A turbine blade profile multi-working condition aerodynamic proxy optimization method based on principal component analysis
Patent Information
- Application Number
- CN202611099720.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-23
- Publication Date
- 2026-10-13
AI Technical Summary
现有方法未对Pareto前沿样本的几何变化模式进行系统挖掘，一方面使得Pareto前沿样本中隐含的主导几何变化规律未被提取和利用，限制了样本利用效率的进一步提升；另一方面，前沿解集对应的叶型几何变化与气动性能变化之间的关联难以被定量揭示，降低了优化结果的可解释性
1、提高优化效率：通过在样本集数量达到预设阈值后启动主成分分析，使代理优化能够沿Pareto前沿样本所表征的几何协同变化方向展开，提高了样本利用效率和优化搜索效率。实施例数据表明，在达到相同Pareto前沿质量的情况下，本方法所需数值仿真样本数量较原始空间优化减少约46%。
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Figure CN122904447A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of turbine blade profile optimization technology, and more specifically to a multi-condition aerodynamic proxy optimization method for turbine blade profiles based on principal component analysis. Background Technology
[0002] Multi-condition aerodynamic optimization of turbine blade profiles is one of the core issues in turbomachinery design. In practical engineering, turbine blades typically need to operate under multiple conditions: for example, different angles of attack, different expansion ratios, or different guide vane openings—all requiring high aerodynamic efficiency. Therefore, turbine blade profile design cannot be optimized around a single design point, but needs to obtain a compromise solution that takes into account the performance of multiple representative operating conditions.
[0003] Currently, turbine blade aerodynamic surrogate optimization typically employs a combined approach of "parametric modeling—numerical simulation—surrogate model—multi-objective optimization." In parametric modeling, researchers usually use mathematical tools such as Bezier curves, B-spline curves, or non-uniform rational B-splines (NURBS) to parametrically describe the blade geometry, controlling the generation and deformation of the blade profile through several design variables. Based on this, initial samples are generated using design of experiments methods (such as Latin hypercube sampling). For each sample, blade design and computational fluid dynamics (CFD) numerical simulations are performed to calculate aerodynamic performance indicators (such as total pressure loss coefficient and isentropic efficiency) under various operating conditions, forming a sample set. Subsequently, using the design variables from the sample set as input and the objective function value as output, a surrogate model is constructed to approximate the high-cost numerical simulation. Commonly used surrogate models include Kriging models, response surface models, and artificial neural networks. Based on this, a multi-objective optimization algorithm (such as the non-dominated sorting genetic algorithm NSGA-II) is used to search the surrogate model to obtain Pareto candidate samples. These candidate samples are then validated through blade design and numerical simulation, updating the sample set. The above process iterates to continuously enrich the sample set and improve the accuracy of the surrogate model, gradually approaching the true Pareto frontier.
[0004] However, existing turbine blade profile surrogate optimization methods still have two shortcomings:
[0005] First, the coupling relationship between design variables restricts the modeling accuracy and search efficiency of surrogate models: the geometric parameters of turbine blades usually have strong synergistic relationships. For example, the changes in parameters such as blade installation angle, trailing edge turning angle, and inlet / outlet configuration angle are not independent but jointly affect the blade load distribution and loss characteristics. Directly establishing a surrogate model in the original variable space and performing optimization search makes it difficult to effectively identify the impact of the synergistic changes between geometric parameters on aerodynamic performance, thus limiting the prediction accuracy and optimization search efficiency of the surrogate model. In recent years, researchers have attempted to introduce dimensionality reduction methods such as principal component analysis (PCA) into the field of turbomachinery optimization. For example, Huang Pengfei et al. combined direct manipulated free deformation (DFFD) with PCA to map the 36-dimensional design space to a 10-dimensional basic modal coefficient space, and established a surrogate model in the dimensionality-reduced space to complete the optimization; some studies have also applied PCA to rotor blade design space exploration and multi-point multi-objective optimization of rotor airfoils. The above studies mainly use PCA as a design space dimensionality reduction tool to perform dimensionality reduction processing on design variables in the optimization initiation stage.
[0006] Secondly, the geometric variation information implicit in the Pareto front samples has not been fully utilized: In multi-objective optimization, the Pareto front typically only provides a few compromise configurations and their corresponding objective function values, mainly reflecting the trade-offs between performance under different operating conditions. However, the Pareto front samples themselves contain high-quality geometric information selected during the optimization process. These samples represent design schemes retained under different performance trade-offs, and the variation patterns of their geometric parameters reflect the response characteristics of aerodynamic performance to the coordinated changes in airfoil geometry. Existing methods have not systematically mined the geometric variation patterns of Pareto front samples. On the one hand, this prevents the extraction and utilization of the dominant geometric variation patterns implicit in the Pareto front samples, limiting further improvement in sample utilization efficiency; on the other hand, the correlation between the airfoil geometry changes corresponding to the front solution set and the changes in aerodynamic performance is difficult to reveal quantitatively, reducing the interpretability of the optimization results.
[0007] In summary, how to fully utilize the high-quality geometric information implicit in the Pareto front samples to extract the dominant and collaborative change directions among design variables during the multi-condition aerodynamic surrogate optimization of turbine blades, and use this information to guide subsequent surrogate modeling and optimization search, while enhancing the physical interpretability of the optimization results, is a technical problem that urgently needs to be solved in this field. Summary of the Invention
[0008] In view of this, the present invention provides a multi-condition aerodynamic proxy optimization method for turbine blade profiles based on principal component analysis, aiming to solve the above-mentioned technical problems.
[0009] To achieve the above objectives, the present invention adopts the following technical solution: A multi-condition aerodynamic proxy optimization method for turbine blade profiles based on principal component analysis includes: Initial samples are generated based on Latin hypercube sampling. The objective function values of each sample under multiple working conditions are calculated through leaf shape design and numerical simulation to form an initial sample set. A Kriging surrogate model is constructed based on the initial sample set, and multi-objective optimization is performed on the Kriging surrogate model. The obtained Pareto candidate samples are subjected to leaf shape design and numerical simulation to calculate their objective function values. The calculation results are added to the initial sample set to update the sample set. In response to the number of samples in the sample set reaching a preset threshold, Pareto front samples are selected from the sample set, and the design variable matrix of the Pareto front samples is normalized and centered. Singular value decomposition is performed on the centered design variable matrix to obtain principal component basis. Based on the principal component basis, all samples in the sample set are mapped to the principal component space. A Kriging surrogate model is constructed in the principal component space and multi-objective optimization is performed. The Pareto candidate samples in the principal component space are inversely mapped to the original design variables. The samples obtained by inverse mapping are subjected to leaf shape design and numerical simulation to calculate their objective function values. The calculation results are added to the sample set and the sample set is updated.
[0010] Through the above technical solution, this invention improves sample utilization efficiency and optimization search efficiency by initiating principal component analysis only after the sample set reaches a preset threshold, enabling surrogate optimization to proceed along the direction of geometric cooperative change represented by the Pareto front samples, rather than relying solely on the coordinate direction of the original variables. Simultaneously, by performing singular value decomposition on the Pareto front sample design variable matrix, the dominant cooperative change law among turbine blade design variables is extracted, quantitatively revealing the correlation between geometric changes and aerodynamic losses, thus enhancing the interpretability of the optimization results. Furthermore, this technical solution forms a closed-loop iteration between principal component analysis and surrogate optimization, making it suitable for the iterative design process of multi-condition aerodynamic optimization of turbine blades.
[0011] Preferably, in the above-mentioned turbine blade profile multi-condition aerodynamic proxy optimization method based on principal component analysis, the objective function value is the total pressure loss coefficient under different operating conditions: ; in, p t,in Indicates the total import pressure. p t,out Indicates the total export pressure. p out Indicates the outlet static pressure.
[0012] Preferably, in the above-mentioned turbine blade profile multi-condition aerodynamic proxy optimization method based on principal component analysis, constructing the Kriging proxy model based on the sample set specifically includes: For different working conditions, the Kriging surrogate model for the objective function of the sample is constructed by taking the design variable vector of the sample as input and the objective function value of a working condition as output.
[0013] Preferably, in the above-mentioned turbine blade profile multi-condition aerodynamic proxy optimization method based on principal component analysis, the construction of the Kriging proxy model corresponding to the objective function of the operating conditions specifically includes: Determine sample correlation based on the correlation matrix between training samples; Relevant hyperparameters are determined based on a global optimization algorithm; The predicted value of the objective function for the new input point is obtained based on the correlation vector between the new input point and the training samples, the correlation matrix, and the training response vector.
[0014] Preferably, in the above-mentioned turbine blade profile multi-condition aerodynamic surrogate optimization method based on principal component analysis, the multi-objective optimization on the Kriging surrogate model specifically includes: Initialize the population with the variable vectors in the current optimization space; The Kriging surrogate model is used to predict multiple objective function values for individuals in the population. Based on the multiple objective function values, perform non-dominated sorting, selection, crossover, mutation, and population update; Repeat the iteration until the preset maximum number of generations is reached, and use the final population as Pareto candidate samples.
[0015] Preferably, in the above-mentioned turbine blade profile multi-condition aerodynamic proxy optimization method based on principal component analysis, selecting Pareto front samples from the sample set specifically includes: The samples in the sample set are sorted by multiple objective function values corresponding to each sample, and the first non-dominated front sample is taken as the Pareto front sample.
[0016] Preferably, in the above-mentioned turbine blade profile multi-condition aerodynamic proxy optimization method based on principal component analysis, the normalization and centering of the design variable matrix of the Pareto front sample specifically includes: The normalization range is determined by the minimum and maximum values of each design variable in the Pareto front sample; Each design variable is normalized to a dimensionless variable to obtain a normalized design variable matrix; Obtain the column mean vector of the normalized design variable matrix; Subtracting the column mean vector from the normalized design variable matrix yields the centered design variable matrix.
[0017] Preferably, in the above-mentioned turbine blade profile multi-condition aerodynamic proxy optimization method based on principal component analysis, the inverse mapping of Pareto candidate samples in the principal component space to the original design variables specifically includes: Based on the principal component basis and the column mean vector in the centering process, the Pareto candidate samples in the principal component space are converted into normalized design variables; Based on the normalization range, the normalized design variables are denormalized to obtain the original design variables.
[0018] Preferably, in the above-mentioned turbine blade profile multi-condition aerodynamic proxy optimization method based on principal component analysis, the design variables include the blade profile installation angle, trailing edge turning angle, inlet configuration angle, outlet configuration angle, outlet trailing edge half-wedge angle, and axial position of the control point inside the Bézier curve corresponding to the first condition.
[0019] Preferably, in the above-mentioned turbine blade multi-condition aerodynamic proxy optimization method based on principal component analysis, after updating the sample set, Pareto front samples are reselected from the updated sample set, and the design variable matrix of the reselected Pareto front samples is normalized, centered, and decomposed again to update the principal component basis.
[0020] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a turbine blade profile multi-condition aerodynamic proxy optimization method based on principal component analysis, which has the following beneficial effects: 1. Improved optimization efficiency: By initiating principal component analysis after the sample set reaches a preset threshold, surrogate optimization can proceed along the geometric co-variation direction represented by the Pareto front samples, improving sample utilization efficiency and optimization search efficiency. Example data shows that, to achieve the same Pareto front quality, this method requires approximately 46% fewer numerical simulation samples than the original spatial optimization.
[0021] 2. Enhanced interpretability of results: By performing singular value decomposition on the design variable matrix of the Pareto front sample, the dominant synergistic variation law among turbine blade design variables can be extracted. This can quantitatively reveal the correlation between geometric parameter changes and blade load distribution and loss changes, providing a quantitative interpretation basis for multi-condition optimization design of turbine blades.
[0022] 3. Forming an optimization closed loop: Principal component analysis and surrogate optimization are combined into a closed-loop iteration. By continuously updating the sample set and re-performing principal component analysis to update the principal component basis, it is suitable for the iterative design process of turbine blade aerodynamic optimization under multiple working conditions. Attached Figure Description
[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0024] Figure 1 The attached figure is a flowchart of the turbine blade profile multi-condition aerodynamic proxy optimization method based on principal component analysis provided by the present invention. Detailed Implementation
[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0026] Example 1 like Figure 1 As shown, this invention discloses a multi-condition aerodynamic proxy optimization method for turbine blade profiles based on principal component analysis, comprising: Initial samples are generated based on Latin hypercube sampling. The objective function values of each sample under multiple working conditions are calculated through leaf shape design and numerical simulation to form an initial sample set. A Kriging surrogate model is constructed based on the initial sample set, and multi-objective optimization is performed on the Kriging surrogate model. The obtained Pareto candidate samples are subjected to leaf shape design and numerical simulation to calculate their objective function values. The calculation results are added to the initial sample set and the sample set is updated. In response to the number of samples in the sample set reaching a preset threshold, Pareto front samples are selected from the sample set. The design variable matrix of the Pareto front samples is normalized and centered. The singular value decomposition is performed on the centered design variable matrix to obtain the principal component basis. Based on the principal component basis, all samples in the sample set are mapped to the principal component space. A Kriging surrogate model is constructed in the principal component space and multi-objective optimization is performed. The Pareto candidate samples in the principal component space are inversely mapped to the original design variables. The samples obtained by inverse mapping are subjected to leaf shape design and numerical simulation to calculate their objective function values. The calculation results are added to the sample set and the sample set is updated.
[0027] Example 2 This invention discloses a multi-condition aerodynamic proxy optimization method for turbine blade profiles based on principal component analysis, comprising: Initial samples are generated based on Latin hypercube sampling. The objective function values of each sample under multiple operating conditions are calculated through leaf shape design and numerical simulation to form an initial sample set.
[0028] The objective function value is the total pressure loss coefficient under different operating conditions.
[0029] The total pressure loss coefficient is: ; in, p t,in Indicates the total import pressure. p t,out Indicates the total export pressure. p out Indicates the outlet static pressure.
[0030] A Kriging surrogate model is constructed based on the initial sample set, and multi-objective optimization is performed on the Kriging surrogate model. The obtained Pareto candidate samples are subjected to leaf shape design and numerical simulation to calculate their objective function values. The calculation results are added to the initial sample set and the sample set is updated.
[0031] In this embodiment, constructing the Kriging proxy model based on the sample set specifically includes: For different working conditions, the Kriging surrogate model for the objective function of the sample is constructed by taking the design variable vector of the sample as input and the objective function value of a working condition as output.
[0032] In this embodiment, constructing the Kriging proxy model corresponding to the objective function of the working condition specifically includes: Determine sample correlation based on the correlation matrix between training samples; Relevant hyperparameters are determined based on a global optimization algorithm; The predicted value of the objective function for the new input point is obtained based on the correlation vector, correlation matrix, and training response vector between the new input point and the training samples.
[0033] Specifically, for the Kriging surrogate model with any objective function under any working condition, let the training sample be the... i The first sample and the first j The design variable vectors for each sample are as follows: Xi and Xj The correlation between the two can be expressed as: ; in, R ij Represents the correlation matrix R The elements in θ (l) Indicates the first l The relevant hyperparameters for each design variable direction m This indicates the dimension of the design variables.
[0034] The relevant hyperparameters are determined through a global optimization algorithm, and the hyperparameter training process is represented as follows: ; in, n Indicates the number of samples, 1 n Represents a column vector consisting entirely of 1s. β Represented as: ; For new input points x The correlation vector between it and the training samples is represented as: ; in, r j Represents the correlation vector r The elements in.
[0035] New input point x The corresponding objective function prediction value is expressed as:
[0036] Therefore, the objective function for each working condition has an independent Kriging surrogate model, and can predict the objective function value for the corresponding working condition based on the input design variables.
[0037] Multi-objective optimization on the Kriging surrogate model specifically includes: Initialize the population with the variable vectors in the current optimization space; The Kriging surrogate model is used to predict multiple objective function values for individuals in the population. Non-dominated sorting, selection, crossover, mutation, and population update are performed based on multiple objective function values. Repeat the iteration until the preset maximum number of generations is reached, and use the final population as Pareto candidate samples.
[0038] In response to the number of samples in the sample set reaching a preset threshold, Pareto front samples are selected from the sample set. The design variable matrix of the Pareto front samples is normalized and centered. The singular value decomposition is performed on the centered design variable matrix to obtain the principal component basis.
[0039] In this embodiment, selecting Pareto front samples from the sample set specifically includes: Based on the multiple objective function values corresponding to each sample in the sample set, the samples are sorted by non-dominated order, and the first non-dominated front sample is taken as the Pareto front sample.
[0040] In this embodiment, the normalization and centering of the design variable matrix of the Pareto front sample specifically includes: The normalization range is determined by the minimum and maximum values of each design variable in the Pareto front sample; Each design variable is normalized to a dimensionless variable to obtain a normalized design variable matrix; Obtain the column mean vector of the normalized design variable matrix; Subtract the column mean vector from the normalized design variable matrix to obtain the centered design variable matrix.
[0041] Specifically, let the original design variable matrix in the sample set be... X , X Include n One sample and m One design variable; set F This represents the set of indices for the Pareto front samples. For the... j The design variables are minimized in the Pareto front sample. m j and maximum value M j And normalize according to the following formula:
[0042] in, X ij Indicates the first i The first sample j One design variable, This represents the normalized design variables.
[0043] Furthermore, the normalized design variable matrix is centered:
[0044] in, This represents the column mean vector of the normalized design variable matrix. This represents a matrix of centralized design variables.
[0045] Furthermore, singular value decomposition is performed on the centralized design variable matrix corresponding to the Pareto front samples:
[0046] in, V The column vectors are principal component vectors, σ1 to σ mFor the corresponding singular values.
[0047] Based on the principal component basis, all samples in the sample set are mapped to the principal component space. A Kriging surrogate model is constructed in the principal component space and multi-objective optimization is performed. The Pareto candidate samples in the principal component space are inversely mapped to the original design variables. The samples obtained by inverse mapping are subjected to leaf shape design and numerical simulation to calculate their objective function values. The calculation results are added to the sample set and the sample set is updated.
[0048] Based on the principal component basis, the samples in the sample set are mapped to the principal component space as follows:
[0049] in, Z This represents the coordinates of the sample in the principal component space.
[0050] In this embodiment, the inverse mapping of Pareto candidate samples in the principal component space to the original design variables specifically includes: Based on the principal component basis and the column mean vector in the centering process, the Pareto candidate samples in the principal component space are converted into normalized design variables; The normalized design variables are denormalized based on the normalization range to obtain the original design variables.
[0051] Candidate points are obtained from the principal component space. z The inverse mapping to normalized design variables is represented as follows:
[0052] The normalized design variables are denormalized back to the original design variables as follows:
[0053] Through the above inverse mapping process, candidate points in the principal component space can be converted into a complete vector of original design variables, which can then be directly used for turbine blade design and numerical simulation.
[0054] Example 3 This embodiment illustrates the application of the method of the present invention in multi-condition aerodynamic proxy optimization of variable geometry turbine guide vanes. The object to be optimized is a variable geometry turbine guide vane, and multiple operating conditions are determined by the changes in the target outlet airflow angle and the total static expansion ratio, as shown in Table 1. The target outlet airflow angle under different operating conditions is achieved by rotating the guide vane.
[0055] Table 1 Optimized operating parameters for variable geometry turbine guide vanes under multiple operating conditions
[0056] The design variables in this embodiment may include the airfoil installation angle, trailing edge bend angle, inlet configuration angle, outlet configuration angle, outlet trailing edge half-wedge angle, and axial position of the control points inside the Bézier curve corresponding to the first operating condition. The total pressure loss coefficients for the first and second operating conditions are used as two objective functions to be minimized. For any candidate guide vane airfoil, numerical simulations are performed under both the first and second operating conditions to obtain the corresponding total pressure loss coefficients.
[0057] Based on the aforementioned operating parameters and objective function, optimization is first performed in the original design variable space. A Latin hypercube experimental design is used to generate 50 initial samples. For each sample, a leaf shape design is performed, and numerical simulations are conducted under the first and second operating conditions to obtain the corresponding objective function values. Subsequently, a Kriging surrogate model is trained for each of the two operating conditions, and a non-dominated sorting genetic algorithm is used to perform multi-objective search on the surrogate model. In this embodiment, the maximum number of generations for Kriging hyperparameter optimization is set to 100. The maximum number of generations for multi-objective optimization is also set to 100, and the population size is 10. After each round of surrogate optimization, guide vane design and numerical simulations are performed on the candidate samples obtained from the multi-objective search, the objective function values are calculated, and these are added to the sample set.
[0058] After accumulating 200 evaluated guide vane design samples in the original design variable space, a surrogate optimization strategy based on principal component analysis is initiated.
[0059] Specifically, Pareto front samples were selected from the 200 evaluated guide vane design samples mentioned above. Their design variable matrices were normalized and centered, and singular value decomposition was performed to obtain principal component bases.
[0060] The 200 evaluated guide vane design samples are mapped to the obtained principal component space. In the principal component space, the Kriging surrogate model of the objective function for each working condition is trained, and multi-objective optimization, inverse mapping, airfoil design and numerical simulation are performed until 200 new evaluated designs are obtained. These are then merged with the previous 200 designs to form 400 evaluated designs.
[0061] Pareto frontier samples were selected from the 400 evaluated designs above, and a second principal component analysis was performed to update the principal component bases.
[0062] The 400 evaluated guide vane design samples are mapped to the obtained principal component space. In the principal component space, the Kriging surrogate model of the objective function for each working condition is trained, and multi-objective optimization, inverse mapping, airfoil design and numerical simulation are performed until 200 new evaluated designs are obtained. These are then merged with the aforementioned 400 designs to form 600 evaluated designs.
[0063] In this embodiment, a hypervolume can be used to evaluate the convergence and distribution of the Pareto front. The hypervolume is represented as:
[0064] in, A i Indicates the first i The target space region is defined by a non-dominated design and a reference point. The larger the HV, the better the Pareto front is in terms of convergence and distribution.
[0065] To evaluate the efficiency of principal component space optimization, this embodiment uses 200 evaluated guide vane design samples as a common basis when principal component analysis is started, and continues to perform surrogate optimization in the original design variable space until it reaches the same hypervolume level as principal component space optimization.
[0066] Table 2. Comparison of efficiency between principal component space optimization and original variable space optimization
[0067] As shown in Table 2, when achieving the same hypervolume, optimization directly in the original design variable space requires 1110 samples, while optimization based on the principal component space can achieve the same hypervolume with only 600 samples. This is equivalent to reducing the number of numerical simulation samples by about 46% while maintaining comparable Pareto front quality.
[0068] Furthermore, after performing principal component analysis based on the Pareto front samples of the guide vane, the direction of the first principal component can be projected onto the original design variable space to quantitatively explain the coordinated changes in the geometric parameters of the variable geometry turbine guide vane. The projection vector of the first principal component can be written as: v 1,ori=[0.291, 2.717, 0.317, -1.251, 0.372, -0.004, -0.005, -0.005, 0.012, 0.016]. The components of the above vector represent, in turn, the changes in the blade installation angle, trailing edge turning angle, inlet configuration angle, outlet configuration angle, outlet trailing edge half-wedge angle, and the axial positions of the five control points within the Bézier curves corresponding to the first operating condition. When changing along the positive direction of the first principal component, the trailing edge turning angle increases and the outlet configuration angle decreases, while the curvature of the guide vane throat to the trailing edge region increases and the radius of curvature decreases. Since the pressure gradient required for flow turning increases as the radius of curvature decreases, under the same total pressure and downstream pressure conditions, the local static pressure on the blade surface decreases and the local velocity peak increases, thereby increasing the maximum isentropic Mach number. Under the first operating condition, this change will form a stronger shock wave and a larger post-shock separation zone, making shock wave loss dominant and increasing total pressure loss. When the first principal component changes in the negative direction, the tail edge turning angle decreases and the exit structure angle increases. The shock wave intensity weakens under the first working condition, but under the second working condition, the reverse pressure gradient region near the tail edge increases, the boundary layer thickens, and the loss under the second working condition increases.
[0069] Therefore, principal component analysis can not only improve the efficiency of surrogate optimization, but also link geometric changes, blade load distribution and total pressure loss changes, providing a quantitative interpretation basis for multi-condition optimization design of turbine blades.
[0070] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.
[0071] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A multi-condition aerodynamic proxy optimization method for turbine blade profiles based on principal component analysis, characterized in that, include: Initial samples are generated based on Latin hypercube sampling. The objective function values of each sample under multiple working conditions are calculated through leaf shape design and numerical simulation to form an initial sample set. A Kriging surrogate model is constructed based on the initial sample set, and multi-objective optimization is performed on the Kriging surrogate model. The obtained Pareto candidate samples are subjected to leaf shape design and numerical simulation to calculate their objective function values. The calculation results are added to the initial sample set to update the sample set. In response to the number of samples in the sample set reaching a preset threshold, Pareto front samples are selected from the sample set, and the design variable matrix of the Pareto front samples is normalized and centered. Singular value decomposition is performed on the centered design variable matrix to obtain principal component basis. Based on the principal component basis, all samples in the sample set are mapped to the principal component space. A Kriging surrogate model is constructed in the principal component space and multi-objective optimization is performed. The Pareto candidate samples in the principal component space are inversely mapped to the original design variables. The samples obtained by inverse mapping are subjected to leaf shape design and numerical simulation to calculate their objective function values. The calculation results are added to the sample set and the sample set is updated.
2. The turbine blade profile multi-condition aerodynamic proxy optimization method based on principal component analysis according to claim 1, characterized in that, The objective function value is the total pressure loss coefficient under different operating conditions: ； in, p t,in Indicates the total import pressure. p t,out Indicates the total export pressure. p out Indicates the outlet static pressure.
3. The multi-condition aerodynamic proxy optimization method for turbine blade profiles based on principal component analysis according to claim 1, characterized in that, Constructing the Kriging proxy model based on the aforementioned sample set specifically includes: For different working conditions, the Kriging surrogate model for the objective function of the sample is constructed by taking the design variable vector of the sample as input and the objective function value of a working condition as output.
4. The multi-condition aerodynamic proxy optimization method for turbine blade profiles based on principal component analysis according to claim 3, characterized in that, The specific steps for constructing the Kriging surrogate model for the corresponding working condition objective function include: Determine sample correlation based on the correlation matrix between training samples; Relevant hyperparameters are determined based on a global optimization algorithm; The predicted value of the objective function for the new input point is obtained based on the correlation vector between the new input point and the training samples, the correlation matrix, and the training response vector.
5. The multi-condition aerodynamic proxy optimization method for turbine blade profiles based on principal component analysis according to claim 1, characterized in that, Multi-objective optimization on the Kriging surrogate model specifically includes: Initialize the population with the variable vectors in the current optimization space; The Kriging surrogate model is used to predict multiple objective function values for individuals in the population. Based on the multiple objective function values, perform non-dominated sorting, selection, crossover, mutation, and population update; Repeat the iteration until the preset maximum number of generations is reached, and use the final population as Pareto candidate samples.
6. The turbine blade profile multi-condition aerodynamic proxy optimization method based on principal component analysis according to claim 1, characterized in that, Selecting Pareto frontier samples from the aforementioned sample set specifically includes: The samples in the sample set are sorted by multiple objective function values corresponding to each sample, and the first non-dominated front sample is taken as the Pareto front sample.
7. The multi-condition aerodynamic proxy optimization method for turbine blade profiles based on principal component analysis according to claim 1, characterized in that, The normalization and centering of the design variable matrix of the Pareto front sample specifically includes: The normalization range is determined by the minimum and maximum values of each design variable in the Pareto front sample; Each design variable is normalized to a dimensionless variable to obtain a normalized design variable matrix; Obtain the column mean vector of the normalized design variable matrix; Subtracting the column mean vector from the normalized design variable matrix yields the centered design variable matrix.
8. The turbine blade profile multi-condition aerodynamic proxy optimization method based on principal component analysis according to claim 1, characterized in that, The inverse mapping of Pareto candidate samples in the principal component space to the original design variables specifically includes: Based on the principal component basis and the column mean vector in the centering process, the Pareto candidate samples in the principal component space are converted into normalized design variables; Based on the normalization range, the normalized design variables are denormalized to obtain the original design variables.
9. The multi-condition aerodynamic proxy optimization method for turbine blade profiles based on principal component analysis according to claim 1, characterized in that, The design variables include the blade installation angle, trailing edge turning angle, inlet construction angle, outlet construction angle, outlet trailing edge half-wedge angle, and axial position of the control point inside the Bézier curve corresponding to the first operating condition.
10. The multi-condition aerodynamic proxy optimization method for turbine blade profiles based on principal component analysis according to claim 1, characterized in that, After updating the sample set, Pareto front samples are reselected from the updated sample set, and the design variable matrix of the reselected Pareto front samples is normalized, centered, and decomposed again to update the principal component basis.