A large wind turbine shaft integrated multi-objective structural optimization design method considering ultimate and fatigue strength

Abstract

The application discloses a large wind turbine shaft integrated multi-objective structure optimization design method considering limit and fatigue strength. The method takes the whole shaft as a design object, obtains multiple lightweight design schemes meeting requirements by a three-stage integrated design process of concept design, configuration design and size optimization under the condition of considering the interaction of the low-speed shaft, the bearing seat and the base, and taking the limit strength and the fatigue strength as constraints, and significantly shortens the design cycle and reduces the requirement for the experience of engineers.

Description

Technical Field

[0001] This invention belongs to the field of wind turbine generator structure design technology, specifically relating to an integrated multi-objective structural optimization design method for the shaft system of a large wind turbine generator considering ultimate strength and fatigue strength. In particular, it relates to an integrated multi-objective optimization design method for the shaft system of a large wind turbine generator considering the interaction between the low-speed shaft, bearing housing, and base, with ultimate strength and fatigue strength as constraints. Background Technology

[0002] As the capacity of wind turbine units continues to increase, the shaft system, as the core load-bearing component connecting the rotor to the gearbox or generator, directly affects the safety and economy of the entire unit. Currently, the structural design of wind turbine shaft systems typically treats the low-speed shaft, bearing housing, and base as independent components for separate design and verification, while other components are merely simplified as constraints, neglecting the load transfer coupling effect between components. This leads to overly conservative design results. Furthermore, traditional design requires repeated adjustments to geometric parameters and iterative calculations of limits and fatigue strength, resulting in long design cycles and reliance on personal experience. When there are more than ten parameters, it is difficult to guarantee optimality. In addition, shaft system design must simultaneously consider multiple conflicting objectives. Traditional weighted single-objective methods are highly subjective and cannot provide a Pareto optimal solution set for decision-making. Topology optimization and dimensional optimization are also often disconnected, lacking a complete optimization chain from conceptual design to detailed design.

[0003] Therefore, there is an urgent need for a multi-objective structural optimization design method that can take into account the interaction effects between shaft components and simultaneously meet the requirements of ultimate strength and fatigue strength. Summary of the Invention

[0004] This invention addresses the shortcomings of existing technologies by providing a multi-objective structural optimization design method for the integrated shaft system of large wind turbines, considering ultimate strength and fatigue strength. This method takes the entire shaft system as the design object and, through a three-stage integrated design process of conceptual design, configuration design, and dimensional optimization, obtains multiple lightweight design schemes that meet the requirements, while considering the interaction between the low-speed shaft, bearing housing, and base, and using ultimate strength and fatigue strength as constraints. This significantly shortens the design cycle and reduces the requirements for engineers' experience.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A multi-objective structural optimization design method for the integrated shaft system of a large wind turbine considering ultimate and fatigue strength includes the following steps: Step S1: Conceptual Design and Overall Modeling S1.1. Based on the wind turbine's rated power, rotor diameter, cut-in / cut-out wind speed, and extreme wind speed, determine the technical route and initial geometric model of the shaft system. The initial geometric model includes components such as the hub, low-speed shaft, bearing housing, bearings, base, and part of the tower. The connection methods between the components are as follows: the low-speed shaft is connected to the bearing housing via the main bearing, the bearing housing is connected to the base via high-strength bolts, and the rest are all connected by binding.

[0006] S1.2 Establish the global finite element model of the initial geometric model, including: 1) The model is discretized using tetrahedral mesh as the main component and hexahedral mesh as the auxiliary component, and the mesh is refined locally for key parts; 2) The main bearing roller is simulated by using rod elements. The stiffness of the roller is simulated by setting the material properties and cross-sectional area of ​​the elements, and the unidirectional bearing characteristics of bearing only pressure and not tension are reflected. 3) Beam elements are used to simulate bolts and screws, and multi-body constraint elements are used to connect the screws and nuts to simulate the thread meshing effect. The bolt preload and the friction between the contact surfaces of each component are also taken into account in the calculation. 4) The torsional stiffness of the gearbox is simulated by using a torsion spring unit.

[0007] S1.3 Apply the calculated ultimate load and equivalent fatigue load to the hub center respectively. The load includes forces (axial thrust Fx, horizontal force Fy, vertical force Fz) and bending moments (torsional moment Mx, pitching moment My, yaw moment Mz) in three spatial directions. Set the bottom of the tower as a fixed constraint and then perform simulation calculations.

[0008] Step S2, Configuration Design S2.1 Based on the initial geometric model from step S1, determine the design variables for topology optimization. The design variables include: 1) Control parameters for low-speed shaft: span SFL, journal radius SFR, flange thickness SFD1, thickness at front bearing SFD2, thickness at rear bearing SFD3; 2) Control parameters of bearing housing: width ZCZK, main body thickness ZCZD1, support beam thickness ZCZD2, support beam height ZCZH; 3) Control parameters of the base: thickness DZD1, support beam thickness DZD2, height DZH.

[0009] S2.2. Taking the minimum compliance as the objective of topology optimization, topology optimization calculations are performed with the constraints that the global maximum equivalent stress calculated under extreme conditions does not exceed the allowable stress of the material, the maximum equivalent stress calculated under fatigue conditions does not exceed the allowable fatigue stress amplitude of the material, and the optimized mass is 60%~80% of the initial mass.

[0010] S2.3. Based on the material density distribution cloud map obtained from topology optimization, identify the load-bearing area and the area where material can be reduced; adjust the model control parameters according to the topology optimization results, and reconstruct the shaft system geometric model, including: adding unloading grooves at stress concentration points and reducing the thickness of non-load-bearing areas.

[0011] Step S3, Size Optimization S3.1 Perform parametric modeling on the geometric model reconstructed in step S2 to determine the design input parameters for fine-tuning the dimensional parameters. The input parameters include, but are not limited to: the thickness of the front and rear bearing connection parts of the bearing housing, the thickness of the support beam, the height of the support beam, the thickness of the main body, the span of the low-speed shaft, the journal radius, the maximum radius of the central cavity, the thickness at the rear bearing, the thickness at the front bearing, the flange thickness, the height and thickness of the base, and the thickness of the support beam.

[0012] S3.2. Sample the design parameters from step S3.1 using experimental design methods to generate N sample points within the design space. The experimental design methods include, but are not limited to, any of the following: (a) Optimal Space-Filling Design (OSF) can distribute design parameters evenly throughout the design space; (b) Latin Hypercube Sampling (LHS) achieves stratified sampling across all parameter dimensions to ensure spatial coverage of the samples; (c) Uniform Design, which is suitable for situations with multidimensional parameter spaces and limited sample size; (d) Sampling methods for low-difference sequences such as Sobol or Halton sequences have better space-filling performance.

[0013] Preferably, the optimal space-filling design method is adopted, and the number of sample points N = 50~60.

[0014] S3.3 Substitute the parameter values ​​of each sample point from step S3.2 into the shaft system geometric model one by one, perform finite element static calculation, and obtain the output parameter values ​​corresponding to each sample point. The output parameters include: the maximum equivalent stress of the low-speed shaft, base, and bearing housing under all ultimate load conditions and equivalent fatigue load conditions, as well as the mass of the bearing housing, the mass of the low-speed shaft, and the mass of the base.

[0015] S3.4. Based on the sample data from step S3.3, establish the mapping relationship between input parameters and output parameters using a surrogate model method. The surrogate model method includes, but is not limited to, any one or more combinations of the following: (a) Nonparametric regression methods (such as Kriging model and radial basis function RBF) have good nonlinear fitting ability and prediction variance estimation ability; (b) The Polynomial Response Surface Method (PRSM) is suitable for problems with low nonlinearity and has high modeling efficiency; (c) Support Vector Regression (SVR) achieves nonlinear regression through kernel function mapping and has good generalization performance under small sample conditions; (d) Gaussian Process Regression (GPR) can provide quantification of the uncertainty of prediction results and is suitable for situations that require confidence interval assessment. (e) Artificial Neural Networks (ANNs), including feedforward neural networks (BP neural networks) and radial basis function neural networks (RBFNNs), fit the complex mapping relationship between input and output through multi-layer nonlinear transformations, and are suitable for modeling the response of highly nonlinear and strongly coupled systems; (f) Deep Neural Network (DNN) extracts high-order features through a multi-layer hidden layer structure and is suitable for building surrogate models when the sample size is sufficient and the input parameters have a high dimension. (g) Ensemble learning methods, including Random Forest, Gradient Boosting Regression Tree (GBRT), and Extreme Gradient Boosting (XGBoost), improve prediction accuracy and robustness by combining multiple weak learners. They are suitable for situations with large sample sizes and interactive effects between input parameters. (h) The surrogate model method based on transfer learning uses simulation data of existing similar axis system designs to pre-train the model and achieve rapid modeling under small sample conditions.

[0016] Randomly select several verification points (preferably 5-8) and substitute them into the real finite element model for verification. When the coefficient of determination R² > 0.99 and the maximum relative residual δ > 0.99, the verification is successful. max If the accuracy of the surrogate model is less than 1% and the relative root mean square error (RRMSE) is less than 1%, the accuracy of the surrogate model is deemed to meet the requirements. If the accuracy does not meet the requirements, the number of sample points is increased and the surrogate model is retrained.

[0017] S3.5. Based on the surrogate model established in step S3.4, with the minimization of low-speed shaft mass, bearing housing mass, and base mass as the three optimization objectives, and with the constraints that the maximum equivalent stress of each component under ultimate load does not exceed the allowable stress of the material, and the maximum equivalent stress under equivalent fatigue load does not exceed the allowable fatigue stress amplitude of the material, a multi-objective optimization algorithm is used to solve the problem and obtain the Pareto front solution set. The multi-objective optimization algorithm includes, but is not limited to, any of the following: (a) Non-dominated sorting genetic algorithm (NSGA-II), which adopts fast non-dominated sorting and crowding distance mechanism, has fast convergence speed and uniform solution set distribution; (b) The multi-objective evolutionary algorithm based on decomposition (MOEA / D) decomposes the multi-objective problem into several single-objective sub-problems and optimizes them simultaneously; (c) Multi-objective particle swarm optimization algorithm (MOPSO) has a fast convergence speed and is suitable for continuous design space; (d) Intensive Pareto Evolutionary Algorithm (SPEA2) uses external archives to preserve non-dominated solutions, resulting in better solution distribution.

[0018] Preferably, the NSGA-II algorithm is used.

[0019] S3.6 Select several candidate schemes (preferably 4-6) from the Pareto front obtained in step S3.5. Substitute the design parameters of the candidate schemes into the real finite element model to verify the ultimate strength and fatigue strength. After ensuring that each scheme meets the ultimate strength and fatigue strength requirements, output the design parameters and corresponding mass and stress data of each candidate scheme for designers to select the final scheme according to actual needs. If the verification strength is not met, repeat step S3.5 or add sample points and repeat steps S3.4 to S3.5.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. The interaction between shaft system components was taken into consideration. This invention employs a holistic finite element model for simulation calculations, and uses rod elements, beam elements, and MPC184 elements to accurately simulate the nonlinear contact behavior of bearing rollers and bolt connections, thus realistically reflecting the load transmission coupling effect between the low-speed shaft, bearing housing, and base. Sensitivity analysis shows that the stress and mass of each component are not only affected by its own geometry but also significantly influenced by the geometry of other components, proving the necessity of the holistic design method of this invention. 2. Incorporate both ultimate strength and fatigue strength into the constraint conditions. In the entire process of topology optimization, surrogate model construction and multi-objective optimization, this invention uses limit strength and fatigue strength as constraints to ensure that the optimization results have sufficient static strength reserve and fatigue life at the same time, thus avoiding the problem of the disconnect between limit design and fatigue design in traditional methods. 3. Significantly shortens the design cycle and reduces reliance on experience. This invention replaces a large amount of time-consuming finite element calculations with a proxy model and automatically searches for the optimal parameter combination through a genetic algorithm, eliminating the need for engineers to repeatedly try and adjust, thus significantly shortening the traditional design cycle. 4. Provide Pareto optimal solution sets to support design decisions This invention employs a multi-objective algorithm to directly obtain the Pareto front of three conflicting mass objectives. It can simultaneously output multiple lightweight schemes that meet both ultimate strength and fatigue strength constraints, allowing designers to flexibly choose according to their preferences. Verification through examples shows that the optimized scheme reduces the total mass by 20% to 20.9% compared to the initial scheme. 5. Seamless integration of topology optimization and fine-grained optimization of dimensional parameters This invention forms a complete design chain of "conceptual design → topology optimization → size optimization". First, the optimal force transmission path is determined through topology optimization, and then the lightweight is maximized through detailed optimization of size parameters. Attached Figure Description

[0021] Figure 1 This is an overall flowchart of the method in this invention; Figure 2 This is a schematic diagram of the overall finite element model of the shaft system in an embodiment of the present invention; Figure 3 This is a schematic diagram of bearing roller simulation in an embodiment of the present invention (Link180 unit); Figure 4 This is a schematic diagram simulating bolt connection and thread engagement in an embodiment of the present invention (beam element + MPC184 element). Figure 5 This is a diagram of the main control parameters in an embodiment of the present invention; Figure 6 This is the Pareto front plot of the target parameter in this embodiment of the invention. Detailed Implementation

[0022] The present invention will be further described below with reference to specific embodiments. These embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0023] This embodiment provides a specific implementation process for optimizing the shaft system design of a 3MW wind turbine using the above method. The optimization design method is as follows: Figure 1 As shown.

[0024] The first step is to determine the overall parameters: rated power 3000kW, rotor diameter 155m, cut-in wind speed 2.5m / s, rated wind speed 8.7m / s, cut-out wind speed 19m / s, extreme wind speed 32.5m / s, and design life 20 years.

[0025] The second step is to establish the following steps according to step S1: Figure 2 The overall finite element model is shown. (See example.) Figure 3 , 4 The figures shown are simulation diagrams of the bearing rollers, bolt connections, and threaded engagement in the overall finite element model. The mesh size was set to 1,027,506 (after mesh independence verification, the stress error at this order of magnitude is <2%). The low-speed shaft material is QT450 (allowable stress 236MPa), and the bearing housing and base material is QT400 (allowable stress 200MPa).

[0026] The third step is to perform initial strength verification. The ultimate strength verification results show that the maximum stress on the low-speed shaft is 196.31 MPa (<236 MPa), the maximum stress on the bearing housing is 188.09 MPa (<200 MPa), and the maximum stress on the base is 184.1 MPa (<200 MPa). The fatigue strength verification results show that the fatigue damage of each component is less than 1 (0.81 for the low-speed shaft, 0.71 for the bearing housing, and 0.86 for the base), and the initial model meets the ultimate strength and fatigue strength requirements.

[0027] The fourth step is to perform topology optimization. For example... Figure 5 The diagram shows the main control parameters. With constraints that the global maximum stress does not exceed the allowable stress of the material, the maximum stress under fatigue conditions does not exceed the allowable stress amplitude of material fatigue, and 70% of the mass is retained, after obtaining the topology optimization density cloud map, unloading grooves are added and non-load-bearing parts are thinned. After reconstruction, the model mass is reduced by about 10.5%.

[0028] The fifth step involves generating 55 sample points using the OSF method to establish a surrogate model between the input and output parameters. The input parameters consist of nine geometric design variables for the shaft system, including: thickness P8 at the bearing connection points before and after the bearing housing, thickness P9 of the bearing housing support beam, thickness P10 of the bearing housing body, span P11 of the low-speed shaft, journal radius P12 of the low-speed shaft, maximum radius of the central cavity of the low-speed shaft P13, thickness P14 at the rear bearing of the low-speed shaft, thickness P15 at the front bearing of the low-speed shaft, and flange thickness P16 of the low-speed shaft.

[0029] The output parameters are divided into two categories: ultimate strength response and fatigue strength response. Ultimate strength output parameters include: the maximum equivalent stress P1 of the low-speed shaft, the maximum equivalent stress P2 of the base, and the maximum equivalent stress P3 of the bearing housing under all extreme working conditions, as well as the mass of the bearing housing P4, the mass of the low-speed shaft P5, and the mass of the base P6. Fatigue strength output parameters include: the maximum equivalent stress P7 of the low-speed shaft, the maximum equivalent stress P8 of the base, and the maximum equivalent stress P9 of the bearing housing under all equivalent fatigue load conditions.

[0030] The accuracy verification results of the surrogate model are as follows: the coefficient of determination R² for each output parameter is greater than 0.997, the maximum relative residual is less than 0.431%, the relative root mean square error is less than 0.364%, and the maximum error at the verification point is less than 0.378%, indicating that the accuracy of the surrogate model meets the requirements.

[0031] Step 6: The NSGA-II algorithm (initial sample size 9000, maximum iterations 20, crossover probability 0.98, mutation probability 0.01) is used for multi-objective optimization. The optimization objectives are minimizing P4, P5, and P6, with limit strength constraints of P1≤236MPa, P2≤200MPa, and P3≤200MPa, and fatigue strength constraints of P7≤158MPa, P8≤123MPa, and P9≤123MPa. The solution yields the following results: Figure 6 The Pareto front plot of the target parameters shown converged in step 8, yielding 5 candidate schemes. The total mass of each scheme is 41.50~41.91t, which is 9.5%~10.4% lighter than the 46.30t of the topology optimization model. Verification using a real finite element model confirmed that all schemes simultaneously meet the requirements for ultimate strength and fatigue strength.

[0032] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A multi-objective structural optimization design method for the integrated shaft system of a large wind turbine considering ultimate limits and fatigue strength, characterized in that, Includes the following steps: S1. Conceptual Design and Overall Modeling Based on the overall parameters of the wind turbine, the initial geometric model of the shaft system is determined; the overall finite element model of the initial geometric model is established, and the ultimate load, equivalent fatigue load, and boundary conditions are applied. S2, Configuration Design Based on the initial geometric model, the design variables for topology optimization are determined; the minimum compliance calculated in the simulation is taken as the objective of topology optimization, and topology optimization calculations are performed based on the constraints; the shaft system geometric model is reconstructed based on the material density distribution cloud map obtained from topology optimization. S3, Size Optimization Based on the reconstructed shaft system geometric model, a proxy model is used to replace finite element calculation. With mass and strength as optimization objectives and constraints, a multi-objective algorithm is used to automatically search for the optimal combination of dimensional parameters, and a feasible solution is output after verification by real simulation.

2. The integrated multi-objective structural optimization design method for the shaft system of a large wind turbine considering ultimate limits and fatigue strength, as described in claim 1, is characterized in that... Step S1 specifically includes: S11. Based on the overall parameters of the wind turbine, determine the initial geometric model of the shaft system; the initial geometric model includes the hub, low-speed shaft, bearing housing, bearing, base and part of the tower. The low-speed shaft is connected to the bearing housing through the main bearing, the bearing housing is connected to the base through high-strength bolts, and the remaining components are connected by binding. S12. Establish the overall finite element model of the initial geometric model, including: a. Discretize the initial geometric model using tetrahedral mesh as the main component and hexahedral mesh as the auxiliary component, and refine the local mesh for key parts; b. The main bearing roller is simulated by using rod elements. The stiffness of the roller is simulated by setting the material properties and cross-sectional area of ​​the elements, and the unidirectional bearing characteristics of bearing only pressure and not tension are reflected. c. Beam elements are used to simulate bolts and screws, and multi-body constraint elements are used to connect the screws and nuts to simulate the thread meshing effect. The bolt preload and the friction between the contact surfaces of each component are also taken into account in the calculation. d. The torsional stiffness of the gearbox is simulated using a torsion spring unit; S13. Apply the calculated ultimate load and equivalent fatigue load to the hub center; the ultimate load and equivalent fatigue load include forces and moments in three spatial directions, namely axial thrust Fx, horizontal force Fy, vertical force Fz, torsional moment Mx, pitching moment My, and yaw moment Mz; and set the bottom of the tower as a fixed constraint.

3. The integrated multi-objective structural optimization design method for the shaft system of a large wind turbine considering ultimate and fatigue strength as described in claim 1, characterized in that, Step S2 specifically includes: S21. Based on the initial geometric model, determine the design variables for topology optimization; the design variables include the control parameters of the low-speed shaft, the control parameters of the bearing housing, and the control parameters of the base; the control parameters of the low-speed shaft include the span, journal radius, flange thickness, thickness at the front bearing, and thickness at the rear bearing; the control parameters of the bearing housing include the bearing housing width, main body thickness, bearing housing support beam thickness, and bearing housing support beam height; the control parameters of the base include the base thickness, base support beam thickness, and base height. S22. The goal of topology optimization is to minimize the compliance calculated by simulation, and topology optimization calculation is performed based on constraints. The constraints include: the global maximum equivalent stress calculated under extreme conditions does not exceed the allowable stress of the material; the maximum equivalent stress calculated under fatigue conditions does not exceed the allowable stress amplitude of material fatigue; and the mass retained after optimization is 60-80% of the initial mass. S23. Based on the material density distribution cloud map obtained from topology optimization, identify the load-bearing area and the area where material can be reduced; adjust the model control parameters according to the topology optimization results, add unloading grooves at stress concentration points, and reduce the thickness of non-load-bearing areas to reconstruct the shaft system geometric model.

4. The integrated multi-objective structural optimization design method for the shaft system of a large wind turbine considering ultimate and fatigue strength as described in claim 1, characterized in that, Step S3 specifically includes: S31. Perform parametric modeling on the reconstructed shaft system geometric model to determine the design input parameters for fine-tuning the dimensional parameters; S32. Using experimental design methods, sample points are generated in the design space, finite element static calculations are performed on each sample point, and the corresponding output parameters are obtained as sample data. S33. Based on sample data, establish a surrogate model to characterize the mapping relationship between design input parameters and output parameters; S34. Based on the surrogate model, the optimization objective is to minimize the mass of the low-speed shaft, bearing housing, and base. The constraint is that the global maximum equivalent stress calculated under extreme conditions does not exceed the allowable stress of the material, and the maximum equivalent stress calculated under fatigue conditions does not exceed the allowable fatigue stress amplitude of the material. A multi-objective optimization algorithm is used to solve the problem and obtain the Pareto front solution set. S35. Select candidate solutions from the Pareto front solution set, and after verification by the real finite element model, output the candidate solutions that meet the requirements of ultimate strength and fatigue strength.

5. The integrated multi-objective structural optimization design method for the shaft system of a large wind turbine considering ultimate and fatigue strength, as described in claim 4, is characterized in that... The design input parameters in step S31 include the thickness of the front and rear bearing connection parts of the bearing housing, the thickness of the support beam, the height of the support beam, the thickness of the main body, the span of the low-speed shaft, the journal radius, the maximum radius of the central cavity, the thickness of the rear bearing, the thickness of the front bearing, the flange thickness, the height and thickness of the base, and the thickness of the support beam.

6. The integrated multi-objective structural optimization design method for the shaft system of a large wind turbine considering ultimate and fatigue strength, as described in claim 5, is characterized in that... The experimental design method used in step S32 is any one of the following: optimal space-filling design, Latin hypercube sampling, uniform design, or low-difference sequence sampling methods such as Sobol or Halton sequences. The output parameters include the maximum equivalent stress of the low-speed shaft, base, and bearing housing under all extreme load conditions and equivalent fatigue load conditions, as well as the mass of the bearing housing, the mass of the low-speed shaft, and the mass of the base.

7. The integrated multi-objective structural optimization design method for the shaft system of a large wind turbine considering ultimate and fatigue strength, as described in claim 6, is characterized in that... The surrogate model in step S33 is any one or more of the following: nonparametric regression model, multinomial response surface model, support vector regression model, Gaussian process regression model, artificial neural network model, deep neural network model, ensemble learning model, and surrogate model based on transfer learning.

8. The integrated multi-objective structural optimization design method for the shaft system of a large wind turbine considering ultimate and fatigue strength, as described in claim 7, is characterized in that... The multi-objective optimization algorithm used in step S34 is any one of the following: non-dominated sorting genetic algorithm, decomposition-based multi-objective evolutionary algorithm, multi-objective particle swarm optimization algorithm, and intensity Pareto evolutionary algorithm.

9. The integrated multi-objective structural optimization design method for the shaft system of a large wind turbine considering ultimate and fatigue strength, as described in claim 4, is characterized in that... Step S33 further includes: Several verification points were randomly selected and substituted into the real finite element model for verification. When the coefficient of determination R² > 0.99 and the maximum relative residual δ > 0.99, the verification was successful. max If the accuracy of the surrogate model is less than 1% and the relative root mean square error (RRMSE) is less than 1%, the accuracy of the surrogate model is deemed to meet the requirements. If the accuracy does not meet the requirements, the number of sample points is increased and the surrogate model is retrained.

10. The integrated multi-objective structural optimization design method for the shaft system of a large wind turbine considering ultimate and fatigue strength, as described in claim 4, is characterized in that... Step S35 further includes: If the verification strength is not met, repeat step S34 or add sample points and then repeat steps S33 and S34.

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