Modeling method of aero-engine high-dimensional airborne steady-state model

Abstract

The invention discloses a modeling method for a high-dimensional airborne steady-state model of an aero-engine. According to the method, an HDMR is used for approximating an aero-engine high-dimensional airborne steady-state model; the self-adaptive sampling method comprises the following steps: step 1, on the basis of an initial cut point, sampling at a design space boundary point to form an initial sample point; 2, on the basis of known sample points, finding out a group of pre-sampling points with the maximum dispersion from a design space; thirdly, gradient estimation is conducted on the pre-sampling points through output of known sample points; 4, when a new sample point needs to be added, M pre-sampling points with the maximum gradient are selected from the current pre-sampling points for sampling, and the required new sample point is obtained; and if the pre-sampling points still need to be newly added after sampling is completed, turning to the step 2. Compared with the prior art, the method has the advantage that the high-dimensional airborne steady-state model of the aero-engine can be constructed at lower modeling cost.

Description

Technical Field

[0001] The present invention relates to a method for modeling an aircraft-borne steady-state model of an aeroengine, and particularly to a method for modeling a high-dimensional aircraft-borne steady-state model of an aeroengine, belonging to the technical field of aeroengine control. Background Art

[0002] The aircraft-borne steady-state model of an aeroengine is used to calculate the key performance parameters of the engine in real time, and has received extensive attention and application in engine control. Flight-propulsion integrated control uses the on-board model to estimate the engine state in real time and adaptively optimize the control parameters to exploit the performance potential of the engine; fault-tolerant control uses the on-board model to diagnose the gas path faults of the engine in real time; model predictive control uses the on-board model to predict the dynamic response of the engine in real time and obtains the optimal control strategy through online rolling optimization. Therefore, it is very important to establish an on-board model with excellent performance.

[0003] Currently, the widely used onboard models mainly include linear parameter-varying models [Orme, John, and Glenn Gilyard. "Preliminary supersonic flight test evaluation of performance seeking control." 29th joint propulsion conference and exhibit. 1993.][Lu, Feng, et al. "In-flight adaptive modeling using polynomial LPV approach for turbofan engine dynamic behavior." Aerospace Science and Technology 64(2017):223-236.], physical models [Pang, Shuwei, Qiuhong Li, and Hailong Feng. "A hybrid onboard adaptive model for aero-engine parameter prediction." Aerospace Science and Technology 105(2020):105951.][Xu, Maojun, et al. "An improved hybrid modeling method based on extreme learning machine for gas turbine engine." Aerospace Science and Technology 107(2020):106333.] and data-driven models [Palmé, Thomas, Francois Liard, and Dan Cameron. "Hybrid modeling of heavy duty gas turbines for on-line performance monitoring." Turbo Expo: Power for Land, Sea, and Air. Vol. 45752. American Society of Mechanical Engineers, 2014.][Brunton, Steven L., et al. "Data-driven aerospace engineering: reframing the industry with machine learning."AIAA Journal 59.8(2021):2820-2847.", etc. Among them, the linear variable parameter model is established by building linear models at a finite number of operating points and then through interpolation or fitting, and usually ignores engine performance degradation and individual differences. Therefore, there will inevitably be certain modeling errors. The mechanism model is finely modeled based on accurate component characteristics and physical laws, and can accurately describe the true aerodynamic and thermodynamic characteristics of the engine. However, the development cost of such models is high, the cycle is long, there is a large computational burden, and the real-time performance of the model is difficult to meet the requirements. The data-driven model can describe the known operating points of the engine with a lower computational pressure by learning the historical operating data of the engine, and has good real-time performance and accuracy. However, the data required to train the data-driven model is huge. In actual situations, the integrity of the data is often difficult to meet, and the accuracy of the model is difficult to guarantee for the flight envelopes and operating states not covered. Therefore, it is still difficult to establish a high-fidelity real-time airborne model of the engine.

[0004] Moreover, the requirements faced by modern aero-engines are constantly increasing. They not only need to expand the operating envelope and adapt to various operating conditions, but also need to meet new requirements such as low emissions and low noise. For example Figure 1As shown, since the advent of turbojet engines in the 1940s, aero-engines have become increasingly complex, and the number of control variables has gradually increased [Wang Bin, Xiao Yi, Liu Feng. Looking at the future development of aero-engine control technology from adaptive cycle engine [J]. Aerospace Power, 2019, (03): 48-51.]. This trend has brought unprecedented challenges to on-board models: for mechanism models, the matrices used for iterative solution have become increasingly large, further exacerbating the already heavy computational burden [Wang Yuan, Li Qiu-hong, Huang Xiang-hua. Numerical calculation of aero-engine model based on self-tuning Broyden quasi-Newton method [J]. Journal of Aerospace Power, 2016, 31(1): 249-256. doi:10.13224 / j.cnki.jasp.2016.01.032]; for LPV models and data-driven models, the number of samples required for model training increases exponentially [Pang, Bo, et al. "Data-driven surrogate model for aerodynamic design using separable shape tensor method." Chinese Journal of Aeronautics 37.9(2024): 41-58.][Siyu, Ding, et al. "Data-driven surrogate modeling and optimization of supercritical jet into supersonic crossflow." Chinese Journal of Aeronautics 37.12(2024): 139-155.], resulting in excessive modeling costs. Existing modeling methods are stretched when dealing with on-board engine models with more control variables. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a method for modeling a high-dimensional on-board steady-state model of an aero-engine, which can construct a high-dimensional on-board steady-state model of an aero-engine at a lower modeling cost.

[0006] The present invention specifically adopts the following technical solutions to solve the above technical problems:

[0007] A method for modeling a high-dimensional airborne steady-state model of an aeroengine decomposes the input variables of the high-dimensional airborne steady-state model of the aeroengine using the high-dimensional model representation method (HDMR), and approximates the high-dimensional airborne steady-state model of the aeroengine as a form of the sum of a 0th-order membership function to an Nth-order membership function, where N is an integer greater than or equal to 2; when constructing the ith-order membership function, adaptive sampling is performed by the method of maximum dispersion and gradient-based adaptive sequential sampling (MDGASS), 1 ≤ i ≤ N, and the MDGASS method is specifically as follows:

[0008] Step 1. Based on the initial cut point, sample at the boundary points of the design space to form initial sample points;

[0009] Step 2. Based on the known sample points, find a set of pre-sampling points with the maximum dispersion from the design space;

[0010] Step 3. Use the outputs of the known sample points to perform gradient estimation on the pre-sampling points respectively;

[0011] Step 4. When new sample points are needed, select the M pre-sampling points with the maximum gradient from the current pre-sampling points for sampling to obtain the required new sample points, where M is a positive integer; if new sample points are still needed after all the pre-sampling points have been sampled, go to Step 2.

[0012] Preferably, the ith-order membership function is constructed using the basis spline (BS) method.

[0013] Preferably, the Delaunay triangulation algorithm is used to find the set of pre-sampling points with the maximum dispersion.

[0014] Preferably, the value of M is 1.

[0015] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0016] The present invention introduces the high-dimensional model representation method (HDMR) into the aero-engine modeling. The input variables of the high-dimensional airborne steady-state model of the aero-engine are decomposed by HDMR, and the high-dimensional airborne steady-state model of the aero-engine is approximated as the sum of multiple membership functions. And the adaptive sequential sampling (MDGASS) method based on the maximum scatter and gradient is adopted in HDMR for adaptive sampling, so that the construction of the high-dimensional airborne steady-state model of the aero-engine can be completed at a lower modeling cost. Experiments show that under the same accuracy conditions, compared with the existing NN-PSM method, the MDGASS-BS-HDMR method proposed by the present invention reduces the required number of sampling points by more than 90% under ten-dimensional input variables. The technical solution of the present invention has good engineering application prospects and can be extended to the modeling of high-dimensional systems such as gas turbines and spacecraft propulsion systems. Description of the Drawings

[0017] Figure 1 It is a trend chart of the change in the number of aero-engine control variables;

[0018] Figure 2 It is a schematic diagram of a specific implementation process of the adaptive sequential sampling (MDGASS) method based on the maximum scatter and gradient;

[0019] Figure 3 It is an example diagram of dividing the two-dimensional design space by the Voronoi diagram method;

[0020] Figure 4 It is a schematic diagram of gradient estimation in one-dimensional case;

[0021] Figure 5 It is a schematic diagram of gradient estimation in two-dimensional case;

[0022] Figure 6 It is a schematic diagram of the pre-sampling sequence and the sequence sampling process; Figure 7 It is a schematic diagram of the principle of the MDGASS-BS-HDMR algorithm proposed by the present invention; Figure 8 It is an error diagram of the airborne steady-state model;

[0023] Figure 9 It is a collection diagram of sampling points of each performance parameter;

[0024] Figure 10(a) to Figure 10(c) It is a schematic diagram of the influence of NoE on the accuracy of the NN-PSM model. Detailed Embodiment

[0025] Aiming at the technical problems of the existing high-dimensional airborne steady-state model modeling technology for aero-engines, such as the excessive number of required samples and modeling costs, the solution idea of the present invention is to introduce the high-dimensional model representation method (HDMR) into aero-engine modeling, decompose the input variables of the high-dimensional airborne steady-state model of the aero-engine by using HDMR, approximate the high-dimensional airborne steady-state model of the aero-engine as the sum of multiple membership functions, and adopt the maximum dispersion and gradient-based adaptive sequential sampling (MDGASS) method in HDMR for adaptive sampling, so as to complete the construction of the high-dimensional airborne steady-state model of the aero-engine at a lower modeling cost.

[0026] The principle of HDMR is to decompose a high-dimensional function into multiple low-order membership functions. Taking an n-dimensional black-box system f(x) with an input of x = [x1, x2,..., x n ∈ R n as an example, the mathematical expression of HDMR is:

[0027]

[0028] In the formula, f0 is the zero-order membership function of the model, which is a constant; f i (x i ) is the first-order membership function of the model, indicating the influence of each input variable acting alone on the output; f ij (x i , x j ) is the second-order membership function of the model, indicating the influence of the interaction between the input variables x i and x j on the output (1 ≤ i ≠ j ≤ n); the subsequent terms are the high-order membership functions of the model, indicating the influence of the interaction of multiple input variables on the output. For a system with n-dimensional input, Equation (1) has a total of summation terms.

[0029] The sampling strategy of HDMR directly determines the modeling efficiency and accuracy. Taking the classical cut-HDMR method as an example, this method selects a cut point x0 within the range of input variables, and forms an approximate representation of the original system by constructing membership functions of each order passing through this point. For the selected cut point x0, the membership functions in the HDMR expansion are expressed as follows:

[0030]

[0031] In the formula, (x i |x0) represents the value x i of the i-th variable in the original system input x, and the other variables are the same as the selected cut point x0, where x i is generated within the range of the i-th dimension input through the sampling strategy; similarly, (x i , xj |x0) means that the i-th and j-th variables in the original system input x take values x i and x j respectively, and the other variables are the same as the selected cut point x0, where x i and x j are generated respectively within the input ranges of the i-th and j-th dimensions through the sampling strategy, and so on.

[0032] The purpose of the sampling method (or experimental design method) is to obtain a set of sample points within the design space in order to understand some laws of the original system. Common sampling methods include full factorial design, Latin hypercube sampling, Monte Carlo sampling, Sobol sequence sampling, and subdivided rectangle sampling, etc. Using sequential sampling methods rather than one-time sampling will help reduce the number of sampling points. The adaptive sampling strategies adopted by the existing cut-HDMR methods include random sampling and dichotomy sampling based on cross-validation, subdivided rectangle sampling, Sobol sequence sampling, and Hammersley sequence sampling, etc. Among them, random sampling may lead to uneven distribution of sampling points, insufficient coverage, and in high-dimensional spaces, a large sample size is required to obtain a good approximation effect, and the computational cost is high; for non-uniformly distributed objective functions, dichotomy sampling and subdivided rectangle sampling may not be able to effectively capture local characteristics; Sobol sequence sampling and Hammersley sequence sampling require determining the sampling quantity in advance, and the uniformity of sampling cannot be dynamically adjusted according to the characteristics of the objective function, which is likely to cause waste of sampling points in some areas.

[0033] To solve the problems existing in the above-mentioned adaptive sampling strategies, for the high-dimensional airborne steady-state model of aeroengines, considering the different influencing capabilities of the aeroengine system inputs on various performance parameters, based on the cut-HDMR method, an adaptive sequential sampling (MDGASS) method based on maximum dispersion and gradient is proposed to perform adaptive sampling on other member functions except the 0th-order member function. The specific MDGASS method is as follows:

[0034] Step 1: Based on the initial cut point, sample at the boundary points of the design space to form initial sample points;

[0035] Step 2: Based on the known sample points, find a set of pre-sampling points with the maximum dispersion from the design space;

[0036] Step 3: Use the outputs of the known sample points to perform gradient estimation on the pre-sampling points respectively;

[0037] Step 4. When new sample points need to be added, select the M pre-sampled points with the largest gradient from the current pre-sampled points for sampling to obtain the required new sample points, where M is a positive integer; if new sample points are still needed after all the pre-sampled points have been sampled, go to Step 2.

[0038] The construction of the i-th order membership function can adopt methods such as linear regression, polynomial fitting, support vector regression, neural network, least squares method, etc. In order to construct a membership function with maximized non-linear expression ability with the smallest number of samples, preferably, the basic spline method is used to construct the i-th order membership function.

[0039] The pre-sampled points with the largest dispersion can be found by methods such as the maximum-minimum distance method, grid search method, numerical optimization, maximum entropy method based on Gaussian process, etc. Preferably, the Delaunay triangulation algorithm is used to find the set of pre-sampled points with the largest dispersion.

[0040] In order to complete the modeling with as few samples as possible, the present invention preferably adopts the method of adding sampling points one by one each time; that is, the value of M is preferably 1.

[0041] A preferred implementation manner of the MDGASS method is as Figure 2 shown, in which the Delaunay triangulation algorithm (for its detailed content, reference can be made to the literature [Lee, Der-Tsai, and Bruce J. Schachter. "Two algorithms for constructing a Delaunay triangulation." International Journal of Computer & Information Sciences 9.3 (1980): 219-242.]) is used to form Voronoi partitions, so as to find a set of pre-sampled points with the largest dispersion; and the method of adding sampling points one by one each time is adopted. The specific process is as follows:

[0042] Step 1. Based on the initial cut point, sample at the boundary points of the design space to form initial sample points:

[0043] One of the purposes of selecting the boundary points of the design space is to ensure that the next points with the largest dispersion are located inside the design space; on the other hand, it is beneficial to further establish the HDMR membership function using the BS method without considering the generalization of the model.

[0044] Step 2. Based on the known sample points, find a set of pre-sampled points with the largest dispersion from the design space;

[0045] Assume there are p initial sample points The Voronoi method divides the design space into p Voronoi polygons according to p sample points It is expressed as:

[0046]

[0047] In the formula, dom(x i ,x j ) represents the closed half-plane enclosed by the perpendicular bisector of the line connecting points x i and x j

[0048] Figure 3 Fig. shows an example of dividing the two-dimensional design space by the Voronoi diagram method, where the initial sample points are randomly generated. Any point within polygon C i in the figure is closer to sample point x i than to other sample points. The dot is the Voronoi vertex, which is the center of the circumcircle of the sample points that form this point and is the sample point with the largest dispersion. Sampling should be preferentially performed on it to obtain uniformly distributed samples within the design space.

[0049] Step 3: Respectively perform gradient estimation on the pre-sampled points by using the outputs of the known sample points;

[0050] Since the design space of the present invention is a hypercube and the selection of the initial sampling points has certain particularity, the dispersion degrees of the pre-sampled points are the same, and gradient estimation needs to be performed respectively.

[0051] As Figure 4 shown, in the one-dimensional case, the distances from points P 12 ,P 23 to the known sample points P1, P2, P3 are equal, and the dispersion degree is the largest. As shown in Equation (4), using the finite difference method, the gradient of P 12 can be estimated from P1 and P2. It should be noted that although a smaller difference step size is what we hope for, considering some basic properties of the actual physical system (for example, as the main fuel flow increases, the engine speed, temperature, thrust, etc. are all monotonically increasing), and at the same time to reduce the additional sampling calculation cost, the known sample points are used for gradient estimation.

[0052]

[0053] In the two-dimensional case, first perform normalization processing on the design space. As Figure 5 ​As shown, there are always two situations in the dispersion iteration process. In situation 1, the maximum dispersion point is at the center of the square area formed by the known points, and there are no known sample points in its horizontal and vertical directions. Denote the points as P1, P2, P3, P4 in sequence, and estimate the magnitude of the directional derivative of point P0 through equations (5) and (6). In situation 2, the known sample points are all located in the horizontal and vertical coordinate axes directions of the maximum dispersion point. In this case, if there are no missing points among the known sample points, the directional derivative can be directly estimated by equations (7) and (8). If there is a missing point (always one point) among the known sample points, the output of the missing point can be first estimated by equation (9), and then the directional derivative of point P0 can be calculated according to equation (7) (or equation (8) if the missing point is in the horizontal axis direction) and equation (10). Finally, after anti-normalizing the directional derivative, the gradient of this point can be obtained by equation (11).

[0054] The gradient estimation algorithm for higher dimensions is the same. The order required for the construction of HDMR (which determines the sampling dimension) has been discussed before, so it will not be elaborated here anymore. In summary, although the gradient estimation involves finite differences in multi-dimensional space, based on the symmetry of the hypercube design space and the uniformity of the initial sampling, the gradients of the pre-sampled points can be effectively estimated through the output values of the known sample points.

[0055]

[0056] Step 4: When new sample points are needed, select the M pre-sampled points with the largest gradients from the current pre-sampled points for sampling to obtain the required new sample points, where M is a positive integer; if new sample points are still needed after all the pre-sampled points have been sampled, go to Step 2;

[0057] In this embodiment, the pre-sampled points are sorted from largest to smallest according to the gradient to form a pre-sampling sequence. Then, when new sample points are needed, the pre-sampled points are selected one by one in sequence from the pre-sampling sequence for sampling to form a new sample point; the schematic diagram of the pre-sampling sequence and the sequence sampling process is shown in Figure 6 .

[0058] For the convenience of public understanding, the technical solution of the present invention will be described in detail through a specific embodiment below:

[0059] For a turbofan engine, the flight altitude H and Mach number Ma determine the inlet conditions of the engine, and the main fuel flow rate W fb and the nozzle throat area A8 are the main control variables for the turbofan engine to adjust its own working state. The influence of these four input variables on the engine operation is the most significant. In addition, the turbofan engine also has fan guide vanes and low-pressure turbine guide vanes to adjust the component working characteristics; the performance of rotating components will also degrade. Select the compressor component flow degradation and turbine component efficiency degradation as the health parameters. Therefore, increasing the fan guide vane angle αf , the angle α of the low-pressure turbine guide vane l , the fan degradation D f , the compressor degradation D c , the high-pressure turbine degradation D h and the low-pressure turbine degradation D l Six input variables. At H = 8 - 13 km, Ma = 0.8 - 1.3, W fb,cor = 0.6 - 2.6 kg / s, A8 = 0.25 - 0.33 m 2 , the guide vane angles of each component vary by ±5°, and the degradation degrees of each component vary in the range of 0 - 2%.

[0060] This embodiment is directed to the above-mentioned airborne steady-state model of a turbofan engine. As Figure 7 shown, the high-dimensional function is decomposed into multiple low-order member functions through the high-dimensional model representation (HDMR), the sample distribution is optimized by combining the maximum dispersion and gradient-based adaptive sequential sampling (MDGASS) strategy, and the member functions are constructed with small samples using the basis spline (BS). Finally, an approximation of the original model is formed by combination. To distinguish it from the prior art, this modeling method is called MDGASS-BS-HDMR. Using this method, the key performance parameters of the turbofan engine, such as the fan speed N f , the compressor speed N c , the fan surge margin S mf , the compressor surge margin S mc , the thrust F and the turbine inlet temperature T4, an airborne steady-state model of the engine is established. In addition, since the modeling error of the second-order HDMR model is acceptable, this embodiment only considers the second-order interaction effects of the input variables.

[0061] The high-dimensional record steady-state modeling method of the aeroengine in this embodiment is as follows:

[0062] Step 1. Construct the HDMR zero-order member function:

[0063] Select the center point of the design space as the cut point x0, and calculate the output f0 at the x0 point as the HDMR zero-order member function;

[0064] Step 2. Construct the HDMR first-order member function:

[0065] Step 2.1. For each input variable x i , the initial sampling points are generated by the MDGASS algorithm, and the initial first-order member function f i (x i ) of the HDMR is constructed based on the BS method;

[0066] Step 2.2. Check whether the pre-sampling sequence is empty. If it is empty, go to Step 2.3; otherwise, go to Step 2.4;

[0067] Step 2.3. Continue to extend the pre-sampled sequence by the MDGASS algorithm;

[0068] Step 2.4. Use leave-one-out cross-validation to check the accuracy of the first-order membership functions. If the accuracy of all first-order membership functions meets the set threshold, the construction of the first-order membership functions of HDMR is completed; otherwise, go to Step 2.5.

[0069] Step 2.5. Perform sequence sampling by the MDGASS algorithm, add a sample point, reconstruct the first-order membership functions based on the BS method, and go to Step 2.4.

[0070] Step 3. Check the strength of the second-order interaction of the system;

[0071] Step 4. Construct the second-order membership functions of HDMR for the two-variable combinations with strong second-order interactions:

[0072] Step 4.1. For each combination of input variables x i and x j , generate initial sampling points by the MDGASS algorithm and construct the initial second-order membership function f ij (x i ,x j ) of HDMR based on the BS method;

[0073] Step 4.2. Check whether the pre-sampled sequence is empty. If it is empty, go to Step 4.3; otherwise, go to Step 4.4.

[0074] Step 4.3. Continue to extend the pre-sampled sequence by the MDGASS algorithm;

[0075] Step 4.4. Use leave-one-out cross-validation to check the accuracy of the second-order membership functions. If the accuracy of all second-order membership functions meets the set threshold, the construction of the second-order membership functions of HDMR is completed; otherwise, go to Step 4.5.

[0076] Step 4.5. Perform sequence sampling by the MDGASS algorithm, add a sample point, reconstruct the second-order membership functions based on the BS method, and go to Step 4.4.

[0077] Step 5. Check the strength of the third-order interaction of the system;

[0078] Step 6. Construct the third-order membership functions of HDMR:

[0079] The construction method is the same as that in Steps 2 and 4 and will not be repeated here;

[0080] Step 7. Combine the membership functions of each order according to Equation (1) to form the HDMR model.

[0081] To verify the effectiveness of the technical solution of the present invention, the Monte Carlo method was used to generate 500,000 test samples to detect the accuracy of the generated aircraft on - state model, and the relative error is as Figure 8 shown, and the performance indicators are shown in Table 1. As Figure 8 shown, the modeling errors of the fan speed, compressor speed and thrust are within 3.7%, the modeling errors of the fan surge margin and compressor surge margin are within 4.6%, and the modeling error of the turbine inlet temperature is within 1.9%. In addition, the errors of each performance parameter are concentrated near 0. Combining with Table 1, it can be seen that the R - square of all performance parameters is close to 1, and both RAAE and RMAE are small. The model has a high degree of fitting, and the modeling accuracy of the proposed method is high.

[0082] Table 1 Performance indicators of the aircraft on - state model based on MDGASS - BS - HDMR

[0083]

[0084] For different engine performance parameters, sampling and meta - modeling were carried out in sequence in this example, and multiple multi - input single - output models were established. However, the sampling points of different performance parameters may overlap, and the total modeling cost of the aircraft model is not simply the sum of the number of sampling points of each performance parameter. For the overlapping sampling points existing in the modeling of different parameters, they should only be calculated once. Therefore, an upset plot was drawn as Figure 9 shown. This figure is a set visualization method that can display the intersections, unions and their size distributions of multiple sets. Compared with the Venn diagram, it can show the combination of multiple sets more clearly. As Figure 9 shown, the number of sampling points required for modeling different parameters is listed on the left, totaling 1355. Among them, there are only 553 different sampling points, and only 229 sampling points are completely non - overlapping (only used once), accounting for about 41% of the total number of sampling points. The remaining 59% of the sampling points are used more than once in the modeling of different parameters. There are 56 sampling points that are used in the modeling of each parameter, accounting for about 10% of the total number of sampling points. The aircraft model established in this example includes multiple performance parameters. The number of samples required for the surge margin modeling is the largest, and many of these sample points are not required for the modeling of other parameters. When the surge margin model does not need to be established, the number of sampling points required becomes 330 (553 - 59 - 164). In summary, when establishing meta - models for different parameters of a multi - output system, the sampling points are highly overlapping, and there is a cost advantage in performing meta - modeling for multiple output parameters.

[0085] To further compare with other airborne model modeling methods, a simulation analysis of the airborne model modeling method based on the NN-PSM method was carried out [Song, J., Wang, Y., Ji, C. and Zhang, H. Real-time optimization control of variable rotor speed based on Helicopter / turboshaft engine on-board composite system. Energy, 2024. 301, p. 131701.][Cai, C., Zheng, Q., Wang, Y., Chen, H. and Zhang, H. Predictive control method for mode transition process of multi-mode turbine engine based on onboard adaptive composite model. Energy, 2024, p. 131748.][Zheng, Q., Xiang, D., Chen, C. and Zhang, H. Research on aero-engine performance seeking control based on the NN-PSM on-board model. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2022, 236(16), pp. 3505-3517.]. This method uses a neural network to establish a baseline model, mapping the relationship between flight conditions and main control variables and engine output. Then, based on the small deviation linearization method, the propulsion system matrix is extracted to correct the influence of guide vane angle and component degradation on engine output.

[0086] Accuracy verification was carried out at the same test sample points as the MDGASS-BS-HDMR method to obtain the influence of different NoE on the accuracy of the NN-PSM model. Related performance indicators such as Figure 10(a) to Figure 10(c)As shown in the figure. The asterisks in the shaded area of the figure represent the performance indicators of the MDGASS-BS-HDMR method. It can be seen that as the NoE increases, the R-square of the NN-PSM model gradually increases. Except for the compressor surge margin, the R-square of other parameters gradually approaches 1, the RAAE gradually decreases, the RMAE shows a decreasing trend, and the prediction error of the model gradually decreases. Combining with the simulation data of MDGASS-BS-HDMR, under the same accuracy index, the NoE of the proposed method is reduced by more than 90% compared with the NN-PSM model, significantly reducing the number of samples.

Claims

1. A method for modeling a high-dimensional airborne steady-state model of an aeroengine, characterized in that Decompose the input variables of the high-dimensional airborne steady-state model of an aero-engine using the high-dimensional model representation method HDMR, and approximate the high-dimensional airborne steady-state model of the aero-engine as a form of the sum of the 0th-order member function to the Nth-order member function, where N is an integer greater than or equal to 2; When constructing the ith-order member function, perform adaptive sampling through the maximum dispersion and gradient-based adaptive sequential sampling MDGASS method, where 1 ≤ i ≤ N, and the MDGASS method is specifically as follows: Step 1: Based on the initial cut point, sample at the boundary points of the design space to form initial sample points; Step 2: Based on the known sample points, find a set of pre-sampling points with the maximum dispersion from the design space; Step 3: Use the outputs of the known sample points to perform gradient estimation on the pre-sampling points respectively; Step 4: When new sample points are needed, select the M pre-sampling points with the largest gradient from the current pre-sampling points for sampling to obtain the required new sample points, where M is a positive integer; if new sample points are still needed after all the pre-sampling points have been sampled, go to Step 2.

2. The method for modeling a high-dimensional airborne steady-state model of an aeroengine according to claim 1, wherein Construct the ith-order member function using the basic spline method.

3. The method for modeling the high-dimensional airborne steady-state model of an aeroengine according to claim 1, characterized in that, Use the Delaunay triangulation algorithm to find the set of pre-sampling points with the maximum dispersion.

4. The method for modeling a high-dimensional airborne steady-state model of an aeroengine according to claim 1, wherein The value of M is 1.

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