Aerodynamic stability quantification method and system based on coupling of flow mechanism and deep learning

Abstract

The application relates to a method and system for quantifying aerodynamic stability based on coupling of flow mechanism and deep learning. The method first compresses high-dimensional point cloud data of a manufactured blade into low-dimensional base modes based on principal component analysis, effectively alleviating the variable dimension disaster problem caused by geometric uncertainty. Then, by taking the low-dimensional base mode weight as input, embedding the key physical feature of the tip leakage flow volume ratio into the deep neural network hidden layer, and taking the compressor stability margin change as output, a physical constraint and data-driven collaborative optimization framework is constructed, which significantly improves the prediction accuracy of the compressor aerodynamic stability under small sample conditions. The method provides a quantitative tool with high precision and physical credibility for solving the performance degradation problem of the CAES multi-stage axial flow compressor under non-design conditions caused by geometric deviation, and provides key technical support for realizing robust design.

Description

Technical Field

[0001] This invention belongs to the field of compressor technology, specifically relating to a method and system for quantifying aerodynamic stability based on the coupling of flow mechanism and deep learning. Background Technology

[0002] Compressed air energy storage (CAES), as a core solution for large-scale energy storage technology, has attracted significant attention under the global carbon neutrality goal due to its high capacity, long lifespan, and environmental friendliness. CAES systems effectively improve grid stability by storing excess renewable energy and releasing it during peak electricity demand. However, in actual operation, CAES systems often operate outside their design conditions due to load fluctuations, changes in gas pressure, and environmental factors, leading to a significant reduction in system efficiency and operational flexibility. Against this backdrop, the aerodynamic stability of the multi-stage axial compressor, as a core component of the CAES system, becomes crucial for ensuring the safe and economical operation of the system.

[0003] Manufacturing tolerances leading to blade geometric uncertainties are a significant factor affecting the performance of multistage compressors. Even within tolerance limits, geometric deviations can alter the internal flow field structure, causing flow separation, increased losses, and decreased surge margin. Studies have shown that in transonic compressors, geometric deviations exacerbate tip leakage, amplify flow disturbances, and further degrade compressor performance under near-stall conditions. For CAES systems, the compressor needs to operate over a wide storage pressure range; geometric uncertainties can easily lead the system into suboptimal conditions, increasing energy consumption and diminishing its energy-saving advantages. However, existing research largely focuses on performance parameters (such as efficiency and total pressure ratio), and the quantitative impact mechanism on stability margin remains unclear, particularly lacking a nonlinear correlation model between geometric uncertainty and surge margin.

[0004] To quantify the impact of geometric uncertainties on the performance of multi-stage compressors, researchers have developed various uncertainty quantification methods, including Monte Carlo methods, polynomial chaotic expansion, and deep learning techniques. While the Monte Carlo method is fundamental, its slow convergence speed makes it difficult to apply to high-dimensional nonlinear problems; adjoint methods are more efficient, but their prediction accuracy for large-scale geometric variations is insufficient. Polynomial chaotic expansion and deep learning have become mainstream methods, but polynomial chaotic expansion faces the "curse of dimensionality," while deep learning requires a large number of computational samples in high-dimensional input spaces. Furthermore, traditional deep learning techniques lack physical constraints, rely on large amounts of data for convergence, and suffer from insufficient prediction accuracy under sparse sample conditions. The current standard method for determining the compressor stability boundary is to gradually increase the outlet back pressure until the computational fluid dynamics simulation diverges. This means that each sample used to train the polynomial chaotic expansion model or deep learning model needs to undergo multiple computational fluid dynamics (CFD) simulations to obtain the compressor stability boundary. This approach incurs significant numerical computation costs, which will further increase the computational burden on geometric uncertainty quantification studies that rely on a large number of samples (Statistical evaluation of stability margin of a multi-stage compressor with geometric variability using adaptive polynomial chaos-Kriging model [J]. Phys of Fluids, 2023, 35, 076114.).

[0005] In summary, current technology has the following key gaps: There is a lack of efficient and high-precision quantitative assessment techniques for the impact of blade geometric uncertainties caused by manufacturing tolerances on compressor aerodynamic stability. Traditional uncertainty quantification techniques have high computational costs when establishing quantitative models of the impact of geometric uncertainties on aerodynamic stability, and data-driven models lack physical constraints, making it difficult to accurately predict nonlinear responses with a small number of training samples (An analytical method for the impact of rotor blade geometric deviations on compressor stability: CN117034584A). Summary of the Invention

[0006] To address the problems existing in the traditional methods mentioned above, this invention proposes an aerodynamic stability quantification method and system based on the coupling of flow mechanism and deep learning. This method directly embeds key flow features affecting compressor aerodynamic stability into the hidden layer of a deep learning network, enhancing the physical interpretability of the deep learning network during training. It achieves high-precision compressor aerodynamic stability prediction with a small number of training samples, providing a technical means for robust compressor design considering blade geometric uncertainties, and better achieving global carbon neutrality.

[0007] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:

[0008] On the one hand, a method for quantifying aerodynamic stability based on the coupling of flow mechanism and deep learning is provided, including the following steps:

[0009] Principal component analysis was used to compress the high-dimensional point cloud data of the actual processed blades into low-dimensional basic modes, and the weight coefficients of the low-dimensional basic modes were obtained.

[0010] We used low-difference sequences to design and sample low-dimensional modal weight coefficients. For each sample, we used CFD to calculate the stability parameters and flow mechanism quantification parameters of the compressor maneuver. Based on the calculation results, we constructed a dataset and divided it into training and test sets.

[0011] A flow mechanism embedded deep neural network was constructed and trained and tested using training and testing sets to obtain a trained flow mechanism embedded deep neural network. The flow mechanism embedded deep neural network includes network block 1 and network block 2. Network block 1 is used to learn the relationship between low-dimensional modal weight coefficients and flow mechanism quantization parameters through nonlinear mapping. Network block 2 is used to process the spliced ​​low-dimensional modal weight coefficients and flow mechanism quantization parameters using a nonlinear layer to obtain the predicted values ​​of aerodynamic stability parameters. The loss function in the training process simultaneously constrains the prediction errors of flow mechanism quantization parameters and aerodynamic stability parameters.

[0012] Monte Carlo sampling is used based on low-dimensional modal weight coefficients. The sampled samples are input into a trained flow mechanism embedded deep neural network to obtain multiple sets of predicted values ​​of aerodynamic stability parameters. Uncertainty analysis is then performed on the predicted values ​​of aerodynamic stability parameters.

[0013] On the other hand, an aerodynamic stability quantification system based on the coupling of flow mechanism and deep learning is also provided, including:

[0014] The module for determining the uncertainty parameters of the blade set is used to compress the high-dimensional point cloud data of the actual processed blades into low-dimensional basic modes using principal component analysis, and obtain the weight coefficients of the low-dimensional basic modes.

[0015] The dataset construction module is used to design and sample low-dimensional modal weight coefficients using low-discrepancy sequences. For each sample, CFD is used to calculate the stability parameters and flow mechanism quantification parameters of the compressor maneuver. The dataset is constructed based on the calculation results and divided into training and test sets.

[0016] A module for constructing and training a flow mechanism embedded deep neural network is included. This module is used to construct a flow mechanism embedded deep neural network and train and test it using training and testing sets to obtain a trained flow mechanism embedded deep neural network. The flow mechanism embedded deep neural network includes network block 1 and network block 2. Network block 1 is used to learn the relationship between low-dimensional modal weight coefficients and flow mechanism quantization parameters through nonlinear mapping. Network block 2 is used to process the concatenated low-dimensional modal weight coefficients and flow mechanism quantization parameters using a nonlinear layer to obtain predicted values ​​of aerodynamic stability parameters. The loss function in the training process simultaneously constrains the prediction errors of the flow mechanism quantization parameters and aerodynamic stability parameters.

[0017] The aerodynamic stability quantification analysis module is used to perform Monte Carlo sampling based on low-dimensional modal weight coefficients, input the sampled samples into a trained flow mechanism embedded deep neural network, obtain multiple sets of predicted aerodynamic stability parameters, and perform uncertainty analysis on the predicted aerodynamic stability parameters.

[0018] One of the above technical solutions has the following advantages and beneficial effects:

[0019] The aforementioned aerodynamic stability quantification method and system, based on the coupling of flow mechanism and deep learning, firstly compresses the high-dimensional point cloud data of the manufactured blades into low-dimensional basic modes using principal component analysis, effectively mitigating the curse of dimensionality caused by geometric uncertainty. Then, by using the weights of the low-dimensional basic modes as input, the key physical feature of tip leakage flow ratio is directly embedded into the hidden layer of a deep neural network, with the compressor stability margin change as output, constructing a co-optimization framework of physical constraints and data-driven approaches. This significantly improves the accuracy of compressor aerodynamic stability prediction under small sample conditions. This method provides a highly accurate and physically reliable quantitative tool for addressing the performance degradation problem caused by geometric deviations in CAES multi-stage axial compressors under off-design conditions, providing key technical support for achieving robust design. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application or the conventional technology, the drawings used in the description of the embodiments or the conventional technology will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating an aerodynamic stability quantification method based on the coupling of flow mechanism and deep learning in one embodiment.

[0022] Figure 2This is a geometric model diagram of an 8-stage compressor designed for a large CAES in one embodiment;

[0023] Figure 3 This is a graph showing the cumulative energy percentage as a function of the number of fundamental modes, obtained from principal component analysis of R1 in one embodiment.

[0024] Figure 4 This is a schematic diagram of the main integral surface and the tip clearance surface in one embodiment;

[0025] Figure 5 Here is a CFD computational domain mesh diagram from one embodiment;

[0026] Figure 6 This is a nominal compressor mass flow rate-total pressure ratio characteristic diagram obtained based on CFD in one embodiment;

[0027] Figure 7 In one example, the training sample size is 200. r M With Δ SM The correlation analysis results are shown in the figure. Figure 7 (a) is r M With Δ SM Scatter plot; Figure 7 (b) is Δ SM and r M Linear fitting error analysis diagram;

[0028] Figure 8 This is a schematic diagram of a deep neural network structure with embedded flow mechanism in one embodiment;

[0029] Figure 9 This is a flowchart of the training process for a deep neural network with embedded flow mechanism in one embodiment;

[0030] Figure 10 In one embodiment, the Δ values ​​of four models for 100 test samples are given. SM Predicted results; Figure 10 (a) is a diagram showing the predicted effect of the present invention; Figure 10 (b) shows the prediction results of the traditional neural network model; Figure 10 (c) shows the prediction results of the sparse polynomial chaotic expansion model based on minimum angle vector regression; Figure 10 (d) shows the prediction results of the sparse polynomial chaotic expansion model based on pan-kriging;

[0031] Figure 11 Four models for Δ in one embodiment SM The graph shows how the relative error of the prediction changes with the number of training samples.

[0032] Figure 12 Δ obtained by the method of the present invention in one embodiment SM The statistical distribution chart. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0034] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0035] It should be noted that, in this document, the reference to "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The presentation of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. Those skilled in the art will understand that the embodiments described herein can be combined with other embodiments. The term "and / or" as used herein refers to any combination of one or more of the associated listed items, and all possible combinations, including such combinations.

[0036] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0037] In one embodiment, such as Figure 1 As shown, an aerodynamic stability quantification method based on the coupling of flow mechanism and deep learning is provided, which may include the following processing steps 1 to 4:

[0038] Step 1: Principal component analysis is used to compress the high-dimensional point cloud data of the actual processed blades into low-dimensional modes, and the weight coefficients of the low-dimensional modes are obtained.

[0039] Specifically, point cloud data of actual processed blades is obtained using a multi-axis rotating overspeed measurement system. Principal component analysis is used to compress the high-dimensional point cloud data into low-dimensional basic modes. The weight coefficients corresponding to the low-dimensional basic modes are used as input variables for subsequent model training, effectively reducing the dimensionality of variables.

[0040] Step 2: Experimental design sampling is carried out on the low-dimensional modal weight coefficients using low-discrepancy sequences. For each sample, CFD is used to calculate the stability parameters and flow mechanism quantification parameters of the compressor maneuver. Based on the calculation results, a dataset is constructed and divided into training and test sets.

[0041] Specifically, low-difference sequences were used to sample low-dimensional modal weighting coefficients in experimental design. Near-stall conditions for each sample were obtained through CFD simulations with progressively increasing outlet back pressure. The compressor stability margin change was calculated, and the axial momentum ratio of the tip leakage flow for each sample was extracted as a quantitative parameter of the flow mechanism.

[0042] Step 3: Construct a flow mechanism embedded deep neural network, and train and test it using training and testing sets to obtain a trained flow mechanism embedded deep neural network. The flow mechanism embedded deep neural network includes network block 1 and network block 2. Network block 1 is used to learn the relationship between low-dimensional modal weight coefficients and flow mechanism quantization parameters through nonlinear mapping. Network block 2 is used to process the spliced ​​low-dimensional modal weight coefficients and flow mechanism quantization parameters using a nonlinear layer to obtain the predicted values ​​of aerodynamic stability parameters. The loss function in the training process simultaneously constrains the prediction errors of flow mechanism quantization parameters and aerodynamic stability parameters.

[0043] Specifically, the low-dimensional modal weight coefficients are used as inputs to the flow mechanism embedded deep neural network, and the compressor stability margin variation is used as the output of the flow mechanism embedded deep neural network. At the same time, the flow mechanism quantification parameters and geometric uncertainty features are directly embedded into the hidden layer. The prediction errors of physical mechanisms and aerodynamic stability parameters are constrained in the network loss function, so as to achieve collaborative modeling of physical laws and data-driven approaches.

[0044] The flow mechanism embedded deep neural network was trained using a training set and then tested using a test set. Through rigorous accuracy verification and multi-model comparison, it was demonstrated that the constructed flow mechanism embedded deep neural network has prediction accuracy and sample efficiency far exceeding traditional methods, thus confirming its applicability for subsequent large-scale, high-reliability probabilistic analysis.

[0045] By directly embedding key flow features affecting compressor aerodynamic stability into the hidden layer of a deep learning network, the physical interpretability of the deep learning network during training is enhanced. High-precision compressor aerodynamic stability prediction is achieved with a small number of training samples, providing a technical means for robust compressor design that considers blade geometric uncertainties, and better achieving global carbon neutrality.

[0046] Step 4: Monte Carlo sampling is performed based on the low-dimensional modal weight coefficients. The sampled samples are input into the trained flow mechanism embedded deep neural network to obtain multiple sets of predicted values ​​of aerodynamic stability parameters. Uncertainty analysis is then performed on the predicted values ​​of aerodynamic stability parameters.

[0047] Specifically, Monte Carlo sampling is performed based on a deep neural network model embedded in the flow mechanism to obtain the probability distribution characteristics of stability margin changes, obtain extreme variation values ​​of stability margin, and analyze whether the compressor has sufficient margin for stable operation.

[0048] The aforementioned aerodynamic stability quantification method, based on the coupling of flow mechanism and deep learning, firstly compresses the high-dimensional point cloud data of the manufactured blades into low-dimensional basic modes using principal component analysis, effectively mitigating the curse of dimensionality caused by geometric uncertainty. Then, by using the weights of the low-dimensional basic modes as input, the key physical feature of tip leakage flow ratio is directly embedded into the hidden layer of a deep neural network, with the compressor stability margin change as output, constructing a co-optimization framework of physical constraints and data-driven approaches. This significantly improves the accuracy of compressor aerodynamic stability prediction under small sample conditions. This method provides a highly accurate and physically reliable quantitative tool for addressing the performance degradation problem caused by geometric deviations in CAES multi-stage axial compressors under off-design conditions, providing key technical support for achieving robust design.

[0049] In one embodiment, step 1 includes: acquiring high-dimensional point cloud data of the actual processed blade; constructing a scatter matrix based on the high-dimensional point cloud data; performing singular value decomposition on the scatter matrix to obtain the eigenvalues ​​corresponding to the fundamental modes; and representing the blade's geometric random deviations as... p The high-dimensional point cloud data of the blade is compressed by summing a finite number of fundamental modes and their corresponding eigenvalues ​​into a weighted linear sum and the average geometric change of the blade. p Each fundamental mode weight coefficient; where p The value is taken when the cumulative energy percentage is not less than a preset threshold. k The value; where the cumulative energy percentage is:

[0050] (1)

[0051] in, Indicates the percentage of cumulative energy. Indicates the first i The energy percentage of low-dimensional modes diagonal eigenvalue matrix Elements on the diagonal.

[0052] In one embodiment, the scatter matrix is ​​constructed based on the high-dimensional point cloud data as follows:

[0053] (2)

[0054] Where S is a scatter matrix, To generate the geometric deviation matrix of the blade after decentering, the superscript... T This is a matrix transpose operation. n This indicates the number of blades manufactured.m This indicates the number of scan points for each leaf; Indicates the first i Geometric deviations after decentering of blades in blade manufacturing Indicates the first i Geometric deviations in blade manufacturing Indicates the first j The average geometric change at each scan point; and They represent the first i The nominal coordinate vector of the blade and the coordinate vector of the blade.

[0055] Specifically, after obtaining the point cloud data of the actual processed blades, the high-dimensional point cloud data compression step based on principal component analysis consists of three steps. First, a scatter matrix S is constructed as shown in formula (2); second, the singular value decomposition of the scatter matrix is ​​performed to obtain the eigenvalues ​​corresponding to the basic modes. Singular value decomposition of the above scatter matrix S yields:

[0056] (3)

[0057] Where Q = [ q 1, q 2, …, q n ] is the eigenvector matrix, This is the diagonal eigenvalue matrix. Finally, the geometric uncertainty of the blade is characterized by a linear combination of the fundamental modes of the geometric deviations. Based on the obtained fundamental modes and eigenvalues, the random geometric deviations of the blade can be... Represented as p A finite number of weighted linear combinations of fundamental modes:

[0058] (4)

[0059] Among them, since geometric deviations originate from random manufacturing processes, the weighting coefficients of all fundamental modes z i All are treated as random variables, jointly representing geometric uncertainty, and the weighting coefficients of each fundamental mode are... z i It follows a standard normal distribution. At this point, the high-dimensional point cloud data of the blade is compressed to... p The random geometric deviation of the blade can be obtained based on formula (4) by using the random perturbation of the fundamental mode weight coefficients. p Through the cumulative energy percentage of the fundamental mode AP k Determine the cumulative energy percentage of the fundamental mode. AP k As shown in formula (1).

[0060] In order to balance data compression effectiveness and accuracy, AP k ≥90% k As p The value of represents p One basic mode can effectively capture most (over 90%) of the geometric uncertainty information. This truncation not only significantly reduces the dimensionality of geometric uncertainty modeling, avoiding the "curse of dimensionality," but also ensures a high-fidelity approximation of geometric uncertainty models to geometric deviations.

[0061] This embodiment analyzes an 8-stage axial compressor designed for large-scale CAES (Computer-Aided Systems) applications. The geometric model is as follows: Figure 2 As shown, the first-stage rotor contains 36 blades, with an inlet hub ratio of approximately 0.55 and an outlet hub ratio of approximately 0.58. To suppress flutter, a trailing edge chamfer design is used at the blade tips. Although the compressor's design speed is 4700 rpm, factory tests revealed that surge is prone to occur around approximately 75% of the design speed. Therefore, this paper focuses on analyzing the impact of geometric uncertainties on aerodynamic stability at this operating speed.

[0062] Based on the manufacturer's maintenance experience, the aerodynamic stability of this compressor is mainly affected by the geometric deviations of its first three rotor stages. To study the uncertainty impact of these geometric deviations on compressor stability, a geometric uncertainty model of each rotor stage needs to be established through deviation measurements. Three-dimensional point cloud data of the actual blades were acquired using a multi-axis rotating overspeed measurement system. This system achieves accurate reconstruction of blade geometry through multi-angle image acquisition and a synchronous digital measurement module. During the measurement process, 100 sets of measurements were taken for each rotor, with multiple spanwise sections measured for each rotor. The first-stage rotor (R1) had 11 sections, the second-stage rotor (R2) had 10 sections, and the third-stage rotor (R3) had 8 sections.

[0063] Principal component analysis based on R1 measurement data Figure 3 The cumulative energy percentage is given. AP k As the number of fundamental modes changes, it can be seen that the cumulative energy of the first 6 fundamental modes accounts for more than 90%, indicating that these 6 fundamental modes can capture more than 90% of the geometric uncertainty information. Therefore, R1 truncates equation (3) when modeling geometric uncertainty, and takes the truncation parameter. p =6. Further analysis of the measurement data of R2 and R3 shows that the cumulative energy proportions of the first 6 PCA modes reach 94.5% and 93.2% respectively, which also meet the requirements for efficiently characterizing geometric uncertainty. Therefore, in this embodiment, the first 6 basic modes of each of the first 3 levels are selected to jointly construct the geometric uncertainty model, that is, 18 geometric uncertainty parameters. Z= [z 1, z 2,…, z 18 The first 6 are the fundamental modes of R1, the middle 6 are the fundamental modes of R2, and the last 6 are the fundamental modes of R3.

[0064] In one embodiment, step 2 includes: using Halton low-difference random sequences to perform experimental design sampling in the probability space of low wiki mode weight coefficients to generate a set of sample points; obtaining the near-stall conditions of each sample point through CFD simulation with gradually increasing outlet back pressure, calculating the compressor stability margin change, and extracting the tip leakage axial momentum ratio of each sample near-stall condition as a flow mechanism quantification parameter.

[0065] In one embodiment, the compressor stability margin changes as follows:

[0066] (5)

[0067] in, This indicates the change in compressor stability margin. and These represent the total pressure ratio and flow rate of the compressor in near-stall conditions, respectively. The subscript "deviation" indicates a compressor with geometric deviation, and the subscript "nominal" indicates a nominal reference compressor without geometric deviation.

[0068] In one embodiment, the axial momentum ratio of the tip leakage flow is:

[0069] (6)

[0070] in, This indicates the axial momentum ratio of the tip leakage flow. and These represent the axial momentum and main flow of the tip leakage flow, respectively.

[0071] Specifically, to quantify the impact of geometric deviations on the aerodynamic stability of the compressor, the compressor stability margin change is defined as shown in formula (5). By introducing a percentage change expression, Δ SM It can intuitively reflect the relative change in stability margin caused by geometric deviation: when Δ SM When Δ > 0, it indicates that the geometric deviation actually increases the stability margin; when Δ SM When <0, it indicates that the geometric deviation has led to a deterioration of the stability margin. In practical applications, the characteristic curves of the nominal compressor and the compressor with geometric deviation are first obtained by CFD, and then the near-stall point parameters of each are determined. Finally, the specific change in stability margin is calculated by substituting them into equation (5).

[0072] Changes in blade geometry alter the axial momentum of the rotor tip leakage flow through complex flow interactions, thus affecting the compressor's aerodynamic stability. Therefore, the axial momentum ratio of the tip leakage flow under near-stall conditions is crucial. r M This parameter, used as a quantitative parameter of the flow mechanism, characterizes the mechanism of changes in compressor aerodynamic stability. It effectively characterizes the momentum exchange intensity between the tip leakage flow and the mainstream, and its negative value reflects the impediment effect of the leakage flow on the mainstream. When geometric deviations cause the negative value to increase (i.e., r M When the negative value increases, it indicates that the leakage flow is increasingly interfering with the mainstream, which will increase the blockage of the leakage flow in the blade tip passage and reduce the stability margin.

[0073] Axial momentum ratio of tip leakage flow r M The definition is shown in formula (6). Main flow M x,in Integrating at the top region (90%–100% blade height) of a single rotor passage at the rotor inlet:

[0074] (7)

[0075] In the formula, ρ It is the fluid density. V x It is the axial velocity of the airflow. A It is the mainstream integral surface. Figure 4 Schematic diagrams of the main integral surface and the tip clearance surface are provided. Considering that the tip leakage flow originates in the leading edge of the clearance region, its axial momentum... M x,tip Axial momentum of leakage flow per unit chord length m x Integrating over the first half of the blade tip clearance surface yields:

[0076] (8)

[0077] In the formula, l Given the tip chord length, the axial momentum of the leakage flow per unit chord length. m x Defined as:

[0078] (9)

[0079] In the formula, V n The absolute velocity of the airflow perpendicular to the blade tip clearance surface. α This indicates the angle of inclination of the clearance surface relative to the axial direction. r This indicates the radial coordinates of the compressor, with "tip" and "casing" representing the blade tip and casing positions, respectively.

[0080] In this embodiment, after obtaining the 18 geometric uncertainty parameters after dimensionality reduction, an experimental design is performed using Halton low-discrepancy random sequences in the probability space of the geometric uncertainty parameters to generate a set of training sample points. ,in N s The number of samples. By... Substitute into formula (4) to obtain the specific geometric deviation distribution, and then obtain the blade geometry corresponding to each training sample by superimposing the geometric deviation distribution onto the nominal reference blade.

[0081] The compressor stability boundary was obtained using a rigorously validated CFD method. First, a hybrid mesh was generated, employing an HO-type mesh topology in the tip clearance region and an O4H-type mesh structure on the blade surface, ensuring the near-wall mesh height was controlled at 10. -6 Within meters, the dimensionless mesh thickness of all near-wall surfaces y + All values ​​are less than 1. Mesh independence verification was performed using five different mesh density configurations, with the total mesh count gradually increasing from 2.75 million to 9.4 million. Ultimately, a mesh count of 6.44 million was determined to meet the computational accuracy requirements. Figure 5 A CFD computational domain mesh diagram of an example is given.

[0082] For each sample, the numerical solution is based on the three-dimensional Reynolds-averaged Navier-Stokes equations, spatially discretized using a second-order Jameson finite volume scheme, and time-integrated using a second-order upwind method. The Spalart-Allmaras model is selected as the turbulence model. Convergence acceleration is achieved through multigrid method, local time step, and implicit residual smoothing techniques. Boundary conditions are set including an inlet total pressure of 101.325 kPa and a total temperature of 288.2 K, with a circumferentially averaged hydrostatic pressure boundary at the outlet. The stall condition is approximated by gradually increasing the back pressure (in 100 Pa steps). The near-stall condition is the last stable operating point before the sudden drop in mass flow rate. Based on the above CFD method, Figure 6 The mass flow rate-total pressure ratio characteristic curve of the nominal reference compressor is given.

[0083] After the CFD calculations for all samples are completed, the stability margin change Δ for all samples is calculated according to formula (5). SM The axial momentum ratio of the tip leakage flow under near-stall conditions for all samples was calculated according to formulas (6) to (9). Ultimately forming a size of The dataset provides data support for the subsequent construction of deep neural networks that embed flow mechanisms.

[0084] The research object of this embodiment is an 8-stage axial compressor designed for large-scale CAES, and the aerodynamic stability of this compressor is mainly affected by the geometric deviations of its first 3 rotor stages. Therefore, for this embodiment, the axial momentum ratio of the tip leakage flow is... This is the sum of the axial momentum ratios of the leakage flow at the tips of the first three rotor stages, i.e.:

[0085] (10)

[0086] In the formula, r M,R1 , r M,R2 and r M,R3 These represent the axial momentum ratios of the leakage flow at the tips of the first three rotor stages.

[0087] Figure 7 This embodiment is given. N s =200 hours With Δ SM The correlation analysis results. Figure 7 The scatter plot results in (a) show that Δ SM and There is a significant linear statistical association between them, and the relationship can be expressed as follows: Coefficient of determination R 2 It reached 0.903. However, Figure 7 Error analysis in (b) shows that Δ SM – y With Δ SM The maximum ratio is approximately 3, meaning the maximum relative error is 300%. This indicates that despite the significant statistical correlation, it is difficult to accurately predict changes in stability margin by directly relying on this flow mechanism parameter.

[0088] Figure 7 The analysis further reveals the complex mechanism by which geometric uncertainty affects stability: blade manufacturing deviations alter the characteristics of tip leakage flow, leading to changes in compressor stability margin. However, this process involves strong nonlinear flow effects and interactions of higher-order parameters. Therefore, it is necessary to develop more advanced prediction methods that can simultaneously capture both the flow mechanism and the nonlinear effects of geometric deviations. This also provides a theoretical basis for the subsequent development of prediction models that integrate flow mechanisms and deep learning.

[0089] In one embodiment, in a flow mechanism embedded deep neural network: the low-dimensional modality weight coefficients are input into the input layer of network block 1, and then processed through several fully connected hidden layers to obtain the predicted value of the flow mechanism quantization parameter; the flow mechanism quantization parameter and the low-dimensional modality weight coefficients are concatenated to obtain the composite input feature; the composite input feature is input into the input layer of network block 2, and then processed through several fully connected hidden layers to obtain the predicted value of the change in the stability margin of the target variable.

[0090] Specifically, flow mechanism embedded deep neural network structures such as Figure 8 As shown. This network innovatively increases the axial momentum ratio of the tip leakage flow. and p Each fundamental mode weight coefficient ( z 1. z 2 、 ... 、z p-1 、z p These features are jointly embedded into a dedicated hidden layer for feature fusion. The neural network is divided into two blocks. In network block 1, [the following is not specified:] p The weight coefficients of each basic mode are used as the initial input features. As output features, through N A fully connected hidden layer performs nonlinear mapping. This network block specifically learns the relationship between geometric uncertainty features and flow mechanism quantification parameters. In network block 2, the output features of the previous network block are concatenated with the geometric uncertainty features to form a 1+ p 3D composite input features ( and p (Each basic mode weight coefficient). This network block learns the nonlinear coupling relationship between geometric uncertainty features and momentum ratio through joint learning. N The two fully connected hidden layers directly output the change in the stability margin Δ of the target variable. SM Both network blocks employ the ReLU activation function in their fully connected layers. This design effectively mitigates the vanishing gradient problem while maintaining nonlinear mapping capability, and improves computational efficiency through sparsity constraints. The number of neurons in each layer is determined through hyperparameter optimization.

[0091] The training process of a deep neural network with embedded flow mechanism is as follows: Figure 9 The training process mainly consists of four steps. First, the input / output data is standardized using the Min-Max normalization method. Second, the AdamW optimizer is used for weight updates, balancing training speed and convergence stability. Then, when the training error value is less than 10 for five consecutive training epochs... -5 Training may terminate when the maximum number of training epochs (2000) is reached. Finally, a Bayesian optimization method is used to minimize...k The mean squared error of cross-validation is used as an indicator to search for the optimal network configuration, determining the number of hidden layers and hidden neurons in each network block, as well as the learning rate for neural network training, to maximize the model's generalization ability. The search domain for network configuration is defined as follows: number of hidden layers in each network block ∈ {1, 2, 3}, number of hidden neurons ∈ {32, 40, 48, 56, 64}, and learning rate ∈ {0.01, 0.001, 0.0001}.

[0092] In this embodiment, a flow mechanism embedded deep neural network model is constructed based on 200 sets of training samples within the PyTorch framework. The input to network block 1 consists of 18 base mode weight coefficients. Z= [ z 1, z 2,…, z 18 The output is the axial momentum ratio of the tip leakage flow calculated by formula (10). r M The input to network block 2 is... r M and Z= [ z 1, z 2,…, z 18 The output is the stability margin change Δ. SM The optimal hyperparameters determined through Bayesian optimization are as follows: learning rate 0.001; network block 1 includes... N Block 1 has 2 hidden layers and 32 / 48 neurons; Block 2 of the network includes... N 2 = 1 hidden layer, 32 neurons. Test results on the normalized training set show a mean squared error of 10. -5 Coefficient of determination R 2 The accuracy reached 0.991, indicating that the model has extremely high prediction accuracy.

[0093] In one embodiment, the loss function for the training process is:

[0094] (11)

[0095] in, L The loss function representing the training process. This represents the axial momentum ratio of the tip leakage flow. The superscripts "predicted" and "actual" indicate the network prediction and the actual value in the training data, respectively. The number of training samples in the training set. This represents the change in compressor stability margin. This design, through equal weighting, ensures that the model learns the correlation between aerodynamic stability and physical mechanisms in a balanced manner during training.

[0096] In one embodiment, the process of testing the trained flow mechanism embedded deep neural network with the test set in step 3 includes: inputting test samples from the test set into the trained flow mechanism embedded deep neural network to obtain the predicted value of the change in the stability margin of the target variable; and calculating the statistical relative error based on the predicted value of the change in the stability margin of the target variable and the CFD calculated value of the change in the stability margin of the target variable corresponding to the test sample.

[0097] (12)

[0098] in, Indicates statistical relative error. Indicates the test sample size. This represents the sample mean of the CFD calculated values. Indicates the first i Predicted values ​​of the change in the stability margin of the target variable for each test sample. Indicates the first i The CFD calculation value of the change in the stability margin of the target variable for each test sample.

[0099] The accuracy of the trained flow mechanism embedded deep neural network is verified by statistical relative error, and the trained flow mechanism embedded deep neural network is obtained.

[0100] Specifically, through rigorous accuracy verification and multi-model comparison, it is demonstrated that the constructed flow mechanism embedded deep neural network has prediction accuracy and sample efficiency far exceeding traditional methods, thus confirming its applicability for subsequent large-scale, high-reliability probabilistic analysis.

[0101] To verify the prediction accuracy and generalization ability of the flow mechanism embedded deep neural network model, an independent test set was used for evaluation. Based on the independent test samples, the statistical relative error (SRE) was calculated using formula (12) as the core evaluation index. For this embodiment, N t =100.

[0102] In this embodiment, to verify the effectiveness of the flow mechanism embedding, three comparative models were trained simultaneously: a traditional neural network model (network structure with three hidden layers (32-48-32 neurons)), a sparse polynomial chaotic expansion model based on minimum angle vector regression, and a sparse polynomial chaotic expansion model based on pan-kriging. All four models are derived from... N s=Trained with 200 training samples. The Δ values ​​of the four models on 100 test samples. SM Predicted results diagram as follows Figure 10 As shown, where Figure 10 (a) is a diagram showing the predicted effect of the present invention; Figure 10 (b) shows the prediction results of the traditional neural network model; Figure 10 (c) shows the prediction results of the sparse polynomial chaotic expansion model based on minimum angle vector regression; Figure 10 (d) shows the prediction results of the sparse polynomial chaotic expansion model based on generalized kriging, comparing the four models. N t =Δ of 100 test samples SM Prediction results show that the predicted points of this invention are closely distributed near the 45° ideal line, while the comparison model exhibits significant dispersion. Quantitative analysis shows that the SRE in this embodiment is 0.89%, which is nearly an order of magnitude lower than the SRE of the traditional neural network model (7.11%), the sparse polynomial chaotic expansion model based on minimum angle vector regression (6.81%), and the sparse polynomial chaotic expansion model based on generalized kriging (7.09%), confirming that the flow mechanism constraint effectively improves the prediction accuracy.

[0103] By reducing the number of training samples in the training set N s The performance of the four models was analyzed under different data scales, and the results are as follows: Figure 11 As shown, the SRE of this invention is significantly lower than that of the comparison model under different training sample sizes. This demonstrates that this invention has a significant advantage with small sample sizes.

[0104] Figure 10 and Figure 11 The research results show that when the training sample size N s When the value reaches 200, the present invention addresses the change in stability margin Δ. SM The statistical relative prediction error is below 1%, fully meeting the accuracy requirements of geometric bias uncertainty analysis based on large-sample statistics. Although there are still non-negligible deviations between individual predicted values ​​and CFD calculation results, relevant literature shows that these errors exhibit a random distribution and can cancel each other out in ensemble statistics. According to error propagation theory, the prediction error of the statistical moments of the response will decrease with the increase of the prediction sample size. However, the study also found that although increasing the training sample size can improve the point prediction accuracy of the machine learning model, its effect on improving the accuracy of the statistical inference of the output response is relatively limited. Therefore, adopting... N s The accuracy of the flow mechanism embedded deep neural network model established by =200 fully meets the requirements of subsequent uncertainty quantification analysis.

[0105] In one embodiment, the specific process of compressor stability margin change prediction and probabilistic characteristic analysis includes: using the weighting coefficients of 18 fundamental modes... Z= [ z 1, z 2,…, z 18 Within the probability space of , perform 10 on it. 5 A Monte Carlo simulation was performed, and these samples were fed into a trained deep neural network embedded in the flow mechanism to predict 10... 5 Group stability margin change Δ SM Perform uncertainty quantification analysis. Figure 12 It shows Δ SM The statistical distribution of Δ is obtained through probability distribution analysis. SM The mean was 0.1976%, and the standard deviation was 0.4618%. This result indicates that, statistically speaking, manufacturing-induced geometric deviations on average shift the compressor's aerodynamic stability towards improvement. Cumulative distribution analysis can estimate the probability of extreme deterioration in aerodynamic stability under the influence of geometric deviations, providing crucial guidance for robust aerodynamic stability design of compressor blades. Specifically, Δ... SM The probability of a random change exceeding -1% is approximately 1.143%, and the probability of exceeding -2% is approximately 0.016%.

[0106] Table 1 lists Δ SM The first four statistical moments. Analysis results show a skewness of -0.4289% and a kurtosis of 0.4683%. Since the Gaussian distribution has a skewness of 0 and a kurtosis of 3, Δ... SM The statistical histogram shows a significant deviation from the Gaussian distribution. Compared to the Gaussian distribution, this probability distribution exhibits a significant right skewness (negative skewness) and low kurtosis. This strong deviation from the Gaussian distribution indicates a highly nonlinear dependence of compressor aerodynamic stability on geometric deviations. This finding has important implications for robust compressor design: traditional tolerance analysis methods based on the Gaussian assumption may underestimate the risk of extreme stability losses, while the non-Gaussian characteristics revealed in this study require the use of more accurate probabilistic assessment methods during the design process. Manufacturers can establish corresponding quality control standards based on an extreme deterioration probability of 1.143% (1% is currently the standard for high-load compressors) to ensure that aerodynamic stability risks are controlled within acceptable limits during mass production.

[0107] Table 1 Δ in this embodiment SM First four statistical moments

[0108]

[0109] The efficient uncertainty quantification achieved by embedding deep neural networks into flow mechanisms provides a scientific basis for the reliability design of multi-stage axial compressors for CAES, making it possible to predict and control aerodynamic stability deterioration during the manufacturing stage.

[0110] It should be understood that, although the above Figure 1 The steps are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise explicitly stated in this document, there is no strict order in which these steps are executed; they can be performed in other orders. Furthermore, the above... Figure 1 At least some of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0111] In one embodiment, an aerodynamic stability quantification system based on the coupling of flow mechanism and deep learning is also provided, comprising:

[0112] The module for determining the uncertainty parameters of the blade set is used to compress the high-dimensional point cloud data of the actual processed blades into low-dimensional basic modes using principal component analysis, and obtain the weight coefficients of the low-dimensional basic modes.

[0113] The dataset construction module is used to design and sample low-dimensional modal weight coefficients using low-discrepancy sequences. For each sample, CFD is used to calculate the stability parameters and flow mechanism quantification parameters of the compressor maneuver. The dataset is constructed based on the calculation results and divided into training and test sets.

[0114] A module for constructing and training a flow mechanism embedded deep neural network is included. This module is used to construct a flow mechanism embedded deep neural network and train and test it using training and testing sets to obtain a trained flow mechanism embedded deep neural network. The flow mechanism embedded deep neural network includes network block 1 and network block 2. Network block 1 is used to learn the relationship between low-dimensional modal weight coefficients and flow mechanism quantization parameters through nonlinear mapping. Network block 2 is used to process the concatenated low-dimensional modal weight coefficients and flow mechanism quantization parameters using a nonlinear layer to obtain predicted values ​​of aerodynamic stability parameters. The loss function in the training process simultaneously constrains the prediction errors of the flow mechanism quantization parameters and aerodynamic stability parameters.

[0115] The aerodynamic stability quantification analysis module is used to perform Monte Carlo sampling based on low-dimensional modal weight coefficients, input the sampled samples into a trained flow mechanism embedded deep neural network, obtain multiple sets of predicted aerodynamic stability parameters, and perform uncertainty analysis on the predicted aerodynamic stability parameters.

[0116] In one embodiment, the blade set uncertainty parameter determination module is further configured to acquire high-dimensional point cloud data of the actual processed blades; construct a scatter matrix based on the high-dimensional point cloud data; perform singular value decomposition on the scatter matrix to obtain the eigenvalues ​​corresponding to the fundamental modes; and represent the blade geometric random deviations as... p The high-dimensional point cloud data of the blade is compressed by summing a finite number of fundamental modes and their corresponding eigenvalues ​​into a weighted linear sum and the average geometric change of the blade. p Each fundamental mode weight coefficient; where p The value is taken when the cumulative energy percentage is not less than a preset threshold. k The value of ; where the cumulative energy accounts for as shown in formula (1).

[0117] In one embodiment, the blade set uncertainty parameter determination module is also used to construct a scatter matrix as shown in formula (2) based on high-dimensional point cloud data.

[0118] In one embodiment, the dataset construction module is also used to perform experimental design sampling using Halton low-difference random sequences in a probability space with low wiki mode weight coefficients to generate a set of sample points; to obtain the near-stall conditions of each sample point through CFD simulation with gradually increasing outlet back pressure, to calculate the compressor stability margin change, and to extract the tip leakage axial momentum ratio of each sample near-stall condition as a flow mechanism quantification parameter.

[0119] In one embodiment, the compressor stability margin variation in the dataset construction module is shown in Equation (5).

[0120] In one embodiment, the axial momentum of the tip leakage flow in the dataset building module is as shown in Equation (6).

[0121] In one embodiment, the flow mechanism embedded deep neural network construction and training module is further configured to: input low-dimensional modality weight coefficients into the input layer of network block 1, and then process them through several fully connected hidden layers to obtain the predicted value of the flow mechanism quantization parameter; concatenate the flow mechanism quantization parameter and the low-dimensional modality weight coefficients to obtain the composite input feature; input the composite input feature into the input layer of network block 2, and then process it through several fully connected hidden layers to obtain the predicted value of the change in the stability margin of the target variable.

[0122] In one embodiment, the loss function of the training process in the flow mechanism embedded deep neural network construction and training module is shown in Equation (11).

[0123] In one embodiment, the process of testing the trained deep neural network with embedded flow mechanism using a test set in the construction and training module of the flow mechanism embedded deep neural network includes: inputting test samples from the test set into the trained deep neural network with embedded flow mechanism to obtain the predicted value of the change in the stability margin of the target variable; calculating the statistical relative error using formula (12) based on the predicted value of the change in the stability margin of the target variable and the CFD calculation value of the change in the stability margin of the target variable corresponding to the test sample; and performing accuracy verification on the trained deep neural network with embedded flow mechanism based on the statistical relative error to obtain the trained deep neural network with embedded flow mechanism.

[0124] It is understood that for a detailed explanation of the aerodynamic stability quantification system based on the coupling of flow mechanism and deep learning, please refer to the corresponding explanations of the various embodiments of the aerodynamic stability quantification method based on the coupling of flow mechanism and deep learning mentioned above, and will not be repeated here. Each module in the above-mentioned aerodynamic stability quantification system based on the coupling of flow mechanism and deep learning can be implemented entirely or partially through software, hardware, or a combination thereof. Each module can be embedded in hardware or independently of a device with data processing capabilities, or it can be stored in software in the memory of the aforementioned device, so that the processor can call and execute the operations corresponding to each module. The aforementioned device can be, but is not limited to, various types of data processing computer devices already existing in the art.

[0125] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0126] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of protection of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and all such modifications and improvements fall within the scope of protection of this application.

Claims

1. A method for quantifying aerodynamic stability based on the coupling of flow mechanism and deep learning, characterized in that, Including the following steps: Principal component analysis is used to compress the high-dimensional point cloud data of actual processed blades into low-dimensional basic modes, obtaining the weight coefficients of the low-dimensional basic modes. Specifically, this includes: acquiring high-dimensional point cloud data of actual processed blades; constructing a scatter matrix based on the high-dimensional point cloud data; performing singular value decomposition on the scatter matrix to obtain the eigenvalues ​​corresponding to the basic modes; and representing the blade's geometric random deviations as... p The high-dimensional point cloud data of the blade is compressed by summing a finite number of fundamental modes and their corresponding eigenvalues ​​into a weighted linear sum and the average geometric change of the blade. p Each fundamental mode weight coefficient; where p The value of is determined based on the cumulative energy ratio of the fundamental mode and a preset threshold; Experimental design sampling was conducted using low-difference sequences for low-dimensional modal weighting coefficients. For each sample, CFD was used to calculate the stability parameters and flow mechanism quantification parameters of the compressor maneuver. A dataset was constructed based on the calculation results and divided into a training set and a test set. The flow mechanism quantification parameter is the axial momentum ratio of the tip leakage flow under near-stall conditions for each sample. A flow mechanism embedded deep neural network is constructed and trained and tested using the training and testing sets to obtain a trained flow mechanism embedded deep neural network. The flow mechanism embedded deep neural network includes network block 1 and network block 2. Network block 1 is used to learn the relationship between low-dimensional modal weight coefficients and flow mechanism quantization parameters through nonlinear mapping. Network block 2 is used to process the concatenated low-dimensional modal weight coefficients and flow mechanism quantization parameters using a nonlinear layer to obtain predicted values ​​of aerodynamic stability parameters. The loss function during training simultaneously constrains the prediction errors of both the flow mechanism quantization parameters and the aerodynamic stability parameters. The predicted values ​​of the aerodynamic stability parameters are the predicted values ​​of the compressor stability margin variation. Monte Carlo sampling is used based on low-dimensional modal weight coefficients. The sampled samples are input into a trained flow mechanism embedded deep neural network to obtain multiple sets of predicted values ​​of aerodynamic stability parameters. Uncertainty analysis is then performed on the predicted values ​​of aerodynamic stability parameters.

2. The aerodynamic stability quantification method based on the coupling of flow mechanism and deep learning according to claim 1, characterized in that, Based on the high-dimensional point cloud data, the scatter matrix is ​​constructed as follows: Where S is a scatter matrix, To generate the geometric deviation matrix of the blade after decentering, the superscript... T This is a matrix transpose operation. n This indicates the number of blades manufactured. m This indicates the number of scan points for each leaf; Indicates the first i Geometric deviations after decentering of blades in blade manufacturing Indicates the first i Geometric deviations in blade manufacturing Indicates the first j The average geometric change at each scan point; and They represent the first i The nominal coordinate vector of the blade and the coordinate vector of the nominal blade; p The value is taken when the cumulative energy percentage is not less than a preset threshold. k The value; wherein the percentage of accumulated energy is: in, Indicates the percentage of cumulative energy. Indicates the first i The energy percentage of low-dimensional modes diagonal eigenvalue matrix Elements on the diagonal.

3. The aerodynamic stability quantification method based on the coupling of flow mechanism and deep learning according to claim 1, characterized in that, Experimental design sampling was performed on low-discrepancy sequences for low-dimensional modal weighting coefficients. For each sample, CFD was used to calculate the aerodynamic stability parameters and flow mechanism quantification parameters of the compressor. Based on the calculation results, a dataset was constructed, which was then divided into a training set and a test set, including: We use Halton low-discrepancy random sequences to design and sample in the probability space of low-dimensional modal weight coefficients to generate a set of sample points; By gradually increasing the outlet back pressure, CFD simulations were used to obtain near-stall conditions at each sample point, and the compressor stability margin changes were calculated. At the same time, the axial momentum ratio of the tip leakage flow in the near-stall conditions of each sample was extracted as a quantitative parameter of the flow mechanism.

4. The aerodynamic stability quantification method based on the coupling of flow mechanism and deep learning according to claim 3, characterized in that, The compressor stability margin change is as follows: in, This indicates the change in compressor stability margin. and These represent the total pressure ratio and flow rate of the compressor in near-stall conditions, respectively. The subscript "deviation" indicates a compressor with geometric deviation, and the subscript "nominal" indicates a nominal reference compressor without geometric deviation.

5. The aerodynamic stability quantification method based on the coupling of flow mechanism and deep learning according to claim 3, characterized in that, The axial momentum ratio of the tip leakage flow is: in, This indicates the axial momentum ratio of the tip leakage flow. and These represent the axial momentum and main flow of the tip leakage flow, respectively.

6. The aerodynamic stability quantification method based on the coupling of flow mechanism and deep learning according to claim 1, characterized in that, In the flow mechanism embedded deep neural network: The low-dimensional modal weight coefficients are input into the input layer of network block 1, and then processed through several fully connected hidden layers to obtain the predicted values ​​of the flow mechanism quantification parameters. The flow mechanism quantization parameters and the low-dimensional mode weight coefficients are concatenated to obtain composite input features; The composite input features are input into the input layer of network block 2, and then processed through several fully connected hidden layers to obtain the predicted value of the change in the stability margin of the target variable.

7. The aerodynamic stability quantification method based on the coupling of flow mechanism and deep learning according to claim 1, characterized in that, The loss function for the training process is: in, L The loss function representing the training process. This represents the axial momentum ratio of the tip leakage flow. The superscripts "predicted" and "actual" indicate the network prediction and the actual value in the training data, respectively. The number of training samples in the training set. This indicates the change in compressor stability margin.

8. The aerodynamic stability quantification method based on the coupling of flow mechanism and deep learning according to claim 1, characterized in that, The trained flow mechanism embedded deep neural network is used to perform accuracy verification on the test set to obtain the trained flow mechanism embedded deep neural network, including: The test samples in the test set are input into a trained flow mechanism embedded deep neural network to obtain the predicted value of the change in the stability margin of the target variable. Based on the predicted value of the change in the stability margin of the target variable and the CFD calculated value of the change in the stability margin of the target variable corresponding to the test sample, the statistical relative error is calculated as follows: in, Indicates statistical relative error. Indicates the test sample size. This represents the sample mean of the CFD calculated values. Indicates the first i Predicted values ​​of the change in the stability margin of the target variable for each test sample. Indicates the first i CFD calculation of the change in the stability margin of the target variable for each test sample; The accuracy of the trained flow mechanism embedded deep neural network is verified based on the statistical relative error to obtain the trained flow mechanism embedded deep neural network.

9. An aerodynamic stability quantification system based on the coupling of flow mechanism and deep learning, characterized in that, include: The blade set uncertainty parameter determination module is used to compress the high-dimensional point cloud data of the actual processed blades into low-dimensional basic modes using principal component analysis, and obtain the weight coefficients of the low-dimensional basic modes. Specifically, it includes: acquiring the high-dimensional point cloud data of the actual processed blades; constructing a scatter matrix based on the high-dimensional point cloud data; performing singular value decomposition on the scatter matrix to obtain the eigenvalues ​​corresponding to the basic modes; and representing the blade geometric random deviations as... p The high-dimensional point cloud data of the blade is compressed by summing a finite number of fundamental modes and their corresponding eigenvalues ​​into a weighted linear sum and the average geometric change of the blade. p Each fundamental mode weight coefficient; where p The value of is determined based on the cumulative energy ratio of the fundamental mode and a preset threshold; The dataset construction module is used to design and sample low-dimensional modal weighting coefficients using low-difference sequences. For each sample, CFD is used to calculate the stability parameters and flow mechanism quantification parameters of the compressor maneuver. The dataset is constructed based on the calculation results and divided into training and testing sets. The flow mechanism quantification parameters are the axial momentum ratio of the tip leakage flow in the near-stall condition of each sample. A flow mechanism embedded deep neural network construction and training module is used to construct a flow mechanism embedded deep neural network and train and test it using the training set and test set to obtain a trained flow mechanism embedded deep neural network. The flow mechanism embedded deep neural network includes network block 1 and network block 2. Network block 1 is used to learn the relationship between low-dimensional modal weight coefficients and flow mechanism quantization parameters through nonlinear mapping. Network block 2 is used to process the spliced ​​low-dimensional modal weight coefficients and flow mechanism quantization parameters using a nonlinear layer to obtain predicted values ​​of aerodynamic stability parameters. The loss function in the training process simultaneously constrains the prediction errors of the flow mechanism quantization parameters and aerodynamic stability parameters. The predicted values ​​of aerodynamic stability parameters are the predicted values ​​of the compressor stability margin changes. The aerodynamic stability quantification analysis module is used to perform Monte Carlo sampling based on low-dimensional modal weight coefficients, input the sampled samples into a trained flow mechanism embedded deep neural network, obtain multiple sets of predicted aerodynamic stability parameters, and perform uncertainty analysis on the predicted aerodynamic stability parameters.

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