Dynamic size flow field interpolation method based on full convolution and residual network
By using a flow field interpolation method based on fully convolutional and residual networks, the problems of insufficient interpolation accuracy and high computational complexity are solved, achieving high-precision and fast flow field interpolation, which is applicable to fields such as engineering design, weather forecasting, and environmental simulation.
Patent Information
- Application Number
- CN202511067694.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-31
- Publication Date
- 2025-11-07
AI Technical Summary
Existing flow field interpolation methods are not accurate enough when dealing with complex flow fields, have high computational complexity, and the interpolation results are not smooth enough. Excessive oscillations are prone to occur at the boundaries, resulting in inaccurate interpolation results.
A dynamic dimensional flow field interpolation method based on fully convolutional and residual networks is adopted. By constructing a flow field interpolation network model, training the network with turbulence simulation data, using the Adam optimizer and RMSE loss function, and combining a random mask for mask region prediction, features are extracted using fully convolutional and residual downsampling modules to perform high-precision flow field interpolation.
It improves the accuracy and computational efficiency of flow field interpolation, supports dynamic multi-scale input and output, enhances the robustness and training speed of the model, and can provide more accurate interpolation predictions in flow fields with high nonlinearity and high gradient changes.
Smart Images
Figure CN120912425A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of fluid mechanics, in particular to a dynamic size flow field interpolation method based on full convolution and residual network. BACKGROUND
[0002] Flow field interpolation is an important problem in fluid mechanics and computational fluid dynamics, and is widely used in engineering design, weather forecasting and environmental simulation. Traditional flow field interpolation methods mainly rely on mathematical models and numerical methods, such as nearest neighbor interpolation, linear interpolation, spline interpolation, and Kriging interpolation. These methods often have problems of insufficient accuracy and high computational complexity when dealing with complex flow fields. In recent years, deep learning-based methods have gradually become a new technology in the field of flow field interpolation, with high accuracy, fast calculation speed, and good robustness and generalization ability.
[0003] Existing interpolation methods are traditional classic methods, which have relatively low accuracy when dealing with complex flow fields, especially in areas with large data changes. In addition, the interpolation results may still not be smooth enough, and some unrealistic transitions may occur. In addition, excessive oscillation may occur at the boundary, resulting in inaccurate interpolation results, which requires special boundary conditions to handle. SUMMARY
[0004] To solve the technical problems of the prior art, the present application provides a dynamic size flow field interpolation method based on full convolution and residual network, which solves the technical problems of high computational complexity, insufficient interpolation accuracy and unsatisfactory boundary condition handling in existing flow field interpolation methods, to improve the accuracy and efficiency of flow field interpolation.
[0005] To solve the above technical problems, the present application provides the following technical solutions: a dynamic size flow field interpolation method based on full convolution and residual network, the method comprising the following steps: S1, obtaining turbulent flow simulation data about the flow field through an open source database, and generating flow field simulation data using a simulation method to form a flow field data set, and dividing it into a training set and a test set; S2, constructing a flow field interpolation network model for reading in double frame images and outputting flow field interpolation results of the same size as the images; S3, training the flow field interpolation network model using the preprocessed training set, and using the Adam optimizer and RMSE as the loss function to optimize the model parameters of the flow field interpolation network model; S4, reading the flow field data file during training and randomly generating a polygon mask as a mask area; S5, inputting the test set containing the mask area to be interpolated into the trained flow field interpolation network model to obtain high-precision flow field interpolation results.
[0006] Further, the flow field interpolation network model comprises a residual down-sampling module for obtaining the encoded features 、 Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. and Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. and and Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. and Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed. Two parallel Stem convolution layers for preliminary feature extraction to align spatial features are synchronously performed.
[0007] Further, the cross-correlation module is used to obtain a dimensional feature map to highlight the motion or change area of the tracer particles in the flow field according to the cross-correlation coefficient between each pixel position in all channels.
[0008] Further, the residual down-sampling module is used to obtain the encoded features and with the spatial resolution reduced to and , respectively, while the number of channels is multiplied accordingly and the encoded features have high-level semantic features.
[0009] Further, the calculation formula of the cross-correlation coefficient is as follows: wherein, represents an image region in the particle original image ; represents an image region in the particle original image ; is the total number of pixels in the image region; , are the average values of the image regions and , respectively.
[0010] Further, the loss function adopted in the training and result evaluation of the flow field interpolation network model is the root mean square error (RMSE) of the mask region predicted flow field, and for the flow field predicted by the mask region, the RMSE loss is calculated for all points in the region, and the expression is: In the formula, , are the resolutions in the height and width directions of the mask region, respectively; is the horizontal velocity predicted by the flow field interpolation network model; is the observed horizontal velocity; is the vertical velocity predicted by the flow field interpolation network model; is the observed vertical velocity.
[0011] Further, in step S4, the flow field data file is read by using python, and the flow field data is in a text format of [x, y, u, v], wherein x and y represent pixel positions, and u and v represent the particle velocity vector of the pixel position.
[0012] By means of the above technical scheme, the application provides a dynamic size flow field interpolation method based on a full convolution and residual network, which has at least the following beneficial effects: 1. The flow field interpolation network model constructed by the application has a plurality of nonlinear activation functions and convolution kernels, and can autonomously learn the complex spatial features of various scales (large eddies, shear layers, small scale vortex cores, etc.) in the flow field. This ability to directly learn complex flow field structures from data enables the flow field interpolation network model to give more accurate interpolation predictions when facing high nonlinearity and high gradient changes in real flow fields, thereby improving the accuracy and computational efficiency of flow field interpolation.
[0013] 2. The input and output of the flow field interpolation network model in the application support dynamic multi-scale, that is, the input of the model is not fixed in size like other neural networks. The flow field interpolation network model supports flow field data of any width and height, and the size of the flow field output by deconvolution is consistent with the size of the input flow field.
[0014] 3、The application adopts random mask as a mask to let the flow field interpolation network model predict the masked part, and the function of the random mask improves the robustness of the flow field interpolation network model.
[0015] 4、The structure of the flow field interpolation network model in the application is reasonably designed, the parameter tuning is relatively simple, and the training and reasoning speed is greatly improved. BRIEF DESCRIPTION OF DRAWINGS
[0016] The drawings described herein are used to provide further understanding of the present application, and form a part of the present application, the illustrative embodiments of the present application and the description thereof are used to explain the present application, and do not constitute improper limitation on the present application. In the drawings: Figure 1 A flow chart of the dynamic size flow field interpolation method in the application; Figure 2 A network structure diagram of the flow field interpolation network model in the application; Figure 3 A comparison result diagram of real flow field data distribution and flow field distribution after interpolation processing in the application. DETAILED DESCRIPTION
[0017] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below in combination with the drawings and specific embodiments. The realization process of how to apply technical means to solve technical problems and achieve technical effects of the present application can be fully understood and implemented.
[0018] The embodiment proposes a dynamic size flow field interpolation method based on full convolution and residual network. When facing high nonlinearity and high gradient change in real flow field, more accurate interpolation prediction can be given, so as to improve the accuracy and calculation efficiency of flow field interpolation. As shown in the figure, the method comprises the following steps: Figure 1 S1, obtain the turbulent flow simulation data of the flow field through the open source database, and generate the flow field simulation data by using the simulation method to constitute the flow field data set, and divide it into training set and test set. In the embodiment, small balls with random size are constructed based on the Blender software as tracer particles in the flow field, and the number of tracer particles is not less than 2000. The tracer particles move in the space of the set size, and the virtual camera is used for virtual shooting to obtain the flow field simulation data containing the motion of the tracer particles.
[0019] In this embodiment, the open-source database comes from Johns Hopkins Turbulence Database (JHTDB), an open numerical turbulence laboratory provided by Johns Hopkins University, aiming to make high-fidelity turbulence simulation data accessible to global researchers.
[0020] S2, a flow field interpolation network model for reading in double-frame images and outputting interpolation results of the same size as the flow field is constructed based on a full convolution network (FCN) and a residual network, as shown in FIG. 2. Figure 2
[0021] Further, the flow field interpolation network model provided in this embodiment includes two parallel Stem convolution layers for synchronously performing preliminary feature extraction to align spatial features. 、
[0022] First, the particle original images of any two adjacent frames are subjected to unified normalization preprocessing. Subsequently, the particle original images are subjected to preliminary feature extraction through a combination of a 7x7 convolution layer (with a stride of 2 and padding of 3), batch normalization (Batch Norm) and a ReLU activation function. The channel number of the particle original images is 1, and the height and width are The Stem convolution layer not only provides a large receptive field to capture macro flow field information, but also ensures the alignment of the feature spaces of the two frames of images when entering the downstream network through shared weights.
[0023] A residual down-sampling module for twice down-sampling operation on the parallel two-way output features is used to obtain encoded features with high-level semantic features and , with the spatial resolution reduced to and , respectively, and the channel number multiplied accordingly.
[0024] In this embodiment, a typical residual unit (Residual Block) can be represented as: wherein, is the input feature; is the output feature; and Residual function representing several layers (e.g. two layers of 3x3 convolution + Batch Norm + ReLU) inside this unit; i.e. "shortcut connection" or "skip connection", which means adding the input directly back to the output.
[0025] The residual structure introduces an identity shortcut, so that the deep network has a "non-blocking" path in both forward and backward propagation. The channel number of the output feature of the Stem convolution layer is 64, and the height and width are , respectively. The feature enters two layers of residual down-sampling modules (Res Block), each of which contains two 3x3 convolutions, batch normalization, and ReLU activation function combination. The residual down-sampling module in this embodiment robustly captures high-level semantic information and retains the residual path to alleviate gradient disappearance, so it effectively alleviates the gradient disappearance problem of the deep network and speeds up the model convergence, thereby robustly extracting high-level semantic features at different scales.
[0026] The encoded features and are pixel-wise inner products in the channel dimension, which are used to measure the cross-correlation of any two adjacent frames of encoded features and in the spatial position, which is used to obtain a dimension feature map that highlights the motion or change area of the tracer particles in the flow field . This embodiment directly measures the similarity distribution of the encoded features and in space through cross-correlation operation, highlighting the motion or change area, where the calculation formula of the cross-correlation coefficient is: wherein, represents the image area in the original image of the particle ; represents the image area in the original image of the particle ; is the total number of pixels in the image area; , are the average values of the image areas and , respectively.
[0027] This operation measures the cross-correlation of any two adjacent frames of encoded features and The local similarity in spatial position is obtained after the cross-correlation calculation, and the cross-correlation coefficient of each pixel position of all channels is obtained, and finally a dimensional feature map .
[0028] The feature map is spliced with the encoded features and of any two adjacent frames along the channel dimension to obtain a multi-source fusion feature , and the expression is: wherein, represents a splicing operation; , and represents the number of channels.
[0029] This fusion strategy splices the two-frame encoded features and with the feature map representing the similarity, which not only retains the respective semantic expression, but also introduces the corresponding relationship between the encoded features and , and simultaneously introduces the cross-frame corresponding relationship into the subsequent decoding process, thereby improving the accuracy and robustness of the flow field estimation.
[0030] The multi-source fusion feature is deconvolved step by step to restore the original resolution of three layers of transposed convolution layers, which are used to output the flow field estimation results with the same size as the input. ConvTranspose2d is deconvolution, which realizes the learnable mapping from low resolution to high resolution through the combination of zero insertion, padding, expansion and ordinary convolution. The output size is determined by the stride, padding, expansion and output padding.
[0031] In this embodiment, three layers of transposed convolution layers are set to gradually restore the multi-source fusion feature ( ) to the original resolution (i.e. ) by deconvolution, so that the flow field interpolation network model can output the flow field interpolation or motion estimation results with the same size as the input. This method establishes a close relationship between multi-scale semantic extraction, pixel-level geometric matching and full convolution decoding recovery, and realizes high-precision interpolation and estimation of PIV flow field.
[0032] The embodiment combines the advantages of the full convolution network and the residual network, improves the accuracy and calculation efficiency of the flow field interpolation. Compared with the flow field data interpolation algorithm, the flow field interpolation network model in the embodiment has a multi-layer nonlinear activation function and a convolution kernel, and can autonomously learn the complex spatial features of various scales (large eddy, shear layer, small-scale vortex core, etc.) in the flow field. This ability to directly learn complex flow field structures from data enables the flow field interpolation network model to give more accurate interpolation predictions when facing high nonlinearity and high gradient changes in real flow fields.
[0033] The "skip connection" in the residual structure alleviates the gradient vanishing and gradient explosion problems of deep networks, making it possible to stack more convolution layers to capture larger receptive fields and deeper features. The flow field interpolation network model can still maintain the stability and convergence speed of model training while greatly improving the accuracy.
[0034] Traditional interpolation is often point-to-point or local window calculation, which is difficult to fully utilize modern hardware; while convolution and deconvolution are highly parallel matrix operations that can be executed at high throughput on GPUs.
[0035] S3, the preprocessed training set is used to train the flow field interpolation network model, and the Adam optimizer and the RMSE are used as the loss function to optimize the model parameters of the flow field interpolation network model. In the embodiment, the Adam optimizer is a first-order gradient optimization algorithm suitable for non-convex optimization problems with large-scale data and parameters. It improves the speed and stability of training by adaptively adjusting the learning rate of each parameter.
[0036] The loss function used for training and result evaluation of the flow field interpolation network model is the mean square error RMSE of the mask area predicted flow field. The loss function RMSE is used to quantify the overall difference between the predicted velocity field and the real velocity field, and the smaller the value, the more accurate the prediction. The expression is: In the formula, 、 are the resolution in the height direction and the width direction in the mask area, respectively; is the horizontal velocity predicted by the flow field interpolation network model; is the observed horizontal velocity; is the vertical velocity predicted by the flow field interpolation network model; is the observed vertical velocity.
[0037] S4, read the flow field data file in the training process, and randomly generate a polygon mask as a mask area, so that the flow field interpolation network model performs prediction. The flow field data file is read by using python, and the data structure of the flow field is usually in text format, which includes: [x, y, u, v], wherein x and y represent pixel positions, and u and v represent particle velocity vectors at the pixel positions. The random polygon mask is generated by using random numbers, and the random effect is achieved by randomly generating circles with different radii and rectangles with different lengths and widths.
[0038] In this embodiment, the random mask is used as a mask to allow the flow field interpolation network model to predict the masked part, and the random mask improves the robustness of the flow field interpolation network model.
[0039] S5, input the test set containing the mask area to be interpolated into the trained flow field interpolation network model to obtain a high-precision flow field interpolation result. The trained flow field interpolation network model is used to read in double-frame images and predict the flow field of the mask area, that is, to predict the u, v value of each pixel position x, y. The mask area mentioned here is the polygon mask generated by using random numbers, and the (u, v) value of the pixel position x, y predicted by the flow field interpolation network model is the high-precision flow field interpolation result, as shown in Figure 3
[0040] The input and output of the flow field interpolation network model support dynamic multi-scale, that is, the input of the model is not fixed in size like other neural networks, and the flow field interpolation network model supports flow field data with any width and height, and the size of the flow field output by deconvolution is consistent with the size of the input flow field.
[0041] Since the convolution kernel of the flow field interpolation network model is spatially invariant and does not depend on the absolute size of the input feature map, it can receive any width x height input, and the output will also change dynamically. All operations (convolution, pooling, deconvolution, splicing) are only window sliding or local calculation, and the specific value of H and W does not need to be known in advance, so that it can be automatically expanded to any size.
[0042] For the technical solution of the application, other deep learning models such as U-Net, GAN, etc. can also be used for flow field interpolation. These methods can also achieve similar interpolation effects under certain conditions, but need to be optimized and adjusted according to actual conditions in specific implementation.
[0043] Those skilled in the art can understand that all or part of the steps in the above-mentioned embodiment methods can be completed by instructing relevant hardware through programs, therefore, the present application can adopt a completely hardware embodiment, a completely software embodiment, or an embodiment in the form of a combination of software and hardware aspects. Moreover, the present application can adopt a computer program product in the form of being implemented on one or more computer usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) containing computer usable program codes.
[0044] Each of the embodiments in the specification is described in a progressive manner, and each embodiment focuses on the difference from other embodiments, and the same or similar parts between the embodiments can be referred to each other. For the above embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the part of the method embodiments.
[0045] The above embodiments have been described in detail, and the principles and implementation manners of the present application are described by applying specific examples; the above embodiment is only used to help understand the method of the present application and its core idea; meanwhile, for those skilled in the art, according to the idea of the present application, the specific implementation manner and application range can be changed, and the above description should not be understood as the limitation of the present application.
Claims
1. A dynamic size flow field interpolation method based on full convolution and residual network, characterized in that, The method comprises the following steps: S1, obtaining turbulent flow simulation data about the flow field through an open source database, and generating flow field simulation data by using a simulation method to form a flow field data set, and dividing the flow field data set into a training set and a test set; S2, constructing a flow field interpolation network model for reading in a double-frame image and outputting a flow field interpolation result with the same size as the double-frame image; S3, training the flow field interpolation network model using the preprocessed training set, and using an Adam optimizer and RMSE as a loss function to optimize the model parameters of the flow field interpolation network model; S4, reading a flow field data file and randomly generating a polygon mask as a mask region during the training process; S5, inputting the test set containing the mask region to be interpolated into the trained flow field interpolation network model to obtain a high-precision flow field interpolation result.
2. The dynamic size flow field interpolation method of claim 1, wherein, The flow field interpolation network model includes processing any two adjacent frames of original particle images. , Two parallel Stem convolutional layers are used to simultaneously perform preliminary feature extraction to align spatial features; The feature output from the Stem convolutional layer is taken as input to perform twice down-sampling operation on two parallel output features and output the encoded features and a residual down-sampling module and, pixel-wise inner product of the encoded features and in the channel dimension, to compute a correlation measure of the encoded features and in spatial location and output a feature map of the two adjacent frames and the feature map encoded features of any two adjacent frames and concatenating along the channel dimension to obtain multi-source fusion features , the expression is: wherein represents a concatenation operation; represents the number of channels; and, to multi-source fusion features The three-layer transposed convolutional layers that perform deconvolution gradually recover to the original resolution to output the flow field estimation results with the same size as the input.
3. The dynamic size flow field interpolation method of claim 2, wherein, The cross-correlation module is used to obtain a dimensional feature map highlighting regions of tracer particle motion or change in the flow field .
4. The dynamic size flow field interpolation method of claim 2, wherein, The residual down-sampling module is used to obtain spatial resolution reduced by 2 With At the same time, the number of channels is multiplied by 2 and the encoding features have high-level semantic features And .
5. The dynamic size flow field interpolation method of claim 3, wherein, The cross-correlation coefficient The formula for calculating the cross-correlation coefficient is: wherein denotes the image region in the particle raw image ; denotes the image region in the particle raw image ; is the total number of pixels within the image region; , are the average values of the image regions and , respectively.
6. The dynamic size flow field interpolation method of claim 1, wherein, The loss function used in the training and result evaluation of the flow field interpolation network model is the mean square error RMSE of the predicted flow field in the mask region. For the predicted flow field in the mask region, the RMSE loss is calculated for all points in the region, and the expression is: In the formula, , are the resolution in height and width direction in the mask region, respectively; is the horizontal velocity predicted by the flow field interpolation network model; is the real observed horizontal velocity; is the vertical velocity predicted by the flow field interpolation network model; is the real observed vertical velocity.
7. The dynamic size flow field interpolation method of claim 1, wherein, In step S4, the flow field data file is read by using python, and the flow field data is in a text format of [x, y, u, v], wherein x and y represent pixel positions, and u and v represent particle velocity vectors of the pixel positions.