Composite angle hole single-exhaust film cooling efficiency two-dimensional distribution prediction method based on POD mode decomposition

Abstract

The invention discloses a compound angle hole single-exhaust film cooling efficiency two-dimensional distribution prediction method based on POD mode decomposition, and belongs to the field of thermal protection of aero-engine high-temperature parts. According to the method, aiming at the problems that an existing prediction model is low in precision of film holes with compound angles, depends on a large number of samples and is weak in generalization ability, a hybrid neural network model comprising a hole pattern adaptive POD mode decomposition and reconstruction module and a conditional residual error U-Net correction module is constructed. The method comprises the following steps: firstly, carrying out dimensionality reduction on a cooling efficiency field of each hole pattern through a POD module, and converting two-dimensional field prediction into low-dimensional coefficient prediction; then, learning and correcting a nonlinear residual error between the POD preliminary prediction and a real field by using a U-Net module taking an input parameter as a condition; and respectively optimizing the two modules by adopting a two-stage progressive training strategy. According to the method, under the condition of limited training samples, high-precision and strong-generalization prediction of downstream complex two-dimensional cooling efficiency distribution of the film hole with the compound angle is achieved.

Description

Technical Field

[0001] This invention belongs to the field of thermal protection technology for high-temperature components of aero-engines, specifically relating to a method for predicting film cooling efficiency, and more specifically to a method for predicting the two-dimensional distribution of film cooling efficiency with composite angles by combining POD mode decomposition and neural networks. Background Technology

[0002] Film cooling (FSR) is a key technology for ensuring the reliable operation of hot-end components such as turbine blades and combustion chambers in aero-engines under extreme high-temperature environments. It works by creating film cooling holes on a high-temperature wall surface and introducing a low-temperature cooling airflow to form a protective film that isolates the high-temperature combustion gases, thereby effectively reducing the wall surface temperature. The two-dimensional spatial distribution of FSR efficiency is the core basis for evaluating cooling performance and optimizing the layout of film cooling holes and the cooling airflow. Inaccurate predictions or improper design can lead to localized overheating, seriously threatening component lifespan and engine safety.

[0003] Currently, methods for predicting the distribution of two-dimensional film cooling efficiency based on one-dimensional parameters are mainly divided into two categories: empirical fitting methods and data-driven artificial intelligence (AI) methods.

[0004] Empirical fitting methods establish empirical correlations to fit the distribution of cooling efficiency along the centerline and its lateral standard deviation, thereby synthesizing a two-dimensional field. These methods often rely on introducing a large number of intermediate variables and model parameters that need to be experimentally calibrated, resulting in complex model structures, poor universality, and difficulty in applying them to situations where geometric parameters (especially the composite angle) vary greatly.

[0005] Artificial intelligence-based methods offer new avenues for rapid prediction, but existing technologies still have significant limitations. For example, Chinese patent CN112084597A proposes a fully connected neural network prediction method based on the assumption of a bell curve (i.e., Gaussian distribution). This method forces the predicted output to conform to a specific bell curve shape. However, for film cooling orifices with compound angles, the downstream cooling efficiency distribution is severely distorted due to the complex vortex structure, no longer conforming to the Gaussian distribution assumption, causing the method to completely fail. Another approach is the hybrid AI framework used in the paper "Hybrid AI framework for the predictions of film cooling effectiveness distribution with various surface curvatures and compound angles, APPLIED THERMAL ENGINEERING, 2024, 257". This framework first uses a feedforward neural network to predict the downstream cooling efficiency distribution of film cooling orifices without compound angles, and then uses a U-net network to transform it into a film cooling efficiency distribution with compound angles based on the compound angle parameters. While such methods address the compound angle problem to some extent, the errors accumulate step by step due to their two-step prediction process. Furthermore, these methods typically require a massive amount of training samples with high coverage to ensure accuracy. In practical engineering scenarios with limited sample data, the model is prone to overfitting, and the robustness and generalization ability of the predictions (such as the ability to transfer across different aperture types) decrease significantly.

[0006] In summary, existing technologies have not yet effectively solved the following two key problems: First, for film vents with complex angles, there is a lack of effective mathematical models or descriptive foundations that can accurately characterize their complex two-dimensional cooling efficiency distribution; Second, existing data-driven prediction models generally suffer from strong dependence on the number of samples and weak generalization ability across vent types. Summary of the Invention

[0007] The purpose of this invention is to address the problems in existing technologies, such as the lack of an effective mathematical model to describe the complex distribution of cooling efficiency with composite-angle film vents, and the reliance on large samples and weak generalization ability of data-driven models. This invention proposes a novel prediction framework based on a combination of Proper Orthogonal Decomposition (POD) mode decomposition and a conditional residual U-Net neural network. The core of this method lies in firstly, using an aperture-adaptive POD mode decomposition and reconstruction module to map the high-dimensional cooling efficiency field into a linear combination of low-dimensional modes, thereby simplifying the prediction problem; then, through a residual U-Net correction module conditioned on input parameters, accurately learning and compensating for the nonlinear deviation between the above linear reconstruction process and the real complex field; ultimately achieving high-precision and strong generalization prediction of the two-dimensional distribution of cooling efficiency with composite-angle film vents under finite sample conditions.

[0008] To achieve the above objectives, the technical solution provided by this invention is:

[0009] A two-dimensional distribution prediction method for composite corner-hole single-exhaust film cooling efficiency based on POD mode decomposition is provided, including the following steps:

[0010] Step 1: Obtain training samples. Each set of sample data includes a film cooling pore parameter vector composed of structural parameters and aerodynamic parameters, as well as the corresponding two-dimensional distribution real field of film cooling efficiency.

[0011] Step 2: Construct a hybrid neural network model. The model takes the air film pore parameter vector as input and the two-dimensional distribution prediction field of air film cooling efficiency as output. It includes an input parameter preprocessing module, an pore type adaptive POD mode decomposition and reconstruction module, and a conditional residual U-Net correction module connected in sequence.

[0012] The input parameter preprocessing module is used to process the air film pore parameter vector into a normalized parameter vector;

[0013] The pore type adaptive POD mode decomposition and reconstruction module is used to establish a POD reduced-order model based on training samples for different air film pore types, and predict the POD coefficients according to the normalized parameter vector, thereby reconstructing the preliminary prediction field of the two-dimensional distribution of air film cooling efficiency.

[0014] The conditional residual U-Net correction module uses the normalized parameter vector as a condition to perform residual correction on the preliminary prediction field and outputs the final two-dimensional distribution prediction field of the air film cooling efficiency.

[0015] Step 3: Train the hybrid neural network model using a two-stage progressive training strategy;

[0016] Step 4: For the air film cooling scheme to be predicted, obtain its air film pore parameter vector and input it into the trained hybrid neural network model to obtain the two-dimensional distribution prediction result of air film cooling efficiency.

[0017] Furthermore, the structural parameters include the air film pore shape and the ratio of the air film pore outlet width to diameter. and air film pore composite angle Aerodynamic parameters include airflow ratio. .

[0018] Furthermore, the input parameter preprocessing module processes the ratio of the outlet width to the diameter of the continuous film gas vent. air film pore composite angle Compared to blowing air Z-score normalization is performed to encode the discrete air film pore patterns using one-hot encoding, forming a five-dimensional normalized parameter vector.

[0019] Furthermore, the air film pore types include cylindrical pores and fan-shaped pores; the pore type adaptive POD mode decomposition and reconstruction module constructs an independent POD reduction model for the training samples of each pore type.

[0020] Furthermore, the execution process of the aperture-adaptive POD mode decomposition and reconstruction module includes:

[0021] For each aperture type, the average cooling efficiency field is calculated based on its training samples;

[0022] Singular value decomposition is performed on the centered sample data to extract the dominant modes, and the number of modes to be retained is determined based on a preset energy threshold. ;

[0023] Construct a multilayer perceptron network and map the five-dimensional normalized parameter vector to... A dimensional POD coefficient prediction vector;

[0024] The predicted POD coefficients are linearly combined with the retained POD modes, and then superimposed with the average cooling efficiency field to obtain the preliminary prediction field.

[0025] Furthermore, the energy threshold is set to a cumulative energy percentage of over 95%.

[0026] Furthermore, the conditional residual U-Net correction module includes a parametric encoder, a U-Net network, and an output layer. The parametric encoder consists of a multilayer perceptron, used to map the normalized parameter vector to a higher-dimensional feature space to form a conditional feature vector. The U-Net network is an encoder-decoder structure. Its encoder part extracts multi-scale spatial features of the preliminary prediction field through multiple downsamplings and injects the conditional feature vector at each level through feature projection. Its decoder part gradually restores the spatial resolution of the feature map through multiple upsamplings and skip connections. The output layer performs convolution processing on the final output of the U-Net network to generate a residual field with the same size as the preliminary prediction field. The residual field is added to the preliminary prediction field to obtain the final two-dimensional distribution prediction field of the film cooling efficiency.

[0027] Furthermore, the conditional feature vectors are injected into each layer of the U-Net encoder through feature projection. Specifically, the conditional feature vectors are projected to the same number of channels as the feature map of the corresponding layer of the encoder through 1×1 convolution, and then fused with the feature map of that layer through nearest neighbor interpolation.

[0028] Furthermore, the bottleneck layer of the U-Net network integrates a Transformer self-attention mechanism to capture the global spatial dependencies of feature maps.

[0029] Furthermore, the two-stage progressive training strategy includes:

[0030] Phase 1: Train the aperture adaptive POD mode decomposition and reconstruction module, and freeze the parameters of the conditional residual U-Net correction module at the same time;

[0031] Phase 2: Train the conditional residual U-Net correction module, and freeze the parameters of the aperture adaptive POD mode decomposition and reconstruction module.

[0032] The advantages of this invention are:

[0033] This invention provides a two-dimensional distribution prediction method for single-exhaust film cooling efficiency based on POD mode decomposition for composite corner orifices. First, an orifice-adaptive POD mode decomposition and reconstruction module transforms the high-dimensional data characterizing the two-dimensional distribution of cooling efficiency into a low-dimensional representation problem linearly reconstructed from a small number of dominant modes and their coefficients. This significantly reduces model learning complexity and dependence on massive training data. Subsequently, a residual U-Net correction module, conditional on input parameters, specifically captures and corrects the nonlinear residuals between the POD linear reconstruction results and the actual complex distribution. This collaborative architecture enables the model to learn the complex flow and heat transfer characteristics caused by composite angles more accurately under limited sample conditions. The entire method avoids prior assumptions about the efficiency distribution shape (such as Gaussian distribution) in existing technologies, fundamentally overcoming the problem of prediction inaccuracies caused by composite angles. Simultaneously, its structured design enhances the model's generalization ability to different orifice shapes and operating conditions, providing a reliable tool for efficient and accurate two-dimensional efficiency distribution prediction and scheme optimization in aero-engine film cooling design. Attached Figure Description

[0034] The above and / or other features and advantages of the present invention will become more readily understood from the following description with reference to the accompanying drawings, in which:

[0035] Figure 1 This is a schematic diagram of the overall structure of the hybrid neural network model provided in an embodiment of the present invention;

[0036] Figure 2 This is a schematic diagram of the air film pore structure parameters in an embodiment of the present invention, wherein (a), (b), (c) and (d) are respectively a front view of the forward-tilted fan-shaped hole, a top view of the forward-tilted fan-shaped hole, a front view of the cylindrical hole, and a top view of the cylindrical hole;

[0037] Figure 3 This is a schematic diagram of the fluid domain model in an embodiment of the present invention;

[0038] Figure 4 This is a schematic diagram of the neural network model architecture based on POD mode decomposition and reconstruction in an embodiment of the present invention;

[0039] Figure 5 This is a schematic diagram illustrating the principle of the conditional injection mechanism in an embodiment of the present invention;

[0040] Figure 6 This is a schematic diagram of the network structure of the conditional residual U-Net correction module in an embodiment of the present invention;

[0041] Figure 7 This is a loss convergence curve of the first stage training process in an embodiment of the present invention;

[0042] Figure 8This is a loss convergence curve of the second stage training process in an embodiment of the present invention;

[0043] Figure 9 The above is a comparison chart of the actual results of four test samples, the prediction results of the traditional model, and the prediction results of the method of the present invention in this embodiment of the invention. (a), (b), (c) and (d) are the actual cooling efficiency distribution cloud maps of samples 1 to 4, respectively. (a1), (b1), (c1) and (d1) are the prediction result cloud maps of the traditional model for samples 1 to 4, respectively. (a2), (b2), (c2) and (d2) are the prediction result cloud maps of the method of the present invention for samples 1 to 4, respectively.

[0044] Figure 10 This is a comparison chart of the difference between the prediction results of the traditional model and the method of the present invention for four test samples and the actual cloud map in an embodiment of the present invention. (a1), (b1), (c1) and (d1) are the absolute error cloud maps of the prediction results of the traditional model for samples 1 to 4 and the actual values, respectively. (a2), (b2), (c2) and (d2) are the absolute error cloud maps of the prediction results of the method of the present invention for samples 1 to 4 and the actual values, respectively.

[0045] Figure 11 This is a comparison chart of the prediction errors of the traditional model and the method of the present invention on four typical test samples in an embodiment of the present invention. Detailed Implementation

[0046] The present invention will now be described in detail with reference to the accompanying drawings and exemplary embodiments thereof. It should be noted that the following detailed description of the present invention is for illustrative purposes only and is not intended to limit the scope of the invention.

[0047] Reference Figure 1 The core process of the two-dimensional distribution prediction method for composite corner-hole single-exhaust film cooling efficiency based on POD mode decomposition, as an exemplary embodiment of the present invention, is as follows: First, obtain a one-dimensional parameter vector composed of film pore structure parameters and aerodynamic parameters and its corresponding two-dimensional cooling efficiency distribution real field as training samples; second, construct as follows... Figure 1 The cascaded neural network model shown sequentially preprocesses the input parameters, performs initial predictions through the POD mode decomposition and reconstruction module, and then refines them through the conditional residual U-Net correction module. Next, a specific two-stage progressive strategy is used to train the model. Finally, by inputting the parameters of the new design scheme into the trained model, the predicted results of its two-dimensional cooling efficiency distribution can be obtained quickly and accurately. This architecture decomposes the complex two-dimensional field prediction problem into two relatively simple sub-problems: linear main body reconstruction and nonlinear residual correction, thus significantly reducing the learning difficulty. The steps of this method will now be described in detail.

[0048] Step S1: Training Sample Acquisition and Parameter Definition

[0049] To train and validate the model, sufficient sample data must first be obtained through numerical simulation. Specifically, the 3D model of the film cooling pores and fluid domain created in UG software is imported into Fluent software for CFD calculation. After the simulation is completed, the 2D distribution cloud map of the film cooling efficiency is extracted from Tecplot software and saved.

[0050] See Figure 2 It shows the key structural parameters of the studied film pores, including the pore shape and the pore outlet width. The inclination angle between the axis of the air film orifice and the outlet plane Expansion angle of the air film pore expansion section Forward tilt angle of the air film pore expansion section Length of air film pores and the length of the expansion segment .

[0051] See Figure 3 It shows a fluid domain model including film pores, which includes film pore structure parameters and the composite angle of the film pores. and the spacing between two adjacent air film pores Among them, the length parameter is represented by the aperture. Dimensionless transformation is performed by setting the expansion angle of the air film pore expansion section. and the forward tilt angle of the film pore expansion section equal, and It can be used Therefore, the final structural parameters of the input model are: the shape of the film air vent (e.g., cylindrical vent, forward-tilted fan-shaped vent), and the ratio of the vent outlet width to the diameter. and air film pore composite angle Table 1 shows the range of structural parameters for the sample data in this embodiment:

[0052] Table 1 Range of Structural Parameter Values

[0053]

[0054] Table 2 shows the aerodynamic parameter range for the sample group. In this embodiment, the blow ratio, a commonly used aerodynamic parameter in studying film cooling efficiency, was selected. As input parameters, other aerodynamic parameters are defined as density ratios. turbulence As input. Indicates gas density, Indicates airflow velocity, subscript and These represent the secondary flow and the mainstream, respectively. This indicates the mainstream pulsation speed.

[0055] Table 2 Range of pneumatic parameters

[0056]

[0057] The final training samples include a film cooling efficiency distribution image of the film cooling efficiency obtained by experimental testing of the film cooling pores, consisting of a parameter vector of three structural parameters and one aerodynamic parameter.

[0058] Step S2: Construction of Hybrid Neural Network Model

[0059] The model constructed in this invention includes three core modules: an input parameter preprocessing module, an aperture-adaptive POD mode decomposition and reconstruction module, and a conditional residual U-Net correction module. Figure 1 As shown.

[0060] The input parameter preprocessing module receives the raw film pore parameter vector. For the blowing ratio... Composite angle The ratio of outlet width to diameter These three continuously varying parameters are processed using the Z-score normalization method, and the calculation formula is as follows:

[0061] (1)

[0062] In the formula, These are the original parameter values. The mean of this parameter in the training set, Standard deviation These are the standardized parameter values. For the discrete parameter of the air film pore shape, one-hot encoding is used; for example, cylindrical pores are encoded as [1, 0], and sector pores are encoded as [0, 1]. After processing, a 5-dimensional normalized parameter vector is formed, providing a scale-uniform input for subsequent networks.

[0063] The aperture-type adaptive POD mode decomposition and reconstruction module is the key to achieving dimensionality reduction and preliminary prediction in this invention. Its detailed working principle is as follows: Figure 4 As shown, the POD method can extract the most energy-concentrated set of orthogonal bases (called modes) from a set of high-dimensional data (i.e., many two-dimensional cooling efficiency fields), and thus approximate any sample with a linear combination of a small number of modes.

[0064] For different orifice types such as cylindrical orifices and sector orifices, since their flow and heat transfer mechanisms differ, this invention establishes an independent POD model for each orifice type. This is achieved by recognizing the one-hot encoding in the input parameters, thereby realizing "orifice type adaptation".

[0065] (2)

[0066] (3)

[0067] (4)

[0068] (5)

[0069] (6)

[0070] The specific establishment process is as follows: First, for a specific hole type... The average cooling efficiency field is calculated using formula (2) for each training sample. ,in, For the first The cooling efficiency field of each training sample is calculated; subsequently, the decentralized fluctuation field is obtained by subtracting the average cooling efficiency field from the cooling efficiency fields of all training samples. The matrices are stacked into a matrix, and singular value decomposition is performed on the matrix using formula (3) to extract the POD modes. In formula (3), The matrix is ​​formed by stacking the cooling efficiency fields of all training samples. The characteristic matrix in the spatial direction, The characteristic matrix in the time direction, The singular value matrix is ​​then used; the number of dominant modes retained is determined according to formula (4) based on the energy contribution rate. That is, the cumulative energy above the preset energy threshold. In this embodiment, the energy threshold is set to a cumulative energy percentage of over 95%, where in formula (4), The index of the number of candidate modes. The maximum number of modes of the POD. For the first The singular values ​​corresponding to each mode. This process compresses high-dimensional two-dimensional field data into a set of low-dimensional bases (modes) and a mean field.

[0071] During prediction, a multilayer perceptron network is constructed according to formula (5), and the input of the network is a five-dimensional normalized parameter vector. The output is dimensional POD coefficient prediction vector , and These represent the weights and bias parameters of the neural network, respectively. The multilayer perceptron has two hidden layers, with 64 and 128 neurons in each layer. The number of neurons in the output layer is equal to the value calculated according to formula (4). The number of neurons in the output layer is selected based on the one-hot encoding of the input aperture. Finally, using formula (6), the predicted coefficient vector is... By linearly combining (multiplying) the pre-extracted POD modes and adding the average cooling efficiency field, a preliminary cooling efficiency distribution prediction field can be reconstructed, where in formula (6), For the first One POD spatial mode. These are the corresponding modal coefficients. In this way, the model does not need to directly learn complex image-to-image mappings, but instead learns simpler mappings from parameters to low-dimensional coefficients, greatly reducing model complexity and data requirements.

[0072] The purpose of the orifice-type adaptive POD mode decomposition and reconstruction module is to initially and quickly predict the film cooling efficiency field. It predicts the linear part of the film cooling efficiency distribution, while the remaining nonlinear part and the part with inaccurate prediction need to be predicted by the conditional residual U-Net correction module.

[0073] The conditional residual U-Net correction module uses the above-mentioned normalized parameter vector as a condition to perform residual correction on the preliminary prediction field and outputs the final two-dimensional distribution prediction field of the air film cooling efficiency.

[0074] Specifically, this module first maps a five-dimensional normalized parameter vector to a higher-dimensional feature space using a parametric encoder, forming a conditional feature vector. This encoder is a three-layer feedforward neural network with 64, 128, and 256 neurons in each layer, thus expanding the input dimension from 5 to 256. This conditional feature needs to be effectively integrated into the image correction process; this invention employs a feature projection injection mechanism, such as... Figure 5 As shown, this mechanism first projects the abstract 256-dimensional conditional feature vectors onto the spatial dimensions corresponding to each layer of the U-Net encoder through dimensionality expansion and broadcasting, generating 256-channel matrices of 512×512, 256×256, 128×128, and 64×64. Subsequently, 1×1 convolutions are used to transform the number of channels in these matrices from 256 to the number of channels matching each layer of the U-Net encoder: 32, 64, 128, and 256, respectively, to complete the adaptation of feature projection.

[0075] Reference Figure 6This module employs a U-Net encoder-decoder architecture. Its input is the preliminary prediction field output from the POD module, corresponding to a 512×512 matrix. The specific process is as follows: This matrix first passes through two 3×3 convolutional blocks to obtain a 512×512 feature map with 32 channels. This feature map is then fused with a conditional feature map of the same size and number of channels obtained through the projection mechanism described above using nearest neighbor interpolation. The fused feature map is downsampled through a 2×2 max pooling layer, and then processed through two 3×3 convolutional blocks to obtain a 256×256 feature map with 64 channels. This feature map is then fused with the 64-channel conditional feature map obtained through projection using nearest neighbor interpolation, completing the first downsampling stage. Subsequently, the feature map undergoes a second 2×2 max pooling downsampling, and then passes through two 3×3 convolutions to obtain a 128×128 image feature map with 128 channels. This feature map is then fused with the 128-channel and 128×128 conditional feature maps obtained through projection using nearest neighbor interpolation, completing the second downsampling stage. Next, the feature map undergoes a third downsampling and convolution to obtain 256-channel 64×64 image features, which are then fused with the corresponding conditional feature map, completing the third downsampling stage and reaching the bottleneck layer of the encoder. The U-Net encoder extracts multi-scale spatial features progressively in this manner, incorporating input parameter conditions into each layer.

[0076] Specifically, at the bottleneck layer of U-Net (i.e., after obtaining a 64×64 feature map with 256 channels), this invention integrates a Transformer self-attention mechanism, such as... Figure 6 As shown, it is specifically an 8-head, 256-channel multi-head attention mechanism with positional encoding, used to capture the global spatial dependencies of the feature map, and still obtains a 64×64 matrix with 256 channels after processing.

[0077] The decoder recovers spatial details through upsampling and skip connections. First, it upsamples through a 2×2 transposed convolutional block to obtain a 128-channel 128×128 feature map. This map is then skip-connected to the 128×128 feature map saved after the second downsampling in the encoding stage, merging them into a 256-channel 128×128 feature map. Next, it upsamples again through a 2×2 transposed convolution and passes through two 3×3 convolutional blocks to obtain a 64-channel 256×256 feature map. This is skip-connected to the 256×256 feature map saved after the first downsampling in the encoding stage, resulting in a 128-channel 256×256 feature map. Finally, it upsamples a third time through a 2×2 transposed convolution and passes through two 3×3 convolutional blocks to obtain a 32-channel 512×512 feature map. This is skip-connected to the initial 32-channel feature map, resulting in a 64-channel 512×512 feature map.

[0078] Finally, the feature is sequentially reduced to 32 channels through two 3×3 convolutional blocks, and then reduced to a single channel through two more 3×3 convolutional blocks. The Tanh activation function is then used to constrain the output value to the [-1, 1] interval, thus generating the residual field. The learning objective of the entire correction module is the difference between the actual cooling efficiency field and the initial POD prediction field. This design allows U-Net to focus on learning the nonlinear error components that are difficult to represent by linear models. Adding the generated residual field directly to the initial POD prediction field yields the final two-dimensional distribution prediction field of the film cooling efficiency. This cascaded approach of "initial prediction + residual correction" synergistically leverages the dual advantages of the POD method's efficient and stable linear reconstruction and the U-Net model's powerful nonlinear fitting capability.

[0079] Step S3, Model Training

[0080] In this embodiment, a total of 290 sets of samples were used for model training and evaluation, including 40 sets of cylindrical holes and 250 sets of forward-tilting fan-shaped holes. To ensure the reliability of model evaluation, all samples were randomly divided into training, validation, and test sets in a ratio of 7:1.5:1.5. The model was implemented using the Python programming language, with AdamW as the optimizer and its weight decay set to... The decay rate for the first moment estimate was set to 0.9, and the decay rate for the second moment estimate was set to 0.999. Due to the limited total sample size, an early stopping strategy was introduced during training to prevent overfitting and ensure the model achieves optimal generalization performance. Training was terminated when the validation set loss no longer decreased over several consecutive training epochs, thus ensuring the saved model performs best on the validation set. The loss function used for model training was L1 loss, calculated as follows:

[0081] (7)

[0082] In the formula, This represents the number of discrete sampling points in the film cooling efficiency field. and Each is for the first The data includes sampling points, the actual value of the film cooling efficiency obtained from numerical simulation, and the film cooling efficiency value predicted by the model.

[0083] Training employs the aforementioned two-stage progressive strategy to ensure each module learns sufficiently and avoids optimization conflicts. The first stage focuses on training the multilayer perceptron network in the aperture adaptive POD mode decomposition and reconstruction module. During this stage, all parameters of the conditional residual U-Net correction module are frozen and do not participate in gradient updates. The training objective is to minimize the L1 loss between the initial predicted field output by the POD module and the true field. The initial learning rate for this stage is set to... The learning rate was dynamically adjusted using a cosine annealing scheduling strategy, with a total training epoch of 2000. The second stage focused on training the conditional residual U-Net correction module. At this stage, all parameters of the POD module were frozen, and the training objective was to minimize the L1 loss between the final output of the entire model (i.e., the residual field from the initial POD prediction plus the U-Net output) and the true field. The initial learning rate for this stage was set to... The same cosine annealing scheduling was used, with a total of 1500 training rounds. The convergence process and performance of the loss functions in these two training phases on the training and validation sets are described below. Figure 7 and Figure 8 As shown, this phased and differentiated training strategy effectively ensures the stable optimization of each sub-module and the overall performance improvement of the model.

[0084] Step S4: Predictive Implementation and Effect Verification

[0085] After model training, for a new film cooling design, it is only necessary to obtain its film pore parameters and input them into the trained hybrid neural network model. The model will automatically perform forward propagation, sequentially undergoing preprocessing, POD reconstruction, and U-Net correction, outputting the predicted two-dimensional cooling efficiency distribution cloud map within milliseconds. To verify the superiority of the method of this invention, its prediction results were compared with those of traditional models. The specific parameters of the four typical test samples used for comparison are shown in the table below:

[0086] Table 3 Test Sample Parameters

[0087]

[0088] Figure 9 The comparison results of four typical test samples with different compound angles, aperture shapes, and blowing ratios are shown, where (a)-(d) are the real fields, (a1)-(d1) are the predicted fields of the traditional AI model, and (a2)-(d2) are the predicted fields of the method of this invention. It can be seen that the distribution pattern predicted by the method of this invention is closer to the real field.

[0089] Figure 10 The comparison between the predicted results and the actual cloud map is further shown, and it can be seen that the error area of ​​the method of the present invention ((a2)-(d2)) is much smaller than that of the traditional model ((a1)-(d1)).

[0090] Figure 11 The root mean square error (MAE) of prediction for four samples was quantitatively compared. The data showed that the method of this invention reduced the prediction error by 33.1% to 55.8% compared with the traditional model, which fully demonstrates its significant effect in improving prediction accuracy.

[0091] In summary, this invention successfully constructs an intelligent model capable of predicting the two-dimensional cooling efficiency distribution of composite angle air film holes with high accuracy and strong generalization under limited sample conditions through hole shape adaptive POD dimensionality reduction, conditionally injected residual U-Net correction, and a two-stage training strategy. This provides an efficient tool for the rapid optimization design of high-temperature components of aero-engines.

[0092] Finally, it should be noted that the features mentioned and / or shown in the above description of exemplary embodiments of the present invention can be combined in the same or similar manner with one or more other embodiments, combined with or substituted for corresponding features in other embodiments. These combined or substituted technical solutions should also be considered to be included within the scope of protection of the present invention.

Claims

1. A two-dimensional distribution prediction method for composite corner-hole single-exhaust film cooling efficiency based on POD mode decomposition, characterized in that, Includes the following steps: Step 1: Obtain training samples. Each set of sample data includes a film cooling pore parameter vector composed of structural parameters and aerodynamic parameters, as well as the corresponding two-dimensional distribution real field of film cooling efficiency. Step 2: Construct a hybrid neural network model. The model takes the air film pore parameter vector as input and the two-dimensional distribution prediction field of air film cooling efficiency as output. It includes an input parameter preprocessing module, an pore type adaptive POD mode decomposition and reconstruction module, and a conditional residual U-Net correction module connected in sequence. The input parameter preprocessing module is used to process the air film pore parameter vector into a normalized parameter vector. The pore type adaptive POD mode decomposition and reconstruction module is used to establish a POD reduction model based on training samples for different air film pore types, and predict the POD coefficients according to the normalized parameter vector, thereby reconstructing the preliminary prediction field of the two-dimensional distribution of air film cooling efficiency. The conditional residual U-Net correction module uses the normalized parameter vector as a condition to perform residual correction on the preliminary prediction field and outputs the final two-dimensional distribution prediction field of air film cooling efficiency. Step 3: Train the hybrid neural network model using a two-stage progressive training strategy; Step 4: For the air film cooling scheme to be predicted, obtain its air film pore parameter vector and input it into the trained hybrid neural network model to obtain the two-dimensional distribution prediction result of air film cooling efficiency.

2. The method for predicting the two-dimensional distribution of composite corner-hole single-exhaust film cooling efficiency based on POD mode decomposition according to claim 1, characterized in that: The structural parameters include the air film pore shape and the ratio of the air film pore outlet width to the diameter. and air film pore composite angle The aerodynamic parameters include the air blowing ratio. .

3. The two-dimensional distribution prediction method for composite corner-hole single-exhaust film cooling efficiency based on POD mode decomposition according to claim 2, characterized in that: The input parameter preprocessing module processes the continuous parameters of the air film pore outlet width and diameter ratio. air film pore composite angle Compared to blowing air Z-score normalization is performed to encode the discrete air film pore patterns using one-hot encoding, forming a five-dimensional normalized parameter vector.

4. The two-dimensional distribution prediction method for composite corner-hole single-exhaust film cooling efficiency based on POD mode decomposition according to claim 3, characterized in that: The air film pore types include cylindrical pores and fan-shaped pores; the pore type adaptive POD mode decomposition and reconstruction module constructs an independent POD reduction model for the training samples of each pore type.

5. The method for predicting the two-dimensional distribution of composite corner-hole single-exhaust film cooling efficiency based on POD mode decomposition according to claim 4, characterized in that, The execution process of the aperture-adaptive POD mode decomposition and reconstruction module includes: For each aperture type, the average cooling efficiency field is calculated based on its training samples; Singular value decomposition is performed on the centered sample data to extract the dominant modes, and the number of modes to be retained is determined based on a preset energy threshold. ; Construct a multilayer perceptron network and map the five-dimensional normalized parameter vector to... A dimensional POD coefficient prediction vector; The predicted POD coefficients are linearly combined with the retained POD modes, and then superimposed with the average cooling efficiency field to obtain the preliminary prediction field.

6. The two-dimensional distribution prediction method for composite corner-hole single-exhaust film cooling efficiency based on POD mode decomposition according to claim 5, characterized in that: The energy threshold is set to a cumulative energy percentage of 95% or higher.

7. The two-dimensional distribution prediction method for composite corner-hole single-exhaust film cooling efficiency based on POD mode decomposition according to claim 1, characterized in that: The conditional residual U-Net correction module includes a parameter encoder, a U-Net network, and an output layer; The parameter encoder consists of a multilayer sensing mechanism, used to map the normalized parameter vector to a higher-dimensional feature space to form a conditional feature vector; The U-Net network is an encoder-decoder structure. Its encoder part extracts the multi-scale spatial features of the preliminary prediction field through multiple downsamplings, and injects the conditional feature vector at each level through feature projection. Its decoder part gradually restores the spatial resolution of the feature map by upsampling multiple times and combining skip connections; The output layer performs convolution processing on the final output of the U-Net network to generate a residual field with the same size as the initial prediction field. The residual field is added to the initial prediction field to obtain the final two-dimensional distribution prediction field of the air film cooling efficiency.

8. The method for predicting the two-dimensional distribution of composite corner-hole single-exhaust film cooling efficiency based on POD mode decomposition according to claim 7, characterized in that, The conditional feature vector is injected into each layer of the U-Net encoder via feature projection. Specifically, the conditional feature vector is projected to the same number of channels as the feature map of the corresponding layer of the encoder through a 1×1 convolution, and then fused with the feature map of that layer through nearest neighbor interpolation.

9. The method for predicting the two-dimensional distribution of composite corner-hole single-exhaust film cooling efficiency based on POD mode decomposition according to claim 7 or 8, characterized in that: The bottleneck layer of the U-Net network integrates a Transformer self-attention mechanism to capture the global spatial dependencies of feature maps.

10. The method for predicting the two-dimensional distribution of composite corner-hole single-exhaust film cooling efficiency based on POD mode decomposition according to claim 1, characterized in that, The two-stage progressive training strategy includes: Phase 1: Train the aperture adaptive POD mode decomposition and reconstruction module, while freezing the parameters of the conditional residual U-Net correction module; The second stage involves training the conditional residual U-Net correction module while simultaneously freezing the parameters of the aperture adaptive POD mode decomposition and reconstruction module.

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