A method, program, equipment, and storage medium for extracting the dominant modes of flow field in a centrifugal fan impeller based on fast sparse dynamic mode decomposition.

Abstract

This invention belongs to the field of numerical calculation technology of centrifugal fan impeller flow field, specifically involving a method, program, device, and storage medium for extracting the dominant modes of centrifugal fan impeller flow field based on fast sparse dynamic mode decomposition (DMD). This invention takes the multi-mode amplitude of a certain physical quantity of a centrifugal fan impeller as the objective, obtains unsteady flow field snapshots of this physical quantity, performs dynamic mode decomposition on adjacent time snapshot matrices to obtain DMD reconstructed modes and time eigenvalues, uses the reconstruction residual of the total data matrix of all time snapshots as data constraints, introduces an L1 regularization term, establishes a sparse optimization function for mode amplitude, and transforms it into a low-dimensional convex optimization problem. A fast iterative threshold shrinkage algorithm is used, combined with Nesterov momentum update, gradient descent, and soft thresholding to iteratively solve the low-dimensional convex optimization problem. After iterative convergence, a subspace is determined based on the non-zero modes, and a least-squares problem without regularization terms is resolved in the subspace to obtain the multi-mode amplitude of the target physical quantity.

Description

Technical Field

[0001] This invention belongs to the field of numerical calculation technology of centrifugal fan impeller flow field, specifically involving a method, program, equipment and storage medium for extracting the dominant modes of centrifugal fan impeller flow field based on fast sparse dynamic mode decomposition. Background Technology

[0002] During the operation of a centrifugal fan, the high-speed rotation of the impeller causes periodic flow separation, jet-wake evolution, and non-uniform flow at the outlet within the blade flow channel. The resulting velocity and pressure pulsations affect the fan's operational stability, the periodic load on the blades, and the aerodynamic noise level.

[0003] Transient numerical calculations of impeller pressure and velocity fields are characterized by high spatial degrees of freedom and a large number of time snapshots, making direct analysis of the entire flow field computationally intensive. Conventional dynamic mode decomposition (DMD) determines mode amplitudes based on the initial flow field, which is susceptible to interference from the initial state and rapidly decaying modes, leading to inaccurate identification of the dominant flow structure related to the impeller shaft frequency. Existing sparse dynamic mode decomposition methods also suffer from long solution times when dealing with high-dimensional impeller flow fields. Summary of the Invention

[0004] The purpose of this invention is to provide a method, program, device, and storage medium for extracting the dominant modes of flow field in a centrifugal fan impeller based on fast sparse dynamic mode decomposition.

[0005] A method for extracting the dominant modes of flow field in a centrifugal fan impeller based on fast sparse dynamic mode decomposition includes the following steps: Taking the multi-mode amplitude of a certain physical quantity of a centrifugal fan impeller as the target, the unsteady flow field snapshot of the physical quantity is obtained, and the total data matrix of all time snapshots is constructed. The first sampling time and the last sampling time are removed respectively to construct the adjacent time snapshot matrix. Dynamic mode decomposition is performed on adjacent time snapshot matrices to obtain DMD reconstructed modes and time eigenvalues. A time evolution Vandermonde matrix is ​​constructed based on the time eigenvalues. The total data matrix of all time snapshots is reconstructed by multiplying the DMD reconstructed modes, the multi-mode amplitude diagonal matrix, and the time evolution Vandermonde matrix. Using the reconstructed residuals of the total data matrix from all time snapshots as data constraints, we introduce... Regularization term, establish modal amplitude sparse optimization function; decompose modal amplitude sparse optimization function into smooth data fitting term and non-smooth regularization term, transform into low-dimensional convex optimization problem; A fast iterative shrinking threshold algorithm is adopted, which combines Nesterov momentum update, gradient descent and soft thresholding to iteratively solve the low-dimensional convex optimization problem. After the iteration converges, the subspace is determined according to the non-zero modes, and the least squares problem without regularization terms is resolved in the subspace to obtain the multi-mode amplitude of the target physical quantity.

[0006] Furthermore, the step of performing dynamic mode decomposition on adjacent time snapshot matrices to obtain DMD reconstructed mode and temporal feature values ​​specifically involves: The adjacent time snapshot matrix includes a first adjacent time snapshot matrix excluding the last sampling time, and a second adjacent time snapshot matrix excluding the first sampling time; Using the modal order as the truncation threshold, truncated singular value decomposition is performed on the first adjacent time snapshot matrix to obtain the left singular matrix, the truncated singular value diagonal matrix and the right singular matrix. The low-dimensional matrix is ​​obtained by multiplying the conjugate transpose of the left singular matrix, the second adjacent time snapshot matrix, the right singular matrix, and the inverse of the truncated singular value diagonal matrix. Perform eigenvalue decomposition on a low-dimensional matrix to obtain an eigenvalue diagonal matrix and an eigenvector matrix. The diagonal elements of the eigenvalue diagonal matrix are the time eigenvalues. The DMD reconstructed mode is obtained by multiplying the second adjacent time snapshot matrix, the right singular matrix, the inverse of the truncated singular value diagonal matrix, and the eigenvector matrix.

[0007] Furthermore, the reconstructed residuals of the total data matrix from all time snapshots are used as data constraints, and this is introduced... The regularization term establishes a sparse optimization function for modal amplitudes, specifically: in, For the target vector, , For the target physical quantity of centrifugal fan impeller First-order modal amplitude; The total data matrix for all time snapshots; Reconstructing modes for DMD; for Diagonal matrix of modal amplitudes, ; For time-evolving Vandermonde matrix; This indicates the calculation of the Frobenius norm; Indicates calculation Norm; This is the regularization parameter.

[0008] Furthermore, the process of decomposing the modal amplitude sparse optimization function into smooth data fitting terms and non-smooth regularization terms, transforming it into a low-dimensional convex optimization problem, specifically involves: in, For smooth data fitting, ; It is a non-smooth regularization term. ; , ; superscript " " indicates conjugate transpose. symbol" " represents the Hadamard product, and the overline indicates the complex conjugate. This represents the computation of the trace of a matrix; The truncated singular value diagonal matrix is ​​obtained by performing truncated singular value decomposition on the first adjacent time snapshot matrix.

[0009] Furthermore, the fast iterative shrinkage thresholding algorithm, combined with Nesterov momentum update, gradient descent, and soft thresholding, is used to iteratively solve the low-dimensional convex optimization problem, specifically as follows: Starting from the third iteration, the target vector is updated based on the previous two iterations. and Update momentum auxiliary variable ; in, For the number of iterations, To accelerate the step size factor, ; Calculate the smooth data fitting term in the momentum auxiliary variable gradient at ; Searching along the negative gradient direction yields intermediate variables. ; in, For smooth data fitting term The Lipschitz constant; Processing intermediate variables using the soft threshold operator , obtained the The target vector updated in the next iteration .

[0010] Furthermore, the soft threshold operator is: The soft threshold operator intermediate variables Medium modulus length less than threshold The modal amplitude is forcibly set to zero to achieve automatic sparse screening of modes.

[0011] Furthermore, after the iteration converges, a subspace is determined based on the non-zero modes, and the least squares problem without regularization terms is resolved in the subspace to obtain the multi-mode amplitudes of the target physical quantity, specifically: If the first The target vector updated in the next iteration If convergence is achieved, the target vector is extracted. Construct a set of non-zero modal amplitudes from all non-zero modal amplitudes. ; In the set of non-zero modal amplitudes Within a defined subspace, the least squares problem without regularization terms is resolved to obtain the final objective vector. This yields the multi-mode amplitudes of the target physical quantity. .

[0012] A computer device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described method for extracting the dominant modes of a centrifugal fan impeller flow field based on fast sparse dynamic mode decomposition.

[0013] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method for extracting the dominant modes of a centrifugal fan impeller flow field based on fast sparse dynamic mode decomposition.

[0014] A computer program product includes computer instructions that, when executed by a processor, implement the steps of the above-described method for extracting the dominant modes of a centrifugal fan impeller flow field based on fast sparse dynamic mode decomposition.

[0015] The beneficial effects of this invention are as follows: This invention acquires transient flow field snapshots at preset sampling time intervals and obtains spatial modes, discrete-time eigenvalues, and their temporal evolution relationships through dynamic mode decomposition. To reduce the influence of initial flow field states and rapidly decaying modes on the dominant structure identification results, this invention uses the overall fitting residuals of all time snapshots as data constraints and introduces... The regularization term establishes a modal amplitude sparse optimization model, enabling modal selection to comprehensively consider the overall contribution of each mode within the complete sampling time.

[0016] To address the sparse optimization problem, this invention employs Nesterov momentum update, gradient descent, and soft thresholding. A fast iterative threshold shrinkage algorithm is used to solve the problem, gradually shrinking the amplitudes of low-contribution modes to zero. After iterative convergence, the dominant mode set is determined based on the non-zero modes, and a least-squares problem without regularization terms is resolved in the subspace corresponding to this set to correct the amplitudes of the retained modes.

[0017] This invention can reduce the computation time for extracting sparse modes of high-dimensional impeller flow fields, providing a basis for the analysis of unsteady flow characteristics of centrifugal fans. Attached Figure Description

[0018] Figure 1 Scatter plots of the modal distributions of standard DMD and F-DMD.

[0019] Figure 2 This is a standard DMD reconstruction error cloud map.

[0020] Figure 3 Reconstruct the error contour map for F-DMD.

[0021] Figure 4 The contribution distribution diagram of the second-order pressure mode of the pressure field of the centrifugal fan impeller.

[0022] Figure 5 The contribution distribution diagram of the third-order pressure mode of the pressure field of the centrifugal fan impeller.

[0023] Figure 6 Table of dominant modal growth rate and Strouhal number data.

[0024] Figure 7 This table compares the computation speeds of SPDMD and F-DMD in different computational examples.

[0025] Figure 8 Table of dominant modal growth rate and frequency data.

[0026] Figure 9 This is the overall flowchart of the present invention. Detailed Implementation

[0027] The present invention will now be further described with reference to the accompanying drawings.

[0028] This invention provides a method for extracting the dominant modes of flow field in a centrifugal fan impeller based on fast sparse dynamic mode decomposition, comprising the following steps: Step 1: Using the multi-mode amplitude of a certain physical quantity of the centrifugal fan impeller as the target, establish a computational domain model of the centrifugal fan impeller and its fluid. Set the impeller speed, flow rate boundary conditions, and fluid property parameters, and perform unsteady flow field calculations on the impeller rotation region. After the flow field enters a periodically stable state, acquire the physical quantity according to the preset sampling time interval. A snapshot of the unsteady flow field at each sampling time; Construct the total data matrix of all time snapshots : in, For sampling time index, , This represents the total number of sampling moments; the physical quantities include velocity, pressure, vorticity, etc. For the first Spatial distribution of physical quantities in the flow field at the sampling time. for 3D column vector, For spatial degrees of freedom; Remove the last sampling time and construct the first adjacent time snapshot matrix. : Remove the first sampling time. Construct the second adjacent time snapshot matrix. : Step 2: Perform dynamic mode decomposition on adjacent time snapshot matrices to obtain DMD reconstructed modes and temporal feature values; Assume that adjacent flow field snapshots satisfy an approximately linear mapping relationship: modal order As a truncation threshold, the first adjacent time snapshot matrix Perform truncated singular value decomposition to obtain the left singular matrix. 1. Truncate singular value diagonal matrices With right singular matrix ; Among them, the singular value diagonal matrix is ​​truncated. The diagonal elements are the first adjacent time snapshot matrix. The first non-zero singular value; the superscript " " indicates conjugate transpose; Compute the conjugate transpose of a left singular matrix Second adjacent time snapshot matrix Right singular matrix 1. Truncate the inverse of a singular value diagonal matrix The product of these terms yields a low-dimensional matrix. ; Among them, low-dimensional matrix It is a linear mapping matrix The result of projecting onto a lower-dimensional subspace; For low-dimensional matrices Perform eigenvalue decomposition to obtain the eigenvalue diagonal matrix. With eigenvector matrix ; Among them, the eigenvalue diagonal matrix The diagonal elements are the time characteristic values. ,Right now ; Calculate the second adjacent time snapshot matrix Right singular matrix 1. Truncate the inverse of a singular value diagonal matrix and eigenvector matrix The product of these terms yields the DMD reconstruction modes in the original high-dimensional space. ; Step 3: Based on time characteristic values Constructing the time evolution Vandermonde matrix ; DMD reconstructed mode Multimodal amplitude diagonal matrix and the time evolution Vandermonde matrix The product of these components is used to reconstruct the total data matrix of all time snapshots. Using the reconstructed residuals of the total data matrix from all time snapshots as data constraints, we introduce... Regularization term, establishing a sparse optimization function for modal amplitude; ; in, For the target vector, , For the target physical quantity of centrifugal fan impeller First-order modal amplitude; This indicates the calculation of the Frobenius norm; Indicates calculation Norm; This is a regularization parameter used to control system sparsity. The regularization parameter is adjusted accordingly. This shrinks the amplitude of modes that contribute less to the evolution of the complete flow field to zero, while retaining the dynamic modes that contribute the most to the evolution of the unsteady flow field. Step 4: Decompose the modal amplitude sparse optimization function into smooth data fitting terms and non-smooth regularization terms, transforming it into a low-dimensional convex optimization problem; in, For smooth data fitting, It is a non-smooth regularization term; Among them, the symbol " " represents the Hadamard product, and the overline indicates the complex conjugate. This represents the computation of the trace of a matrix; Obviously, , and All with Irrelevant, meaning not following the search for optimization. Changes have occurred; Step 5: The fast iterative shrinking threshold algorithm is used, combined with Nesterov momentum update, gradient descent and soft thresholding to iteratively solve the low-dimensional convex optimization problem. After the iteration converges, the subspace is determined according to the non-zero modes. The least squares problem without regularization terms is solved again in the subspace to obtain the multi-mode amplitude of the target physical quantity. Step 5.1: Set the convergence threshold Initialize the number of iterations Initialize the target vector Initialize the acceleration step size factor ; Step 5.2: Perform two iterations to obtain the updated target vector. and ,at this time Proceed to step 5.3; Step 5.3: Update the target vector based on the previous two iterations. and Update momentum auxiliary variable ; in, ; Step 5.4: Calculate the smooth data fit term in the momentum auxiliary variable gradient at ; Searching along the negative gradient direction yields intermediate variables. ; in, For smooth data fitting term The Lipschitz constant can be taken as a matrix. The largest eigenvalue; Step 5.5: Process intermediate variables using a soft threshold operator , obtained the The target vector updated in the next iteration ; The soft threshold operator implements the handling of non-smooth regularization terms. Sparse truncation; The soft threshold operator is defined as: Soft threshold operator intermediate variables Medium modulus length less than threshold The modal amplitude is forcibly set to zero to achieve automatic sparse filtering of modes; Step 5.6: If the target vector converges, i.e., or If the iteration stops, proceed to step 5.7; otherwise, let... Return to step 5.3; Step 5.7: Perform a polishing step to eliminate the bias caused by regularization; because While regularization introduces sparsity, it can also lead to smaller amplitudes of non-zero modes. Therefore, a polishing step is needed after the algorithm converges to eliminate the bias caused by regularization. After the iteration converges, the target vector is extracted. Construct a set of non-zero modal amplitudes from all non-zero modal amplitudes. In the set of non-zero mode amplitudes Within a defined subspace, the least squares problem without regularization terms is resolved to obtain the final objective vector. This yields the multi-mode amplitudes of the target physical quantity. Step 6: Further processing based on the multi-mode amplitudes of the target physical quantity: (1) If the physical quantity is pressure, then what is obtained is The amplitude of the first pressure mode can be set to... , ; To convert the final modal amplitude vector into an output with physical meaning of centrifugal fan flow, the optimized modal amplitude can be combined with the corresponding spatial mode.

[0029] For the The pressure mode contribution field is defined as follows: Its modal contribution amplitude is: in, For the first Pressure space mode; when the input pressure snapshot uses dimensional pressure data. The unit is Pa.

[0030] (2) If the physical quantity is velocity, then what is obtained is The amplitude of the first velocity mode can be set to... ; Similarly, for the first The velocity mode contribution field is defined as follows: Its modal contribution amplitude is: in, For the first First-order velocity space mode; when the input velocity snapshot uses dimensional velocity data. The unit is m / s.

[0031] By rapidly screening the dominant modes of the centrifugal fan impeller pressure and velocity fields, and based on the correspondence between the mode frequencies and the impeller shaft frequencies, the periodic pressure and velocity coherent structures within the centrifugal fan impeller are identified. Furthermore, the spatial distribution of the dominant modes in the blade flow channel and impeller outlet region is determined through the pressure and velocity field mode cloud maps.

[0032] The applications of other physical quantities will not be listed in detail here.

[0033] Example 1: Flow around a cylinder with a low Reynolds number; This embodiment uses the Navier-Stokes equations to obtain a snapshot of the unsteady flow field around a two-dimensional cylinder, with the Reynolds number set to 60. Dynamic mode decomposition is performed on the flow field data during the linear instability growth phase, extracting the first five dominant modes obtained from the standard DMD and F-DMD under this condition. Their dynamic parameters are as follows: Figure 6 As shown. The F-DMD method of this invention identifies the first five modal frequencies and growth rates in line with the standard DMD method. Specifically, the first-order zero-frequency mode corresponds to the average current; the second-order mode has a Strouhal number of 0.121 and a growth rate of... This corresponds to the dominant vortex shedding structure in the cylindrical wake; the 3rd to 5th modes have negative growth rates and belong to high-frequency structures that decay rapidly over time.

[0034] Although the frequency characteristics extracted by both are the same, the modal amplitudes differ. There are significant differences in energy distribution. Figure 1 The amplitude values ​​of each mode of the standard DMD are given. and the corresponding Strauhal number The invention also presents the first five modes retained by the F-DMD. The standard DMD determines the mode amplitudes based on the initial state, making the initial amplitudes of the 3rd to 5th rapidly decaying modes similar in magnitude to those of the dominant vortex shedding mode, which easily leads to an overestimation of their contribution to the overall flow field evolution. This invention, by minimizing the overall reconstruction residuals of all time snapshots and applying sparsity constraints, suppresses the amplitudes of the rapidly decaying modes while retaining the mean flow mode and the dominant vortex shedding mode.

[0035] To quantify the reconstruction accuracy of the two methods, the root mean square error between the reconstructed flow field and the original flow field is defined as: In the formula, Represents the number of snapshots. and Representing the first The original flow field matrix and modal reconstruction matrix at each time step. Figure 2 and Figure 3 The spatial distribution cloud map based on the reconstruction error of the first 5 modes is shown. The results show that the reconstruction error of the present invention in the cylindrical wake region is lower than that of the standard DMD, indicating that the full time history amplitude optimization and polishing correction can reduce the error accumulation caused by the initial snapshot fitting.

[0036] The conventional SPDMD method based on the alternating direction multiplier method is used as a comparison method, and the calculation results are as follows: Figure 7 As shown. The computation time of the method of this invention is shorter than that of the ADMM-based SPDMD method, achieving a speedup of 4.9.

[0037] The aforementioned difference in computational efficiency mainly stems from the fact that the SPDMD method based on the alternating direction multiplier method requires repeated solving of linear equations during variable alternation updates, resulting in high cost per iteration. This invention transforms the sparse modal amplitude problem into a low-dimensional modal space and employs gradient calculation, Nesterov momentum updates, and complex soft thresholding to complete the iterations, avoiding matrix inversion or high-cost linear system solutions in each iteration. Therefore, this invention significantly reduces the processing time for high-dimensional unsteady flow field data while maintaining the ability to identify dominant modal frequencies and perform sparse filtering.

[0038] Example 2: Application verification of centrifugal fan impeller flow field; The application effect of this invention in complex rotating flow fields is verified by using unsteady calculation results of the centrifugal fan impeller rotation region. Figure 8The first five modal frequencies and growth rates extracted by standard DMD and F-DMD are presented. The second to fifth dynamic modal frequencies extracted in this invention are 44.6 Hz, 87.4 Hz, 130.1 Hz, and 177.4 Hz, respectively, close to the impeller shaft frequency and its 2nd to 4th harmonics, indicating that the proposed method can identify the main coherent flow structures generated by the periodic rotation of the impeller. In contrast, the first five modes of standard DMD show rapidly decaying components with large negative growth rates, such as 56.5 Hz, 287.3 Hz, and 585.0 Hz, and the key shaft frequency and its harmonics are disturbed by modes with no physical meaning or low contribution. This invention reduces the amplitude of the above-mentioned disturbing modes through full-time history sparsity optimization, resulting in a clearer correspondence between the retained modes and the impeller rotation frequency, which can be used for the identification of periodic flow structures and unsteady excitation characteristics in rotating machinery.

[0039] The pressure mode optimization amplitude obtained by F-DMD is multiplied by the corresponding pressure space mode to obtain the pressure mode contribution field. Figure 4 and Figure 5 The axial frequency and 2x axial frequency modes of the impeller pressure field are presented based on optimized modal amplitude weighting. The RF spatial pressure mode exhibits two spatial lobes with opposite phases in the impeller region, with the flow field phase reversing every 180°. This phenomenon is caused by the non-axisymmetric nature of the volute geometry disrupting the uniformity of the circumferential aerodynamic load on the impeller; with each rotation of the impeller, a single blade only brushes past the volute tongue once, thus undergoing a complete "compression-expansion" pressure pulsation cycle, thereby exciting a coherent structure with RF as the fundamental frequency within the rotating system. The 2RF spatial pressure mode distribution is more fragmented and less regular, but still exhibits four alternating spatial lobes overall, with the phase reversing every 90° between flow channels. This indicates that as the excitation frequency increases, the non-uniform potential flow disturbance caused by the volute tongue induces more complex higher-order unsteady responses within the impeller.

[0040] By combining the optimized modal amplitude with the pressure space mode, the modal analysis results are transformed from an abstract amplitude vector into a spatial contribution distribution with pressure dimensions, which can be used to identify regions with strong periodic pressure inside the impeller.

Claims

1. A method for extracting the dominant modes of flow field in a centrifugal fan impeller based on fast sparse dynamic mode decomposition, characterized in that: Taking the multi-mode amplitude of a certain physical quantity of a centrifugal fan impeller as the target, the unsteady flow field snapshot of the physical quantity is obtained, and the total data matrix of all time snapshots is constructed. The first sampling time and the last sampling time are removed respectively to construct the adjacent time snapshot matrix. Dynamic mode decomposition is performed on adjacent time snapshot matrices to obtain DMD reconstructed modes and time eigenvalues. A time evolution Vandermonde matrix is ​​constructed based on the time eigenvalues. The total data matrix of all time snapshots is reconstructed by multiplying the DMD reconstructed modes, the multi-mode amplitude diagonal matrix, and the time evolution Vandermonde matrix. Using the reconstructed residuals of the total data matrix from all time snapshots as data constraints, we introduce... Regularization term, establishing a sparse optimization function for modal amplitude; The modal amplitude sparse optimization function is decomposed into smooth data fitting terms and non-smooth regularization terms, and transformed into a low-dimensional convex optimization problem. A fast iterative shrinking threshold algorithm is adopted, which combines Nesterov momentum update, gradient descent and soft thresholding to iteratively solve the low-dimensional convex optimization problem. After the iteration converges, the subspace is determined according to the non-zero modes, and the least squares problem without regularization terms is resolved in the subspace to obtain the multi-mode amplitude of the target physical quantity.

2. The method for extracting the dominant modes of a centrifugal fan impeller flow field based on fast sparse dynamic mode decomposition according to claim 1, characterized in that: The process of performing dynamic mode decomposition on adjacent time snapshot matrices to obtain DMD reconstructed mode and temporal feature values ​​is as follows: The adjacent time snapshot matrix includes a first adjacent time snapshot matrix excluding the last sampling time, and a second adjacent time snapshot matrix excluding the first sampling time; Using the modal order as the truncation threshold, truncated singular value decomposition is performed on the first adjacent time snapshot matrix to obtain the left singular matrix, the truncated singular value diagonal matrix and the right singular matrix. The low-dimensional matrix is ​​obtained by multiplying the conjugate transpose of the left singular matrix, the second adjacent time snapshot matrix, the right singular matrix, and the inverse of the truncated singular value diagonal matrix. Perform eigenvalue decomposition on a low-dimensional matrix to obtain an eigenvalue diagonal matrix and an eigenvector matrix. The diagonal elements of the eigenvalue diagonal matrix are the time eigenvalues. The DMD reconstructed mode is obtained by multiplying the second adjacent time snapshot matrix, the right singular matrix, the inverse of the truncated singular value diagonal matrix, and the eigenvector matrix.

3. The method for extracting the dominant modes of a centrifugal fan impeller flow field based on fast sparse dynamic mode decomposition according to claim 2, characterized in that: The reconstructed residuals of the total data matrix from all time snapshots are used as data constraints, and the following is introduced: The regularization term establishes a sparse optimization function for modal amplitudes, specifically: in, For the target vector, , For the target physical quantity of centrifugal fan impeller First-order modal amplitude; The total data matrix for all time snapshots; Reconstructing modes for DMD; for Diagonal matrix of modal amplitudes, ; For time-evolving Vandermonde matrix; This indicates the calculation of the Frobenius norm; Indicates calculation Norm; This is the regularization parameter.

4. The method for extracting the dominant modes of a centrifugal fan impeller flow field based on fast sparse dynamic mode decomposition according to claim 3, characterized in that: The process of decomposing the modal amplitude sparse optimization function into smooth data fitting terms and non-smooth regularization terms, transforming it into a low-dimensional convex optimization problem, is as follows: in, For smooth data fitting, ; It is a non-smooth regularization term. ; , ; superscript " " indicates conjugate transpose. symbol" " represents the Hadamard product, and the overline indicates the complex conjugate. This represents the computation of the trace of a matrix; The truncated singular value diagonal matrix is ​​obtained by performing truncated singular value decomposition on the first adjacent time snapshot matrix.

5. The method for extracting the dominant modes of a centrifugal fan impeller flow field based on fast sparse dynamic mode decomposition according to claim 4, characterized in that: The method employs a fast iterative shrinking threshold algorithm, combined with Nesterov momentum update, gradient descent, and soft thresholding to iteratively solve the low-dimensional convex optimization problem. Specifically: Starting from the third iteration, the target vector is updated based on the previous two iterations. and Update momentum auxiliary variable ; in, For the number of iterations, To accelerate the step size factor, ; Calculate the smooth data fitting term in the momentum auxiliary variable gradient at ; Searching along the negative gradient direction yields intermediate variables. ; in, For smooth data fitting term The Lipschitz constant; Processing intermediate variables using the soft threshold operator , obtained the The target vector updated in the next iteration .

6. The method for extracting the dominant modes of a centrifugal fan impeller flow field based on fast sparse dynamic mode decomposition according to claim 5, characterized in that: The soft threshold operator is: The soft threshold operator intermediate variables Medium modulus length less than threshold The modal amplitude is forcibly set to zero to achieve automatic sparse screening of modes.

7. The method for extracting the dominant modes of a centrifugal fan impeller flow field based on fast sparse dynamic mode decomposition according to claim 6, characterized in that: After the iteration converges, a subspace is determined based on the non-zero modes. The least squares problem without regularization terms is then resolved in this subspace to obtain the multi-mode amplitudes of the target physical quantity. Specifically: If the first The target vector updated in the next iteration If convergence is achieved, the target vector is extracted. Construct a set of non-zero modal amplitudes from all non-zero modal amplitudes. ; In the set of non-zero modal amplitudes Within a defined subspace, the least squares problem without regularization terms is resolved to obtain the final objective vector. This yields the multi-mode amplitudes of the target physical quantity. 。 8. A computer device, comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When executed by a processor, the computer program implements the steps of the method according to any one of claims 1 to 7.

10. A computer program product comprising computer instructions, characterized in that: When executed by a processor, the computer instructions implement the steps of the method according to any one of claims 1 to 7.

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