A Multi-Objective Optimization Method for Overall Performance of Aero-engines Based on a Proxy Model
By using the pointwise combined surrogate model (PEHE-OP) based on the hybrid error criterion and the multi-objective optimization algorithm MODE, the problems of high computational cost and low efficiency in the overall performance optimization of aero-engines are solved, achieving low-cost and high-efficiency multi-objective optimization and improving model accuracy and stability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2024-02-04
- Publication Date
- 2026-05-26
AI Technical Summary
The current overall performance optimization of aero-engines is computationally expensive and time-consuming, and traditional proxy models are inefficient in multi-dimensional design spaces, failing to effectively consider the optimization of multiple performance parameters.
A point-by-point combined surrogate model based on the hybrid error criterion (PEHE-OP) is adopted, which combines optimal Latin hypercube design (OLHS) to generate sample points, uses CV-Voronio adaptive point addition update, and combines the multi-objective optimization algorithm MODE to establish a surrogate model with higher accuracy and better stability, and comprehensively considers multiple performance parameters.
It achieves low computational cost and rapid optimization convergence, effectively explores the design space in the early stage and makes fine adjustments in the later stage, provides more optimization options, improves model accuracy and stability, and significantly enhances optimization results.
Smart Images
Figure CN117932960B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of aero-engines, specifically relating to a multi-objective optimization method for the overall performance of aero-engines based on a surrogate model. Background Technology
[0002] Aero-engines are highly precise and complex thermodynamic machines. With the continuous development of aircraft design and control, the coupling relationships between various aero-engine components are constantly strengthening, the engine structure is becoming increasingly complex, and the demand for advanced control technologies is constantly increasing. For specific problems related to the overall performance optimization of aero-engines, experiments or simulations are needed to evaluate the impact of different design parameters on actual performance. As the number of aero-engine design parameters and constraints increases, directly solving the original model requires a significant computational cost. To improve optimization efficiency, a certain degree of accuracy can be sacrificed within acceptable limits, using a surrogate model to replace the original model, and optimization is performed based on the surrogate model (SBO).
[0003] Traditional aero-engine surrogate models typically use Latin hypercube design (LHS) to generate initial sample points. For LHS with multi-dimensional control variables, generating the required initial sample points is computationally slow, and the space-filling capability decreases with increasing dimensionality. Furthermore, the generated sample points do not consider their actual output values, making it impossible to add more sample points in highly nonlinear design space regions. This invention uses optimal Latin hypercube design (OLHS) with better space-filling performance to generate initial sample points, and employs CV-Voronio to add more sample points in highly nonlinear design space regions. Traditional aero-engine surrogate models are usually single or combined Kriging surrogate models, radial basis function neural networks, etc. Single models have unavoidable drawbacks, while combined models rely on the weight determination method for effectiveness and have high computational costs.
[0004] Traditional surrogate model-based optimization of aero-engine overall performance typically focuses on the optimal achievement of single performance parameters such as thrust and fuel consumption rate. This invention provides a multi-objective optimization method based on a surrogate model, which can be used in the overall performance optimization of aero-engines with high evaluation costs. It adopts the multi-objective optimization algorithm MODE to comprehensively consider various performance parameters and provide more options. Summary of the Invention
[0005] The technical problem to be solved:
[0006] To overcome the shortcomings of existing technologies, this invention provides a multi-objective optimization method for the overall performance of aero-engines based on a surrogate model. It employs a point-by-point combination surrogate model (PEHE-OP) based on a hybrid error criterion as the surrogate model for the aero-engine. This surrogate model method offers higher accuracy and better stability for different problems. It can effectively explore the design space in the early stages and finely adjust the model later to improve accuracy. This invention provides a more accurate and stable surrogate model establishment method, solving the problems of high optimization costs and long computation times in existing technologies.
[0007] The technical solution of this invention is: a multi-objective optimization method for the overall performance of aero-engines based on a surrogate model, the specific steps of which are as follows:
[0008] Determine the overall performance parameters, control variables, and constraint variables of the aero-engine;
[0009] Within the design space defined by the range of values of the design variables, the optimal Latin hypercube design OLHS is used to generate initial sample points for the training set and to randomly generate sample points for the test set.
[0010] The actual performance parameter response values of the initial sample points in the training set and the actual performance parameter response values of the sample points in the test set are obtained through experimental or simulation programs.
[0011] The actual performance parameter response values of the initial sample points in the training set and the actual performance parameter response values of the sample points in the test set are normalized to obtain the normalized dataset.
[0012] Based on the normalized training set data, a PEHE-OP proxy model is established;
[0013] The accuracy of the established PEHE-OP surrogate model is verified using normalized test set data. If the accuracy meets the standard or the maximum number of sample point evaluations is reached, the process continues; otherwise, the training set data is updated by adaptive addition of points using CV-Voronio, and the establishment and verification of the PEHE-OP surrogate model are repeated.
[0014] Based on the validated PEHE-OP surrogate model, the MODE method is used to optimize the overall performance parameters of the aero-engine;
[0015] The optimization is complete, and the output is the optimized solution set of the overall performance parameters of the aero-engine using the MODE method.
[0016] A further technical solution of the present invention is as follows: the overall performance parameters of the aero-engine include unit thrust Fs and unit fuel consumption rate sfc; the control variables include the relative equivalent speed of the high and low pressure compressors, the cross-sectional area of the turbine guide vane, the combustion chamber outlet temperature, the cross-sectional area of the tail nozzle throat, and the inlet guide vane angle of the compression component; the constraint variables include the surge margin of the compression component not being lower than a set value, the relative equivalent speed of the high and low pressure compressors not being higher than a set value, and the combustion chamber outlet temperature not being higher than a set value.
[0017] A further technical solution of the present invention is: the method for modeling the PEHE-OP proxy model is as follows:
[0018] A six-component proxy model was established based on the training set data;
[0019] Calculate the cross-validation error of each component surrogate model at each training set sample point, and establish an error estimation vector.
[0020] By introducing the k-nearest approach and employing distance correction and global error GMSE correction, the corrected error estimation vector is obtained.
[0021] Based on the error estimation vector An optimization method was used to obtain the point-by-point weights of the component surrogate models at each sample point, and the component surrogate models with the largest cross-validation error at each sample point were temporarily removed to improve the accuracy of the combined surrogate model.
[0022] The weights at non-sample points are determined using the inverse square Euclidean distance method, thus completing the establishment of the combined surrogate model PEHE-OP.
[0023] A further technical solution of the present invention is that the six component proxy models include two Kriging proxy models, three RBF proxy models, and one PRS proxy model.
[0024] A further technical solution of the present invention is: the corrected error estimation vector The formula is as follows:
[0025]
[0026] in:
[0027]
[0028]
[0029]
[0030] In the formula, d(x) k ,x j) represents the sample point x k With x j The distance between them, d averge d represents the average distance between sample points. averge d represents the average distance between sample points. 25prctile This represents the 25th percentile of the distance between sample points.
[0031] A further technical solution of the present invention is: the component surrogate model weight formula at each sample point is as follows:
[0032]
[0033] In the formula, w i (x) represents the weight of the surrogate model for the i-th component at the point prediction point x, w ik Let be the weight of the surrogate model for the i-th component at the k-th sample point.
[0034] A further technical solution of the present invention is: the method for adaptively updating the training set data using CV-Voronio point-by-point addition is as follows:
[0035] Based on the surrogate model PEHE-OP established using the current sample set, the design space is divided into a series of Thiessen polygons using the Thiessen graphical method. Each polygon is approximated by a set of random points using the Monte Carlo method.
[0036] The prediction error of the polygon is calculated using round-robin cross-validation, thereby identifying sensitive polygons. From the set of random points corresponding to the sensitive polygons, a new point is selected as the random point furthest from the center point.
[0037] Update the sample set and rebuild the model until the model meets the required accuracy or reaches the maximum number of evaluations.
[0038] A further technical solution of the present invention is: the method for optimizing the overall performance parameters of an aero-engine using the MODE method is as follows:
[0039] An initial population of size 100 was randomly generated and evaluated using the established surrogate model to obtain multiple objective function values;
[0040] Offspring populations are obtained through crossover, mutation, and selection operations, and individual assessments are performed.
[0041] The Pareto front is obtained by performing non-dominated sorting and crowding calculation on the offspring population;
[0042] Repeat the generation of offspring until the Pareto optimal solution meets the requirements or the maximum number of population iterations is reached. The maximum number of population iterations is set to 100.
[0043] A further technical solution of the present invention is: the constraint condition processing method for optimizing the overall performance parameters of aero-engines using the MODE method adopts the penalty function method.
[0044] Beneficial effects
[0045] The beneficial effects of this invention are as follows: The multi-objective optimization method for overall aero-engine performance based on a surrogate model, as proposed in this invention, has low computational cost, fast optimization convergence speed, and can comprehensively consider multiple performance parameters in the optimization problem, providing more options. Firstly, it can obtain a surrogate model with higher accuracy and better stability; secondly, the experimental design method proposed in this invention can effectively explore the design space in the early stages and finely adjust it in the later stages to improve model accuracy; finally, the multi-objective optimization based on the established surrogate model has low computational cost, fast optimization convergence speed, and good optimization effect, and can comprehensively consider various performance parameters, providing more options. A detailed analysis follows:
[0046] (a) The surrogate model PEHE-OP has higher accuracy and better stability:
[0047] The proposed combined surrogate model method was tested using a design point performance modeling problem for a three-bypass adaptive cycle engine. The modeling objects were the design point thrust and fuel consumption rate of the three-bypass adaptive cycle engine. First, a sample point set was generated using Latin hypercube design (LHS) as input parameters for calling the overall performance simulation model of the three-bypass adaptive cycle engine. These input parameters included: fan pressure ratio, fan bypass ratio, CDFS pressure ratio, CDFS bypass ratio, compressor pressure ratio, and combustion chamber outlet total temperature. Then, the engine performance parameters—thrust and fuel consumption rate—were obtained by calling the overall performance simulation model of the three-bypass adaptive cycle engine. Afterward, a corresponding surrogate model was established based on the input parameters and performance parameters. The selected design parameters and their value ranges for the three-bypass adaptive cycle engine design point performance modeling are shown in Table 1, and the values of some other parameters under the design state of the three-bypass adaptive cycle engine are shown in Table 2. When establishing the surrogate model, sample set sizes of 12 times and 24 times the dimension of the design variables were selected, i.e., sample set sizes of 72 and 144 were chosen for the study.
[0048] Table 1. Design parameters and their value ranges for the three-external-bypass adaptive cycle engine.
[0049]
[0050] Table 2. Values of some other parameters for the three-external-bypass adaptive cycle engine under design conditions.
[0051]
[0052] The root mean square error (RMSE) of each surrogate model was selected as the accuracy metric for testing. For ease of comparison, the RMSE of the most accurate component surrogate model was used, and the RMSE of the combined surrogate model was normalized. The normalized root mean square error (NRMSE) of the combined surrogate model was then used as its performance metric. The classic single surrogate model methods used in constructing the combined surrogate model included the Kriging surrogate model, the RBF surrogate model, and the PRS surrogate model. In establishing the Kriging surrogate model, two different Kriging surrogate models were established using a constant trend model and a linear trend model, denoted as KRG0 and KRG1, respectively. In establishing the RBF surrogate model, inverse multi-quadric (IMQ), thin-plate spline (TPS), and Gaussian (G) basis functions were used, and the resulting RBF surrogate models were denoted as IMQ, TPS, and G, respectively. Therefore, the combined surrogate model consisted of six component surrogate models. When testing the accuracy of the combined proxy model, four combined proxy models were selected from the published literature for comparison: EG proposed by Goel et al. in 2007, Od proposed by Viana et al. in 2009, SP proposed by Acar et al. in 2010, and PV proposed by Sanchez et al. in 2007.
[0053] The test results are shown in Table 3 and Figure 3 As shown, PEHE-OP improves accuracy by 6.3% compared to the most accurate component surrogate model and by 3.9% compared to the most accurate classical combinatorial surrogate model method.
[0054] Table 3. NRMSE of each agent modeling during modeling under the design state of the three-external-bypass adaptive cycle engine.
[0055]
[0056] (II) Experimental Design Methods:
[0057] The experimental design method proposed in this invention, compared with traditional experimental design methods, can effectively explore the design space in the early stages and make fine adjustments in the later stages to improve the accuracy of the surrogate model. For example... Figure 4 As shown in (a), the experimental design method proposed in this invention establishes a more accurate performance proxy model for the three-external-bypass adaptive cycle engine design point; as Figure 4 As shown in (b), the experimental design method proposed in this invention achieves faster accuracy convergence.
[0058] (III) The Proxy Model-Based Optimization Method Offers Low Computational Cost, Fast Convergence, and Good Optimization Results: This invention utilizes a Proxy Model (MODE) for multi-objective optimization, resulting in lower computational cost, faster convergence, and better optimization results compared to traditional optimization methods. The performance optimization problem of a three-bypass adaptive cycle engine at the design point is verified. The selected design parameters and their value ranges are shown in Table 1, and the values of some other parameters under the three-bypass adaptive cycle engine design state are shown in Table 2. The optimization results are as follows: Figure 5 As shown in Table 4, the SBO optimization method based on the surrogate model proposed in this invention, compared with the Pareto optimal solution set obtained by using only the MODE method, produces greater thrust and lower fuel consumption, has a larger number of solutions in the optimal solution set, and requires a shorter optimization time. Furthermore, compared with the single-objective optimization methods used in traditional aero-engine performance optimization, the optimization method proposed in this invention can comprehensively consider various performance parameters, providing more options.
[0059] Table 4 Comparison of Design Point Performance Optimization for Three-Benefit Adaptive Cycle Engines
[0060] Attached Figure Description
[0061] Figure 1 This is a schematic diagram of a multi-objective optimization method for overall performance of aero-engines based on a proxy model, which is optional according to an embodiment of the present invention.
[0062] Figure 2 This is a schematic diagram of an optional PEHE-OP modeling process according to an embodiment of the present invention;
[0063] Figure 3 These are thrust modeling examples and fuel consumption rate modeling examples for a three-external-root adaptive cycle engine; (a) thrust modeling example for a three-external-root adaptive cycle engine, (b) fuel consumption rate modeling example for a three-external-root adaptive cycle engine.
[0064] Figure 4 These are NRMSE bar charts and line graphs; (a) NRMSE bar charts for three experimental design methods; (b) NRMSE line graphs for the sequential addition process;
[0065] Figure 5 This is a comparison chart of the SBO optimization method based on the surrogate model proposed in this invention and the Pareto optimal solution set obtained by using only the MODE method. Detailed Implementation
[0066] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.
[0067] Given the unavoidable limitations of single models in existing technologies, and the high computational cost of combined models due to their reliance on weight determination methods, this invention provides a multi-objective optimization method for the overall performance of aero-engines based on a surrogate model. It employs a point-by-point combination surrogate model (PEHE-OP) based on a hybrid error criterion optimization method as the surrogate model for the aero-engine. This surrogate model method offers higher accuracy and better stability for different problems. Traditional aero-engine overall performance optimization based on surrogate models typically focuses on the optimal achievement of single performance parameters such as thrust and fuel consumption rate. This invention uses a multi-objective optimization algorithm (MODE) to comprehensively consider various performance parameters, providing more options. The specific method steps are as follows:
[0068] Step one: Determine the overall performance parameters, control variables, and constraint variables of the aero-engine. Performance parameters typically include unit thrust Fs and unit fuel consumption rate sfc. Control variables include, but are not limited to, the relative equivalent speeds of the high and low pressure compressors, the cross-sectional area of the turbine guide vanes, the combustion chamber outlet temperature, the cross-sectional area of the exhaust nozzle throat, and the inlet guide vane angle of the compression components. Constraint variables typically include a compression component surge margin not lower than a certain value, a relative equivalent speed of the high and low pressure compressors not higher than a certain value, and a combustion chamber outlet temperature not higher than a certain value. The actual constraint variables and values are determined by the designer based on the specific problem.
[0069] Step 2: In the design space determined by the range of values of the design variables, the initial sample points of the training set are generated using the optimal Latin hypercube design (OLHS), and the sample points of the test set are randomly generated.
[0070] Step 3: Calculate the actual performance parameter response values of the initial sample points in the training set and the actual performance parameter response values of the sample points in the test set through experiments or simulation programs.
[0071] Step four: Normalize the dataset obtained in step three to obtain the normalized dataset.
[0072] Step 5: Based on the normalized training set data obtained in Step 4, establish the PEHE-OP surrogate model.
[0073] Step 6: Use the normalized test set data obtained in Step 4 to verify the accuracy of the PEHE-OP surrogate model established in Step 5. If the accuracy meets the standard or the maximum number of sample point evaluations is reached, proceed to Step 7; otherwise, use CV-Voronio adaptive point addition to update the training set data and repeat Steps 5 and 6.
[0074] Furthermore, based on the surrogate model PEHE-OP established using the current sample set, the design space is divided into a series of Thiessen polygons using the Thiessen graphical method. Each polygon is approximated using a Monte Carlo method with a set of random points. Round-trip cross-validation is used to calculate the polygon prediction error, thereby identifying sensitive polygons. From the set of random points corresponding to the sensitive polygons, a random point farthest from the center point is selected as a new point. The sample set is updated, and the model is rebuilt until the model meets the required accuracy or reaches the maximum number of evaluations.
[0075] Step 7: Based on the PEHE-OP surrogate model obtained in Step 6, the overall performance parameters of the aero-engine are optimized using the MODE method, wherein the penalty function method is used to handle the constraints.
[0076] Step 8: Optimization complete. Output the optimized solution set obtained in Step 7.
[0077] The above technical solution will be further explained with reference to the accompanying drawings and examples:
[0078] Reference Figure 1 As shown, a specific embodiment of a multi-objective optimization method for overall performance of aero-engines based on a surrogate model includes the following steps:
[0079] Step one: Determine the overall performance parameters, control variables, and constraint variables of the aero-engine. Performance parameters typically include unit thrust Fs and unit fuel consumption rate sfc. Control variables include, but are not limited to, the relative equivalent speeds of the high and low pressure compressors, the cross-sectional area of the turbine guide vanes, the combustion chamber outlet temperature, the cross-sectional area of the exhaust nozzle throat, and the inlet guide vane angle of the compression components. Constraint variables typically include a compression component surge margin not lower than a certain value, a relative equivalent speed of the high and low pressure compressors not higher than a certain value, and a combustion chamber outlet temperature not higher than a certain value. The actual constraint variables and values are determined by the designer based on the specific problem.
[0080] Step 2: In the design space determined by the range of values of the design variables, the initial sample points of the training set are generated using the optimal Latin hypercube design (OLHS), and the sample points of the test set are randomly generated.
[0081] Step 3: Calculate the actual performance parameter response values of the initial sample points in the training set and the actual performance parameter response values of the sample points in the test set through experiments or simulation programs.
[0082] Step four: Normalize the dataset obtained in step three to obtain the normalized dataset.
[0083] Step 5: Based on the normalized training set data obtained in Step 4, establish the PEHE-OP surrogate model.
[0084] Reference Figure 2 As shown, the PEHE-OP surrogate model modeling process is as follows: First, based on the training set data, six component surrogate models are established, including two Kriging surrogate models, three RBF surrogate models, and one PRS surrogate model; then, the cross-validation error of each component surrogate model at each training set sample point is calculated, and an error estimation vector is established. Then, the k-nearest error estimation vector is introduced, and distance correction and global error GMSE correction are used to obtain the corrected error estimation vector. Then, based on the error estimation vector The component surrogate model weights at each sample point are obtained by an optimization method. To improve the accuracy of the combined surrogate model, the component surrogate model with the largest cross-validation error at the sample point is temporarily removed. Finally, the weights at non-sample points are determined by the inverse square Euclidean distance method, and the combined surrogate model PEHE-OP can be established.
[0085] Corrected error estimation vector
[0086]
[0087] in:
[0088]
[0089]
[0090]
[0091] In the formula, d(x) k ,x j ) represents the sample point x k With x j The distance between them, d averge d represents the average distance between sample points. averge d represents the average distance between sample points. 25prctile This represents the 25th percentile of the distance between sample points.
[0092] The local error of the combined surrogate model in the region near the sample point can be expressed as:
[0093]
[0094] C(x k ) represents the component surrogate model at the k-th sample point x k The error estimation matrix for the nearby region can be estimated using the following formula:
[0095]
[0096] In the formula, For the surrogate model of the i-th component at the k-th sample point x k The local error estimation vector at point m is the number of sample points.
[0097] For local error E local (x k Establish a minimization optimization problem:
[0098]
[0099] st1 T w(x k ) = 1
[0100] The theoretical solution can be obtained using the Lagrange multiplier method:
[0101]
[0102] The component surrogate model weights at sample points can be obtained from the above formula. The component surrogate model weights at non-sample points can be determined by using the inverse square Euclidean distance method, as shown in the following formula:
[0103]
[0104] In the formula, w i (x) represents the weight of the surrogate model for the i-th component at the point prediction point x, w ik Let be the weight of the surrogate model for the i-th component at the k-th sample point.
[0105] Step Six: Using the normalized test set data obtained in Step Four, verify the accuracy of the PEHE-OP surrogate model established in Step Five. If the accuracy meets the standard or the maximum number of evaluations per sample point is reached, proceed to Step Seven; otherwise, use CV-Voronio adaptive point addition to update the training set data and repeat Steps Five and Six. The CV-Voronio adaptive point addition process is as follows: Based on the surrogate model PEHE-OP established using the current sample set, the design space is divided into a series of Thiessen polygons using the Thiessen diagram method. Each polygon is approximated using a Monte Carlo method with a set of random points. The polygon prediction error is calculated using round-trip cross-validation to identify sensitive polygons. From the set of random points corresponding to the sensitive polygons, select the random point farthest from the center point as the new point. Update the sample set and rebuild the model until the model meets the required accuracy or the maximum number of evaluations is reached.
[0106] Step 7: Based on the PEHE-OP surrogate model obtained in Step 6, the MODE method is used to optimize the overall performance parameters of the aero-engine, with the penalty function method used for constraint handling. The MODE algorithm is as follows: First, an initial population of size 100 is randomly generated and evaluated using the established surrogate model to obtain multiple objective function values; then, offspring populations are obtained through crossover, mutation, and selection operations, and individual evaluations are performed; subsequently, the offspring populations are sorted non-dominated and crowding is calculated to obtain the Pareto front; offspring generation is repeated until the Pareto optimal solution meets the requirements or the maximum number of population iterations is reached, which is set to 100.
[0107] Step 8: Optimization complete. Output the optimized solution set obtained in Step 7.
[0108] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.
Claims
1. A multi-objective optimization method for the overall performance of an aero-engine based on a surrogate model, characterized in that... The specific steps are as follows: Determine the overall performance parameters, control variables, and constraint variables of the aero-engine; Within the design space defined by the range of values of the design variables, the optimal Latin hypercube design OLHS is used to generate initial sample points for the training set and to randomly generate sample points for the test set. The actual performance parameter response values of the initial sample points in the training set and the actual performance parameter response values of the sample points in the test set are obtained through experimental or simulation programs. The actual performance parameter response values of the initial sample points in the training set and the actual performance parameter response values of the sample points in the test set are normalized to obtain the normalized dataset. Based on the normalized training set data, a PEHE-OP proxy model is established; The accuracy of the established PEHE-OP surrogate model is verified using normalized test set data. If the accuracy meets the standard or the maximum number of sample point evaluations is reached, the process continues; otherwise, the training set data is updated by adaptive addition of points using CV-Voronio, and the establishment and verification of the PEHE-OP surrogate model are repeated. Based on the validated PEHE-OP surrogate model, the MODE method is used to optimize the overall performance parameters of the aero-engine; The optimization is complete, and the output is the optimized solution set of the overall performance parameters of the aero-engine using the MODE method.
2. The multi-objective optimization method for overall performance of aero-engines based on a surrogate model according to claim 1, characterized in that: The overall performance parameters of the aero-engine include unit thrust Fs and unit fuel consumption rate sfc; the control variables include the relative equivalent speed of the high and low pressure compressors, the cross-sectional area of the turbine guide vane, the combustion chamber outlet temperature, the cross-sectional area of the tail nozzle throat, and the inlet guide vane angle of the compression component; the constraint variables include the compression component surge margin not being lower than the set value, the relative equivalent speed of the high and low pressure compressors not being higher than the set value, and the combustion chamber outlet temperature not being higher than the set value.
3. The multi-objective optimization method for overall performance of aero-engines based on a surrogate model according to claim 1, characterized in that: The method for modeling the PEHE-OP proxy model is as follows: A six-component proxy model was established based on the training set data; Calculate the cross-validation error of each component surrogate model at each training set sample point, and establish an error estimation vector. By introducing the k-nearest approach and employing distance correction and global error GMSE correction, the corrected error estimation vector is obtained. Based on the error estimation vector An optimization method was used to obtain the point-by-point weights of the component surrogate models at each sample point, and the component surrogate models with the largest cross-validation error at each sample point were temporarily removed to improve the accuracy of the combined surrogate model. The weights at non-sample points are determined using the inverse square Euclidean distance method, thus completing the establishment of the combined surrogate model PEHE-OP.
4. The multi-objective optimization method for overall performance of aero-engines based on a surrogate model according to claim 3, characterized in that: The six component proxy models include two Kriging proxy models, three RBF proxy models, and one PRS proxy model.
5. The multi-objective optimization method for overall performance of aero-engines based on a surrogate model according to claim 4, characterized in that: The corrected error estimation vector The formula is as follows: in: In the formula, d(x) k ,x j ) represents the sample point x k With x j The distance between them, d averge d represents the average distance between sample points. averge d represents the average distance between sample points. 25prctile This represents the 25th percentile of the distance between sample points.
6. The multi-objective optimization method for overall performance of aero-engines based on a surrogate model according to claim 5, characterized in that: The component surrogate model weight formulas for each sample point are as follows: In the formula, w i (x) represents the weight of the surrogate model for the i-th component at the point prediction point x, w ik Let be the weight of the surrogate model for the i-th component at the k-th sample point.
7. The multi-objective optimization method for overall performance of aero-engines based on a surrogate model according to claim 6, characterized in that: The CV-Voronio adaptive point-addition update method for training set data is as follows: Based on the surrogate model PEHE-OP established using the current sample set, the design space is divided into a series of Thiessen polygons using the Thiessen graphical method. Each polygon is approximated by a set of random points using the Monte Carlo method. The polygon prediction error is calculated using round-robin cross-validation to identify sensitive polygons; a random point farthest from the center point is selected from the set of random points corresponding to the sensitive polygon as a new point. Update the sample set and rebuild the model until the model meets the required accuracy or reaches the maximum number of evaluations.
8. The multi-objective optimization method for overall performance of aero-engines based on a surrogate model according to claim 7, characterized in that: The method for optimizing the overall performance parameters of an aero-engine using the MODE method is as follows: An initial population of size 100 was randomly generated and evaluated using the established surrogate model to obtain multiple objective function values; Offspring populations are obtained through crossover, mutation, and selection operations, and individual assessments are performed. The Pareto front is obtained by performing non-dominated sorting and crowding calculation on the offspring population; Repeat the generation of offspring until the Pareto optimal solution meets the requirements or the maximum number of population iterations is reached. The maximum number of population iterations is set to 100.
9. The multi-objective optimization method for overall performance of aero-engines based on a surrogate model according to claim 8, characterized in that: The constraint handling method for optimizing the overall performance parameters of aero-engines using the MODE method employs the penalty function method.