Method and device for back-calculating boundary conditions of turbine cascade test based on sparse measurement data

Abstract

Method and device for back-calculating boundary conditions of turbine cascade test based on sparse measurement data, belonging to the technical field of gas turbine turbine test data processing, and particularly relating to the back-calculation of boundary conditions of cascade test; solving the problems existing in the prior art, such as large computational amount, only focusing on low Reynolds number flow or relatively simple three-dimensional or even two-dimensional flow patterns, and only being able to handle the scenario where the number and position of sensors remain unchanged; the method includes the following steps: a step for obtaining a spatial analysis network structure built based on a self-attention unit and a Transformer encoder; a step for inputting the normalized sparse measurement data into the trained spatial analysis network structure to obtain the corresponding test boundary conditions. The method and device for back-calculating boundary conditions of turbine cascade test based on sparse measurement data are applicable to back-calculating boundary conditions of turbine cascade test.

Description

Technical Field

[0001] The present invention relates to the technical field of gas turbine turbine test data processing, and particularly relates to the back-calculation of boundary conditions for cascade tests. Background Art

[0002] A gas turbine is an important energy conversion device and plays a very crucial role in aviation power, ship propulsion, ground power generation, and other industrial fields. The compressor, turbine, and combustion chamber are the three main components of a gas turbine. To meet the performance requirements of a new generation of gas turbines, each component must be carefully designed to improve thermal efficiency and reduce emissions of greenhouse gases such as carbon dioxide. In traditional design and optimization processes, a large number of tests and numerical simulations are carried out to evaluate candidate design schemes. Each method has its own advantages and disadvantages. On the one hand, although test data can provide information closer to basic physics, it is usually unable to cover the design parameter domain and the spatial domain of interest due to measurement technology and cost limitations. Therefore, test data usually exhibits low spatio-temporal resolution. On the other hand, numerical simulations are usually used to supplement unperformed tests due to their flexibility. However, achieving high-fidelity simulations requires complex modeling, a large amount of computing resources, and a considerable amount of time investment. Most importantly, accurate boundary conditions are required to match the test environment. To reduce the acquisition cost of high-value data, a method capable of back-calculating test boundary conditions from sparse test data must be developed.

[0003] Existing sparse reconstruction techniques based on limited measurement data include methods based on linear theory and nonlinear methods based on machine learning.

[0004] Linear methods are computationally faster and have strong applicability to most problems. However, linear methods still have some limitations:

[0005] (1) The computational cost required to perform POD in a big data scenario is unaffordable, and at the same time, it limits the space for its continuous update and evolution;

[0006] (2) The process of extracting simplified basis vectors requires that the measurement points must be included in the dataset for constructing the reference basis vectors, which limits the flexibility of the measurement positions;

[0007] (3) The mathematical essence of the POD method is linear operation. When the application involves strong nonlinear dynamics, its accuracy will be challenged.

[0008] Machine learning methods have also been widely applied to improve the ability of the model to handle nonlinear problems.

[0009] Most of the existing technologies focus on low Reynolds number flows (Re < 500), or relatively simple three-dimensional or even two-dimensional flow patterns. However, the internal flow field in turbomachinery usually exhibits complex three-dimensional flow characteristics. The existence of complex wave systems (such as shock waves and expansion waves) leads to the formation of complex pressure and temperature distribution stripes on the surface of turbine blades. In addition, existing technologies usually can only handle scenarios where the number and position of sensors remain unchanged. Summary of the Invention

[0010] The present invention proposes a method and device for back-calculating the boundary conditions of a turbine cascade test based on sparse measurement data, which solves the problems existing in the prior art, such as large computational complexity, only focusing on low Reynolds number flows or relatively simple three-dimensional or even two-dimensional flow patterns, and only being able to handle scenarios where the number and position of sensors remain unchanged.

[0011] The method for back-calculating the boundary conditions of a turbine cascade test based on sparse measurement data according to the present invention has the following technical solutions:

[0012] The method includes the following steps:

[0013] A step for obtaining a spatial analysis network structure built based on a self-attention unit and a Transformer encoder;

[0014] The spatial analysis network structure includes a position encoding module, a multi-layer perceptron, a Transformer encoder, and an average pooling layer, where:

[0015] The multi-head self-attention unit is an improved scaled dot-product attention:

[0016] Given a series of queries Q and key-value pairs K-V, the scaled dot-product attention is calculated using formula (6); where d k is the feature number of the query and the key; the superscript T is the matrix transpose; softmax(·) is a normalization activation function that normalizes the calculated attention scores into a probability distribution with a sum of 1;

[0017]

[0018] In the self-attention calculation, Q, K, and V are the same values;

[0019] For the multi-head self-attention, multiple attention calculations are performed in parallel to capture features from different scales, and the information is aggregated by concatenating the calculation results, as shown in formula (7); where head i is the i-th attention head:

[0020]

[0021] Steps for training the spatial analysis network structure, optimizing model parameters, and calculating the corresponding residuals using the mean square error:

[0022]

[0023] Steps for obtaining the trained spatial analysis network structure:

[0024] Mathematical form description of the trained spatial analysis network structure:

[0025]

[0026] where s is the experimental observation data, is the supervised learning model, θ is the model hyperparameter, is the actual boundary condition, and the superscript * represents the optimal solution;

[0027] Steps for inputting the normalized sparse measurement data into the trained spatial analysis network structure to obtain the corresponding experimental boundary conditions.

[0028] Furthermore, a preferred implementation is provided, where the position encoding module is used for position encoding;

[0029] The position encoding implies relative position encoding and absolute position encoding:

[0030]

[0031] The relative position encoding is used for embedding position information in the spatial domain; the absolute position encoding is used for embedding position information in the feature domain;

[0032] The relative position encoding is implemented through a trigonometric function matrix:

[0033]

[0034] The absolute position encoding stems from the characteristics of binary calculation: the alternating frequency of higher-order numerical values is lower than that of lower-order numerical values. Since the feature vector itself does not have the position information of the Euclidean space, the sequential position of the feature vector is abstractly described with reference to the binary rule;

[0035] The multi-layer perceptron is a series of stacked fully connected layers, which is essentially a continuous linear operation; the parameters of each layer of neurons include the weight matrix and the bias vector where m is the number of neurons in the current layer and n is the size of the input data;

[0036] Let ζ(·) be the activation function, then the output of the neurons in the l-th layer is:

[0037]

[0038] Select the leaky ReLU function, which satisfies the mathematical relationship described as follows:

[0039]

[0040] The Transformer encoder includes 6 identical network blocks; each network block consists of two layer normalizations, a multi-head self-attention unit, and a multi-layer perceptron;

[0041] The average pooling layer is an aggregation function.

[0042] Furthermore, a preferred embodiment is provided, in which the Adam algorithm is used to train the spatial analysis network structure.

[0043] Furthermore, a preferred embodiment is provided, in which the spatial analysis network structure is established based on uniform grid division of the turbine blade surface, and the sampled grid nodes are used as the sensor arrangement positions; at least 32 sampling points are arranged on each of the suction side and the pressure side of the blade.

[0044] Furthermore, a preferred embodiment is provided, in which 128 sampling points are arranged on the suction side of the blade and 256 sampling points are arranged on the pressure side of the blade.

[0045] Furthermore, a preferred embodiment is provided, in the step of training the spatial analysis network structure to optimize the model parameters and calculating the corresponding residuals using the mean square error:

[0046] Adopt the random sampling strategy of adjoint training:

[0047] The sensor positions are re-randomly sampled in each round of training iteration, and each sampling process is independent of each other.

[0048] The present invention also proposes a device for inverse calculation of the test boundary conditions of a turbine cascade based on sparse measurement data, and its technical solution is as follows:

[0049] The device includes the following modules:

[0050] A module for obtaining a spatial analysis network structure built based on a self-attention unit and a Transformer encoder;

[0051] The spatial analysis network structure includes a position encoding module, a multi-layer perceptron, a Transformer encoder, and an average pooling layer, where:

[0052] The multi-head self-attention unit is an improved scaled dot-product attention:

[0053] Given a series of queries Q and key-value pairs K-V, the scaled dot-product attention is calculated using formula (6); where, d kis the number of features of the query and the key; the superscript T is the matrix transpose; softmax(·) is the normalization activation function that normalizes the calculated attention scores into a probability distribution with a sum of 1;

[0054]

[0055] In self-attention calculation, Q, K, and V are the same values;

[0056] For multi-head self-attention, multiple attention calculations are performed in parallel to capture features from different scales, and the information is aggregated by concatenating the calculation results, as shown in Equation (7); where head i is the i-th attention head:

[0057]

[0058] A module for training the spatial analysis network structure, optimizing the model parameters, and calculating the corresponding residuals using the mean squared error:

[0059]

[0060] A module for obtaining the trained spatial analysis network structure:

[0061] Mathematical form description of the trained spatial analysis network structure:

[0062]

[0063] where s is the experimental observation data, is the supervised learning model, θ is the model hyperparameter, is the actual boundary condition, and the superscript * represents the optimal solution;

[0064] A module for inputting the normalized sparse measurement data into the trained spatial analysis network structure to obtain the corresponding experimental boundary condition.

[0065] The present invention also proposes a computer device, and its technical solution is as follows:

[0066] A computer device, including: a processor and a memory, the memory is used to store the executable instructions of the processor, and the processor is configured to execute the above-mentioned method for inverse calculation of the experimental boundary condition of the turbine cascade based on sparse measurement data via executing the executable instructions.

[0067] The present invention also proposes a computer storage medium, and its technical solution is as follows:

[0068] A computer storage medium stores a computer program which, when running, executes the above-mentioned method for inverse calculation of turbine cascade test boundary conditions based on sparse measurement data.

[0069] The present invention also proposes a computer program product, and its technical solution is as follows:

[0070] A computer program product includes computer programs / instructions which, when executed by a processor, implement the steps of the above-mentioned method for inverse calculation of turbine cascade test boundary conditions based on sparse measurement data.

[0071] The present invention has the following beneficial effects:

[0072] 1. For the method for inverse calculation of turbine cascade test boundary conditions based on sparse measurement data of the present invention, the proposed spatial analysis network structure (model) has permutation invariance.

[0073] 2. For the method for inverse calculation of turbine cascade test boundary conditions based on sparse measurement data of the present invention, the random sampling strategy through adjoint training will effectively improve the coverage rate of training data for the sample domain, and improve the generalization and robustness of the model.

[0074] 3. For the method for inverse calculation of turbine cascade test boundary conditions based on sparse measurement data of the present invention, using the supervised learning method in machine learning, a spatial analysis network structure based on the self-attention mechanism is proposed. For the sparse discrete measurement data in the gas turbine turbine cascade test, it can effectively process the data from any number of randomly arranged sensors, and extract key features therefrom to inverse calculate the boundary conditions of the flow.

[0075] 4. The core contribution of the method for inverse calculation of turbine cascade test boundary conditions based on sparse measurement data of the present invention lies in proposing a new architecture applicable to the complex flow field data of gas turbine turbines, a targeted design applicable to any number of randomly arranged sensors, and a training strategy for obtaining the optimal model parameters θ *

[0076] 5. The method for inverse calculation of turbine cascade test boundary conditions based on sparse measurement data of the present invention can be applied to aero-engine and gas turbine turbine blades to extract features from sparse test data and inverse calculate the boundary conditions of the cascade test.

[0077] 6. The method for inverse calculation of turbine cascade test boundary conditions based on sparse measurement data of the present invention can effectively reduce the cost of obtaining high-quality data in the cascade test.

[0078] 7. The method for inverse calculation of the boundary conditions of the turbine cascade test based on sparse measurement data according to the present invention can also provide solutions to key problems in the development process of the digital twin system. The scenario often faced in the operation and maintenance stage of the digital twin system is to evaluate the current operating condition of the unit from limited sensor data. The method can comprehensively process the measurement data of discrete and limited sensors, inverse calculate the current inlet and outlet flow conditions of the unit, assist in evaluating possible operating risks, and provide numerical support for the decision-making of the control system.

[0079] The method and device for inverse calculation of the boundary conditions of the turbine cascade test based on sparse measurement data according to the present invention are applicable to inverse calculation of the boundary conditions of the turbine cascade test. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0081] Figure 1 For an embodiment of the present invention, it is a schematic diagram of the spatial analysis network structure;

[0082] Figure 2 For an embodiment of the present invention, it is a schematic diagram of the relative position encoding principle;

[0083] Figure 3 For an embodiment of the present invention, it is a schematic diagram of the performance of the model (spatial analysis network structure) on the training set;

[0084] Figure 4 For an embodiment of the present invention, it is a schematic diagram of the performance of the model (spatial analysis network structure) on the test set;

[0085] Figure 5 For an embodiment of the present invention, it is the number N of different sensors s A schematic diagram of the influence on the performance of the model (spatial analysis network structure);

[0086] Figure 6 For an embodiment of the present invention, it is the number N of different attention heads h A schematic diagram of the performance of the model (spatial analysis network structure);

[0087] Figure 7 For an embodiment of the present invention, it is a schematic diagram of the data processing method. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0088] To make the technical solutions and advantages of the present invention more clearly described, the following will further describe in detail and completely the specific embodiments of the present invention with reference to the accompanying drawings. The following described various embodiments are only a part of the preferred embodiments of the present invention, rather than all the implementation schemes; each of the following described embodiments is intended to explain the present invention and should not be construed as a limitation of the present invention; the reasonable combination of the technical features defined in each of the embodiments of the present invention, and all other embodiments obtained by those of ordinary skill in the art without creative efforts based on the embodiments of the present invention, fall within the scope of protection of the present invention.

[0089] In one embodiment, a method for back-calculating the test boundary conditions of a turbine cascade based on sparse measurement data is provided:

[0090] The method includes the following steps:

[0091] A step for obtaining a spatial analysis network structure built based on a self-attention unit and a Transformer encoder;

[0092] The spatial analysis network structure includes a position encoding module, a multi-layer perceptron, a Transformer encoder, and an average pooling layer, where:

[0093] The multi-head self-attention unit is an improved scaled dot-product attention:

[0094] Given a series of queries Q and key-value pairs K-V, the scaled dot-product attention is calculated using formula (6); where d k is the number of features of the query and the key; the superscript T is the matrix transpose; softmax(·) is a normalization activation function that normalizes the calculated attention scores into a probability distribution with a sum of 1;

[0095]

[0096] In the self-attention calculation, Q, K, and V are the same values;

[0097] For the multi-head self-attention, multiple attention calculations are performed in parallel to capture features from different scales, and the information is aggregated by concatenating the calculation results, as shown in formula (7); where head i is the i-th attention head:

[0098]

[0099] A step for training the spatial analysis network structure, optimizing the model parameters, and calculating the corresponding residuals using the mean square error;

[0100]

[0101] Steps for obtaining the trained spatial analysis network structure:

[0102] Mathematical form description of the trained spatial analysis network structure:

[0103]

[0104] where s is the experimental observation data, is the supervised learning model, θ is the model hyperparameter, is the actual boundary condition, and the superscript * represents the optimal solution;

[0105] Steps for inputting the normalized sparse measurement data into the trained spatial analysis network structure to obtain the corresponding experimental boundary conditions.

[0106] It should be noted that for any two points with a spatial interval of δ, their position encodings are obtained by mutual conversion through the sum and difference formulas, that is, the position encodings calculated according to Equation (2) naturally contain the relative spatial position information of the two points.

[0107] In this embodiment, the basic structure of the spatial analysis network structure is as Figure 1 shown.

[0108] In this embodiment, the absolute position encoding is as Figure 2 shown.

[0109] In this embodiment, the multi-layer perceptron is an important basic component of the neural network.

[0110] In this embodiment, the structure of each network block is as Figure 1 (c) shown.

[0111] In this embodiment, the multi-head self-attention unit is the core computational component of the encoder.

[0112] It should be emphasized that regardless of the arrangement order of the sparse observations, the calculated boundary conditions should remain unchanged, which is called the permutation invariance of the calculation results. The spatial analysis network structure (model) proposed by the method in this embodiment has permutation invariance, and the following derivation proves this property:

[0113] The input tensor is organized as a matrix where n is the number of sensors, and d is the number of physical quantities measured;

[0114] First, the weights of the multi-layer perceptron are shared for all sensors and naturally have permutation invariance;

[0115] The activation function and regularization operations are essentially scaling operations and are independent of the order of the data;

[0116] Equation (8) proves the permutation invariance of the scaled dot - product attention calculation, where is the observation value of a specific point;

[0117] Finally, the mean - pooling layer is an aggregation function that is independent of the order of the data;

[0118] In summary, it has been proven that the proposed spatial analysis network structure (model) has permutation invariance.

[0119]

[0120] In addition, in one embodiment, the position encoding module is used for position encoding;

[0121] The position encoding implies relative position encoding and absolute position encoding:

[0122]

[0123] The relative position encoding is used for embedding position information in the spatial domain; the absolute position encoding is used for embedding position information in the feature domain;

[0124] The relative position encoding is implemented through a trigonometric function matrix:

[0125]

[0126] The absolute position encoding stems from the characteristics of binary calculation: the alternating frequency of higher - order numerical values is lower than that of lower - order numerical values. Since the feature vector itself does not have position information in Euclidean space, the sequential position of the feature vector is abstractly described with reference to the binary rule;

[0127] The multi - layer perceptron is a series of stacked fully - connected layers, which is essentially a continuous linear operation; the parameters of each layer of neurons include a weight matrix and a bias vector where m is the number of neurons in the current layer and n is the size of the input data;

[0128] Let ζ(·) be the activation function, then the output of the l - th layer of neurons is:

[0129]

[0130] The leaky ReLU function is selected to satisfy the mathematical relationship described as follows:

[0131]

[0132] The Transformer encoder consists of 6 identical network blocks; each network block is composed of two layer normalizations, a multi - head self - attention unit, and a multi - layer perceptron;

[0133] The average pooling layer is an aggregation function.

[0134] In addition, in one embodiment, the Adam algorithm is used to train the spatial analysis network structure.

[0135] In addition, in one embodiment, the spatial analysis network structure is established on the basis of uniformly meshing the surface of the turbine blade, and the sampled grid nodes are used as the sensor layout positions; at least 32 sampling points are arranged on each of the suction side and the pressure side of the blade.

[0136] In addition, in one embodiment, 128 sampling points are arranged on the suction side of the blade and 256 sampling points are arranged on the pressure side of the blade.

[0137] In this embodiment, a total of 128×256 sampling points are arranged. Assuming the number of sensors to be arranged is N s , then the total number of possible selection methods is kinds, which means that the problem to be solved has a very large sample domain.

[0138] In addition, in one embodiment, in the step of training the spatial analysis network structure and optimizing the model parameters by using the mean square error to calculate the corresponding residuals:

[0139] Adopt a random sampling strategy for adjoint training:

[0140] Randomly resample the sensor positions in each round of training iteration, and each sampling process is independent of each other.

[0141] In this embodiment, the random sampling strategy for adjoint training will effectively improve the coverage rate of the training data for the sample domain, and improve the generalization and robustness of the model.

[0142] In this embodiment, the method can also provide solutions to the key problems in the development process of the digital twin system. The scenario often faced in the operation and maintenance stage of the digital twin system is to evaluate the current operating condition of the unit from limited sensor data. The method can comprehensively process the measurement data of the limited discretely arranged sensors, reverse calculate the current inlet and outlet flow conditions of the unit, assist in evaluating the possible operating risks, and provide numerical support for the control system decision-making.

[0143] In this embodiment, the method uses the supervised learning method in machine learning, proposes a spatial analysis network structure based on the self-attention mechanism, and can effectively process the data from any number of randomly arranged sensors for the sparse discrete measurement data in the gas turbine turbine cascade test, and extract key features from it to reverse calculate the boundary conditions of the flow.

[0144] In this embodiment, the core contribution of the method lies in proposing a new architecture applicable to the complex flow field data of gas turbine turbines, a targeted design applicable to any number of randomly arranged sensors, and a training strategy for obtaining the optimal model parameter θ * .

[0145] In addition, in one embodiment, a device for back-calculating the boundary conditions of a turbine cascade test based on sparse measurement data is provided:

[0146] The device includes the following modules:

[0147] A module for obtaining a spatial analysis network structure built based on a self-attention unit and a Transformer encoder;

[0148] The spatial analysis network structure includes a position encoding module, a multi-layer perceptron, a Transformer encoder, and an average pooling layer, where:

[0149] The multi-head self-attention unit is an improved scaled dot-product attention:

[0150] Given a series of queries Q and key-value pairs K-V, the scaled dot-product attention is calculated using formula (6); where d k is the number of features of the query and the key; the superscript T is the matrix transpose; softmax(·) is a normalization activation function that normalizes the calculated attention scores into a probability distribution with a sum of 1;

[0151]

[0152] In self-attention calculation, Q, K, and V are the same values;

[0153] For multi-head self-attention, multiple attention calculations are performed in parallel to capture features from different scales, and the information is aggregated by concatenating the calculation results, as shown in formula (7); where head i is the i-th attention head:

[0154]

[0155] A module for training the spatial analysis network structure, optimizing the model parameters, and calculating the corresponding residuals using the mean square error;

[0156]

[0157] A module for obtaining the trained spatial analysis network structure;

[0158] Mathematical form description of the trained spatial analysis network structure:

[0159]

[0160] where s is the experimental observation data, is the supervised learning model, and θ is the model hyperparameter, is the actual boundary condition, and the superscript * represents the optimal solution;

[0161] A module for inputting the normalized sparse measurement data into the trained spatial analysis network structure to obtain the corresponding experimental boundary conditions.

[0162] In addition, in one embodiment, a specific embodiment of a method for inverse calculation of the experimental boundary conditions of a turbine cascade based on sparse measurement data is provided:

[0163] Step 1, data preparation:

[0164] In practical applications, if targeted training of the network is required, sufficient experimental data should be prepared and data extraction and preprocessing should be carried out.

[0165] First, uniformly distributed sampling points are arranged on the surface of the turbine blade. The surface of the turbine blade is evenly cut into 128 cross-sections along the span direction, and 256 sampling points are evenly arranged on the suction side and the pressure side along the blade profile arc respectively. Starting from the trailing edge of the pressure side, crossing the leading edge line until the trailing edge of the suction side, the three-dimensional blade surface is unfolded into a matrix-like two-dimensional plane. Finally, each complete blade surface field is constructed into an array with a shape of 2×128×512, storing the pressure P and temperature data T on the blade surface.

[0166] Figure 7 shows the process of data extraction. Then, according to the statistical characteristics of the data, the data is normalized based on the following formula:

[0167]

[0168] where μ is the mean value and σ is the standard deviation.

[0169] The preparation of the experimental data should consider the requirements of the proposed spatial analysis network structure. At least 32 measurement sensors should be installed on the suction side and the pressure side respectively. The digitization of the sensor positions should select the closest node relative positions with reference to the 128×512 sampling grid. The experimental measurement data and the boundary conditions are constructed into training and test data sets in one-to-one correspondence.

[0170] Step 2, model training:

[0171] Both the network and the attached code can be written in the Python language and built based on the open-source deep learning framework PaddlePaddle. The network is trained on a computer platform equipped with specific hardware devices. Usually, it is recommended to use the Adam optimizer and use the default parameters.

[0172] Step 3, Performance Verification:

[0173] After the model is completed, the performance of the model on the dataset is evaluated by the mean square error and the relative error.

[0174] Step 4, Model Prediction:

[0175] When the model is completed training, in the prediction phase, only the normalized test data needs to be provided, and the corresponding test boundary conditions can be obtained by importing the model. Among them, the normalization index should adopt the statistical characteristics of the CFD data in the training set.

[0176] In addition, in an embodiment, the performance of the method for inverse calculation of the test boundary conditions of the turbine cascade based on sparse measurement data is verified:

[0177] To evaluate the performance of the proposed model, the mean square error and the relative error are used to evaluate the deviation between the predicted value and the reference value.

[0178]

[0179] The scatter plot shows the overall performance of the model on the training and test datasets to more clearly demonstrate the inversion ability of the spatial analysis network structure (or the spatial analysis model).

[0180] Figure 3 and Figure 4 respectively show the scatter plots of the predicted values and the actual values of the model on the training and test datasets. Due to the different ranges of the angle of attack AOA and the exit isentropic Mach number Ma 2s , the absolute deviation and the relative deviation are respectively used to evaluate the prediction accuracy of the model. In the training set, except for a few outliers, the absolute error between the predicted value and the true value of AOA for most samples is less than ±1°, while the relative error of Ma 2s prediction is less than ±2%. The model shows a prediction accuracy comparable to that of the training set in the test, confirming the good generalization ability of the proposed method.

[0181] Figure 5 shows the curves of the mean square error and the relative error under different numbers of sensors N s . As N s decreases, the prediction error shows a significant upward trend. It is worth noting that when N s changes from 32 to 16, both the mean square error and the relative error increase sharply. For the case of N s > 32, the mean square error is below 10 -3 , the relative error is below 2%, and the average relative error is below 0.5%. However, when N s < 32, the average mean square error increases to 10 -3Magnitude, and the maximum mean square error even increases significantly to 10 -1 Magnitude. Correspondingly, the maximum and average RE increase to 3.5% and 1% respectively. This indicates that the proposed method requires at least 32 sensors to be arranged on the suction side and pressure side of the blade respectively for sufficiently accurate back-calculation of boundary conditions.

[0182] Three models with different numbers of attention heads were further configured, while other hyperparameters remained unchanged.

[0183] Figure 6 The survey results are shown. On the one hand, the relationship between the prediction errors of the three models with different N h and N s is very consistent with the trend shown Figure 5 . Specifically, as N s decreases, the lack of information that can be extracted from observations leads to a sharp increase in the reconstruction error. On the other hand, regardless of the value of N s , when N h = 8, the model can achieve the best performance. Therefore, a model with N s = 8 trained on data with N h = 32 can be adopted.

[0184] The technical solutions provided by the present invention are further described in detail through several specific embodiments above to highlight the advantages and beneficial effects of the technical solutions provided by the present invention. However, the several specific embodiments described above are not used as limitations on the present invention. Any reasonable changes and improvements to the present invention, reasonable combinations of implementation manners, equivalent replacements, etc. within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for back-calculating the boundary conditions of a turbine cascade based on sparse measurement data, characterized in that The method includes the following steps: A step for obtaining a spatial analysis network structure built based on a self-attention unit and a Transformer encoder; The spatial analysis network structure includes a position encoding module, a multi-layer perceptron, a Transformer encoder, and an average pooling layer. The Transformer encoder includes 6 identical network blocks; each network block consists of two layer normalizations, a multi-head self-attention unit, and a multi-layer perceptron; Wherein: The multi-head self-attention unit is an improved scaled dot-product attention: Given a series of queries Q and key-value pairs K-V, calculate the scaled dot-product attention using Equation (6); where, d k is the number of features of the query and the key; the superscript T is the matrix transpose; is the normalization activation function that normalizes the calculated attention scores into a probability distribution with a sum of 1; （6） In self-attention calculation, Q, K, and V are the same values; For multi-head self-attention, multiple attention calculations are performed in parallel to capture features at different scales, and the information is aggregated by concatenating the calculation results, as shown in Equation (7); where, head i is the i th attention head: （7）； A step for training the spatial analysis network structure, optimizing model parameters, and calculating the corresponding residuals using mean squared error; （9） A step for obtaining the trained spatial analysis network structure; Mathematical form description of the trained spatial analysis network structure; （1） where is the test observation data, is the supervised learning model, is the model hyperparameter, is the actual boundary condition, and the superscript represents the optimal solution; A step for inputting the normalized sparse measurement data into the trained spatial analysis network structure to obtain the corresponding experimental boundary conditions; The spatial analysis network structure is established based on uniform grid division of the turbine blade surface, and the sampling grid nodes are used as sensor layout positions; at least 32 sampling points are arranged on each of the suction side and the pressure side of the blade.

2. The method for back-calculating the test boundary conditions of a turbine cascade based on sparse measurement data according to claim 1, wherein The position encoding module is used for position encoding; The position encoding implies relative position encoding and absolute position encoding: （2） The relative position encoding is used for embedding position information in the spatial domain; the absolute position encoding is used for embedding position information in the feature domain; The relative position encoding is realized through a trigonometric function matrix; （3） The absolute position encoding stems from the characteristics of binary calculation: the alternating frequency of higher-order numerical values is lower than that of lower-order numerical values. Since the feature vector itself does not have the position information of the Euclidean space, the sequence position of the feature vector is abstractly described with reference to the binary rule; A multi-layer perceptron is a series of stacked fully-connected layers, which are essentially continuous linear operations; the parameters of each layer of neurons include a weight matrix W ∈ℝ m×n and a bias vector b ∈ℝ m , where m is the number of neurons in the current layer, n is the size of the input data; Let ζ(·) be the activation function, then the output of the neurons in the l layer is: Select the leaky ReLU function, satisfying the mathematical relationship described as follows: （5） The average pooling layer is an aggregation function.

3. The method for back-calculating the test boundary conditions of a turbine cascade based on sparse measurement data according to claim 2, wherein The Adam algorithm is used to train the spatial analysis network structure.

4. The method for back-calculating the test boundary conditions of a turbine cascade based on sparse measurement data according to claim 3, wherein 128 sampling points are arranged on the suction side of the blade, and 256 sampling points are arranged on the pressure side of the blade.

5. The method for back-calculating the test boundary conditions of a turbine cascade based on sparse measurement data according to claim 3, wherein In the step for training the spatial analysis network structure, optimizing model parameters, and calculating the corresponding residuals using mean squared error: Adopt a random sampling strategy for adjoint training: In each round of training iteration, the sensor positions are randomly resampled, and each sampling process is independent of each other.

6. An inverse calculation device for the boundary conditions of a turbine cascade based on sparse measurement data, characterized in that The device includes the following modules: A module for obtaining a spatial analysis network structure built based on a self-attention unit and a Transformer encoder; The spatial analysis network structure includes a position encoding module, a multi-layer perceptron, a Transformer encoder, and an average pooling layer. The Transformer encoder includes 6 identical network blocks; each network block consists of two layer normalizations, a multi-head self-attention unit, and a multi-layer perceptron; Wherein: The multi-head self-attention unit is an improved scaled dot-product attention: Given a series of queries Q and key-value pairs K-V, calculate the scaled dot-product attention using formula (6); where, d k is the number of features of the query and the key; the superscript T is the matrix transpose; is the normalization activation function that normalizes the calculated attention scores into a probability distribution with a sum of 1; （6） In self-attention calculation, Q, K, and V are the same values; For multi-head self-attention, multiple attention calculations are performed in parallel to capture features at different scales, and the information is aggregated by concatenating the calculation results, as shown in Equation (7); where, head i is the i th attention head: （7）； A module for training a spatial analysis network structure, optimizing model parameters, and calculating corresponding residuals using mean square error: （9） A module for obtaining the trained spatial analysis network structure: Mathematical form description of the trained spatial analysis network structure: （1） wherein is the test observation data, is the supervised learning model, is the model hyperparameter, is the actual boundary condition, and the superscript represents the optimal solution; A module for inputting the normalized sparse measurement data into the trained spatial analysis network structure to obtain the corresponding test boundary conditions; The spatial analysis network structure is based on a uniform grid division of the turbine blade surface, and the sampling grid nodes are used as the sensor layout positions; at least 32 sampling points are arranged on each of the suction side and the pressure side of the blade.

7. A computer device, comprising: A processor and a memory, wherein the memory is used to store executable instructions of the processor, and the processor is configured to execute the method for inverse calculation of test boundary conditions of a turbine cascade based on sparse measurement data according to any one of claims 1-5 by executing the executable instructions.

8. A computer storage medium, characterized in that, A computer program is stored in the storage medium, and when the computer program runs, it executes the method for inverse calculation of test boundary conditions of a turbine cascade based on sparse measurement data according to any one of claims 1-5.

9. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, the steps of the method for inverse calculation of test boundary conditions of a turbine cascade based on sparse measurement data according to any one of claims 1-5 are implemented.

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