A PIV flow field missing data compensation method and device and storage medium

Abstract

The application relates to a PIV flow field missing data compensation method and device based on data fusion and a storage medium, wherein the method comprises the following steps: step 1) acquiring PIV flow field data sets with different data missing areas; step 2) performing data preprocessing on the first PIV flow field data set; step 3) performing intrinsic orthogonal decomposition on the preprocessed first PIV flow field data set to obtain a POD mode; step 4) respectively performing masking on the POD mode and the second PIV flow field data set to obtain a masked POD mode and a masked data set; step 5) projecting the masked data set onto the masked POD mode based on least square regression to obtain reconstructed time coefficients; step 6) reconstructing a flow field; and step 7) sequentially moving the data corresponding to the data missing area in the second PIV flow field data set in the reconstructed flow field into the second PIV flow field data set in time sequence to obtain a fusion data field after data compensation. Compared with the prior art, the application has the advantages of good data compensation effect and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of flow field data processing, and particularly to a PIV flow field missing data compensation method and device based on data fusion and a storage medium. BACKGROUND

[0002] Particle image velocimetry (PIV) is a mature optical flow field testing technology with high spatial resolution. In PIV optical measurement technology, light and data are often missing due to the obstruction of solid boundaries, such as the obstruction of the flow field directly below the solid cylinder in the flow around the cylinder. Even if a transparent solid material (such as acrylic) is used, the refractive index of light will change due to the sharp change in the curvature of the boundary, so that even if the brightness is not completely lost, obvious shadows will be caused in the imaging, making the post-processing result of the image extremely inaccurate.

[0003] In the face of such a common data missing problem, the most direct idea is to use the characteristics of the flow field itself to compensate for the missing data, such as using the symmetry and periodicity of the flow field. However, the disadvantage of this method is that if the data missing area is symmetric about the center line, the above method will be completely ineffective. SUMMARY

[0004] The purpose of the present application is to provide a PIV flow field missing data compensation method and device based on data fusion and a storage medium, which improves the data compensation effect and can be applied to various data missing scenarios.

[0005] The purpose of the present application can be achieved by the following technical solutions:

[0006] A PIV flow field missing data compensation method based on data fusion, comprising the following steps:

[0007] Step 1) obtaining a first PIV flow field data set and a second PIV flow field data set with different data missing areas;

[0008] Step 2) data preprocessing of the first PIV flow field data set;

[0009] Step 3) intrinsic orthogonal decomposition of the preprocessed first PIV flow field data set to obtain a POD mode;

[0010] Step 4) masking the POD mode and the second PIV flow field data set respectively to obtain a masked POD mode and a masked data set;

[0011] Step 5) projecting the masked data set onto the masked POD mode based on least squares regression to obtain reconstructed time coefficients;

[0012] Step 6) determining a reconstructed flow field based on the reconstructed time coefficient and the POD mode;

[0013] Step 7) sequentially translating the data in the reconstructed flow field corresponding to the data missing area in the second PIV flow field data set in time sequence into the second PIV flow field data set to obtain the fusion data field after data compensation.

[0014] The data preprocessing is removing the time average component.

[0015] The proper orthogonal decomposition is:

[0016]

[0017] wherein g is the data of the PIV flow field data set G at a certain time, represents the average flow field, π i represents the spatial mode, and ∑π is the POD mode, represents the time coefficient corresponding to the spatial mode π i , and w represents the total number of spatial modes.

[0018] The time coefficient is calculated based on singular value decomposition:

[0019]

[0020] wherein, is the two-norm of the time coefficient , C represents a matrix obtained by performing spatial cross-correlation calculation on the inner product (G, G') of the flow data set G, λ is a sequence of eigenvalues, and represents the energy occupied by the mode π.

[0021] The step 4) comprises the following steps:

[0022] determining a mask matrix;

[0023] multiplying the mask matrix and the POD mode point by point to obtain a masked POD mode;

[0024] multiplying the mask matrix and the second PIV flow field data set point by point to obtain a masked data set.

[0025] The mask matrix has the same dimension as the first PIV flow field data set and the second PIV flow field data set.

[0026] The matrix elements of the mask matrix are 0 or 1, wherein the elements corresponding to the data missing area in the first PIV flow field data set and the second PIV flow field data set are 0.

[0027] The data missing area of the POD mode is the same as the data missing area of the first PIV flow field data set.

[0028] A PIV flow field missing data compensation device based on data fusion comprises a memory, a processor, and a program stored in the memory, and the processor implements the method as described above when executing the program.

[0029] A storage medium has a program stored thereon, and the program implements the method as described above when executed.

[0030] Compared with the prior art, the present application has the following beneficial effects:

[0031] (1) The present application performs data fusion operation on data sets with different missing regions based on the common properties of the overlapping parts, and compensates for the missing data based on the non-missing parts of other data sets, so as to obtain complete data sets and achieve good data compensation effect.

[0032] (2) The present application only needs to move the position of the light source to obtain flow field data sets with different missing regions, and can compensate for the missing data through data fusion, which is suitable for various types of data missing scenarios. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 The method flowchart of the present application is shown in the figure;

[0034] Figure 2 The data processing flowchart of the present application is shown in the figure;

[0035] Figure 3 The PIV flow field schematic diagram is shown in the figure; wherein (a) is the true value of the whole flow field, (b) is the flow field schematic diagram in data set 1, and (c) is the flow field schematic diagram in data set 2;

[0036] Figure 4 The curve graph of the influence of the modal number used for reconstruction on the reconstruction error is shown in the figure;

[0037] Figure 5 The data compensation result comparison graph of the flow field in the streamwise velocity in an embodiment is shown in the figure, wherein (a) is the fusion result graph after processing by the method of the present application, and (b) is the flow field true data;

[0038] Figure 6 The data compensation result comparison graph of the flow field in the spanwise velocity in an embodiment is shown in the figure, wherein (a) is the fusion result graph after processing by the method of the present application, and (b) is the flow field true data. DETAILED DESCRIPTION

[0039] The present application will be described in detail below in combination with the drawings and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present application, and detailed implementation modes and specific operation processes are given, but the protection scope of the present application is not limited to the following embodiments.

[0040] A PIV flow field data missing compensation method based on data fusion, as shown in the figure, comprising the following steps: Figure 1

[0041] Step 1) Obtain a first PIV flow field data set and a second PIV flow field data set with different data missing areas;

[0042] Step 2) Remove the time average component of the first PIV flow field data set;

[0043] In an embodiment, removing the time average component refers to removing the constant part of the PIV flow field data set in the time domain, and retaining the data that fluctuates with time.

[0044] Step 3) Perform intrinsic orthogonal decomposition on the first PIV flow field data set after removing the time average component to obtain the POD mode;

[0045] The intrinsic orthogonal decomposition is:

[0046]

[0047] Where g is the data of the PIV flow field data set G at a certain time, represents the average flow field, π i represents the spatial mode, and ∑π is the POD mode, represents the time coefficient corresponding to the spatial mode π i , and w represents the total number of spatial modes.

[0048] The time coefficient is calculated based on singular value decomposition:

[0049]

[0050] Where, is the two-norm of the time coefficient , C represents a matrix obtained by performing spatial cross-correlation calculation on the inner product (G, G') of the flow data set G, λ is the eigenvalue sequence, and represents the energy occupied by the mode π. The energy proportion occupied by the mode is usually denoted as

[0051] The data missing area of the POD mode obtained by intrinsic orthogonal decomposition is the same as the data missing area of the first PIV flow field data set.

[0052] Step 4) Mask the POD mode and the second PIV flow field data set respectively to obtain a masked POD mode and a masked data set;

[0053] Step 4-1) Determine the mask matrix; ​

[0054] The dimension of the mask matrix is the same as that of the first PIV flow field data set and the second PIV flow field data set, and the matrix elements are 0 or 1, wherein the elements corresponding to the data missing area in the first PIV flow field data set and the second PIV flow field data set are 0;

[0055] Step 4-2) Point-by-point multiplication of the mask matrix and the POD mode to obtain a masked POD mode, and the masked POD mode thus obtained only has data in the common area of the first PIV flow field data set and the second PIV flow field data set;

[0056] Step 4-3) Point-by-point multiplication of the mask matrix and the second PIV flow field data set to obtain a masked data set, and the masked data set thus obtained only has data in the common area of the first PIV flow field data set and the second PIV flow field data set.

[0057] Step 5) Projection of the masked data set onto the masked POD mode based on least square regression to obtain reconstructed time coefficients;

[0058] In this embodiment, the reconstructed time coefficients are solved by pseudo-inverse.

[0059] Step 6) Multiplication of the reconstructed time coefficients and the POD mode to obtain a reconstructed flow field having the same time evolution rule as the second PIV flow field data set;

[0060] At this time, the reconstructed flow field is obtained by multiplying the POD mode without masking, so the reconstructed flow field only has a common missing area with the first PIV flow field data set, and the missing area part in the second PIV flow field data set is complete.

[0061] Step 7) Sequentially shifting the data corresponding to the data missing area in the second PIV flow field data set in the reconstructed flow field in time sequence into the second PIV flow field data set to obtain the fused data field after data compensation.

[0062] The data processing flowchart based on the above method is shown in Figure 2 .

[0063] If the above functions are realized in the form of software function units and sold or used as independent products, they can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the parts of the prior art that make contributions or parts of the technical solutions can be embodied in the form of software products. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present application. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various media that can store program codes.

[0064] In this embodiment, a flow field around a cylinder is taken as an example for illustration.

[0065] The flow field data is measured by TR-PIV in an open water tunnel with a turbulence intensity less than 1%. The test section of the water tunnel is 150mm wide, 250mm high and 1050mm long. The cylinder is 15mm in diameter and is placed across the width of the water tunnel. The free stream velocity is 0.12m / s, which gives a Reynolds number of 1.8×103 based on the diameter of the cylinder and a vortex shedding frequency of 1.68Hz. The camera is operated at a frame rate of 250Hz, which is sufficient to resolve the flow field characteristics over a vortex shedding period. The cross-correlation window for PIV post-processing is 16mm×16mm with a 50% overlap. A total of 6000 time-resolved instantaneous flow fields are obtained, which contain 14 complete vortex shedding periods. Figure 3 (a) shows the real data of a certain instantaneous flow field of the data set, while Figure 3 (b) and Figure 3 (c) represent the data sets with data missing in different regions, respectively. The regions shown by the vertical strips in the figures are the missing regions. 5000 of the 6000 instantaneous fields measured in the experiment are allocated to data set 1 to meet the convergence requirement of the algorithm, and the remaining 1000 instantaneous fields are allocated to data set 2.

[0066] In this embodiment, the influence of the number of modes used for reconstruction on the reconstruction error is discussed. The reconstruction error is the time-averaged value on the 1000 instantaneous fields of data set 2. From Figure 4(a) shows that in the overlapping region of the two data sets, i.e. the region where neither of the two data sets has missing data, the reconstruction error of the flow field of data set 2 reconstructed by the POD modes from data set 1 gradually tends to 0 with the increase of the number of modes used. This is because the POD modes are arranged in descending order of energy, and when all modes are used, the reconstruction error must be exactly (within the rounding error of the computer) equal to 0. However, a non-monotonic change trend appears in the missing region unique to data set 2 - with the increase of the number of modes used, the reconstruction error first gradually decreases from 6.6% when using 2-order modes to 4.9% when using 200-order modes, and then rapidly increases until divergence if the number of modes used for reconstruction is further increased. The significant difference in the change trend between the overlapping region and the missing region of data set 2 is because the overlapping region itself is the data used in the regression step of the POD algorithm, and the reconstruction of the data in the overlapping region is equivalent to evaluating the error on the training set of machine learning, so obviously, the more features (i.e. the number of POD modes used) used for fitting, the better the model constructed can predict the training set; however, the missing region of data set 2 does not participate in the regression step of the algorithm, and the reconstruction of the data in this range is equivalent to evaluating the error on the test set of machine learning, and the more POD modes used for reconstruction, the more complex the features of the model constructed, which will inevitably lead to the trend of first optimization and then deterioration on the test set, which is actually the trend from underfitting to overfitting, as shown in Figure 4 (b) shows. Therefore, when masking the POD modes, the optimal number of modes needs to be selected to optimize the performance of the algorithm. In this embodiment, the number of modes selected is 200, i.e. r = 200 in the following pseudo code.

[0067] The pseudo code based on the above method is as follows:

[0068]

[0069] The data compensation results of this embodiment are shown in Figure 5 and Figure 6 It can be found that even if the transient field has strong turbulent fluctuations, the data compensation algorithm based on the method can still restore the flow field details in the missing region (in the black vertical box) well, and the data compensation effect is good.

[0070] The above describes the preferred embodiments of the present application in detail. It should be understood that those skilled in the art can make many modifications and changes without creative labor according to the concept of the present application. Therefore, any technical solutions obtained by logical analysis, reasoning or limited experiments by those skilled in the art on the basis of the prior art according to the concept of the present application shall be within the protection scope determined by the claims.

Claims

1. A method for compensating for missing data in a PIV flow field based on data fusion, characterized in that, Includes the following steps: Step 1) Obtain the first PIV flow field dataset and the second PIV flow field dataset with different data missing regions; Step 2) Perform data preprocessing on the first PIV flow field dataset; Step 3) Perform intrinsic orthogonal decomposition on the preprocessed first PIV flow field dataset to obtain the POD modes; Step 4) Mask the POD mode and the second PIV flow field dataset respectively to obtain the masked POD mode and the masked dataset; Step 4) includes the following steps: Determine the mask matrix; the dimension of the mask matrix is ​​the same as the dimension of the first PIV flow field dataset and the second PIV flow field dataset, and the matrix elements of the mask matrix are 0 or 1, wherein the elements corresponding to the missing data regions in the first PIV flow field dataset and the second PIV flow field dataset are 0; The masked POD mode is obtained by multiplying the mask matrix and the POD mode point by point; The mask dataset is obtained by multiplying the mask matrix and the second PIV flow field dataset point by point. Step 5) Project the masked dataset onto the masked POD mode based on least squares regression to obtain the reconstruction time coefficients; Step 6) Determine the reconstructed flow field based on the reconstruction time coefficient and the POD mode; Step 7) The data corresponding to the missing data regions in the reconstructed flow field and the second PIV flow field dataset are sequentially shifted to the second PIV flow field dataset in chronological order to obtain the fused data field after data compensation.

2. The method for compensating for missing PIV flow field data based on data fusion according to claim 1, characterized in that, The data preprocessing involves removing the time-averaged component.

3. The method for compensating for missing PIV flow field data based on data fusion according to claim 1, characterized in that, The intrinsic orthogonal decomposition is as follows: in, For PIV flow field dataset Data at a certain point in time, Indicates the average flow field. Representing spatial modes, For POD mode, Represents the corresponding spatial modes time coefficient, This represents the total number of spatial modes.

4. The method for compensating for missing PIV flow field data based on data fusion according to claim 3, characterized in that, The time coefficient Based on singular value decomposition calculations: in, , Time coefficient The 2-norm, Represents the flow dataset inner product The matrix obtained by performing spatial cross-correlation calculations. The sequence of eigenvalues ​​represents the modes. The energy possessed.

5. The method for compensating for missing PIV flow field data based on data fusion according to claim 1, characterized in that, The missing data region of the POD mode is the same as the missing data region of the first PIV flow field dataset.

6. A PIV flow field missing data compensation device based on data fusion, comprising a memory, a processor, and a program stored in the memory, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1-5.

7. A storage medium having a program stored thereon, characterized in that, When the program is executed, it implements the method as described in any one of claims 1-5.

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