Feature learning and data fusion based on neural operator for film cooling prediction

Abstract

The application discloses a feature learning and data fusion air film cooling prediction method based on a neural operator, and comprises the following steps: obtaining a basic data set for feature learning, establishing different geometric models through a parameterized hole distribution and a blowing ratio condition, and obtaining surface temperature distribution data; extracting surface adiabatic cooling efficiency data as output data and drawing surface geometric data as input data; setting the total sample quantity, reading input and output data division labels, and dividing a training set and a test set; building an iterative neural operator framework based on FNO, simulating an operator solving process, and learning air film cooling features; inputting test set input set data into a training model, verifying the model by using test set output set data, and obtaining a prediction model. The application solves the problem of efficiently, quickly and accurately predicting air film cooling distribution through sparse point array data of one sample.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of engineering thermophysics, and particularly relates to a feature learning and data fusion air film cooling prediction method based on a neural operator. BACKGROUND

[0002] Air film cooling technology is an important means for improving the high-temperature resistance of key components such as turbine blades in an aero-engine. With the continuous increase of the working temperature of modern aero-engines, traditional cooling technology gradually fails to meet the demand. Air film cooling forms a layer of air film on the surface of the engine blade in the hot area, effectively preventing the high-temperature gas flow from directly contacting the blade surface, thereby achieving the cooling of the blade. Air film cooling plays a crucial role in improving the working efficiency of the engine, prolonging the service life of the engine and ensuring flight safety. Especially in the high-pressure turbine and combustion chamber area, the design and optimization of air film cooling become the key to the development of aero-engine technology. Accurate control of air film cooling distribution and optimization of the cooling scheme are one of the core research topics in current engineering thermophysical technology.

[0003] The method for obtaining air film cooling distribution mainly relies on experimental measurement and numerical simulation. Experimental measurement methods, such as thermocouples, infrared thermometers, etc., although can provide real-time surface temperature data, are limited by measurement accuracy, sensor arrangement, test environment and other factors, and are difficult to fully obtain the distribution of air film cooling. In addition, experiments usually cannot provide dynamic changes under real operating conditions. Numerical simulation methods, especially simulation techniques based on CFD, can provide comprehensive cooling field data, but the calculation cost is very high, especially under complex flow field conditions, the simulation time and computing resource consumption are large. In addition, low-precision numerical simulation often cannot obtain sufficient prediction accuracy, which makes the air film cooling distribution prediction based on these methods have great limitations. Therefore, how to realize fast, accurate and low-cost air film cooling distribution prediction has become a technical challenge to be solved.

[0004] With the rapid development of deep learning technology, more and more research attempts to apply deep learning methods to the prediction of gas film adiabatic cooling efficiency. For example, convolutional neural network (CNN) and recurrent neural network (RNN) are used to predict the gas film cooling distribution through historical data and experimental measurement data. Although these methods have achieved good results when the data volume is large and the quality is high, they still have obvious shortcomings. First, deep learning models usually require a large amount of high-quality training data, which is very difficult in actual engineering applications, especially when dealing with complex physical processes, high-quality training data is often scarce and difficult to obtain. Second, many deep learning models lack sufficient physical knowledge integration, resulting in insufficient model generalization and extrapolation ability. This makes it difficult for these methods to provide accurate predictions when faced with new cooling conditions or special working conditions. Finally, the training process of deep learning models is complex and consumes a lot of computing resources, making it difficult to efficiently apply them in actual engineering. Therefore, how to reduce the dependence on high-quality data while improving the model's generalization ability and accuracy is still an important challenge for deep learning in gas film cooling prediction.

[0005] Neural operator (NO) method as a new deep learning technology has made significant achievements in solving many physical problems, especially in fluid dynamics, heat conduction, etc. Fourier neural operator (FNO) is a kind of neural operator method, which combines convolutional neural network with Fourier transform to realize efficient modeling and solving of complex physical systems. The advantage of FNO method is that it can handle data with periodic boundary conditions and high-dimensional input-output, and effectively utilize the prior knowledge of physical models to improve the accuracy and generalization ability of the model. Compared with traditional deep learning models, FNO processes in the frequency domain through Fourier transform, significantly reducing the computational load and improving the computational efficiency. Especially in the face of complex nonlinear problems, FNO shows better performance and efficiency. However, although FNO has good performance, its application in gas film cooling distribution prediction still faces the problem of large sample demand. In order to better apply in actual engineering, how to predict the gas film cooling distribution from a small amount of sample sparse data even one sample has high research significance. SUMMARY

[0006] In order to solve the problem of efficiently, quickly and accurately predicting the gas film cooling distribution through a sample of sparse point array data, the purpose of the present application is to provide a feature learning and data fusion gas film cooling prediction method based on neural operator, which learns the adiabatic gas film cooling distribution features through feature learning of classical examples. At the same time, the learned features and sparse point array data of a single sample are fused to predict the gas film cooling distribution under different conditions by using data fusion method.

[0007] In order to achieve the above object, the present application is realized by the following technical solutions:

[0008] A feature learning and data fusion air film cooling prediction method based on neural operator, comprising the following steps:

[0009] Step 1: Obtain the basic data set for feature learning, establish different geometric models by parameterizing the hole distribution and blowing ratio conditions, and calculate to obtain the surface temperature distribution data.

[0010] Step 2: Extract the surface adiabatic cooling efficiency data as the output data, draw the surface geometric data as the input data, and calculate the adiabatic cooling efficiency according to the wall temperature as shown in the formula below:

[0011]

[0012] Where T m represents the main flow inlet temperature, T c represents the cold gas flow inlet temperature, and T w represents the cooling wall temperature.

[0013] Step 3: Set the total number of samples, read the input and output data of step 2, divide the labels, and divide the training set and test set.

[0014] Step 4: Build an iterative neural operator framework based on FNO, simulate the operator solving process, predict the air film cooling evolution process, obtain the training model, and learn the air film cooling features.

[0015] Step 5: Input the input set data of the test set into the training model, use the output set data of the test set to verify the model, obtain the prediction model, and compare the prediction results.

[0016] Step 6: Input the blowing ratio, geometric condition and air film cooling data scatter of the new sample into the prediction model, use the data fusion method, and use the scatter data as the constraint to predict the complete air film cooling distribution.

[0017] Further, the specific steps of obtaining the basic data set in step 1 include:

[0018] Step 1-1: The total number of samples is 70, and 70 groups of different flat plate air film hole distribution point cloud data are randomly generated using the Latin hypercube sampling method, and 70 groups of blowing ratio conditions are randomly generated.

[0019] Step 1-2: According to the point cloud data, use ug software for automatic modeling to generate different geometric models

[0020] Step 1-3: Automatic meshing using fluent meshing software according to the generated geometric model, and automatic calculation using fluent software combined with different blowing ratio conditions.

[0021] Step 1-4: Extracting surface temperature distribution as a txt file according to the calculation results.

[0022] Further, the specific steps of step 4 include:

[0023] Step 4-1: Build an iterative neural operator framework based on FNO, and the model expression of FNO operator is as follows:

[0024] v t (x)=σ(W*v t-1 (x)+∫ D k(x,y,a(x),a(y))*v x (dy))

[0025] Where v t represents the inlet temperature distribution data of different diffusion processes, σ represents the activation function, W represents the linear transformation part of the predicted value between adjacent two diffusion processes, k represents the Fourier transform and inverse transform process, and a represents the boundary condition. Therefore, the overall FNO operator model can represent the spatial diffusion evolution process.

[0026] Step 4-2: Input blank initial value and boundary condition (geometric condition and blowing ratio condition), and data passes through multiple FNO modules until the predicted result tends to be stable, and the loop is stopped. In the prediction of steady-state results, this loop iteration process represents the convergence process of the operator space solution result. The blank initial value gradually changes to the accurate prediction result. Combined with FNO operator and loop iteration process, the spatial diffusion and operator solution convergence process are simulated, so as to obtain accurate prediction result.

[0027] Step 4-3: Import input and output data, perform standardization processing, and randomly shuffle the input model framework for calculation.

[0028] Step 4-4: Use small batch random gradient descent algorithm, set batch to 8. Calculate model error by forward propagation; update model parameters by back propagation, and stop training after loss is stable.

[0029] Further, the specific steps of step 6 include:

[0030] Step 6-1: Save the feature learning model, freeze most of the parameters in the feature learning model, keep other parameters unchanged, and thaw the last two layers of parameters of the model layer by layer.

[0031] Step 6-2: Re-train the last two layers of parameters with the geometric conditions and blowing ratio conditions of the new sample as input, and the scatter data as supervised values to constrain the prediction results.

[0032] Step 6-3: After the loss is stable, output the prediction results, i.e. the complete film cooling distribution results in the new sample, thereby realizing the function of predicting the complete film cooling distribution from the scatter data of a single sample.

[0033] Advantages of the present application:

[0034] 1. The present application can learn the characteristics of film cooling according to classical examples, and transfer the characteristics to new film cooling models with different boundary conditions to predict the adiabatic cooling effect. For a new film cooling model, only a small amount of scatter data of a sample is needed to complete fast, efficient and accurate prediction, thereby reducing the sample quantity demand for predicting the results of new research objects; at the same time, the demand for data point resolution in the sample is reduced, and only a small amount (5%) of scatter data can complete accurate prediction.

[0035] 2. The present application takes pixel difference as an index: in single pixel point result comparison, the error of the adiabatic cooling efficiency prediction result of the training result is less than 0.01; the error of the adiabatic cooling efficiency prediction result of the test result is less than 0.04; in the average result comparison of all pixel points in a sample, the error of the adiabatic cooling efficiency prediction result of the training result is less than 0.01; the error of the adiabatic cooling efficiency prediction result of the test result is less than 0.02. In a single sample with completely different inlet conditions and geometric conditions, when there are only 5% of the detection data points, the error is less than 0.05, and a single sample can complete efficient and accurate prediction. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 Latin hypercube sampling hole distribution result graph.

[0037] Figure 2 Film cooling calculation model schematic diagram.

[0038] Figure 3 Full surface temperature distribution result.

[0039] Figure 4 Full surface adiabatic cooling efficiency distribution result.

[0040] Figure 5 Operator framework graph based on FNO.

[0041] Figure 6 Iteration neural operator framework graph based on FNO.

[0042] Figure 7 Sample iteration process schematic diagram.

[0043] Figure 8 Figure 1 shows a comparison of prediction results of the first test sample.

[0044] Figure 9 Figure 2 shows a comparison of prediction results of the second test sample.

[0045] Figure 10 Figure 3 shows a comparison of prediction results of the third test sample.

[0046] Figure 11 Figure 4 shows a comparison of prediction results of the fourth test sample.

[0047] Figure 12 Figure 5 shows a geometry diagram of a new sample.

[0048] Figure 13 Figure 6 shows a scatter plot of data distribution results.

[0049] Figure 14 Figure 7 shows a prediction result diagram of a single sample. DETAILED DESCRIPTION

[0050] The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present application, and cannot be understood as limiting the present application.

[0051] The embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0052] A feature learning and data fusion gas film cooling prediction method based on a neural operator includes the following steps:

[0053] Step 1: First, determine the mathematical representation of the variable by parameterizing the hole distribution and blowing ratio conditions, combine the Latin hypercube sampling method, and randomly generate 70 different plate gas film hole distribution point cloud data (part of the sample is shown in Figure 1 The point cloud data is used to automatically model using the ug software, and different geometric models are generated, in which the hole diameter is 1mm, the inclination angle is 30°, and the number of holes is randomly generated in the range of 10-15. According to the generated geometric model, the fluent meshing software is used to automatically draw the grid, and the fluent software is used to automatically calculate combined with different blowing ratio conditions. As shown in Figure 2 The model's cold and hot gas flow inlet and outlet and geometric shape are labeled, Figure 3 The full-surface temperature distribution diagram of the 70 samples is shown in

[0054] Step 2: As shown in Figure 4 The surface adiabatic cooling efficiency data is extracted as output data, the surface geometric data is drawn as input data, and the adiabatic cooling efficiency formula is calculated according to the temperature as shown below:

[0055]

[0056] Where T m Indicates the mainstream inlet temperature, T c T represents the inlet temperature of the cold airflow. w This indicates the temperature of the cooling wall surface.

[0057] Step 3: Set the total number of samples to 70. Read the input and output data from Step 2, label them, and divide them into training and test sets. The training set contains 60 samples, and the test set contains 10 samples.

[0058] Step 4: Build an iterative neural operator framework based on FNO. Figure 5 Based on the operator framework diagram of FNO, the model expression of the FNO operator is shown below:

[0059] v t (x)=σ(W*v t-1 (x)+∫ D k(x, y, a(x), a(y))*v x (dy))

[0060] Where v t The FNO operator model represents the spatial diffusion process, with inlet temperature distribution data, σ representing the activation function, W representing the linear transformation of the predicted values ​​between two adjacent diffusion steps, k representing the Fourier transform and inverse transform processes, and a representing the boundary conditions. Therefore, the overall FNO operator model can represent the spatial diffusion evolution process.

[0061] like Figure 6 As shown, an iterative neural operator framework based on FNO is constructed to simulate the operator solution process, predict the evolution of film cooling, obtain a training model, and learn the characteristics of film cooling. Initial values ​​and boundary conditions (geometric and blowing ratio conditions) are input blankly. The data passes through multiple FNO modules until the prediction results stabilize, at which point the loop stops. In the prediction of steady-state results, this iterative process represents the convergence of the operator space solution results. The blank initial values ​​gradually change to accurate prediction results. The hyperparameter of the iteration count in this invention was tested for 5, 10, and 20 iterations. It was ultimately found that five iterations basically reached stability (e.g., ...). Figure 7 (As shown). By combining the FNO operator and the iterative process, the spatial diffusion and the process of solving the operator solution for convergence were simulated, thus obtaining accurate prediction results.

[0062] Input and output data are imported, standardized, and randomly shuffled before computation within the model framework. Mini-batch stochastic gradient descent is used with a batch size of 8. Model error is calculated via forward propagation, and model parameters are updated via backpropagation. Training stops once the loss stabilizes. Each training iteration takes approximately 1.6 seconds, and the loss function stops decreasing after 100 training iterations.

[0063] Step 5: input the input set data of the test set into the trained model, verify the model with the output set data of the test set, obtain the prediction model, and compare the prediction results (such as Figures 8 to 11 ).

[0064] Step 6: input the blowing ratio, geometric condition and film cooling data of the new sample into the prediction model, use the data fusion method, and predict the complete film cooling distribution with the scatter point data as the constraint. The comparison between the basic 70 sample working conditions and the working conditions of the new sample is as follows:

[0065]

[0066] The geometric model of the new sample is shown in Figure 12 , the characteristic learning model is saved, most of the parameters in the characteristic learning model are frozen, other parameters remain unchanged, and the last two layers of parameters of the model are thawed layer by layer. Take the geometric condition and blowing ratio condition of the new sample as input, and the scatter point data as supervision value (as shown in Figure 13 , only 5% of the total point ratio of the scatter point, generated by a random function), constrain the prediction result, retrain the last two layers of parameters. When the loss function calculation result is stable, the prediction result is output, that is, the complete film cooling distribution result in the new sample, as shown in Figure 14 , which realizes the function of predicting the complete film cooling distribution from the scatter point data of a single sample.

[0067] The present application learns the adiabatic film cooling distribution characteristics through the characteristic learning of the classical example. At the same time, the learned characteristics and the sparse point array data of a single sample are fused by using the data fusion method to predict the film cooling distribution under different conditions, which solves the problem of efficiently, quickly and accurately predicting the film cooling distribution from the sparse point array data of a single sample.

Claims

1. A method for predicting film cooling based on feature learning and data fusion using neural operators, characterized in that, Includes the following steps: Step 1: Obtain the basic dataset for feature learning. By parameterizing the hole distribution and blowing ratio conditions, establish different geometric models and perform calculations to obtain surface temperature distribution data. Step 2: Extract the surface adiabatic cooling efficiency data as output data, and plot the surface geometry data as input data. The formula for calculating the adiabatic cooling efficiency based on the wall temperature is shown below: Where T m Indicates the mainstream inlet temperature, T c T represents the inlet temperature of the cold airflow. w Indicates the temperature of the cooled wall surface; Step 3: Set the total number of samples, read the input and output data from Step 2, label them, and divide them into training and test sets; Step 4: Build an iterative neural operator framework based on FNO, simulate the operator solution process, predict the evolution process of film cooling, obtain a training model, and learn the characteristics of film cooling. Step 5: Input the input set data of the test set into the training model, use the output set data of the test set to validate the model, obtain the prediction model, and compare the prediction results; Step 6: Input the air-blowing ratio, geometric conditions, and film cooling data scatter points of the new sample into the prediction model, and use the data fusion method with the scatter point data as constraints to predict the complete film cooling distribution.

2. The air film cooling prediction method based on neural operator feature learning and data fusion according to claim 1, characterized in that, The specific steps to obtain the basic dataset in Step 1 include: Step 1-1: The total number of samples is 70. The Latin hypercube sampling method is used to randomly generate 70 different sets of point cloud data of pore distribution of flat plate air film, and 70 sets of blowing ratio conditions are also randomly generated. Steps 1-2: Use UG software to perform automated modeling based on point cloud data to generate different geometric models; Steps 1-3: Use Fluent meshing software to automatically draw the mesh based on the generated geometric model, and use Fluent software to automatically calculate based on different wind ratio conditions; Steps 1-4: Extract the surface temperature distribution into a txt file based on the calculation results.

3. The air film cooling prediction method based on neural operator feature learning and data fusion according to claim 1, characterized in that, The specific training steps in step 4 include: Step 4-1: Build an iterative neural operator framework based on FNO. The model expression of the FNO operator is shown below: Where v t The FNO operator model represents the spatial diffusion evolution process, where σ represents the inlet temperature distribution data for different diffusion processes, W represents the linear transformation part of the predicted value between two adjacent diffusion processes, k represents the Fourier transform and inverse transform process, and a represents the boundary condition. Step 4-2: Input blank initial values ​​and boundary conditions. The data passes through multiple sets of FNO modules until the prediction results tend to stabilize, and then the loop stops. In the prediction of steady-state results, this iterative process represents the convergence process of the operator space solution results. The blank initial values ​​gradually change into accurate prediction results. Combining the FNO operator and the iterative process, the spatial diffusion and the process of solving the convergent operator solution are simulated, thereby obtaining accurate prediction results. Step 4-3: Import input and output data, perform standardization processing, and randomly shuffle the input model framework for calculation; Step 4-4: Use the mini-batch stochastic gradient descent algorithm, set the batch size to 8, calculate the model error through forward propagation, update the model parameters through backpropagation, and stop training after the loss stabilizes.

4. The air film cooling prediction method based on neural operator feature learning and data fusion according to claim 1, characterized in that, The specific steps of fusion in step 6 include: Step 6-1: Save the feature learning model, freeze most of the parameters in the feature learning model, keep other parameters unchanged, and unfreeze the parameters of the last two layers of the model layer by layer. Step 6-2: Using the geometric conditions and wind ratio conditions of the new sample as input, and the scatter data as supervision values, constrain the prediction results and retrain the parameters of the last two layers. Step 6-3: After the loss stabilizes, output the prediction result, that is, the complete gas film cooling distribution result in the new sample, thereby realizing the function of predicting the complete gas film cooling distribution from the scatter data of a single sample.

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