Supersonic three-hole probe data calibration method based on transfer learning theory

Abstract

The invention discloses a supersonic probe calibration method of a multi-fidelity transfer learning algorithm based on an empirical curve, and belongs to the technical field of aerodynamic performance testing. According to the method, based on a low-fidelity data set constructed by rich numerical simulation and expert experience and a small amount of high-fidelity data obtained based on pneumatic testing, data which is obtained by numerical simulation and conforms to physical rules are migrated to a probe of real data calibrated by a multi-degree-of-freedom probe in a standard wind tunnel by utilizing a transfer learning theory; and establishing a multi-fidelity neural network with generalization for predicting calibration parameters of the supersonic probe. According to the method, low-fidelity simulation data and high-fidelity test data are combined, a multi-fidelity transfer learning algorithm is utilized, a large amount of experimental data and time needed by a traditional calibration method are remarkably reduced, and therefore the efficiency of supersonic probe data calibration is improved. Through the transfer learning technology, the calibration model not only has good performance under specific conditions, but also can adapt to different flow field conditions, and the generalization ability of the model is enhanced.

Description

Technical Field

[0001] The invention relates to the technical field of fine testing of turbine engine impeller machinery, and relates to a supersonic three-hole pneumatic probe rapid calibration method based on experience curve and transfer learning technology. Background Art

[0002] The supersonic three-hole probe is a measurement tool commonly used in pneumatics and fluid dynamics. It is widely used in aerodynamics, fluid mechanics and other fields to measure fluid velocity, pressure and other parameters. Due to the complex flow characteristics of the internal channels of the impeller machinery, the directional calibration method has great limitations. In order to ensure the accuracy of the measurement data, the supersonic three-hole probe needs to be calibrated non-directionally before actual measurement. Non-directional calibration refers to obtaining the calibration results of the probe through indirect methods, which usually does not directly rely on standard fluids or known flow field conditions.

[0003] At present, traditional probe data calibration processing methods usually rely on complex test equipment and a large amount of test sample data for interpolation fitting to establish the mapping relationship between the pressure of each hole of the probe and the actual flow field parameters under various working conditions. This interpolation method is not only time-consuming and costly, but also in practical applications, due to changes in flow field conditions, the generalization of the calibration results may not be guaranteed. Summary of the invention

[0004] In order to solve the problems existing in the prior art, the present invention provides a supersonic three-hole probe data calibration method based on transfer learning theory. Through simulation and transfer learning technology, the demand for physical resources such as wind tunnel tests is reduced, and the consumption of experimental resources is reduced. The existing simulation data and a small amount of experimental data are fully utilized, the utilization rate of data is improved, and the data calibration process is made more efficient.

[0005] The technical solution adopted to achieve the purpose of the present invention is: a supersonic probe data calibration method based on a multi-fidelity transfer learning algorithm, comprising the following steps:

[0006] Step 1 simplifies the physical model of the three-hole probe, sets up the numerical simulation and obtains simulation data, and constructs a low-fidelity data set with physical laws.

[0007] Step 2 is to conduct a three-hole probe calibration test, set the incoming flow Mach number, and collect pressure data at different deflection angles.

[0008] Step 3: Obtain data based on numerical simulation and experiments, and establish a transfer learning theory that conforms to the laws of physics.

[0009] Step 4: Based on the transfer learning model, a transfer variable fidelity agent model based on physical laws is established.

[0010] Step 5 verifies the accuracy of the variable-fidelity proxy model based on the test set.

[0011] The method specifically comprises the following steps:

[0012] Step 1: Simplify the physical model of the three-hole probe, set up the numerical simulation and obtain simulation data, and construct a low-fidelity data set with physical laws; specifically, it includes the simplification of the physical model of the three-hole probe, numerical simulation and parameter setting, the establishment of a low-fidelity data set, and the processing of low-fidelity simulation data;

[0013] Step 1.1: simplifying the physical model of the three-hole probe, wherein the three-hole probe uses a probe support rod (1) to support a head support rod (3), and a wedge-shaped probe head (2) is arranged on the head support rod (3); a pressure measuring middle hole (4), a pressure measuring left hole (5) and a pressure measuring right hole (6) are arranged on the end surface of the probe head (2); simplifying the three-hole pressure measuring probe, and simplifying the physical structure of the wedge-shaped probe head (2) into a combination of an equilateral triangle and a rectangle for subsequent numerical simulation;

[0014] Step 1.2: Numerical simulation and parameter setting, by setting the incoming flow Mach number to achieve the total inlet pressure P t The aerodynamic parameters are regulated by setting the proportion of the flow direction in the X direction and the Y direction, and regulating the angle between the incoming flow velocity and the simulation model, i.e., the deflection angle β. The range of the deflection angle is [-βm ,βm ];

[0015] Step 1.3: Establish a low-fidelity data set, conduct numerical simulations under different Mach number settings, record the distribution law of the simplified model flow field of the probe under different deflection angles β, obtain the numerical simulation results of the probe pressure hole layout area in the calibration flow field, and record the pressure of the left pressure hole (5) under different working conditions. , Pressure measuring center hole (4) pressure And the pressure of the right hole (6) , Total inflow pressure , static pressure of incoming flow and the distribution of the deflection angle β set by the simulation; generate the calculation condition matrix of the simplified model with different Mach numbers and different deflection angles, carry out numerical simulation and generate a data set; the data set is defined as a low-fidelity data set;

[0016] Step 1.4: Processing of low-fidelity simulation data: Use dimensionless calibration coefficients to simplify the calibration data, reflecting the regularity between the pressure at the monitoring point of the numerical simulation model and the total pressure, static pressure and airflow deflection angle of the incoming flow. Substitute the pressure data into equations (1), (2) and (3) to obtain the total pressure calibration coefficient, static pressure coefficient and angle coefficient. The specific dimensionless calibration coefficient is defined as follows:

[0017] Total pressure calibration factor:

[0018] (1)

[0019] Static pressure coefficient:

[0020] (2)

[0021] Angle factor:

[0022] (3)

[0023] In the formula, is the total incoming flow pressure, is the static pressure of the incoming flow;

[0024] Step 2: Conduct a three-hole probe calibration test, set the incoming flow Mach number, and collect pressure data at different deflection angles;

[0025] A three-hole probe calibration test is conducted. Based on the calculation condition matrix in the low-fidelity data set, random sampling is performed to generate the incoming flow Mach number Ma and the angle β between the probe and the incoming flow required for the three-hole probe calibration test, and the calibration test condition matrix is ​​set; during the test, the aerodynamic test calibration of different angles at the same Mach number is completed in sequence; during the calibration process, the three-hole probe under different test conditions is recorded, and the pressure of the left hole (5) is measured. , Pressure measuring center hole (4) pressure And the pressure of the right hole (6) And the total pressure of the incoming flow , static pressure The data set obtained by the pneumatic calibration of the real three-hole probe is defined as the high-fidelity data set;

[0026] Step 3: Based on the data obtained from numerical simulation and experiments, establish a transfer learning theory that conforms to the laws of physics, including the division and preprocessing of data sets, the pre-training stage, and the physical transfer law stage;

[0027] Step 3.1: Dataset division and preprocessing: The high-precision dataset obtained by calibration is divided into a training set and a test set. The training set is used to fine-tune the pre-trained model, and the test set is used to compare the results predicted by the migration model, calculate the relative error, and evaluate the model prediction effect.

[0028] Step 3.2: Pre-training stage, low-fidelity data feature learning, input and output settings: set the airflow deflection angle to , the calibration coefficient is set to ; Using low-fidelity data ( , ) Perform preliminary training on the model, use the neural network to preprocess the data of the calibration coefficients to learn the characteristic trend of the target data; initialize the neural network: set 1 neuron in the input layer, n neurons in the hidden layer, m hidden layers, and 1 neuron in the output layer;

[0029] Loss function calculation:

[0030]

[0031] in, is the number of low-fidelity samples, Indicated by the parameter The neural network model defined, For the pre-training phase Parameters;

[0032]

[0033] Use the Adam optimization algorithm and set the initial learning rate =lr, and set weight decay weight_decay to prevent overfitting;

[0034] Step 3.3: Use high-fidelity data to adjust neural network parameters in the physical migration law stage. Input and output settings: Divide the high-fidelity data set into a training set and a test set, and use the training set data to input x hi and output y hi Use neural networks to fine-tune pre-trained models;

[0035] Mean square error loss function calculation:

[0036]

[0037] in is the number of high-fidelity samples, For this fine-tuning phase Parameters;

[0038]

[0039] is the learning rate for high-fidelity samples, used to fine-tune a good initialization obtained from pre-training;

[0040] Step 4: Based on the transfer learning model, a variable-fidelity proxy model based on physical law migration is established, including the low-fidelity data and its derivative information training model model_h, the construction of a hybrid model that integrates high-fidelity and low-fidelity data, and the joint training model;

[0041] Step 4.1: Train the model model_h with low-fidelity data and its derivative information, reinitialize model_h, and train it with low-fidelity data and its derivative information; define a loss function that comprehensively considers prediction error and gradient matching:

[0042]

[0043] is the prediction error term, expressed as:

[0044]

[0045] in, Indicates that low-quality data input is used in this stage. For the corresponding output, For this time Parameters;

[0046] is the gradient matching term, expressed as:

[0047]

[0048] in,

[0049] is a learnable parameter that balances the contribution between prediction error and gradient matching;

[0050]

[0051] The learning rate for this training phase is used to update Parameters ;

[0052] Step 4.2: Build a hybrid model that integrates high-fidelity and low-fidelity data, define two new models model3 and model4, and combine them with the pre-trained model_h; the specific hybrid model is:

[0053]

[0054] in: represents the high-fidelity data input used in this stage, They are the neural network models defined by model3 and model4 respectively. is a learnable parameter that controls the ratio of the two model outputs;

[0055] Step 4.3: Joint training model, constructing a joint loss function during training:

[0056]

[0057] in,

[0058] The loss function for high-fidelity data is defined as:

[0059]

[0060] It is a loss function based on low-fidelity data and its derivative information;

[0061] Weight update rule:

[0062]

[0063]

[0064]

[0065]

[0066] in, Joint training phase Parameters, is the learning rate, and It is divided into updating the parameters of model3 and model4;

[0067] In each training iteration, model_h is used to make predictions on low-fidelity data, and the difference between the predicted value and the actual value is calculated as part of the loss; model3 and model4 are used to make predictions on high-fidelity data, and trainable parameters are combined The weighted fusion is performed; the weighted prediction result is used to calculate the difference between the actual high-fidelity output and the actual high-fidelity output as the other part of the loss; the two parts of the loss are added to obtain the total loss value, and all model parameters and learnable parameter;

[0068] Step 5: Verify the accuracy of the variable-fidelity proxy model based on the test set:

[0069] The final predicted exported results are compared with the results in the test set to calculate the corresponding relative error; if the performance of the model meets the preset accuracy requirements, it can be used in practical applications; if the performance of the model does not meet the preset accuracy requirements, it is necessary to re-perform the three-hole probe pneumatic calibration to collect high-fidelity data, and re-divide the data set to retrain the model.

[0070] The beneficial effects of the present invention are:

[0071] This method is mainly based on a low-fidelity data set constructed by rich numerical simulation and expert experience and a small amount of high-fidelity data obtained from aerodynamic tests. The data obtained by numerical simulation that conforms to physical laws are transferred to the probe of real data of multi-degree-of-freedom probe calibration in a standard wind tunnel using transfer learning theory, and a generalized multi-fidelity neural network is established to predict the calibration parameters of supersonic probes. First, the flow calculation and analysis area of ​​the probe pressure measurement area is determined, and numerical calculations are performed; secondly, the law of probe pressure change is determined based on the numerical simulation results, and the low-fidelity data obtained by numerical simulation is used to pre-train the model to learn the characteristics of low-precision data, so that the model learns the basic relationship and pattern between input data and output data, so that it has a basic understanding of the characteristics of the target data. Then, in view of the individual differences of supersonic probes caused by materials, processing, etc., the model that has learned that the low-precision data characteristics conform to physical laws is adjusted based on a small amount of calibration data, so that the model is more adapted to the characteristics of high-fidelity data and improves the prediction performance of the model on high-fidelity tasks. Finally, the transfer learning part provides a good foundation for the subsequent training of the multi-fidelity model, and the multi-fidelity proxy model is used to make the final prediction of the target data. By combining low-fidelity simulation data and high-fidelity test data, the present invention uses a multi-fidelity transfer learning algorithm to significantly reduce the large amount of experimental data and time required for traditional calibration methods, thereby improving the efficiency of supersonic probe data calibration. Through transfer learning technology, the calibration model not only performs well under specific conditions, but also can adapt to different flow field conditions, enhancing the generalization ability of the model.

[0072] Transfer learning can transfer the knowledge of an existing model in one field to another field to reduce the need for a large number of experimental samples. Using the idea of ​​transfer learning, the amount of experimental data required for the calibration of the supersonic three-hole probe can be reduced by training in an existing data set, while improving its adaptability under new conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 is a flow chart of the method.

[0074] Figure 2 It is a schematic diagram of the structure of a three-hole pressure probe.

[0075] Figure 3 yes Figure 2 Right side view of the probe head.

[0076] Figure 4 It is the angle definition of supersonic three-hole probe.

[0077] Figure 5 This is the mesh of the simplified model of the supersonic three-hole probe pressure measurement area.

[0078] Figure 6 It is a numerical simulation pressure cloud diagram of the airflow deviation angle of 25 degrees in the supersonic three-hole probe pressure measurement area.

[0079] Figure 7 It is the simulation data of supersonic probe total pressure calibration coefficient and the aerodynamic calibration data result.

[0080] Figure 8 It is a polynomial fit calibration curve of a small amount of calibration data.

[0081] Fig. 9 This is the total pressure prediction curve at 1.387Ma calibrated by the supersonic probe based on transfer learning.

[0082] Fig.10 This is the total pressure prediction curve at 0.6Ma calibrated by the supersonic probe based on transfer learning.

[0083] Fig.11 It is the prediction curve of the supersonic probe calibration angle coefficient based on transfer learning.

[0084] Fig.12 It is a static pressure prediction curve of supersonic probe calibration based on transfer learning. DETAILED DESCRIPTION

[0085] Example: The calibration process of a certain supersonic three-hole probe is as follows:

[0086] Step 1: Determine the construction of a low-fidelity data set with physical laws, including simplification of the three-hole probe physical model, numerical simulation and parameter setting, establishment of a low-fidelity data set, and processing of low-fidelity simulation data.

[0087] Step 1.1: Simplify the physical model of the three-hole probe. The three-hole probe captures the flow field characteristics based on the pressure difference principle (such as Figure 2 , Figure 3 As shown in the figure, its main structure includes a probe support rod 1, a probe head 2, a head support rod 3, a pressure measuring middle hole 4, a pressure measuring left hole 5, a pressure measuring right hole 6, a pressure lead pipe channel 7, and a pressure lead pipe 8. Different probe head structural designs and pressure measuring hole position arrangements have a great influence on the measurement results. In order to obtain this physical law, the three-hole pressure measuring probe is simplified, and the physical structure of the wedge-type probe head is simplified to a combination of an equilateral triangle and a rectangle for subsequent numerical simulation.

[0088] Step 1.2: Numerical simulation and parameter setting. The calculation area is set to 300 to 500 times the model size to ensure the full development of flow characteristics. The inlet boundary condition is set to the pressure far field, and the inlet total pressure P is achieved by setting the incoming flow Mach number. tThe aerodynamic parameters are regulated by setting the proportion of the flow direction in the X direction and the Y direction to regulate the angle between the incoming flow velocity and the simulation model, also known as the deflection angle β. The deflection angle range is [-21°, 21°].

[0089] Step 1.3: Establish a low-fidelity data set, carry out numerical simulation under different settings of the incoming flow Mach number, record the distribution law of the simplified model flow field of the probe under different deflection angles β, obtain the numerical simulation results of the probe pressure measuring hole arrangement area in the calibration flow field, and record the pressure of the left pressure measuring hole 5 under different working conditions. , Pressure measuring center hole 4 pressure And measure the pressure of right hole 6 , Total inflow pressure , static pressure of incoming flow And the distribution of the deflection angle β set in the simulation. Generate the calculation condition matrix of different Mach numbers and different deflection angles of the simplified model, carry out numerical simulation and generate a data set. Due to the difference between the simplified model and the real three-hole probe model, this data set is defined as a low-fidelity data set, and the data in the data set are uniformly represented by the subscript lo.

[0090] Step 1.4: Processing of low-fidelity simulation data. Based on the numerical simulation of the simplified model of the probe probe area in step 1.3, the probe pressure and the characteristic parameters of the corresponding simulated flow field are known. The dimensionless calibration coefficient is used to simplify the calibration data to reflect the regularity between the measuring point pressure at the monitoring point of the numerical simulation model and the total pressure, static pressure and airflow deflection angle of the incoming flow. Substituting the pressure data into equations (1), (2) and (3) can obtain the total pressure calibration coefficient, static pressure coefficient and angle coefficient. The specific dimensionless calibration coefficient is defined as follows:

[0091] Total pressure calibration factor:

[0092] (1)

[0093] Static pressure coefficient:

[0094] (2)

[0095] Angle factor:

[0096] (3)

[0097] In the formula, is the total incoming flow pressure, The static pressure of the incoming flow.

[0098] Step 2: Conduct a three-hole probe calibration test. During the probe calibration test, the measurement position of the three-hole probe is located downstream of the calibration wind tunnel. To reduce the test cost and time, based on the calculation condition matrix in the low-fidelity data set in step 1.3, random sampling is performed to generate the incoming flow Mach number Ma and the angle β between the probe and the incoming flow required for the three-hole probe calibration test, and the calibration test condition matrix is ​​set. During the test, the aerodynamic test calibrations at different angles at the same Mach number are completed in sequence. During the calibration process, the three-hole probe under different test conditions is recorded, and the pressure of the left hole 5 is measured. , Pressure measuring center hole 4 pressure And measure the pressure of right hole 6 And the total pressure of the incoming flow , static pressure Before each calibration, it is necessary to verify whether the pressure values ​​of the upper and lower pressure measuring holes are consistent when the probe is horizontal at zero degrees, and to repair the probes with inconsistent pressure values ​​of the upper and lower pressure measuring holes. The data set obtained by the pneumatic calibration of the real three-hole probe is defined as a high-fidelity data set, and the data in this data set are uniformly represented by hi.

[0099] Table 1 Pneumatic test results

[0100]

[0101] Table 2 High-precision calibration coefficients

[0102]

[0103] Step 3: Transfer of physical laws, including the division and preprocessing of the data set, the pre-training (learning low-fidelity data features) stage, and the physical law transfer (adjusting neural network parameters using high-fidelity data) stage.

[0104] Step 3.1: Dataset division and preprocessing: divide the high-precision data set obtained by calibration into training set and test set. Select X% of the high-precision data as the training set to fine-tune the pre-trained model to improve its accuracy and efficiency in data calibration. The remaining (1-X)% is used as the test set to compare with the results predicted by the migration model, calculate the relative error, and evaluate the model prediction effect. , total pressure coefficient and static pressure coefficient The data is amplified to enhance the model's ability to learn key features.

[0105] Step 3.2: Pre-training (low-fidelity data feature learning) stage, input and output settings: Set the airflow deflection angle to , the calibration coefficient is set to . Using low-fidelity data ( , ) Perform preliminary training on the model and use the neural network to preprocess the data of the calibration coefficients to learn the characteristic trends of the target data. The main steps of neural network initialization include setting 1 neuron in the input layer, 50 neurons in the hidden layer, 6 hidden layers, and 1 neuron in the output layer.

[0106] Loss function calculation:

[0107]

[0108] in, is the number of low-fidelity samples, Indicated by the parameter , For the pre-training phase Parameters;

[0109]

[0110] Use the Adam optimization algorithm and set the initial learning rate =lr=1e-3, and weight decay (L2 regularization) weight_decay is set to 1e-3 to prevent overfitting. Based on the test data recorded by S1, the dimensionless coefficients obtained by supersonic probe calibration are calculated according to equations (1) to (3);

[0111] Step 3.3: In the physical migration law stage, use high-fidelity data to adjust the neural network parameter input and output settings: divide the high-fidelity data into training set and test set, select X% of high-precision data as the training set, and use the training set data to input x hi and output y hi Fine-tune the pre-trained model using a neural network.

[0112] Mean square error loss function calculation:

[0113]

[0114] in, is the number of high-fidelity samples, For this fine-tuning phase Parameters;

[0115]

[0116] is the learning rate for high-fidelity samples used for fine-tuning to avoid the good initialization obtained by pre-training

[0117] Setting the learning rate lr to 1e-4 and keeping the weight decay weight_decay to 1e-4 helps to fine-tune the pre-trained model parameters and improve its accuracy and efficiency in data calibration. The remaining (1-X)% is used as a test set to evaluate the prediction accuracy and generalization ability of the multi-fidelity model.

[0118] Step 4: Establish a variable-fidelity proxy model based on physical law migration, including training the model model_h with low-fidelity data and its derivative information, building a hybrid model that integrates high- and low-fidelity data, and jointly training the model.

[0119] Step 4.1: Training model model_h with low-fidelity data and its derivative information, reinitialize model_h and train it with low-fidelity data and its derivative information. At this stage, we define a loss function that takes into account prediction error and gradient matching:

[0120]

[0121] in

[0122] is the prediction error term, expressed as:

[0123]

[0124] in, Indicates that low-quality data input is used in this stage. For the corresponding output, For this time Parameters;

[0125] is the gradient matching term, expressed as:

[0126]

[0127] in,

[0128] ;

[0129]

[0130] The learning rate for this training phase is used to update Parameters ;

[0131] In this way, we not only consider the low-fidelity data points themselves, but also introduce their derivative information to enhance the learning effect of the model.

[0132] Step 4.2: Build a hybrid model that fuses high-fidelity and low-fidelity data. In order to better fuse the information of high-fidelity and low-fidelity data, two new models model3 and model4 are defined. These two models will be used to process additional information from high-fidelity data and combine with the pre-trained model_h. Specifically, we designed a hybrid model output:

[0133]

[0134] in: represents the high-fidelity data input used in this stage, They are the neural network models defined by model3 and model4 respectively. is a learnable parameter that controls the ratio of the two model outputs;

[0135] Step 4.3: Joint training model, we use a model containing model3, model4 and model_h and trainable parameters The joint loss function is constructed during the training process:

[0136]

[0137] in,

[0138] The loss function for high-fidelity data is defined as:

[0139]

[0140] It is a loss function based on low-fidelity data and its derivative information;

[0141] Weight update rule:

[0142]

[0143]

[0144]

[0145]

[0146] in, Joint training phase Parameters, is the learning rate, and It is divided into updating the parameters of model3 and model4;

[0147] In each training iteration, we first use model_h to predict the low-fidelity data and calculate the difference between the predicted value and the actual value as part of the loss. This part of the loss reflects the performance of the model on the low-fidelity data and includes considerations of prediction error and gradient matching. Next, we use model3 and model4 to predict the high-fidelity data and perform weighted fusion with the trainable parameter alpha. The weighted prediction result is used to calculate the difference with the actual high-fidelity output as another part of the loss. Finally, we add these two parts of the loss to obtain the total loss value, and update all model parameters and learnable parameters through the back-propagation algorithm. After sufficient training, we use the trained model to make predictions for the entire input range. At this point, the model has learned how to effectively combine the characteristics of high-fidelity and low-fidelity data to provide more accurate and reliable prediction results.

[0148] Step 5: Verify the accuracy of the variable-fidelity proxy model based on the test set, compare the final predicted export results with the results in the test set, and calculate the corresponding relative error. If the performance of the model meets the preset accuracy requirements, it can be used for practical applications. Stop further training and testing cycles, and do not apply the model to actual scenarios. If the performance of the model does not meet the preset accuracy requirements, it is necessary to recalibrate the wind tunnel platform to carry out supersonic probe aerodynamic test calibration, take high-precision data, and re-divide the data set to retrain the model.

[0149] Table 3 Model prediction results and relative errors

[0150]

[0151] The above comparison between the present invention and polynomial fitting based on the same high-fidelity data sample yields a comparison of the results. Figure 8 and Fig. 9 As shown, it is obvious that the prediction effect of the present invention is more accurate, and the time cost of the present invention is one-third of that of the polynomial fitting, showing and describing the basic principles and main features of the present invention and the advantages of the present invention. For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive, and the scope of the present invention is defined by the attached claims rather than the above description, so it is intended to include all changes within the meaning and scope of the equivalent elements of the claims in the present invention. Any figure mark in the claims should not be regarded as limiting the claims involved.

[0152] The above contents are further detailed descriptions of the present invention in combination with specific preferred technical solutions, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the protection scope of the present invention.

[0153] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the attached claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention. Any figure mark in the claims should not be regarded as limiting the claims involved.

[0154] The above contents are further detailed descriptions of the present invention in combination with specific preferred technical solutions, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the protection scope of the present invention.

Claims

1. A method for supersonic probe data calibration based on a multi-fidelity transfer learning algorithm, characterized in that: The steps include: Step 1: Simplify the physical model of the three-hole probe, set up the numerical simulation and obtain simulation data, and construct a low-fidelity data set with physical laws; specifically, it includes the simplification of the physical model of the three-hole probe, numerical simulation and parameter setting, the establishment of a low-fidelity data set, and the processing of low-fidelity simulation data; Step 1.1: simplifying the physical model of the three-hole probe, wherein the three-hole probe uses a probe support rod (1) to support a head support rod (3), and a wedge-shaped probe head (2) is arranged on the head support rod (3); a pressure measuring middle hole (4), a pressure measuring left hole (5) and a pressure measuring right hole (6) are arranged on the end surface of the probe head (2); simplifying the three-hole pressure measuring probe, and simplifying the physical structure of the wedge-shaped probe head (2) into a combination of an equilateral triangle and a rectangle for subsequent numerical simulation; Step 1.2: Numerical simulation and parameter setting, by setting the incoming flow Mach number to achieve the total inlet pressure P t The aerodynamic parameters are regulated by setting the proportion of the flow direction in the X direction and the Y direction, and regulating the angle between the incoming flow velocity and the simulation model, i.e., the deflection angle β. The range of the deflection angle is [-βm ,βm ]; Step 1.3: Establish a low-fidelity data set, conduct numerical simulations under different Mach number settings, record the distribution law of the simplified model flow field of the probe under different deflection angles β, obtain the numerical simulation results of the probe pressure hole layout area in the calibration flow field, and record the pressure of the left pressure hole (5) under different working conditions. , Pressure measuring center hole (4) pressure And the pressure of the right hole (6) , Total inflow pressure , static pressure of incoming flow and the distribution of the deflection angle β set by the simulation; Generate the calculation condition matrix of the simplified model with different Mach numbers and different deflection angles, carry out numerical simulation and generate a data set; the data set is defined as a low-fidelity data set; Step 1.4: Processing of low-fidelity simulation data: Use dimensionless calibration coefficients to simplify the calibration data, reflecting the regularity between the pressure at the monitoring point of the numerical simulation model and the total pressure, static pressure and airflow deflection angle of the incoming flow. Substitute the pressure data into equations (1), (2) and (3) to obtain the total pressure calibration coefficient, static pressure coefficient and angle coefficient. The specific dimensionless calibration coefficient is defined as follows: Total pressure calibration factor: （1） Static pressure coefficient: （2） Angle factor: （3） In the formula, is the total incoming flow pressure, is the static pressure of the incoming flow; Step 2: Conduct a three-hole probe calibration test, set the incoming flow Mach number, and collect pressure data at different deflection angles; A three-hole probe calibration test is conducted. Based on the calculation condition matrix in the low-fidelity data set, random sampling is performed to generate the incoming flow Mach number Ma and the angle β between the probe and the incoming flow required for the three-hole probe calibration test, and the calibration test condition matrix is ​​set; during the test, the aerodynamic test calibration of different angles at the same Mach number is completed in sequence; during the calibration process, the three-hole probe under different test conditions is recorded, and the pressure of the left hole (5) is measured. , Pressure measuring center hole (4) pressure And the pressure of the right hole (6) And the total pressure of the incoming flow , static pressure The data set obtained by the pneumatic calibration of the real three-hole probe is defined as the high-fidelity data set; Step 3: Based on the data obtained from numerical simulation and experiments, establish a transfer learning theory that conforms to the laws of physics, including the division and preprocessing of data sets, the pre-training stage, and the physical transfer law stage; Step 3.1: Dataset division and preprocessing: The high-precision dataset obtained by calibration is divided into a training set and a test set. The training set is used to fine-tune the pre-trained model, and the test set is used to compare the results predicted by the migration model, calculate the relative error, and evaluate the model prediction effect. Step 3.2: Pre-training stage, low-fidelity data feature learning, input and output settings: set the airflow deflection angle to , the calibration coefficient is set to ; Using low-fidelity data ( , ) Conduct preliminary training on the model and use a neural network to preprocess the data of the calibration coefficients to learn the characteristic trends of the target data; Initialize the neural network: set 1 neuron in the input layer, n neurons in the hidden layer, m hidden layers, and 1 neuron in the output layer; Loss function calculation: ； in, is the number of low-fidelity samples, Indicated by the parameter The neural network model defined, For the pre-training phase Parameters; ； Use the Adam optimization algorithm and set the initial learning rate =lr, and set weight decay weight_decay to prevent overfitting; Step 3.3: In the physical migration law stage, high-fidelity data is used to adjust the neural network parameters and input and output settings: the high-fidelity data set is divided into a training set and a test set, and the training set data input xhi and output yhi are used to adjust the pre-trained model with a neural network; Mean square error loss function calculation: ； in is the number of high-fidelity samples, For this fine-tuning phase Parameters; ； is the learning rate for high-fidelity samples, used to fine-tune a good initialization obtained from pre-training; Step 4: Based on the transfer learning model, a variable-fidelity proxy model based on physical law migration is established, including the low-fidelity data and its derivative information training model model_h, the construction of a hybrid model that integrates high-fidelity and low-fidelity data, and the joint training model; Step 4.1: Train the model model_h with low-fidelity data and its derivative information, reinitialize model_h, and train it with low-fidelity data and its derivative information; define a loss function that comprehensively considers prediction error and gradient matching: ； is the prediction error term, expressed as: ； in, Indicates that low-quality data input is used in this stage. For the corresponding output, For this time Parameters; is the gradient matching term, expressed as: ； in, ; is a learnable parameter that balances the contribution between prediction error and gradient matching; ； The learning rate for this training phase is used to update Parameters ; Step 4.2: Build a hybrid model that integrates high-fidelity and low-fidelity data, define two new models model3 and model4, and combine them with the pre-trained model_h; the specific hybrid model is: ； in: represents the high-fidelity data input used in this stage, They are the neural network models defined by model3 and model4 respectively. is a learnable parameter that controls the ratio of the two model outputs; Step 4.3: Joint training model, constructing a joint loss function during training: ； in, The loss function for high-fidelity data is defined as: ； It is a loss function based on low-fidelity data and its derivative information; Weight update rule: ； ； ； ； in, Joint training phase Parameters, is the learning rate, and It is divided into updating the parameters of model3 and model4; In each training iteration, model_h is used to make predictions on low-fidelity data, and the difference between the predicted value and the actual value is calculated as part of the loss; model3 and model4 are used to make predictions on high-fidelity data, and trainable parameters are combined The weighted fusion is performed; the weighted prediction result is used to calculate the difference between the actual high-fidelity output and the actual high-fidelity output as the other part of the loss; the two parts of the loss are added to obtain the total loss value, and all model parameters and learnable parameter; Step 5: Verify the accuracy of the variable-fidelity proxy model based on the test set: The final predicted exported results are compared with the results in the test set to find the corresponding relative error; if the performance of the model meets the preset accuracy requirements, it can be used in practical applications; if the performance of the model does not meet the preset accuracy requirements, it is necessary to re-perform the three-hole probe pneumatic calibration to collect high-fidelity data, and re-divide the data set to retrain the model.

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