Flow field reconstruction and PIV measurement method based on physical information neural network

Abstract

The invention discloses a flow field reconstruction and PIV (particle image velocimetry) measurement method based on a physical information neural network, which belongs to the technical field of fluid mechanics, deep learning, computer vision and PIV crossing and comprises the steps of low-cost experimental system construction, experimental data processing and period identification, simulation synchronization and data set construction and physical information neural network flow field reconstruction. According to the invention, the problems of high cost and non-real time of the traditional PIV technology are solved, a novel low-cost solution is provided for flow field measurement, and the popularization and application of the PIV technology in basic scientific research and teaching are promoted.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary fields of fluid mechanics, deep learning, computer vision and PIV, and specifically relates to a flow field reconstruction and PIV measurement method based on physical information neural network. Background Technology

[0002] Particle image velocimetry (PIV) is the most commonly used non-contact, full-field velocimetry technique in fluid mechanics research. Its principle involves injecting tracer particles into the fluid, recording images of the particles' motion at different times using a camera system, and then calculating particle displacement using algorithms such as image cross-correlation and particle tracking to reconstruct the velocity distribution of the flow field. Because PIV technology can simultaneously acquire velocity information at all points in the flow field, it is widely used in aerospace, automotive engineering, biomedicine, and other fields, and is a key tool for studying flow structures (such as vortex shedding and boundary layer separation).

[0003] The core components of a traditional PIV system include a dual-pulse laser (used to generate high-brightness sheet light to illuminate the tracer particles), a high-speed camera (used to capture images of particle motion, typically at a frame rate of ≥1000fps), and specialized image processing software (used to calculate the velocity field). However, these components are extremely expensive: dual-pulse lasers can cost hundreds of thousands of yuan, and high-speed cameras also cost hundreds of thousands of yuan, and they have stringent requirements for the experimental environment (such as needing a darkroom and a stable power supply). This high cost limits the application of traditional PIV technology to well-funded settings such as research institutes and large enterprises, making it difficult to popularize it in low-cost scenarios such as teaching laboratories and small and medium-sized enterprises.

[0004] To reduce the cost of PIV systems, existing technologies attempt to replace high-speed cameras with ordinary cameras (such as mobile phones and industrial cameras, with frame rates ≤30fps), improving image quality by increasing the shooting frame rate (e.g., using multi-frame overlay) or optimizing image processing algorithms (e.g., improving the cross-correlation window size). However, the frame rate of ordinary cameras is much lower than that of high-speed cameras, resulting in large errors in particle displacement measurement (e.g., inability to capture particle motion in high-speed flow); at the same time, ordinary cameras have high image noise, making it difficult for traditional cross-correlation algorithms to accurately extract particle motion information, thus making the flow field reconstruction accuracy (e.g., velocity error) unable to meet engineering requirements (typically requiring an error ≤5%).

[0005] Furthermore, numerical simulation (such as COMSOL Multiphysics and ANSYS Fluent) is an important means of obtaining high-fidelity flow field data. By solving the Navier-Stokes (NS) equations, it can output detailed information such as velocity and pressure of the flow field. However, the simulation process has two major drawbacks: First, the computational cost is high, requiring high-performance computers (such as GPU clusters), and each simulation requires resetting boundary conditions (such as inlet velocity and geometry), making it unable to adapt to dynamically changing experimental environments (such as inlet wind speed fluctuations and particle concentration changes); second, spatiotemporal synchronization is difficult, and the temporal and spatial matching of simulation results with experimental data requires a lot of post-processing (such as frame matching and coordinate transformation), making it difficult to directly use for real-time reconstruction of experimental flow fields.

[0006] In recent years, deep learning techniques (such as convolutional neural networks (CNN) and U-Net) have been applied to PIV flow field reconstruction, achieving end-to-end mapping from images to velocity fields by training on a "particle image-velocity field" dataset. While this method can improve reconstruction speed, the purely data-driven model lacks physical constraints (such as not embedding the Navier-Stokes equations), which may cause the output flow field to not conform to the laws of fluid dynamics.

[0007] In summary, existing PIV technology suffers from problems such as high cost, poor real-time performance, and insufficient physical consistency. There is an urgent need for a low-cost, real-time, and physically consistent flow field reconstruction and PIV measurement method to meet the needs of teaching, scientific research, and industrial applications. Summary of the Invention

[0008] This invention addresses the problems of high cost (reliant on high-speed cameras and dual-pulse lasers), poor real-time performance (slow traditional algorithms or simulation calculations), and insufficient physical consistency (pure data-driven models do not conform to the laws of fluid mechanics) of existing PIV technologies. Combining deep learning and prior knowledge of fluid mechanics physics, this invention proposes a flow field reconstruction system and a low-cost PIV measurement method based on Physical Information Neural Network (PINN). This achieves a closed loop of "low-cost image acquisition - real-time physical flow field output", which is suitable for flow field measurement needs in teaching, scientific research, and industrial fields.

[0009] To achieve the aforementioned objectives, the present invention employs the following technical solution: a flow field reconstruction and PIV measurement method based on a physical information neural network, comprising the following steps: S1: Build a low-cost experimental system, generate flow phenomena containing tracer particles based on the low-cost experimental system, and collect video of tracer particle flow. S2: Import the tracer particle flow video into a computer and extract flow characteristics, including eddy shedding period and Strouhal number, by analyzing it frame by frame. S3: Establish a simulation model based on the actual experimental parameters, perform high-fidelity numerical simulation, and export a velocity field animation consistent with the experimental perspective. S4: Select experimental reference frames from the experimental video and simulation frames synchronized with the experimental reference frames from the simulation animation. Establish a linear mapping relationship between experimental time and simulation time to form an experimental image-simulation velocity field paired dataset. S5: Construct a physical information neural network model, using experimental images as input and simulated velocity fields as labels, and train the physical information neural network model. After training, realize the real-time reconstruction of the entire field velocity field from the experimental images to the physical consistency.

[0010] Furthermore, the fabrication of the low-cost experimental system in S1 includes: A transparent cuboid fluid cavity is constructed, with an inlet and a particle generator at one end and an outlet at the other end. A cylindrical obstacle is vertically fixed inside the cavity at a predetermined distance from the inlet. A sheet light source is set horizontally in the fluid cavity to illuminate the central cross-section of the cavity. The flow of tracer particles is driven by air blowing through the inlet, and a video of the tracer particle flow is captured using a regular camera or mobile phone. The transparent cuboid fluid cavity is made of acrylic material; the particle generating device is an atomizer that produces tracer particles with a particle size of 10–50 μm; the sheet light source is a 532nm laser or a high-brightness LED light source with a thickness of no more than 1 mm; and the frame rate of the ordinary camera or mobile phone is no less than 30fps.

[0011] Further, the flow characteristics are extracted in S2, including: Calculate the structural similarity and mean square error between consecutive frames of the tracer particle flow video. When the structural similarity is greater than or equal to 0.9 and the mean square error is less than or equal to 0.05, the two frames are determined to be in the same periodic state. Calculate the vortex shedding period and the Strauhall number. The vortex shedding cycle for: in, The number of frames at the periodic interval. This refers to the time interval between video frames. The Strauhal number for: in, The diameter of the cylindrical obstacle. The inlet average flow velocity is denoted as .

[0012] Furthermore, the selection of physics fields for the simulation model in S3 includes: When Reynolds number When laminar flow is used, a laminar flow model is employed; when When k-ε or k-ω turbulence models are used, where, For fluid kinematic viscosity, The diameter of the cylindrical obstacle. The inlet average flow velocity is denoted as .

[0013] Furthermore, the selection of the experimental reference frame in S4 specifically involves selecting the initial time frame from the experimental video as the experimental reference frame; The selection of simulation frames is as follows: in the simulation animation, the structural similarity and mean square error between the experimental reference frame and each simulation frame are calculated. When the structural similarity is greater than or equal to 0.85 and the mean square error is less than or equal to 0.1, the current simulation frame is determined to be a simulation frame synchronized with the experimental reference frame. The linear mapping relationship between experimental time and simulation time is established as follows: in, The simulation time after synchronization. For the simulation reference frame time, The video duration in the experiment. For the experimental reference frame time, The time interval between video frames. This is the experimental frame number.

[0014] Furthermore, the physical information neural network model in S5 includes: The encoder section employs a convolutional neural network, consisting of four convolutional layers and two max-pooling layers, to extract image features. Decoder section: It adopts a U-Net structure, including 4 deconvolutional layers and 2 skip connections, to map image features to the full-field velocity field; Loss function: Includes data loss term and physical loss term, where the physical loss term is the norm of the Navier-Stokes equation residuals, including the continuity equation residuals. and momentum equation residuals ; in, To predict speed, For gradient, This is the predicted value of the pressure. For fluid density, is the kinematic viscosity of the fluid.

[0015] Furthermore, the loss function for: in, For data loss, For physical loss, For physical constraint weights, The number of pixels. For the first Prediction speed per pixel For the first The simulated true value of each pixel.

[0016] The beneficial effects of this invention are: Low cost: The experimental system uses a mobile phone / ordinary camera (cost ≤ 2000 yuan) instead of the high-speed camera of the traditional PIV (cost ≥ 1 million yuan), and uses LED (cost ≤ 500 yuan) instead of dual-pulse laser (cost ≥ 500,000 yuan) for the light source, reducing the hardware cost of the PIV system by more than 99%.

[0017] Real-time performance: After the PINN model is trained, the inference time for a single frame image is ≤0.1 seconds (based on NVIDIA GTX1080 GPU), achieving the effect of "shooting video → real-time viewing of flow field", solving the "slow computation" problem of traditional PIV or simulation.

[0018] Physical consistency: PINN incorporates the Navier-Stokes equations as constraints, and the output velocity field strictly satisfies the continuity equation and the momentum equation (physical residual ≤ 0.01). Even if the input image contains noise (such as motion blur from a mobile phone), the noise can be "corrected" through physical constraints to output a reasonable flow field.

[0019] High precision: The MSE of the velocity field predicted by PINN is ≤0.02 (velocity error ≤5%) compared with the true value of COMSOL simulation, and the error of the Strouhal number compared with the experimental value is ≤5%, meeting the precision requirements of engineering and scientific research. Attached Figure Description

[0020] Figure 1 This is a flowchart of the flow field reconstruction and PIV measurement method based on physical information neural network of the present invention.

[0021] Figure 2 This is a schematic diagram of a measuring device provided in an embodiment of the present invention.

[0022] Figure 3 Comparison of PINN flow field reconstruction results. Detailed Implementation

[0023] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0024] like Figure 1 As shown, a flow field reconstruction and PIV measurement method based on a physical information neural network includes the following steps: S1: Build a low-cost experimental system, generate flow phenomena containing tracer particles based on the low-cost experimental system, and collect video of tracer particle flow. The fabrication of the low-cost experimental system includes: A transparent cuboid fluid cavity (length × width × height ≥ 150cm × 20cm × 20cm) was constructed. One end of the cavity had an inlet (connected to a fan / speed-regulating fan) and a particle generator, while the other end was an outlet (open to maintain atmospheric pressure). A cylindrical obstacle with a diameter of 1.2cm was vertically fixed inside the cavity at a predetermined distance (20cm) from the inlet (to induce vortex shedding and verify the flow field reconstruction effect). A sheet light source was set horizontally in the fluid cavity to illuminate the central cross-section of the cavity. The tracer particles were driven to flow by air blowing through the inlet, and the flow of the tracer particles was recorded using a regular camera or mobile phone. The transparent cuboid fluid cavity is made of acrylic material. The particle generating device is an atomizer (such as an ultrasonic atomizer) that produces tracer particles with a particle size of 10–50 μm (the particle size is smaller than the thickness of the light sheet to ensure clear imaging). The light sheet is a 532nm laser or a high-brightness LED (with a cylindrical lens) light source with a thickness of no more than 1 mm, producing a sheet of light with a thickness of ≤1 mm to illuminate the central cross-section (XY plane) of the cavity, ensuring that the particle movement is imaged in the same plane. The ordinary camera or mobile phone has a frame rate of no less than 30fps and a resolution of ≥1920×1080, is fixed on a tripod, and has its lens perpendicular to the light sheet plane to capture video of the tracer particle movement.

[0025] S2: Import the tracer particle flow video into a computer and extract flow characteristics, including eddy shedding period and Strouhal number, by analyzing it frame by frame. First, video preprocessing is performed: the video shot by the mobile phone is imported into the computer, and background subtraction (using the particle-free frame as a reference to remove noise such as reflections from the cavity wall) is performed using MATLAB, ROI cropping (keeping the 20cm×20cm area around the cylinder to reduce the amount of computation), and image normalization (mapping grayscale values ​​to the range of 0-1).

[0026] The flow characteristics extracted in S2 include: Calculate the structural similarity and mean square error between consecutive frames of the tracer particle flow video. When the structural similarity is greater than or equal to 0.9 and the mean square error is less than or equal to 0.05, the two frames are determined to be in the same period (repeated vortex shedding mode). Calculate the vortex shedding period and the Strauhall number. The vortex shedding cycle for: in, The number of frames at the periodic interval. The time interval between video frames, at 30fps Second; The Strauhal number (The relationship between vortex shedding frequency and flow parameters) is as follows: in, The diameter of the cylindrical obstacle. The inlet average flow velocity is denoted as .

[0027] S3: Establish a simulation model based on the actual experimental parameters, perform high-fidelity numerical simulation, and export a velocity field animation consistent with the experimental perspective. The simulation model, used to generate high-resolution flow field data that matches the experiments (as training labels for PINN), is implemented using COMSOL Multiphysics software, with the following settings: Geometric model: Completely replicates the dimensions of the experimental chamber and cylinder (e.g., chamber length 150cm, width 20cm, height 20cm, cylinder diameter 1.2cm, distance from the entrance 20cm).

[0028] The selection of physics fields for the simulation model in S3 includes: When Reynolds number When laminar flow is used, a laminar flow model is employed; when When k-ε or k-ω turbulence models are used, where, For fluid kinematic viscosity, The diameter of the cylindrical obstacle. The inlet average flow velocity is denoted as .

[0029] There is a proportional relationship between the two. , For fluid density, For the inlet velocity of the incoming flow, The kinematic viscosity of a fluid, such as air at 22°C. , , =1.5×10 -5 m2 / s.

[0030] Boundary conditions: The inlet is given a velocity boundary (consistent with the experimentally calibrated U), the outlet is given a pressure boundary (0 Pa gauge pressure), and the cavity wall and cylinder are given a no-slip boundary.

[0031] Mesh and Time Step: Refine the mesh around the cylinder (first layer mesh height ≤ 0.3mm, ensuring y⁺≈1 for accurate simulation of viscous sublayer flow); Time Step like seconds, (seconds) to ensure the capture of the periodic details of vortex shedding.

[0032] Output settings: Export a 2D velocity field animation consistent with the experimental viewpoint (frame rate consistent with the experimental video, such as 30fps), and save the full-field velocity field data at each moment. , ).

[0033] S4: Select experimental reference frames from the experimental video and simulation frames synchronized with the experimental reference frames from the simulation animation. Establish a linear mapping relationship between experimental time and simulation time to form an experimental image-simulation velocity field paired dataset. The selection of the experimental reference frame in S4 specifically involves selecting the initial time frame (e.g., frame 1) from the experimental video. (as experimental reference frame) ; The selection of simulation frames specifically involves: traversing the simulation animation and calculating the experimental reference frames. With each simulation frame The structural similarity and mean square error are considered. When the structural similarity is greater than or equal to 0.85 and the mean square error is less than or equal to 0.1, the current simulation frame is determined. For simulation frames synchronized with the experimental reference frame, their simulation time is recorded. ; The linear mapping relationship between experimental time and simulation time is established as follows: in, The simulation time after synchronization. For the simulation reference frame time, The video duration in the experiment. For the experimental reference frame time, The time interval between video frames. This is the experimental frame number.

[0034] Through this mapping, any frame in the experimental video... Each of these can be mapped to a unique moment in the simulation. And extract the simulated velocity field at that moment. .

[0035] S5: Construct a Physical Information Neural Network (PINN) model, using experimental images as input and simulated velocity fields as labels, and train the PINN model. After training, real-time reconstruction of the entire field velocity field from experimental images to physical consistency is achieved.

[0036] The physical information neural network model in S5 includes: The encoder section employs a convolutional neural network, consisting of four convolutional layers (each with 32 3×3 convolutional kernels and ReLU activation function) and two max-pooling layers (2×2 pooling windows) to extract image features. The decoder section employs a U-Net architecture, comprising four deconvolutional layers (each with 32 3×3 deconvolutional kernels and ReLU activation function) and two skip connections (connecting feature maps from the corresponding encoder layers) to map image features to a full-field velocity field (output size 1920×1080×2, corresponding to...). , ); Loss function: Includes data loss term and physical loss term, where the physical loss term is the norm of the Navier-Stokes equation residuals, including the continuity equation residuals. and momentum equation residuals ; in, To predict speed, For gradient, This is the predicted value of the pressure. For fluid density, is the kinematic viscosity of the fluid.

[0037] The Navier-Stokes (NS) equation residuals are embedded in the loss function to ensure that the output velocity field conforms to the laws of hydrodynamics. The loss function... for: in, For data loss, denoted as , and for mean square error (MSE) between the PINN predicted velocity field and the simulation true value. For physical loss, The physical constraint weights (values ​​range from 1 to 10, determined through cross-validation to ensure a balance between data loss and physical loss) are used. The number of pixels. To predict speed, This is the simulated true value.

[0038] The training and inference process of PINN is as follows: Dataset construction: Through spatiotemporal synchronization, 1000 frames of images (input) in the experimental video are paired with 1000 frames of velocity fields (labels) at the corresponding simulation time to form an "image-velocity field" training dataset (80% for training and 20% for validation).

[0039] Model training: Adam optimizer was used (learning rate 1×10⁻⁶). −4To minimize the loss function, train for 50-100 epochs (processing 20 batches per epoch, with each batch containing 10 frames). During training, monitor the velocity field MSE (target ≤ 0.02) and physical residual (target ≤ 0.01) on the validation set to ensure model convergence.

[0040] Flow field reconstruction: For new experimental images (not used in training), input the trained PINN model, and output the full-field velocity field at the corresponding time moment in real time. , The output resolution is consistent with the experimental image (≥1920×1080 pixels).

[0041] In one embodiment of the present invention, to better understand the technical means of the present invention, an example of flow around a cylinder is given below, along with accompanying drawings ( Figure 2 This is a schematic diagram of the experimental system. Figure 3 (A comparison chart of PINN flow field reconstruction results) This article details the implementation process of the present invention. Experimental setup: Transparent cavity 50cm long, 10cm wide, 10cm high; cylinder diameter 1.2cm, 20cm from the inlet; inlet wind speed... U = 1 m / s (Reynolds number) Re=800, laminar flow); the atomizer produces 20μm glycerol droplets; video was shot with a mobile phone (iPhone 14 Pro) (60fps, 1920×1080).

[0042] Experimental approach: Identifying the eddy shedding period using MATLAB seconds, calculation .

[0043] Simulation settings: COMSOL uses a laminar flow model, with mesh refinement to [specific detail needed]. Time step Seconds; Export simulated velocity field animation (30fps).

[0044] Spatiotemporal synchronization: Experiment Frame 1 ( ) and simulation frame 50 ( =0.1 seconds) matching (SSIM=0.88, MSE=0.08), establish time mapping .

[0045] PINN Training: PINN is trained using 1000 frames of "image-velocity field" data. After training for 80 epochs, the validation set MSE=0.015 and the physical residual=0.008.

[0046] Flow field reconstruction: Input experiment frame 100 ( =1.67 seconds), PINN output velocity field ( , ), compared to the COMSOL simulation value of MSE=0.018, the Strouhal number (Error of 1.7% compared to experimental value).

[0047] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of the invention.

Claims

1. A flow field reconstruction and PIV measurement method based on physical information neural network, characterized in that, Includes the following steps: S1: Build a low-cost experimental system, generate flow phenomena containing tracer particles based on the low-cost experimental system, and collect video of tracer particle flow. S2: Import the tracer particle flow video into a computer and extract flow characteristics, including eddy shedding period and Strouhal number, by analyzing it frame by frame. S3: Establish a simulation model based on the actual experimental parameters, perform high-fidelity numerical simulation, and export a velocity field animation consistent with the experimental perspective. S4: Select experimental reference frames from the experimental video and simulation frames synchronized with the experimental reference frames from the simulation animation. Establish a linear mapping relationship between experimental time and simulation time to form an experimental image-simulation velocity field paired dataset. S5: Construct a physical information neural network model, using experimental images as input and simulated velocity fields as labels, and train the physical information neural network model. After training, realize the real-time reconstruction of the entire field velocity field from the experimental images to the physical consistency.

2. The flow field reconstruction and PIV measurement method based on physical information neural network according to claim 1, characterized in that, The fabrication of the low-cost experimental system in S1 includes: A transparent cuboid fluid cavity is constructed, with an inlet and a particle generator at one end and an outlet at the other end. A cylindrical obstacle is vertically fixed inside the cavity at a predetermined distance from the inlet. A sheet light source is set horizontally in the fluid cavity to illuminate the central cross-section of the cavity. The flow of tracer particles is driven by air blowing through the inlet, and a video of the tracer particle flow is captured using a regular camera or mobile phone. The transparent cuboid fluid cavity is made of acrylic material; the particle generating device is an atomizer that produces tracer particles with a particle size of 10–50 μm; the sheet light source is a 532nm laser or a high-brightness LED light source with a thickness of no more than 1 mm; and the frame rate of the ordinary camera or mobile phone is no less than 30fps.

3. The flow field reconstruction and PIV measurement method based on physical information neural network according to claim 1, characterized in that, The flow characteristics extracted in S2 include: Calculate the structural similarity and mean square error between consecutive frames of the tracer particle flow video. When the structural similarity is greater than or equal to 0.9 and the mean square error is less than or equal to 0.05, the two frames are determined to be in the same periodic state. Calculate the vortex shedding period and the Strauhall number. The vortex shedding cycle for: in, The number of frames at the periodic interval. This refers to the time interval between video frames. The Strauhal number for: in, The diameter of the cylindrical obstacle. The inlet average flow velocity is denoted as .

4. The flow field reconstruction and PIV measurement method based on physical information neural network according to claim 1, characterized in that, The selection of physics fields for the simulation model in S3 includes: When Reynolds number When laminar flow is used, a laminar flow model is employed; when When k-ε or k-ω turbulence models are used, where, For fluid kinematic viscosity, The diameter of the cylindrical obstacle. The inlet average flow velocity is denoted as .

5. The flow field reconstruction and PIV measurement method based on physical information neural network according to claim 1, characterized in that, The selection of the experimental reference frame in S4 specifically involves selecting the initial time frame from the experimental video as the experimental reference frame. The selection of simulation frames is as follows: in the simulation animation, the structural similarity and mean square error between the experimental reference frame and each simulation frame are calculated. When the structural similarity is greater than or equal to 0.85 and the mean square error is less than or equal to 0.1, the current simulation frame is determined to be a simulation frame synchronized with the experimental reference frame. The linear mapping relationship between experimental time and simulation time is established as follows: in, The simulation time after synchronization. For the simulation reference frame time, The video duration in the experiment. For the experimental reference frame time, The time interval between video frames. This is the experimental frame number.

6. The flow field reconstruction and PIV measurement method based on physical information neural network according to claim 1, characterized in that, The physical information neural network model in S5 includes: The encoder section employs a convolutional neural network, consisting of four convolutional layers and two max-pooling layers, to extract image features. Decoder section: It adopts a U-Net structure, including 4 deconvolutional layers and 2 skip connections, to map image features to the full-field velocity field; Loss function: Includes data loss term and physical loss term, where the physical loss term is the norm of the Navier-Stokes equation residuals, including the continuity equation residuals. and momentum equation residuals ; in, To predict speed, For gradient, This is the predicted value of the pressure. For fluid density, is the kinematic viscosity of the fluid.

7. The flow field reconstruction and PIV measurement method based on physical information neural network according to claim 6, characterized in that, The loss function for: in, For data loss, For physical loss, For physical constraint weights, The number of pixels. For the first Prediction speed per pixel For the first The simulated true value of each pixel.

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