Multi-stage turbomachinery optimization method based on global sensitivity analysis

Abstract

The method for optimizing multistage turbomachinery based on global sensitivity analysis comprises the following steps: establishing a design space; obtaining a plurality of samples uniformly distributed in the established design space; establishing a data table recording the interaction between all variable data; screening out a plurality of variable combinations that are more likely to be related according to the global sensitivity analysis results, generating r sub-tasks on the basis of the preliminary decomposition scheme, and optimizing the r sub-questions respectively; updating the search boundary of the sub-questions, verifying the variable combinations screened out in the sub-questions, and confirming the correlation between two variables according to the sub-question proxy model obtained after optimization; repeating the above steps until the evaluation times of all samples reach the set upper limit. The method effectively improves the optimization efficiency, and the way of gradually exploring the design space in the optimization process also makes the data mining results have higher robustness and accuracy compared with one-time data mining.

Description

Technical Field

[0001] This invention belongs to the field of turbomachinery optimization, and specifically relates to a multi-stage turbomachinery optimization method based on global sensitivity analysis. Background Technology

[0002] In recent years, automated optimization design methods have been increasingly widely used in the field of turbomachinery. Automated optimization design methods require the manual definition of a parametric design space. In this space, each coordinate corresponds to a specific geometric design scheme. The results of computational fluid dynamics (CFD) simulations serve as the optimization target, and with the aid of specific optimization algorithms, high-performance turbomachinery components can be designed automatically. The use of automated design methods can effectively reduce the reliance on designer experience, enabling rapid and high-quality design completion. In this process, the optimization algorithm is often the key factor determining the efficiency of automated optimization design methods.

[0003] However, due to their often curved surfaces and complex design details, turbomachinery blades typically require dozens of design variables to represent. When designing multi-stage turbomachinery, the number of design variables increases dramatically when several or even a dozen rows of blades need to be designed together, and the area to be explored in the design space increases exponentially. Therefore, directly treating the high-dimensional space as a black box for optimization will inevitably fail due to insufficient sample size. Thus, in the design of multi-stage turbomachinery, existing methods often involve optimizing each stage or row of blades separately. This separate design effectively reduces the difficulty of optimization, but its drawback is that it cannot account for inter-stage interference, limiting further performance improvements.

[0004] To achieve efficient and high-performance optimized design of multi-stage turbomachinery, new design methods are needed. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for optimizing multi-stage turbomachinery based on global sensitivity analysis, in order to solve the problem that the inability to take into account inter-stage interference and other factors limits further performance improvement.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] The multi-stage turbomachinery optimization method based on global sensitivity analysis includes the following steps:

[0008] Taking multi-stage impeller mechanical components as the design object, the adjustment parameters of each three-dimensional blade are obtained, and the design space is established;

[0009] In the established design space, obtain the coordinates of several uniformly distributed samples, and evaluate their performance to obtain the optimization target evaluation value of these several design samples.

[0010] Establish a global chaotic polynomial PCE fitting model using the obtained sample coordinates and optimization objective evaluation values; establish an interaction data table that records the interaction relationships between all pairs of variable data;

[0011] Generate a preliminary decomposition plan based on the current interaction data table; generate r sub-tasks based on the sensitivity values provided by the global chaotic polynomial PCE model, and optimize the r sub-problems separately;

[0012] Update the search boundaries of the sub-problems, verify the variable combinations screened out initially in the sub-problems, and confirm the interaction relationship between two variables based on the optimized sub-problem surrogate model after optimization;

[0013] Repeat the above steps until the number of evaluations of all samples reaches the set upper limit, select the sample with the best sample value from the sample data set as the optimization result, and obtain the interaction information knowledge of this design task from the interaction data set.

[0014] Furthermore, use the Latin Hypercube LHS sampling method in the established design space to obtain several sample coordinates with a relatively uniform distribution; in the design space, a group of determined design parameters corresponds to obtaining a geometric design.

[0015] Furthermore, establish a PCE fitting model using the obtained sample coordinates and optimization objective evaluation values The coefficient of the PCE fitting model represents the magnitude of the Sobol sensitivity of this term. Extract the coefficients of all quadratic terms and denote them as S jk (1 ≤ j < k ≤ D), representing the variable x j and the variable x k The degree of interaction in the entire space.

[0016] Furthermore, establish an interaction data table that records the interaction relationships between all pairs of variable data. For a D-dimensional problem, there are a total of D(D - 1) / 2 pairs of pairwise interaction relationships; where I jk (1 ≤ j < k ≤ D) represents whether an interaction relationship is identified between the variable x j and the variable x k during the optimization process; if there is an interaction relationship, then I jk = 1; if there is no interaction relationship, I jk = 0; in the initial state, it is default that all variables are not correlated and are all recorded as 0.

[0017] Furthermore, generate a preliminary decomposition plan according to the current interaction data I: allocate D variables to sub-problems. If two variables x a and x bAn interaction relationship has been confirmed between them, namely I ab If the value is 1, then these two variables are assigned to the same subproblem. In this case, the D variables are decomposed into r. temp Group.

[0018] Furthermore, the elements in S, representing the degree of interaction between variables, are arranged in descending order to select pairs of variables that meet the following requirements: 1) These pairs of variables are not in the same group in the initial decomposition scheme; 2) The sum of the dimensions of the two subproblems in which these pairs of variables reside does not exceed 5. [D / 5] pairs of initially screened interactive variables are selected in sequence, and the two subproblems in which these pairs of variables reside are aggregated into one subproblem to obtain the final decomposition scheme for this round of optimization. At this point, D variables are decomposed into r groups.

[0019] Furthermore, generate r subtasks: select the coordinates of the sample with the best target performance among all currently evaluated samples as the core point x. * Based on the final decomposition scheme, the high-dimensional global problem is decomposed into r low-dimensional problems. Assuming that variables x1, x2, and x3 are grouped together, their corresponding subproblems are:

[0020]

[0021] Furthermore, the EGO algorithm is used to optimize each of the r subproblems: A complete and independent optimization search is performed within the subproblem space using the Kriging surrogate model and the Expected Value Optimization (EI) criterion, yielding the optimization result x. best,j The Kriging model at the end of optimization is After optimization, all samples generated during the optimization of subtasks are saved to a sample dataset.

[0022] Update the search boundary of the subproblem: First, collect N samples within the current boundary range. test Given a sample set X, calculate the predicted value for each sample. Select the [N] with the best evaluation value test ·ω] sample sets X s The new upper and lower search boundaries U and L are respectively:

[0023]

[0024] Both are sets X s The samples in N test The values ​​of ω and ω are set to 10000 and 0.5 respectively; the sampling method used is Latin hypercube sampling.

[0025] Furthermore, the initially screened variable combinations are validated in the sub-problems; after optimization, the interaction relationship between the two variables needs to be confirmed based on the sub-problem proxy model obtained from the optimization.

[0026] We used one-minus-cross-validation to analyze the accuracy of the surrogate model;

[0027]

[0028] in, This indicates a model built using samples other than the i-th sample;

[0029] Use perturbation methods to confirm the correlation between two variables;

[0030]

[0031]

[0032] Where, N test The values ​​of and h are set to 10000 and 0.0001 respectively; the sampling method used is Latin hypercube sampling; when the R of the surrogate model 2 Value greater than 0.8 and H ij If the value is greater than 0.2, it is confirmed that there is an interaction relationship between the two variables, and this result is stored in a data table that records the interaction relationships between all pairs of variable data.

[0033] Furthermore, a multi-stage turbomachinery optimization system based on global sensitivity analysis includes:

[0034] The design space module is used to obtain the adjustment parameters of three-dimensional blades and establish a design space by taking the impeller mechanical components as the design object.

[0035] The performance evaluation module is used to obtain several uniformly distributed sample coordinates in the established design space, and to evaluate the performance of these sample coordinates to obtain the optimization target evaluation value of these sample designs.

[0036] The model building module is used to build a global chaotic multinomial PCE fitting model using the obtained sample coordinates and optimization target evaluation values; and to build an interactive data table that records the pairwise interactions between all variable data.

[0037] The decomposition module is used to generate a preliminary decomposition scheme based on the current interactive data table; and to generate a final decomposition scheme based on the sensitivity values ​​provided by the global chaotic polynomial PCE model.

[0038] The optimization module generates r subtasks, optimizes each of the r subproblems, updates the search boundaries of the subproblems, verifies the initially screened variable combinations in the subproblems, and confirms the interaction relationship between two variables based on the optimized subproblem proxy model after optimization.

[0039] Compared with the prior art, the present invention has the following technical effects:

[0040] This invention provides an optimization method for multi-stage turbomachinery based on global sensitivity analysis. In this method, design variables related to different blades of the multi-stage turbomachinery are placed in a high-dimensional design space for joint optimization. Data mining technology acquires design space knowledge in real time and applies this knowledge to the optimization process in the form of a spatial decomposition scheme, effectively improving optimization efficiency. Furthermore, the gradual increase in samples during the optimization process, accumulating knowledge of the design space, makes the data mining results more robust and accurate compared to one-time data mining. The two methods mutually reinforce each other.

[0041] In engineering practice, the method proposed in this invention avoids the difficulties in resource allocation between optimization and data mining, and improves the efficiency of optimization design. Regarding data mining to explore problem structure, this invention adopts a "preliminary screening-confirmation" interaction effect analysis model, combining and improving upon traditional interaction effect analysis methods. "Preliminary screening" uses a low-cost, low-precision surrogate model-based method to select sample combinations with interactive meanings; "confirmation" examines the interactivity of the selected sample combinations individually in a low-dimensional space. The combination of these two methods effectively improves accuracy and reduces costs. Furthermore, the entire process is highly coupled with optimization. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of an embodiment of the present invention.

[0043] Figure 2 The curve diagram shows the optimization target of the booster stage of the fan engine in an embodiment of the present invention. Detailed Implementation

[0044] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings and examples.

[0045] like Figure 1 As shown, this embodiment provides a multi-stage turbomachinery optimization method based on global sensitivity analysis and applies it to the optimization design of compressor rotor blades. Specifically, it includes the following steps:

[0046] 1) Establishment of design space.

[0047] This embodiment selects the booster stage of a turbofan engine as the object of optimization (see...). Figure 2The booster stage contains five blades, denoted as: IGV inlet guide vane, R1 first-stage moving blade, S1 first-stage stationary blade, R2 second-stage moving blade, and S2 second-stage stationary blade. Because the flow of the compressor blades exhibits strong three-dimensional effects, the blade profile changes significantly with the blade height, requiring more design variables to accurately describe the three-dimensional shape of the compressor blades, thus increasing the number of design variables.

[0048] Here, only the profiles of the four blade rows other than the inlet guide vanes are adjusted and design variables are set. For each blade row, three sections are taken at 0%, 50%, and 100% of the blade height as characteristic sections for shaping. For the moving blades R1 and R2, five control points are selected on the suction surface of each section to adjust the shape of the suction surface curve. Three design parameters are also selected to adjust the bending and sweeping states when the three-dimensional blades are stacked. For the stationary blades S1 and S2, since the stationary blades have a relatively small impact on aerodynamic efficiency, only three control points are selected on the suction surface of each section to adjust the shape of the suction surface curve. Three design parameters are also selected to adjust the bending and sweeping states when the three-dimensional blades are stacked. As mentioned above, this design space includes a total of 60 design variables, significantly exceeding the feasible range of design variables for common optimization design methods.

[0049] 2) Establishment of performance evaluation model

[0050] In this study, compressor stage efficiency was chosen as the target parameter for optimization design, aiming to design a blade cascade geometry model with higher stage efficiency. Commercial computational fluid dynamics (CFD) software was used to evaluate the stage efficiency of the geometric design model.

[0051] 3) Determine the user-defined variables in the algorithm

[0052] In this example, the initial global sample size is selected as 150, and the distribution method is Latin hypercube sampling (LHS); the highest order of the chaotic polynomial is selected as 6; the initial sample size of the sub-optimization is selected as twice the dimension of the corresponding subspace; the maximum number of iterations of the sub-optimization is selected as six times the dimension of the corresponding subspace; and the maximum sample size of the entire algorithm is determined to be 1000.

[0053] The specific process of optimization design

[0054] refer to Figure 1 The specific process is as follows:

[0055] 4a. Using the LHS method within the established design space, obtain the coordinates of 150 relatively evenly distributed samples. Evaluate the performance of these 50 design samples to obtain their level efficiency values. (Since the default optimization objective is to minimize the value, the sample evaluation values ​​are set to level efficiency multiplied by -1.)

[0056] 4b. Initialize the interaction data table, with all interaction relationships between variables set to 0; initialize the boundary data table, setting the search range for all variables to [0,1].

[0057] 4c. Using the sample coordinates and values ​​obtained in 4a, establish a 60-dimensional PCE fitting model. After the model is established, obtain the coefficients of each second-order term of the model as estimates of the 1770 Sobol coefficients between pairwise variables in the overall design space. jk (1≤j <k≤D)。

[0058] 4d. Obtain the initial decomposition scheme for this round of optimization based on the interaction data table of variables. The method to obtain the initial scheme is to put all variables marked as having interaction relationships in the table into the same group.

[0059] 4e. Based on the Sobol coefficients obtained from the PCE, generate the final decomposition scheme for this round of optimization based on the initial decomposition scheme. Select the 12 largest Sobol coefficients from the 1770 coefficients in descending order. If the two variables corresponding to these coefficients meet the following conditions, they are set as "initial screening variable combinations": 1) The two variables are not in the same group in the initial decomposition scheme; 2) The sum of the number of variables in the current group of the two variables is less than 5. A total of 20 "initial screening variable combinations" are selected using the above method, and these pairs of variables are grouped together to obtain the final decomposition scheme.

[0060] 4f. Select the sample with the best evaluation value from all currently evaluated samples as the core point for this round of optimization. Decompose the original optimization task into r sub-optimization tasks using the core point and the final decomposition scheme. In a sub-task, only a few corresponding variables change for optimization, while the values ​​of the remaining variables remain consistent with the core point.

[0061] 4g. The Efficient Global Optimization (EGO) algorithm is used to optimize each of the r sub-optimization tasks. The initial number of optimization points is 5d, and the maximum number of iterations is 6d, where d represents the dimension of the sub-problem. After optimization, all evaluated samples are recorded in a sample data table, and the final generation of the Kriging model is obtained for subsequent analysis.

[0062] 4h. Update the variable boundaries based on the Kriging surrogate model, taking ω = 0.5 to narrow the upper and lower bounds of each variable so that the top 50% of the samples in terms of evaluation value are still within the new boundary range;

[0063] 4i. Perform reduced-one cross-validation (LooCV) on the samples within the new boundary range to obtain their Ri. 2 value.

[0064] 4j. Perform perturbation analysis within the new variable boundaries to obtain the interaction effect parameter H between the two variables. ij For a d-dimensional sub-optimization, d(d-1) / 2 interaction effect parameters can be obtained.

[0065] 4k. When the cross-validation parameter is greater than 0.9 and the interaction effect parameter between the two variables is greater than 0.2, an interaction effect can be considered to exist between the two variables. Verify the interaction relationships between variables in all sub-optimization tasks and record the newly discovered interaction relationships in the interaction data table.

[0066] 4l. Steps 4c to 4k constitute a complete optimization process. Repeat the above optimization process until the total number of sample evaluations reaches 1000.

[0067] 4m. Optimization ends, output the optimal solution result and the interaction relationship results between variables.

[0068] Optimization Design Results

[0069] A total of 1,000 samples were used in this optimization process, and the final stage efficiency was 89.16%, which is 1.01% higher than the stage efficiency of 88.15% of the reference design, a significant improvement.

[0070] Table 1: Details of Optimization Results

[0071] Sample size Optimal efficiency Efficiency improvement / 88.15％ / 150 88.15％ 0.00％ 300 88.53％ 0.38％ 450 88.62％ 0.47％ 600 88.96％ 0.81％ 750 89.04％ 0.89％ 900 89.14％ 0.99％ 1000 89.16％ 1.01％

[0072] The principle of this invention is as follows:

[0073] The most significant features and innovations of this invention are: 1) combining the problem structure decomposition stage and the problem optimization stage of high-dimensional problem optimization; 2) combining high-dimensional global models and low-dimensional local models, and achieving low-cost variable interaction effect analysis through the "initial screening-confirmation" method.

[0074] Traditional high-dimensional problem decomposition and optimization methods typically involve first fully analyzing the problem, then decomposing it according to the analysis results, and optimizing each sub-problem one by one. However, this introduces the problem of computational cost allocation. If the decomposition phase consumes a large amount of computational resources, resulting in insufficient usable samples for optimization, the optimization cannot proceed smoothly; conversely, if the decomposition phase uses insufficient resources, leading to inaccurate analysis results, it cannot be corrected in subsequent optimizations. This invention, by combining problem structure decomposition and the optimization process, solves this problem. It deepens the understanding of the problem gradually during optimization, updating the decomposition scheme based on the obtained interaction effect data in each iteration. This solves both the resource allocation problem and improves optimization efficiency.

[0075] The "initial screening-confirmation" interaction effect analysis model proposed in this invention combines and improves upon traditional interaction effect analysis methods. Traditional methods, based on models, can obtain the interaction relationships between all variables at once; however, their accuracy depends on the precision of the problem and often fails to guarantee accuracy in problems with more than 20 dimensions. Methods that analyze pairs of variables are accurate but very costly. This invention uses a model-based method for initial screening, initially selecting variable pairs that may have interaction relationships. Then, it confirms whether these variable pairs actually have interaction relationships using a low-dimensional Kriging surrogate model, which requires only a small number of samples for high-precision modeling. Since the Kriging surrogate model used is itself a legacy from EGO optimization, the actual decomposition and analysis process in this invention does not require additional sample consumption, greatly improving optimization efficiency.

Claims

1. A method for multistage turbomachinery optimization based on global sensitivity analysis, characterized in that, The method comprises the following steps: A multi-stage impeller component is taken as a design object to obtain adjustment parameters of each three-dimensional blade, and a design space is established; A plurality of sample coordinates uniformly distributed in the established design space are obtained, and performance evaluation is performed on the sample coordinates to obtain optimal objective evaluation values of the plurality of design samples; A global chaotic polynomial PCE fitting model is established using the obtained sample coordinates and optimal objective evaluation values, and an interaction data table recording interaction relationships between all variable data is established; A preliminary decomposition scheme is generated according to the current interaction data table, and r sub-tasks are generated based on the preliminary decomposition scheme according to sensitivity values provided by the global chaotic polynomial PCE model, and the r sub-tasks are optimized respectively; Search boundaries of the sub-tasks are updated, the variable combinations preliminarily screened out are verified in the sub-tasks, and interaction relationships between two variables are confirmed according to a sub-task proxy model obtained after optimization; The above steps are repeated until a set upper limit of sample evaluation times is reached, a sample with optimal sample value is selected from a sample data set as an optimization result, and interaction information knowledge of the design task is obtained from an interaction data set; The variable combinations preliminarily screened out are verified in the sub-tasks, and the interaction relationships between two variables are confirmed according to the sub-task proxy model obtained after optimization; Precision of the proxy model is analyzed using leave-one-out cross validation; wherein, represents a model established using samples other than the first sample; A perturbation method is used to confirm the correlation relationship between the two variables; wherein, and are set to 10000 and 0.0001, respectively; the method used for sampling is Latin hypercube sampling; when the value of the is greater than 0.8 and the value of the is greater than 0.2, it is confirmed that there is an interaction between the two variables, and this result is stored in a data table recording the interaction between all variables two by two.

2. The multi-stage turbomachinery optimization method based on global sensitivity analysis of claim 1, wherein, A plurality of sample coordinates uniformly distributed in the established design space are obtained using a Latin hypercube LHS sampling method; in the design space, a group of determined design parameters correspond to a geometric design obtained.

3. The multi-stage turbomachinery optimization method based on global sensitivity analysis of claim 1, wherein, A PCE fitting model is established using the obtained sample coordinates and the optimization target evaluation values The coefficients of the PCE fitting model represent the numerical size of the Sobol sensitivity of the term, and the coefficients of all the quadratic terms are extracted and denoted as , which represent the interaction degree of the variable and the variable in the entire space.

4. The multi-stage turbomachinery optimization method based on global sensitivity analysis of claim 1, wherein, An interaction data table is established to record the interaction between all variables, which is used to coexist in the same problem two-by-two interaction; wherein the interaction between variables is identified during the optimization process; if the interaction exists, then and variables ; if the interaction exists, then ; If there is no interaction ; all variables are initially assumed to be independent of each other and are recorded as 0.

5. The multi-stage turbomachinery optimization method based on global sensitivity analysis of claim 1, wherein, According to the current interaction data , a preliminary decomposition scheme is generated: the variables are assigned to sub-problems, if the interaction between two variables and has been confirmed, i.e. , then these two variables are assigned to the same sub-problem, at this time variables are decomposed into groups.

6. The multi-stage turbomachinery optimization method based on global sensitivity analysis of claim 1, wherein, This represents the degree of interaction between variables. Arrange the elements in descending order and select pairs of variables that meet the following requirements: 1) These pairs of variables are not in the same group in the initial decomposition scheme; 2) The sum of the dimensions of the two subproblems containing these pairs of variables does not exceed 5. Filter them in order. For the initial screening of interaction variables, the two subproblems containing these paired variables are aggregated into one subproblem, resulting in the final decomposition scheme for this round of optimization. The variables are decomposed into Group.

7. The multi-stage turbomachinery optimization method based on global sensitivity analysis of claim 1, wherein, Generate r sub-tasks: select the sample coordinate with the optimal target performance among all the samples that have been evaluated as the core point , according to the final decomposition scheme, the high-dimensional global problem is decomposed into low-dimensional problems, assuming that the variables are divided into the same group, then the corresponding sub-problem is: 。 8. The multi-stage turbomachinery optimization method based on global sensitivity analysis of claim 1, wherein, The EGO algorithm is used to optimize r sub-problems respectively: a complete independent optimization search is completed in the sub-problem space using the Kriging surrogate model and the maximum expected improvement adding point criterion EI, and the result obtained by optimization is The Kriging model at the end of optimization is After the optimization ends, all samples generated in the optimization process of the sub-tasks are saved into a sample data set; updating the search boundary of the sub-problem: first collect samples in the current boundary range to obtain a sample set , and respectively calculate the predicted values of these samples ; The sample set with the optimal evaluation value is selected The sample set with the optimal evaluation value is selected The new search upper and lower boundaries , Respectively: ， ； are all sets of samples, and the values of which are set to 10000 and 0.5, respectively; the method used for sampling is Latin hypercube sampling.

9. A multi-stage turbomachinery optimization system based on global sensitivity analysis, characterized in that, The method comprises: A design space module is configured to take an impeller component as a design object, obtain adjustment parameters of a three-dimensional blade, and establish a design space; A performance evaluation module is configured to obtain a plurality of sample coordinates uniformly distributed in the established design space, and perform performance evaluation on the sample coordinates to obtain optimal objective evaluation values of the plurality of design samples; A model establishment module is configured to establish a global chaotic polynomial PCE fitting model using the obtained sample coordinates and optimal objective evaluation values, and establish an interaction data table recording interaction relationships between all variable data; A decomposition module is configured to generate a preliminary decomposition scheme according to the current interaction data table; A final decomposition scheme is generated based on the preliminary decomposition scheme according to sensitivity values provided by the global chaotic polynomial PCE model; An optimization module is configured to generate r sub-tasks, and optimize the r sub-tasks respectively; Search boundaries of the sub-tasks are updated, the variable combinations preliminarily screened out are verified in the sub-tasks, and interaction relationships between two variables are confirmed according to a sub-task proxy model obtained after optimization; The variable combinations preliminarily screened out are verified in the sub-tasks, and the interaction relationships between two variables are confirmed according to the sub-task proxy model obtained after optimization; Precision of the proxy model is analyzed using leave-one-out cross validation; wherein, represents a model established using samples other than the first sample; A perturbation method is used to confirm the correlation relationship between the two variables; wherein, and are set to 10000 and 0.0001, respectively; the method used for sampling is Latin hypercube sampling; when the value of the of the proxy model is greater than 0.8 and the value of the is greater than 0.2, it is confirmed that there is an interaction between the two variables, and this result is stored in the data table recording the interaction between all variables.

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