Optimization analysis method of steel structure frame

Abstract

The invention discloses an optimization analysis method for a cold box steel structure frame, which comprises the following steps of: 1, establishing a steel structure frame finite element analysis model, performing statics analysis on a target steel structure, and determining a target needing to be optimized and structure parameters of the target structure; 2, finite element analysis is carried out, and a constraint function of each optimization target is determined; 3, designing a sensitivity relationship between the structural parameters and a calculation result according to a finite element calculation result, generating an experimental group, and designing a change range of the structural size according to the sensitivity to generate a plurality of sample experimental groups; 4, constructing a difference algorithm model, and substituting the plurality of experimental groups into the optimization analysis model according to the constraint function to obtain a response relationship between the change of each sample and the change of the target function in the optimization process; and 5, carrying out multi-target optimization on the model by adopting a genetic algorithm, and modifying the structure size of each target structure to achieve the optimal combination of the structure parameters.

Description

Technical Field

[0001] This invention relates to the field of optimization design and analysis technology for steel structures of cold boxes, and in particular to an optimization analysis method for steel structure frames. Background Technology

[0002] An air separation cold box, also known as an air separation cold box, is a device used for gas separation. It is a landmark project of air separation plants, primarily used to separate gases such as oxygen and nitrogen from the air. It is widely used in industrial production and scientific research. The cold box consists of two parts: an internal core air separation unit and a large steel-shell insulated box. The external steel-shell insulated box has a steel frame structure. Steel frame structures are a common type of steel structure used in Chinese construction. As a modern building structure, compared to other materials, it has advantages such as high strength, high rigidity, high stability, and light weight, making it suitable for high-rise building structural systems.

[0003] Currently, most steel structure design software does not adopt optimized design while meeting the requirements of the national design code GB-50017, thus ignoring the principle of economy (optimization). The existing optimized design schemes also have imperfections, such as the incompatibility between the load-bearing capacity of components and the internal calculation mode of the structure, and the inability to predict the load-bearing capacity of the overall structure.

[0004] Currently, structural optimization in theory is divided into size optimization, shape optimization, and topology optimization. Structural optimization does not simply minimize the geometric parameters of individual components, but rather adjusts the relationships between these components to an optimal state, ensuring that the geometric parameters of each structure reach their optimal values ​​while satisfying certain predetermined constraints. Steel structure optimization design is a systematic and complex task. The design concept needs to be clear and explicit, and the selection of structural forms must conform to reality. Therefore, after the initial design in steel structure design software, optimization design is added to improve the practical performance of steel and better meet the requirements of engineering construction. This is precisely the necessity of optimizing steel structures. Summary of the Invention

[0005] To address the aforementioned technical problems in existing technologies, this invention proposes an optimization analysis method for steel structure frames. A finite element analysis model of the steel structure frame is established, the influence of different structural dimensions on the response structural quality is investigated, a prediction model is established using the Kriging interpolation method, and a genetic algorithm is employed for multi-objective optimization of the frame structure.

[0006] An optimization analysis method for steel structure frames includes the following steps:

[0007] Step 1: Based on CAE technology, establish a finite element analysis model of the steel structure frame, perform static analysis on the target steel structure, and determine the target to be optimized and the structural parameters of the target structure.

[0008] Step 2: Perform finite element analysis on the steel structure frame of the cold box under relevant working conditions, obtain the convergence criteria based on the calculation results, and determine the constraint functions of each optimization objective;

[0009] Step 3: Based on the finite element calculation results, design the sensitivity relationship between the structural parameters and the calculation results through Box-Behnken experiments. Generate an experimental group using the initial size parameters of the structural parameters, and then design the variation range of the structural dimensions according to the sensitivity to generate multiple sample experimental groups.

[0010] Step 4: Construct the Kriging difference algorithm model. Based on the constraint function set in Step 2 and the multiple experimental groups designed in Step 3, the response relationship between the changes in the sample experiment and the changes in the objective function can be obtained.

[0011] Step 5: Use a genetic algorithm to perform multi-objective optimization on the Kriging model, and modify the structural dimensions of each objective structure to achieve the optimal combination of various structural parameters.

[0012] Furthermore, step one includes the following steps:

[0013] Static analysis of the target structure was performed using finite element simulation software. The components to be optimized were selected, and their structural dimensions and mass were recorded. The structural dimensions were used as design variables, which were independent variables, represented as: x = (x1 x2 … x n ) T The quality of the target structure is taken as the optimization objective and expressed as y = y(x);

[0014] Furthermore, step two includes the following steps:

[0015] The structural calculation results, such as the maximum tensile stress, maximum compressive stress, and maximum deformation of the entire structure, obtained from finite element analysis, are used as constraint functions for the constraint optimization objective. These functions can be expressed as s. imin <<s i (x) << s imax ;

[0016] Furthermore, step three includes the following steps:

[0017] Based on finite element method (FEM) calculations, a sensitivity relationship between structural parameters and calculation results was designed using a Box-Behnken experiment. The structural parameters include the length, width, and thickness of the structure. An experimental group was generated based on the range of parameter variations. Multiple sample experimental groups were then generated by designing various ranges of variation for the structural dimensions according to the sensitivity. These sample experimental groups formed the correlation matrix of the correlation function for known points, R = R(x). n ) T .

[0018] Furthermore, step four includes the following steps:

[0019] The objective function of the Kriging prediction model is as follows:

[0020]

[0021] Where F(x) represents the objective function with variable x; ω represents the weighting coefficient of the objective function; y represents the response exponent related to variable x; the weighting coefficient ω can be regarded as a Gaussian static random process, and its expression is:

[0022] Y(x) = β0 + Z(x)

[0023] Where Y(x) represents the predicted value of the Kriging prediction model; β0 is the correlation coefficient, representing the expected value of Y(x); Z(x) is a Gaussian static random function with a mean of zero and a variance expression of:

[0024]

[0025] Where, σ 2 Indicates process variance;

[0026] The spatial covariance function of Z(x) is:

[0027]

[0028] Among them, Cov(z(x) i ),z(x j R represents the covariance of Z(x); R represents the correlation function, whose value is inversely proportional to the distance, and is 0 when the distance is infinitely far; R(x) i ,x j θ represents the correlation function between any two predicted values. n Represents the correlation coefficient; x represents i The nth component; x represents j The nth component, where n represents the kth dimension of the design variable;

[0029] Based on the obtained experimental data, the regression coefficients and correlation coefficients are calculated, and the predicted values ​​and their root mean square errors for unknown points are determined. The functional expression is as follows:

[0030]

[0031]

[0032] β=(F T R -1 F) -1 F T R -1 y,

[0033] Where, x * To represent an unknown point, Represented as x * The predicted value at that location; R represents the estimated regression coefficients; R represents the correlation function between known points; R -1 represents the inverse of the correlation matrix between known points; y represents the observed response vector, which is the mass value of the target structure in the finite element simulation results; s 2 (x * ) represents the predicted value x * The mean squared error at point n; p represents a column vector containing component n0; p T represents the transpose of the design matrix; r represents the correlation vector between x and other sample points.

[0034] The above calculations can predict the response relationship between changes in the experimental samples and the objective function.

[0035] Furthermore, step five, the genetic algorithm optimization process, includes the following steps:

[0036] Step 5.1: Obtain the length, width, and thickness parameters of the target structure to be optimized to obtain the initial individual;

[0037] Step 5.2: Use Latin hypercube sampling to randomly generate the initial population;

[0038] Step 5.3: Eliminate individuals that do not meet the nonlinear constraints through constraint functions to ensure that all individuals in the population are in the initial population;

[0039] Step 5.4: Using the target structure quality predicted by the Kriging model as the objective, construct a normalized multi-objective fitness function, evaluate the normalized multi-objective fitness function, and select excellent individuals from the first generation.

[0040] Step 5.5: Based on the principle of survival of the fittest, select the best individuals to generate the second generation of individuals;

[0041] Step 5.6: Perform mutation and crossover on the second-generation individuals to generate the next generation of individuals;

[0042] Step 5.7: Repeat steps 5.3 to 5.6 until the maximum number of iterations is reached or convergence is achieved;

[0043] 1. The multi-objective optimization analysis method for a steel structure frame according to claim 6, characterized in that the initial population size is set to 5000, the maximum number of iterations is 100, the chromosome dimension is N, the number of samples in each iteration is 1000, the crossover probability P = 0.97, and the mutation probability is 0.01.

[0044] The present invention can achieve the following beneficial effects:

[0045] 1) By finite element simulation calculation of relevant parameters of steel structure frame, the corresponding objective function and constraint conditions were obtained. The sensitivity relationship between parameters and calculation results was analyzed by Box-Behnken experimental design. The analysis found that the size of the beam has a greater impact on compressive stress, and the size of the diagonal brace has a greater impact on tensile stress.

[0046] 2) Based on the Kriging difference algorithm, in addition to the Kriging prediction model of the objective function of the cold box steel structure frame, a genetic algorithm was used to optimize the upper beam, lower beam and diagonal bracing for multiple objectives. Finally, the optimal combination of structural parameters was obtained. The total mass of the optimized structure was significantly reduced, which improved the economy of the project. Attached Figure Description

[0047] The accompanying drawings, which constitute a part of this invention, 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 undue limitation of the invention. In the drawings:

[0048] Figure 1 This is a flowchart of the cold box steel structure optimization analysis method provided in the embodiments of the present invention;

[0049] Figure 2 This is the finite element analysis model of the cold box steel structure optimization analysis method provided in the embodiments of the present invention;

[0050] Figure 3 This is a load diagram of the cold box steel structure frame under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0051] Figure 4 This is the maximum tensile-compressive stress cloud diagram of the cold box steel structure frame under full load conditions, provided by the cold box steel structure optimization analysis method in this embodiment of the invention.

[0052] Figure 5This is the maximum deformation cloud map of the cold box steel structure frame under full load conditions, provided by the cold box steel structure optimization analysis method in this embodiment of the invention.

[0053] Figure 6 This diagram shows the tensile-compressive stress cloud diagram of the upper crossbeam of the cold box steel structure frame under wind pressure conditions.

[0054] Figure 7 This diagram shows the tensile-compressive stress cloud diagram of the lower crossbeam of the cold box steel structure frame under wind pressure conditions.

[0055] Figure 8 This diagram shows the tension-compression stress cloud diagram of the diagonal bracing of the steel frame of the cold box under wind pressure conditions.

[0056] Figure 9 This diagram shows the tensile-compressive stress contours of the main beams of the cold box steel structure frame under wind pressure conditions.

[0057] Figure 10 This is a sensitivity diagram of the upper crossbeam size and maximum deformation under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0058] Figure 11 This is a sensitivity diagram of the upper beam dimensions and maximum tensile stress under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0059] Figure 12 This is a sensitivity diagram of the upper beam dimensions and maximum compressive stress under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0060] Figure 13 This is a sensitivity diagram of the lower section beam size and maximum deformation under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0061] Figure 14 This is a sensitivity diagram of the lower section beam dimensions and maximum tensile stress under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0062] Figure 15 This is a sensitivity diagram of the lower section beam dimensions and maximum compressive stress under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0063] Figure 16 This is a sensitivity diagram of the diagonal support dimensions and maximum deformation under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0064] Figure 17This is a sensitivity diagram of the diagonal support dimensions and maximum tensile stress under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0065] Figure 18 This is a sensitivity diagram of the diagonal support dimensions and maximum compressive stress under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0066] Figure 19 This is a spatial response surface diagram showing the relationship between the upper crossbeam dimensions and maximum deformation under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0067] Figure 20 This is a spatial response surface diagram showing the relationship between the upper beam dimensions and the maximum tensile stress under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0068] Figure 21 This is a spatial response surface diagram showing the relationship between the upper beam dimensions and the maximum compressive stress under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0069] Figure 22 This is a spatial response surface diagram showing the relationship between the dimensions of the lower crossbeam and the maximum deformation under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0070] Figure 23 This is a spatial response surface diagram showing the relationship between the dimensions of the lower crossbeam and the maximum tensile stress under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0071] Figure 24 This is a spatial response surface diagram showing the relationship between the dimensions of the lower crossbeam and the maximum compressive stress under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0072] Figure 25 This is a diagram showing the planar response relationship between the diagonal support dimensions and the maximum deformation under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0073] Figure 26 This is a plane response diagram showing the relationship between the diagonal support dimensions and the maximum tensile stress under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0074] Figure 27 This is a plane response diagram showing the relationship between the diagonal support dimensions and the maximum compressive stress under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0075] Figure 28This is the maximum deformation cloud map of the optimized steel structure frame under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0076] Figure 29 This is the maximum tensile-compressive stress cloud diagram of the optimized steel structure frame under full load conditions, based on the cold box steel structure optimization analysis method provided in this embodiment of the invention.

[0077] Figure 30 This is a flowchart of a genetic algorithm provided according to an embodiment of the present invention. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the described embodiments are merely some, not all, of the embodiments of this invention. The specific embodiments described herein are for illustrative purposes only and do not constitute a limitation thereof.

[0079] The invention will now be described in detail with reference to specific embodiments.

[0080] like Figures 1 to 30 As shown in the figure, an optimization analysis method for a cold box steel structure frame provided by an embodiment of the present invention includes the following steps:

[0081] Step 1: Based on CAE (Computer-Aided Engineering) technology, model the structure using CAD software, then import it into finite element analysis software, assign element properties, and establish the corresponding finite element analysis model of the steel structure frame (e.g., Figure 2 (As shown), determine the target to be optimized and the structural parameters of the target structure;

[0082] Step Two: Apply wind pressure loads to the cold box steel structure frame and perform finite element analysis. Based on the finite element analysis model of the cold box steel structure frame established in Step One, apply full constraints to the bottom of the cold box steel structure model to fix the model. Apply corresponding wind loads to the windward side, leeward side, and both sides of the cold box. Apply live load and dead load to the top of the cold box. Apply perlite load and nitrogen pressure load (e.g., ...) inside the cold box. Figure 3 As shown), the maximum tensile-compressive stress contour diagram is obtained based on the calculation results (as shown). Figure 4 (As shown) to determine the maximum stress value and its distribution location of the cold box steel structure frame, and the maximum deformation cloud map of the structure (as shown). Figure 5 (As shown) to determine the maximum deformation value and location of the cold box steel structure frame, thereby determining the optimization constraints. Based on the maximum stress value and distribution location of each load-bearing main beam of the cold box steel structure frame under wind pressure conditions, the optimization objective and optimization parameters are determined. Figures 4 to 9 As shown

[0083] Figure 4 The diagram shows the maximum tensile-compressive stress cloud diagram of the steel structure frame of the cold box under wind pressure conditions. The maximum tensile stress is 152.24 MPa and the maximum compressive stress is 166.61 MPa.

[0084] Figure 5 The diagram shows the maximum deformation of the steel frame of the cold box under wind pressure conditions, with a maximum deformation of 207.01 mm.

[0085] Figure 6 The diagram shows the tensile-compressive stress cloud diagram of the upper crossbeam of the cold box steel structure frame under wind pressure conditions. The maximum tensile stress is 7.31 MPa and the maximum compressive stress is 5.33 MPa.

[0086] Figure 7 The diagram shows the tensile-compressive stress cloud diagram of the lower crossbeam of the cold box steel structure frame under wind pressure conditions. The maximum tensile stress is 32.37 MPa and the maximum compressive stress is 13.98 MPa.

[0087] Figure 8 The diagram shows the tensile-compressive stress cloud diagram of the diagonal support of the cold box steel structure frame under wind pressure conditions. The maximum tensile stress is 34.04 MPa and the maximum compressive stress is 17.89 MPa.

[0088] Figure 9 The diagram shows the tensile-compressive stress cloud diagram of the main beam of the cold box steel structure frame under wind pressure conditions. The maximum tensile stress is 152.24 MPa and the maximum compressive stress is 166.61 MPa.

[0089] As can be seen from the above, the main beam bears more tensile and compressive stress, while the upper and lower crossbeams and the diagonal support bear less tensile and compressive stress, indicating room for optimization. Therefore, the mass of the upper and lower crossbeams and the diagonal support are taken as optimization targets. The upper crossbeam is a hollow square tube with a cross-sectional dimension of 250*250*8, the lower crossbeam is a hollow square tube with a cross-sectional dimension of 250*250*10, and the diagonal support is a hollow circular tube with a cross-sectional dimension of 168.3*8. The cross-sectional length and thickness of the upper and lower crossbeams and the outer diameter of the diagonal support are taken as optimization parameters.

[0090] Step 3: Based on the optimization objectives determined in Step 2, the sensitivity relationships between the cross-sectional parameters of the upper beam and the maximum deformation, maximum tensile stress, and maximum compressive stress are obtained through Box-Behnken experimental design (e.g., Figures 10 to 12 As shown), the sensitivity relationship between the cross-sectional parameters of the lower beam and the maximum deformation, maximum tensile stress, and maximum compressive stress (e.g.) Figures 13 to 15 As shown), the sensitivity relationship between the cross-sectional parameters of the diagonal brace and the maximum deformation, maximum tensile stress, and maximum compressive stress (e.g.) Figures 16 to 18 (As shown).

[0091] Based on the sensitivity relationships of various parameters, it can be concluded that the thickness of the upper beam has a greater positive correlation with tensile stress compared to other structural parameters, while the thickness of the lower beam has a greater negative correlation with tensile stress. The thickness of the lower beam has a greater positive correlation with compressive stress compared to other structural parameters, while the outer diameter of the diagonal brace has a greater negative correlation with compressive stress compared to other structural parameters. The thickness of the upper beam has a greater positive correlation with deformation compared to other structural parameters, while the length of the lower beam has a greater negative correlation with deformation compared to other structural parameters. Based on this, 27 experimental samples were designed (as shown in Table 1).

[0092] Table 1 Sample Experimental Design

[0093]

[0094] Step 4: Construct the Kriging interpolation algorithm to establish a prediction model. Introduce the multiple experimental groups designed in Step 3 into the optimization analysis model to obtain the response relationship between the changes of each sample and the changes of the objective function during the optimization process.

[0095] Specifically, the Kriging prediction model takes the length and thickness of the upper crossbeam, the length and thickness of the lower crossbeam, and the outer diameter of the diagonal brace as input, and predicts the maximum tensile stress, compressive stress, and deformation of the cold box steel structure frame through interpolation. The mass of the upper crossbeam, the mass of the lower crossbeam, and the mass of the diagonal brace are optimized using a multi-objective genetic algorithm. The expression for the predicted value of the Kriging prediction model is:

[0096] Y(x) = β0 + Z(x)

[0097] Where Y(x) represents the predicted value of the Kriging prediction model; β0 is the correlation coefficient, representing the expected value of Y(x); Z(x) is a Gaussian static random function with a mean of zero and a variance expression of:

[0098]

[0099] Where, σ 2 Indicates process variance;

[0100] The spatial covariance function of Z(x) is:

[0101]

[0102] Among them, Cov(z(x) i ),z(x j R represents the covariance of Z(x); R represents the correlation function, whose value is inversely proportional to the distance, and is 0 when the distance is infinitely far; R(x) i ,x jθ represents the correlation function between any two predicted values. n Represents the correlation coefficient; x represents i The nth component; x represents j The nth component, where n represents the kth dimension of the design variable. In this embodiment, n is 5.

[0103] Based on the obtained experimental data, the regression coefficients and correlation coefficients are calculated, and the predicted values ​​and their root mean square errors for unknown points are determined. The functional expression is as follows:

[0104]

[0105]

[0106] β=(F T R -1 F) -1 F T R -1 y,

[0107] Where, x * To represent an unknown point, Represented as x * The predicted value at that location; R represents the estimated regression coefficients; R represents the correlation function between known points; R -1 represents the inverse of the correlation matrix between known points; y represents the observed response vector, which is the mass value of the target structure in the finite element simulation results; s 2 (x * ) represents the predicted value x * The mean squared error at point n; p represents a column vector containing component n0; p T represents the transpose of the design matrix; r represents the correlation vector between x and other sample points.

[0108] The above calculations can predict the response relationship between the experimental sample changes and the objective function. These are: the spatial response surface diagram of the relationship between the upper beam dimensions and the maximum deformation (e.g., ...). Figure 19 (As shown); Spatial response surface diagram of the upper beam dimensions and maximum tensile stress (as shown). Figure 20 (as shown); Spatial response surface diagram of the upper beam dimensions and maximum compressive stress (as shown). Figure 21 (as shown); Spatial response surface diagram of the lower beam dimensions and maximum deformation (as shown). Figure 22 (as shown); Spatial response surface diagram of the lower beam dimensions and maximum tensile stress (as shown). Figure 23 (as shown); Spatial response surface diagram of the lower beam dimensions and maximum compressive stress (as shown). Figure 24 (as shown); A diagram showing the relationship between the dimensions of the diagonal brace and the plane response to the maximum deformation (as shown). Figure 25 (as shown); Plane response diagram of diagonal brace dimensions and maximum tensile stress (as shown). Figure 26 (as shown); Plane response diagram of diagonal brace dimensions and maximum compressive stress (as shown). Figure 27 (as shown);

[0109] Step 5: The genetic algorithm optimization process includes the following steps:

[0110] Step 5.1: The length and thickness of the upper crossbeam, the length and thickness of the lower crossbeam, and the outer diameter of the diagonal support are obtained by taking points on the response surface and using real number encoding to obtain parameterized individuals. These individuals are represented as chromosome individuals in the genetic space. Each chromosome individual is composed of multiple genes, and the gene values ​​correspond to the actual physical quantities of the optimization variables.

[0111] Step 5.2: Use Latin hypercube sampling to randomly generate the initial population.

[0112] Specifically, Latin hypercube sampling is used to randomly generate an initial population on the response surface as the initial solution to the optimization problem. The initial population size is 5000, the maximum number of iterations is 100, the chromosome dimension is 5, the number of samples in each iteration is 1000, the crossover probability P = 0.97, and the mutation probability is 0.01.

[0113] Step 5.3: Process individuals that do not meet the nonlinear constraints through constraint functions to ensure that all individuals in the population are in the initial population.

[0114] Specifically, the constraints for each chromosome within the population are verified. Constraint functions are used to handle chromosomes that do not meet the nonlinear constraints, ensuring that all individuals in the population are within the initial population. In this embodiment, the nonlinear constraints are the maximum tensile stress, maximum compressive stress, and maximum deformation of the cold box steel structure.

[0115] Step 5.4: With the quality of the Kriging prediction model as the objective, construct a normalized objective fitness function, evaluate the normalized multi-objective fitness function, and select the best individuals from the parent generation.

[0116] Specifically, with the quality of the Kriging prediction model as the objective, a normalized multi-objective fitness function is constructed to form Pareto front candidate solutions in the objective space. An elite retention strategy is adopted to extract Pareto optimal solutions from the population. The fitness of stored chromosome individuals is used as a parameter to evaluate the objective fitness function. It is used to select superior chromosome individuals from the parents.

[0117] Step 5.5: Based on the principle of survival of the fittest, select the best individuals to generate the second generation of individuals.

[0118] Step 5.6: Perform crossover and mutation on the second-generation individuals to generate the third-generation individuals.

[0119] Step 5.7: Repeat steps 5.3 to 5.4 until the maximum number of iterations or individual convergence is reached.

[0120] Compared to the original model, the overall displacement of the optimized cold box steel structure model remains unchanged (e.g., Figure 28 As shown), the optimized tensile stress change is 152.24 MPa, with an error of approximately 0.3%, and the optimized compressive stress change is 166.7 MPa, with an error of approximately 0.05% (as shown). Figure 29 (As shown). The total structural mass before optimization was 35.517 tons, and the total mass after optimization was 29.191 tons, a reduction of approximately 17.8%. Specifically, the total mass of the upper crossbeam before optimization was 10.979 tons, and after optimization it was 4.325 tons, a reduction of approximately 60.6%. The total mass of the lower crossbeam before optimization was 12.598 tons, and after optimization it was 14.928 tons, an increase of approximately 18.5%. The mass of the diagonal brace before optimization was 11.94 tons, and after optimization it was 8.938 tons, a reduction of approximately 25.1%.

[0121] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements within the theory and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A multi-objective optimization analysis method for a steel structure frame of a cold box, characterized in that... Includes the following steps: Step 1: Based on CAE technology, establish a finite element analysis model of the steel structure frame, perform static analysis on the target steel structure, and determine the target to be optimized and the structural parameters of the target structure. Step 2: Apply loads under the corresponding working conditions to the steel structure frame of the cold box and perform finite element analysis. Obtain the convergence criteria based on the calculation results and determine the constraint functions of each optimization objective. Step 3: Based on the finite element calculation results, design the sensitivity relationship between the structural parameters and the calculation results through Box-Behnken experiments. Generate an experimental group using the initial size parameters of the structural parameters, and then design the variation range of the structural dimensions according to the sensitivity to generate multiple sample experimental groups. Step 4: Construct the Kriging interpolation algorithm model. Based on the constraint function set in Step 2 and the multiple experimental groups designed in Step 3, input them into the optimization analysis model to obtain the response relationship between the changes of each sample and the changes of the objective function during the optimization process. Step 5: Use a genetic algorithm to perform multi-objective optimization on the Kriging model, and modify the structural dimensions of each objective structure to achieve the optimal combination of various structural parameters.

2. The multi-objective optimization analysis method for a steel structure frame according to claim 1, characterized in that, In step one, a static analysis of the target structure is performed using finite element simulation software. The component to be optimized is selected, and its structural dimensions and mass are read. The structural dimensions are used as design variables, which are independent variables, expressed as: x = (x1 x2 … x n ) T The quality of the target structure is taken as the optimization objective and is represented as y = y(x).

3. The multi-objective optimization analysis method for a steel structure frame according to claim 1, characterized in that, In step two, the structural calculation results, such as the maximum stress value, maximum compressive stress value, and maximum deformation value of the overall structure obtained from the finite element calculation, are used as constraint functions for the constraint optimization objective. These can be expressed as follows:

4. The multi-objective optimization analysis method for a steel structure frame according to claim 1, characterized in that, In step three, based on the finite element calculation results, a sensitivity relationship between the structural parameters and the calculation results is designed using a Box-Behnken experiment. The structural parameters include the length, width, and thickness of the structure. An experimental group is generated based on the range of parameter variations. Multiple sample experimental groups are generated by designing various ranges of variation for the structural dimensions according to the sensitivity. These sample experimental groups form the correlation matrix of the correlation function for known points, R = R(x). n ) T .

5. The multi-objective optimization analysis method for a steel structure frame according to claim 1, characterized in that, In step four, the Kriging prediction model is constructed, and its objective function formula is: Where F(x) represents the objective function with variable x; ω represents the weighting coefficient of the objective function; and y represents the response exponent related to variable x. The weighting coefficient ω can be viewed as a Gaussian static random process, and its expression is: Y(x) = β0 + Z(x) Where Y(x) represents the predicted value of the Kriging prediction model; β0 is the correlation coefficient, representing the expected value of Y(x); Z(x) is a Gaussian static random function with a mean of zero and a variance expression of: Where, σ 2 Indicates process variance; The spatial covariance function of Z(x) is: Among them, Cov(z(x) i ),z(x j R represents the covariance of Z(x); R represents the correlation function, whose value is inversely proportional to the distance, and is 0 when the distance is infinitely far; R(x) i ,x j θ represents the correlation function between any two predicted values. n Represents the correlation coefficient; x represents i The nth component; x represents j The nth component, where n represents the kth dimension of the design variable; Based on the obtained experimental data, the regression coefficients and correlation coefficients are calculated, and the predicted values ​​and their root mean square errors for unknown points are determined. The functional expression is as follows: β=(F T R -1 F) -1 F T R -1 y, Where, x * To represent an unknown point, Represented as x * The predicted value at that location; R represents the estimated regression coefficients; R represents the correlation function between known points; R -1 represents the inverse of the correlation matrix between known points; y represents the observed response vector, which is the mass value of the target structure in the finite element simulation results; s 2 (x * ) represents the predicted value x * The mean squared error at point n; p represents a column vector containing component n0; p T represents the transpose of the design matrix; r represents the correlation vector between x and other sample points.

6. The multi-objective optimization analysis method for a steel structure frame according to claim 1, characterized in that, In step five, the genetic algorithm optimization process includes the following steps: Step 5.1: Obtain the length, width, and thickness parameters of the target structure to be optimized to obtain the initial individual; Step 5.2: Use Latin hypercube sampling to randomly generate the initial population; Step 5.3: Eliminate individuals that do not meet the nonlinear constraints through constraint functions to ensure that all individuals in the population are in the initial population; Step 5.4: Using the target structure quality predicted by the Kriging model as the objective, construct a normalized multi-objective fitness function, evaluate the normalized multi-objective fitness function, and select excellent individuals from the first generation. Step 5.5: Based on the principle of survival of the fittest, select the best individuals to generate the second generation of individuals; Step 5.6: Perform mutation and crossover on the second-generation individuals to generate the next generation of individuals; Step 5.7: Repeat steps 5.3 to 5.6 until the maximum number of iterations is reached or convergence is achieved.

7. The multi-objective optimization analysis method for a steel structure frame according to claim 6, characterized in that, The initial population size is 5000, the maximum number of iterations is 100, the chromosome dimension is N, the number of samples in each iteration is 1000, the crossover probability P = 0.97, and the mutation probability is 0.01.

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