An unsteady flow field dynamic characteristic analysis method and system combining best mode decomposition and 2D-FFT wave number spectrum

Abstract

A method and system for analyzing the dynamic characteristics of unsteady flow fields, combining optimal mode decomposition (OMD) and 2D-FFT wavenumber spectrum, is disclosed, relating to the field of flow field dynamics characteristic analysis. This method solves the existing problems of accurately decoupling the coherent structure dominating the flow field evolution from a raw flow field characterized by strong noise, multi-scale features, and extremely high nonlinearity, and quantifying its spatiotemporal evolution properties. The method includes: acquiring time-series flow field data based on experimental images captured by a high-speed camera; constructing an OMD-based dynamic model; performing spatial mode reconstruction on the constructed OMD-based dynamic model, mapping low-dimensional feature vectors back to high-dimensional physical space to obtain OMD spatial modes; calculating the weight coefficients of each mode and combining them with the time evolution term to calculate the total energy; rearranging the column vectors of the calculated weight coefficients of each mode into a two-dimensional matrix, and performing a two-dimensional fast Fourier transform. This method is also applicable to fields such as fluid mechanics and underwater robotics.

Description

Technical Field

[0001] This invention relates to the field of flow field dynamics feature analysis technology, specifically to a method for extracting spatiotemporal features and analyzing the evolution of flow fields based on Optimal Mode Decomposition (OMD) and Two-Dimensional Fast Fourier Transform (2D-FFT). Background Technology

[0002] Extracting and analyzing the evolution of unsteady flow field dynamics is a core research area in experimental fluid mechanics, aerospace aerodynamic design, and energy and power engineering. With the widespread adoption of high-frequency particle image velocimetry (TR-PIV) and high-fidelity numerical simulation (DNS / LES) techniques, researchers can acquire flow field data sequences containing massive amounts of spatiotemporal information. However, accurately decoupling the coherent structures that dominate the flow field evolution from the original flow field, which is characterized by strong noise, multi-scale features, and extremely high nonlinearity, and quantifying its spatiotemporal evolution properties, remains a challenge in the field of fluid mechanics post-processing.

[0003] Currently, the mainstream methods for flow field modal decomposition include intrinsic orthogonal decomposition (POD) and dynamic mode decomposition (DMD). POD extracts the main energy modes of the flow field through singular value decomposition (SVD), but its essence is a linear dimensionality reduction of spatial correlation. A single mode often contains multiple frequency components, making it difficult to directly correspond to the physical dynamic evolution process. While DMD can extract single-frequency modes through eigenvalue analysis of linear operators, it exhibits poor robustness when facing complex flow fields containing measurement noise or broad-spectrum features (such as cavitation flow and unsteady separated flow). It often suffers from eigenvalue deviation, disordered mode ordering, and unclear energy definitions, leading to an inability to accurately reconstruct the dynamic essence of the flow field.

[0004] Therefore, in response to the above problems, this invention proposes an unsteady flow field analysis method that can take into account dynamic evolution stability, high-contrast spatial identification, and refined wavenumber spectrum quantization, which has important scientific significance and engineering value for revealing complex flow mechanisms. Summary of the Invention

[0005] This invention addresses the challenge of accurately decoupling the coherent structure dominating the flow field evolution from a raw flow field characterized by strong noise, multi-scale features, and extremely high nonlinearity, and quantifying its spatiotemporal evolution properties—a persistent difficulty in current fluid mechanics post-processing. To this end, this invention proposes a method and system for analyzing the dynamic characteristics of unsteady flow fields, combining optimal mode decomposition and 2D-FFT wavenumber spectroscopy. This method provides a reliable analytical tool for the dynamic characteristics of unsteady flow fields, aiming to improve the robustness of dynamic mode extraction under complex noise backgrounds. Furthermore, through spatiotemporal decoupling analysis, it accurately quantifies the characteristic frequencies and spatial wavenumber distributions of the flow field structure. To solve the aforementioned technical problems, this invention achieves its goals through the following technical solutions: Option 1: This invention proposes a method for analyzing the dynamic characteristics of unsteady flow fields by combining optimal mode decomposition and 2D-FFT wavenumber spectrum. The method includes the following steps: Step 1: Obtain time-series flow field data based on experimental images captured by a high-speed camera; Step 2: Based on the time-series flow field data obtained in Step 1, construct a dynamic model based on OMD; Step 3: Perform spatial modal reconstruction on the OMD-based dynamic model constructed in Step 2, mapping the low-dimensional feature vectors back to the high-dimensional physical space to obtain the OMD spatial modes, and calculate the weight coefficients of each mode. And calculate the total energy by combining the time evolution term. ; Step 4: Calculate the weighting coefficients for each mode in Step 3. The column vectors are rearranged as Two-dimensional matrix and to Two-dimensional fast Fourier transform is performed to complete the dynamic characteristic analysis of unsteady flow fields by combining optimal mode decomposition and 2D-FFT wavenumber spectrum.

[0006] Furthermore, a preferred embodiment is provided, wherein step 1 specifically includes: Step 1.1: Based on the experimental images captured by the high-speed camera, flatten each frame of the two-dimensional flow field image into a one-dimensional column vector. Frame vectors are arranged horizontally to construct the original snapshot matrix. Calculate the time-averaged flow field And peel off;

[0007] in, The flow field matrix is ​​pulsating. The index number of the time series snapshot. .

[0008] Furthermore, a preferred embodiment is provided, wherein the method for constructing the OMD-based dynamic model in step 2 is as follows: Step 2.1: Apply singular value decomposition to the time-averaged flow field calculated in Step 1. To process, that is,

[0009] in, It is a spatial eigenorthogonal basis; It is a singular value matrix; For time coefficient; Step 2.2: Define flow field snapshot pairs and The low-dimensional evolution operator is solved by minimizing the objective function using the conjugate gradient method. ; Step 2.3: Solve for the low-dimensional evolution operator eigenvalues and eigenvectors Calculate the complex frequency in continuous time. .

[0010] Furthermore, a preferred embodiment is provided in which the objective function is minimized in step 2.2 to solve for the low-dimensional evolution operator using the conjugate gradient method. The method is as follows:

[0011] in, Actively describe the flow field state in low-dimensional space from arrive The best linear mapping.

[0012] Furthermore, a preferred embodiment is provided, wherein in step 2.3, the low-dimensional evolution operator is solved. eigenvalues and eigenvectors Calculate the complex frequency in continuous time. The method is as follows:

[0013] in, Modal growth rate / decrease rate; This refers to the physical frequency.

[0014] Furthermore, a preferred embodiment is provided, wherein step 3 specifically includes: Step 3.1: Map the low-dimensional feature vectors back to the high-dimensional physical space to obtain the OMD space mode:

[0015] in, For the eigenvector The matrix formed Each column in the table represents a spatial coherence structure at a specific frequency; Step 3.2: Calculate the weighting coefficients for each mode. And calculate the total energy by combining the time evolution term. :

[0016] in, Total analysis time; For the first The first spatial mode is in the first order. The amplitude of each spatial point.

[0017] Furthermore, a preferred embodiment is provided, wherein in step 4... The method for performing a two-dimensional fast Fourier transform is as follows:

[0018] in, These are the normalized wavenumbers for the horizontal and vertical directions, respectively; This represents the modal mean.

[0019] Option 2: A system for analyzing the dynamic characteristics of unsteady flow fields by combining optimal mode decomposition and 2D-FFT wavenumber spectrum, the system comprising: The data acquisition module is used to acquire time-series flow field data based on experimental images captured by a high-speed camera; The OMD dynamics model building module is used to build a dynamics model based on OMD based on the time series flow field data acquired by the data acquisition module. The spatial modal reconstruction module is used to reconstruct the spatial modes of the OMD-based dynamic model constructed by the OMD-based dynamic model construction module. It maps low-dimensional feature vectors back to high-dimensional physical space to obtain OMD spatial modes and calculates the weight coefficients of each mode. And calculate the total energy by combining the time evolution term. ; The unsteady flow field dynamics characteristic analysis module is used to convert the weighting coefficients of each mode calculated in the spatial mode reconstruction module. The column vectors are rearranged as Two-dimensional matrix and to Two-dimensional fast Fourier transform is performed to complete the dynamic characteristic analysis of unsteady flow fields by combining optimal mode decomposition and 2D-FFT wavenumber spectrum.

[0020] Option 3: A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described in Option 1.

[0021] Option 4: A computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the method described in Option 1.

[0022] The advantages of this invention are: The present invention describes a method and system for analyzing the dynamic characteristics of unsteady flow fields that combines optimal mode decomposition (OMD) and 2D-FFT wavenumber spectroscopy. In terms of robustness and physical accuracy in dynamic mode extraction, the method employs the OMD algorithm. By optimizing linear operators using the conjugate gradient method in a low-dimensional projected space, it effectively solves the numerical instability problem of traditional DMD methods when processing high-noise flow field data. This method can more accurately identify the dominant frequencies and growth rates in unsteady flow fields. Even in complex cavitation or separated flow backgrounds, it maintains a high degree of consistency between the eigenvalue evolution law and physical reality, ensuring the reliability of dynamic mode extraction.

[0023] The unsteady flow field dynamics characteristic analysis method and system described in this invention, combining optimal mode decomposition and 2D-FFT wavenumber spectrum, features a comprehensive energy assessment system and long-term characteristic identification. It introduces an energy reconstruction model considering the evolution integral across the entire time domain, correcting the limitation of traditional methods that rely solely on initial amplitude for sorting. By comprehensively considering both spatial modal intensity and time-varying evolution rate, this system can accurately identify core structures with small initial amplitudes but significant long-range dynamic influence. This allows for the priority screening of physical mechanisms that contribute most to flow field fluctuations, thus revealing the true nature of the energy distribution in unsteady flow fields more realistically and comprehensively.

[0024] The present invention describes a method and system for analyzing unsteady flow field dynamics by combining optimal mode decomposition (OMD) and 2D-FFT wavenumber spectroscopy, achieving spectral quantification and multidimensional feature correlation of spatial topology. By combining OMD and 2D-FFT techniques, complex spatial modal topologies are mapped to the normalized wavenumber spectral domain, enabling a leap from qualitative geometric observation to quantitative spectral feature extraction of the coherent flow field structure. This scheme can accurately decouple the characteristic wavelengths of modes in the flow direction and normal direction, constructing complete spatiotemporal evolution characteristics indices for the flow field. This provides rigorous mathematical support for identifying dominant flow regimes, secondary unstable structures, and assessing spatial evolution scales, filling the gap in the quantitative characterization of spatial structures using traditional methods.

[0025] This invention is also applicable to fields such as fluid mechanics, multiphase flow, underwater robots, marine engineering, aerospace and energy engineering, and is especially applicable to the analysis of non-stationary and transient signals with complex gas-liquid interface evolution behaviors, such as cavitation, transmedium, and jets. Attached Figure Description

[0026] Fig. 1 This is a flowchart illustrating the unsteady flow field dynamics characteristic analysis method combining optimal mode decomposition and 2D-FFT wavenumber spectrum as described in Implementation Method 1.

[0027] Fig. 2 This is a bar chart showing the energy distribution of the first 20 modes as described in Implementation Method 1.

[0028] Fig. 3 This is a typical flow field spatial mode diagram as described in Implementation Method 1.

[0029] Among them, (a) is the spatial modal diagram of the first mode flow field, (b) is the spatial modal diagram of the fifth mode flow field, and (c) is the spatial modal diagram of the tenth mode flow field.

[0030] Fig. 4 This is the 2D-FFT spectrum heatmap described in Implementation Method 1.

[0031] Among them, (a) is the 2D-FFT spectrum heatmap of the first mode, (b) is the 2D-FFT spectrum heatmap of the fifth mode, and (c) is the 2D-FFT spectrum heatmap of the tenth mode. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them.

[0033] Implementation Method 1, see [link] Figs. 1 to 4 This embodiment describes a method for analyzing the dynamic characteristics of unsteady flow fields that combines optimal mode decomposition and 2D-FFT wavenumber spectrum. The method includes the following steps: 1. Flow field data acquisition and structuring Time-series flow field data are obtained through experiments or CFD numerical simulations. In this invention, the data originates from experimental images captured by a high-speed camera. Each frame of the two-dimensional flow field image (resolution) is processed... Flatten it into a one-dimensional column vector. Frame vectors are arranged horizontally to construct the original snapshot matrix. Calculate the time-averaged flow field and strip it:

[0034] in, The pulsating flow field matrix is ​​physically defined as filtering out the steady base current and retaining only the unsteady fluctuation component that evolves over time.

[0035] 2. Dynamic Modeling Based on OMD The first step is to perform spatial dimensionality reduction (SVD). This is done by using singular value decomposition to... Processing:

[0036] in, It is a spatial eigenorthogonal basis; It is a singular value matrix (energy distribution); The time coefficient. Based on the truncated rank. Before keeping Order basis, defining the orthogonal projection matrix after dimensionality reduction. .

[0037] The second step is to perform operator optimization. Define flow field snapshot pairs. and The low-dimensional evolution operator is solved by minimizing the following objective function using the conjugate gradient method. :

[0038] in, Describing the flow field state in low-dimensional space from arrive The best linear mapping.

[0039] The third step involves feature extraction and physical frequency calculation. Solving... eigenvalues and eigenvectors Calculate the complex frequency in continuous time. :

[0040] in, Modal growth rate / decrease rate; The physical frequency (Hz).

[0041] 3. Modal reconstruction and energy assessment The first step is spatial mode reconstruction. Low-dimensional feature vectors are mapped back to high-dimensional physical space to obtain the OMD spatial modes:

[0042] in, For the eigenvector The matrix formed. Each column in the diagram represents a spatial coherence structure at a specific frequency.

[0043] The second step involves energy calculation based on evolutionary integrals. This includes calculating the weighting coefficients for each mode. (pass (Obtained), and the total energy is calculated by combining the time evolution term. :

[0044] in, Total analysis time; For the first The first spatial mode is in the first order. The amplitude at each spatial point. This considers not only the initial intensity but also the spatiotemporal integral energy of the mode over the entire period.

[0045] 4. Visualization Enhancement and Wavenumber Spectrum Analysis Enhanced visualization of spatial modalities. The column vectors are rearranged as Two-dimensional matrix Apply contrast enhancement factor :

[0046] Set the color mapping range to This makes the faint fluctuation stripes that were previously hidden by strong signals visible.

[0047] 2D-FFT wavenumber spectrum calculation. Perform a two-dimensional fast Fourier transform:

[0048] in, These are the normalized wavenumbers for the horizontal and vertical directions, respectively; This is the modal mean (DC component).

[0049] 5. Results Output The output results include, but are not limited to, energy distribution histograms, typical flow field spatial mode diagrams, and 2D-FFT spectral thermograms corresponding to the modes.

[0050] Those skilled in the art will understand that the above description is merely a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims of this disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. This is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0051] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.

Claims

1. A method for analyzing the dynamic characteristics of unsteady flow fields by combining optimal mode decomposition and 2D-FFT wavenumber spectrum, characterized in that, The method includes the following steps: Step 1: Obtain time-series flow field data based on experimental images captured by a high-speed camera; Step 2: Based on the time-series flow field data obtained in Step 1, construct a dynamic model based on OMD; Step 3: Perform spatial modal reconstruction on the OMD-based dynamic model constructed in Step 2, mapping the low-dimensional feature vectors back to the high-dimensional physical space to obtain the OMD spatial modes, and calculate the weight coefficients of each mode. And calculate the total energy by combining the time evolution term. ; Step 4: Calculate the weighting coefficients for each mode in Step 3. The column vectors are rearranged as Two-dimensional matrix and to Two-dimensional fast Fourier transform is performed to complete the dynamic characteristic analysis of unsteady flow fields by combining optimal mode decomposition and 2D-FFT wavenumber spectrum.

2. The method for analyzing the dynamic characteristics of unsteady flow fields combining optimal mode decomposition and 2D-FFT wavenumber spectrum as described in claim 1, is characterized in that, Step 1 specifically involves: Step 1.1: Based on the experimental images captured by the high-speed camera, flatten each frame of the two-dimensional flow field image into a one-dimensional column vector. Frame vectors are arranged horizontally to construct the original snapshot matrix. Calculate the time-averaged flow field And peel off; in, The flow field matrix is ​​pulsating. The index number of the time series snapshot. .

3. The method for analyzing the dynamic characteristics of unsteady flow fields combining optimal mode decomposition and 2D-FFT wavenumber spectrum as described in claim 2, is characterized in that, The method for constructing the OMD-based dynamic model in step 2 is as follows: Step 2.1: Apply singular value decomposition to the time-averaged flow field calculated in Step 1. To process, that is, in, It is a spatial eigenorthogonal basis; It is a singular value matrix; For time coefficient; Step 2.2: Define flow field snapshot pairs and The low-dimensional evolution operator is solved by minimizing the objective function using the conjugate gradient method. ; Step 2.3: Solve for the low-dimensional evolution operator eigenvalues and eigenvectors Calculate the complex frequency in continuous time. .

4. The method for analyzing the dynamic characteristics of unsteady flow fields combining optimal mode decomposition and 2D-FFT wavenumber spectrum as described in claim 3, is characterized in that, In step 2.2, the objective function is minimized using the conjugate gradient method to solve for the low-dimensional evolution operator. The method is as follows: in, Actively describe the flow field state in low-dimensional space from arrive The best linear mapping.

5. The method for analyzing the dynamic characteristics of unsteady flow fields combining optimal mode decomposition and 2D-FFT wavenumber spectrum as described in claim 3, is characterized in that, Step 2.3: Solving for the low-dimensional evolution operator eigenvalues and eigenvectors Calculate the complex frequency in continuous time. The method is as follows: in, Modal growth rate / decrease rate; This refers to the physical frequency.

6. The method for analyzing the dynamic characteristics of unsteady flow fields combining optimal mode decomposition and 2D-FFT wavenumber spectrum as described in claim 1, characterized in that, Step 3 specifically includes: Step 3.1: Map the low-dimensional feature vectors back to the high-dimensional physical space to obtain the OMD space mode: in, For the eigenvector The matrix formed Each column in the table represents a spatial coherence structure at a specific frequency; Step 3.2: Calculate the weighting coefficients for each mode. And calculate the total energy by combining the time evolution term. : in, Total analysis time; For the first The first spatial mode is in the first order. The amplitude of each spatial point.

7. The method for analyzing the dynamic characteristics of unsteady flow fields combining optimal mode decomposition and 2D-FFT wavenumber spectrum as described in claim 1, characterized in that, In step 4, The method for performing a two-dimensional fast Fourier transform is as follows: in, These are the normalized wavenumbers for the horizontal and vertical directions, respectively; This represents the modal mean.

8. A system for analyzing the dynamic characteristics of unsteady flow fields by combining optimal mode decomposition and 2D-FFT wavenumber spectrum, characterized in that, The system includes: The data acquisition module is used to acquire time-series flow field data based on experimental images captured by a high-speed camera; The OMD dynamics model building module is used to build a dynamics model based on OMD based on the time series flow field data acquired by the data acquisition module. The spatial modal reconstruction module is used to reconstruct the spatial modes of the OMD-based dynamic model constructed by the OMD-based dynamic model construction module. It maps low-dimensional feature vectors back to high-dimensional physical space to obtain OMD spatial modes and calculates the weight coefficients of each mode. And calculate the total energy by combining the time evolution term. ; The unsteady flow field dynamics characteristic analysis module is used to convert the weighting coefficients of each mode calculated in the spatial mode reconstruction module. The column vectors are rearranged as Two-dimensional matrix and to Two-dimensional fast Fourier transform is performed to complete the dynamic characteristic analysis of unsteady flow fields by combining optimal mode decomposition and 2D-FFT wavenumber spectrum.

9. A computer storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1-7.

10. A computer device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the program to implement the method of any one of claims 1-7.

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