Multi-objective optimization method for structural size of portable gantry crane

Abstract

The invention discloses a portable gantry crane structure size multi-objective optimization method, which comprises the following steps of: (1) establishing a portable gantry crane structure parameterization finite element model by taking the cross section size of a main bearing component of a gantry crane as a design variable, and preprocessing the portable gantry crane structure parameterization finite element model; (2) generating a sample point data set by adopting an optimal space filling design of a maximum and minimum distance criterion; (3) increasing parameter boundary sample points; (4) parameter correlation analysis and sensitivity analysis are carried out, and design variables are screened; (5) constructing a Kriging response surface of the structural quality, the safety coefficient and the deformation of the portable gantry crane; and (6) carrying out multi-objective optimization on the structure size of the gantry crane by adopting a multi-objective genetic algorithm and taking the structure quality as an important objective and the safety coefficient and the deformation as secondary objectives. Parameter boundary sample points are added to avoid optimal space filling design defects, a Kriging model is adopted to improve efficiency, and a multi-target genetic algorithm is adopted to realize multi-target optimization of structural quality, safety coefficient and deformation.

Description

Technical Field

[0001] The present invention relates to a multi-objective size optimization method, and particularly to a multi-objective size optimization method for a portable gantry crane based on a Kriging response surface, belonging to the technical field of structural size optimization. Background Art

[0002] As a light and flexible lifting equipment, the portable gantry crane is widely used in construction sites, warehouses, workshops and other places for material handling, equipment installation and maintenance operations. Its structure usually consists of components such as columns, beams, legs, and traveling mechanisms, and has the characteristics of simple structure, convenient disassembly and assembly, and flexible movement. In the traditional design of portable gantry cranes, in order to meet the load-bearing requirements under different working conditions, larger structural sizes are often adopted, resulting in heavy equipment, inconvenient transportation and installation, and it is difficult to give full play to the advantages of portable gantry cranes; traditional designs mostly rely on empirical formulas or single-objective optimization, and it is difficult to comprehensively consider multiple factors such as structural strength, stiffness, stability, weight, and cost, resulting in the design scheme being difficult to achieve the optimum; the traditional design process is cumbersome, requiring a large amount of manual calculations and experimental verifications, with a long design cycle and high costs, and it is difficult to meet the rapidly changing market demands.

[0003] In recent years, with the development of computer technology and optimization algorithms, structural size optimization methods have been widely used in engineering design. However, when the existing structural size optimization methods are applied to the design of portable gantry cranes, there are still some deficiencies. The traditional optimization method based on finite element analysis requires a large number of iterative calculations, with low computational efficiency and difficulty in meeting the actual engineering requirements; the design of portable gantry cranes needs to consider multiple conflicting objectives, such as structural weight, safety factor, deformation amount, etc., and the traditional optimization methods are difficult to effectively handle multi-objective optimization problems; moreover, the traditional optimization methods usually assume that the model is deterministic and ignore the uncertainty of model parameters, resulting in possible deviations in the optimization results. Summary of the Invention

[0004] Aiming at the deficiencies of the existing structural size optimization methods for portable gantry cranes, such as low computational efficiency, difficulty in handling multi-objective optimization problems, and lack of consideration of model uncertainty, the present invention proposes a multi-objective size optimization method for a portable gantry crane based on a Kriging response surface. This method takes the cross-sectional sizes of the main load-bearing members of the gantry crane as design variables, establishes a parametric finite element model of the portable gantry crane structure, generates sample point data through the best space filling design with the maximum minimum distance criterion, and adds a boundary sample band to make up for sampling defects, completes parameter correlation analysis and sensitivity analysis, screens the design variables, reduces the dimension of the optimization problem, constructs a high-precision Kriging response surface, and combines with a multi-objective genetic algorithm to achieve efficient and reliable optimization of the structural size of the portable gantry crane.

[0005] The multi-objective optimization method for the structural dimensions of a portable gantry crane includes the following steps: (1) Taking the cross-sectional dimensions of the main load-bearing members of the gantry crane as design variables, establishing a parametric finite element model of the portable gantry crane structure and preprocessing it; (2) Generating a sample point data set using the optimal space-filling design based on the maximum-minimum distance criterion; (3) Adding parameter boundary sample points; (4) Conducting parameter correlation analysis and sensitivity analysis and screening the design variables; (5) Constructing Kriging response surfaces for the structure mass, safety factor, and deformation of the portable gantry crane; (6) Using a multi-objective genetic algorithm, taking the structure mass as the primary objective and the safety factor and deformation as secondary objectives, to conduct multi-objective optimization of the gantry crane structure dimensions.

[0006] The beneficial technical effects of the present invention: (1) After generating a sample point data set using the optimal space-filling design based on the maximum-minimum distance criterion, adding parameter boundary sample points to the sample point data set, that is, sample points where the design variables take upper and lower limit values, compensates for the defect that the optimal space-filling design cannot obtain boundary sample points, avoids large errors in the Kriging response surface in the boundary region, and improves the prediction accuracy of the model; (2) Using the Kriging response surface to construct the mapping relationship between the design variables and the objective function, verifying its high-precision characteristics, providing a reliable basis for the optimization design, effectively reducing the influence of model uncertainty on the optimization results. Avoiding a large number of finite element iterative calculations significantly improves the calculation efficiency; (3) Using a multi-objective genetic algorithm can simultaneously optimize multiple objective functions, obtain the Pareto optimal solution set, provide multiple design scheme options. Through multi-objective optimization, under the premise of meeting the constraint conditions, multi-objective optimizations such as the lightest structure weight and the lowest cost can be achieved, thereby improving the performance and market competitiveness of the portable gantry crane. Description of the Drawings

[0007] Figure 1 is the flowchart of the multi-objective optimization method for the structural dimensions of the portable gantry crane of the present invention; Figure 2 is the working state of the unfolded portable gantry crane structure of the present invention; Figure 3 is the folded and stored state of the portable gantry crane structure of the present invention; Figure 4 is the correlation matrix diagram of the parameter correlation analysis of the present invention; Figure 5 is the sensitivity analysis result of the gantry crane design variables and output responses of the present invention; Figure 6 is the response surface model of the key design variables and output responses of the present invention; Figure 7 is the Kriging response surface quality verification result of the present invention; Figure 8 is the Pareto front of the output responses after multi-objective optimization of the present invention; Figure 9 is the finite element verification data result of the optimization candidate points of the present invention. Detailed implementation manners

[0008] Combined with the attached Figures 1 to 8 , illustrate the steps and specific operations of the present invention.

[0009] The present invention conducts multi-objective size optimization on a portable gantry crane, establishes a parametric finite element model, constructs a mapping relationship between design variables and objective functions by using the efficient surrogate model Kriging response surface, and completes the multi-objective size optimization of the portable gantry crane by using a multi-objective genetic algorithm. The working state and folding state of the mechanical structure of the portable gantry crane in the optimization example are as Figure 2 , Figure 3 shown.

[0010] The multi-objective size optimization method for the structure size of a portable gantry crane includes the following steps: (1) Taking the cross-sectional sizes of the main load-bearing members of the gantry crane as design variables, establishing a parametric finite element model of the portable gantry crane structure and preprocessing it; (2) Generating a sample point data set by using the best space filling design with the maximum minimum distance criterion; (3) Adding parameter boundary sample points; (4) Conducting parameter correlation analysis and sensitivity analysis and screening design variables; (5) Constructing Kriging response surfaces for the structure quality, safety factor, and deformation of the portable gantry crane structure; (6) Using a multi-objective genetic algorithm, taking the structure quality as the important objective and the safety factor and deformation as the secondary objectives, to conduct multi-objective optimization on the structure size of the gantry crane.

[0011] The operation process of the multi-objective size optimization method for the structure size of the portable gantry crane of the present invention is as follows: 1. Establishing a parametric finite element model of the portable gantry crane structure and preprocessing it (1) Determining design variables: Determining the main load-bearing members of the portable gantry crane and the parts that have a greater impact on the structure quality, including columns, main beams, legs, connecting plate members, etc., and taking the cross-sectional sizes of these members as design variables.

[0012] (2)Determine the range of design variables: According to national standards and design requirements, determine the value range of each design variable. Note that the national standard requires that the minimum thickness of the load-bearing metal structure of the crane is not less than 3 mm. For each design variable, determine its upper and lower limits. For example, the range of the inner width of the inclined leg is set between 88 mm and 94 mm. The main design variables and their upper and lower limits of the example portable gantry crane are shown in Table 1.

[0013]

[0014] (3)Construct a parametric finite element model: Use the 3D modeling software SolidWorks to complete the initial model construction of the portable gantry crane. Connect SolidWorks with the finite element analysis software ANSYS. In SolidWorks, perform parametric settings for parts. When creating features, modify the format of their feature names and part dimension parameter names. Add the "DS-" identification code prefix before the dimension parameter names of the design variables. For the design variables corresponding to the feature dimensions, call the tool equation in the overall structure model, set global variables, add identification code information and assign values, and delete the initial feature settings. Enter in the form of global variables in the dimension input. Open ANSYS Workbench from the SolidWorks plug-in, select the Static Structural module, import the geometric model, and then start Mechanical. In the geometric structure control, select the CAD parameters set for the parts to generate a parameter set and establish a parametric finite element model of the portable gantry crane.

[0015] (4)Model preprocessing: Establish a custom material property library in the engineering data source of the Static Structural module in ANSYS Workbench, add properties such as elastic modulus, Poisson's ratio, and density of materials such as aluminum alloy 6061T6, 6063T5, 6063T6, and 7075, and assign the corresponding materials to the parts in the parametric finite element model. Use solid elements for meshing, set the contact between connectors as rigid connection, perform adaptive mesh division on the gantry crane structure, adjust the mesh size to 15 mm, apply boundary conditions with the leg grounding support surface as the fixed constraint. Determine the load state according to national standards and the design requirements of the gantry crane. Take the dangerous working condition as the design analysis standard, add a standard gravity field, add a load of 9800 N to the hook section at the mid-span of the main beam, calculate and add wind load according to national standard requirements, and add uniformly distributed loads of 310 N and 160 N to the main beam and each leg.

[0016] 2. Generate a sample point data set using the optimal space filling design (1)Set the maximum and minimum distance criteria: In ANSYS Workbench, use the Design of Experiments module, select the "Optimal Space-Filling Design" method, and set the Maximin Distance Criterion to ensure that the generated sample points are evenly distributed within the design space, avoiding over-concentration or sparsity of sample points.

[0017] (2)Generate a sample point data set: Determine the number of generated sample points according to the number and complexity of design variables. The number of sample points should be large enough to ensure the accuracy of the subsequent Kriging response surface. In this example, 200 sets of sample points are generated within the design space for the portable gantry crane. Run the DOE module in ANSYS to generate a sample point data set, where each sample point corresponds to a set of design variable value combinations.

[0018] (3)Define the output response: Define the output response in ANSYS, that is, the optimization objective function. Use the mass, safety factor, and deformation of the gantry crane structure as the output responses and add them to the parameter set for use in subsequent analyses.

[0019] (4)Calculate sample point data: The hardware configuration used in the present invention is CPU: Intel Core i7-12700H; CPU main frequency: 2.69 GHz; memory: 16G; GPU: NVIDIA GeForce GTX 1660 Ti. In ANSYS, run finite element simulations for each generated sample point to calculate its output response, and export the design variable values and corresponding output responses of each sample point as a CSV format file.

[0020] 3. Add sample points for parameter boundaries (1)Generate boundary sample points: Determine the sample point boundaries according to the upper and lower bound values of the design variables. Use the DOE module, change the random generator seed setting to 3 to prevent duplication with the sample points generated by the optimal space-filling design, generate 50 sets of sample points, export the generated design variable data as a CSV format file, change the single design variable of the sample points in the output CSV file to be close to its upper and lower bound values, and keep the other parameters unchanged. Each set of sample points in the modified file has design variables close to their boundaries, and save the modification.

[0021] (2)Calculate sample point data: In ANSYS, customize the design points, import the design variable data of the modified boundary sample points from the CSV format, run finite element simulations to calculate their output responses, and output the result CSV data.

[0022] (3) Custom sample data set: Design the custom experiment type, import the CSV data table of boundary sample points and the CSV data table generated by the optimal space filling design of the maximum and minimum distance criteria, and use it as the overall data set for subsequent analysis.

[0023] 4. Conduct parameter correlation analysis and sensitivity analysis and screen design variables (1) Correlation matrix calculation: In ANSYS Workbench, import the previously generated sample point data set, which contains design variables and corresponding output responses (structural mass, safety factor, deformation), select the "Design of Experiments" (DOE) module, enter the "Parameter Correlation" tool, and select the Spearman correlation coefficient as the correlation analysis method. The Spearman correlation coefficient is applicable to non-normal distribution data and can effectively evaluate the non-linear relationship between design variables and output responses. Its calculation formula is: , where r s is the Spearman correlation coefficient, R X and R Y are the ranks of variables X and Y respectively, Cov( R X , R Y ) is the covariance of R X and R Y , σ RX and σ RY are the standard deviations of variables R X and R Y respectively, d is R X and R Y is the rank difference of Figure 4 as shown.

[0024] ​​(2) Sensitivity analysis: In ANSYS Workbench, select the "Sensitivity Analysis" tool, choose the local sensitivity analysis method, calculate the partial derivatives of the design variables at the reference point, evaluate the influence degree of each design variable on the output response. Taking the dimension parameters of the gantry crane as the input variables and the mass, safety factor, and deformation of the gantry crane as the output variables, select the initial sample point data as the reference point, run the sensitivity analysis, calculate the sensitivity coefficients of each design variable to the output response, normalize the sensitivity coefficients, and judge the influence degree of each parameter on the output response. The parameter sensitivity results obtained for the portable gantry crane are as Figure 5 shown.

[0025] (3) Parameter screening: Select the design variables that have a significant impact on the objective function according to the values of the Spearman correlation coefficient and the sensitivity coefficient. Among the design variables of the portable gantry crane, the lengths of the 0-8 branch pipes, the inner circle 1 diameter of the 0-10 support plates, and the thickness of the 0-10 support plates have extremely small impacts on the output response in the parameter correlation analysis and sensitivity analysis, and are non-important design variables, which can be ignored in the subsequent optimization operations to reduce the dimension of the optimization problem.

[0026] 5. Construct the Kriging response surface of the portable gantry crane (1) Kriging response surface construction: In ANSYS Workbench, select the "Response Surface" module, enter the "Kriging Model" tool, and use the sample point data to construct the Kriging response surfaces of the structural mass, safety factor, and deformation of the portable gantry crane in the finite element analysis software. The type of kernel variable is set to variable, and its fitting result can capture the global trend of the input variables on the structural mass, improving the fitting accuracy of the model. Use the sample point data set to train the Kriging response surface. According to the input design variables and output responses, automatically construct the Kriging response surface. During the training process, the Kriging response surface will fit the mapping relationship between the design variables and the output responses, generating a high-precision response surface.

[0027] (2) Response surface quality verification: Use Goodness of Fit to evaluate the quality of the response surface, and use the root mean square error, relative maximum absolute error, and relative mean absolute error to evaluate the fitting quality of the response surface. Customize and introduce three verification points that are not included in the experimental design and cover different regions of the design space, calculate the response output and predicted output of the verification points, normalize the values of the response surface prediction points and the verification points, and verify the goodness of fit of the response surface. The results are as Figure 7As shown, the maximum value of the verified root mean square error is controlled within 0.06, the relative maximum absolute error does not exceed 5%, and the relative average absolute error is limited within 3%. The response surface has high quality and accurate prediction, and can be used for subsequent optimization calculations.

[0028] 6. Use the multi-objective genetic algorithm to perform multi-objective optimization on the structure size of the gantry crane (1)Select the optimization algorithm: The present invention uses the MOGA method (multi-objective genetic algorithm), a variant of the popular NSGA-II (Non-dominated Sorting Genetic Algorithm II) based on the concept of controlled elitism, for multi-objective optimization calculations. It supports multiple objectives and constraints and searches for the global optimal solution.

[0029] (2)Determine the optimization objectives: According to the actual design requirements, the structure mass of the gantry crane is taken as the important optimization objective, and the safety factor and deformation amount are taken as the secondary optimization objectives.

[0030] (3)Set the algorithm parameters: Use the MOGA algorithm for optimization. The initial sample number and the sample number for each iteration are set to 1000. The maximum allowable Pareto percentage is 70 to retain more Pareto optimal solutions and improve the diversity of the optimization results. The convergence stability percentage is 2, the maximum number of iterations is 20, the maximum number of candidates is 3, the crossover probability is 0.9, and the mutation probability is 0.1.

[0031] (4)Iteratively run the calculation: Run the multi-objective genetic algorithm. After 9 iterations and 8860 times of objective evaluation, the result converges. The Pareto percentage is 0.1 and the stability percentage is 1.53. The obtained Pareto optimal solution set is as Figure 8 shown.

[0032] (5)Result analysis and verification: Analyze the generated candidate points, select the candidate point with the minimum mass, and select the candidate point with better other indicators when the masses are the same. Perform simulation verification on the candidate points, change the parametric model with it as the design point, and compare the key indicators such as the safety factor, deformation condition, and weight with the traditional design and the theoretical expected values to ensure the reliability and safety of the optimization results in practical applications. The verification results are as Figure 9 shown. The final result shows that the safety factor decreases by 5.4%, the deformation amount of the main girder increases by 5.6%, and the mass decreases by 10.3%. While meeting the national standard requirements, the structural lightening is achieved through multi-objective size optimization.

Claims

1. A multi-objective optimization method for the structural dimensions of a portable gantry crane is used for the lightweight design of a portable gantry crane, and includes the following steps: (1) Taking the cross-sectional dimensions of the main load-bearing components of the gantry crane as the design variables, a parametric finite element model of the portable gantry crane structure was established and preprocessed; (2) Generate a sample point data set using the optimal space filling design based on the maximum and minimum distance criteria; (3) Add boundary sample points for taking upper and lower limit values ​​of design variables; (4) Perform parameter correlation analysis and sensitivity analysis, and screen design variables based on the values ​​of the Spearman correlation coefficient and sensitivity coefficient; (5) Construct the Kriging response surface of the portable gantry crane's structural mass, safety factor, and deformation; (6) A multi-objective genetic algorithm is used to optimize the structural dimensions of the gantry crane with structural quality as the main objective and safety factor and deformation as secondary objectives.

2. The multi-objective optimization method for the structure size of a portable gantry crane according to claim 1 is characterized in that: The design variables of step (1) are selected from the main load-bearing components of the portable gantry crane, including columns, main beams, legs, connecting plates, and the cross-sectional dimensions of the parts that have a greater impact on the structural quality. The value range of each design variable is determined according to national standards and design requirements. The dangerous working condition is used as the design analysis standard, a standard gravity field is added, and the wind load is calculated and added according to the national standard requirements.

3. The multi-objective optimization method for the structure size of a portable gantry crane according to claim 1 is characterized in that: The data set for correlation analysis in step (4) contains the output responses corresponding to the design variables and structural quality, safety factor, and deformation. The calculation formula is: ,in r s is the Spearman correlation coefficient, R X and R Y The variables are X and Y The rank of Cov( R X , R Y )yes R X and R Y The covariance of σ RX and σ RY The variables are R X and R Y The standard deviation of d yes R X and R Y The rank difference of .

4. The multi-objective optimization method for the structure size of a portable gantry crane according to claim 1 is characterized in that: The initial sample number and iteration number of the multi-objective genetic algorithm in step (6) are adjusted according to the computing resources, with the maximum allowed Pareto percentage of 70, the convergence stability percentage of 2, the maximum number of candidates of 3, the crossover probability of 0.9, and the mutation probability of 0.1.

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