Compression method of CFD data based on dynamic mode decomposition and frequency domain transformation

Abstract

The invention relates to the technical field of fluid mechanics, and discloses a CFD data compression method based on dynamic mode decomposition and frequency domain transformation, and the method comprises the steps: decomposing a CFD data set into low-frequency part data and high-frequency part data based on a preset frequency threshold; decomposing the low-frequency part data by utilizing dynamic mode decomposition to obtain a low-frequency modal parameter, and performing quantization coding on the high-frequency part data to obtain a high-frequency coded stream; and performing mixed compression on the low-frequency modal parameter and the high-frequency coding stream to obtain a compressed file of the CFD data set. Through frequency domain pre-separation of high-frequency and low-frequency data, the calculation complexity is reduced, the data scale of dynamic mode decomposition processing is reduced, the calculation efficiency is improved, an adaptive compression strategy is selected according to the physical characteristics of the high-frequency and low-frequency data, a good compression effect can be kept for flow fields with different complexities, and the compression efficiency is improved. Better compression ratio and quality are achieved, and optimal balance of calculation efficiency, compression ratio and data fidelity is realized.

Description

Technical Field

[0001] This invention relates to the field of fluid mechanics, and more specifically to a method for compressing CFD data based on dynamic mode decomposition and frequency domain transformation. Background Technology

[0002] Computational Fluid Dynamics (CFD) simulations generate data characterized by high dimensionality, multi-scale, and strong spatiotemporal correlation. With the continuous development of high-performance computing technology, the spatiotemporal resolution of CFD simulations has been continuously improved, allowing single simulations to generate terabytes (TB) or even petabytes (PB) of data. However, the storage requirements for large-scale CFD data exceed the capacity of conventional storage systems, leading to a sharp increase in storage costs and increased complexity in data management. Furthermore, in distributed computing environments, CFD data transmission has become a severe bottleneck, limiting the realization of remote visualization, collaborative analysis, and real-time monitoring.

[0003] Common CFD data compression methods include: (1) Integrating algorithms such as GZIP and LZMA into scientific data formats such as HDF5, which is a lossless compression scheme. However, since these compression algorithms are general algorithms and do not utilize the physical characteristics of CFD data, they cannot achieve high compression rates. (2) Schemes based on frequency domain transformation and threshold quantization, such as Discrete Cosine Transform (DCT) / Discrete Wavelet Transform (DWT), are usually used for image and video compression. They are less commonly used in CFD data and can only cover the spatial static relationship at a single time point. They cannot effectively encode the dynamic relationship at a time, and their compression effect on time series continuous data is limited. (3) Dynamic Mode Decomposition (DMD) can capture the dynamic evolution mode of the flow field. However, it is not directly designed as a compression algorithm. If mode selection and dimensionality reduction are not performed, the storage space requirement will increase. Moreover, it does not perform well in preserving small-scale turbulence details after reconstruction. At the same time, the computational load is large, and if used globally, it requires high computational resources. Existing technologies for compressing CFD data cannot achieve an optimal balance between computational efficiency, compression ratio, and data fidelity. Summary of the Invention

[0004] In view of this, the present invention provides a compression method for CFD data based on dynamic mode decomposition and frequency domain transformation to solve the problem of failing to achieve an optimal balance between computational efficiency, compression ratio and data fidelity.

[0005] In a first aspect, the present invention provides a method for compressing CFD data based on dynamic mode decomposition and frequency domain transformation, the method comprising:

[0006] Acquire the CFD dataset and decompose it into low-frequency and high-frequency data based on a preset frequency threshold;

[0007] The low-frequency data is decomposed using dynamic mode decomposition to obtain low-frequency mode parameters, and the high-frequency data is quantized and encoded to obtain a high-frequency encoded stream.

[0008] The low-frequency modal parameters and high-frequency encoded streams are mixed and compressed to obtain a compressed file of the CFD dataset.

[0009] The CFD data compression method based on dynamic mode decomposition and frequency domain transformation provided by this invention reduces computational complexity and the data scale of dynamic mode decomposition by pre-separating high-frequency and low-frequency data in the frequency domain. It supports parallel computing architecture, improves data computation efficiency, and selects an appropriate compression strategy according to the physical characteristics of high-frequency and low-frequency data. It can maintain good compression effect for flow fields of different complexities, achieve better compression ratio and quality, and realize an optimized balance between computational efficiency, compression ratio and data fidelity.

[0010] In one optional implementation, the CFD dataset is decomposed into low-frequency and high-frequency components based on a preset frequency threshold, including:

[0011] The time-domain data in the CFD dataset is transformed into the frequency domain to obtain the frequency domain data corresponding to each time-domain data.

[0012] By comparing the frequency of each frequency domain data with the preset frequency threshold, high-frequency data and low-frequency data in the frequency domain are obtained.

[0013] Perform an inverse transform on the high-frequency data in the frequency domain to obtain the high-frequency part of the corresponding time domain data, and perform an inverse transform on the low-frequency data in the frequency domain to obtain the low-frequency part of the corresponding time domain data.

[0014] The CFD data compression method based on dynamic mode decomposition and frequency domain transformation provided by this invention utilizes DMD to capture the temporal dynamic characteristics of low-frequency data, reducing the storage requirements of the time dimension. At the same time, it compresses the temporal evolution mode of the flow field, maintains the continuity and periodicity of physical phenomena, and completely preserves the main flow structure of CFD data. Quantization encoding is used for high-frequency data to reduce storage requirements. Through differential processing, key physical features are preserved under high compression ratios, and reconstruction errors are mainly concentrated in high-frequency turbulence details that have little impact on analysis.

[0015] In one optional implementation, the low-frequency modal parameters include: low-frequency mode, modal frequency, modal amplitude, and initial state. The low-frequency data is decomposed using dynamic mode decomposition to obtain the low-frequency modal parameters, including:

[0016] The low-frequency data is reshaped into a matrix, and singular value decomposition is performed on the matrix.

[0017] A simplified dynamical system is constructed using the results of singular value decomposition, and eigenvalue decomposition is performed on the simplified dynamical system to obtain eigenvalues ​​and eigenvectors;

[0018] The low-frequency modes are reconstructed based on eigenvalues ​​and eigenvectors, and the modal frequencies, modal amplitudes, and initial states are determined based on the low-frequency modes.

[0019] In one optional implementation, after determining the modal frequency, modal amplitude, and initial state based on the low-frequency mode, the method further includes:

[0020] The preset number of low-frequency modes to be retained is determined based on the target compression ratio;

[0021] Based on the magnitude of the modal amplitude, the reconstructed low-frequency modes are sorted from largest to smallest, and a preset number of low-frequency modes are selected and retained as the main modes.

[0022] The CFD data compression method based on dynamic mode decomposition and frequency domain transformation provided by this invention uses dynamic mode decomposition to process low-frequency data, accurately extracts key dynamic structures of the flow field, reduces data storage dimensionality, selects main modes to retain core information, reduces redundancy, and improves data processing efficiency. It provides a simpler and more effective low-frequency feature representation for flow field analysis, and helps efficient and accurate dynamic research and application.

[0023] In one optional implementation, a high-frequency encoded stream is obtained by quantizing and encoding the high-frequency portion of the data, including:

[0024] Obtain the target compression ratio of the CFD dataset and set the quantization threshold based on the target compression ratio;

[0025] Based on the quantization threshold, the data with coefficients less than the quantization threshold in the high-frequency part of the data are set to zero, thus obtaining a sparse representation of the high-frequency part of the data. The sparse representation contains the non-zero part of the high-frequency part of the data.

[0026] The location information of the non-zero data is determined, and the non-zero data and its corresponding location information are encoded to obtain a high-frequency encoded stream.

[0027] The CFD data compression method based on dynamic mode decomposition and frequency domain transformation provided by this invention precisely controls the degree of compression by adapting the target compression rate to the quantization threshold, balancing storage and accuracy requirements, achieving data sparsity by setting small coefficients to zero, filtering redundant information, highlighting key high-frequency features, encoding non-zero data and locations, significantly compressing the data volume, improving storage and transmission efficiency, minimizing and controlling the loss of high-frequency data, and efficiently compressing CFD high-frequency data to facilitate detailed flow field analysis and engineering applications.

[0028] In one alternative implementation, the low-frequency modal parameters and the high-frequency encoded stream are mixed and compressed, including:

[0029] Record the low-frequency modal parameters and the global parameters of the high-frequency encoded stream. The global parameters include: dimension, time step, and preset frequency threshold.

[0030] Record the total number of low-frequency modes, perform singular value decomposition on the mode matrix in the low-frequency mode parameters, and encode and compress the modal frequency and modal amplitude in the low-frequency mode parameters to obtain low-frequency compressed data;

[0031] The high-frequency encoded stream is compressed according to the high-frequency encoding protocol to obtain high-frequency compressed data;

[0032] The low-frequency compressed data and high-frequency compressed data are combined, and metadata indexes are added to both to obtain a compressed file.

[0033] The present invention provides a CFD data compression method based on dynamic mode decomposition and frequency domain transformation. It records global parameters to provide basic information for decompression and data understanding; it performs secondary SVD and parameter encoding on the low-frequency mode matrix to efficiently compress key structural data; it compresses high-frequency streams according to protocols to retain details; and it combines data and adds metadata indexes to achieve both high- and low-frequency data collaborative compression and supports random access. While ensuring the integrity of the physical characteristics of the flow field, it significantly reduces storage requirements, improves data management and retrieval efficiency, and adapts to the complex characteristics and analysis needs of CFD data.

[0034] In an optional implementation, the method further includes: decompressing the compressed file of the CFD dataset, including:

[0035] Parse global parameters, metadata indexes, low-frequency compressed data, and high-frequency compressed data from compressed files;

[0036] Based on global parameters, low-frequency compressed data is decoded and reconstructed to obtain low-frequency data, and high-frequency compressed data is decoded and reconstructed to obtain high-frequency data.

[0037] By merging low-frequency and high-frequency data based on metadata, the original CFD dataset is obtained.

[0038] The CFD data compression method based on dynamic mode decomposition and frequency domain transformation provided by this invention obtains various types of data by parsing the compressed file, accurately decodes and reconstructs high and low frequency data based on global parameters, and then uses metadata index fusion to efficiently reconstruct the original CFD dataset, ensuring complete data recovery. It utilizes the advantages of layered processing in the early compression stage to make the decoding process orderly and accurate, achieving a good balance between data storage and reuse, and improving the efficiency of the entire CFD data processing process.

[0039] Secondly, the present invention provides a compression device for CFD data based on dynamic mode decomposition and frequency domain transformation, the device comprising:

[0040] The frequency domain separation module is used to acquire CFD datasets and decompose them into low-frequency and high-frequency data based on preset frequency thresholds.

[0041] The data encoding module is used to decompose the low-frequency part of the data using dynamic mode decomposition to obtain low-frequency mode parameters, and to quantize and encode the high-frequency part of the data to obtain a high-frequency encoded stream.

[0042] The hybrid compression module is used to compress low-frequency modal parameters and high-frequency encoded streams to obtain compressed files of CFD datasets.

[0043] Thirdly, the present invention provides a computer device, comprising: a memory and a processor, the memory and the processor being communicatively connected to each other, the memory storing computer instructions, and the processor executing the computer instructions to perform the method described in the first aspect or any corresponding embodiment thereof.

[0044] Fourthly, the present invention provides a computer-readable storage medium storing computer instructions for causing a computer to perform the method described in the first aspect or any corresponding embodiment thereof. Attached Figure Description

[0045] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0046] Figure 1 This is a flowchart illustrating a CFD data compression method based on dynamic mode decomposition and frequency domain transformation according to an embodiment of the present invention.

[0047] Figure 2This is a flowchart illustrating another method for compressing CFD data based on dynamic mode decomposition and frequency domain transformation according to an embodiment of the present invention.

[0048] Figure 3 This is a structural block diagram of a CFD data compression device based on dynamic mode decomposition and frequency domain transformation according to an embodiment of the present invention.

[0049] Figure 4 This is a schematic diagram of the hardware structure of a computer device according to an embodiment of the present invention. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] This invention provides a method for compressing CFD data based on dynamic mode decomposition and frequency domain transformation. By separating and differentiating the frequency domain of CFD data, it achieves an optimized balance between computational efficiency, compression ratio, and data fidelity.

[0052] According to an embodiment of the present invention, a method for compressing CFD data based on dynamic mode decomposition and frequency domain transformation is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0053] This embodiment provides a CFD data compression method based on dynamic mode decomposition and frequency domain transformation, which can be used in the aforementioned computer system. Figure 1 This is a flowchart of a CFD data compression method based on dynamic mode decomposition and frequency domain transformation according to an embodiment of the present invention, as shown below. Figure 1 As shown, the process includes the following steps:

[0054] Step S101: Obtain the CFD dataset and decompose the CFD dataset into low-frequency data and high-frequency data based on a preset frequency threshold.

[0055] Specifically, in this embodiment, the CFD dataset is time-series data. CFD data is characterized by high dimensionality, multiple scales, and strong spatiotemporal correlation. Therefore, the CFD dataset can be represented as: in, Let l represent the set of real numbers, l×m×n represent the spatial dimension (including but not limited to two-dimensional or three-dimensional space); t represents the time step, which refers to the total number of time steps selected and retained throughout the entire simulation process.

[0056] Based on storage device requirements or bandwidth for remote visualization, limitations similar to those used in video streaming are applied to determine the target compression rate. This process can be accomplished using mature, existing technologies and will not be elaborated upon here. The preset frequency threshold is then dynamically adjusted based on the target compression rate.

[0057] Based on the physical scene simulated by CFD, the characteristic frequencies that dominate large-scale motion can be extracted and used as preset frequency thresholds. The CFD dataset is then decomposed in the frequency domain according to these preset frequency thresholds, distinguishing between the low-frequency components containing the main flow field structure and the high-frequency components representing local details.

[0058] By using thresholds to distinguish between "large-scale dominant motion" and "small-scale details," the subsequent use of DMD to compress low-frequency data can be more focused on physical modes, and high-frequency coding can be more efficient in processing local pulsations.

[0059] Step S102: Decompose the low-frequency data using dynamic mode decomposition to obtain low-frequency mode parameters, and quantize and encode the high-frequency data to obtain a high-frequency encoded stream.

[0060] Specifically, different compression strategies are used for the low-frequency and high-frequency data to perform differentiated processing. The low-frequency data focuses on the capture time evolution characteristics, while the high-frequency data focuses on the spatial distribution characteristics.

[0061] For low-frequency data, the DMD captures the time dynamics, elevating it from an analysis tool to a core component of the compression algorithm. This reduces the storage requirements for the time dimension. After filtering out high-frequency signals, the DMD captures nonlinear dynamic systems more accurately and performs better. For high-frequency data, its sparsity is utilized through threshold quantization, entropy coding, or run-length encoding (RLE) to preserve turbulence details while improving compression ratio with lossless or low-loss processing.

[0062] Step S103: Mix and compress the low-frequency modal parameters and the high-frequency encoded stream to obtain a compressed file of the CFD dataset.

[0063] Specifically, different compression methods are used for low-frequency modal parameters and high-frequency encoded streams. For the low-frequency part, the low-rank property of the modality is utilized, along with quadratic singular value decomposition and parametric encoding, to compress structured information. For the high-frequency part, the redundancy of details is utilized, along with threshold quantization and entropy encoding, to compress local data. After compressing the low-frequency and high-frequency parts separately, they are directly combined to obtain the compressed file of the CFD dataset.

[0064] The CFD data compression method based on dynamic mode decomposition and frequency domain transformation provided in this embodiment reduces computational complexity and the data scale of dynamic mode decomposition processing by pre-separating high-frequency and low-frequency data in the frequency domain. It supports parallel computing architecture, improves data computation efficiency, and selects an appropriate compression strategy according to the physical characteristics of high-frequency and low-frequency data. It can maintain good compression effect for flow fields of different complexities, achieve better compression ratio and quality, and realize an optimized balance between computational efficiency, compression ratio and data fidelity.

[0065] This embodiment provides a CFD data compression method based on dynamic mode decomposition and frequency domain transformation, which can be used in the aforementioned computer system. Figure 2 This is a flowchart of a CFD data compression method based on dynamic mode decomposition and frequency domain transformation according to an embodiment of the present invention, as shown below. Figure 2 As shown, the process includes the following steps:

[0066] Step S201: Obtain the CFD dataset and decompose the CFD dataset into low-frequency data and high-frequency data based on a preset frequency threshold.

[0067] Specifically, step S201 includes:

[0068] Step S2011: Perform time-domain-frequency domain transformation on each time-domain data in the CFD dataset to obtain the frequency domain data corresponding to each time-domain data.

[0069] Specifically, the time-domain frequency-domain transformation method can employ conversion methods such as DCT or DWT. This embodiment uses DCT as an example for illustration, but it is not limited to this. All data in the CFD dataset are in time-domain format. Based on the spatial dimension of each time-domain data, a two-dimensional or three-dimensional discrete cosine transform is performed on the time-domain data X(:,:,:,i) at each time step to obtain the frequency-domain representation of each time-domain data: F(:,:,:,i). The data represented in the frequency domain is the corresponding frequency-domain data for each time-domain data. The dimension of the time-domain data is 1×m×n, and the dimension of the frequency-domain data is m×n×t. The process of discrete cosine transform is a mature existing technology and will not be elaborated here.

[0070] Step S2012: Compare the frequency of each frequency domain data with the preset frequency threshold to obtain high-frequency data and low-frequency data in the frequency domain.

[0071] Specifically, a preset frequency threshold is set as θ. The frequency of each frequency domain data is compared with the preset frequency threshold. Frequency domain data with a frequency greater than the preset frequency threshold is frequency domain high-frequency data F_H, and frequency domain data with a frequency not greater than the preset frequency threshold is frequency domain low-frequency data F_L.

[0072] Step S2013: Perform an inverse transform on the high-frequency data in the frequency domain to obtain the high-frequency part of the corresponding time domain data, and perform an inverse transform on the low-frequency data in the frequency domain to obtain the low-frequency part of the corresponding time domain data.

[0073] Specifically, the inverse discrete cosine transform (ICD) is performed on the high-frequency data F_H in the frequency domain to obtain the high-frequency data in the time domain, which is the high-frequency part of the original data X_H; the inverse discrete cosine transform (ICD) is performed on the low-frequency data F_L in the frequency domain to obtain the low-frequency data in the time domain, which is the low-frequency part of the original data X_L. The inverse discrete cosine transform is a mature existing technology and will not be elaborated here.

[0074] The CFD data compression method based on dynamic mode decomposition and frequency domain transformation provided in this embodiment utilizes DMD to capture the temporal dynamic characteristics of low-frequency data, reducing the storage requirements of the time dimension. At the same time, it compresses the temporal evolution mode of the flow field, maintains the continuity and periodicity of physical phenomena, and completely preserves the main flow structure of CFD data. Quantization encoding is used for high-frequency data to reduce storage requirements. Through differential processing, key physical features are preserved under high compression ratios, and reconstruction errors are mainly concentrated in high-frequency turbulence details that have little impact on the analysis.

[0075] Step S202: Decompose the low-frequency data using dynamic mode decomposition to obtain low-frequency mode parameters, and quantize and encode the high-frequency data to obtain a high-frequency encoded stream.

[0076] Specifically, the low-frequency modal parameters include: low-frequency mode, modal frequency, modal amplitude, and initial state. In step S202 above, dynamic mode decomposition is used to decompose the low-frequency data to obtain the low-frequency modal parameters, including:

[0077] Step S2021: Reshape the low-frequency data into a matrix and perform singular value decomposition on the matrix.

[0078] Specifically, the spatial dimension is flattened: X = reshape(X,L,(m*n,t), which reshapes the low-frequency data X_L into a matrix, such as X1 = [X_1,X_2,...,X_(t-1)] and X2 = [X_2,X_3,...,X_t], where t represents the time step.

[0079] Perform Singular Value Decomposition (SVD) on the reshaped matrix to calculate the optimal approximation matrix: A≈U∑V * Where U represents the left singular vector matrix, ∑ represents the diagonal singular value matrix, and V * Let ∑ be the conjugate transpose of the right singular vector matrix, and ∑ be the elements on the diagonal. iThese are the singular values ​​of A. The specific process of singular value decomposition is a mature existing technology and will not be elaborated here.

[0080] Step S2022: Construct a simplified dynamical system using the results of singular value decomposition, and perform eigenvalue decomposition on the simplified dynamical system to obtain eigenvalues ​​and eigenvectors.

[0081] Specifically, a simplified dynamical system is constructed based on the results of singular value decomposition, yielding: For simplified power system Perform eigenvalue decomposition to obtain eigenvalues ​​λ_i and eigenvectors w_i.

[0082] Step S2023: Reconstruct the low-frequency mode based on the eigenvalues ​​and eigenvectors, and determine the modal frequency, modal amplitude and initial state based on the low-frequency mode.

[0083] Specifically, the essence of dynamic mode decomposition is to extract the coherent structure (i.e., DMD modes) of the flow field that evolves over time through eigenvalue decomposition of a linear system. The goal of the reconstruction process is to use the eigenvalues ​​and eigenvectors of the simplified system to back-calculate the dynamic modes of the flow field in the original high-dimensional space. These modes can characterize the physically meaningful dynamic features of the flow field, such as vortex structures and wave propagation. The complete DMD modes are reconstructed based on the eigenvalues ​​and eigenvectors: Φ_i=X_2*V*Σ^(-1)*w_i. Based on the DMD modes, the modal frequency ω_i=ln(λ_i) / Δt is calculated through the eigenvalues. The modal amplitude and initial state are calculated to make Φb=X0, where ω_i represents the modal frequency, b represents the modal amplitude, and X0 represents the initial state.

[0084] In some optional implementations, after determining the modal frequency, modal amplitude, and initial state based on the low-frequency mode, the method further includes:

[0085] The preset number of low-frequency modes to be retained is determined based on the target compression ratio;

[0086] Based on the magnitude of the modal amplitude, the reconstructed low-frequency modes are sorted from largest to smallest, and a preset number of low-frequency modes are selected and retained as the main modes.

[0087] Specifically, before each compression, the target compression ratio for the low-frequency portion is determined based on the target compression ratio of the CFD dataset. Then, the number of low-frequency modes to be retained is determined based on the target compression ratio for the low-frequency portion, and this number is used as the preset number r of low-frequency modes. Reducing the number of modes can directly and linearly reduce the amount of data. For example, retaining only 1 / 8 or 1 / 16 of the low-frequency modes is equivalent to performing lossy compression directly. Each mode corresponds to an independent dynamic pattern, such as vortex shedding or wave propagation. By calculating the importance index of each mode, based on the magnitude of the mode amplitude or the mode importance, the top r main modes are selected for retention, achieving lossy compression and reducing the amount of data while retaining the main flow characteristics.

[0088] The CFD data compression method based on dynamic mode decomposition and frequency domain transformation provided in this embodiment uses dynamic mode decomposition to process low-frequency data, accurately extracts key dynamic structures of the flow field, reduces data storage dimensionality, filters main modes to retain core information, reduces redundancy, and improves data processing efficiency. It provides a simpler and more effective low-frequency feature representation for flow field analysis, and helps efficient and accurate dynamic research and application.

[0089] In step S202 above, the high-frequency data is quantized and encoded to obtain a high-frequency encoded stream, including:

[0090] Step S2024: Obtain the target compression ratio of the CFD dataset and set the quantization threshold based on the target compression ratio.

[0091] Specifically, when quantizing and encoding the high-frequency data, the input is the high-frequency data X_H, and the output is the quantized and encoded high-frequency stream C_H. The target compression ratio of the CFD dataset is obtained, and the target compression ratios for the high-frequency and low-frequency components are determined based on the actual compression target. This process is a mature existing technology and will not be elaborated here. A quantization threshold is then set based on the target compression ratio of the high-frequency component.

[0092] Step S2025: Based on the quantization threshold, set the coefficients of the high-frequency data that are less than the quantization threshold to zero to obtain a sparse representation of the high-frequency data. The sparse representation includes the non-zero part of the high-frequency data.

[0093] Specifically, based on the quantization threshold, the coefficients of data with coefficients less than the quantization threshold in the high-frequency part of the data are set to zero, while the "important coefficients" with larger absolute values ​​are retained to form a sparse representation X_H'.

[0094] For example, in one specific embodiment, CFD simulation of the turbulent boundary layer of an airfoil at a Reynolds number Re = 106 is used to obtain wall pressure fluctuation data p(y,t), where y is the spanwise position and t is time. First, a four-level discrete wavelet transform (DWT) is performed on p(y,t) using the Daubechies-4 wavelet basis to obtain the high-frequency coefficients at each level: approximately 85% of the high-frequency coefficients have absolute values ​​less than 0.05 Pa; only 5% of the coefficients have absolute values ​​exceeding 0.2 Pa. Then, an adaptive calculation of the quantization threshold is used to estimate the noise standard deviation σ = 0.03 Pa, and the calculated... All |D j Coefficients with a value less than 0.12 are set to zero, and the remaining 15% of coefficients are retained, where D j This represents the coefficients after DWT conversion.

[0095] Step S2026: Determine the location information of the non-zero data and encode the non-zero data and its corresponding location information to obtain a high-frequency encoded stream.

[0096] Specifically, the non-zero coefficients are uniformly quantized, and the positions of the quantized non-zero coefficients and the corresponding non-zero data are encoded using entropy coding (e.g., arithmetic coding). The probability distribution characteristics of the data are used to reduce redundancy, resulting in a high-frequency coded stream C_H.

[0097] By using threshold quantization to filter key information and combining entropy coding or RLE to reduce redundant data, efficient compression is achieved while ensuring the physical fidelity of high-frequency details such as turbulence.

[0098] The CFD data compression method based on dynamic mode decomposition and frequency domain transformation provided in this embodiment precisely controls the degree of compression by adapting the target compression rate to the quantization threshold, balancing storage and accuracy requirements, achieving data sparsity by setting small coefficients to zero, filtering redundant information, highlighting key high-frequency features, encoding non-zero data and locations, significantly compressing the data volume, improving storage and transmission efficiency, minimizing and controlling the loss of high-frequency data, and efficiently compressing CFD high-frequency data to facilitate detailed flow field analysis and engineering applications.

[0099] Step S203: The low-frequency modal parameters and the high-frequency encoded stream are mixed and compressed to obtain a compressed file of the CFD dataset.

[0100] Specifically, step S203 includes:

[0101] Step S2031: Record the low-frequency modal parameters and the global parameters of the high-frequency encoded stream. The global parameters include: dimension, time step, and preset frequency threshold.

[0102] Specifically, by designing a header file containing global parameters to record global data attributes, the decoding end can clearly define the original data dimension and spatiotemporal scale, ensuring correct decompression. During decoding, reading the header file first can initialize memory and confirm decompression parameters.

[0103] Step S2032: Record the total number of low-frequency modes, perform singular value decomposition on the mode matrix in the low-frequency mode parameters, and encode and compress the mode frequency and mode amplitude in the low-frequency mode parameters to obtain low-frequency compressed data.

[0104] Specifically, the total number of low-mode features retained is recorded, such as the top r major modes, which need to be reconstructed according to this dimension during decoding. Singular value decomposition is performed on the mode matrix corresponding to the low modes, replacing the original matrix with low-rank decomposition, significantly reducing storage while preserving the spatial distribution characteristics of the modes. Modal frequencies are essentially complex numbers (containing frequency / damping information) and can be encoded according to floating-point precision requirements (e.g., single-precision / half-precision), or redundancy can be compressed using entropy coding. For modal amplitudes, entropy coding after quantization can be used, further compressing them by leveraging the "sparseness" of modal amplitudes (most modal amplitudes are small and can be truncated with a threshold).

[0105] DMD has compressed the time dimension through "modal segmentation + dimensionality reduction" and then compressed the spatial mode through secondary SVD to achieve structured compression, preserving the physical mode rather than simply data redundancy.

[0106] Step S2033: Compress the high-frequency encoded stream according to the high-frequency encoding protocol to obtain high-frequency compressed data.

[0107] Specifically, the data mainly consists of small-scale turbulent structures and noise. After threshold quantization (setting small coefficients to zero) and entropy encoding, a high-frequency encoded stream C_H with "sparseness + redundancy compression" is formed. It can be directly stored according to the high-frequency encoding protocol (e.g., marking encoding type, quantization threshold, and other metadata), ensuring that the encoding rules can be identified and the high-frequency coefficients can be restored during decoding.

[0108] Step S2034: Combine the low-frequency compressed data and the high-frequency compressed data, and add metadata indexes to the low-frequency compressed data and the high-frequency compressed data to obtain a compressed file.

[0109] Specifically, the system records the "start position, length, and type marker" of each encoded segment, supporting random access and allowing for quick location of encoded data at a specific moment / mode. If only low-frequency mode evolution needs to be viewed, the user can directly jump to the DMD encoded segment; if high-frequency details need to be verified, the high-frequency segment is read. Different decoding threads can independently process low-frequency / high-frequency segments by index, improving decompression efficiency.

[0110] The CFD data compression method provided in this embodiment, based on dynamic mode decomposition and frequency domain transformation, records global parameters to provide basic information for decompression and data understanding; it performs secondary SVD and parameter encoding on the low-frequency mode matrix to efficiently compress key structural data; it compresses high-frequency streams according to protocols while preserving details; and it combines data and adds metadata indexes to achieve both high- and low-frequency data collaborative compression and support for random access. While ensuring the integrity of the flow field's physical characteristics, it significantly reduces storage requirements, improves data management and retrieval efficiency, and adapts to the complex characteristics and analysis needs of CFD data.

[0111] In some alternative implementations, the method further includes: decompressing the compressed file of the CFD dataset, including:

[0112] Step S204: Parse global parameters, metadata index, low-frequency compressed data and high-frequency compressed data from the compressed file.

[0113] Specifically, a compressed file typically contains a header file for storing global parameters, a low-frequency encoded segment, a high-frequency encoded segment, and a metadata index. By reading the header file, dimensions, time steps, preset frequency thresholds, and quantization thresholds are extracted to initialize the decoding environment. The index table is parsed to determine the bytes contained in the low-frequency encoded segment (encoding type SVD+entropy coding) and the bytes contained in the high-frequency encoded segment (encoding type can be RLE+Huffman coding). Based on the metadata index, low-frequency compressed data (e.g., DMD modes, amplitudes, frequencies, etc.) and high-frequency compressed data (e.g., a list of sparse coefficient positions, and a non-zero high-frequency encoded stream) are extracted from the compressed file.

[0114] Step S205: Based on global parameters, decode and reconstruct the low-frequency compressed data to obtain the low-frequency data portion, and decode and reconstruct the high-frequency compressed data to obtain the high-frequency data portion.

[0115] Specifically, the low-frequency compressed data is decoded based on the target time step. The decoding algorithm is the same as the encoding algorithm, and the low-frequency data is obtained: in, This represents the reconstructed low-frequency data, where i represents the corresponding time step, b_i represents the amplitude at the i-th time step, and ω_i represents the frequency at the i-th time step.

[0116] The high-frequency compressed data is decoded and reconstructed using the same decoding algorithm as the encoding algorithm. Specifically, this includes converting the non-zero value encoded stream in the high-frequency encoded stream into the original numerical values ​​(e.g., looking up the corresponding coefficients from the Huffman code table), filling the all-zero matrix with non-zero data based on the position information, and recovering the coefficient data matrix.

[0117] Step S206: Based on the metadata, merge the low-frequency part of the data and the high-frequency part of the data to obtain the original CFD dataset.

[0118] Specifically, the metadata index records the spatial / temporal alignment information of the low-frequency and high-frequency data (e.g., whether it is stored in blocks according to grid blocks or time steps), and the dimensional mapping of the original data (e.g., the low-frequency data has a dimension of l×m×n×t, and the high-frequency data is a residual of the same dimension). The high-frequency and low-frequency data are directly combined to obtain the original CFD dataset. Aligning the high- and low-frequency data through the metadata index ensures that the large-scale structure of low frequencies and the small-scale details of high frequencies are accurately superimposed in time and space, thus restoring the physical characteristics of the original flow field.

[0119] The CFD data compression method based on dynamic mode decomposition and frequency domain transformation provided in this embodiment obtains various types of data by parsing the compressed file, accurately decodes and reconstructs high and low frequency data based on global parameters, and then uses metadata index fusion to efficiently reconstruct the original CFD dataset, ensuring complete data recovery. By leveraging the advantages of layered processing in the early compression stage, the decoding process is orderly and accurate, achieving a good balance between data storage and reuse, and improving the efficiency of the entire CFD data processing process.

[0120] This embodiment also provides a CFD data compression apparatus based on dynamic mode decomposition and frequency domain transformation. This apparatus is used to implement the above embodiments and preferred embodiments, and details already described will not be repeated. As used below, the term "module" can refer to a combination of software and / or hardware that performs a predetermined function. Although the apparatus described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0121] This embodiment provides a compression device for CFD data based on dynamic mode decomposition and frequency domain transformation, such as... Figure 3 As shown, it includes:

[0122] The frequency domain separation module 301 is used to acquire the CFD dataset and decompose the CFD dataset into low-frequency data and high-frequency data based on a preset frequency threshold.

[0123] The data encoding module 302 is used to decompose the low-frequency part of the data using dynamic mode decomposition to obtain low-frequency mode parameters, and to quantize and encode the high-frequency part of the data to obtain a high-frequency encoded stream.

[0124] The hybrid compression module 303 is used to mix and compress low-frequency modal parameters and high-frequency encoded streams to obtain a compressed file of the CFD dataset.

[0125] In some alternative implementations, the frequency domain separation module 301 includes:

[0126] The time-frequency conversion unit is used to perform discrete cosine transform on each time-domain data in the CFD dataset to obtain the corresponding frequency-domain data.

[0127] The frequency comparison unit is used to compare the frequency of each frequency domain data with the preset frequency threshold to obtain high-frequency data and low-frequency data in the frequency domain.

[0128] The inverse data transformation unit is used to perform inverse discrete cosine transform on high-frequency data in the frequency domain to obtain the high-frequency part of the corresponding time domain data, and to perform inverse discrete cosine transform on low-frequency data in the low-frequency domain to obtain the low-frequency part of the corresponding time domain data.

[0129] In some alternative implementations, the data encoding module 302 includes:

[0130] The singular value decomposition unit is used to reshape the low-frequency data into a matrix and perform singular value decomposition on the matrix.

[0131] The eigenvalue decomposition unit is used to construct a simplified dynamical system using the results of singular value decomposition, and to perform eigenvalue decomposition on the simplified dynamical system to obtain eigenvalues ​​and eigenvectors.

[0132] The low-frequency mode reconstruction unit is used to reconstruct low-frequency modes based on eigenvalues ​​and eigenvectors, and to determine the modal frequency, modal amplitude, and initial state based on the low-frequency modes.

[0133] The quantization threshold setting unit is used to obtain the target compression ratio of the CFD dataset and set the quantization threshold according to the target compression ratio.

[0134] The coefficient zeroing unit is used to set the coefficients of the high-frequency data to zero according to the quantization threshold, so as to obtain a sparse representation of the high-frequency data. The sparse representation contains the non-zero part of the high-frequency data.

[0135] The non-zero data encoding unit is used to determine the position information of the non-zero data and encode the non-zero data and its corresponding position information to obtain a high-frequency encoded stream.

[0136] In some alternative implementations, the hybrid compression module 303 includes:

[0137] The parameter recording unit is used to record low-frequency modal parameters and global parameters of the high-frequency encoded stream. The global parameters include: dimension, time step, and preset frequency threshold.

[0138] The low-frequency data compression unit is used to record the total number of low-frequency modes, perform singular value decomposition on the mode matrix in the low-frequency mode parameters, and encode and compress the mode frequency and mode amplitude in the low-frequency mode parameters to obtain low-frequency compressed data.

[0139] The high-frequency data compression unit is used to compress the high-frequency encoded stream according to the high-frequency encoding protocol to obtain high-frequency compressed data.

[0140] The combined compression unit is used to combine low-frequency compressed data and high-frequency compressed data, and add metadata indexes to the low-frequency compressed data and high-frequency compressed data to obtain a compressed file.

[0141] Further functional descriptions of the above modules and units are the same as those in the corresponding embodiments described above, and will not be repeated here.

[0142] In this embodiment, the CFD data compression device based on dynamic mode decomposition and frequency domain transformation is presented in the form of a functional unit. Here, a unit refers to an ASIC (Application Specific Integrated Circuit) circuit, a processor and memory that execute one or more software or fixed programs, and / or other devices that can provide the above functions.

[0143] This invention also provides a computer device having the above-described features. Figure 3 The device shown is a compression device for CFD data based on dynamic mode decomposition and frequency domain transformation.

[0144] Please see Figure 4 , Figure 4 This is a schematic diagram of the structure of a computer device provided in an optional embodiment of the present invention, such as... Figure 4 As shown, the computer device includes one or more processors 10, memory 20, and interfaces for connecting the components, including high-speed interfaces and low-speed interfaces. The components communicate with each other via different buses and can be mounted on a common motherboard or otherwise installed as needed. The processors can process instructions executed within the computer device, including instructions stored in or on memory to display graphical information of a GUI on external input / output devices (such as display devices coupled to the interfaces). In some alternative implementations, multiple processors and / or multiple buses can be used with multiple memories and multiple memory modules, if desired. Similarly, multiple computer devices can be connected, each providing some of the necessary operations (e.g., as a server array, a group of blade servers, or a multiprocessor system). Figure 4 Take a processor 10 as an example.

[0145] Processor 10 may be a central processing unit, a network processor, or a combination thereof. Processor 10 may further include a hardware chip. The hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The programmable logic device may be a complex programmable logic device (CAMP), a field-programmable gate array (FPGA), a general-purpose array logic (GDA), or any combination thereof.

[0146] The memory 20 stores instructions executable by at least one processor 10 to cause the at least one processor 10 to perform the method shown in the above embodiments.

[0147] The memory 20 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the computer device. Furthermore, the memory 20 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some alternative embodiments, the memory 20 may optionally include memory remotely located relative to the processor 10, and these remote memories may be connected to the computer device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0148] The memory 20 may include volatile memory, such as random access memory; the memory may also include non-volatile memory, such as flash memory, hard disk or solid-state drive; the memory 20 may also include a combination of the above types of memory.

[0149] The computer device also includes a communication interface 30 for communicating with other devices or communication networks.

[0150] This invention also provides a computer-readable storage medium. The methods described above according to embodiments of the invention can be implemented in hardware or firmware, or implemented as computer code that can be recorded on a storage medium, or implemented as computer code downloaded via a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and then stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code, which, when accessed and executed by the computer, processor, or hardware, implements the methods shown in the above embodiments.

[0151] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A method for compressing CFD data based on dynamic mode decomposition and frequency domain transformation, characterized in that, The method includes: Acquire a CFD dataset and decompose the CFD dataset into low-frequency data and high-frequency data based on a preset frequency threshold; The low-frequency data is decomposed using dynamic mode decomposition to obtain low-frequency mode parameters, and the high-frequency data is quantized and encoded to obtain a high-frequency encoded stream. The low-frequency modal parameters and the high-frequency encoded stream are mixed and compressed to obtain the compressed file of the CFD dataset.

2. The method according to claim 1, characterized in that, The CFD dataset is decomposed into low-frequency and high-frequency components based on a preset frequency threshold, including: The time-domain data in the CFD dataset is transformed into the frequency domain to obtain the frequency domain data corresponding to each time-domain data. By comparing the frequency of each frequency domain data with the preset frequency threshold, high-frequency data and low-frequency data in the frequency domain are obtained. The high-frequency data in the frequency domain is inversely transformed to obtain the high-frequency part of the corresponding time domain data, and the low-frequency data in the frequency domain is inversely transformed to obtain the low-frequency part of the corresponding time domain data.

3. The method according to claim 1, characterized in that, The low-frequency modal parameters include: low-frequency mode, modal frequency, modal amplitude, and initial state. The low-frequency data is decomposed using dynamic mode decomposition to obtain the low-frequency modal parameters, including: The low-frequency data is reshaped into a matrix, and singular value decomposition is performed on the matrix. A simplified dynamical system is constructed using the results of singular value decomposition, and eigenvalue decomposition is performed on the simplified dynamical system to obtain eigenvalues ​​and eigenvectors; The low-frequency mode is reconstructed based on the eigenvalues ​​and eigenvectors, and the modal frequency, modal amplitude, and initial state are determined based on the low-frequency mode.

4. The method according to claim 3, characterized in that, After determining the modal frequency, modal amplitude, and initial state based on the low-frequency mode, the method further includes: The preset number of low-frequency modes to be retained is determined based on the target compression ratio; Based on the magnitude of the modal amplitude, the reconstructed low-frequency modes are sorted from largest to smallest, and a preset number of low-frequency modes are selected and retained as the main modes.

5. The method according to claim 1, characterized in that, By quantizing and encoding the high-frequency data, a high-frequency encoded stream is obtained, including: Obtain the target compression ratio of the CFD dataset, and set a quantization threshold based on the target compression ratio; Based on the quantization threshold, the data with coefficients less than the quantization threshold in the high-frequency part of the data are set to zero to obtain a sparse representation of the high-frequency part of the data, wherein the sparse representation includes the non-zero part of the high-frequency part of the data. The location information of the non-zero data portion is determined, and the non-zero data portion and its corresponding location information are encoded to obtain a high-frequency encoded stream.

6. The method according to claim 1, characterized in that, The low-frequency modal parameters and the high-frequency encoded stream are mixed and compressed, including: Record the low-frequency modal parameters and the global parameters of the high-frequency encoded stream. The global parameters include: dimension, time step, and preset frequency threshold. Record the total number of low-frequency modes, perform singular value decomposition on the mode matrix in the low-frequency mode parameters, and encode and compress the mode frequency and mode amplitude in the low-frequency mode parameters to obtain low-frequency compressed data; The high-frequency encoded stream is compressed according to a high-frequency encoding protocol to obtain high-frequency compressed data; The low-frequency compressed data and the high-frequency compressed data are combined, and metadata indexes are added to the low-frequency compressed data and the high-frequency compressed data to obtain a compressed file.

7. The method according to claim 6, characterized in that, The method further includes: Decompressing the compressed file of the CFD dataset includes: Parse global parameters, metadata indexes, low-frequency compressed data, and high-frequency compressed data from the compressed file; Based on the global parameters, the low-frequency compressed data is decoded and reconstructed to obtain the low-frequency data portion, and the high-frequency compressed data is decoded and reconstructed to obtain the high-frequency data portion. Based on the aforementioned metadata, the low-frequency and high-frequency data are combined to obtain the original CFD dataset.

8. A compression device for CFD data based on dynamic mode decomposition and frequency domain transformation, characterized in that, The device includes: The frequency domain separation module is used to acquire the CFD dataset and decompose the CFD dataset into low-frequency data and high-frequency data based on a preset frequency threshold. The data encoding module is used to decompose the low-frequency data using dynamic mode decomposition to obtain low-frequency mode parameters, and to quantize and encode the high-frequency data to obtain a high-frequency encoded stream. The hybrid compression module is used to mix and compress the low-frequency modal parameters and the high-frequency encoded stream to obtain a compressed file of the CFD dataset.

9. A computer device, characterized in that, include: A memory and a processor, the memory and the processor being communicatively connected to each other, the memory storing computer instructions, the processor executing the computer instructions to perform the method of any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing the computer to perform the method of any one of claims 1 to 7.

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