed. Step 3: Perform analysis and calculation based on the finite element model and sample matrix to obtain the stress data corresponding to each group of sample data in each sample matrix. Combine each group of sample data and its corresponding stress data to form a dataset. The dataset includes datasets obtained from single-factor variables and datasets obtained from multi-factor variables. Step 4: Train the RSM surrogate model based on the dataset to obtain the single-factor-stress surrogate model and the multi-factor-stress surrogate model respectively; Step 5: Based on the single-factor stress surrogate model trained in Step 4 and the sample matrix obtained in Step 2, correct the multi-factor stress surrogate model to improve the accuracy of the model and facilitate the rapid and accurate acquisition of stress for different parameters.
2. The rapid stress assessment method for trolley frame angular structures based on adaptive response surface model according to claim 1, characterized in that, In step 1, the boundary conditions are set as follows: the load is applied to the bending plate position, and constraints are applied to the pin connection position in the finite element model.
3. The rapid stress assessment method for trolley frame angular structures based on adaptive response surface model according to claim 1, characterized in that, In step 1, the key parameters include: the thickness t1 of the trolley frame angled structure bending plate, the radius r of the bending plate arc, and the thickness t2 of the web plate.
4. The rapid stress assessment method for a trolley frame angle structure based on adaptive response surface model according to claim 1, characterized in that, In step 2, the output variable is the maximum stress at the arc connection of the angular structure.
5. The rapid stress assessment method for trolley frame angular structures based on adaptive response surface model according to claim 1, characterized in that, In step 2, the Latin hypercube sampling method is used to extract samples, ensuring that the sample variables are uniform and independent, thus achieving higher estimation accuracy.
6. The rapid stress assessment method for a trolley frame angle structure based on adaptive response surface model according to claim 1, characterized in that, In step 2, the sample data are data pairs in the sample variable space where the input variables and output variables correspond one-to-one.
7. The rapid stress assessment method for a trolley frame angle structure based on adaptive response surface model according to claim 1, characterized in that, In step 4, the surrogate model adopts the RSM model to obtain a polynomial approximation model of the input and output variables; single-factor stress surrogate models M1(t1), M2(t2), M3(r) and multi-factor stress surrogate model M4(t1,t2,r), with sample matrix S={t 1m ,t 2n ,r q ,σ mnq };t 1m t 2n r q Let σ represent a single data point from t1, t2, and r respectively. mnq For t 1m t 2n r q The maximum stress at the arc connection of the corresponding angular structure.
8. The rapid stress assessment method for a trolley frame angle structure based on adaptive response surface model according to claim 1, characterized in that, In step 5 of the process of modifying the multi-factor-stress surrogate model, the weights of each coefficient in the model are determined based on the single-factor-stress surrogate model. A sparse screening method is used to remove redundant terms with small weights in the multi-factor-stress surrogate model and optimize the multi-factor-stress surrogate model.
9. The rapid stress assessment method for a trolley frame angle structure based on adaptive response surface model according to claim 1, characterized in that, In step 5, during the process of correcting the multi-factor-stress surrogate model, the physical constraints of the single-factor-stress surrogate model are extracted, the physical constraints are embedded into the alternating direction multiplier algorithm, the anti-interference coefficients that satisfy the physical constraints are obtained, and the multi-factor-stress surrogate model is further corrected.
10. The rapid stress assessment method for a trolley frame angular structure based on adaptive response surface model according to claim 1, characterized in that, Furthermore, in step 5, during the process of modifying the multi-factor-stress surrogate model, a dynamic equilibrium iterative weight adjustment mechanism is constructed.