Mine large-scale bucket lightweight design method based on topology-size joint optimization

Abstract

The application provides a mine large-scale bucket lightweight design method based on topological-size joint optimization, belongs to the technical field of mine equipment lightweight, and specifically comprises the following steps: modular design is conducted on the mine large-scale bucket; a lining plate arrangement mode is selected; finite element static simulation is conducted on the bucket box of the mine large-scale bucket; a geometric model of the bucket box after topological optimization is obtained through preliminary topological optimization; design parameters, optimization targets and constraint conditions of size optimization are defined based on the topological optimization result; a bucket box proxy model based on a Fourier neural operator is constructed; and the optimal design parameters of the bucket box are solved based on the proxy model; the method can find the optimal bucket structure design scheme and the optimal lightweight model of the lightweight result in a specified interval through multi-stage lightweight optimization of the bucket.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of lightweight technology of mine equipment, and particularly relates to a lightweight design method of a large mine bucket based on topology-size joint optimization. BACKGROUND

[0002] The bucket is one of the main equipment of mine hoisting, and is applied to the hoisting and transportation of coal in the main shaft and sometimes to the hoisting of people. Due to the rapid development of industry, the coal consumption is still increasing, and the scale of the bucket is developing towards large and super large, which also makes the tonnage of the bucket increase continuously. The traditional bucket often contains redundant structures, and the gain of the redundant structures to the strength of the bucket is far less than the loss caused by the increase of energy consumption, so it is necessary to solve the redundancy of the bucket structure and realize the lightweight design of the large-capacity mine.

[0003] The lightweight design of the large mine bucket is realized through structural topology optimization, shape optimization or size optimization. It is difficult to obtain the optimal structural design scheme by using a single structural optimization method. SUMMARY

[0004] The purpose of the present application is to provide a lightweight design method of a large mine bucket based on topology-size joint optimization, which can find the optimal bucket structure design scheme by performing multi-stage lightweight optimization on the large mine bucket, and can find the optimal lightweight model of the lightweight result in the specified interval.

[0005] In order to achieve the above-mentioned purpose of the application, the technical scheme adopted by the present application is as follows:

[0006] The present application provides a lightweight design method of a large mine bucket based on topology-size joint optimization, comprising the following steps:

[0007] S1, modular analysis is performed on the structure of the large mine bucket; the large mine bucket is divided into a bearing module, a lifting module and an intelligent monitoring module, and the design process is simplified through modular analysis;

[0008] S2, selecting a lining plate arrangement mode; the wear of the lining plate of the large mine bucket is simulated and analyzed to determine the position of the lining plate wear, and the thickness of the lining plate is increased;

[0009] S3, finite element static simulation is performed on the bucket box of the large mine bucket; a three-dimensional model Model1 is established, and finite element static analysis is performed on the three-dimensional model of the bucket box;

[0010] S4, preliminary topology optimization; the SIMP model variable density method is selected to perform topology optimization with the minimum volume of the bucket box material as the optimization target, and the best force transmission path and the optimal distribution of the material of the bucket box are obtained; through the preliminary topology optimization, the geometric model of the bucket box after the topology optimization is obtained;

[0011] S5, define the size-optimized design parameters, optimization objectives and constraints, the bucket design parameters include bucket length x1, bucket width x2, rib thickness x3; three parts together constitute the design optimization variable x, x = [x1, x2, x3];

[0012] The optimization objective is to minimize the material weight f1 of the bucket, maximize the bucket capacity f2, and minimize the maximum stress f3;

[0013] The constraint condition is the allowable stress [σ] of the material, which is calculated by the following formula:

[0014]

[0015] [σ] is the allowable stress of the material, σ s is the ultimate stress of the material, S is the safety factor;

[0016] S6, size optimization; construct a bucket stress field surrogate model based on Fourier neural operator, based on the surrogate model to solve the optimal design parameters x i of the bucket.

[0017] Preferably, in step S1, the bearing module includes a bucket and a lining plate, the lifting module includes an ear and a lifting ring, and the intelligent monitoring module includes a built-in pressure sensor and a displacement sensor.

[0018] Preferably, step S2 specifically includes:

[0019] S2-1: use EDEM to establish a bucket geometry model;

[0020] S2-2: define material properties, coal characteristics parameters are set as: bulk density 1000 kg / m 3 , angle of repose 30°, sliding angle 60°, moisture content 20%; in addition, wear-resistant hardfacing plate is selected as the lining plate material;

[0021] S2-3: select the Archard wear model in the material property setting of EDEM;

[0022] S2-4: set the simulation parameters, the simulation is a total of 15s, the first 4s simulate the process of 30 tons of material flowing into the bucket through the chute and moving in the bucket;

[0023] S2-5: run the simulation; EDEM will output the wear amount of each contact point of the bucket, and generate a surface wear distribution map; according to the wear position, increase the lining plate thickness by 5mm.

[0024] Preferably, step S3 specifically is:

[0025] S3-1. Import the initial three-dimensional model of the bucket box into Ansys Workbench, define the material properties of the bucket box, including the Young's modulus, Poisson's ratio and density, and use tetrahedral element type SOLID187 to mesh the bucket box model;

[0026] S3-2. Set the load condition, as the bucket box is under the working condition of lifting, the load is the pressure of the coal blocks on the inner wall of the bucket box, set the load to be applied at the corresponding position of the model;

[0027] S3-3. Solve the response of the stress and strain of the bucket box under the above load condition, and prepare for subsequent topology optimization.

[0028] Preferably, step S4 specifically comprises:

[0029] S4-1. Set the main part of the bucket box as the design domain, and set the local structure including the bucket box ear and the base as the non-design area, divide the design domain entity model of the bucket box into N grid elements to obtain the design domain grid model of the front cabin base;

[0030] S4-2. Based on the SIMP model variable density method, do the minimum volume topology optimization of the bucket box material f1, take the relative density l of each element as the optimization object, take the allowable stress [σ] of the material in step S2 as the constraint condition, and take the minimum volume f1 of the bucket box material as the optimization target, and the mathematical model formula of topology optimization is as follows:

[0031] search L=[l1,l2,l3...l N ]0<l i <1

[0032]

[0033] s.t.σ i ≤[σ]

[0034] In the formula, N represents the N grid elements of the bucket box design domain, search() represents searching for design variables, L=[l1,l2,l3...l N ] represents the design variable vector of the relative density of the element, l i represents the relative density of the i-th element, i=1,2…N; min() represents the minimization of the objective function, f1 is the material volume of the bucket box, V0 represents the effective volume of the structure under the condition that the topology design variable takes the relative density of 1; s.t.() represents the constraint condition, σ i represents the stress value of the i-th element, and [σ] represents the allowable stress of the material;

[0035] S4-3. Reconstruct the model Model1 to obtain a topologically optimized geometric model Model2 using the topological optimization result.

[0036] Preferably, step S5 is specifically:

[0037] The three sub-objective optimal weight values are allocated by using the combination weighting method, and the three sub-objects are normalized by using the compromise programming method to obtain an optimized comprehensive objective function u, that is:

[0038] u = ω1f1 + ω2f2 + ω3f3;

[0039] In the formula, the optimization parameter x is an input, u is an output, x corresponding to the minimum u is an optimal parameter solution, ω1, ω2, and ω3 are optimal weight values of the sub-objects f1, f2, and f3, respectively;

[0040] Preferably, step S6 is specifically:

[0041] S6-1. Construct a proxy model data set based on a Fourier neural operator, and the specific content is as follows:

[0042] The value interval range of the bucket box length x1 is [1.5, 2.5], the unit is m, the value interval range of the bucket box width x2 is [1.5, 2.5], the unit is m, and the value interval range of the rib plate thickness x3 is [15, 25], the unit is mm; x1 is taken as an interval with a step length of 0.1 in its interval, x2 is taken as an interval with a step length of 0.1 in its interval, and x3 is taken as an interval with a step length of 1 in its interval; the values of x1, x2, and x3 are combined to obtain 100x100x10 groups of sample points to constitute a data set D x , and the stress field σ of the bucket box is obtained based on the finite element simulation of step S3 to obtain a corresponding data set D y ; the data set D x is combined with the corresponding D y to obtain a data set D, and the data set D is divided into a training set D train and a test set D test in a ratio of 7:3, wherein the training set includes and

[0043] S6-2. Define the data set composed of x as the network input , and the output σ is composed of The calculation formula of the proxy model is as follows:

[0044] σ = FNO(x)

[0045] Wherein, FNO represents a proxy model based on a Fourier neural operator;

[0046] S6-3: Constructing a Fourier neural operator network architecture, performing Fourier transform on the network input x in the input layer to obtain S(ω), selecting a traditional 4-layer fully connected neural network structure in the hidden layer, and finally performing inverse Fourier transform in the output layer to output back to the original spatial domain; the Fourier forward transform formula is as follows:

[0047]

[0048] Where S() is the Fourier transformed feature, k is the Fourier coefficient, omega is the frequency, and x is the network input variable;

[0049] S6-4. The Adam algorithm is used to optimize the loss function, the automatic differentiation tool TensorFlow or PyTorch is used to calculate the gradient of the loss function, and the network weights are updated by back propagation; the test set D test is used to evaluate the model performance;

[0050] S6-5. The maximum stress f3 of the size parameter x is calculated based on the proxy model, and the target function u is further calculated, and the particle swarm algorithm is used to solve the minimum value u * of the optimization target u * and the optimization variable x * corresponding to the minimum value; the global optimal solution mathematical expression is as follows:

[0051] (u * ,x * ) = argmin phi (u, x)

[0052] Where (u * ,x * ) is the global optimal solution, and phi (u, x) is the optimization target evaluation index at the predicted solution x.

[0053] Compared with the prior art, the beneficial effects of the present application are:

[0054] 1. The present application effectively improves the problem that it is difficult to find the optimal bucket structure design scheme by using a single optimization method through multi-stage optimization of the fusion topology-size of the mine large-scale bucket, and can effectively improve the reliability of the lightweight design result.

[0055] 2. The present application establishes a stress field proxy model of the mine large-scale bucket based on the Fourier neural operator, which can provide high-precision and high-reliability model support for size optimization, and can greatly reduce the time of optimization design. DETAILED DESCRIPTION

[0056] The accompanying drawings are used to provide a further understanding of the present application, and constitute a part of the specification, together with the embodiments of the present application, to explain the present application, and do not constitute a limitation of the present application.

[0057] Figure 1 Flow chart for lightweight design method of mine large-scale bucket;

[0058] Figure 2 Flow chart for topology optimization;

[0059] Figure 3 Flow chart for size optimization of bucket box.

[0060] Figure 4 Frame chart for Fourier neural operator. DETAILED DESCRIPTION

[0061] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. Of course, the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application.

[0062] The embodiment of the present application provides a lightweight design method of mine large-scale bucket based on topology-size joint optimization, comprising the following steps:

[0063] S1. Modular analysis is performed on the structure of the mine large-scale bucket; the mine large-scale bucket comprises modular structures such as a bearing module, a lifting module, and an intelligent monitoring module, and the design process is simplified through modular analysis. The bearing module comprises a bucket box, a lining plate, etc., the lifting module comprises an ear, a ring, etc., and the intelligent monitoring module comprises a built-in sensor, a communication device, etc.

[0064] S2. Selecting a lining plate arrangement; the wear condition of the lining plate of the mine large-scale bucket is simulated and analyzed by using EDEM discrete element simulation software, the position where the lining plate mainly wears is further determined, and the thickness of the lining plate is further increased.

[0065] Specifically, it comprises:

[0066] S2-1: Establishing a bucket geometric model by using EDEM

[0067] S2-2: Defining material properties, and setting the coal block characteristic parameters as follows: bulk density 1000 kg / m 3 , angle of repose 30°, sliding angle 60°, and moisture content 20%. In addition, a wear-resistant hardfacing plate is selected as the lining plate material.

[0068] S2-3: Selecting to use the Archard wear model in the material property setting of EDEM.

[0069] S2-4: Setting simulation parameters, and simulating a total of 15 seconds, wherein the first 4 seconds simulate the process that 30 tons of materials flow into the bucket through a chute and move in the bucket.

[0070] S2-5: Run the simulation. EDEM will output the wear amount of each contact point of the bucket, and generate a surface wear distribution map. According to the wear position, increase the thickness of the liner by 5mm.

[0071] S3. Perform finite element static simulation on the bucket of a large mine bucket; establish a three-dimensional model Model1, and perform finite element static analysis on the three-dimensional model of the bucket;

[0072] Specifically, it includes:

[0073] S3-1. Import the initial three-dimensional model of the bucket into Ansys Workbench, define the material properties of the bucket, including Young's modulus, Poisson's ratio and density, and use tetrahedral element type SOLID187 to mesh the bucket model;

[0074] S3-2. Set the load condition, as the bucket has the maximum load in the lifting working condition, the load is the pressure of the coal blocks on the inner wall of the bucket, and the load is applied at the corresponding position of the model;

[0075] S3-3. Solve the stress-strain response of the bucket under the above load condition, and prepare for subsequent topology optimization.

[0076] S4. Preliminary topology optimization; select the SIMP model variable density method to minimize the volume of the bucket material as the optimization target for topology optimization, and obtain the optimal force transmission path and optimal material distribution of the bucket. Through preliminary topology optimization, the geometric model of the bucket after topology optimization is obtained;

[0077] Specifically, it includes:

[0078] S4-1. Set the main part of the bucket as the design domain, and set the local structure including the bucket ear and base as the non-design area. Divide the design domain entity model of the bucket into N grid elements to obtain the design domain grid model of the front cabin base;

[0079] S4-2. Based on the SIMP model variable density method, the minimum volume f1 of the bucket material is optimized, the relative density l of each element is taken as the optimization object, the allowable stress [σ] of the material in step S2 is taken as the constraint condition, and the minimum volume f1 of the bucket material in step S2 is taken as the optimization target. The mathematical model formula of topology optimization is as follows:

[0080] search L=[l1,l2,l3...l N ]0<l i <1

[0081]

[0082] s.t.σ i ≤[σ]

[0083] In the formula, N represents N grid units of the hopper design domain, search() represents searching for design variables, L=[l1, l2, l3...l N ] represents a design variable vector of unit relative density, l i represents the relative density of the i-th unit, i=1, 2...N; min() represents minimization of the objective function, f1 is the volume of the hopper material, V0 represents the effective volume of the structure when the topological design variable takes the state of the relative density being 1; s.t.() represents a constraint condition, σ i represents the stress value of the i-th unit, [σ] represents the allowable stress of the material;

[0084] S4-3. Reconstruct Model1 to obtain Model2 using the topological optimization result.

[0085] S5. Define the design parameters, optimization objectives and constraint conditions of size optimization, the hopper design parameters include hopper length x1, hopper width x2 and rib plate thickness x3; the three parts together constitute the design optimization variable x, x=[x1, x2, x3];

[0086] The optimization objectives are to minimize the material weight f1 of the hopper, maximize the hopper capacity f2 and minimize the maximum stress f3;

[0087] The constraint condition is the allowable stress [σ] of the material, which is calculated by the following formula:

[0088]

[0089] [σ] is the allowable stress of the material, σ s is the ultimate stress of the material, and S is the safety factor;

[0090] Specifically:

[0091] The three sub-objective optimal weight values are distributed by using the combination weighting method, the three sub-objects are normalized by using the compromise programming method, and the optimization comprehensive objective function u is obtained, that is:

[0092] u=ω1f1+ω2f2+ω3f3;

[0093] In the formula: the optimization parameter x is input, u is output, the x corresponding to the minimum u is the optimal parameter solution, ω1, ω2 and ω3 are optimal weight values of the sub-objects f1, f2 and f3 respectively;

[0094] S6. Size optimization; construct a hopper stress field proxy model based on a Fourier neural operator, and further solve the optimal design parameter x i of the hopper based on the proxy model. Specifically:

[0095] 6-1. Construct a proxy model dataset based on Fourier neural operator, the specific content is as follows:

[0096] The value interval range of the bucket length x1 is [1.5, 2.5], the unit is m, the value interval range of the bucket width x2 is [1.5, 2.5], the unit is m, the value interval range of the rib plate thickness x3 is [15, 25], the unit is mm. x1 takes values in its interval with a step size of 0.1, x2 takes values in its interval with a step size of 0.1, and x3 takes values in its interval with a step size of 1. Combining the values of x1, x2, and x3, 100x100x10 groups of sample points are obtained to form the dataset D x , and based on the finite element simulation of step S3, the bucket stress field σ is obtained, and the corresponding dataset D composed of σ is obtained y ; the dataset D x is combined with the corresponding D y to obtain the dataset D, and the dataset D is divided into a training set D train and a test set D test in a ratio of 7:3, wherein the training set includes and

[0097] S6-2 defines the network input as the dataset x , and the output σ composed of The calculation formula of the proxy model is as follows:

[0098] σ=FNO(x)

[0099] Where FNO represents the proxy model based on Fourier neural operator.

[0100] S6-3: Construct a Fourier neural operator (FNO) network architecture, perform Fourier transform on the network input x in the input layer to obtain S(ω), select a traditional 4-layer fully connected neural network structure in the hidden layer, and finally perform inverse Fourier transform in the output layer to output back to the original spatial domain; the Fourier transform formula is as follows:

[0101]

[0102] Where S() is the Fourier transformed feature, k is the Fourier coefficient, ω is the frequency, and x is the network input variable;

[0103] S7-4. Use the Adam algorithm to optimize the loss function, use the automatic differentiation tool TensorFlow or PyTorch to calculate the gradient of the loss function, and perform backpropagation to update the network weights; use the test set D test to evaluate the performance of the model.

[0104] S6-5. Calculate the maximum stress f3 when the size parameter is x based on the agent model, and further calculate the objective function u, and solve the minimum value u of the optimization objective u by using the particle swarm algorithm * , and the minimum value u * corresponding to the optimization variable x * ; the global optimal solution is mathematically expressed as follows:

[0105] (u * ,x * )=argminφ(u,x)

[0106] In the formula, (u * ,x * ) is the global optimal solution, and φ(u,x) is the optimization objective evaluation index at the predicted solution x.

[0107] The present application effectively improves the problem that it is difficult to find the optimal bucket structure design scheme by using a single optimization method by carrying out multi-stage optimization of the fusion topology-size of the large mine bucket, and can effectively improve the reliability of the lightweight design result. The present application establishes a stress field agent model of the large mine bucket based on the Fourier neural operator, which can provide high-precision and high-reliability model support for size optimization, and can greatly reduce the time of optimization design.

[0108] The above only describes the preferred embodiments of the present application, and is not intended to limit the present application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for lightweight design of a large-scale mine hopper based on topological-size joint optimization, characterized in that, The method comprises the following steps: S1, modular analysis is performed on the structure of the large mine bucket; the large mine bucket is divided into a bearing module, a lifting module and an intelligent monitoring module, and the design process is simplified through modular analysis; S2, a lining plate arrangement mode is selected; the wear condition of the lining plate of the large mine bucket is simulated and analyzed to determine the position of the lining plate wear, and the thickness of the lining plate is increased; S3, finite element static simulation is performed on the bucket box of the large mine bucket; a three-dimensional model Model1 is established, and finite element static analysis is performed on the three-dimensional model of the bucket box; S4, preliminary topology optimization; the SIMP model variable density method is selected to take the minimum volume of the bucket box material as the optimization target to perform topology optimization, and the best force transmission path and the optimal distribution of the material of the bucket box are obtained; through the preliminary topology optimization, the geometric model of the bucket box after the topology optimization is obtained; S5, the design parameters, the optimization target and the constraint conditions of the size optimization are defined, the design parameters of the bucket box include the length x1 of the bucket box, the width x2 of the bucket box and the thickness x3 of the rib plate; the three parts jointly constitute the design optimization variable x, x=[x1,x2,x3]; The optimization target is to minimize the material volume f1 of the bucket box, maximize the capacity f2 of the bucket box and minimize the maximum stress f3; The constraint condition is the allowable stress [σ] of the material, which is calculated through the following formula: [σ] is the allowable stress of the material, σ s is the ultimate stress of the material, S is the safety factor; S6、size optimization; construct a hopper stress field surrogate model based on the Fourier neural operator, and solve the optimal design parameters x of the hopper based on the surrogate model i .

2. The method of claim 1, wherein, In step S1, the bearing module includes the bucket box and the lining plate, the lifting module includes the lifting lug and the lifting ring, and the intelligent monitoring module includes the built-in pressure sensor and the displacement sensor.

3. The method of claim 2, wherein, Step S2 specifically includes: S2-1: a bucket geometry model is established by using EDEM; S2-2: Define material properties, coal block characteristic parameters are set as: bulk density 1000 kg / m 3 , angle of repose 30°, angle of slide 60°, moisture content 20%; in addition, wear-resistant hardfacing plate is selected as the lining material; S2-3: in the material property setting of EDEM, the Archard wear model is selected for use; S2-4: simulation parameters are set, and the simulation is a total of 15s, the first 4s simulate the process that 30 tons of materials flow into the bucket through the chute and move in the bucket; S2-5: run the simulation; EDEM will output the wear amount of each contact point of the bucket, and generate a surface wear distribution map; according to the wear position, the thickness of the lining plate is increased by 5mm.

4. The method of claim 3, wherein, Step S3 specifically includes: S3-1. Import the initial three-dimensional model of the bucket box into Ansys Workbench, define the material properties of the bucket box, including the Young's modulus, Poisson's ratio and density of the material, and divide the bucket box model into a tetrahedral element type SOLID187 through meshing; S3-2. Set the load condition, because the maximum load of the bucket box is in the lifting working condition, the load is the pressure of the coal block on the inner wall of the bucket box, and the load is applied at the corresponding position of the model; S3-3. Under the above load condition, the stress-strain response of the bucket box is solved, which prepares for subsequent topology optimization.

5. The method of claim 4, wherein, Step S4 specifically includes: S4-1. Set the main part of the bucket box as the design domain, and set the local structure including the bucket ear and the base as the non-design area, divide the design domain entity model of the bucket box into N grid units to obtain the design domain grid model of the front cabin base; S4-2. Based on the SIMP model variable density method, the bucket box material volume f1 is minimized for topology optimization, the relative density l of each unit is taken as the optimization object, the allowable stress [σ] of the material in step S5 is taken as the constraint condition, the minimum volume f1 of the bucket box material in step S5 is taken as the optimization goal, and the mathematical model formula of topology optimization is as follows: search L=[l1,l2,l3...l N ] 0<l i <1 s.t.σ i ≤[σ] In the formula, N represents N grid units of the hopper design domain, search() represents searching for design variables, L = [l1, l2, l3…l N ] represents a design variable vector of unit relative density, l i represents the relative density of the i-th unit, i = 1, 2…N; min() represents minimization of the objective function, f1 is the volume of the hopper material, V0 represents the effective volume of the structure when the topology design variable takes the state of the relative density being 1; s.t.() represents a constraint condition, σ i represents the stress value of the i-th unit, [σ] represents the allowable stress of the material; S4-3. The topology optimization results are used to reconstruct the model Model1 to obtain the geometric model Model2 after topology optimization.

6. The method of claim 5, wherein, Step S5 is specifically: The three sub-objective optimal weight values are allocated by using the combination weighting method, the three sub-objects are normalized by using the compromise programming method, and the optimization comprehensive objective function u is obtained, that is: u=ω1f1+ω2f2+ω3f3; In the formula: the optimization parameter x is input, u is output, the x corresponding to the minimum u is the optimal parameter solution, ω1, ω2, ω3 are the optimal weight values of the sub-objects f1, f2, f3 respectively.

7. The method of claim 6, wherein, Step S6 is specifically: S6-1, construct a proxy model data set based on the Fourier neural operator, and the specific content is as follows: The value interval range of the bucket box length x1 is [1.5, 2.5], the unit is m, the value interval range of the bucket box width x2 is [1.5, 2.5], the unit is m, the value interval range of the rib plate thickness x3 is [15, 25], the unit is mm; x1 takes values in its interval with a step of 0.1, x2 takes values in its interval with a step of 0.1, x3 takes values in its interval with a step of 1, the values of x1, x2 and x3 are combined to obtain 100*100*10 groups of sample points to constitute a data set D x , and based on the finite element simulation of the S3 step, the bucket stress field sigma is solved to obtain a corresponding data set D composed of sigma y ; the data set D x is combined with the corresponding D y to obtain a data set D, and the data set D is divided into a training set D train and a test set D test in a ratio of 7:3, wherein the training set includes and S6-2 defines the data set consisting of network inputs x Output σ consists of The calculation formula of the agent model is as follows: σ=FNO(x) Wherein, FNO represents the proxy model based on the Fourier neural operator; S6-3: Construct the Fourier neural operator network architecture, perform Fourier transform on the network input x in the input layer to obtain S(ω), select a traditional 4-layer fully connected neural network structure in the hidden layer, and finally output back to the original spatial domain through inverse Fourier transform in the output layer; The Fourier transform formula is as follows: Wherein, S() is the Fourier transformed feature, k is the Fourier coefficient, ω is the frequency, and x is the network input variable; S6-4. The Adam algorithm is used to optimize the loss function, and the automatic differentiation tools TensorFlow or PyTorch are used to calculate the gradient of the loss function, and the network weights are updated by backpropagation; the test set D test Evaluate the performance of the model; S6-5 calculate the maximum stress f3 when the size parameter is x based on the agent model, and further calculate the objective function u, and use the particle swarm algorithm to solve the minimum value u of the optimization objective u * , and the minimum value u * Corresponding to the optimization variable x * ; the mathematical expression of the global optimal solution is as follows: (u * ,x * )=argminφ(u,x) where (u * ,x * ) is the global optimal solution, and φ(u,x) is the objective evaluation index of optimization at the predicted solution x.

Images