Transmission shaft fatigue strength optimization method and system, storage medium and computing equipment

Abstract

The invention relates to the field of mechanical fatigue strength optimization design, and discloses a transmission shaft fatigue strength optimization method and system, a storage medium and computing device.The transmission shaft fatigue strength optimization method comprises the steps that the contribution degree of key structure parameters to transmission shaft output response is calculated, and the structure parameter with the highest contribution degree serves as a design variable of transmission shaft fatigue strength optimization design; establishing a mathematical model of transmission shaft fatigue strength optimization design to calculate and obtain a performance response value of a transmission shaft model; constructing an initial Kriging agent model based on the selected design variables and the corresponding performance response values, setting a control function based on Bayesian posterior characteristics, and introducing the control function into a classical expectation point adding strategy to establish a Kriging agent model of Bayesian expectation improvement control; the maximum service life of the transmission shaft is taken as a target, the fatigue strength of the transmission shaft is optimally designed on the basis of a Kriging agent model of Bayesian expectation improvement control, global search is carried out by adopting a genetic algorithm, and the optimal structure parameters and fatigue life of the transmission shaft meeting constraint conditions are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical fatigue strength optimization design, and in particular to a transmission shaft fatigue strength optimization method, system, storage medium and computing device. Background Art

[0002] With the rapid development of finite element technology, a large number of computer-aided software has been widely used in structural optimization design. However, the difficulty of the fatigue strength optimization design of the transmission shaft lies mainly in the complexity of its finite element analysis process. A structural finite element static analysis will take a long time, and fatigue strength analysis requires a large sample size structural analysis, which often requires dozens or even hundreds of iterative calculations to obtain an optimization solution. Applying approximate models to fit complex and high-precision numerical simulation calculation models, constructing approximate objective functions or constraint functions to characterize the performance response of the structure, and then using evolutionary algorithms to optimize and solve it can effectively reduce the calculation cost and time of the optimization design.

[0003] A variety of methods have been proposed to solve the fatigue strength optimization design problem of the transmission shaft, mainly including the finite element topology method and the proxy model method. The former is to find the optimal distribution of materials or the optimal load transfer path under the given design area and constraints, so as to obtain a structure that meets various performance requirements and is light in weight. Its forms of expression include homogenization method, variable density method and variable thickness method. The latter mostly uses the DOE test method to sample the key design variables of the mechanical structure, establishes an approximate model that meets the accuracy requirements after sensitivity analysis and screening of the design variables, and uses relevant algorithms to optimize and solve multiple objectives of the mechanical structure to achieve the best comprehensive performance of the structure. Currently commonly used proxy models include response surface model, radial basis model, Kriging model, etc.

[0004] Although the finite element topological structure optimization method achieves lightweight structure by removing materials, in order to obtain the analytical mathematical model as the fitness function, it needs to rely on the existing design experience to conduct repeated simulation experiments and model corrections in the specific operation process. Not only does it take a long time to model and the optimization efficiency is low, but the boundaries of the topological structure are not clear enough, and the sensitivity calculation of the optimization process is also relatively complicated. Therefore, it lacks universality and reliability. In recent years, researchers have widely used surrogate model approximation models to fit complex and high-precision numerical simulation calculation models, and to construct approximate objective functions or constraint functions to characterize the performance response of the structure. However, the existing approximate models have low accuracy and poor generalization ability, and there is still much room for improvement in solution efficiency. Summary of the invention

[0005] In view of the above problems, the purpose of the present invention is to provide a method, system, storage medium and computing device for optimizing the fatigue strength of a transmission shaft, which overcomes the difficult situation that the existing fatigue strength optimization design is difficult to deal with, such as high cost and low efficiency. On the premise of ensuring the accuracy of the fatigue strength optimization design, the computing cost is reduced, the computing efficiency is improved, and the efficient fatigue strength optimization design of the transmission shaft is realized.

[0006] To achieve the above-mentioned purpose, in the first aspect, the technical solution adopted by the present invention is: a method for optimizing fatigue strength of a transmission shaft, which comprises: based on an established parameterized model of the transmission shaft, using the entropy weight TOPSIS method to calculate the contribution of key structural parameters to the output response of the transmission shaft, taking the structural parameters with the highest contribution as the design variables for the fatigue strength optimization design of the transmission shaft, establishing a mathematical model for the fatigue strength optimization design of the transmission shaft, so as to calculate the performance response value of the transmission shaft model, and the performance response value includes stress, strain and life; constructing an initial Kriging proxy model based on the selected design variables and the corresponding performance response values, and setting a control function based on the Bayesian posterior characteristics, introducing it into the classic expectation plus point strategy to establish a Kriging proxy model of Bayesian expectation improved control; taking the maximum life of the transmission shaft as the goal, optimizing the fatigue strength of the transmission shaft based on the Kriging proxy model of the Bayesian expectation improved control, and using a genetic algorithm for global search to solve the optimal structural parameters and fatigue life of the transmission shaft that meet the constraints.

[0007] Furthermore, the entropy weight TOPSIS method is used to calculate the contribution of key structural parameters to the output response of the transmission shaft, and the structural parameters with the highest contribution are used as the design variables for the fatigue strength optimization design of the transmission shaft, including:

[0008] Combined with boundary constraints and loads, according to the material properties of the transmission shaft, the finite element analysis of the initial simplified model of the transmission shaft was performed to obtain the stress distribution cloud map and deformation cloud map results;

[0009] Finite element analysis is used to select parameters that can improve structural strength and service life, and the single contribution of the parameters to each response index is calculated by the entropy weight TOPSIS method. Further calculations are made based on the results of the single contribution of each evaluation index to obtain the comprehensive contribution of each response index. The structural parameters with the highest comprehensive contribution are used as design variables.

[0010] Furthermore, a mathematical model for the optimal design of transmission shaft fatigue strength is established, including:

[0011] The selected design variables are used as input parameters, and the mass of the transmission shaft and the performance response obtained after finite element analysis are used as constraints;

[0012] The fatigue life of the transmission shaft is solved based on the critical surface multi-axial fatigue damage model of normal strain, and the calculated maximum fatigue life is used as the optimization target to establish a mathematical model.

[0013] Furthermore, the performance response value of the transmission shaft model is calculated, including:

[0014] The Latin hypercube sampling method is used to extract sample points within the range of design variables to establish the design space;

[0015] The extracted sample point data are input into the mathematical model in sequence, and the performance response value of the drive shaft model is obtained through finite element analysis and numerical calculation.

[0016] Furthermore, a Kriging agent model for Bayesian expectation-improved control is established, including:

[0017] Determine whether the accuracy of the initial Kriging surrogate model meets the set requirements. If it does, the optimal design variables and the corresponding optimal response values ​​are output. Otherwise, the control function is set based on the Bayesian posterior characteristics and introduced into the classic expectation plus point strategy to obtain the Kriging surrogate model of Bayesian expectation improved control.

[0018] Furthermore, with the goal of maximizing the life of the transmission shaft, the Kriging surrogate model based on the Bayesian expectation improved control is used to optimize the fatigue strength of the transmission shaft, including:

[0019] The Bayesian expectation improvement strategy is used as the optimization point addition criterion to guide the addition of new sample points and solve the response values ​​corresponding to the new sample points;

[0020] Get the maximum value of the Bayesian expected change of the current surrogate model and determine whether its value meets the accuracy condition; if so, the optimization is terminated and the optimal solution of the current surrogate model is the optimal solution of the design space; if not, the calculation requires adding new sample points.

[0021] Furthermore, a genetic algorithm is used for global search to solve the optimal structural parameters and fatigue life of the transmission shaft under the constraints, including:

[0022] Taking the agent model as the fitness function, the genetic algorithm is used to find the optimal solution in the given design space;

[0023] The termination condition is set. If the termination condition is met, the optimization process ends, the optimized transmission shaft size parameters are output, and the accuracy of the method is verified by numerical simulation method. If it is not met, the parameters are updated through evolutionary operation and the optimization is performed again until the termination condition is met and the optimization process ends.

[0024] In the second aspect, the technical solution adopted by the present invention is: a transmission shaft fatigue strength optimization system, which includes: an optimization design module, based on the established parameterized model of the transmission shaft, using the entropy weight TOPSIS method to calculate the contribution of key structural parameters to the output response of the transmission shaft, and taking the structural parameters with the highest contribution as the design variables for the fatigue strength optimization design of the transmission shaft, and establishing a mathematical model for the fatigue strength optimization design of the transmission shaft to calculate the performance response value of the transmission shaft model, the performance response value includes stress, strain and life; an agent model construction module, constructing an initial Kriging agent model based on the selected design variables and the corresponding performance response values, and setting a control function based on the Bayesian posterior characteristics, introducing it into the classic expectation plus point strategy to establish a Kriging agent model of Bayesian expectation improved control; an optimization result determination module, taking the maximum life of the transmission shaft as the goal, optimizing the fatigue strength of the transmission shaft based on the Kriging agent model of the Bayesian expectation improved control, and using a genetic algorithm for global search to solve the optimal structural parameters and fatigue life of the transmission shaft that meets the constraints.

[0025] In a third aspect, the technical solution adopted by the present invention is: a computer-readable storage medium storing one or more programs, wherein the one or more programs include instructions, and when the instructions are executed by a computing device, the computing device executes any one of the above methods.

[0026] In a fourth aspect, the technical solution adopted by the present invention is: a computing device, comprising: one or more processors, a memory and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for executing any of the above methods.

[0027] The present invention adopts the above technical solution, which has the following advantages:

[0028] 1. The transmission shaft fatigue strength simulation optimization design method based on the improved Kriging proxy model combined with the genetic algorithm adopts the entropy weight TOPSIS method to quickly solve the contribution of key structural dimensions to the output response of the transmission shaft parametric model to reduce the input parameter dimension, so as to achieve rapid modeling of the analysis object and effective dimensionality reduction of the optimization design problem.

[0029] 2. The present invention adopts a control function and introduces a classical expectation adding point strategy to establish a Kriging proxy model of Bayesian improved expectation control to improve the iteration speed, stability and calculation accuracy of the Kriging proxy model.

[0030] 3. The present invention adopts an improved proxy model to fit the implicit relationship between design variables and constraints, carries out low-cycle fatigue strength optimization design with the optimization goal of maximizing the life of the transmission shaft, and uses a genetic algorithm for optimization and solution, which can effectively improve the fatigue life of the transmission shaft. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a flow chart of a method for optimizing fatigue strength of a transmission shaft according to an embodiment of the present invention;

[0032] Figure 2 is a schematic diagram of the interface of the transmission shaft modeling plug-in in an embodiment of the present invention;

[0033] Figure 3 is a stress-strain cloud diagram obtained by numerical simulation calculation of the transmission shaft model in an embodiment of the present invention;

[0034] Figure 4 is the single contribution of the design variable in the embodiment of the present invention;

[0035] Figure 5 is the comprehensive contribution of the design variables in the embodiment of the present invention;

[0036] FIG6( a ) is a comparison result of the iteration speed of three strategies using Squared as the test function in an embodiment of the present invention;

[0037] FIG6( b ) is a comparison result of the iteration speed of three strategies using Branin as the test function in an embodiment of the present invention;

[0038] FIG6( c ) is a comparison result of the iteration speed of three strategies using Paulson as the test function in an embodiment of the present invention;

[0039] FIG. 7( a ) is a robustness comparison result of three strategies using Squared as the test function in an embodiment of the present invention;

[0040] FIG7( b ) is a robustness comparison result of three strategies using Branin as the test function in an embodiment of the present invention;

[0041] FIG. 7( c ) is a robustness comparison result of three strategies using Paulson as the test function in an embodiment of the present invention;

[0042] FIG8( a ) is a comparison result between the predicted value and the simulated calculated value of the quality in an embodiment of the present invention;

[0043] FIG8( b ) is a comparison result of the predicted response value of the natural frequency and the simulation calculated value in the embodiment of the present invention;

[0044] FIG8( c ) is a comparison result of the predicted response value of the maximum deformation and the simulation calculated value in an embodiment of the present invention;

[0045] FIG8( d ) is a comparison result of the predicted response value of the maximum stress and the simulation calculated value in an embodiment of the present invention;

[0046] FIG8( e ) is a comparison result of the predicted value of the life span and the simulation calculated value in the embodiment of the present invention. DETAILED DESCRIPTION

[0047] Most transmission shafts have large structural dimensions and complex service environments, and their fatigue strength and reliability face severe tests. To address this problem, a transmission shaft fatigue strength optimization method, system, storage medium, and computing device are proposed to significantly reduce the calculation time while ensuring the accuracy of the design results. This is of great significance for ensuring the normal, stable, and safe operation of mechanical equipment.

[0048] The present invention takes the transmission shaft of special vehicles as the research object, and carries out the fatigue strength optimization design of the transmission shaft based on finite element analysis combined with the improved Kriging proxy model. Firstly, the parametric model of the transmission shaft is established by secondary development of ABAQUS using Python, and the stress-strain response of the transmission shaft model with existing structural dimensions under typical starting conditions is analyzed quickly and efficiently. Then the entropy weight TOPSIS method is used to calculate the contribution of key structural parameters to the output response of the transmission shaft. Based on the Bayesian posterior characteristics, a control function is proposed, which is introduced into the classic expectation plus point strategy to establish a Kriging proxy model of Bayesian expectation improved control. Finally, the structural parameters with high contribution are used as design variables, and the fatigue strength optimization design of the transmission shaft is carried out based on the improved proxy model with the goal of maximizing the life of the transmission shaft. A genetic algorithm is used for global search to solve the optimal structural parameters and fatigue life of the transmission shaft that meet the constraints.

[0049] In order to make the purpose, technical solution and advantages of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field belong to the scope of protection of the present invention.

[0050] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0051] In one embodiment of the present invention, a method for optimizing the fatigue strength of a transmission shaft is provided. In this embodiment, Figure 1 As shown, the method comprises the following steps:

[0052] 1) Based on the established parametric model of the transmission shaft, the entropy weight TOPSIS method is used to calculate the contribution of key structural parameters to the output response of the transmission shaft. The structural parameters with the highest contribution are used as the design variables for the fatigue strength optimization design of the transmission shaft. A mathematical model for the fatigue strength optimization design of the transmission shaft is established to calculate the performance response values ​​of the transmission shaft model, such as stress, strain and life; among them, the key structural parameters include spline parameters and shaft segment parameters.

[0053] 2) An initial Kriging surrogate model is constructed based on the selected design variables and the corresponding performance response values, and a control function is set based on the Bayesian posterior characteristics, which is introduced into the classic expectation plus point strategy to establish a Kriging surrogate model of Bayesian expectation improved control.

[0054] 3) Taking the maximum life of the transmission shaft as the goal, the fatigue strength of the transmission shaft is optimized based on the Kriging surrogate model of Bayesian expectation improved control, and a genetic algorithm is used for global search to solve the optimal structural parameters and fatigue life of the transmission shaft that meets the constraints.

[0055] In the above step 1), the establishment of the parameterized model of the transmission shaft is specifically as follows:

[0056] According to the basics of mechanical design and mathematical analysis methods, the coordinate parameter equations of the involute and helix series points are established. Based on the secondary development of ABAQUS with Python, the spur involute spline is accurately modeled to accurately and conveniently establish the spur involute spline model, and the transmission shaft modeling plug-in is developed, such as Figure 2 shown.

[0057] In the above step 1), the entropy weight TOPSIS method is used to calculate the contribution of key structural parameters to the output response of the transmission shaft, and the structural parameter with the highest contribution is used as the design variable for the fatigue strength optimization design of the transmission shaft, which includes the following steps:

[0058] 1.1.1) Finite element analysis: The model was reasonably simplified and the cyclic symmetric interaction provided by ABAQUS software was set to further reduce the computational cost.

[0059] For example, the elastic modulus of the material properties is 210GPa, and the Poisson's ratio is 0.3. The middle spline applies a torque of 9815.12Nm (torque corresponding to the maximum output power), and the splines at both ends are fixed (tooth surface displacement constraint). Convergence analysis is performed to determine the appropriate unit model mesh size, and the model is finally divided into 58305 meshes, and the minimum mesh size at the spline root of the short shaft end is 0.0961.

[0060] Combined with the boundary constraints and loads, according to the material properties of the transmission shaft, the finite element analysis of the initial simplified model of the transmission shaft is carried out to obtain the stress distribution cloud map and deformation cloud map results, such as Figure 3 The average stress of the short shaft is significantly higher than that of the long shaft, and the maximum stress occurs at the root of the spline at the short shaft end, which is consistent with the actual crack initiation area obtained from the bench test.

[0061] 1.1.2) Calculate the contribution of parameters: select parameters that can improve structural strength and service life through finite element analysis, and calculate the single contribution of parameters to each response index through the entropy weight TOPSIS method. Further calculation is performed based on the results of the single contribution of each evaluation index to obtain the comprehensive contribution of each response index. The structural parameter with the highest comprehensive contribution is used as the design variable.

[0062] In this embodiment, the key design variables of the special vehicle transmission shaft include spline parameters and shaft section parameters, wherein the spline parameters include the root fillet chigen, the pressure angle alpha1 and the undercut R1, and the shaft section parameters include the inner diameter Radius3, the outer diameter Radius1 and the transition fillet Radius2 of the short shaft. Finite element analysis found that the selection of 30° round root spline can significantly improve the structural strength and service life of the spline. The single contribution of the structural parameters to each response index is calculated by the entropy weight TOPSIS method, and the results are as follows Figure 4 As shown in the figure, M represents the model mass, U represents the maximum deformation of the model, F represents the natural frequency of the model, S represents the maximum stress of the model, and L represents the life of the model. The undercut R1 has the largest contribution to the maximum deformation U of the transmission shaft. Further calculations are made based on the results of the single contribution of each evaluation index to obtain the comprehensive contribution of each response index, as shown in Figure 5 As shown, the short shaft outer diameter Radius1 and the transition fillet Radius2 of the transmission shaft have the highest comprehensive contribution to all response indicators, so they are determined as the design variables for the fatigue strength optimization design of the transmission shaft.

[0063] In the above step 1), a mathematical model for optimizing the fatigue strength of the transmission shaft is established, including the following steps:

[0064] 1.2.1) The selected design variables are used as input parameters, and the mass of the drive shaft and the performance response obtained after finite element analysis are used as constraints;

[0065] In this embodiment, the selected design variables are used as input parameters, the mass of the transmission shaft and the performance response obtained after finite element analysis are used as constraints, and the fatigue life calculation results are used as optimization targets to establish a mathematical model. From the results of the contribution calculation, it can be seen that the main factors affecting the deformation are the outer diameter and transition radius of the transmission shaft stub. Therefore, the outer diameter Radius1 of the transmission shaft stub is the first design variable x1, and the transition radius of the stub is the second design variable x2. The design variables are:

[0066] X=[x1,x2]

[0067] The upper and lower limits of the design variables are obtained by analysis after multiple calculations and can be expressed as:

[0068] 42≤x1≤56

[0069] 3≤x2≤40

[0070] 1.2.2) Calculate fatigue life: The fatigue life of the transmission shaft is solved based on the multi-axial fatigue damage model of the critical surface of normal strain, and the maximum value of the calculated fatigue life is used as the optimization target to establish a mathematical model.

[0071] In this embodiment, although the transmission shaft is subjected to a uniaxial load, there is a multiaxial stress state at the spline tooth root. The present invention uses a critical surface multiaxial fatigue damage model based on normal strain to solve the fatigue life of the transmission shaft. The formula is as follows:

[0072]

[0073] In the formula, Δε max is the normal strain range on the critical plane; σ′ f is the fatigue strength coefficient, b is the fatigue strength index, ε′ f is the fatigue plasticity coefficient, c is the fatigue plasticity index, these four parameters can be obtained by consulting the literature; N f is fatigue life, and E is elastic model.

[0074] In this embodiment, the transmission shaft fatigue strength optimization design is to seek the optimization design with the maximum fatigue life of the transmission shaft, so as to improve the service life of the transmission shaft through the optimization of structure and size. Therefore, the maximum fatigue life is set as the objective function:

[0075] min[-f(x)]

[0076] After fatigue strength optimization design, the mass M, maximum deformation U, natural frequency F and maximum stress S of the transmission shaft all have range requirements, that is, the corresponding constraints are:

[0077] g1(x)≤26.59

[0078] g2(x)≤1.0820

[0079] g3(x)≥104.50

[0080] g4(x)≤2280.63

[0081] Finally, the mathematical model is established as:

[0082] find:X=[x1,x2]

[0083] min:1 / f(x)

[0084] stg1(x)≤26.59

[0085] g2(x)≤1.0820

[0086] g3(x)≥104.50

[0087] g4(x)≤2280.63

[0088] Among them, g1(x) represents the constraint condition of mass M, g2(x) represents the constraint condition of maximum deformation U, g3(x) represents the constraint condition of natural frequency F, and g4(x) represents the constraint condition of maximum stress S.

[0089] In the above step 1), calculating and obtaining the performance response value of the transmission shaft model includes the following steps:

[0090] 1.3.1) Extract initial sample points: Use Latin hypercube sampling method to extract sample points within the range of design variables to establish the design space.

[0091] 1.3.2) Numerical simulation calculation of performance response: The sample point data extracted are input into the mathematical model in sequence, and the performance response values ​​such as stress, strain and life of the drive shaft model are obtained through finite element analysis and numerical calculation.

[0092] In the above step 2), a Kriging proxy model of Bayesian expectation improved control is established, specifically: determine whether the accuracy of the initial Kriging proxy model meets the set requirements, if it does, output the optimal design variables and the corresponding optimal response values, otherwise set the control function based on the Bayesian posterior characteristics, introduce it into the classic expectation plus point strategy, and obtain the Kriging proxy model of Bayesian expectation improved control.

[0093] In this embodiment, an initial Kriging proxy model is constructed based on the extracted design variables and the corresponding performance response values, and the accuracy of the model is verified. If the accuracy meets the requirements, the optimal design variables and the corresponding optimal response values ​​are output. Otherwise, the proxy model is updated according to the point addition strategy.

[0094] In the above step 3), the fatigue strength of the transmission shaft is optimized based on the Kriging surrogate model of the Bayesian expectation improvement control with the goal of maximizing the service life of the transmission shaft, including the following steps:

[0095] 3.1) Using the Bayesian expectation improvement strategy as the optimization point addition criterion, guide the addition of new sample points and solve the response values ​​corresponding to the new sample points;

[0096] 3.2) Obtain the maximum value of the Bayesian expected change of the current surrogate model and determine whether its value meets the accuracy condition; if so, the optimization is terminated and the optimal solution of the current surrogate model is the optimal solution of the design space; if not, the calculation requires the addition of new sample points.

[0097] In this embodiment, the control function is constructed using the Bayesian posterior characteristic as follows:

[0098]

[0099] In the formula, x i is the input sample point, x i+1 is a new sample point, r() is the Gaussian kernel function, and is the hyperparameter to be determined, m is the dimension of the input variable, and d≈1 / m.

[0100] In the actual modeling process, the improvement direction is affected by the randomness of the initial sample design, which may lead to unsatisfactory improvement direction. Therefore, the first maximum expected improvement point generated in the classic expected improvement strategy is selected as the initial reference point to construct a function of the following form:

[0101]

[0102] In the formula, is the approximate value of the predicted point, y min is the smallest true value, Φ represents the probability density function of the standard normal distribution, φ represents the standard normal distribution function, is the standard deviation of the predicted values.

[0103] Finally, the Bayesian expected improvement control optimization strategy is constructed by applying the control function to the EI strategy (expected point addition strategy). The BYEI function (Bayesian function) with constraints can be expressed as:

[0104]

[0105] In the formula, P[G i (x)≤0] is the probability that the constraint is satisfied at any point x.

[0106] The Bayesian expectation improvement strategy is used as the optimization point addition criterion to guide the addition of new sample points and solve the response values ​​corresponding to the new sample points. Then the maximum value of the Bayesian expectation change of the current model is calculated to determine whether its value meets the accuracy condition. If it does, the optimization is terminated, and the optimal solution of the current proxy model is the optimal solution of the design space. If it does not meet the requirements, the calculation requires the addition of new sample points.

[0107] In the above step 3), a genetic algorithm is used to perform a global search to solve the optimal structural parameters and fatigue life of the transmission shaft that meet the constraints, specifically:

[0108] The surrogate model is used as the fitness function, and the genetic algorithm is used to seek the optimal solution in the given design space. The population is set to 200, the crossover rate is 0.8, the mutation rate is 0.05, and the roulette wheel is used as the selection strategy. The termination condition is 3000 iterations or the fitness is less than 0.001. If the termination condition is met, the optimization process ends, the optimized transmission shaft size parameters are output, and the accuracy of the method is verified by numerical simulation methods. If not, the parameters are updated through evolutionary operations and the optimization is performed again until the termination condition is met and the optimization process ends.

[0109] After the above steps are executed, the step of analyzing the superiority of BYEI strategy is also included: taking three test functions, Squared, Branin and Paulson, to compare and analyze the three point adding strategies of EI, WEI and BYEI from the three aspects of number of iterations, model accuracy and robustness, as shown in the figure. Figure 6(a) to Figure 7(c) It is found that the Kriging proxy model under the BYEI improved control strategy of the present invention has faster iteration speed and stronger robustness.

[0110] The root mean square error (RMSE) and mean absolute percent error (MAPE) are selected as the model prediction accuracy indicators. The expressions of RMSE and MAPE are shown in the formula. The smaller the value, the higher the model prediction accuracy:

[0111]

[0112] Among them, f ri and f ki are the true response value obtained for the i-th test sample and the predicted response value of the Kriging model.

[0113] As can be seen from Table 1, the accuracy of the EI and WEI methods is not much different, while the RMSE and MAPE of the BYEI method are significantly smaller than those of the first two methods, indicating that the BYEI strategy has higher calculation accuracy.

[0114] Table 1 Comparison of calculation accuracy of three strategies

[0115]

[0116] After the above steps are executed, the step of analyzing the fitting accuracy of the response value is also included. 20 groups of samples are obtained by optimal Latin hypercube sampling, and the Kriging model controlled by BYEI optimization strategy is used to fit the mass, natural frequency, maximum stress, maximum deformation and life. The optimization model is solved by genetic algorithm, and the error scatter plot of each response value is obtained as shown in the figure. Figure 8(a) to Figure 8(e) As shown, the error points are distributed along the 45° diagonal, indicating that the Kriging model controlled by the BYEI optimization strategy has a good fitting effect.

[0117] The optimization solution results of the proxy model controlled by the BYEI point optimization strategy are shown in Table 2. The calculation results show that the optimized model has an increase in mass and natural frequency compared to the model with the initial value of the design variables, but the local maximum stress and maximum deformation are reduced, and the fatigue life is finally increased. The obtained optimization scheme increases the mass of the transmission shaft by about 2.35% and the natural frequency by about 3.98%, reduces the local maximum stress by 21.33% and the maximum deformation by about 4.12%, thereby increasing the average fatigue life of the transmission shaft structure from 7818 cycles to 12204 cycles, an increase of 56.11%.

[0118] Table 2 Optimization results

[0119]

[0120] In summary, compared with the prior art, the present invention is a transmission shaft fatigue strength simulation optimization design method based on an improved Kriging proxy model combined with a genetic algorithm. This method uses the entropy weight TOPSIS method to quickly solve the contribution of key structural dimensions to the output response of the transmission shaft parameterized model to reduce the input parameter dimension; then a control function is proposed and the classic expectation point addition strategy is introduced to establish a Kriging proxy model of Bayesian improved expectation control to improve the accuracy and efficiency of the proxy model; finally, the improved proxy model is used to fit the implicit relationship between the design variables and the constraints, and the low-cycle fatigue strength optimization design is carried out with the transmission shaft life as large as possible as the optimization goal, and the genetic algorithm is used for optimization and solution.

[0121] Therefore, the method of the present invention has at least the following advantages: (1) rapid modeling of the analysis object; (2) effective dimensionality reduction of the optimization design problem; (3) improving the iteration speed, stability and calculation accuracy of the Kriging proxy model; (4) effectively improving the fatigue life of the transmission shaft. In one embodiment of the present invention, a transmission shaft fatigue strength optimization system is provided, which includes:

[0122] The optimization design module uses the entropy weight TOPSIS method to calculate the contribution of key structural parameters to the output response of the transmission shaft based on the established parametric model of the transmission shaft. The structural parameters with the highest contribution are used as the design variables for the fatigue strength optimization design of the transmission shaft. The mathematical model for the fatigue strength optimization design of the transmission shaft is established to calculate the performance response value of the transmission shaft model, which includes stress, strain and life.

[0123] The surrogate model construction module builds the initial Kriging surrogate model based on the selected design variables and the corresponding performance response values, and sets the control function based on the Bayesian posterior characteristics, which is introduced into the classic expectation plus point strategy to establish the Kriging surrogate model of Bayesian expectation improved control;

[0124] The optimization result determination module takes the maximum life of the transmission shaft as the goal, optimizes the fatigue strength of the transmission shaft based on the Kriging agent model of Bayesian expectation improved control, and uses genetic algorithm for global search to solve the optimal structural parameters and fatigue life of the transmission shaft that meets the constraints.

[0125] In the above embodiment, the entropy weight TOPSIS method is used to calculate the contribution of key structural parameters to the output response of the transmission shaft, and the structural parameter with the highest contribution is used as the design variable for the fatigue strength optimization design of the transmission shaft, including:

[0126] Combined with boundary constraints and loads, according to the material properties of the transmission shaft, the finite element analysis of the initial simplified model of the transmission shaft was performed to obtain the stress distribution cloud map and deformation cloud map results;

[0127] Finite element analysis is used to select parameters that can improve structural strength and service life, and the single contribution of the parameters to each response index is calculated by the entropy weight TOPSIS method. Further calculations are made based on the results of the single contribution of each evaluation index to obtain the comprehensive contribution of each response index. The structural parameters with the highest comprehensive contribution are used as design variables.

[0128] In the above embodiment, a mathematical model for optimizing the fatigue strength design of the transmission shaft is established, including:

[0129] The selected design variables are used as input parameters, and the mass of the transmission shaft and the performance response obtained after finite element analysis are used as constraints;

[0130] The fatigue life of the transmission shaft is solved based on the critical surface multi-axial fatigue damage model of normal strain, and the calculated maximum fatigue life is used as the optimization target to establish a mathematical model.

[0131] In the above embodiment, calculating and obtaining the performance response value of the transmission shaft model includes:

[0132] The Latin hypercube sampling method is used to extract sample points within the range of design variables to establish the design space;

[0133] The extracted sample point data are input into the mathematical model in sequence, and the performance response value of the drive shaft model is obtained through finite element analysis and numerical calculation.

[0134] In the above embodiment, a Kriging agent model of Bayesian expectation improvement control is established, including:

[0135] Determine whether the accuracy of the initial Kriging surrogate model meets the set requirements. If it does, the optimal design variables and the corresponding optimal response values ​​are output. Otherwise, the control function is set based on the Bayesian posterior characteristics and introduced into the classic expectation plus point strategy to obtain the Kriging surrogate model of Bayesian expectation improved control.

[0136] In the above embodiment, the fatigue strength of the transmission shaft is optimized based on the Kriging agent model of the Bayesian expectation improvement control with the goal of maximizing the service life of the transmission shaft, including:

[0137] The Bayesian expectation improvement strategy is used as the optimization point addition criterion to guide the addition of new sample points and solve the response values ​​corresponding to the new sample points;

[0138] Get the maximum value of the Bayesian expected change of the current surrogate model and determine whether its value meets the accuracy condition; if so, the optimization is terminated and the optimal solution of the current surrogate model is the optimal solution of the design space; if not, the calculation requires adding new sample points.

[0139] In the above embodiment, a genetic algorithm is used to perform a global search to solve the optimal structural parameters and fatigue life of the transmission shaft that meet the constraints, including:

[0140] Taking the agent model as the fitness function, the genetic algorithm is used to find the optimal solution in the given design space;

[0141] The termination condition is set. If the termination condition is met, the optimization process ends, the optimized transmission shaft size parameters are output, and the accuracy of the method is verified by numerical simulation method. If it is not met, the parameters are updated through evolutionary operation and the optimization is performed again until the termination condition is met and the optimization process ends.

[0142] The system provided in this embodiment is used to execute the above-mentioned method embodiments. Please refer to the above-mentioned embodiments for specific processes and detailed contents, which will not be repeated here.

[0143] In one embodiment of the present invention, a computing device is provided, which may be a terminal, and may include: a processor, a communication interface, a memory, a display screen, and an input device. Among them, the processor, the communication interface, and the memory communicate with each other through a communication bus. The processor is used to provide computing and control capabilities. The memory includes a non-volatile storage medium and an internal memory, and the non-volatile storage medium stores an operating system and a computer program. When the computer program is executed by the processor, the method in each of the above embodiments is implemented; the internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be implemented through WIFI, a management network, NFC (near field communication) or other technologies. The display screen may be a liquid crystal display screen or an electronic ink display screen, and the input device may be a touch layer covered on the display screen, or a key, trackball or touchpad provided on the housing of the computing device, or an external keyboard, touchpad or mouse, etc. The processor may call the logic instructions in the memory.

[0144] In addition, the logic instructions in the above-mentioned memory can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0145] In one embodiment of the present invention, a computer program product is provided, wherein the computer program product includes a computer program stored on a non-transitory computer-readable storage medium, wherein the computer program includes program instructions. When the program instructions are executed by a computer, the computer can execute the methods provided by the above-mentioned method embodiments.

[0146] In one embodiment of the present invention, a non-transitory computer-readable storage medium is provided, wherein the non-transitory computer-readable storage medium stores server instructions, and the computer instructions enable a computer to execute the methods provided in the above embodiments.

[0147] The above embodiment provides a computer-readable storage medium, whose implementation principle and technical effect are similar to those of the above method embodiment, and will not be repeated here.

[0148] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0149] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0150] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0151] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing fatigue strength of a transmission shaft, characterized in that: include: Based on the established parametric model of the transmission shaft, the entropy weight TOPSIS method is used to calculate the contribution of key structural parameters to the output response of the transmission shaft. The structural parameters with the highest contribution are used as the design variables for the fatigue strength optimization design of the transmission shaft. A mathematical model for the fatigue strength optimization design of the transmission shaft is established to calculate the performance response value of the transmission shaft model, which includes stress, strain and life. The initial Kriging surrogate model is constructed based on the selected design variables and the corresponding performance response values, and the control function is set based on the Bayesian posterior characteristics, which is introduced into the classic expectation plus point strategy to establish the Kriging surrogate model of Bayesian expectation improved control. With the goal of maximizing the life of the transmission shaft, the fatigue strength of the transmission shaft is optimized based on the Kriging surrogate model of Bayesian expectation improved control, and a genetic algorithm is used for global search to solve the optimal structural parameters and fatigue life of the transmission shaft that meets the constraints.

2. The transmission shaft fatigue strength optimization method according to claim 1, characterized in that: The entropy weight TOPSIS method is used to calculate the contribution of key structural parameters to the output response of the transmission shaft, and the structural parameters with the highest contribution are used as the design variables for the fatigue strength optimization design of the transmission shaft, including: Combined with boundary constraints and loads, according to the material properties of the transmission shaft, the finite element analysis of the initial simplified model of the transmission shaft was performed to obtain the stress distribution cloud map and deformation cloud map results; Finite element analysis is used to select parameters that can improve structural strength and service life, and the single contribution of the parameters to each response index is calculated by the entropy weight TOPSIS method. Further calculations are made based on the results of the single contribution of each evaluation index to obtain the comprehensive contribution of each response index. The structural parameters with the highest comprehensive contribution are used as design variables.

3. The transmission shaft fatigue strength optimization method according to claim 1, characterized in that: Establish a mathematical model for the optimal design of transmission shaft fatigue strength, including: The selected design variables are used as input parameters, and the mass of the transmission shaft and the performance response obtained after finite element analysis are used as constraints; The fatigue life of the transmission shaft is solved based on the critical surface multi-axial fatigue damage model of normal strain, and the calculated maximum fatigue life is used as the optimization target to establish a mathematical model.

4. The transmission shaft fatigue strength optimization method according to claim 3, characterized in that: The performance response values ​​of the transmission shaft model are calculated, including: The Latin hypercube sampling method is used to extract sample points within the range of design variables to establish the design space; The extracted sample point data are input into the mathematical model in sequence, and the performance response value of the drive shaft model is obtained through finite element analysis and numerical calculation.

5. The transmission shaft fatigue strength optimization method according to claim 1, characterized in that: Building the Bayesian Phase Hope for improvement and control The Kriging surrogate model is composed of: Determine whether the accuracy of the initial Kriging surrogate model meets the set requirements. If it does, the optimal design variables and the corresponding optimal response values ​​are output. Otherwise, the control function is set based on the Bayesian posterior characteristics and introduced into the classic expectation plus point strategy to obtain the Kriging surrogate model of Bayesian expectation improved control.

6. The transmission shaft fatigue strength optimization method according to claim 5, characterized in that: With the goal of maximizing the life of the transmission shaft, the Kriging surrogate model based on Bayesian expectation improved control is used to optimize the fatigue strength of the transmission shaft, including: The Bayesian expectation improvement strategy is used as the optimization point addition criterion to guide the addition of new sample points and solve the response values ​​corresponding to the new sample points; Get the maximum value of the Bayesian expected change of the current surrogate model and determine whether its value meets the accuracy condition; if so, the optimization is terminated and the optimal solution of the current surrogate model is the optimal solution of the design space; if not, the calculation requires adding new sample points.

7. The transmission shaft fatigue strength optimization method according to claim 1, characterized in that: Genetic algorithm is used for global search to find the optimal structural parameters and fatigue life of the transmission shaft under the constraints, including: Taking the agent model as the fitness function, the genetic algorithm is used to find the optimal solution in the given design space; The termination condition is set. If the termination condition is met, the optimization process ends, the optimized transmission shaft size parameters are output, and the accuracy of the method is verified by numerical simulation method. If it is not met, the parameters are updated through evolutionary operation and the optimization is performed again until the termination condition is met and the optimization process ends.

8. A transmission shaft fatigue strength optimization system, characterized in that: include: The optimization design module uses the entropy weight TOPSIS method to calculate the contribution of key structural parameters to the output response of the transmission shaft based on the established parametric model of the transmission shaft. The structural parameters with the highest contribution are used as the design variables for the fatigue strength optimization design of the transmission shaft. The mathematical model for the fatigue strength optimization design of the transmission shaft is established to calculate the performance response value of the transmission shaft model, which includes stress, strain and life. The surrogate model construction module builds the initial Kriging surrogate model based on the selected design variables and the corresponding performance response values, and sets the control function based on the Bayesian posterior characteristics, which is introduced into the classic expectation plus point strategy to establish the Kriging surrogate model of Bayesian expectation improved control; The optimization result determination module takes the maximum life of the transmission shaft as the goal, optimizes the fatigue strength of the transmission shaft based on the Kriging agent model of Bayesian expectation improved control, and uses genetic algorithm for global search to solve the optimal structural parameters and fatigue life of the transmission shaft that meets the constraints.

9. A computer-readable storage medium storing one or more programs, characterized in that: The one or more programs include instructions, which, when executed by a computing device, cause the computing device to perform any one of the methods of claims 1 to 7.

10. A computing device, characterized in that include: One or more processors, memory and one or more Programs, One or more programs are stored in the memory and configured as one or more processors Execution, the one or more programs include instructions for executing any one of the methods according to claims 1 to 7.

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