A method for dynamic reconstruction and monitoring of unsteady flow field based on sparse measurement points

Abstract

This invention discloses a method for dynamic reconstruction and monitoring of unsteady flow fields based on sparse measurement points. The method first acquires snapshot data of physical quantities of the target flow field at continuous time steps; selects a small number of snapshots and extracts a reference frequency set through dynamic mode decomposition (DMD); forms a candidate measurement point set through high-order moment feature construction and K-means clustering; performs DMD fine screening on the candidate measurement point combination based on frequency domain consistency constraints to determine the optimal sparse measurement point set; constructs a measurement matrix to achieve sparse observation, and combines compressed dynamic mode decomposition (cDMD) to complete the full-field flow field reconstruction and time-domain evolution monitoring. This invention achieves robust capture of dominant dynamic frequencies with very few observation channels, reduces sensing costs and computational load, and improves the stability and real-time performance of reconstruction under complex conditions. It is applicable to flow field monitoring needs in aerospace, marine observation, and other fields.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to a method for dynamic reconstruction and monitoring of unsteady flow fields based on sparse measurement points. Background Technology

[0002] In engineering fluid mechanics research and applications, obtaining high-precision, time-varying full-field flow information is a core requirement for revealing turbulence mechanisms, optimizing aerodynamic / hydrodynamic characteristics, and realizing online monitoring and control of systems. However, traditional experimental measurement methods have significant bottlenecks in complex engineering environments: while digital particle image velocimetry (PIV) can provide a full-field view, it is prone to deviations near walls or in obstructed areas due to calibration difficulties and uneven particle concentration, and its spatial and temporal resolution is insufficient to meet high-order statistical requirements; laser Doppler velocimetry (LDV) offers high single-point measurement accuracy, but its sparse data points, limited by optical channels and measurement volume, result in insufficient overall flow field coverage; particle tracking velocimetry (PTV) also suffers from significant systematic errors near walls or in severely obstructed areas. These experimental methods generally face challenges such as high deployment costs, limited coverage, difficulty in error control, and poor engineering applicability.

[0003] Existing related technologies also have obvious limitations. For example, the patent CN117875220A discloses "a data monitoring method, device and medium based on flow field numerical simulation". Although it improves the flexibility of monitoring local flow field characteristic variables through grid partitioning and coordinate mapping mechanism, the solution is limited to data reading and storage of known grid points, relies on manual preset monitoring area, and does not involve a closed-loop process from a small number of observations to dynamic prediction of the whole field. It cannot meet the online and noise-resistant real-time monitoring needs under complex working conditions.

[0004] In summary, the common shortcomings of existing technologies are mainly reflected in the following aspects: the selection of observation points lacks dynamic basis, making it difficult to balance representativeness and economy; the ability to reconstruct the entire field is insufficient, making it impossible to predict the temporal evolution of unsteady flow fields; and the stability against noise interference and operating condition drift is poor, making engineering implementation difficult. To address these issues, there is an urgent need for a technical solution that can achieve high-fidelity flow field reconstruction and monitoring with a small number of measurement points. Summary of the Invention

[0005] This invention was made in view of the above-mentioned existing situation, and aims to solve the problems of insufficient representativeness of measurement points, low reconstruction accuracy, and poor noise and drift resistance in existing flow field monitoring and reconstruction technologies. It proposes a low-channel-number flow field monitoring and reconstruction method with frequency domain reference as the core.

[0006] This invention provides a method for dynamic reconstruction and monitoring of unsteady flow fields based on sparse measuring points, comprising the following steps:

[0007] S1. Obtain snapshot data of the physical quantity distribution of the target flow field over continuous time steps and record the sampling interval;

[0008] S2. Reference spectrum extraction: Select several snapshot data to perform dynamic mode decomposition (DMD), and use the mode frequencies obtained by the DMD as a set of reference frequencies;

[0009] S3. K-means Clustering Initial Screening: For the time series of each grid point, calculate the higher-order moments for selected physical quantities. Construct a feature vector based on the calculated higher-order moments. After standardizing the feature vector, perform K-means clustering to compress all grid points into a single array. K Each cluster is further divided into two groups, and representative points are selected from each cluster to form a candidate set. C ;

[0010] S4. Frequency Domain Consistency Refinement: For the candidate set C The DMD is performed on different combinations of observation points to extract the main spectrum corresponding to each combination, and the consistency distance between the main spectrum and the reference frequency set is calculated. D Under the preset constraint of the number of measurement points, the consistency distance is selected through greedy search or heuristic search. D Minimal set of observation points S ;

[0011] S5. Measurement Matrix Construction and Sparse Observation: A measurement matrix is ​​constructed based on the grid positions corresponding to the observation point set S, and a sparse observation layout is formed based on the measurement matrix for online monitoring;

[0012] S6. Flow Field Reconstruction and Evolution Monitoring: Singular value decomposition (SVD) and eigenvalue decomposition are performed on the sparse observation snapshot sequence obtained from the sparse observation layout to obtain compressed spatial modes and eigenvalues. The full-field modes are recovered according to the backpropagation relationship of standard compressed dynamic mode decomposition (cDMD). Least square inversion or regularized inversion model is established using the measurement point observation data obtained from the sparse observation layout to solve for the modal coefficients. The full-field flow field reconstruction and time-domain evolution monitoring are realized based on the modal coefficients, the compressed spatial modes and the eigenvalues.

[0013] In step S2, the extraction of the reference spectrum is assisted by the Welch method or the short-time Fourier transform (STFT) method to achieve spectrum estimation.

[0014] In step S3, the K-means clustering can be replaced by hierarchical clustering, density clustering (DBSCAN), or spectral clustering.

[0015] In step S2 and step S4, the DMD can be replaced by extended dynamic mode decomposition (EDMD), delayed dynamic mode decomposition (Delay-DMD), or spectral eigenorthogonal decomposition combined with dynamic mode decomposition (SPOD-DMD fusion).

[0016] In step S4, the consistency distance is calculated using a weighted L2 norm, and the weighting coefficients of the weighted L2 norm are determined based on the energy proportion of each frequency in the reference frequency set.

[0017] The flow field reconstruction process described in step S6 can be combined with algorithms such as Gappy-POD, compressed sensing technology, and recursive least squares.

[0018] The selected physical quantity in step S3 includes at least one of Reynolds shear stress, vorticity, and pressure.

[0019] In step S6, the time-domain evolution monitoring process adopts a sliding window mechanism and an online update mechanism. The sliding window mechanism is used to update the observation snapshot sequence in real time, and the online update mechanism is used to adjust the compressed spatial mode and the feature value based on the updated observation snapshot sequence to adapt to operating condition drift and noise interference.

[0020] The expression for the feature vector in step S3 is as follows:

[0021]

[0022] in For Reynolds shear stress, vorticity, For pressure, The second moment of the Reynolds shear stress. The third moment of the Reynolds shear stress. The second moment of vorticity. Let be the second moment of the pressure.

[0023] Among them, the higher-order moments mentioned in step S3 The value can be any integer from 1 to 5. The fluctuations involved in the calculation of the higher-order moments are expressed as the variance of the physical quantity, the bandpass energy, or the variance after detrending.

[0024] The unsteady flow field dynamic reconstruction and monitoring method based on sparse measurement points provided by this invention organically integrates spectrum anchoring, K-means clustering compression based on physical moment, DMD fine screening with frequency domain consistency constraints, and compressed DMD reconstruction. Compared with traditional methods that rely on large-scale full-field measurements or static modal libraries, this method can stably capture the dominant dynamic frequencies and maintain the consistency of modal characteristics with very few observation channels, thereby effectively improving the physical representativeness and information coverage of the observation points for the main modes.

[0025] First, in the frequency domain anchoring stage, this invention establishes a reference frequency set by initially acquiring only a small number of flow field snapshots and directly extracting the characteristic frequencies of the dominant modes using dynamic mode decomposition (DMD). Combined with a candidate compression strategy based on high-order statistical moment clustering, the computational scale of frequency domain fine-tuning can be significantly reduced while maintaining dynamic fidelity, thus facilitating efficient deployment in real-time or online scenarios.

[0026] Secondly, in the measurement point optimization stage, frequency domain consistency is introduced as a direct constraint for DMD selection. This ensures that the final sensor layout is not only reasonable in terms of spatial coverage but also maintains a high similarity to the reference mode at the spectral level. Therefore, even with changes in operating conditions, noise interference, or limited measurement points, it can still robustly identify the dominant frequency and key modes. This mechanism compensates for the shortcomings of existing sparse deployment methods that neglect frequency constraints, significantly enhancing sensitivity to dominant dynamics and anti-interference capabilities.

[0027] In the flow field reconstruction stage, this invention utilizes compressed DMD combined with a small number of measured points and an initial time slice to achieve rapid recovery of the full-field modes and prediction of temporal evolution. Furthermore, it can adapt to operational condition drift during long-term monitoring through sliding windows and online updates. Compared to deep learning methods that rely on large amounts of prior data or require long training times, this approach has lower dependence on prior data, shorter deployment cycles, and lower computational resource consumption, making it more suitable for long-term online operation in engineering sites.

[0028] This invention has strong potential for widespread application, both theoretically and practically. It not only provides a low-cost, highly robust approach to full-field monitoring and reconstruction, but also serves as an important tool for sensor deployment optimization, closed-loop control strategy design, and monitoring of multi-physics coupled systems. In fields such as aerospace aerodynamic optimization, ocean and atmospheric observation, combustion flow field diagnostics, wind engineering, and complex equipment operation monitoring, this method can significantly improve observation and modeling efficiency, providing solid technical support for the understanding, prediction, and control of complex flow fields. Attached Figure Description

[0029] Figure 1 A flowchart illustrating the unsteady flow field dynamic reconstruction and monitoring method based on sparse measuring points according to an embodiment of the present invention is shown.

[0030] Figure 2 A schematic diagram of the Reynolds shear stress distribution in the unsteady flow field dynamic reconstruction and monitoring method based on sparse measuring points, as described in the embodiments of the present invention, is shown.

[0031] Figure 3 This diagram illustrates the frequency distance variation with the number of grid points in the unsteady flow field dynamic reconstruction and monitoring method based on sparse measuring points according to an embodiment of the present invention.

[0032] Figure 4 A schematic diagram of the point selection distribution of the unsteady flow field dynamic reconstruction and monitoring method based on sparse measuring points involved in the embodiments of the present invention is shown.

[0033] Figure 5 The diagram illustrates the root mean square velocity field variation over time in the unsteady flow field dynamic reconstruction and monitoring method based on sparse measuring points, as described in the embodiments of the present invention. Detailed Implementation

[0034] Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the following description, the same reference numerals are used for the same parts, and repeated descriptions are omitted. Furthermore, the drawings are merely schematic diagrams, and the proportions of the parts or the shapes of the parts may differ from the actual figures.

[0035] The embodiments of the present invention use Reynolds number Taking the flow around a two-dimensional cylinder as the research object, this flow field exhibits obvious unsteady characteristics of vortex shedding, making it a typical scenario for verifying flow field reconstruction methods. The TAU software (second-order finite volume flow solver) from the German Aerospace Center (DLR) was used to generate a sequence of transient snapshots of the flow field. Specific parameters are as follows: time step... =0.0025 (dimensionless), total simulation time T=6.0, total number of flow field snapshots 300, number of grid points N=36474; the first 30 snapshots are used for the selection of measurement points and model construction of the method of the present invention, and the last 270 snapshots are used for the verification of reconstruction effect.

[0036] like Figure 1 As shown, the present invention provides a method for dynamic reconstruction and monitoring of unsteady flow fields based on sparse measuring points, comprising the following steps:

[0037] S1. Obtain snapshot data of the physical quantity distribution of the target flow field at continuous time steps, and record the sampling interval. ;

[0038] The TAU software directly outputs snapshot data of the velocity field in the u direction of the flow field around the cylinder at 300 consecutive time steps, forming a data matrix. Each column represents the global velocity distribution at a given time step, recording the sampling interval. = 0.0025. The snapshot data obtained in this step provides the basis for all subsequent analyses, and its temporal and spatial resolutions meet the requirements of high-order statistics and mode decomposition.

[0039] S2. Reference Spectrum Extraction: Select several snapshot data sets for Dynamic Mode Decomposition (DMD), and use the mode frequencies obtained through the DMD as a reference frequency set. ;

[0040] Select the first 30 snapshots (denoted as the data matrix) Dynamic mode decomposition (DMD) is performed. The DMD method extracts the modal frequencies and modal shapes of the flow field by performing singular value decomposition (SVD) and eigenvalue decomposition on the data matrix.

[0041] In this embodiment, the DMD extracts three dominant mode frequencies, forming a reference frequency set. To verify the reliability of the reference spectrum, it was compared with the standard frequency calculated from a complete set of 300 snapshots. The relative errors were 0.005%, 0.057%, and 0.032%, respectively (see Table 1). The errors were extremely small, indicating that a small number of snapshots were sufficient to accurately capture the dominant frequency of the flow field, thus achieving the technical goal of "establishing a reliable reference with a small amount of data".

[0042] Table 1. Comparison of Standard Frequency and Reference Frequency

[0043]

[0044] S3. K-means clustering initial screening: Calculate higher-order moments for selected physical quantities on the time series of each grid point;

[0045] The formula for calculating the higher-order moments is:

[0046]

[0047] in, T The length of the time series. For grid points in The physical quantity value at a given time. The time average of the physical quantity at this grid point is used as the basis for constructing a feature vector based on the calculated higher-order moments. After standardizing the feature vector, K-means clustering is performed to compress the entire field grid points into [database values]. K Each cluster is further divided into two groups, and representative points are selected from each cluster to form a candidate set. C。

[0048] The core of this step is to construct feature vectors based on higher-order moments of physical quantities, and then compress all grid points through K-means clustering to form a set of candidate measurement points.

[0049] First, select the Reynolds shear stress. As a core physical quantity, it can effectively reveal the correlation between vorticity transport and velocity fluctuations, and locate active regions of the flow field. The time-averaged velocity field is calculated using the instantaneous velocity field (u, v). , The formula is:

[0050] ,

[0051] Extracting pulsation components:

[0052] ,

[0053] Final calculation of Reynolds shear stress:

[0054]

[0055] in The fluid density is taken as 1.0 in this embodiment, and the calculation results are as follows: Figure 2 As shown, the wake region The value is significantly higher than in other regions.

[0056] Then, higher-order moments are calculated to construct eigenvectors, selecting moments of order n=2nd and 3rd, and the second moment:

[0057]

[0058] Reflecting the wave intensity of τ,

[0059] Third moment:

[0060]

[0061] Characterizing the asymmetry of the τ distribution;

[0062] Simultaneously introducing vorticity second moment With pressure second moment , forming feature vectors The feature vectors of all grid points are standardized (mean is 0, variance is 1) to eliminate the influence of dimensions.

[0063] Perform K-means clustering with the following parameters: number of clusters K=100 (balancing compression and computational efficiency), initialization method K-means++ (to avoid local optima), and convergence condition of centroid change < 10. -4 After clustering, the grid point closest to the centroid is selected from each cluster as the representative point, forming a candidate set C containing 100 measurement points, thus achieving efficient compression of the entire field of 36,474 grid points.

[0064] S4. Frequency Domain Consistency Refinement: For the candidate set C The DMD is performed on different combinations of observation points to extract the main spectrum corresponding to each combination. Calculate the main spectrum and the reference frequency set. Consistency distance D。 The consistency distance D The calculation formula is:

[0065]

[0066] in For the first i The frequency obtained by combining the observation points through the DMD.

[0067] This step selects the optimal set of measurement points S from the candidate set C. The core principle is to ensure the dynamic representativeness of the measurement points through frequency domain consistency constraints. A constraint of 30 measurement points is set (a common upper limit for sensor deployment in engineering). A greedy search strategy is used for step-by-step selection: starting with 100 candidate points, the target number of points is decreased by a step size of 1. For each target number s, all... For each combination of measuring points, perform the following operations:

[0068] (1) Extract 30 snapshot data corresponding to each measuring point in the combination to form a data matrix. ;

[0069] (2) To Perform DMD to extract the 7 dominant frequency components. ;

[0070] (3) Calculate the consistency distance. In this embodiment, the L2 norm is used, and the formula is: .

[0071] During the screening process, the frequency distance D changes with the number of grid points as follows: Figure 3 As shown, when the number of measuring points decreases from 100 to 30, the D value slightly increases from 0.08 to 0.12, still within the low error range; further reducing the number of measuring points causes the D value to rise sharply. Therefore, 30 measuring points are determined as the optimal set S, and its spatial distribution is as follows. Figure 4 As shown, the stress is mainly concentrated in the high-stress region of the wake, which is consistent with the physical characteristics of the flow field.

[0072] S5. Measurement Matrix Construction and Sparse Observation: A measurement matrix is ​​constructed based on the grid positions corresponding to the observation point set S, and a sparse observation layout is formed based on the measurement matrix for online monitoring.

[0073] A measurement matrix C (30×36474) is constructed using the grid positions of the optimal measurement point set S. The elements corresponding to the grid points in S are set to 1, and the remaining elements are set to 0. (If the j-th grid point belongs to S), otherwise The measurement matrix is ​​essentially a selection matrix, and sparse observation data can be directly obtained by multiplying it with the full-field data matrix. This simulates the sparse sampling process of sensors in engineering, providing input for subsequent reconstruction.

[0074] S6. Flow Field Reconstruction and Evolution Monitoring: Based on the sparse observation snapshot sequence obtained from the sparse observation layout, singular value decomposition (SVD) and eigenvalue decomposition are performed to obtain the compressed spatial modes. With eigenvalues The full-field modes are recovered according to the backward relationship of standard compressed dynamic mode decomposition (cDMD). A least-squares inversion or regularized inversion model is established using the measurement data obtained from the sparse observation layout, and the mode coefficients are solved. ; through formula Achieve full-field flow field reconstruction and temporal evolution monitoring, among which for The distribution of physical quantities in the entire flow field at time t. For It is a diagonal matrix with diagonal elements.

[0075] Reconstruction is achieved using compressed dynamic mode decomposition (cDMD), and stability is improved by combining a sliding window and an online update mechanism.

[0076] (1) Sparse observation data based on the first 30 snapshots Perform SVD and eigenvalue decomposition to obtain compressed space modes. (r=10, the effective modal order) and eigenvalues ;

[0077] (2) Enable the sliding window mechanism (window length 30) to update the observation snapshot sequence in real time; for the observation data y of the last 270 verification time steps future The modal coefficients are solved by least squares. ;

[0078] (3) Through the formula The entire flow field is reconstructed, and an online update mechanism is adopted (updating once every 10 time steps). and Adapt to possible operating condition drift;

[0079] (4) To improve noise immunity, this embodiment combines gappy-POD, compressed sensing, and Kalman filtering. Gappy-POD completes missing modal information, compressed sensing optimizes sparse signal recovery, and Kalman filtering corrects observation noise in real time. The final reconstruction error is as follows: Figure 5 As shown, the RMS value of the velocity field remained stable below 0.15 for a long time, while the absolute velocity of the flow field was about 66, with a relative error of less than 0.23%, which verified the high accuracy and stability of the method.

[0080] This embodiment verifies the method using a cylindrical flow scenario, achieving full-field flow reconstruction from 30 sparse measurement points to 36,474 grid points. The reconstruction error is small and stable over a long period, demonstrating that the method can capture the dominant dynamic characteristics of the flow field with a very small number of measurement points, solving the problems of traditional methods such as numerous measurement points, high cost, and insufficient representativeness. Furthermore, the combination of clustering initial screening and frequency domain fine screening significantly reduces the computational load, and the online update mechanism improves engineering applicability, providing a feasible solution for low-cost, high-precision monitoring of complex flow fields.

[0081] The embodiments described above do not constitute a limitation on the scope of protection of this technical solution. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the above embodiments should be included within the scope of protection of this technical solution.

Claims

1. A method for dynamic reconstruction and monitoring of unsteady flow fields based on sparse measuring points, characterized in that, Includes the following steps: S1. Obtain snapshot data of the physical quantity distribution of the target flow field over continuous time steps and record the sampling interval; S2. Reference spectrum extraction: Select several snapshot data to perform dynamic mode decomposition (DMD), and use the mode frequencies obtained by the DMD as a set of reference frequencies; S3. K-means Clustering Initial Screening: For the time series at each grid point, calculate the higher-order moments for the selected physical quantities and construct feature vectors. Then, use K-means clustering to obtain the candidate set. C ; S4. Frequency Domain Consistency Refinement: For the candidate set C The DMD is performed on different combinations of observation points to extract the main spectrum and calculate the consistency distance between the main spectrum and the reference frequency set. D Under the preset constraint of the number of measurement points, the consistency distance is selected through greedy search or heuristic search. D Minimal set of observation points S ; S5. Measurement Matrix Construction and Sparse Observation: A measurement matrix is ​​constructed based on the grid positions corresponding to the observation point set S, and a sparse observation layout is formed based on the measurement matrix for online monitoring; S6. Flow Field Reconstruction and Evolution Monitoring: Based on the snapshot sequence obtained from the sparse observation layout, singular value decomposition (SVD) and eigenvalue decomposition are performed to obtain compressed spatial modes and eigenvalues. The full-field modes are recovered according to the backpropagation relationship of standard compressed dynamic mode decomposition (cDMD). The least squares inversion or regularized inversion model is established using the measurement point observation data obtained from the sparse observation layout to solve for the modal coefficients. The full-field flow field reconstruction and time-domain evolution monitoring are realized based on the modal coefficients, the compressed spatial modes and the eigenvalues.

2. The method for dynamic reconstruction and monitoring of unsteady flow fields based on sparse measuring points according to claim 1, characterized in that, In the process of extracting the reference spectrum in step S2, the Welch method or the short-time Fourier transform (STFT) method is used to assist in spectrum estimation.

3. The method for dynamic reconstruction and monitoring of unsteady flow fields based on sparse measuring points according to claim 1, characterized in that, The K-means clustering described in step S3 can be replaced by hierarchical clustering, density clustering (DBSCAN), or spectral clustering.

4. The method for dynamic reconstruction and monitoring of unsteady flow fields based on sparse measuring points according to claim 1, characterized in that, The DMD mentioned in steps S2 and S4 can be replaced by extended dynamic mode decomposition (EDMD), delayed dynamic mode decomposition (Delay-DMD), or spectral eigenorthogonal decomposition combined with dynamic mode decomposition.

5. The method for dynamic reconstruction and monitoring of unsteady flow fields based on sparse measuring points according to claim 1, characterized in that, The consistency distance in step S4 is calculated using a weighted L2 norm, and the weighting coefficients of the weighted L2 norm are determined based on the energy proportion of each frequency in the reference frequency set.

6. The method for dynamic reconstruction and monitoring of unsteady flow fields based on sparse measuring points according to claim 1, characterized in that, The flow field reconstruction process described in step S6 can combine Gappy-POD (Gap Eigenorthogonal Decomposition), compressed sensing technology, and recursive least squares algorithm.

7. The method for dynamic reconstruction and monitoring of unsteady flow fields based on sparse measuring points according to claim 1, characterized in that, The selected physical quantity in step S3 includes at least one of Reynolds shear stress, vorticity, and pressure.

8. The method for dynamic reconstruction and monitoring of unsteady flow fields based on sparse measuring points according to claim 1, characterized in that, The time-domain evolution monitoring process described in step S6 employs a sliding window mechanism and an online update mechanism. The sliding window mechanism is used to update the observation snapshot sequence in real time, and the online update mechanism is used to adjust the compressed spatial mode and the feature value based on the updated observation snapshot sequence.

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