Titanium matrix composite blisk structure design method based on sequential sampling global optimization

Abstract

The application relates to the technical field of aero-engines and discloses a titanium-based composite material integral shroud structure design method based on sequential sampling global optimization. Latin hypercube sampling is used to generate initial sample points in the design space of design variables of a titanium-based composite material integral shroud, output responses of the sample points are obtained through simulation, a training data set is constructed, a proxy model is built to represent the mapping relationship between the design variables and the target and the constraint conditions; and then the proxy model is iteratively optimized by using a sequential sampling strategy to obtain an optimal design variable combination. The application guides sampling by using a modified maximum expected criterion function based on the characteristics of anisotropic materials, automatically balances between global exploration and local development, avoids falling into a local optimal solution, efficiently obtains a global optimal structure parameter meeting multiple constraint conditions under limited computing resources, speeds up the optimization process, and greatly reduces the computing cost.

Description

Technical Field

[0001] This invention relates to the field of aero-engine technology and discloses a design method for an integral blade ring structure of titanium-based composite materials based on sequential sampling global optimization. Background Technology

[0002] Titanium-based composite integral blade rings are key components for achieving significant weight reduction in aero engines, and their optimized design typically relies on traditional global optimization methods such as finite element simulation and genetic algorithms.

[0003] However, existing methods have the following shortcomings:

[0004] 1. High-fidelity simulation of integral blade rings of titanium-based composite materials (including fiber / matrix interface damage, anisotropic constitutive model, and thermo-mechanical coupling analysis) has extremely high computational costs, with a single evaluation taking several hours. Traditional global optimization algorithms require thousands of simulations, resulting in optimization cycles of several months, which is difficult to meet the timeliness requirements of engineering research and development. 2. This optimization problem is characterized by high nonlinearity, multimodality, and multiple constraint coupling. Gradient-based local optimization methods are prone to getting trapped in local optima, while traditional global optimization algorithms, although possessing certain global search capabilities, have insufficient convergence accuracy under limited computational budgets and are difficult to obtain the true optimal structural parameters. 3. Existing surrogate model-assisted optimization methods are mostly designed for isotropic homogeneous materials, and lack adaptive sampling strategies for the anisotropic characteristics of titanium-based composite materials and the damage response at the fiber / matrix interface. They are unable to balance global exploration and local development during the optimization process. Summary of the Invention

[0005] The purpose of this invention is to provide a design method for the overall blade ring structure of titanium-based composite materials based on sequential sampling global optimization. This method can automatically balance global exploration and local development, avoid getting trapped in local optima, and efficiently obtain globally optimal structural parameters that satisfy multiple constraints under limited computing resources, thereby accelerating the optimization process and significantly reducing computational costs.

[0006] To achieve the above-mentioned technical effects, the technical solution adopted by the present invention is as follows: A design method for an integral blade ring structure of titanium-based composite materials based on sequential sampling and global optimization includes: Step 1: Determine the design variables, objective function, and constraints of the integral blade ring made of titanium-based composite material; the design variables include one or more of the following: volume fraction of titanium-based composite material and structural dimensions of the integral blade ring; the objective function includes minimizing the mass of the integral blade ring or maximizing the limiting speed; the constraints include one or more of the following: strength constraints, stiffness constraints, maximum failure speed constraints, vibration frequency avoidance constraints, and manufacturability constraints. Step 2: Use the Latin hypercube sampling method to generate an initial set of sample points in the design space of the design variables, and call the simulation model to perform simulation analysis on each sample point to obtain the corresponding objective function response value and constraint response value, and construct the initial training dataset; Step 3: Based on the initial training dataset, construct a surrogate model to represent the mapping relationship between the objective function response value, constraint response value and design variables; Step 4: Adaptive iterative optimization is performed using a sequential sampling strategy. In each iteration, a sampling function is constructed based on the current surrogate model. New sample points are generated with the goal of maximizing the sampling function, and simulation analysis is performed. The training dataset and surrogate model are updated synchronously. Step 5: Determine whether the updated surrogate model meets the convergence condition. If it does, output the optimal combination of design variables corresponding to the current surrogate model. Otherwise, repeat step 4 until the updated surrogate model meets the convergence condition. If it does, output the optimal combination of design variables corresponding to the current surrogate model.

[0007] Furthermore, the simulation model includes an anisotropic constitutive model of titanium-based composite materials and a matrix interface cohesive model.

[0008] Furthermore, the surrogate model is a Kriging model or a support vector regression model.

[0009] Furthermore, the constructed acquisition function is a modified maximization expectation criterion function that considers the properties of anisotropic materials, and its expression is: ,in For the sample points of the design variables, The value of the acquisition function; Let be the minimum value of the objective function. For sample points Predicted values ​​in the surrogate model, Let be the probability distribution function of the standard normal distribution. The minimum value predicted by the objective function. The variance of the actual target values ​​for the sample points. The distribution function of the normal distribution. To account for the correction factor of anisotropic materials, The tensile properties of titanium-based composite materials in the main load-bearing direction. The tensile properties of titanium-based composite materials in the direction perpendicular to the main load-bearing direction.

[0010] Furthermore, the conditions for determining whether the updated proxy model meets the convergence criteria include: the change in the minimum value of the objective function after several consecutive iterations is less than a preset threshold, or the preset number of simulation model calls is reached.

[0011] Furthermore, the design space for the design variables includes: The volume fraction of the titanium-based composite material ranges from 35% to 65%. The value range of the inner diameter of the overall blade ring of the titanium-based composite material is 150mm~220mm; The radial thickness of the integral blade ring of the titanium-based composite material ranges from 10 mm to 25 mm; The axial thickness of the overall blade ring of the titanium-based composite material ranges from 10 mm to 30 mm. The thickness of the integral blade ring cladding of the titanium-based composite material ranges from 1 mm to 3.5 mm.

[0012] Furthermore, methods for generating new sample points with the goal of maximizing the acquisition function include: The current surrogate model is globally optimized using a multi-island genetic algorithm or a particle swarm optimization algorithm to obtain a new combination of design variables that satisfies the maximization of the acquisition function.

[0013] Furthermore, the sequential sampling strategy described in step 4 also includes a parallel sampling mechanism, in which multiple new sample points are selected simultaneously in each iteration, and the simulation model is called in parallel to perform simulation analysis using multi-core or multi-node computing resources.

[0014] Compared with existing technologies, the advantages of this invention are as follows: This invention utilizes Latin hypercube sampling to generate initial sample points within the design space of the design variables for the integral blade ring of titanium-based composite materials. The output responses of these sample points are obtained through simulation to construct a training dataset. A surrogate model is then built to represent the mapping relationship between design variables and the response values ​​of the objective function and constraints. A sequential sampling strategy is then used to iteratively optimize the surrogate model to obtain the optimal combination of design variables. This invention relies on the modified maximization expectation criterion function of anisotropic material properties to guide sampling, automatically balancing global exploration and local development, avoiding getting trapped in local optima. This allows for efficient acquisition of globally optimal structural parameters that satisfy multiple constraints under limited computational resources, accelerating the optimization process and significantly reducing computational costs. Attached Figure Description

[0015] Figure 1 This is a flowchart of the design method for the overall blade ring structure of titanium-based composite materials based on sequential sampling global optimization in the embodiments; Figure 2 This is a schematic diagram of the integral blade ring of titanium-based composite material in the embodiment. Detailed Implementation

[0016] The present invention will now be described in further detail with reference to the embodiments and accompanying drawings. However, this should not be construed as limiting the scope of the above-described subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0017] Example 1 See Figure 1 and Figure 2 A design method for an integral blade ring structure of titanium-based composite materials based on sequential sampling and global optimization includes: Step 1: Determine the design variables, objective function, and constraints of the integral blade ring made of titanium-based composite material; the design variables include one or more of the following: volume fraction of titanium-based composite material and structural dimensions of the integral blade ring; the objective function includes minimizing the mass of the integral blade ring or maximizing the limiting speed; the constraints include one or more of the following: strength constraints, stiffness constraints, maximum failure speed constraints, vibration frequency avoidance constraints, and manufacturability constraints. Step 2: Use the Latin hypercube sampling method to generate an initial set of sample points in the design space of the design variables, and call the simulation model to perform simulation analysis on each sample point to obtain the corresponding objective function response value and constraint response value, and construct the initial training dataset; Step 3: Based on the initial training dataset, construct a surrogate model to represent the mapping relationship between the objective function response value, constraint response value and design variables; Step 4: Adaptive iterative optimization is performed using a sequential sampling strategy. In each iteration, a sampling function is constructed based on the current surrogate model. New sample points are generated with the goal of maximizing the sampling function, and simulation analysis is performed. The training dataset and surrogate model are updated synchronously. Step 5: Determine whether the updated surrogate model meets the convergence condition. If it does, output the optimal combination of design variables corresponding to the current surrogate model. Otherwise, repeat step 4 until the updated surrogate model meets the convergence condition. If it does, output the optimal combination of design variables corresponding to the current surrogate model.

[0018] In this embodiment, initial sample points are generated within the design space of the design variables for the integral blade ring of the titanium-based composite material using Latin hypercube sampling. The output responses of these sample points are obtained through simulation to construct a training dataset. A surrogate model is then built to represent the mapping relationship between the design variables and the response values ​​of the objective function and constraints. A sequential sampling strategy is then used to iteratively optimize the surrogate model to obtain the optimal combination of design variables. This invention relies on the modified maximization expectation criterion function of anisotropic material properties to guide sampling, automatically balancing global exploration and local development to avoid getting trapped in local optima. It can effectively find the globally optimal structural parameters of the integral blade ring of the titanium-based composite material under multiple constraints. Furthermore, it can reduce the number of high-fidelity simulation calls from thousands to tens to hundreds, compressing the optimization cycle from months to days, significantly reducing computational costs. It is suitable for ultra-large-scale design variables or multi-objective optimization scenarios.

[0019] Example 2 This embodiment takes the integral blade ring of the first stage compressor of a certain type of aero-engine as the optimization object, and provides a detailed description of the titanium-based composite material integral blade ring structure design method based on sequential sampling global optimization of the present invention. The specific design process is as follows: Step 1: Determine the design variables, objective function, and constraints of the integral blade ring made of titanium-based composite material; the design variables include one or more of the following: volume fraction of titanium-based composite material and structural dimensions of the integral blade ring; the objective function includes minimizing the mass of the integral blade ring or maximizing the limiting speed; the constraints include one or more of the following: strength constraints, stiffness constraints, maximum failure speed constraints, vibration frequency avoidance constraints, and manufacturability constraints. In this embodiment, the titanium-based composite material system is a continuous SiC fiber reinforced Ti2AlNb-based composite material; design variables (5 in total) and their design space are defined: fiber volume fraction Value range: 35%~65%; Overall blade ring inner diameter Value range: 150mm~220mm; Overall blade ring radial thickness Value range: 10mm~25mm; Overall blade ring axial thickness Value range: 10mm~30mm; Overall blade ring casing wall thickness Value range: 1mm~3.5mm.

[0020] Define the objective function: minimize the overall blade ring mass. ; Constraints: Based on the blade ring manufacturing process definition, the manufacturability constraint is set to the integral blade ring shroud wall thickness not being less than 1 mm; other constraints are defined as needed, and will not be detailed here.

[0021] Define constraint response value: This embodiment focuses on examining the response value of the maximum failure speed of the integral blade ring under the constraint conditions. .

[0022] Therefore, the optimization problem can ultimately be defined as:

[0023]

[0024] .

[0025] Step 2: Use the Latin hypercube sampling method to generate an initial sample point set in the design space of the design variables, and call the simulation model to perform simulation analysis for each sample point to obtain the structural response of the overall blade ring corresponding to each sample point under the super-rotation condition, obtain the corresponding objective function value and constraint response value, and construct the initial training dataset. In this embodiment, optimal Latin hypercube sampling is used to generate 20 initial sample points in the design space, and each sample point corresponds to a complete set of 5-dimensional design variables.

[0026] In this embodiment, a finite element simulation model is used for simulation analysis of each sample point. This model includes material properties such as an isotropic elastic constitutive model of the titanium alloy sheath, an anisotropic elastic constitutive model of the composite material ring core, and cohesive elements at the fiber / matrix interface, as well as the over-rotation load. The simulation for each sample point takes approximately 3.5 hours (8-core parallel processing). The initial 20 sample points took approximately 70 hours to construct the initial training dataset. .

[0027] Step 3: Based on the initial training dataset, construct a surrogate model to represent the mapping relationship between the objective function response value, the constraint response value, and the design variables; In this embodiment, the objective function response values ​​are respectively... and constraint response values Establish an independent Kriging model. Use a Gaussian correlation function, and select a second-order polynomial for the regression part.

[0028] Step 4: Adaptive iterative optimization is performed using a sequential sampling strategy. In each iteration, a sampling function is constructed based on the current surrogate model. New sample points are generated with the goal of maximizing the sampling function, and simulation analysis is performed. The training dataset and surrogate model are updated synchronously. In this embodiment, the maximum number of high-fidelity simulation calls is set to 120 (including the initial 20), which means an additional 100 sequential samplings.

[0029] In each iteration: 4.1) Calculate the modified maximization expectation criterion function considering the properties of anisotropic materials, the formula is: ,in For the sample points of the design variables, The value of the acquisition function; Let be the minimum value of the objective function. For sample points Predicted values ​​in the surrogate model, Let be the probability distribution function of the standard normal distribution. The minimum value predicted by the objective function. The variance of the actual objective function values ​​for the sample points. The distribution function of the normal distribution. To account for the correction factor of anisotropic materials, The tensile properties of titanium-based composite materials in the main load-bearing direction. The tensile properties of titanium-based composite materials in the direction perpendicular to the main load-bearing direction.

[0030] For points that do not meet the constraints, a penalty factor is used to... Multiply by the product of the probability of the constraint being satisfied.

[0031] 4.2) Maximize using a multi-island genetic algorithm The acquisition function selects the next evaluation point as a new sample point from the candidate point set. The sequential sampling strategy in this embodiment also includes a parallel sampling mechanism, which selects multiple new sample points simultaneously in each iteration and uses multi-core or multi-node computing resources to call the simulation model in parallel to perform simulation analysis.

[0032] 4.3) Use high-fidelity simulation to obtain the real response value and add it to the training dataset.

[0033] 4.4) Update the Kriging proxy model.

[0034] Step 5: Determine if the convergence condition is met. If not, repeat step 4. If it is met, output the current optimal combination of design variables. In this embodiment, the convergence condition is set as follows: the quality change of the current optimal solution is less than 0.5% in 10 consecutive iterations; or the preset upper limit of 120 simulation model calls is reached.

[0035] Through simulation iterations, in this embodiment, the objective function (overall blade ring mass) has converged to a stable value in the 58th iteration, and a total of 96 high-fidelity simulations were called (less than the preset upper limit of 120).

[0036] The optimal combination of design variables is output after the conditions are met, as shown in Table 1 below: Table 1. Statistical table of the value range of each design variable and the obtained optimal combination of design variables.

[0037] Under this optimal design, the overall blade ring mass is 10.65 kg, which is 32.3% lighter than the initial design (using empirical parameters such as a uniform fiber volume fraction of 35% and a core sheath thickness of 4.0 mm). All constraints are satisfied.

[0038] To highlight the superiority of the present invention, a control group was set up: the same overall leaf ring problem was optimized using a traditional genetic algorithm (population size 50, 100 iterations, 5000 simulations in total), and the high-fidelity simulation model in Example 2 was also used.

[0039] Table 2 Comparison of the Invention Method and Traditional Genetic Algorithm Optimization Design

[0040] The results show that the design method of the present invention achieves better (lighter) design results with only about 1 / 50 of the computational cost, which fully demonstrates the efficiency and accuracy advantages of the sequential sampling surrogate model method.

[0041] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A design method for an integral blade ring structure of titanium-based composite materials based on sequential sampling and global optimization, characterized in that, include: Step 1: Determine the design variables, objective function, and constraints of the integral blade ring of titanium-based composite material; The design variables include one or more of the following: volume fraction of titanium-based composite material and overall blade ring structure dimensions; the objective function includes minimizing the overall blade ring mass or maximizing the limiting speed; the constraints include one or more of the following: strength constraints, stiffness constraints, maximum failure speed constraints, vibration frequency avoidance constraints, and manufacturability constraints. Step 2: Use the Latin hypercube sampling method to generate an initial set of sample points in the design space of the design variables, and call the simulation model to perform simulation analysis on each sample point to obtain the corresponding objective function response value and constraint response value, and construct the initial training dataset; Step 3: Based on the initial training dataset, construct a surrogate model to represent the mapping relationship between the objective function response value, constraint response value and design variables; Step 4: Adaptive iterative optimization is performed using a sequential sampling strategy. In each iteration, a sampling function is constructed based on the current surrogate model. New sample points are generated with the goal of maximizing the sampling function, and simulation analysis is performed. The training dataset and surrogate model are updated synchronously. Step 5: Determine whether the updated surrogate model meets the convergence condition. If it does, output the optimal combination of design variables corresponding to the current surrogate model. Otherwise, repeat step 4 until the updated surrogate model meets the convergence condition. If it does, output the optimal combination of design variables corresponding to the current surrogate model.

2. The design method for the integral blade ring structure of titanium-based composite materials according to claim 1, characterized in that, The simulation model includes an anisotropic constitutive model of titanium-based composite materials and a matrix interface cohesive model.

3. The method for designing an integral blade ring structure of titanium-based composite material according to claim 1, characterized in that, The surrogate model is either the Kriging model or the support vector regression model.

4. The design method for the integral blade ring structure of titanium-based composite materials according to claim 1, characterized in that, The constructed acquisition function is a modified maximization expectation criterion function that considers the properties of anisotropic materials, and its expression is: ,in For the sample points of the design variables, The value of the acquisition function; Let be the minimum value of the objective function. For sample points Predicted values ​​in the surrogate model, Let be the probability distribution function of the standard normal distribution. The minimum value predicted by the objective function. The variance of the actual target values ​​for the sample points. The distribution function of the normal distribution. To account for the correction factor of anisotropic materials, The tensile properties of titanium-based composite materials in the main load-bearing direction. The tensile properties of titanium-based composite materials in the direction perpendicular to the main load-bearing direction.

5. The design method for the integral blade ring structure of titanium-based composite materials according to claim 1, characterized in that, The conditions for determining whether the updated proxy model meets the convergence criteria include: the change in the minimum value of the objective function is less than a preset threshold after several consecutive iterations, or the preset number of simulation model calls is reached.

6. The method for designing an integral blade ring structure of titanium-based composite material according to claim 1, characterized in that, The design space for the design variables includes: The volume fraction of the titanium-based composite material ranges from 35% to 65%. The value range of the inner diameter of the overall blade ring of the titanium-based composite material is 150mm~220mm; The radial thickness of the integral blade ring of the titanium-based composite material ranges from 10 mm to 25 mm; The axial thickness of the overall blade ring of the titanium-based composite material ranges from 10 mm to 30 mm. The thickness of the integral blade ring cladding of the titanium-based composite material ranges from 1 mm to 3.5 mm.

7. The method for designing an integral blade ring structure of titanium-based composite material according to claim 1, characterized in that, Methods for generating new sample points with the goal of maximizing the acquisition function include: The current surrogate model is globally optimized using a multi-island genetic algorithm or a particle swarm optimization algorithm to obtain a new combination of design variables that satisfies the maximization of the acquisition function.

8. The method for designing an integral blade ring structure of titanium-based composite material according to claim 1, characterized in that, The sequential sampling strategy described in step 4 also includes a parallel sampling mechanism, in which multiple new sample points are selected simultaneously in each iteration, and the simulation model is called in parallel to perform simulation analysis using multi-core or multi-node computing resources.

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