Cascade flow field prediction method and device based on sparse promotion modal feature prediction

Abstract

The invention provides a cascade flow field prediction method and device based on sparse promotion modal feature prediction, and belongs to the technical field of gas turbine flow field prediction. According to the method, a flow field snapshot is decomposed into a DMD mode, a mode amplitude matrix and a DMD eigenvalue matrix, and a flow field reconstruction expression is constructed; constructing an objective function, including promoting a sparse term to produce a more sparse solution; the optimal position of the non-zero modal amplitude is solved based on target function optimization, and a modal order corresponding to the non-zero modal amplitude forms a dominant modal representing the dynamic characteristics of the flow field; the modal amplitude and the DMD characteristic value of the unknown working condition are predicted based on the modal amplitude and the DMD characteristic value of the dominant modal of the flow field under the known working condition, and then the flow field of the unknown working condition is predicted by using the inverse process of the DMD. According to the method, control over the number of sparse modes is added into the target function, the mode sparsity is enhanced, and then the mode subset which has remarkable influence on the flow field is better identified.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of gas turbine flow field prediction, in particular to a cascade flow field prediction method and device based on sparse promoting modal characteristic prediction. BACKGROUND

[0002] The gas turbine needs to adjust the airflow under different operating conditions, and the relative angle between the blade and the airflow can be changed by adjusting the pitch angle of the cascade, so as to ensure that the gas turbine maintains high efficiency and stability under different working conditions. The aerodynamic performance of the cascade changes very complicatedly with the pitch angle, and due to the influence of vortex, boundary layer and other factors of the airflow, it is difficult to maintain high precision in these complex aerodynamic environments, thereby affecting the control precision of the cascade pitch angle.

[0003] Therefore, how to predict the cascade flow field distribution in the complex aerodynamic environment and provide the required data for the active control of the variable pitch angle of the cascade is a problem that needs to be solved by the person skilled in the art. SUMMARY

[0004] Therefore, the present application provides a cascade flow field prediction method and device based on sparse promoting modal characteristic prediction, which can predict the flow field distribution state of the variable pitch angle of the cascade under multiple working conditions without complex modeling. Moreover, the present application also improves the dynamic modal decomposition DMD method, enhances the modal sparsity, improves the modal selection efficiency, and thereby better identifies the modal subset which has a significant influence on the flow field. Moreover, the increase in the number of sparse modes can also reduce the calculation cost and improve the calculation speed.

[0005] In order to solve the above technical problems, the present application is implemented as follows.

[0006] A cascade flow field prediction method based on sparse promoting modal characteristic prediction, comprising: Step 1: using dynamic modal decomposition DMD to decompose the flow field snapshot into a DMD modal , a modal amplitude matrix and a DMD eigenvalue matrix , to construct a flow field reconstruction expression; Step 2: constructing a target function, including a truncation error term between the original flow field and the reconstructed flow field and a promoting sparse term; the promoting sparse term is used to punish the number of non-zero elements in the unknown modal amplitude matrix, so as to produce a more sparse solution; based on the target function optimization, the best position of the non-zero modal amplitude is solved, and the modal order corresponding to the non-zero modal amplitude constitutes the dominant modal representing the dynamic characteristics of the flow field; Step 3: Based on the modal amplitude and DMD eigenvalue of the leading mode of the flow field under the known working condition, the modal amplitude and DMD eigenvalue under the unknown working condition are predicted; then, based on the predicted values of the modal amplitude and DMD eigenvalue, the inverse process of the DMD is used to determine the predicted flow field under the unknown working condition.

[0007] Preferably, the step 1 comprises: The data sequence of the flow field snapshot under the known working condition is:

[0008] The data sequence of another flow field snapshot generated by the invariable system is:

[0009] wherein, is the physical quantity snapshot of the flow field at time step t, , is the snapshot number; the flow field at the previous time is obtained by linear transformation of the matrix : ; The flow field is subjected to eigenvalue decomposition: ; and are orthogonal matrices, is a diagonal matrix; then:

[0010]

[0011] wherein, the matrix represents the best low-dimensional representation of the matrix , and represent the eigenvector and eigenvalue of the matrix respectively; the eigenvector is projected to the high dimension, i.e. the DMD mode, using the orthogonal matrix :

[0012] For the flow field , the decomposition into the DMD mode , the modal amplitude matrix and the DMD eigenvalue matrix is obtained, and the flow field reconstruction expression is obtained:

[0013] wherein, r is​rank of the matrix , the first i order singular value decomposition (SVD) mode, the first i order mode amplitude, the first i order DMD eigenvalue; the Vandermonde matrix.

[0014] Preferably, in step 2, the objective function is:

[0015] wherein, is a promotion sparse term, is a truncation error term:

[0016] wherein, is a penalty term for penalizing the number of non-zero elements in the mode amplitude, and a regularization parameter is added , as the increase of , the more zero elements in the mode amplitude matrix , thus producing a more sparse solution; denotes the conjugate transpose of the matrix denotes the two-norm calculation.

[0017] Preferably, the convex optimization problem of the objective function is solved by the alternating direction multiplier method (ADMM).

[0018] Preferably, in step 3, the mode amplitude and DMD eigenvalue of the unknown working condition are predicted based on the mode amplitude and DMD eigenvalue of the dominant mode of the flow field under the known working condition as: According to the DMD mode of the flow field under the known working condition , the SVD mode corresponding to the dominant mode order is extracted, denoted as , to form the basis SVD mode; wherein, m is the total order of the dominant mode; obtain the working condition parameters and the mode amplitude and DMD eigenvalue of the dominant mode under multiple known working conditions; For each dominant mode j , the mapping relationship between the mode amplitude , the DMD eigenvalue and the working condition parameters is determined by fitting; According to the working condition parameters of the unknown working condition, based on the mapping relationship, the mode amplitude prediction value of each dominant mode order j under the unknown working condition is obtained and DMD eigenvalue prediction value .

[0019] Preferably, the DMD mode of the flow field under the known working condition is The SVD mode corresponding to the dominant modal order is extracted and denoted as The basic SVD mode is composed of: Any one known working condition is selected, and the DMD mode of the flow field is The SVD mode corresponding to each dominant modal order is extracted to directly form the basic SVD mode; Or, For multiple known working conditions, the DMD mode of the flow field is The SVD mode corresponding to each dominant modal order is extracted respectively; For each dominant modal order j The SVD mode of multiple known working conditions is found The largest one is taken as the basic SVD mode of the dominant modal order j .

[0020] Preferably, in step 3, the prediction value based on the modal amplitude and the DMD eigenvalue is determined by using the inverse process of the DMD, and the predicted flow field of the unknown working condition is: Flow field prediction value The expression is:

[0021] Wherein, is the flow field prediction value at time step t; is the modal amplitude prediction value of the dominant modal order j is the DMD eigenvalue prediction value of the dominant modal order at time step t, j is the SVD mode of the dominant modal order in the basic SVD mode, j is the total number of dominant modes. m

[0022] The application also provides a cascade flow field prediction device based on sparse promotion modal characteristic prediction, which comprises a sparse optimization module and a flow field prediction module. The sparse optimization module is used for decomposing the flow field snapshot into DMD mode , modal amplitude matrix and DMD eigenvalue matrix ​The flow field reconstruction expression is constructed; an objective function is constructed, including a truncation error term and a sparsity promotion term between the original flow field and the reconstructed flow field; the sparsity promotion term is used to penalize the number of non-zero elements in the unknown modal amplitude to produce a sparser solution; the optimal position of the non-zero modal amplitude is solved based on the objective function, and the modal order composition corresponding to the non-zero modal amplitude represents the dominant mode of the flow field dynamic characteristics; The flow field prediction module is used to predict the modal amplitude and DMD characteristic values ​​of unknown operating conditions based on the dominant mode determined by the sparse optimization module and the modal amplitude and DMD characteristic values ​​of the dominant mode of the flow field under known operating conditions. Then, based on the predicted values ​​of the modal amplitude and DMD characteristic values, the predicted flow field of the unknown operating condition is determined by using the inverse process of DMD.

[0023] Preferably, the sparsity-promoting term in the objective function is a modal amplitude matrix. The sum of the absolute values ​​of the amplitudes of each mode is used to represent the mode, with regularization parameters added. ,along with The increase of modal amplitude matrix The more zero elements there are.

[0024] Preferably, the flow field prediction module includes a basic SVD mode construction module, a mode amplitude mapping relationship construction module, a DMD eigenvalue mapping relationship construction module, and a reconstruction module; The basic SVD mode construction module is used to construct DMD modes based on the flow field under known operating conditions. Extract the SVD mode corresponding to the dominant mode order, denoted as These constitute the basic SVD modes; among them, m The total order of the dominant mode; The modal amplitude mapping relationship construction module is used to obtain the operating parameters and modal amplitudes of the dominant modes under various known operating conditions. For each dominant mode j The modal amplitude is determined by fitting. Mapping relationship with operating parameters; The DMD feature value mapping relationship construction module is used to obtain the operating parameters and DMD feature values ​​of the dominant mode under various known operating conditions. For each dominant mode j DMD feature values ​​were determined through fitting. Mapping relationship with operating parameters; The reconstruction module is used to obtain each dominant mode order under the unknown working condition based on the working condition parameters and the mapping relationship. j Modal amplitude prediction values and DMD eigenvalue prediction Then, based on the modal amplitude prediction values... and DMD eigenvalue prediction The predicted flow field for the unknown operating condition is determined by using the inverse process of DMD.

[0025] Beneficial effects: (1) This invention improves the DMD method by adding control of the number of sparse modes to the objective function, thereby increasing the number of sparse modes, improving mode selection efficiency, enhancing mode sparsity, and thus better identifying the subset of modes that have a significant impact on the flow field. Moreover, increasing the number of sparse modes can also reduce computational costs and increase computational speed.

[0026] (2) This global optimization problem is solved by using the Alternative Direction Multiplayer method (ADMM), thereby enhancing the sparsity of the modes and better identifying the subset of modes that have a significant impact on the flow field. (3) After obtaining the characteristic parameters of the known flow field after order reduction, the characteristic parameters of the flow field under unknown working conditions can be calculated by using regression model or fitting method, thereby realizing the prediction of single-parameter or multi-parameter flow field variables. Attached Figure Description

[0027] Figure 1 This is a flowchart of the flow field prediction method for cascades based on sparse-promoted modal feature prediction according to the present invention.

[0028] Figure 2 This is a schematic diagram of a variable pitch angle rotor blade cascade structure.

[0029] Figure 3 This is a schematic diagram of the prediction boundary of a bivariate prediction scheme in an example.

[0030] Figure 4 This is a block diagram of the flow field prediction device for cascades based on sparse-promoted modal feature prediction according to the present invention. Detailed Implementation

[0031] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0032] This invention provides a method for predicting the flow field of a cascade based on sparse-enhanced modal feature prediction, such as... Figure 1 As shown, it includes the following steps: Step S1: Construct the flow field reconstruction expression.

[0033] First, a data sequence of flow field snapshots at equal time intervals is obtained based on experiments or fluid dynamics simulations. :

[0034] in, For a certain moment t A snapshot of the physical quantities of the flow field. . It is a vector whose elements are physical quantities of the flow field, which may include static pressure, velocity field, pressure field, etc. Describe the M×N matrix space over the complex field. M The number of measurement points (the product of the number of grid points and the number of variables). N For the number of snapshots, .

[0035] Assuming a small time step, the time steps of two adjacent moments are... and A mapping relationship exists:

[0036] in, It is a linear mapping matrix.

[0037] Another flow field snapshot generated by the invariant system :

[0038] If the snapshot is generated by a discrete-time linear system, then:

[0039] Among them These are linear coefficients; the linear coefficients constitute a linear mapping matrix. .

[0040] That is, the flow field at the previous moment can be obtained by linear transformation of the flow field at the next moment:

[0041] The dynamic information of the flow field is contained in the linear mapping matrix. In the middle, through analysis The eigenvalues ​​and other parameters can be used to identify the dynamic characteristics of the entire flow field.

[0042] Linear mapping matrix The expected parameters corresponding to the eigenvalues ​​are obtained through singular value decomposition.

[0043] Convection field Perform eigenvalue decomposition:

[0044]

[0045] Based on similarity matrix The eigenvalues ​​are obtained as follows:

[0046] in, and It is an orthogonal matrix. It is a diagonal matrix. Representation matrix The conjugate transpose of . r Representing a matrix Rank is equal to the singular values ​​(of a matrix). The number of diagonal elements.

[0047] matrix Represents a matrix The best low-dimensional representation, It is a matrix eigenvectors, It is a matrix The eigenvalues. Using a matrix. Can Projecting to higher dimensions, i.e., DMD modes :

[0048] The energy of a mode can be used The norm indicates that the level of modal energy reflects the importance of a mode in the flow field. Specifically, it represents... Projected to By identifying the modes, the modal energy can be obtained. (The level of modal energy reflects the importance of the mode in the flow field):

[0049]

[0050] Since DMD achieves dimensionality reduction of the system, the dynamic relationship in the lower dimension is as follows:

[0051] Snapshot It can be derived from a matrix Approximate mapping to lower dimensions ,and It can be converted to diagonal coordinates:

[0052]

[0053] in, It has a unit length, and , yes The eigenvectors of have the following bioorthogonality condition:

[0054] Then the above formula It can be transformed into:

[0055] In the formula, Represents the i-th mode pair The contribution, and Defined as the amplitude of the corresponding DMD mode. The superscript H indicates the conjugate transpose calculation, and t represents the discrete time step number (i.e., the time index in the Vandermonde matrix). The Vandermonde matrix dominates the temporal evolution of the dynamic mode and describes the state of the mode at discrete time step t; each column of the Vandermonde matrix corresponds to a t.

[0056] Will Mapping to a higher-dimensional space, that is Its matrix form is That is, for a flow field snapshot It can be decomposed into DMD modes. Modal amplitude and DMD eigenvalues This is the expression for flow field reconstruction:

[0057] in, r for rank; For the first i The singular value decomposition (SVD) mode of order 1 is a basis function and an auxiliary mode used to construct the DMD mode; For the first i First mode amplitude, For the first i Modal eigenvalues ​​at discrete time step t, ; For the Vandermonde matrix, the time evolution of its dominant dynamic mode is given.

[0058] Step S2: Construct an objective function, including a truncation error term and a sparsity promotion term between the original flow field and the reconstructed flow field; the sparsity promotion term is used to penalize the number of non-zero elements in the unknown mode amplitude matrix to produce a sparser solution; optimize the solution based on the objective function to find the optimal position of the non-zero mode amplitude, and the mode order corresponding to the non-zero mode amplitude represents the dominant mode of the flow field dynamic characteristics.

[0059] After decomposing the flow field data, the DMD method needs to filter the modes to obtain the optimal subset of modes that can represent the dynamic characteristics of the flow field; these are called dominant modes. The number of active modes directly affects the reconstruction error and computational cost. To balance the computational cost and reconstruction error of DMD, a definition is provided. The error between the reconstructed matrix and the reconstructed matrix is ; because

[0060]

[0061] The error function selected in this invention is: , which represents the difference between the original flow field matrix and the reconstructed matrix, i.e., the truncation error.

[0062] To further sparse the number of modes and improve mode selection efficiency, a penalty term is added to the error function. Constructing coefficient promotion term Therefore, the optimization problem is transformed into: (1) in, The larger the value, the greater the penalty. The purpose of this term is to make... There are more zero elements in it. To introduce regularization parameters, To regulate The sparsity of the sparsity increases with The increase of vector The more zero elements there are, The more zero elements in the vector, the sparser the solution. The goal of this invention is to find the vector that minimizes the objective function. .

[0063] For a vector with unknown magnitude To achieve the optimization of sparsification and reconstruction error, it is equivalent to the convex optimization problem of the above equation (1), and the alternating direction multiplier method (ADMM) is used to solve it.

[0064] After achieving an ideal balance between the accuracy of the flow field approximation and the number of DMD modes, the following constrained convex optimization problem is solved with the sparse structure having an unknown amplitude vector fixed: Objective function: (2) Constraints: (3) The position of the non-zero term in the amplitude vector is obtained by optimizing equation (1), and the optimal value of the non-zero term is obtained by equations (2) and (3) to approximate the original data sequence.

[0065] The detailed solution process is as follows: make For ease of representation, the solution will be... vectors in use Instead, the optimization problem transforms into .

[0066] Introducing the Lagrange function:

[0067] in, and These are the parameters.

[0068] Use superscript k To indicate the iteration round, optimize using the following iteration format:

[0069] The convergence speed of this algorithm is affected by parameters. The influence of this convergence condition is:

[0070] in, and These are convergence thresholds in the ADMM optimization algorithm, used to determine whether the optimization process has converged to a satisfactory solution. Their specific values ​​are usually set according to the accuracy requirements of the practical application, and common value ranges may include... arrive between.

[0071] Step S3: Based on the modal amplitude and DMD characteristic value of the dominant mode of the flow field under known operating conditions, predict the modal amplitude and DMD characteristic value of the unknown operating conditions; then, based on the predicted values ​​of the modal amplitude and DMD characteristic value, use the inverse process of DMD to determine the predicted flow field of the unknown operating conditions.

[0072] After decomposing the flow field using this invention, an approximate flow field can be obtained through flow field reconstruction. If a functional relationship can be established between the characteristic parameters after modal decomposition under different operating conditions, the DMD eigenvalues ​​for unknown operating conditions can be predicted. Modal amplitude This allows us to obtain an approximate flow field for unknown operating conditions.

[0073] As the inverse process of flow field decomposition, flow field prediction can be viewed as reconstructing the flow field using modes and corresponding DMD eigenvalues ​​and mode amplitudes. Therefore, the flow field prediction steps can be expressed as:

[0074] in, For the flow field at time step t, The total order of the dominant mode. Dominant mode j SVD mode, and These represent the dominant mode order.j The DMD eigenvalues ​​and modal amplitudes. j is the order index after rearranging the order of the dominant module.

[0075] To obtain all the above parameters of the predicted flow field, this invention proposes the following two assumptions: Assumption 1: Under changing flow field conditions (such as rotational speed, flow rate, etc.), the dominant mode of the flow field remains unchanged or approximately unchanged. This assumption means that since the dominant mode is constant, the dominant mode of a known operating condition can be selected as the basic mode to predict the flow field under adjacent operating conditions.

[0076] The specific solution is as follows: based on the DMD modes of the flow field under known operating conditions. Extract the SVD modes corresponding to the dominant mode order (1~m), denoted as These form the basic SVD modes. There are two extraction methods: Option 1: Select any known operating condition and analyze the DMD modes of the flow field. Extract the SVD modes corresponding to each dominant mode order and directly form the basic SVD modes.

[0077] Option 2: For multiple known operating conditions, analyze the DMD modes of the flow field under each operating condition. Extract the SVD modes corresponding to each dominant mode order; for each dominant mode order j SVD modes from various known working conditions Find the one with the largest proportion and designate it as the dominant mode. j The basic SVD modes. For example: if for the dominant mode order 1, the mode a1 with the highest proportion is extracted from working conditions 1-3; and for the dominant mode order 2, the mode a3 with the highest proportion is extracted from working conditions 1-3, then the basic modes are {a1, a3}.

[0078] Hypothesis 2: The parameters of the flow field under different operating conditions have a certain functional relationship with the characteristic parameters corresponding to the dominant mode.

[0079] Under various operating conditions related to the dominant mode, there are corresponding relationships between relevant parameters. That is, under different operating conditions, there are functional relationships between operating parameters and modal characteristic values ​​and modal amplitudes. These functional relationships can be found using methods such as polynomial fitting and regression models.

[0080] So for each dominant mode j The modal amplitude is determined by fitting. DMD eigenvalues The mapping relationship between the parameters and the operating conditions. For example, the constructed mapping relationship is as follows:

[0081]

[0082] in, For the predicted DMD eigenvalues ​​of the j-th mode, The modal amplitude of the predicted j-th mode; Operating condition parameters directly determine modal parameters. The pitch angle of the grating blades. For flow coefficient; This represents the mapping relationship between the operating parameters and the eigenvalues ​​of the DMD corresponding to the j-th mode; This represents the mapping relationship between the operating parameters and the modal amplitude for the j-th mode.

[0083] During prediction, based on the operating parameters of the unknown operating condition and the aforementioned mapping relationship, each dominant mode order under the unknown operating condition is obtained. j Modal amplitude prediction values and DMD eigenvalue prediction .

[0084] Based on the above two assumptions, the SVD modes of the flow field under the corresponding unknown working conditions can be obtained. Modal amplitude and DMD eigenvalues By utilizing the inverse process of DMD, the following reconstruction formula can be used to predict the flow field:

[0085] in, For the predicted flow field at time t, Dominant mode j The predicted modal amplitude values, For the dominant mode at time step t j DMD eigenvalue predictions Dominant mode order in basic SVD modes j SVD modes; m The dominant mode order.

[0086] The relationship between the modal amplitudes and eigenvalues ​​of the flow field under different operating conditions is determined through interpolation. For univariate flow field predictions (i.e., where there is a variable parameter, such as the flow coefficient, between the predicted flow field condition and the known flow field), cubic interpolation is used, while for bivariate flow field predictions (such as rotational speed and flow coefficient), surface interpolation is used. Compared to machine learning, interpolation requires less data, which is beneficial for rapid calculation and analysis of the flow field.

[0087] For univariate predictions, such as those using parameters including cascade pitch angle θ and flow coefficient φ, θ can be fixed at a single value, while multiple φ values ​​can be selected to form various known operating conditions. Under each known condition, the modal amplitude and DMD eigenvalue of the dominant flow mode are obtained, and the relationship between φ and modal amplitude is determined. When predicting the [θ,φ'] condition, where φ' is a parameter not covered in the known conditions, the modal amplitude and DMD eigenvalue corresponding to φ' are determined based on the aforementioned relationships and substituted into the reconstruction formula to predict the flow field.

[0088] For bivariate prediction, for example, when the operating parameters include the blade pitch angle θ and the flow coefficient φ, θ is fixed at a single value θ1, and multiple φ values ​​are selected to form various operating parameters; when θ is changed, multiple φ values ​​are selected for each θ value to form various operating parameters. For each known operating condition, the modal amplitude and DMD eigenvalue of the dominant flow field mode are obtained, and a two-dimensional relationship between the modal amplitude and [θ,φ], as well as a two-dimensional relationship between the DMD eigenvalue and [θ,φ], are constructed. When predicting the [θ',φ'] operating condition, θ' and φ' are parameters not involved in the known operating conditions. Therefore, the modal amplitude and DMD eigenvalue corresponding to θ' and φ' are determined based on the above two-dimensional relationship and substituted into the reconstruction formula to predict the flow field.

[0089] The flow field predicted by this invention can be used for active control of variable pitch angle of the blade cascade.

[0090] To verify the above method, a model of a variable pitch angle rotor blade cascade structure was created, as shown in the attached diagram. Figure 2 Where L is defined as the distance from the leading edge point to the pivot point, θ is defined as the pitch angle of the blade around the pivot point, c represents the blade cascade length, and L / c represents the pivot point position of the blade cascade.

[0091] To reduce computational costs, a single-channel mesh model was selected for numerical calculation. The total axial length of the computational domain was 10c, including an inlet section of 3.72c, a rotor section of 0.56c, and an outlet section of 5.72c. The inlet temperature was set to 298K, the number of time steps per unit channel was set to 400, and the rotational speed was set to 10000 rpm.

[0092] To predict the blade pitch angle θ and flow coefficient φ for the gas turbine flow field distribution, a prediction scheme is developed to predict unknown operating conditions from known operating conditions. This scheme is divided into univariate and bivariate prediction schemes. The pivot position of the variable pitch angle blade is set to 0.3c.

[0093] Take θ1=2°, θ2=4°, θ3=6° φ1=0.125, φ2=0.150, φ3=0.175, φ4=0.200, φ5=0.225 φ6=0.250, φ7=0.275, φ8=0.325, φ9=0.325.

[0094] Table 1 below shows the operating parameters for the univariate and bivariate prediction schemes. In the univariate prediction scheme, with a fixed blade pitch angle θ, the flow field distribution under the other two flow coefficients is predicted based on the flow coefficients under three known conditions. In the bivariate prediction scheme, both the blade pitch angle θ and the flow coefficient φ can be varied. Figure 3 The prediction boundary of the bivariate prediction scheme is shown. The quadrilateral region enclosed by ABCD is the predictable region, and its size is limited by the upper and lower boundaries. The results show that the distribution of the spanwise average Mach number along the blade chord predicted by the method described in this paper is highly consistent with the simulation results, indicating that this method can accurately capture the variation trend of flow pressure and velocity along the chord.

[0095] Table 1

[0096] To achieve the above method, the present invention also provides a flow control device for variable pitch angle of a cascade based on sparse-promoted modal feature prediction, such as... Figure 4 As shown, it includes a sparse optimization module and a flow field prediction module; The sparse optimization module is used to decompose the flow field snapshot into DMD modes using Dynamic Mode Decomposition (DMD). Modal amplitude matrix and DMD eigenvalue matrix The flow field reconstruction expression is constructed; an objective function is constructed, including a truncation error term and a sparsity promotion term between the original flow field and the reconstructed flow field; the sparsity promotion term is used to penalize the number of non-zero elements in the unknown modal amplitude to produce a sparser solution; the optimal position of the non-zero modal amplitude is solved based on the objective function, and the modal order corresponding to the non-zero modal amplitude represents the dominant mode of the flow field dynamic characteristics.

[0097] The sparsity promotion term in the objective function is represented by the modal amplitude matrix. The sum of the absolute values ​​of the amplitudes of each mode is used to represent the mode, with regularization parameters added. ,along with The increase of modal amplitude matrix The more zero elements there are.

[0098] The flow field prediction module is used to predict the modal amplitude and DMD characteristic values ​​of unknown operating conditions based on the dominant mode determined by the sparse optimization module and the modal amplitude and DMD characteristic values ​​of the dominant mode of the flow field under known operating conditions. Then, based on the predicted values ​​of the modal amplitude and DMD characteristic values, the predicted flow field of the unknown operating condition is determined by using the inverse process of DMD.

[0099] The flow field prediction module includes a basic SVD mode construction module, a mode amplitude mapping relationship construction module, a DMD eigenvalue mapping relationship construction module, and a reconstruction module. The basic SVD mode construction module is used to construct DMD modes based on the flow field under known operating conditions. Extract the SVD mode corresponding to the dominant mode order, denoted as These constitute the basic SVD modes; among them, m The total order of the dominant mode.

[0100] The modal amplitude mapping relationship construction module is used to obtain the operating parameters and modal amplitudes of the dominant modes under various known operating conditions. For each dominant mode j The modal amplitude is determined by fitting. The mapping relationship between the parameters and the operating conditions.

[0101] The DMD eigenvalue mapping relationship construction module is used to obtain the operating parameters and DMD eigenvalues ​​of the dominant mode under various known operating conditions. For each dominant mode j DMD feature values ​​were determined through fitting. The mapping relationship between the parameters and the operating conditions.

[0102] The reconstruction module is used to obtain each dominant mode order under the unknown working condition based on the working condition parameters and the mapping relationship. j Modal amplitude prediction values and DMD eigenvalue prediction Then, based on the modal amplitude prediction values... and DMD eigenvalue prediction The predicted flow field for the unknown operating condition is determined by using the inverse process of DMD.

[0103] The specific embodiments described above only illustrate the design principles of the present invention. The shapes and names of the components in this description may differ and are not limited. Therefore, those skilled in the art can modify or make equivalent substitutions to the technical solutions described in the foregoing embodiments; and these modifications and substitutions do not depart from the inventive spirit and technical solutions of the present invention, and should all fall within the protection scope of the present invention.

Claims

1. A method for predicting the flow field of a cascade based on sparse-promoted modal feature prediction, characterized in that, include: Step 1: Use Dynamic Mode Decomposition (DMD) to decompose the flow field snapshot into DMD modes. Modal amplitude matrix and DMD eigenvalue matrix Construct the flow field reconstruction expression; Step 2: Construct the objective function, including the truncation error term between the original flow field and the reconstructed flow field, as well as the sparsity promotion term; The term promoting sparsity is used to penalize the number of non-zero elements in the unknown mode amplitude matrix in order to produce a sparser solution. The optimal position of non-zero mode amplitude is obtained by optimizing the objective function. The mode order composition corresponding to the non-zero mode amplitude represents the dominant mode of the dynamic characteristics of the flow field. Step 3: Based on the modal amplitude and DMD eigenvalues ​​of the dominant flow field modes under known operating conditions, predict the modal amplitude and DMD eigenvalues ​​under unknown operating conditions; Then, based on the predicted values ​​of modal amplitude and DMD eigenvalues, the predicted flow field for the unknown operating condition is determined using the inverse process of DMD.

2. The cascade flow field prediction method based on sparse-promoted modal feature prediction as described in claim 1, characterized in that, Step 1 includes: The data sequence for obtaining a snapshot of the flow field under known operating conditions is as follows: Another data sequence of flow field snapshots generated by the invariant system is as follows: In the formula, This is a snapshot of the physical quantities of the flow field at time step t. , For the number of snapshots; Flow field in the previous moment Through matrix The linear transformation yields the flow field at the next time step. : ; Convection field Perform eigenvalue decomposition: ; and It is an orthogonal matrix. If the matrix is ​​diagonal, then: Among them, matrix Represents a matrix The best low-dimensional representation, and Representing matrices respectively Eigenvectors and eigenvalues; using orthogonal matrices eigenvectors Projecting to higher dimensions, i.e., DMD modes: For the flow field It is then decomposed into DMD modes. Modal amplitude matrix and DMD eigenvalue matrix The flow field reconstruction expression is obtained as follows: in, r for rank, For the first i Singular Value Decomposition (SVD) Modes For the first i First mode amplitude, For the first i DMD eigenvalues; This is the Vandermonde matrix.

3. The cascade flow field prediction method based on sparse-promoted modal feature prediction as described in claim 2, characterized in that, In step 2, the objective function is: in, To promote sparse terms, For the truncation error term: In the formula, To penalize the number of non-zero elements in the modal amplitude, a regularization parameter is added. ,along with The increase of modal amplitude matrix The more zero elements there are, the sparser the solutions become; Representation matrix The conjugate transpose of . This indicates the calculation of the L2 norm.

4. The cascade flow field prediction method based on sparse-promoted modal feature prediction as described in claim 3, characterized in that, The convex optimization problem of the objective function is solved by the Alternating Direction Multiplier Method (ADMM).

5. The cascade flow field prediction method based on sparse-promoted modal feature prediction as described in claim 1, characterized in that, In step 3, based on the modal amplitude and DMD characteristic values ​​of the dominant flow field mode under known operating conditions, the modal amplitude and DMD characteristic values ​​for the unknown operating conditions are predicted as follows: Based on the DMD modes of the flow field under known operating conditions Extract the SVD mode corresponding to the dominant mode order, denoted as These constitute the basic SVD modes; among them, m The total order of the dominant mode; Obtain operating parameters and modal amplitudes of the dominant modes under various known operating conditions. and DMD eigenvalues ; For each dominant mode j The modal amplitude is determined by fitting. DMD eigenvalues Mapping relationship with operating parameters; Based on the operating parameters of the unknown operating condition and the mapping relationship, each dominant mode order under the unknown operating condition is obtained. j Modal amplitude prediction values and DMD eigenvalue prediction .

6. The cascade flow field prediction method based on sparse-promoted modal feature prediction as described in claim 5, characterized in that, The DMD mode based on the flow field under known operating conditions Extract the SVD mode corresponding to the dominant mode order, denoted as The basic SVD modes are: Choose any known operating condition and analyze the DMD modes of the flow field. Extract the SVD modes corresponding to each dominant mode order and directly form the basic SVD modes; or, For various known operating conditions, the DMD modes of the flow field are analyzed. Extract the SVD modes corresponding to each dominant mode order; For each dominant mode j SVD modes from various known working conditions Find the one with the largest proportion and designate it as the dominant mode. j The basic SVD mode.

7. The cascade flow field prediction method based on sparse-promoted modal feature prediction as described in claim 5, characterized in that, In step 3, the predicted flow field for the unknown operating condition is determined by using the inverse process of DMD based on the predicted values ​​of modal amplitude and DMD eigenvalues: Flow field prediction The expression is: in, The predicted flow field value at time step t; Dominant mode j The predicted modal amplitude values, The dominant mode order at time step t j DMD eigenvalue predictions Dominant mode order in basic SVD modes j SVD mode, m The total order of the dominant mode.

8. A flow field prediction device for cascades based on sparse-promoted modal feature prediction, characterized in that, It includes a sparse optimization module and a flow field prediction module; The sparse optimization module is used to decompose the flow field snapshot into DMD modes using Dynamic Mode Decomposition (DMD). Modal amplitude matrix and DMD eigenvalue matrix Construct the flow field reconstruction expression; construct the objective function, including the truncation error term and the sparsity promotion term between the original flow field and the reconstructed flow field; The term promoting sparsity is used to penalize the number of non-zero elements in the unknown mode amplitude in order to produce a sparser solution. The optimal position of non-zero mode amplitude is obtained by optimizing the objective function. The mode order composition corresponding to the non-zero mode amplitude represents the dominant mode of the dynamic characteristics of the flow field. The flow field prediction module is used to predict the modal amplitude and DMD characteristic values ​​of unknown operating conditions based on the dominant mode determined by the sparse optimization module and the modal amplitude and DMD characteristic values ​​of the dominant mode of the flow field under known operating conditions. Then, based on the predicted values ​​of the modal amplitude and DMD characteristic values, the predicted flow field of the unknown operating condition is determined by using the inverse process of DMD.

9. The cascade flow field prediction device based on sparse-promoted modal feature prediction as described in claim 8, characterized in that, The sparsity-promoting term in the objective function is represented by the modal amplitude matrix. The sum of the absolute values ​​of the amplitudes of each mode is used to represent the mode, with regularization parameters added. ,along with The increase of modal amplitude matrix The more zero elements there are.

10. The cascade flow field prediction device based on sparse-promoted modal feature prediction as described in claim 8, characterized in that, The flow field prediction module includes a basic SVD mode construction module, a mode amplitude mapping relationship construction module, a DMD eigenvalue mapping relationship construction module, and a reconstruction module; The basic SVD mode construction module is used to construct DMD modes based on the flow field under known operating conditions. Extract the SVD mode corresponding to the dominant mode order, denoted as These constitute the basic SVD modes; among them, m The total order of the dominant mode; The modal amplitude mapping relationship construction module is used to obtain the operating parameters and modal amplitudes of the dominant modes under various known operating conditions. For each dominant mode j The modal amplitude is determined by fitting. Mapping relationship with operating parameters; The DMD feature value mapping relationship construction module is used to obtain the operating parameters and DMD feature values ​​of the dominant mode under various known operating conditions. For each dominant mode j DMD feature values ​​were determined through fitting. Mapping relationship with operating parameters; The reconstruction module is used to obtain each dominant mode order under the unknown working condition based on the working condition parameters and the mapping relationship. j Modal amplitude prediction values and DMD eigenvalue prediction Then, based on the modal amplitude prediction values... and DMD eigenvalue prediction The predicted flow field for the unknown operating condition is determined by using the inverse process of DMD.

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