A multi-row exhaust film cooling effect superposition prediction method based on discrete fourier transform

Abstract

The application discloses a multi-row gas film cooling efficiency superposition prediction method based on discrete Fourier transform, and belongs to the field of thermal protection of high-temperature components of an aero-engine. The method firstly acquires the geometric and aerodynamic parameters of a gas film hole and a single-row hole cooling efficiency curve, and calculates an initial superposition curve based on a Sellers formula; then the initial curve and working condition parameters are input into a pre-trained three-branch neural network model, wherein a time domain branch extracts time domain features through a convolution network, a frequency domain branch performs discrete Fourier transform on the curve to extract frequency domain features, and a residual branch extracts residual correction features; finally, the three features are fused to output a high-precision prediction curve. The application introduces discrete Fourier transform to extract physical priori, and combines a three-branch network structure, so that the defects of low precision, poor generalization and dependence on large data of a pure data-driven model are effectively overcome, and high-precision and strong extrapolation prediction of the cooling efficiency of the multi-row gas film is realized under limited samples.

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 an intelligent method for predicting the cooling efficiency of multiple film cooling holes superimposed. Background Technology

[0002] Film cooling is a key thermal protection technology widely used in high-temperature components of aero-engines, such as combustion chamber walls, turbine blades, and nozzles. Accurate prediction of its cooling efficiency is crucial for optimizing cooling gas usage, ensuring combustion stability, reducing pollutant emissions, and extending the lifespan of hot-end components.

[0003] Currently, the mainstream methods for predicting the superimposed cooling efficiency of multiple exhaust film holes can be categorized into two types: analytical correction methods based on physical models and data-driven neural network methods.

[0004] Among the analytical correction methods based on physical models, the most classic is the Sellers superposition algorithm, which makes predictions based on a simple linear superposition assumption. However, it does not fully consider the flow interference and mixing effects between the orifice rows, resulting in large prediction deviations under complex working conditions. To address this, researchers have proposed various correction schemes to improve its accuracy. For example, Zhu Huiren et al., in "Efficiency of Double-Row Flute-Shaped Orifice Film Cooling and Its Superposition Algorithm (Journal of Aerospace Power, 2006(5): 814-819)," conducted an experimental study on double-row staggered flute orifices and introduced two correction parameters into the Sellers model, achieving accurate prediction for this specific orifice type. Jiang Xingwen, in "Study on Heat Transfer Characteristics of Flat Plate Film Cooling (Tsinghua University, 2015)," introduced a correction coefficient related to the blowing ratio for a three-row orifice model, making the prediction results better match the measured values. However, such correction methods are usually for specific orifice types, specific number of rows, or specific flow conditions. Their correction parameters lack universality, and when extrapolated to other geometric or aerodynamic conditions that have not been specifically calibrated, the prediction performance drops significantly.

[0005] To overcome the structural limitations of analytical models, utilizing the powerful nonlinear mapping capabilities of neural networks for prediction has become a new research approach. For example, Yang L et al.'s work, "Establishment of a long-short-term-memory model to predict film cooling effectiveness under superposition conditions (INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2020, 160: 120-231)," constructed a long short-term memory network model to attempt to learn the transport patterns of upstream flow characteristics downstream, achieving better prediction accuracy in some regions compared to the Sellers model. However, this type of purely data-driven method has two inherent drawbacks: First, its model performance is highly dependent on the quantity and quality of the training dataset, and obtaining high-quality film cooling experiments or high-fidelity numerical simulation data is costly, with limited sample size becoming a bottleneck restricting its application; second, the internal working mechanism of the model lacks clear physical interpretability, resembling a "black box," which is not conducive to researchers understanding and trusting its prediction results, and also increases the difficulty of model debugging, optimization, and evaluation of generalization ability.

[0006] In summary, existing technologies either suffer from weak generalization ability due to the simplification assumptions of physical models, or are hampered by the "black box" nature of data-driven models, resulting in poor interpretability and strong data dependence. Summary of the Invention

[0007] The purpose of this invention is to address the problems of low prediction accuracy, weak extrapolation ability, strong dependence on training data, and insufficient physical interpretability in existing multi-exhaust film cooling efficiency superposition prediction methods. To address these issues, a new method for predicting multi-exhaust film cooling efficiency superposition, integrating physical priors and data-driven intelligent algorithms, is proposed. This method reveals and extracts the quasi-periodic characteristics of the film efficiency distribution by introducing discrete Fourier transform, and based on this, constructs a multi-branch neural network architecture that integrates time-domain, frequency-domain, and operating condition parameters. This achieves high-precision and strong generalization prediction of superposition cooling efficiency under limited data conditions.

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

[0009] A method for predicting the superposition of cooling effects of multiple exhaust films based on discrete Fourier transform is provided, including the following steps:

[0010] Step 1: Obtain the geometric parameters, aerodynamic parameters, and individual cooling efficiency curves of the multiple air film cooling holes of the target air film cooling structure.

[0011] Step 2: Based on the Sellers superposition formula, calculate the initial film cooling efficiency superposition curve according to the individual cooling efficiency curve of each exhaust film hole.

[0012] Step 3: Input the geometric and aerodynamic parameters of the multiple air film cooling holes, as well as the initial air film cooling efficiency superposition curve, into the pre-trained neural network model.

[0013] Neural network models include:

[0014] The residual branch is used to receive geometric and aerodynamic parameters and extract residual correction features;

[0015] The time-domain branch is used to receive the initial film cooling efficiency superposition curve and extract time-domain features;

[0016] The frequency domain branch is used to receive the initial film cooling efficiency superposition curve and perform a discrete Fourier transform on it to extract frequency domain features.

[0017] The neural network model fuses the residual correction feature information output by the residual branch, the time-domain feature information output by the time-domain branch, and the frequency-domain feature information output by the frequency-domain branch.

[0018] Step 4: Output the superimposed prediction curve of the film cooling efficiency generated by the fusion process as the final prediction result.

[0019] Furthermore, the residual branch includes a multi-layer fully connected neural network used to map geometric parameters and aerodynamic parameters into vectors with the same dimension as the temporal feature information, serving as residual correction feature information.

[0020] Furthermore, the residual branch is specifically a network structure consisting of a five-layer fully connected neural network.

[0021] Furthermore, the temporal branch includes a multi-layer one-dimensional convolutional neural network used to extract multi-scale temporal features from the initial film cooling efficiency superposition curve.

[0022] Furthermore, the temporal branch is specifically a network structure consisting of four one-dimensional convolutional layers with a kernel size of 3.

[0023] Furthermore, the frequency domain branch includes:

[0024] The Discrete Fourier Transform module is used to transform the input initial film cooling efficiency superposition curve to obtain frequency domain information.

[0025] The attention mechanism module is used to adaptively weight different frequency components in the frequency domain information to extract key frequency domain features.

[0026] Furthermore, the frequency domain branch also includes an inverse Fourier transform module, which is used to transform the features processed by the attention mechanism module back to the time domain and output them as frequency domain feature information.

[0027] Furthermore, the fusion processing of the neural network model is a weighted summation, and the final superimposed prediction curve of the air film cooling efficiency is obtained by multiplying the time domain feature information and frequency domain feature information by their respective weights, and then adding them to the residual correction feature information.

[0028] Furthermore, the weight multiplied by the time-domain feature information is 0.5, and the weight multiplied by the frequency-domain feature information is also 0.5.

[0029] Furthermore, the pre-trained neural network model is trained using a method that includes the following steps:

[0030] - Construct a training dataset, which includes multiple sets of known geometric parameters, aerodynamic parameters, individual cooling efficiency curves for each exhaust film orifice and their corresponding real superimposed cooling efficiency curves;

[0031] - Construct a neural network model with the structure described in claim 1;

[0032] - The neural network model is trained using a training dataset, where a weighted loss function that assigns higher weights to prediction errors in downstream regions is used to optimize the model parameters.

[0033] The advantages of this invention are:

[0034] 1. The multi-stage film cooling efficiency superposition prediction method based on Discrete Fourier Transform (DFT) provided by this invention integrates the physical priors extracted by DFT with the data-driven capability of neural networks to construct a superposition prediction model for film cooling efficiency that combines high accuracy, strong generalization, and good physical interpretability. Specifically, this invention creatively transforms the quasi-periodic time-domain signal of the superposition of film cooling systems into the frequency domain through DFT for identification and feature extraction, providing physical interpretability for the prediction of the network model. Furthermore, it designs a unique three-branch network architecture encompassing the time domain, frequency domain, and parameter residuals, enabling multi-angle collaborative correction of the initial Sellers prediction curve. This method effectively overcomes the problem that traditional pure data-driven models require a large amount of training data to make up for the lack of physical information, and can still achieve high-precision prediction under limited sample conditions. At the same time, by learning and fusing the dual features of the initial prediction curve in the time domain and frequency domain, it significantly improves the overall prediction accuracy, especially the prediction accuracy in the downstream region. This enables the model to show superior extrapolation and generalization performance when facing complex working conditions such as more hole rows and different hole types that have not been trained, providing an efficient and reliable tool for the rapid optimization of air film cooling design.

[0035] 2. This invention introduces a frequency domain attention mechanism, which adaptively weights different frequency components in the frequency domain information, enabling the model to automatically focus on low-frequency key components containing major physical deviations while ignoring high-frequency noise or minor details. This mechanism not only further improves prediction accuracy but also enhances the model's feature extraction efficiency and robustness, making its learning process more targeted and interpretable. Attached Figure Description

[0036] 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:

[0037] Figure 1 This is a flowchart illustrating the method for predicting the superposition of cooling effects of multiple exhaust films based on discrete Fourier transform, according to an embodiment of the present invention.

[0038] Figure 2 This is a schematic diagram of the structural parameters of the multi-exhaust membrane hole in an embodiment of the present invention, wherein (a) is a schematic diagram of the cylindrical hole structure and (b) is a schematic diagram of the scoop-shaped (fan-shaped) hole structure;

[0039] Figure 3 This is a schematic diagram of the numerical simulation computational domain grid used to generate training samples in an embodiment of the present invention;

[0040] Figure 4 This is a schematic diagram of the superimposed curve of the air film cooling efficiency and its frequency domain characteristics obtained by discrete Fourier transform in an embodiment of the present invention;

[0041] Figure 5 This is an overall architecture diagram of the neural network prediction model based on discrete Fourier transform in an embodiment of the present invention;

[0042] Figure 6 This is a schematic diagram of the specific structure of the residual branch of the neural network model in an embodiment of the present invention;

[0043] Figure 7 This is a schematic diagram of the specific structure of the temporal branch of the neural network model in an embodiment of the present invention;

[0044] Figure 8 This is a schematic diagram of the specific structure of the frequency domain branch of the neural network model in this embodiment of the invention;

[0045] Figure 9 This is a convergence curve of the loss function versus the learning rate during model training in an embodiment of the present invention;

[0046] Figure 10 This is a comparison chart of the prediction results of the present invention with the prediction results of the Sellers model and the actual values ​​on eight different test samples, where (a) to (d) correspond to the comparison results of samples 1 and 2, samples 3 and 4, samples 5 and 6, and samples 7 and 8, respectively.

[0047] Figure 11 This is a comparison and error analysis diagram of the area-average film cooling efficiency predicted by the present invention and the Sellers model with the actual value, where (a) to (d) correspond to the comparison results of four rows of cylindrical holes, four rows of fan-shaped holes, five rows of cylindrical holes, and five rows of fan-shaped holes, respectively. Detailed Implementation

[0048] 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.

[0049] This invention aims to provide a prediction method with high accuracy, strong generalization ability, and clear physical meaning to solve the quantitative prediction problem of complex flow heat transfer issues involving the superposition of cooling efficiencies from multiple exhaust film orifices. The complete implementation process of this method will be described step by step below.

[0050] Reference Figure 1 The multi-row film cooling efficiency superposition prediction method based on discrete Fourier transform, as an exemplary embodiment of the present invention, includes: acquiring the geometric structural parameters, aerodynamic parameters, and individual cooling efficiency curves of the multiple rows of film cooling holes in the target film cooling structure; calculating an initial film cooling efficiency superposition curve based on the classic Sellers superposition formula; inputting the initial curve and operating parameters into a specially designed three-branch neural network model for deep processing; and finally, the model outputs a final high-precision superposition prediction curve by fusing the learning results of the three branches. This process creatively combines physical models, mathematical transformations, and data-driven algorithms.

[0051] See Figure 2 It demonstrates the typical geometric parameters of the multi-exhaust film cooling structure targeted by the present invention. Figure 2 In the diagram, (a) represents a cylindrical hole, and (b) represents a scoop-shaped (fan-shaped) hole. The input parameters required for this method include two categories: one is geometric structural parameters, such as the number of hole rows (e.g., 2 or 3 rows) and the width of the air film outlet. Spacing between adjacent rows of holes Spacing between adjacent holes in the same row And the staggered arrangement between rows (by This indicates that the cross-row is 1 / 2 and the straight-row is 0, etc.; secondly, it refers to gas dynamic parameters, such as the mainstream velocity. mainstream temperature Cooling airflow (secondary flow) temperature Blower than and density ratio In this embodiment, the specific values ​​of these parameters are shown in Tables 1 and 2.

[0052] Table 1 Range of Structural Parameter Values

[0053]

[0054] Table 2 Range of pneumatic parameters

[0055]

[0056] To obtain the data needed for training and testing, a sample library needs to be built through high-fidelity numerical simulations or experiments. See also Figure 3 This paper demonstrates the numerical simulation computational domain setup and mesh generation strategy used to generate training samples. The computational model mainly consists of three parts: the main channel, the cold air branch channels, and the film cooling structure. The main channel inlet is set as a velocity inlet, and the main channel outlet is set as a pressure outlet. The cold air branch inlet is defined as a mass flow rate inlet, and its flow rate is determined according to the blowing ratio. The cooling wall and other walls are all set as adiabatic no-slip walls. Periodic boundary conditions are applied to the sidewalls of the main channel and the cold air channels. The mesh discretization adopts a hybrid mesh: the film cooling holes and their surrounding cavity regions are divided into quadrilateral unstructured meshes, while the main channel and the cold air cavity regions are divided into structured meshes. To ensure computational accuracy, especially the resolution of near-wall flow, the mesh is refined on the lower wall covering the film cooling system and near the outlet of the holes to meet the requirement of y+≈1. With the above settings, the true film cooling efficiency distribution field under various combinations of geometric and aerodynamic parameters can be simulated, and then the spanwise average cooling efficiency curve can be extracted as label data.

[0057] Thus, each sample in the complete training dataset contains three key pieces of information: a set of geometric parameters and gas dynamic parameters; the cooling efficiency curve of each exhaust film orifice when acting alone, obtained through numerical simulation under these parameters (used to calculate Sellers' initial superposition prediction); and the actual superposition cooling efficiency curve when multiple rows of orifices act together under these parameters (serving as the target label for model training).

[0058] In the film cooling superposition problem addressed in this patent, the distribution of multi-row film cooling efficiency along the flow direction exhibits a quasi-periodic characteristic of "attenuation-enhancement" recurrence. Specifically, the film cooling forms a high-efficiency region at the orifice outlet, which then gradually attenuates due to mixing with the mainstream. When the flow reaches the next row of film cooling orifices, newly injected cold air replenishes the film coverage, causing a significant jump in cooling efficiency at that location. The subsequent film cooling then attenuates again along the flow direction, only to be replenished by the next row of orifices, thus repeating the cycle. To effectively utilize this physical characteristic, this invention performs a discrete Fourier transform on the initial film cooling efficiency superposition curve calculated using the Sellers formula. See [link to relevant documentation]. Figure 4Taking a three-row perforated structure as an example, the left side shows the cooling efficiency curve in the time domain, which forms a peak downstream of each perforated row; the right side shows the frequency domain amplitude spectrum obtained after performing a discrete Fourier transform on the curve. It can be seen that the transformed signal exhibits obvious characteristic components in the frequency domain, which are closely related to the physical period of the gas film superposition. By performing the transformation using the following equation (1), the length is... Transforming time-domain sequences into frequency-domain representations :

[0059] (1)

[0060] In the formula, the index This represents the frequency components in the Fourier transform. In this embodiment, both the time-domain sequence and the frequency components are 512-dimensional. This process essentially decomposes the signal into sine and cosine components of different frequencies. Specifically, to calculate the... Frequency components The corresponding complex exponential basis functions need to be constructed. According to Euler's formula, this basis function can be decomposed into sine and cosine components:

[0061] (2)

[0062] Next, the basis function is compared with the 512-point spanning average cooling efficiency sequence. If we calculate the inner product, then... The middle presents the same as the first If multiple complex exponential basis functions exhibit similar changing patterns, then the corresponding frequency components... The amplitude will be larger; conversely, it will be smaller.

[0063] This step transforms complex morphological changes in the time domain into feature patterns in the frequency domain that are easier to analyze and learn, providing strong physical prior guidance for subsequent neural networks.

[0064] Reference Figure 5 The neural network model designed in this invention employs a strategy of three parallel branches (time-domain branch, frequency-domain branch, and residual branch) working collaboratively to correct the initial prediction from different dimensions, and finally outputs the final result through a fusion module. This structure effectively decomposes the learning task and reduces the model complexity.

[0065] Combination Figure 6The residual branch directly processes the input geometric and aerodynamic parameters. These parameters, as systematic factors affecting cooling efficiency, are fed into a subnetwork consisting of multiple fully connected layers; in this embodiment, the network structure comprises a five-layer fully connected neural network. This network maps the input parameters into a 512-dimensional correction vector to perform parameterized residual correction on Sellers' initial prediction. This vector contains condition-specific correction information, enabling targeted compensation for inherent biases in the physical formulas.

[0066] Combination Figure 7 The temporal branch directly processes the initial superimposed curve predicted by the Sellers formula. It comprises a multi-layered one-dimensional convolutional neural network, in this embodiment, consisting of four stacked one-dimensional convolutional layers with a kernel size of 3. Convolutional operations excel at capturing local patterns and dependencies between neighboring points. Through multiple convolutions, this branch is able to extract multi-scale temporal features from the initial curve, learning its local undulations and the parts of the overall shape that need correction. The output of this branch is a curve with the same length dimension as the input (i.e., a 512-dimensional vector).

[0067] Combination Figure 8 The frequency domain branch is the core innovation of this invention. The purpose of this branch is to identify the "quasi-periodic" characteristics of gas film superposition through Fourier transform and then transform it into the frequency domain for feature recognition and extraction. The input of this branch is the initial superposition curve (512-dimensional vector) predicted by the Sellers formula.

[0068] First, the Discrete Fourier Transform module transforms the input curve, outputting real and imaginary vectors (both 512-dimensional) representing the signal phase and amplitude, respectively. Next, positional encoding is added to the real and imaginary parts, and they are combined into matrices to generate the Q, K, and V matrices.

[0069] The signal then enters the attention mechanism module, which adaptively assigns higher weights to key frequencies (typically low-frequency components related to physical periods) by calculating the correlation between different frequency components, while suppressing the influence of minor or noise frequencies. In this embodiment, six such attention structures are stacked to enhance learning capabilities. Finally, the processed signal is reconstructed back into a time-domain curve via an inverse Fourier transform module, forming a 512-dimensional vector as the frequency-domain feature information of this branch. This design enables the model to "understand" and reinforce the core frequency-domain components related to quasi-periodic physical phenomena, significantly improving the relevance and interpretability of the learning.

[0070] The outputs of all three branches are 512-dimensional vectors / curves. Finally, the model's fusion module uses a weighted summation method for feature fusion. In this embodiment, the outputs of the time-domain and frequency-domain branches are each multiplied by a weight of 0.5 before being summed. The result is then directly added to the output vector of the residual branch to generate the final film cooling efficiency superimposed prediction curve for output. This fusion strategy balances the contributions of time-domain and frequency-domain information and directly incorporates residual corrections for operating parameters, ensuring that the final prediction result maintains physical consistency while also conforming to specific conditions.

[0071] Model training is crucial for acquiring predictive capabilities. The training dataset, consisting of 360 samples, was constructed using the aforementioned numerical simulation method. Training was conducted on an Nvidia RTX 4080 Super GPU with 16GB of VRAM, an Intel Core i7 14700K CPU, 64GB of RAM, and Python as the programming language. The Adam optimizer was selected, and the learning rate was adjusted using a cosine annealing strategy. This invention introduces a weighted loss function (Equation (3)) during training. This function assigns higher weights to the prediction errors in downstream regions (Equation (4)), guiding the model to prioritize optimizing the prediction errors in those regions during training, thereby improving overall prediction accuracy.

[0072] (3)

[0073] (4)

[0074] In the formula, This represents the total number of data points in a training sample used to predict the curve. To give the first The weighting coefficients of the prediction error for each data point. For the first The actual film cooling efficiency value (i.e., the label value) at each data point location. For the model to the first Predicted values ​​for each data point.

[0075] See Figure 9 The diagram shows the curves of the loss function versus the learning rate during training. It is evident that after approximately 600 training epochs, the loss converged to a low level, indicating that the model was sufficiently trained. The entire training process took approximately 300 minutes, while the trained model only needs about 0.3 milliseconds to predict a new sample, demonstrating extremely high efficiency.

[0076] To verify the model's performance, complex working conditions with more rows of holes (4 rows and 5 rows) that were not included in the training were selected for testing. The test sample parameters are shown in Table 3.

[0077] Table 3 Test Sample Parameters

[0078]

[0079] First, see Figure 10 The prediction curves of the model of this invention (hereinafter referred to as "the model"), the traditional Sellers model (corresponding to "Model Sellers" in the figure), and the actual values ​​(label values) were compared on eight representative test samples. It can be seen that, regardless of whether it is a cylindrical or fan-shaped orifice, at a blowing ratio of 1.0 or 2.0, the prediction curve of the model of this invention has a much higher degree of agreement with the actual values ​​than the Sellers model. Especially in the far downstream region, the error of the Sellers model increases significantly, while the model of this invention still maintains high accuracy, with prediction errors mostly controlled within 5%, and a maximum local error of only 8%, while the maximum error of the Sellers model is as high as 13%. This fully demonstrates the model's powerful correction capability and high accuracy.

[0080] Further, see Figure 11 A quantitative comparison and error analysis were conducted on the area-average cooling efficiency of cylindrical and fan-shaped holes in four-row and five-row structures. It can be seen that under all test conditions (four combinations of hole types and row numbers), the prediction results of the model of this invention almost coincided with the actual values, and the overall prediction error was stably controlled within 3%. Although the prediction difficulty increased and the error slightly increased with the increase of the airflow ratio, the model consistently demonstrated robust prediction performance. In contrast, the prediction results of the Sellers model showed a significant deviation from the actual values, with a significantly higher error. This confirms that the method of this invention has excellent and robust prediction accuracy and generalization ability for different hole types, different row numbers, and a wide range of airflow ratios.

[0081] In summary, this invention injects physical priors through Discrete Fourier Transform, achieves feature decoupling and efficient learning through a three-branch network structure, and focuses on difficult regions through weighted loss during training, thereby constructing a prediction model that combines high accuracy, strong generalization ability and clear physical meaning. This effectively overcomes the shortcomings of traditional methods, such as low accuracy, reliance on big data, and poor interpretability of data-driven methods.

[0082] 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 method for predicting the superposition of cooling effects of multiple exhaust films based on discrete Fourier transform, characterized in that, Includes the following steps: Step 1: Obtain the geometric parameters, aerodynamic parameters, and individual cooling efficiency curves of the multiple air film cooling holes of the target air film cooling structure. Step 2: Based on the Sellers superposition formula, calculate the initial film cooling efficiency superposition curve according to the individual cooling efficiency curve of each exhaust film hole. Step 3: Input the geometric and aerodynamic parameters of the multiple air film cooling holes, as well as the initial air film cooling efficiency superposition curve, into the pre-trained neural network model. The neural network model includes: The residual branch is used to receive the geometric parameters and aerodynamic parameters, and extract residual correction features; The time-domain branch is used to receive the initial film cooling efficiency superposition curve and extract time-domain features; The frequency domain branch is used to receive the initial film cooling efficiency superposition curve and perform a discrete Fourier transform on it to extract frequency domain features. The neural network model fuses the residual correction feature information output by the residual branch, the time-domain feature information output by the time-domain branch, and the frequency-domain feature information output by the frequency-domain branch. Step 4: Output the superimposed prediction curve of the film cooling efficiency generated by the fusion process as the final prediction result.

2. The method for predicting the superimposed cooling effect of multiple exhaust films according to claim 1, characterized in that: The residual branch includes a multi-layer fully connected neural network, which maps the geometric parameters and aerodynamic parameters into vectors with the same dimension as the time-domain feature information, serving as the residual correction feature information.

3. The method for predicting the superimposed cooling effect of multiple exhaust films according to claim 2, characterized in that: The residual branch is specifically a network structure consisting of a five-layer fully connected neural network.

4. The method for predicting the superimposed cooling effect of multiple exhaust films according to claim 1, characterized in that: The temporal branch includes a multi-layer one-dimensional convolutional neural network, used to extract multi-scale temporal features from the initial film cooling efficiency superposition curve.

5. The method for predicting the superimposed cooling effect of multiple exhaust films according to claim 4, characterized in that: The temporal branch is specifically a network structure consisting of four one-dimensional convolutional layers with a kernel size of 3.

6. The method for predicting the superimposed effect of multi-exhaust film cooling according to claim 1, characterized in that: The frequency domain branch includes: The Discrete Fourier Transform module is used to transform the input initial film cooling efficiency superposition curve to obtain frequency domain information. The attention mechanism module is used to adaptively weight different frequency components in the frequency domain information to extract key frequency domain features.

7. The method for predicting the superimposed cooling effect of multiple exhaust films according to claim 6, characterized in that: The frequency domain branch also includes an inverse Fourier transform module, which is used to transform the features processed by the attention mechanism module back to the time domain and output them as the frequency domain feature information.

8. The method for predicting the superimposed cooling effect of multiple exhaust films according to claim 1, characterized in that, The fusion processing of the neural network model is a weighted summation. The final gas film cooling efficiency superposition prediction curve is obtained by multiplying the time domain feature information and the frequency domain feature information by their respective weights, and then adding them to the residual correction feature information.

9. The method for predicting the superimposed cooling effect of multiple exhaust films according to claim 8, characterized in that: The weight multiplied by the time-domain feature information is 0.5, and the weight multiplied by the frequency-domain feature information is 0.

5.

10. The method for predicting the superimposed cooling effect of multiple exhaust films according to any one of claims 1 to 9, characterized in that, The pre-trained neural network model is obtained by training a method including the following steps: - Construct a training dataset, which includes multiple sets of known geometric parameters, aerodynamic parameters, individual cooling efficiency curves for each exhaust film orifice and their corresponding real superimposed cooling efficiency curves; - Construct a neural network model with the structure described in claim 1; - The neural network model is trained using the training dataset, wherein a weighted loss function that assigns higher weight to the prediction error in the downstream region is used to optimize the model parameters.

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