An intelligent modeling method for migrating and reducing the order of the transient flow field of a turbine blade under multiple working conditions

Abstract

A multi-condition transient flow field migration and reduced-order intelligent modeling method for turbine blades, comprising the following steps: S1, data acquisition and preprocessing, S2, dimensionality reduction encoding, S3, using data augmentation technology to expand the sample training set, S4, obtaining a standard target task training set and a standard auxiliary task training set, S5, modeling and training, S6, dynamic reconstruction. The present invention utilizes the potential connection characteristics existing between the flow field parameters of turbine blades under different conditions, and proposes a transient flow field migration and reduced-order monitoring method for turbine blades based on proper orthogonal decomposition and multi-task Gaussian process. By using multi-condition data fusion, the knowledge learned under auxiliary conditions is migrated to the target task, realizing intelligent modeling and rapid prediction of the evolution of high-dimensional transient flow field parameters of the target task blades, which can greatly reduce the computational cost and improve the R & D efficiency of turbine blades.

Description

Technical Field

[0001] The present invention relates to the field of intelligent modeling of high-dimensional transient flow field data of gas turbine turbine blades, and in particular to a method for intelligent modeling of multi-condition transient flow field migration and reduction order of turbine blades. Background Art

[0002] At present, large and heavy gas turbines play a huge role in the fields of people's livelihood, national defense and military, etc. Their R & D needs to rely on a strong industrial foundation and scientific and technological strength as support, thus driving the progress and development of various fields such as metallurgy, machinery, materials, and chemical engineering.

[0003] As one of the key components of gas turbines, the working environment of turbine blades is extremely harsh. They need to rotate at high speed under high-temperature and high-pressure gas, and the uneven heating on their surfaces is extremely prone to high-temperature creep, resulting in major damage. To improve the service life of turbine blades, many R & D personnel in the industry use experimental or numerical methods to study the related characteristics of turbine blades, which takes a long time, is costly, and has a huge workload. In addition, some researchers use deep neural networks to model and analyze the internal flow field characteristics of turbines, but when the data is scarce, the obtained results are prone to overfitting, resulting in poor generalization performance. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for intelligent modeling of multi-condition transient flow field migration and reduction order of turbine blades, which uses cross-condition knowledge migration to realize intelligent fusion and rapid prediction of high-dimensional transient flow field data of turbine blades under multiple conditions, shortens the blade R & D cycle, and solves problems such as long experimental or simulation cycles under variable condition conditions and difficult prediction of internal flow field parameters in the R & D process of gas turbine turbine blades.

[0005] The technical solution adopted by the present invention to solve the problems of the prior art: A method for intelligent modeling of multi-condition transient flow field migration and reduction order of turbine blades, comprising the following steps:

[0006] S1. Data acquisition and preprocessing: including the following steps:

[0007] S1-1. Collect the training data set of the target flow field: Construct a turbine simulation model, use a preset cross-section in the fluid domain of the turbine simulation model as the monitoring surface, and arbitrarily select n monitoring points {d i} 1≤i≤n ; Under the preset working condition conditions, perform transient calculations on the fluid domain, and extract the m flow field snapshots containing the monitoring parameter p at the monitoring points {d j ≤(m-1)Δt} j∈N at the moment {0≤t i} 1≤i≤n ; Combine the flow field snapshots into a two-dimensional spatio-temporal tensor of the target task in ascending time sequence And use the two-dimensional spatio-temporal tensor P as the training data set of the target flow field; where m > 1, n ≥ 1;

[0008] S1-2. Collect the training data set of the auxiliary flow field: Change the preset working condition, and under K states different from the preset working condition, perform transient calculations on the fluid domain, and extract {0 ≤ t s j ≤ (m K -1)Δt} 1≤s≤K Snapshots of the flow field with monitoring parameters p at the monitoring points {d i} 1≤i≤n at m K time instants, where m K >> m; Combine the flow field snapshots in ascending time sequence into a two-dimensional spatio-temporal tensor And use this two-dimensional spatio-temporal tensor P K ′ as the auxiliary task data set of the target flow field; where m K > 1, j′ ∈ N; Δt is the time interval between adjacent flow field snapshots;

[0009] S2. Dimensionality reduction encoding: Use the proper orthogonal decomposition method to perform dimensionality reduction encoding on the training data set and the auxiliary task data set respectively, and obtain the temporal characteristics of each element in the training data set P and the auxiliary task data set P′ K That is, the modal coefficients α r (t j ) of each element in the training data set P, and the modal coefficients of each element in the auxiliary task data set P′ K Among them, r is the truncated modal order; The modal coefficients α (t r ) form the modal coefficient sequence α j of the training data set P, and use it as the target modal coefficient; The modal coefficients r form the modal coefficient sequence α of the auxiliary task data set P′ K and use it as the auxiliary modal coefficient; r ';

[0010] The specific method is: First, perform time-averaging processing on each element K in the two-dimensional spatio-temporal tensors P and P ′ to obtain the pulsating quantity and where are the time-averaged values of the transient flow fields of each element in the training data set and the auxiliary task data set respectively;

[0011] The pulsating quantities K of each element of the two-dimensional spatio-temporal tensors P and P′ and Process according to the following formula:

[0012]

[0013] where the spatial modal vector is a set of orthogonal bases, are the modal coefficients of the elements in the two-dimensional space-time tensors P and P' respectively, r is the truncated modal order; Z is the highest truncated modal order Z = min(m, m K ) K

[0014] The spatial modal vector

[0015]

[0016] λ r and λ' r are the eigenvalues of the target covariance matrix C r,i and the auxiliary covariance matrix C' r,i respectively. λ r and λ' r represent the magnitude of each modal energy value, and ψ r and ψ' r are the eigenvectors of the target covariance matrix C r,i and the auxiliary covariance matrix C' r,i respectively. ψ r and ψ' r characterize the evolution characteristics of the flow field;

[0017] where the target covariance matrix C r,i is the inner product of the pulsation matrix and its transposed matrix . The target covariance matrix C r,i represents the correlation of physical characteristics between different grid points of the flow field. The specific expression is as follows:

[0018]

[0019] Similarly, the auxiliary covariance matrix C' r,i is:

[0020]

[0021] The pulsation matrix

[0022] S3. Use data augmentation technology to expand the sample training set: Augment the modal coefficient sequences α r , α' r obtained in step S2 to obtain the enhanced target modal coefficient sequence ​With the enhanced auxiliary modal coefficient sequence It includes the following steps:

[0023] Using the enhanced interpolation function for the modal coefficient sequence α r , Perform offline enhancement, that is, refine the time interval Δt into For the target modal coefficient α r And the auxiliary modal coefficient Perform interpolation enhancement respectively to obtain the enhanced target modal coefficient sequence And the enhanced auxiliary modal coefficient sequence

[0024]

[0025] where g r (·) and g′ r (·) are the enhanced interpolation functions, is the number of enhanced snapshots of the target flow field, is the number of enhanced snapshots of the auxiliary flow field, ζ is the number of interpolation points;

[0026] S4. Obtain the standard target task training set and the standard auxiliary task training set

[0027] S4-1 Use the autoregressive strategy to convert the enhanced target modal coefficient sequence and the enhanced auxiliary modal coefficient sequence into labeled type data respectively to obtain the target task training set D r and the auxiliary task training set D r k , including the following steps:

[0028] S4-1-1. Obtain the target task training set D r : Using the sliding window method, preset the sliding window length as W, and translate the window with length W one step backward along the time increasing direction of the enhanced target modal coefficient sequence Perform autoregressive transformation on the enhanced target modal coefficient sequence to obtain the input in the form of single-step prediction as: Output where,

[0029]

[0030] where, is the element value of the enhanced target modal coefficient at the th moment, is the enhanced target modal coefficient the element value at the moment; after fixing the window length W, the window translation can be completed by incrementing the variable i′, that is, marking the enhanced target modal coefficients data as label X r , and marking the enhanced target modal coefficients data outside the window as label Y r , and obtaining the target task training set D r = {X r , Y r} 1≤r≤Z ;

[0031] S4-1-2. Obtain the auxiliary task training set D r k : Using the sliding window method, slide the window of length W one step backward along the time increasing direction of the enhanced auxiliary modal coefficients , and perform autoregressive transformation on the enhanced auxiliary modal coefficients to obtain the input in the form of single-step prediction as follows: Output

[0032]

[0033] Among them, is the element value at the moment in the enhanced auxiliary modal coefficients , is the element value at the moment in the enhanced auxiliary modal coefficients ; after fixing the window length W, the window translation can be completed by incrementing the variable i", that is, marking the enhanced auxiliary modal coefficients data as label X k r , and marking the enhanced auxiliary modal coefficients data outside the window as label Y k r , and obtaining the auxiliary task training set D k r = {X k r , Y k r} 1≤r≤Z,1≤k≤K ;

[0034] S4-2. Respectively perform Z-score standardization processing on the obtained target task training set D r and the auxiliary task training set D r k , and output the standard target task training set and the standard auxiliary task training set

[0035] S5. Modeling and training: Establish a multi-task Gaussian process model to perform transfer prediction on the standard target task training set and the standard auxiliary task training set The specific steps are as follows:

[0036] S5-1. Use the standard target task training set obtained in step S4 and the standard auxiliary task training set to construct r multi-task Gaussian process transfer models M r :

[0037]

[0038] where Z is the highest-order truncated modal order, Z = min(m, m k );

[0039] The expression of the multi-task Gaussian process transfer model M r is:

[0040]

[0041] where, is used as the training data set of the multi-task Gaussian process transfer model M r , is the standardized autoregressive modal coefficient, {y r} 1≤r≤Z is the model output; is Q Gaussian process latent functions subject to zero mean; is H latent functions mapped from the base Gaussian process {f q (·)} 1≤q≤Q to a high-dimensional space, where Q < H; is the linear mixing weight of the latent function of the r-th task; is the independent and identically distributed Gaussian noise term of the r-th task; is the mapping function that varies with the input;

[0042] S5-2. Use the importance weight variational inference to minimize the evidence lower bound L to optimize the hyperparameters The expression is:

[0043]

[0044] where, f = {f q (·)} 1≤q≤Qis a latent variable; KL[q(·)||p(·)]≥0 is the Kullback-Leibler divergence; where q(·) is an approximate distribution of p(·), and the Kullback-Leibler divergence is used to measure the approximation degree of the distribution q(·) to the distribution p(·); the induced variable set δ={δ r} 1≤r≤Z , the multi-task Gaussian process transfer model uses the Adam stochastic gradient optimizer for model training;

[0045] After predicting each training data, return to step S4 and move the sliding window forward one step at a time to update the target task training set and the auxiliary task training set Recursively loop until all the training data in the training dataset are predicted;

[0046] S5-3. Use the r groups of multi-task Gaussian process transfer models trained in step S5-2 to predict the mean value of the Gaussian prediction distribution of the modal coefficients at future time :

[0047]

[0048] where, is the mean value of the Gaussian prediction distribution of the modal coefficients at future time , is the mean value of the Gaussian distribution of the modal coefficients at future time , is the prediction variance, and x r,* is the input of the multi-task Gaussian process transfer model;

[0049] S6. Dynamic reconstruction: Use the mean value of the Gaussian prediction distribution of the modal coefficients obtained in step S5 to perform dynamic reconstruction decoding on the flow field: For the predicted value of the Z-th order modal coefficient of the target task at TΔt and the spatial modal vector to obtain the prediction expression of the parameter field at the inlet section of the turbine moving blade at future time t as:

[0050]

[0051] is the predicted reconstructed flow field of the two-dimensional spatio-temporal tensor temperature field at TΔt, is the time-averaged vector of the monitoring parameters.

[0052] In step S6, select the highest order mode i.e., when r = Z, perform dynamic reconstruction on the instantaneous flow field so as to maximize the restoration of the flow field information.​

[0053] The method of Z-score normalization in step S4-2 is as follows: where τ is the vector to be processed, β is the normalized output result, μ is the mean of the vector to be processed, σ is the standard deviation of the vector to be processed, and the normalized training set is

[0054] In step S4-1, 3 ≤ W ≤ 10.

[0055] The working conditions include turbine speed and outlet pressure; the monitoring parameter p includes temperature.

[0056] The beneficial effects of the present invention are as follows: By utilizing the potential connection characteristics existing among the flow field parameters of turbine blades under different working conditions, the present invention proposes a transient flow field migration and order reduction monitoring method for turbine blades based on proper orthogonal decomposition and multi-task Gaussian process. By using multi-condition data fusion, the knowledge learned under auxiliary conditions is migrated to the target task, realizing intelligent modeling and rapid prediction of the evolution of high-dimensional transient flow field parameters of the target task blades. This method can significantly reduce the computational cost and effectively improve the R & D efficiency of turbine blades. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 is the basic concept flowchart of the present invention.

[0058] Figure 2 is the single-channel model of the turbine blade in the present invention.

[0059] Figure 3 is the modal coefficient prediction diagram of the present invention and the benchmark model (AR-STGP-POD).

[0060] Figure 4 is the model reconstructed flow field and absolute error diagram of the present invention at t = 0.0073 s.

[0061] Figure 5 The RMSE error diagram of the model reconstructed flow field of the present invention at different times. DETAILED DESCRIPTION OF THE INVENTION

[0062] The present invention will be described below in conjunction with the accompanying drawings and specific embodiments:

[0063] The design idea of the present invention is a multi-condition turbine blade transient flow field data migration and order reduction monitoring modeling method based on multi-task Gaussian process. It mainly uses proper orthogonal decomposition to perform order reduction projection on the high-dimensional flow field to obtain orthogonal modes and their modal coefficients; uses data augmentation and autoregressive techniques to reduce the computational cost, handle the spatio-temporal coupling problem, and perform migration prediction on similar tasks through the multi-task Gaussian process model, thereby improving the overall prediction accuracy of the algorithm. The basic operation idea of the present invention is as Figure 1 shown:

[0064] 1. Establish a simulation calculation model for turbine transient off-design conditions.

[0065] 2. Set the model boundary conditions and initial conditions for thermodynamic analysis, and export the initial sample data of the turbine detection surface (including target fluid data and auxiliary fluid data).

[0066] 3. Extract the target task and auxiliary task sample data.

[0067] 4. Perform proper orthogonal decomposition on the high-dimensional transient data to obtain modes and modal coefficients.

[0068] 5. Interpolate and expand the target task modal coefficient set, and use the autoregressive strategy to transform the target and auxiliary task modal coefficients into label data.

[0069] 6. Use the multi-task Gaussian process model to perform transfer learning on the modal coefficients of the target and auxiliary tasks, and update the original training set for single-step rolling prediction.

[0070] 7. Use the predicted modal coefficients for flow field reconstruction and give the error analysis results.

[0071] A multi-condition transient flow field transfer and reduced-order intelligent modeling method for turbine blades includes the following steps:

[0072] S1. Data acquisition and preprocessing: including the following steps:

[0073] S1-1. Collect the training data set of the target flow field: Use the commercial software ANSYS to construct a turbine simulation model, which includes 36 stator blades and 42 rotor blades. Each flow passage is circumferentially symmetric, and the full circumference calculation can be approximated by a single flow passage (only including a pair of stator and rotor blades) to reduce the cost. Figure 2 As shown in the schematic diagram of the turbine single-channel model, the total number of grid nodes of the single-channel model is 30508. The monitored parameter p is temperature, and the preset cross-section in the fluid domain of the turbine simulation model is used as the monitoring surface. As Figure 2 shown, the circumferential cross-section at the rotor inlet is set as the monitoring surface ( Figure 2 the contour shown by the thick black solid line), which includes a total of n = 400 monitoring points {d i} 1≤i≤400 ( Figure 2 the solid dot is the i-th monitoring point). Set the turbine boundary conditions (such as outlet pressure) and initial conditions (such as rotational speed), given a time interval Δt = 10 -4 s, a period T = 1.5×10 -2 s, perform transient calculations on the single-channel model, and export 0 ≤ t jThe first 18 (m = 18) transient snapshots of the temperature field of this cross-section at a moment ≤ 0.0017 s are combined in ascending chronological order into a two-dimensional spatio-temporal tensor as the training set of the target flow field

[0074] S1-2. Collect the training data set of the auxiliary flow field: Change the turbine speed and outlet pressure, that is, set K = 1 group of turbine boundary conditions (such as outlet pressure) and initial value conditions (such as speed) different from those in step S1-1, perform transient calculations on the fluid domain, and extract {0 ≤ t K＝1 j′ ≤ (m K＝1 -1)Δt} the first 100 (m k＝1 = 100) transient snapshots of the temperature field of this cross-section, and combine the flow field snapshots into a two-dimensional spatio-temporal tensor of the target task in ascending chronological order and use this two-dimensional spatio-temporal tensor P′ K as the auxiliary task data set of the target flow field. Table 1 shows the comparison of partial boundary conditions of the transient flow fields of the target flow field and the auxiliary flow field

[0075] Table 1 Comparison table of partial boundary conditions of transient flow fields of target flow field and auxiliary flow field

[0076]

[0077] S2. Dimensionality reduction encoding: Use the proper orthogonal decomposition method to perform dimensionality reduction encoding on the training data set and the auxiliary task data set respectively, and obtain the temporal characteristics of each element in the training data set P and the auxiliary task data set P′ K That is, the modal coefficients α r (t j ) in the training data set P, and the modal coefficients of each element in the auxiliary task data set P′ K Among them, r is the truncated modal order; the modal coefficients α (t r ) constitute the modal coefficient sequence α j of the training data set P, and use it as the target modal coefficient; the modal coefficients r constitute the modal coefficient sequence α′ of the auxiliary task data set P′ K and use it as the auxiliary modal coefficient r ;

[0078] The method of using the proper orthogonal decomposition method to perform dimensionality reduction encoding on the above training data set and auxiliary task data set respectively is: To ensure the robustness of the algorithm, first perform time-averaging processing on each element K in the two-dimensional spatio-temporal tensors P and P′ to obtain the pulsation and where are the time-averaged values of the transient flow fields of the elements in the training dataset and the auxiliary task dataset, respectively;

[0079] The pulsations of the elements of the two-dimensional spatio-temporal tensors P and P′ K are processed according to the following formula: and are processed according to the following formula:

[0080]

[0081] where the spatial mode vector is a set of orthogonal bases, are the modal coefficients of the elements in the two-dimensional spatio-temporal tensors P and P′ K respectively, r is the truncated mode order; usually, the truncated mode order r is selected such that the relative error of the pulsations before and after decomposition is less than 90%. Z is the highest-order truncated mode order Z = min(m, m K ), the larger the value of Z, the higher the approximation degree of the low-dimensional features to the high-dimensional flow field. To maximize the preservation of the temporal development characteristics of the high-dimensional flow field, Z = 18 is preferably selected.

[0082] The spatial mode vector

[0083]

[0084] λ r and λ' r are the eigenvalues of the target covariance matrix C r,i and the auxiliary covariance matrix C' r,i respectively, λ r and λ' r represent the magnitude of each modal energy value, ψ r and ψ' r are the eigenvectors of the target covariance matrix C r,i and the auxiliary covariance matrix C' r,i respectively, ψ r and ψ' r characterize the evolution characteristics of the flow field; 1 ≤ γ ≤ Z.

[0085] where the target covariance matrix C r,i is the inner product of the pulsation matrix and its transpose matrix The target covariance matrix C r,i represents the correlation of physical characteristics between different grid points of the flow field, and the specific expression is as follows:

[0086]

[0087] Similarly, the auxiliary covariance matrix C' can be obtainedr,i is:

[0088]

[0089] Pulsation matrix

[0090] S3. Expand the sample training set using data augmentation techniques: Due to the large computational overhead, the flow field data included in step S1-1 is often very limited. Therefore, it is necessary to augment the existing modal coefficient sequences α r , α′ r to enable the model to accurately mine the dynamic laws behind the data. To reduce the computational overhead, instead of directly augmenting the high-dimensional flow field, the present invention chooses to perform offline augmentation on the modal coefficients after dimensionality reduction encoding. The specific steps are as follows:

[0091] Augment the modal coefficient sequences α r , α′ r obtained in step S2 to obtain the augmented target modal coefficients and the augmented auxiliary modal coefficients including the following steps:

[0092] Use the augmentation interpolation function to perform offline augmentation on the modal coefficient sequences α r , that is, refine the time interval Δt into Perform interpolation augmentation on the target modal coefficient α r and the auxiliary modal coefficient respectively to obtain the augmented target modal coefficient sequence and the augmented auxiliary modal coefficient sequence

[0093] where g r (·) and g′ r (·) are augmentation interpolation functions, is the number of augmented snapshots of the target flow field, is the number of augmented snapshots of the auxiliary flow field, is the number of interpolation points; g r (.) and g' r (.) are preferably cubic spline interpolations provided by interp1d in sklearn. Using the above interpolation functions, given the number of interpolation points ξ, the target modal coefficient α r and the auxiliary modal coefficient α r′ can be interpolated and augmented by (ξ - 1) times to obtain the more informative augmented target modal coefficients and the augmented auxiliary modal coefficients It should be noted that when the number of interpolation points ξ = 1 within the time interval Δt, It is equivalent to not performing data augmentation. Selecting the number of interpolation points ξ = 4, the augmented set can be obtained

[0094] S4. Obtain the standard target task training set and the standard auxiliary task training set

[0095] S4-1. Using the auto-regressive (AR) strategy, respectively convert the enhanced target modal coefficient sequence and the enhanced auxiliary modal coefficient sequence into labeled type data to obtain the target task training set D r and the auxiliary task training set D r k , including the following steps:

[0096] S4-1-1. Obtain the target task training set D r : Obtain the target task training set D r : Using the sliding window method, preset the sliding window length as W, 3 ≤ W ≤ 10. In this embodiment, taking W = 3 as an example, move the window with length W one step backward along the time increasing direction of the enhanced target modal coefficient sequence to perform auto-regressive transformation on the enhanced target modal coefficient sequence to obtain the input in the form of single-step prediction as: Output where,

[0097]

[0098] where, is the element value at the th moment in the enhanced target modal coefficient ; is the element value at the th moment in the enhanced target modal coefficient r ; After fixing the window length W, the window translation can be completed through the self-increment operation of the variable i′, that is, mark the enhanced target modal coefficient data located within the window as label X r , and mark the enhanced target modal coefficient r data located outside the window as label Y r , and obtain the target task training set D r = {X 1≤r≤Z ;

[0099] S4-1-2. Obtain the auxiliary task training set D r k: Using the sliding window method, a window of length W is translated one step backward along the time increasing direction of the enhanced auxiliary modal coefficients to autoregressively transform the enhanced auxiliary modal coefficients to obtain the input in the form of a single-step prediction: Output

[0100]

[0101] where, is the element value at the th moment in the enhanced auxiliary modal coefficients is the element value at the th moment in the enhanced auxiliary modal coefficients; after fixing the window length W, the window translation can be completed by incrementing the variable i″, that is, marking the enhanced auxiliary modal coefficient data within the window as label X k r , and marking the enhanced auxiliary modal coefficient data outside the window as label Y k r , and obtaining the auxiliary task training set D k r ={X k r , Y k r} 1≤r≤Z,1≤k≤K ;

[0102] S4-2. Normalize the obtained target task training set D r and the auxiliary task training set D r k respectively by Z-score normalization, and output the standard target task training set and the standard auxiliary task training set The method of Z-score normalization is: where τ is the vector to be processed, β is the normalized output result, μ is the mean of the vector to be processed, σ is the standard deviation of the vector to be processed, and the normalized training set is

[0103] S5. Modeling and training: Establish a multi-task Gaussian process model (MTGP) to perform transfer prediction on the standard target task training set and the standard auxiliary task training set , specifically including the following steps:

[0104] S5-1. Use the standard target task training set obtained in step S4 and the standard auxiliary task training set to construct r multi-task Gaussian process transfer models M r :

[0105]

[0106] where Z is the highest-order truncated modal order, Z = min(m, m k );

[0107] Since the multi-task Gaussian process model based on neural network regional collaborative embedding (NSVLMC) has strong non-linear representation ability and moderate complexity, this model is selected to complete the transfer learning of multi-modal tasks. Specifically, the expression of the above multi-task Gaussian process transfer model is:

[0108]

[0109] where As the training data set of the multi-task Gaussian process transfer model M r , is the standardized autoregressive modal coefficient, {y r} 1≤r≤Z is the model output; are Q Gaussian process latent functions that follow zero mean; are H latent functions mapped from the base Gaussian process {f q (·)} 1≤q≤Q to the high-dimensional space, where Q < H; is the linear mixing weight of the latent function of the r-th task; is the independent and identically distributed Gaussian noise term of the r-th task; is the mapping function that varies with the input;

[0110] S5-2. Use the variational inference of important weights to minimize the evidence lower bound L to optimize the hyperparameters , and the expression is:

[0111]

[0112] where f = {f q (·)} 1≤q≤Q is the latent variable; KL[q(·)||p(·)] ≥ 0 is the Kullback-Leibler divergence; where q(·) is the approximate distribution of p(·), and the Kullback-Leibler divergence is used to measure the approximation degree of the distribution q(·) to the distribution p(·); use the sparse approximation method to reduce the model complexity, and introduce the induced variable set δ = {δ r}1≤r≤Z As the sufficient statistic of the latent function f q (·), it replaces the latent function for subsequent calculations. The multi-task Gaussian process transfer model uses the Adam stochastic gradient optimizer for model training; the learning rate α = 0.005, and it iteratively calculates 5000 steps;

[0113] After predicting each training data, return to step S4 and move the sliding window forward by one step, updating the target task training set and the auxiliary task training set Recursively loop until the prediction of the training data in the training dataset is completed;

[0114] S5-3. Use the r groups of multi-task Gaussian process transfer models trained in step S5-2 to predict the mean of the Gaussian prediction distribution of the modal coefficients at future times : For prediction:

[0115]

[0116] where, is the mean of the Gaussian prediction distribution of the modal coefficients at future times , is the mean of the Gaussian distribution of the modal coefficients at future times , is the predicted variance, x r,* is the input of the multi-task Gaussian process transfer model;

[0117] Figure 3 is the predicted value of the temperature field modal coefficients of the target task, which is represented by AR-MTGP-POD in the present invention. The cross lines in the figure are the predicted means of the existing AR-STGP-POD model, and the area sandwiched by the upper and lower two dotted lines is the 95% confidence interval of the predicted value; the solid line is the predicted mean of the present invention, and the area sandwiched by the upper and lower two double dotted lines is the 95% confidence interval; the dotted line represents the POD modal coefficients obtained by the spatial modal decomposition of the training data; the solid dots represent the model training points without enhancement. Since m = 18 and W = 3, there are initially only 15 training points. It can be observed that both models have achieved good prediction effects on the mean of the Gaussian prediction distribution of the first-order modal coefficients . However, as the order increases, the mean of the Gaussian prediction distribution of the modal coefficients evolves into more irregular oscillations, such as at this time, it is difficult for AR-STGP-POD to give a reasonable prediction, but the present invention (AR-MTGP-POD) can accurately predict each order coefficient with the help of the auxiliary tasks under other working conditions.

[0118] S6. Dynamic reconstruction: Use the mean of the Gaussian prediction distribution of the modal coefficients obtained in step S5 Performing dynamic reconstruction decoding on the flow field: the predicted value of the Z - order modal coefficient of the target task at time TΔt and the spatial modal vector to obtain the prediction expression of the temperature field at the inlet section of the turbine moving blade at future time t as follows:

[0119]

[0120] where, is the predicted reconstructed flow field of the two - dimensional spatio - temporal tensor temperature field at time TΔt, is the time - averaged temperature vector, is the reconstructed predicted value of the pulsating temperature field at time TΔt.

[0121] To maximize the restoration of flow field information, the highest - order modal coefficient is selected to perform dynamic reconstruction on the instantaneous flow field.

[0122] To ensure that the reconstructed flow field information is fully retained, take Z = 18. Figure 4 is the reconstructed flow field of the AR - STGP - POD model and the AR - MTGP - POD model of the present invention at t = 0.0073s, and the reconstruction result of POD based on the spatial mode of the training data is given as a benchmark. It can be observed that at t = 0.0073s, the reconstructed temperature field details of the model of the present invention (AR - MTGP - POD) are closer to the real temperature field, and the absolute error is smaller.

[0123] Table 2 shows the root mean square error (RMSE) of the reconstructed flow fields of the two models in the time range of 0 - 9.9×10 -3 s. It can be found that the reconstruction error of the model of the present invention (AR - MTGP - POD) is only 18.65% of the reconstruction error of the AR - STGP - POD model, a year - on - year decrease of 81.34%. In addition, Figure 4 shows the RMSE errors of the two models at different times. It can be seen that within the test set range (to the right of the vertical line), the prediction accuracy of the model of the present invention (AR - MTGP - POD) is better than that of the AR - STGP - POD model at each moment.

[0124] Table 2 Mean and standard deviation of RMSE errors of the reconstructed flow fields of the two models

[0125]

[0126] The above content is a further detailed description of the present invention in combination with specific preferred technical solutions. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, which should all be regarded as falling within the protection scope of the present invention.

Claims

1. A multi - condition transient flow field migration and reduced - order intelligent modeling method for turbine blades, characterized in that, it includes the following steps: S1. Data collection and pre - processing: including the following steps: S1-1. Collect the training dataset of the target flow field: Construct a turbine simulation model, use a preset cross-section in the fluid domain of the turbine simulation model as the monitoring surface, and arbitrarily select n monitoring points {d i} 1≤i≤n on this monitoring surface; Under the preset working condition, perform transient calculation on this fluid domain, and extract {0 ≤ t j ≤ (m - 1)Δt} j∈N snapshots of m flow fields containing the monitoring parameter p at the monitoring points {d i} 1≤i≤n ; Combine the flow field snapshots into a two-dimensional spatio-temporal tensor of the target task in ascending time sequence, and use this two-dimensional spatio-temporal tensor P as the training dataset of the target flow field; where m > 1 and n ≥ 1; S1-2. Collect the training data set of the auxiliary flow field: Change the preset working conditions. Under K states different from the preset working conditions, perform transient calculations on the fluid domain, and extract the monitoring points {0 ≤ t s j′ ≤ (m K -1)Δt} 1≤s≤K at the moment, where the monitoring parameter p of the monitoring point {d i} 1≤i≤n contains m K flow field snapshots. Among them, m K >> m; Combine the flow field snapshots into a two-dimensional spatio-temporal tensor of the target task in increasing time sequence and use this two-dimensional spatio-temporal tensor P K ′ as the auxiliary task data set of the target flow field; where m K > 1, j′ ∈ N; Δt is the time interval between adjacent flow field snapshots; S2. Dimensionality reduction encoding: Use the proper orthogonal decomposition method to perform dimensionality reduction encoding on the training data set and the auxiliary task data set respectively, and obtain the temporal features of each element in the training data set P and the auxiliary task data set P K ′, that is, the modal coefficients α r (t j ) of each element in the training data set P, and the modal coefficients of each element in the auxiliary task data set P K ′ where r is the truncated modal order; The modal coefficients α r (t j ) form the modal coefficient sequence α r of the training data set P and are used as the target modal coefficients; The modal coefficients form the modal coefficient sequence α′ K of the auxiliary task data set P′ r and are used as the auxiliary modal coefficients; S3. Expand the sample training set using data augmentation techniques: For the modal coefficient sequences α r , α' r perform augmentation to obtain the enhanced target modal coefficient sequence and the enhanced auxiliary modal coefficient sequence S4. Obtain the standard target task training set and the standard auxiliary task training set S4-1 Use the autoregressive strategy to separately convert the enhanced target modal coefficient sequence and the enhanced auxiliary modal coefficient sequence into labeled type data to obtain the target task training set D r and the auxiliary task training set D r k ; S4-2. Normalize the obtained target task training set D r and the auxiliary task training set D r k using Z-score normalization respectively, and output the standardized target task training set and the standardized auxiliary task training set S5. Modeling and training: Establish a multi-task Gaussian process model to perform transfer prediction on the standard target task training set and the standard auxiliary task training set Specifically, it includes the following steps: S5-1. Use the standard target task training set obtained in step S4 and the standard auxiliary task training set to construct r multi-task Gaussian process transfer models M r : where Z is the highest order of the truncated mode, Z = min(m, m k ); The multi-task Gaussian process transfer model M r has the following expression: Among them, As the training data set of the multi-task Gaussian process transfer model M r ; is the standardized autoregressive modal coefficient, {y r} 1≤r≤Z is the model output; are Q Gaussian process latent functions that follow zero mean; are H latent functions mapped from the base Gaussian process {f q (·)} 1≤q≤Q into a high-dimensional space, where Q < H; is the linear mixing weight of the latent function of the r-th task; is the independent and identically distributed Gaussian noise term of the r-th task; is the mapping function that varies with the input; S5-2. Minimize the evidence lower bound \(L\) with respect to the hyperparameters by using importance weighted variational inference. The expression is as follows: where \(f = \{f q (\cdot)\} 1≤q≤Q is a latent variable; \(KL[q(\cdot)\parallel p(\cdot)]\geq0\) is the Kullback-Leibler divergence; where \(q(\cdot)\) is an approximate distribution of \(p(\cdot)\), and the Kullback-Leibler divergence is used to measure the approximation degree of the distribution \(q(\cdot)\) to the distribution \(p(\cdot)\); the set of induced variables \(\delta=\{\delta r \}\ 1≤r≤Z , and the multi-task Gaussian process transfer model uses the Adam stochastic gradient optimizer for model training; After predicting each piece of training data, return to step S4, move the sliding window forward one step at a time, and update the training set of the target task and the training set of the auxiliary task Repeat this process until all the training data in the training dataset has been predicted; S5-3. Use the r groups of multi-task Gaussian process transfer models trained in step S5-2 at future time to predict the mean of the Gaussian predictive distribution of the modal coefficients as follows: Among them, is the mean of the Gaussian predictive distribution of the modal coefficients at a future time , and is the mean of the Gaussian distribution of the modal coefficients at a future time . is the predictive variance, and x r,* is the input of the multi-task Gaussian process transfer model; S6. Dynamic Reconstruction: Using the mean value of the Gaussian predictive distribution of the modal coefficients obtained in step S5 Perform dynamic reconstruction decoding on the flow field: For the predicted value of the Z-order modal coefficients of the target task at time TΔt and the spatial modal vector Obtain the prediction expression of the parameter field at the inlet section of the turbine moving blade at future time t as follows: is the predicted reconstructed flow field of the two-dimensional spatio-temporal tensor monitoring parameter field at the moment of TΔt, is the time-averaged vector of the monitoring parameter p; The working conditions include turbine speed and outlet pressure; the monitored parameter p includes temperature.

2. The multi - condition transient flow field migration and reduced - order intelligent modeling method for turbine blades according to claim 1, characterized in that, The specific method of dimensionality reduction coding in step S2 is as follows: First, perform time averaging on each element in the two-dimensional spatio-temporal tensors P and P K ′ to obtain the pulsating quantities and and where are the time-averaged values of the transient flow fields of each element in the training data set and the auxiliary task data set, respectively; Process the pulsations of each element of the two-dimensional spacetime tensors P and P K ′ and according to the following formula: Among them, the spatial modal vector is a set of orthogonal bases, which are respectively the modal coefficients of the elements in the two-dimensional space-time tensors P and P K ′, r is the truncated modal order; Z is the highest-order truncated modal order Z = min(m, m K ); Spatial mode vector λ r and λ' r are the eigenvalues of the target covariance matrix C r,i and the auxiliary covariance matrix C' r,i respectively. λ r and λ' r represent the magnitudes of the energy values of each mode. ψ r and ψ' r are the eigenvectors of the target covariance matrix C r,i and the auxiliary covariance matrix C' r,i respectively. ψ r and ψ' r characterize the evolution characteristics of the flow field; Among them, the target covariance matrix C r,i is the pulsation matrix and the inner product of its transpose matrix . The target covariance matrix C r,i represents the correlation of physical characteristics between different grid points in the flow field. The specific expression is as follows: Similarly, the auxiliary covariance matrix C' can be obtained r,i as follows: Pulse momentum matrix 3. The multi - condition transient flow field migration and reduced - order intelligent modeling method for turbine blades according to claim 1, characterized in that, Step S3 includes the following steps: Using an enhanced interpolation function for the modal coefficient sequence α r , perform offline enhancement, that is, refine the time interval Δt into Interpolate and enhance the target modal coefficient α r and the auxiliary modal coefficient respectively to obtain the enhanced target modal coefficient sequence and the enhanced auxiliary modal coefficient sequence Among them, g r (·) and g′ r (·) is an enhanced interpolation function, is the number of enhanced snapshots of the target flow field, is the number of enhanced snapshots of the auxiliary flow field, ζ is the number of interpolation points.

4. The multi - condition transient flow field migration and reduced - order intelligent modeling method for turbine blades according to claim 1, characterized in that, Step S4 - 1 includes the following steps: S4-1-1. Obtain the target task training set D r : Using the sliding window method, preset the sliding window length as W, and move the window with length W one step backward along the time increasing direction of the enhanced target modal coefficient sequence , and perform autoregressive transformation on the enhanced target modal coefficient sequence to obtain the input in the form of single-step prediction as follows: Output wherein, Among them, To enhance the element value of the at the moment in the target modal coefficient is to enhance the element value of the at the moment in the target modal coefficient; after fixing the window length W, the window translation can be completed by incrementing the variable i'. That is, the enhanced target modal coefficient data located within the window is labeled as label X r , and the enhanced target modal coefficient data located outside the window is labeled as label Y r , and the target task training set D r = {X r , Y r} 1≤r≤Z ; S4-1-2. Obtain the auxiliary task training set D r k : Using the sliding window method, slide the window of length W one step backward along the time increasing direction of the enhanced auxiliary modal coefficients to perform autoregressive transformation on the enhanced auxiliary modal coefficients to obtain the input in the form of single-step prediction as follows: Output Among them, is the element value at the th moment in the enhanced auxiliary modal coefficient ; is the element value at the th moment in the enhanced auxiliary modal coefficient ; after fixing the window length W, the window translation can be completed by incrementing the variable i″, that is, marking the enhanced auxiliary modal coefficient k r data within the window as label X and marking the enhanced auxiliary modal coefficient k r data outside the window as label Y k r to obtain the auxiliary task training set D k r = {X k r}, Y 1≤r≤Z,1≤k≤K .

5. The multi - condition transient flow field migration and reduced - order intelligent modeling method for turbine blades according to claim 1, characterized in that, In step S6, the highest-order mode is selected. That is, when r = Z, the instantaneous flow field is dynamically reconstructed so that the flow field information can be restored to the greatest extent.

6. The multi - condition transient flow field migration and reduced - order intelligent modeling method for turbine blades according to claim 1, characterized in that, The method of Z-score normalization in step S4-2 is as follows: where τ is the vector to be processed, β is the standardized output result, μ is the mean of the vector to be processed, σ is the standard deviation of the vector to be processed, and the standardized training set is 7. The multi - condition transient flow field migration and reduced - order intelligent modeling method for turbine blades according to claim 4, characterized in that, 3≤W≤10。

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