Spiral bevel gear pre-forged piece structure optimization method based on self-adaptive E-SVM model

Abstract

The invention discloses a spiral bevel gear pre-forged piece structure optimization method based on a self-adaptive E-SVM model. The method comprises the steps that firstly, a spiral bevel gear pre-forged piece structure parameter optimization model considering design parameter uncertainty is established; secondly, 15 groups of initial structure parameter sample points are selected in a design domain by utilizing the optimal Latin hypercube, and a training sample set is updated by utilizing sequence sampling; a Kriging model of the stroke ratio and an E-SVM model of the maximum forming load are constructed, and the failure probability predicted by the E-SVM model is obtained through Monte Carlo simulation; and solving the spiral bevel gear pre-forged piece structure parameter optimization model by using a genetic algorithm. According to the optimization method, the optimal structural parameter combination of the spiral bevel gear pre-forged piece can be obtained, optimal selection of structural parameters of the pre-forged piece in an uncertain environment is achieved, the minimum stroke ratio is achieved on the basis of meeting the minimum forming load, and the forging precision and efficiency are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of gear forging, and relates to the optimization of the structure of gear pre-forgings. Specifically, it relates to a method for optimizing the structure of spiral bevel gear pre-forgings based on an adaptive E-SVM model. Background Art

[0002] Spiral bevel gears are widely used. At present, the traditional gear cutting processing mode is still used. The metal streamline is cut off during the cutting process, resulting in low fatigue strength. The cutting process is carried out after isothermal normalizing, with a large amount of metal removed, which destroys the stress balance inside the normalized gear blank, leading to large deformation of the tooth surface and serious warping deformation of the mounting surface after carburizing and quenching of the gear. The forging process can effectively solve the above problems. During forging, the workpiece blank is heated to a certain temperature or not heated, and the gear teeth are directly forged based on the die. Only a small amount of cutting or no cutting is required before heat treatment, and the anti-fatigue performance is greatly improved.

[0003] The geometric shape of spiral bevel gears is complex, and the plastic forming process belongs to the category of non-steady large deformation, requiring multi-step forging. During the forging process, the material deformation resistance is large, the material fluidity of the gear teeth is poor, and it is difficult to fill the tooth tip corners, resulting in an excessive forming load during the final forging, which causes excessive local stress and strain in the die, leading to phenomena such as fracture and local wear, seriously hindering the popularization and application of the technology of forging spiral bevel gears. Optimizing and adjusting the structure of the spiral bevel gear pre-forging can effectively reduce the deformation resistance, improve the forging quality, and extend the die life. The optimization method is particularly important. Exploring an optimized design scheme for the structure parameters of spiral bevel gear pre-forgings is a technical problem that needs to be solved urgently. Summary of the Invention

[0004] In view of this, the present invention provides a method for optimizing the structure of spiral bevel gear pre-forgings based on an adaptive E-SVM model. During the forging process, the forming load is used as a constraint to optimize the structural design of the preform of the spiral bevel gear driven wheel, thereby proposing a process plan for forging spiral bevel gears suitable for such products, meeting the technical requirements of small deformation resistance, high forging quality, and long die life, and providing technical support for the popularization and application of forging spiral bevel gears.

[0005] To achieve the above object, the technical solution adopted by the present invention is: A method for optimizing the structure of spiral bevel gear pre-forgings based on an adaptive E-SVM model, comprising the following steps: Step 1: Establish an optimization model for the structural parameters of the spiral bevel gear pre-forging, which takes into account the uncertainty of the design parameters; Define the gear forging process parameters and performance response indicators (stroke ratio and forming load). Among them, the gear forging process parameters are X = [H, h, α, d], where H is the height of the pre-forging, h is the height of the circular arc chord, α is the circular arc chord angle, and d is the distance from the high point of the circular arc to the small end; Step 2: Use the optimal Latin hypercube to select 15 groups of initial structural parameter sample points in the design domain, and obtain the performance response indexes of the sample points through simulation to form a sample set; Step 3: Sequentially sample and update the training sample set, and obtain the performance response indexes of the new sample set through simulation; Step 4: Construct a Kriging model for the stroke ratio, and construct an E-SVM model for the forming load based on the weighted aggregation method of multiple kernel functions to obtain the failure probability P predicted by the E-SVM model predict ; Step 5: Use the genetic algorithm to solve the structural parameter optimization model of the spiral bevel gear preform to obtain the optimal combination of the structural parameters of the gear preform.

[0006] Furthermore, the Kriging model is: ξ(x) = ψ(x) T β + z(x); where ψ(x) is a polynomial of x, β is the regression coefficient of ψ(x), ψ(x) T β represents the mean value of ξ(x), and z(x) is a Gaussian random process with a mean of 0.

[0007] Furthermore, the mathematical expression of the E-SVM model is specifically: where n is the number of initial training sample points (n = 15), λ i is the Lagrange multiplier, x i , x j are two sample points in the original space, y i is the label of the sample point, is the Poly kernel function, the order d, is the RBF kernel function, the width γ, the penalty parameter C, g(x i ) = P(S max (x) ≥ S t is the limit state function.

[0008] Even further, the weighted aggregation method of multiple kernel functions includes the following content: 1. Construct an aggregated kernel function K(x i , x j ), as shown in the following formula: K(x i , x j ) = w 1 K 1 (x i , x j ) + w 2 K 2 (xi , x j ), w 1 +w 2 = 1; Among them, is the Ploy kernel function, is the RBF kernel function, w 1 , w 2 are the aggregation weights of the two respectively. 2. Select the Bayesian optimization algorithm (Bayesian optimization) to calculate the optimal weight w of the Poly kernel function in the aggregation kernel function 1 , and determine the weight coefficient of the kernel function of the E-SVM model; 3. Use K-fold cross-validation to select the optimal hyperparameter combination of the SVM model.

[0009] Furthermore, solve the optimization model (step 5), which specifically includes the following steps: S1. Define the objective function: Minimize the stroke ratio, which is achieved by calling the constructed stroke ratio Kriging model during the optimization process. S2. Define the constraint conditions: The design variables [H, h, α, d] are all within the specified value ranges; the failure probability of the forming load is less than the given value, and this failure probability is achieved by calling the constructed E-SVM model. S3. Define the genetic algorithm parameters: Set the population size to N, the number of iterations to n, the crossover rate to a, and the mutation rate to b. S4. Initialize the population: Randomly generate the initial population according to the range of the design variables. S5. Evaluate the population: For each individual, call the Kriging model to calculate its stroke ratio. S6. Selection: Select according to the fitness of the individual (i.e., the objective function value), and select the individuals with higher fitness (smaller objective function value) as the population of the next generation. S7. Crossover and mutation: Perform crossover and mutation operations on the selected individuals to generate new individuals. S8. Elimination: Call the constructed E-SVM model to calculate the forming load failure probability of the existing population, and eliminate the individuals that do not meet the constraints. S9. Repeat steps S5 - S7 until the specified number of iterations is reached. S10. Output the result: Output the best combination of design variables.

[0010] Optionally, in step 5, when the algorithm starts, the Bayesian optimization algorithm initializes the probability model by randomly selecting a small batch of sample points in the search space; in each iteration, the Bayesian optimization algorithm uses the existing sample data and the prior information of the objective function to update the probability model, and then selects the next candidate point for evaluation by sampling on the model to determine the optimal aggregation weight.

[0011] Furthermore, in step 5, in each iteration, the information parameter points are adaptively selected and added to the training sample set, the E-SVM model is adaptively updated, and the bounded failure probability range [P predict , P upper in each iteration of the sequential sampling process is calculated to quantify the uncertainty in the empirical estimation of the failure probability, and the convergence of P upper is used as the termination criterion for the iteration of the adaptive sampling algorithm: Set a relatively small τ value. When |P upper - P predict < τ, it is considered that P upper converges, and the adaptive sampling algorithm stops iterating; wherein, P upper represents the upper bound of the failure probability, and P predict is the system failure probability.

[0012] Even further, the calculated system failure probability includes the following content: According to the distribution form of the structural parameters, 10 6 sample points are selected near the current design point by using Monte Carlo simulation, and the probability that the forming load is greater than a given value is calculated.

[0013] Even further, in the said step 5, the distance from the Monte Carlo sample to the predicted classification boundary is used as the uncertainty function, and in each iteration process, a new set of training data is selected based on the uncertainty function.

[0014] The beneficial effects of the present invention are as follows: 1. The method of the present invention takes the spiral bevel gear driven wheels with different outer diameters as the object. In order to reduce the final forging forming force and improve the corner filling quality, with the minimization of the stroke ratio as the optimization goal, the structural design of the preform of the spiral bevel gear driven wheel is optimized, and the optimal combination of the structural parameters of the spiral bevel gear pre-forged part is obtained; the optimal selection of the structural parameters of the pre-forged part in the uncertain environment is realized. On the basis of meeting the forming load, the minimum stroke ratio is achieved, and the performance of the forging is guaranteed; 2. The Bayesian optimization algorithm is used to search for the best aggregation weight of the polynomial kernel function and the Gaussian kernel function in the E-SVM. On this basis, the two kernel functions are linearly weighted and aggregated, and the optimal hyperparameter combination of the SVM model is selected by using K-fold cross-validation, effectively improving the fitting accuracy of the E-SVM model; 3. Quantify the uncertainty in the empirical estimation of the failure probability by calculating the bounded failure probability range for each iteration. Select information parameter points in each iteration and add them to the training data to achieve the adaptive update of the E-SVM model. 4. Using the adaptive sampling method, while ensuring the global search ability, it can also focus on the detailed optimization of the local area, ensuring the comprehensiveness and reliability of the optimization results. By combining the Kriging model, the present invention realizes the intelligent optimization design of the pre-forging structure parameters, improving the accuracy and efficiency of the design. 5. The method proposed in the present invention is not only applicable to the optimization of the pre-forging structure parameters, but also can be extended to other fields of structural parameter optimization, with good generality and adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0016] Figure 1 is a flowchart of the gear pre-forging structure optimization method based on the adaptive E-SVM model; Figure 2 is a schematic diagram of the pre-forging structure parameters of the spiral bevel gear of the present invention; Figure 3 is a flowchart of the Bayesian optimization algorithm for searching the optimal weight of the Poly kernel function of the present invention; Figure 4 is a convex hull diagram of the safety domain and failure domain of the E-SVM model of the present invention; Figure 5 is a flowchart of calculating the bounded failure probability range of the present invention; Figure 6 is a flowchart of the genetic algorithm optimization. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0017] The following specific embodiments are given to further clearly, completely and detailedly illustrate the technical solutions of the present invention. The embodiments described in the present invention are only some preferred embodiments of the present invention, and are not used to limit the protection scope of the present invention.

[0018] The present invention provides a method for optimizing the structure of a spiral bevel gear preform based on an adaptive E-SVM model. Taking spiral bevel gear driven wheels with different outer diameters as objects, with the goal of reducing the stroke ratio under the forming load, the structure design of the preform of the spiral bevel gear driven wheel is optimized to obtain the optimal combination of structural parameters of the spiral bevel gear preform.

[0019] As Figure 1 shown, the specific parameter optimization steps of this method are as follows: Step 1: Establish an optimization model for the structural parameters of the spiral bevel gear preform; Select the optimized structural parameters as X = [H, h, α, d], where H is the height of the preform, h is the chord height of the arc, α is the chord angle of the arc, and d is the distance from the high point of the arc to the small end, as specifically Figure 2 shown. The performance response indicators are the percentage of the stroke when the tooth profile is filled in the total stroke (abbreviated as the stroke ratio) and the forming load (constrained by the probability P t that this stress is less than a given value); In actual production, there are certain fluctuations in the structural parameters of the preform, which will affect the performance responses (stroke ratio and forming load). Therefore, when establishing the optimization model for the structural parameters of the spiral bevel gear preform, the uncertainty of the design parameters is considered: Among them, x opt is the optimal structural parameter obtained through optimization, F(d) is the stroke ratio, P(S max (x) ≥ S t ) is the probability that the forming load (S max , unit Mpa) exceeds the allowable value S t during the forging process, P t is the maximum failure probability given by the enterprise, x L and x U are the upper and lower bounds of the variable X respectively, and the optimization initial value is the current forging parameter d 0 .

[0020] Step 2: Construct a sample set: Use the optimal Latin Hypercube Design to select m = 15 (m = (n + 1)(n + 2) / 2, n is the dimension) initial structural parameter sample points in the design domain, and use the DEFORM software for finite element simulation to obtain the stroke ratio and forming load corresponding to different preform structural parameters. The structural parameters and their responses (stroke ratio and forming load) together constitute the sample set. Subsequently, the sample set will be supplemented through sequential sampling and finite element simulation.

[0021] Step 3: Construct the Kriging model of the stroke ratio, and construct the E-SVM model of the forming load based on the weighted aggregation method of multiple kernel functions to obtain the system failure probability P predicted by the E-SVM model predict ; After the sample set is constructed, the Kriging model is used to substitute the implicit relationship between the structure parameters and the stroke ratio, and the E-SVM model is used to substitute the implicit relationship function g(x)=S max -S t for substitution, which specifically includes the following sub-steps: Step 3.1: Construct the E-SVM model; The construction of the E-SVM model is realized by calling the LIBSVM toolbox, and its specific formula is as shown in Equation (2): Among them, n is the number of initial training sample points (n = 15), λ i is the Lagrange multiplier, x i , x j are two sample points in the original space, y i is the label of the sample point, is the Poly kernel function, order d, is the RBF kernel function, width γ, penalty parameter C, g(x i ) = P(S max (x)≥S t is the limit state function. After the model is constructed, the system failure probability P predicted by the E-SVM model is obtained predict .

[0022] Step 3.2: Determine the weight coefficients of the kernel function of the E-SVM model; SVM is a binary classification algorithm. Its basic idea is to find an optimal hyperplane in the dataset to separate samples of different classes, so as to maximize the interval between the two classes. The selection of the kernel function is the key to the construction of SVM, which directly determines the nonlinear fitting ability of the model and the final classification effect. Different kernel functions are suitable for different types of data distributions and complexities. In SVM, common kernel functions include linear kernel, polynomial kernel (Poly kernel), radial basis function kernel (RBF kernel), Sigmoid kernel, etc. Among them, the Poly kernel can efficiently solve linear and non-linearly separable problems, but is not suitable for large-order power problems; the RBF kernel has good local approximation ability and global continuity, but its calculation speed is slow and it is prone to overfitting.

[0023] To make full use of the advantages of different kernel functions, the present invention proposes a weighted aggregation method of multiple kernel functions, and constructs the implicit function g(x)=S on this basis max-S t Aggregated Support Vector Machine (E-SVM) model: Step 3.2.1, construction of the aggregated kernel function; It is proposed to linearly weight and aggregate the Poly kernel and the RBF kernel to take into account the classification advantages of the polynomial kernel function (Poly kernel) and the Gaussian radial basis kernel function (RBF kernel); The aggregated kernel function K(x i , x j ) is constructed as shown in Equation (3): K(x i , x j ) = w 1 K 1 (x i , x j ) + w 2 K 2 (x i , x j ), w 1 + w 2 = 1 (3) Wherein, is the Ploy kernel function, is the RBF kernel function, and w 1 , w 2 are the aggregation weights of the two respectively.

[0024] Step 3.2.1, selection of the aggregation weight; The selection of the aggregation weight is very crucial, as it directly affects the contribution degree of each basic kernel function in the final model. Since the Bayesian optimization algorithm can find the optimal solution within a relatively small number of objective function evaluations, the present invention selects the Bayesian optimization algorithm to calculate the optimal weight w 1 of the Poly kernel function in the aggregated kernel function (the optimal aggregation weight w 2 of the RBF kernel function = 1 - w 1 ), and the specific content is as follows: At the beginning of the algorithm, Bayesian optimization initializes the probability model by randomly selecting a small batch of sample points in the search space. With each iteration, the algorithm updates the probability model using the existing sample data and the prior information of the objective function, and then selects the next candidate point for evaluation by sampling on the model.

[0025] Furthermore, the calculation process of the optimal weight w 1 of the Poly kernel function is as Figure 2 shown, and the specific process is as follows: (1) Taking the minimization of the classification error of the E-SVM model as the objective function, as shown in Equation (4): Among them, y i is the true label of the i-th training sample of the E-SVM model (y i = 1 indicates that g(x) = S max -S t > 0; otherwise y i = 0), is the predicted label of the i-th training sample of the E-SVM model, and n is the number of training samples of the E-SVM model.

[0026] (2) Define the search range of the parameter w to be optimized 1 as [0, 1]. Randomly select 100 points in [0, 1], and calculate the classification error value at each point (Formula 4), and establish an initial Gaussian Process Regression (GP) model to simulate the prior distribution of the objective function; According to the current Gaussian process regression model, use the Bayesian optimization algorithm to select the next most promising sampling point in the parameter space, usually the point with the maximum Expected Improvement (EI), to update the GP model to the greatest extent. The mathematical expression of EI is as shown in Equation (5): Among them, f min is the minimum value of the objective function that has been observed currently, and f(x) is the value of the objective function at the sampling point x to be evaluated; is the sign of the expected value; Δ represents the difference between the two, that is, the improvement amount. If the improvement amount is greater than 0, it means that the sampling point x has improved the value of the objective function. Otherwise, use the max function to set the improvement amount to 0, and max(Δ, 0) means to select a larger value between Δ and 0.

[0027] Furthermore, the specific steps of the EI criterion during execution are as follows: (a) Estimate the mean and variance: Use the current model to estimate the mean μ(x) and variance σ(x) of the objective function in the parameter space; (b) Calculate the standardized improvement: Standardize the improvement amount, and the standardized improvement amount is Z(x): Among them, μ(x) is the mean estimate of the model for the objective function at point x, and σ(x) is the corresponding variance estimate; (c) Calculate the expected improvement: EI(x) = (μ(x) - f min )Φ(Z(x)) + σ(x)φ(Z(x)) (7) where, Φ(·) is the cumulative distribution function of the standard normal distribution, and φ(·) is the probability density function of the standard normal distribution; (d) Calculate the next sampling point: Use the PSO algorithm to select the point with the maximum EI value in [0, 1] as the next evaluation point, i.e., (e) Evaluate the value of the objective function at this point, and add the newly obtained evaluation point to the existing observed values. Based on the new observed values, update the Gaussian process regression model to obtain the posterior distribution of the objective function, and continue to add the new maximum EI value points until the objective function value converges. The specific criteria are as follows: |f k -f k-1 | / |f k +eps|≤10 -3 and |f k-1 -f k-2 | / |f k-1 +eps|≤10 -3 (9) where, f k is the optimal solution of the k-th iteration of formula (4).

[0028] (3) Obtain the optimal solution: When the algorithm converges, select the point with the minimum value of the objective function in all iterations as the optimal solution, and this optimal solution is the required optimal weight w 1 , such as Figure 3 During the iteration process, the Bayesian optimization algorithm continuously utilizes the existing sample information and probability model to dynamically update the sampling points and the GP model, thereby effectively searching for the optimal weight w of the Poly kernel function 1 .

[0029] Step 3.3. Adaptive update of the E-SVM model; SVM can be regarded as finding the maximum margin hyperplane between two convex hulls in the feature space, as Figure 2 shown. The convex hull is a concept in computational geometry, which represents the smallest convex polygon (convex polyhedron in three-dimensional or higher-dimensional problems) that contains all samples in the two-dimensional space. C S corresponds to the convex hull formed by the training sample points in the safe domain, and C f corresponds to the convex hull formed by the training sample points in the failure domain.

[0030] In actual engineering practice, the limit state function is usually difficult to express explicitly. Therefore, the acquisition of the initial training samples needs to cover the entire feature space, which increases the complexity of structural reliability analysis. To solve this problem, based on the aforementioned optimal Latin hypercube sampling, this invention adaptively selects information parameter points in each iteration and adds them to the training sample set to adaptively update the E-SVM model.

[0031] The uncertainty in the empirical estimation of the failure probability is quantified by calculating the bounded failure probability range in each iteration of the sequential sampling process. The bounded failure probability range is represented by [P predict ,P upper , where P upper represents the upper bound of the failure probability; it is assumed that all Monte Carlo samples outside the safety convex hull fall within the failure domain, thereby obtaining the upper bound of the failure probability P upper .

[0032] Furthermore, the specific process of calculating P upper is as follows: 1) Generate Monte Carlo sample points centered on the current design point; 2) Construct the convex hull C S formed by the training sample points in the safety domain in the feature space. The Monte Carlo samples within C S are considered safe; 3) The complement of all safe Monte Carlo samples divided by the total number of Monte Carlo samples can obtain a conservative estimate of the upper bound of the failure probability P upper , as shown in Equation (10): where N represents the total number of Monte Carlo samples, X i is the i-th Monte Carlo sample (i = 1, 2,..., N), F u (X i ) is the modified failure domain function, φ(X i ) is the mapping function, and C S is the safety convex hull; 4) Equation (10) is too conservative, resulting in relatively few Monte Carlo sample points being in the safety domain. To make up for this, a distance l from the classification hyperplane is added. At this distance, the Monte Carlo samples are considered to be within the safety domain regardless of whether they are within C S ; 5) Calculate the distance L(X i ) from all Monte Carlo sample points to the trained classification hyperplane, and select the 10th percentile of the result distribution as l. Then, the process of calculating P upper in Equation (10) is modified to Equation (11): Quantify the uncertainty in the empirical estimate of the failure probability by calculating the bounded failure probability range [P predict , P upper for each iteration, and use the convergence of P upper as the termination criterion for the iteration of the adaptive sampling algorithm; 6) This patent uses the distance from the Monte Carlo samples to the predicted classification boundary as the uncertainty function. In each iteration, a new set of training data is selected based on the uncertainty function.

[0033] Furthermore, the specific termination criterion is as follows: Set a small value of τ. When |P upper - P predict | < τ, it is considered that P upper converges, and the adaptive sampling algorithm stops iterating. Taking different values of τ, the difficulty of convergence of P upper is different. The smaller the value of τ, the more difficult it is for P upper to converge, the more iterations of the adaptive sampling algorithm, the higher the prediction accuracy of the E - SVM model, but the computational cost will also be higher accordingly.

[0034] According to the existing research, in this embodiment, τ = 0.03 is selected.

[0035] Furthermore, in step 6), the specific steps of the adaptive sampling algorithm are as follows: a) At the beginning of each iteration, calculate the distance from all Monte Carlo sample points to the predicted classification boundary. The smaller the distance, the higher the uncertainty score; b) Sort the Monte Carlo sample points according to the uncertainty score, and select the sample point with the highest score as the new training data; c) Update the model using the new training data and recalculate the uncertainty scores of all Monte Carlo sample points; d) Repeat steps 2 and 3 until the stop condition (P upper converges) is met.

[0036] Step 3.4, Calculate the system failure probability P predict ; After the E - SVM model of the implicit function g(x) = S max - S t is constructed, according to the distribution form of the structural parameters, use Monte Carlo simulation to select 10 6 sample points near the current design point, and calculate the probability that the forming load is greater than a given value (i.e., the failure probability). The generation of sample points is realized by calling MATLAB software.

[0037] Step 3.5, The Kriging model of the stroke ratio; There is a certain non-linear relationship between the structural parameters of the pre-forging and the stroke ratio. In the optimization, directly calling the finite element simulation results in an overly high optimization outcome. Therefore, the Kriging model with good fitting performance is used to approximately substitute the implicit relationship between the structural parameters and the performance response. The specific expression of the Kriging model is as shown in Equation (12): ξ(x) = ψ(x) T β + z(x) (12) In the formula, ψ(x) is the polynomial matrix of x, β is the regression coefficient of ψ(x), and ψ(x) T β represents the mean value of ξ(x), providing a global approximation in R s . Generally speaking, ψ(x) T β can be assumed to be of order 0, 1, and 2. And z(x) is a Gaussian random process with a mean of 0.

[0038] Furthermore, to determine the optimal order of ψ(x), based on all the sample points x 1 , x 2 ,..., x M obtained during the construction of the E-SVM model and the corresponding stroke ratios y 1 , y 2 ,..., y M , it is calculated jointly through the error estimation at the test points and the cross-validation error. The specific calculation formula is as follows: e k = e k1 + e k2 , k = 0, 1, 2 (13) Among them, e k represents the error of the k-order polynomial Kriging model. In this patent, the order with the smallest error value is selected as the order of the Kriging model; e k1 is the error estimation at the prediction points of the k-order polynomial Kriging model after normalization. The calculation formula is as follows: Among them, n is the number of test points. In this project, 10 4 evenly distributed sample points are selected as test points. Specifically, each dimension is divided into ten equal parts, and the midpoint of each equal part is taken as the sample point of that dimension. There are a total of 10 4 in four dimensions; is the error estimation of the k-order polynomial Kriging model at the i-th test point, obtained by calling the constructed Kriging model; In formula (13), e k2 is the cross-validation error of the k-order polynomial Kriging model after normalization. The calculation formula is as follows: Among them, M is the number of sample points for constructing the Kriging model; is the predicted value of the k - order polynomial Kriging model constructed after removing the training sample point x i at x i ; f(x i ) is the stroke ratio at the training sample point x i , which is obtained through DEFORM simulation.

[0039] Step 4: Use the genetic algorithm to solve the optimization model of the spiral bevel gear pre - forging structure to obtain the optimal combination of gear pre - forging structure parameters; The specific optimization process is as Figure 5 shown, and the specific process is as follows: (1) Define the objective function: Minimize the stroke ratio, which is realized by calling the Kriging model during the optimization process. (2) Define the constraint conditions: The design variables [H, h, α, d] are all within the specified value ranges; the failure probability of the forming load is less than a given value, and this failure probability is realized by calling the constructed E - SVM model. (3) Define the genetic algorithm parameters: Set the population size to N, the number of iterations to n, the crossover rate to a, and the mutation rate to b. (4) Initialize the population: Randomly generate the initial population according to the range of the design variables. (5) Evaluate the population: For each individual, call the Kriging model to calculate its stroke ratio. (6) Selection: Select according to the fitness of the individual (i.e., the objective function value), and select the individuals with higher fitness (smaller objective function value) as the population of the next generation. (7) Crossover and mutation: Perform crossover and mutation operations on the selected individuals to generate new individuals. (8) Elimination: Call the constructed E - SVM model to calculate the forming load failure probability of the existing population, and eliminate the individuals that do not meet the constraints. (9) Repeat steps 5 - 7 until the specified number of iterations is reached. (10) Output the result: Output the best combination of design variables.

[0040] In summary, the present invention provides a method for optimizing the structure of a spiral bevel gear pre - forging based on an adaptive E - SVM model. By using an adaptive sampling method, combining the Kriging model and the E - SVM model, the optimal combination of the structure parameters of the spiral bevel gear pre - forging is obtained. The present invention realizes the intelligent optimization design of the pre - forging structure parameters, improving the accuracy and efficiency of the design.

[0041] The main features, basic principles and advantages of the present invention have been shown and described above. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will also have various changes and improvements according to the actual situation, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A spiral bevel gear pre-forging structure optimization method based on an adaptive E-SVM model, characterized in that: The following steps are involved: Step 1: construct a structural parameter optimization model for spiral bevel gear pre-forgings, taking into account the uncertainty of design parameters; The gear forging process parameters and performance response indicators are defined. The gear forging process parameters are X = [H, h, α, d], where H is the pre-forging height, h is the arc chord height, α is the arc chord angle, and d is the distance from the arc high point to the small end; the performance response indicators include stroke ratio and forming load; Step 2: Select 15 groups of initial structural parameter sample points in the design domain using optimal Latin hypercube sampling, and use simulation to obtain the performance response indicators of the sample points to form a sample set; Step 3: Update the training sample set by sequence sampling, and use simulation to obtain the performance response index of the new sample set; Step 4: Construct a Kriging model of stroke ratio, and construct an E-SVM model of forming load based on multiple kernel function weighted aggregation methods. The system failure probability P predicted by the E-SVM model is obtained through Monte Carlo simulation. predict ; Step 5: Use genetic algorithm to solve the spiral bevel gear pre-forging structural parameter optimization model to obtain the optimal pre-forging structural parameter combination.

2. The method for optimizing the structure of spiral bevel gear pre-forgings based on the adaptive E-SVM model according to claim 1, characterized in that: The structural parameter optimization model of spiral bevel gear pre-forging is constructed to meet the following formula: Among them, x opt is the optimal structural parameter obtained through optimization, F(d) is the stroke ratio, P(S max (x)≥S t ) is the forming load during forging (S max , unit MPa) exceeds the allowable value S t The probability, P t is the maximum failure probability given by the enterprise, x L and x U are the upper and lower bounds of the variable X respectively, and the initial optimization value is the currently used forging parameter d0.

3. The method for optimizing the structure of spiral bevel gear pre-forgings based on the adaptive E-SVM model according to claim 1, characterized in that: Construct the Kriging model to satisfy the following formula: ξ(x)=ψ(x) T β+z(x); Where ψ(x) is the polynomial of x, β is the regression coefficient of ψ(x), and ψ(x) T β is the mean value of ξ(x), in R s A global approximation is provided in , where z(x) is a random process with mean 0.

4. The method for optimizing the structural parameters of spiral bevel gear pre-forgings based on the adaptive E-SVM model according to claim 1, characterized in that: Construct an E-SVM model that satisfies the following formula: Where n is the number of initial training sample points (n = 15), λ i is the Lagrange multiplier, x i ,x j are two sample points in the original space, y i is the label of the sample point, K1(x i ,x j )=(c+x i T ·x j ) d is the Poly kernel function, order d, is the RBF kernel function, width γ, penalty parameter C, g(x i )=P(S max (x)≥S t is the limit state function.

5. The method for optimizing the structure of spiral bevel gear pre-forgings based on the adaptive E-SVM model according to claim 4, characterized in that: In step 4, an E-SVM model of an implicit function is constructed based on the weighted aggregation method of the multiple kernel functions, including the following contents: A. Constructing the aggregation kernel function K(x i ,x j ), as shown below: K(x i ,x j )=w1K1(x i ,x j )+w2K2(x i ,x j ),w1+w2=1; Among them, K1(x i ,x j )=(c+x i T ·x j ) d is the Ploy kernel function, is the RBF kernel function, w1 and w2 are their aggregation weights respectively. B. Use the Bayesian optimization algorithm to calculate the optimal weight w1 of the Poly kernel function in the aggregation kernel function, and determine the weight coefficient of the E-SVM model kernel function; C. Use K-fold cross validation to select the optimal hyperparameter combination of the SVM model.

6. The method for optimizing the structure of spiral bevel gear pre-forgings based on the adaptive E-SVM model according to any one of claims 1 to 5, characterized in that: In step 5, the optimization model is solved by multiple iterations, which specifically includes the following sub-steps: S1, minimize the stroke ratio, which is achieved by calling the Kriging model during the optimization process; S2, the design variables [H, h, α, d] are all within the specified value range; the failure probability of the forming load is less than the given value, and the failure probability is realized by calling the constructed E-SVM model; S3, set the population size to N, the number of iterations to n, the crossover rate to a, and the mutation rate to b; S4, randomly generate the initial population according to the range of the design variables; S5. For each individual, the Kriging model is called to calculate its stroke ratio; S6. Select individuals based on their fitness and choose individuals with higher fitness as the next generation population; S7, performing crossover and mutation operations on the selected individuals to generate new individuals; S8, calling the constructed E-SVM model to calculate the forming load failure probability of the existing population, and eliminating individuals that do not meet the constraints; S9, repeat steps S5-S7 until the specified number of iterations is reached; S10. Output the best design variable combination.

7. The method for optimizing the structure of spiral bevel gear pre-forgings based on the adaptive E-SVM model according to claim 6, characterized in that: When determining the weight coefficients of the E-SVM model kernel function: First, the Bayesian optimization algorithm initializes the probability model by randomly selecting a small batch of sample points in the search space; in each subsequent iteration, the Bayesian optimization algorithm uses the existing sample data and prior information of the objective function to update the probability model, and then selects the next candidate point for evaluation by sampling on the model to determine the optimal aggregation weight.

8. The method for optimizing the structure of spiral bevel gear pre-forgings based on the adaptive E-SVM model according to claim 6, characterized in that: In each iteration, information parameter points are adaptively selected and added to the training sample set, and the E-SVM model is adaptively updated. By calculating the bounded failure probability range of each iteration in the sequence sampling process [P predict ,P upper ] to quantify the uncertainty in the empirical estimate of failure probability, using P upper The convergence of is used as the termination criterion for the iteration of the adaptive sampling algorithm: Set a smaller τ value, when |P upper -P predict |<τ, it is considered that P upper Convergence, the adaptive sampling algorithm stops iterating; Among them, P upper represents the upper bound of failure probability, P predict To predict the failure probability.

9. The method for optimizing the structure of spiral bevel gear pre-forgings based on the adaptive E-SVM model according to claim 8, characterized in that: According to the distribution form of structural parameters, 10 6 sample points and calculate the probability that the forming load is greater than a given value.

10. According to the method for optimizing the structure of spiral bevel gear pre-forgings based on the adaptive E-SVM model of claim 8, the distance from the Monte Carlo sample to the predicted classification boundary is used as the uncertainty function, and in each iteration process, a new set of training data is selected based on the uncertainty function.

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