A method and system for measuring flow velocity on the surface of a body of water

Abstract

The application relates to a water surface flow velocity measurement method and system. The method comprises the following steps: collecting monocular video sequences of a water area to be measured, and performing flat field correction and contrast-limited adaptive histogram equalization processing to obtain preprocessed videos; performing multi-scale Gaussian difference filtering on the preprocessed videos to extract underwater turbulent speckle of different scales and form a multi-scale turbulent speckle sequence; constructing a turbulent intensity time sequence feature based on the turbulent speckle sequence; inputting the turbulent intensity time sequence feature into a deep learning model with physical information constraints, outputting a preliminary surface flow velocity field and an auxiliary pressure field by a feature extraction network, and approximating spatial and temporal derivatives in the model by a physical constraint layer, combining water density and kinematic viscosity coefficient to calculate mass conservation residual and momentum conservation residual, and applying physical constraints to the preliminary surface flow velocity field to output a water surface flow velocity field. The method reduces the dependence on water surface tracing features, and improves the measurement stability and physical credibility in complex environments.

Description

Technical Field

[0001] This application relates to the field of water surface velocity measurement technology, and in particular to a method and system for measuring water surface velocity. Background Technology

[0002] As hydrological monitoring systems evolve towards digitalization, precision, and real-time capabilities, non-contact optical measurement of river surface velocity has become a crucial foundational capability for flood control scheduling, flood warning, water resource management, and eco-hydrodynamic assessment. Compared to traditional contact-based velocity instruments, visual flow measurement offers advantages such as flexible deployment, wide coverage, and minimal impact on waterways and personnel safety. Among these methods, large-scale particle image velocimetry and spatiotemporal image velocimetry are widely adopted due to their lower implementation costs and mature engineering applications. These methods typically infer the surface velocity field distribution by analyzing the movement trajectories of natural or artificial tracers on the water surface.

[0003] However, existing visual flow measurement techniques still have significant limitations in complex natural environments. First, they lack environmental adaptability. These methods heavily rely on clear, continuous, and stably trackable visible tracer features on the water surface. When encountering calm, windless water, turbid water leading to decreased texture contrast, water surface fragmentation due to raindrop impact or foam coverage, or low illumination at night, tracer features are difficult to extract or track, easily resulting in measurement failure, increased noise, or a sharp decline in accuracy. Second, they utilize only a single dimension of information. Traditional methods often use changes in water surface brightness as the sole source of information, only characterizing two-dimensional surface motion and failing to fully explore the dynamic information of the near-surface region below the water surface. In fact, there is a stable physical correlation between the near-surface turbulent structure and the internal velocity distribution of the water body, but this correlation is often not explicitly modeled and utilized in existing methods, limiting their usability and robustness under weak tracer or strong interference conditions. Third, physical consistency is difficult to guarantee. In recent years, although deep learning-based image-to-flow velocity direct regression schemes have emerged, pure data-driven models have "black box" characteristics, and the output results may violate the basic laws of fluid mechanics. Some studies have adopted physical correction after training or physical equations as posterior constraints for correction, but such loose coupling of "two steps" makes it difficult to achieve deep integration of physical laws and data features within the model, resulting in insufficient generalization ability and low physical reliability of prediction results under complex flow conditions and cross-scenario conditions. Summary of the Invention

[0004] To overcome, to some extent, the problems of visual flow measurement methods in related technologies, such as strong dependence on water surface tracer features, easy failure in complex environments, and lack of physical consistency constraints, this application provides a method and system for measuring water surface velocity.

[0005] The proposed solution is as follows:

[0006] According to a first aspect of the embodiments of this application, a method for measuring the surface velocity of a water body is provided, comprising: Acquire monocular video sequences of the water area to be measured; Flat field correction is performed on the monocular video sequence, and contrast-limited adaptive histogram equalization is performed to obtain a preprocessed video sequence. Multi-scale Gaussian difference filtering is performed on the preprocessed video sequence to obtain a multi-scale turbulence pattern sequence characterizing underwater turbulence patterns at different scales; Based on the multi-scale turbulence pattern sequence, temporal features of turbulence intensity are constructed. The temporal features of the turbulence intensity are input into a pre-trained deep learning model with physical constraints; the deep learning model includes a feature extraction network and a physical constraint layer. The feature extraction network outputs a preliminary surface velocity field and an auxiliary pressure field corresponding to the preliminary surface velocity field. The physical constraint layer calculates the mass conservation residual and momentum conservation residual based on the initial surface velocity field and the auxiliary pressure field; including: performing spatial derivative approximation and time derivative approximation on the initial surface velocity field and the auxiliary pressure field, and using water density and water kinematic viscosity as physical parameter inputs to obtain the mass conservation residual and momentum conservation residual of the corresponding incompressible fluid control equation; The preliminary surface velocity field is constrained based on the mass conservation residual and the momentum conservation residual to output the surface velocity field of the water body to be measured.

[0007] Preferably, the preprocessed video sequence is subjected to multi-scale Gaussian difference filtering to obtain a multi-scale turbulence pattern sequence characterizing underwater turbulence patterns at different scales, including: The preprocessed video sequence is smoothed using multiple sets of Gaussian kernels of different scales to obtain multiple smoothed sequences of corresponding scales. Perform a difference operation on two sets of smoothed sequences at adjacent scales to obtain the difference sequences at the corresponding scales; The difference sequences at each scale are aggregated to form the multi-scale turbulent pattern sequence; wherein the multi-scale turbulent pattern sequence includes at least four difference sequences corresponding to the scales, and the scale ratio between adjacent scales is a preset constant.

[0008] Preferably, constructing temporal features of turbulence intensity based on the multi-scale turbulence pattern sequence includes: For the turbulent pattern images corresponding to each target scale in the multi-scale turbulent pattern sequence, the spatial gradient is calculated in the pixel neighborhood and the structure tensor is constructed accordingly. The maximum eigenvalue of the structure tensor is determined as the texture intensity; Temporal difference processing is performed on the texture intensity of adjacent frames to obtain a characterization of turbulence intensity variation; The turbulence intensity variation characteristics corresponding to each target scale are stacked along the feature channel dimension to form a temporal feature of turbulence intensity.

[0009] Preferably, the method further includes: Training monocular video sequences under different flow velocities and hydrological conditions are collected, and the reference surface flow velocity field corresponding to each training monocular video sequence is collected simultaneously to form a training dataset. The deep learning model is trained using the training dataset.

[0010] Preferably, the feature extraction network adopts an encoder-decoder structure; The encoder comprises a multi-stage downsampling structure, each stage of which includes two consecutive convolutional processing units, and the kernel size of each convolutional processing unit is 3. 3. Each convolutional processing unit sequentially includes convolution processing, batch normalization processing, and linear rectified activation processing; a max-pooling downsampling unit is set after the two consecutive convolutional processing units, and the pooling window of the max-pooling downsampling unit is 2. 2. The downsampling step size is 2; the number of channels of the encoder is doubled after each downsampling stage; The decoder comprises a multi-level upsampling structure, each level of which includes a transposed convolutional upsampling unit with a kernel size of 2. 2; The upsampled features of the transposed convolutional upsampling unit and the features of the corresponding level of the encoder are concatenated through skip connections, and then sequentially processed by two identical convolutional processing units for feature recovery; the kernel size of the convolutional processing unit used for feature recovery is 3. 3, and includes convolution processing, batch normalization processing and linear rectified activation processing in sequence; The decoder end is configured with a convolution kernel size of 1. A 1-mapped convolutional layer is used to output the initial surface velocity field and the auxiliary pressure field corresponding to the initial surface velocity field.

[0011] Preferably, the physical constraint layer is used to construct a physical constraint loss during the training phase, and the physical constraint layer is a network layer without trainable parameters. The physical constraint layer includes a spatial derivative approximation module and a temporal derivative approximation module. The spatial derivative approximation module uses a preset and fixed differentiable convolution operator to calculate the first-order spatial variation of the initial surface velocity field and the auxiliary pressure field, and to calculate the second-order spatial diffusion characterization of the initial surface velocity field, so as to obtain the divergence characterization of the initial surface velocity field, the pressure gradient characterization of the auxiliary pressure field, and the viscous diffusion characterization of the initial surface velocity field. The time derivative approximation module performs inter-frame difference processing on the initial surface velocity field and the auxiliary pressure field corresponding to adjacent time points to obtain the time variation characteristics of the initial surface velocity field and the time variation characteristics of the auxiliary pressure field.

[0012] Preferably, the method further includes: The mass-conserving residual is constructed based on the divergence characterization of the preliminary surface velocity field; The momentum conservation residual is constructed based on the time variation characterization of the initial surface velocity field, the first-order spatial variation of the initial surface velocity field, the pressure gradient characterization of the auxiliary pressure field, and the viscous diffusion characterization of the initial surface velocity field, combined with the water density and the water kinematic viscosity coefficient. The mass conservation residual and the momentum conservation residual are combined according to a preset aggregation rule to construct a physical constraint loss, thereby constraining the model parameter updates of the feature extraction network.

[0013] Preferably, the training of the deep learning model adopts a training objective function consisting of data consistency loss and physical constraint loss; The data consistency loss is used to characterize the difference between the preliminary surface velocity field and the reference surface velocity field acquired synchronously with the training samples; The physical constraint loss is used to characterize the overall deviation between the mass conservation residual and the momentum conservation residual; The training objective function is obtained by weighting the data consistency loss and the physical constraint loss according to preset weights.

[0014] Preferably, the monocular video sequence is acquired by an optical acquisition device deployed above the water area to be measured; The optical acquisition device is equipped with a polarization filter in the imaging optical path to suppress water surface reflection and enhance the contrast of underwater turbulent structures. In addition, an auxiliary lighting device is used to supplement the water area under test when the ambient light is insufficient.

[0015] According to a second aspect of the embodiments of this application, a water surface flow velocity measurement system is provided, comprising: Processor and memory; The processor and memory are connected via a communication bus: The processor is used to call and execute the program stored in the memory; The memory is used to store a program, which is at least used to execute a method for measuring surface flow velocity of a water body as described in any of the preceding claims.

[0016] The technical solution provided in this application may include the following beneficial effects: This technical solution performs flat-field correction and contrast enhancement on monocular video sequences, and uses multi-scale Gaussian difference to extract underwater turbulent patterns and construct temporal features of turbulence intensity. It further introduces a deep learning model that includes a feature extraction network and a physical constraint layer. The model calculates the mass conservation residual and momentum conservation residual and constrains the initial surface velocity field. This enables more stable surface velocity field estimation results even when the water surface tracer features are insufficient or when there is interference from raindrops, foam, low light, etc. At the same time, it improves the consistency between the output velocity field and the laws of incompressible fluids, and enhances the physical reliability and cross-scene generalization ability of the measurement results.

[0017] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0018] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0019] Figure 1 This is a schematic flowchart of a method for measuring surface velocity of water provided in one embodiment of this application. Detailed Implementation

[0020] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0021] Example 1 Traditional non-contact optical methods for measuring river surface velocity, such as large-scale particle image velocimetry and spatiotemporal image velocimetry, heavily rely on clearly visible tracer features on the water surface. However, in complex natural environments such as calm, turbid water, water surfaces impacted by raindrops or covered with foam, and low-light conditions at night, tracer features are difficult to extract or track, leading to measurement failures or decreased accuracy. Furthermore, traditional methods utilize only a single dimension of information, failing to fully explore the dynamic information of the near-surface region below the water surface. Additionally, purely data-driven deep learning models may violate fundamental laws of fluid mechanics, making it difficult to guarantee physical consistency and limiting generalization ability.

[0022] In response, this application proposes a method for measuring surface velocity of water, referring to... Figure 1 ,include: S1. Acquire monocular video sequences of the water area to be measured; S2. Perform flat field correction on the monocular video sequence and perform contrast-limited adaptive histogram equalization to obtain the preprocessed video sequence. S3. Perform multi-scale Gaussian difference filtering on the preprocessed video sequence to obtain a multi-scale turbulence pattern sequence that characterizes underwater turbulence patterns at different scales. S4. Construct temporal features of turbulence intensity based on multi-scale turbulence pattern sequences; S5. Input the temporal features of turbulence intensity into a pre-trained deep learning model with physical constraints; the deep learning model includes a feature extraction network and a physical constraint layer; S6. Output the initial surface velocity field and the corresponding auxiliary pressure field through the feature extraction network; S7. Calculate the mass conservation residual and momentum conservation residual based on the initial surface velocity field and auxiliary pressure field through the physical constraint layer; including: performing spatial derivative approximation and time derivative approximation on the initial surface velocity field and auxiliary pressure field, and using water density and water kinematic viscosity coefficient as physical parameter inputs to obtain the mass conservation residual and momentum conservation residual of the corresponding incompressible fluid control equation; S8. Constrain the preliminary surface velocity field based on the mass conservation residual and the momentum conservation residual to output the surface velocity field of the water body to be measured.

[0023] For ease of understanding, the following explains some key terms in this embodiment: Monocular video sequence: refers to a set of image frames continuously acquired over a period of time by a single camera or optical acquisition device, used to record dynamic visual information of the water body under test.

[0024] In practice, monocular video sequences are acquired by an optical acquisition device deployed above the water area to be measured. A polarization filter is installed on the imaging optical path of the optical acquisition device to suppress mirror reflection on the water surface and enhance the contrast of underwater turbulent structures. An auxiliary lighting device is used to supplement the light of the water area under test when the ambient light is insufficient.

[0025] Flat field correction: refers to a preprocessing operation performed on an image to eliminate image brightness non-uniformity caused by optical non-uniformity of the imaging system or differences in sensor pixel response, in order to obtain a more uniform image background.

[0026] Contrast-limited adaptive histogram equalization: This refers to an image enhancement technique that equalizes the histogram of a local region of an image and limits the magnitude of contrast enhancement during the equalization process to improve local image contrast while avoiding excessive noise amplification.

[0027] Multi-scale Gaussian difference filtering: This refers to applying Gaussian smoothing kernels of different scales to an image and then performing difference operations on the smoothing results to extract texture features or edge information at different scales in the image.

[0028] Turbulent pattern sequence: refers to an image sequence extracted from water body videos using image processing methods, which represents the change of visual textures formed by the projection of underwater turbulent structures onto the water surface over time.

[0029] Temporal characteristics of turbulence intensity: refers to the numerical or vector representation extracted from the turbulence pattern sequence that can quantify the change of water turbulence intensity over time.

[0030] Deep learning model: refers to a model that combines deep learning technology with the physical laws of fluid mechanics. This model learns data features while introducing physical constraints to ensure that its output conforms to basic physical principles.

[0031] Feature extraction network: refers to a component of a deep learning model, responsible for learning and extracting high-level, discriminative feature representations from the temporal features of the input turbulence intensity.

[0032] Physical constraint layer: This refers to a special network layer in a deep learning model that does not contain trainable parameters. Its main function is to calculate the physical residuals based on the output of the feature extraction network according to the basic equations of fluid mechanics, thereby providing physical consistency guidance for the training of the model.

[0033] Preliminary surface velocity field: refers to the preliminary estimate of the surface velocity of the water body under test, which is directly output by the feature extraction network and has not been corrected by physical constraints.

[0034] Auxiliary pressure field: A variable introduced to meet the mathematical requirements of the incompressible fluid control equations. It works together with the initial surface velocity field to calculate the physical residuals, ensuring the physical rationality of the predicted velocity field.

[0035] Mass conservation residuals and momentum conservation residuals: These are quantities calculated based on the governing equations of incompressible fluids, characterizing the degree to which the current velocity and pressure fields deviate from the physical conservation laws. When the residuals approach zero, it indicates that the flow field satisfies the physical conservation laws.

[0036] Spatial derivative approximation and time derivative approximation: These refer to estimating the rate of change of flow field variables in space and time using numerical methods.

[0037] Water density and kinematic viscosity: These are parameters describing the physical properties of water. Water density represents the mass of water per unit volume, while kinematic viscosity represents the water's resistance to shear deformation. These parameters are used in fluid dynamics equations to describe the motion characteristics of fluids.

[0038] Incompressible fluid governing equations: These are the fundamental physical equations describing the motion of incompressible fluids, typically including the mass conservation equation and the momentum conservation equation.

[0039] Water surface velocity field: refers to the vector field that accurately reflects the velocity distribution at various points on the surface of the water body under test after physical constraint correction.

[0040] This embodiment provides a method for measuring the surface velocity of water, specifically including the following steps: First, a monocular video sequence of the water area to be measured is acquired. This video sequence can be obtained by fixing a regular camera above the water area and having it continuously record images of the water surface. For example, the camera can simply be placed on a bridge or bank to record water surface dynamics from a fixed perspective. This acquisition method can provide visual information about the water surface, but it may be affected by factors such as ambient lighting and water surface reflection, resulting in unstable image quality.

[0041] Secondly, flat-field correction is performed on the monocular video sequence, followed by contrast-limited adaptive histogram equalization to obtain a preprocessed video sequence. In practice, a simple global brightness adjustment can be first applied to the acquired video frames to compensate for overall insufficient illumination or overexposure. Subsequently, standard histogram equalization methods can be used to enhance the overall image contrast. However, this global processing approach may not effectively solve the problem of uneven brightness or insufficient contrast in local areas, especially when there are complex light and shadow variations on the water surface.

[0042] Furthermore, multi-scale Gaussian difference filtering is performed on the preprocessed video sequence to obtain a multi-scale turbulent pattern sequence representing underwater turbulent patterns at different scales. For example, a single-scale Gaussian filter can be applied to the preprocessed video frames for smoothing, and then a simple edge detection algorithm can be used to extract the water surface texture. However, the patterns formed on the water surface by underwater turbulent structures have multi-scale characteristics, and single-scale processing may not be able to fully capture these complex dynamic information, resulting in insufficient representation of turbulent features.

[0043] Based on this, a temporal feature of turbulence intensity is constructed using this multi-scale turbulence pattern sequence. Specifically, for each frame of the multi-scale turbulence pattern sequence, the local variance of its pixel grayscale values ​​can be calculated, and this variance can be used as the texture intensity of that region. Subsequently, a simple difference operation is performed on the texture intensity of adjacent frames to characterize the change in turbulence intensity. However, this intensity calculation based on pixel grayscale variance may be sensitive to noise and fails to fully utilize the structural information of the image to accurately reflect the dynamic characteristics of turbulence.

[0044] Subsequently, the temporal features of turbulence intensity are input into a pre-trained deep learning model. This deep learning model includes a feature extraction network and a physical constraint layer. For example, a standard convolutional neural network can be constructed as the feature extraction network and connected to a simple fully connected layer to directly learn and output flow velocity information from the temporal features of turbulence intensity. In this case, the physical constraint layer can be designed as a separate post-processing module to check and correct the physical consistency of the initial flow velocity output by the model. However, this loosely coupled approach may not be able to achieve a deep fusion of physical laws and data features during model training.

[0045] The feature extraction network outputs a preliminary surface velocity field and a corresponding auxiliary pressure field. Specifically, the feature extraction network can be designed to directly output a two-dimensional vector field representing the preliminary surface velocity. Simultaneously, to assist in subsequent physical constraints, the network can also output an additional scalar field as a preliminary estimate of the auxiliary pressure field.

[0046] The physical constraint layer calculates the mass and momentum conservation residuals based on the initial surface velocity field and the auxiliary pressure field. This calculation involves approximating the initial surface velocity field and the auxiliary pressure field using spatial and temporal derivatives, and using water density and kinematic viscosity as input physical parameters to obtain the corresponding mass and momentum conservation residuals for the incompressible fluid control equations. For example, the physical constraint layer can use a simple finite difference method to approximate the spatial gradient and temporal rate of change of the velocity and pressure fields. These approximate derivatives are then directly substituted into simplified fluid dynamics equations to calculate the residuals. However, this simple approximation method may have limitations in terms of accuracy and stability, especially when dealing with complex flow fields.

[0047] Finally, the initial surface velocity field is constrained based on the mass conservation residual and the momentum conservation residual to output the surface velocity field of the water body under test. For example, an iterative optimization algorithm can be used to fine-tune the initial surface velocity field based on the calculated residuals until the residuals converge to below a preset threshold. Alternatively, the residuals can be used as part of the loss function to guide the feature extraction network to adjust its parameters during model training, thereby making the output velocity field more consistent with physical laws.

[0048] This embodiment effectively overcomes the dependence of traditional methods on tracer features in complex natural environments by combining multi-scale turbulent pattern feature extraction with a deep learning model, thus improving environmental adaptability under weak tracer or strong interference conditions. Simultaneously, this method fully exploits the dynamic information of the near-surface region below the water surface and ensures the physical consistency of the output velocity field through a physical constraint layer, thereby enhancing the robustness and reliability of the measurement results.

[0049] Example 2 It should be noted that multi-scale Gaussian difference filtering is performed on the preprocessed video sequence to obtain a multi-scale turbulence pattern sequence representing underwater turbulence patterns at different scales, including: The preprocessed video sequence was smoothed using multiple Gaussian kernels of different scales to obtain multiple smoothed sequences of corresponding scales. Perform a difference operation on two sets of smoothed sequences at adjacent scales to obtain the difference sequences at the corresponding scales; The difference sequences at each scale are aggregated to form a multi-scale turbulent pattern sequence; wherein, the multi-scale turbulent pattern sequence includes at least four difference sequences corresponding to the scales, and the scale ratio between adjacent scales is a preset constant.

[0050] Specifically, when smoothing a preprocessed video sequence using multiple sets of Gaussian kernels of different scales, the Gaussian kernel, a commonly used image smoothing filter, has a weight distribution resembling a Gaussian function, effectively removing image noise and blurring image details. Using multiple sets of Gaussian kernels of different scales aims to extract information from different spatial frequencies in the preprocessed video sequence, i.e., capturing turbulent structures of different sizes. Smaller-scale Gaussian kernels retain more details, corresponding to smaller turbulent patterns; larger-scale Gaussian kernels smooth out more details, highlighting larger-scale turbulent structures. This smoothing process can be achieved through convolution operations. For each frame in the preprocessed video sequence, convolution is performed with multiple preset sets of Gaussian kernels.

[0051] Based on this, a difference operation is performed on two sets of smoothed sequences at adjacent scales to obtain the difference sequences at the corresponding scales. Difference operations, especially Gaussian difference, are commonly used edge detection and feature extraction techniques. By differencing smoothed sequences at adjacent scales, image features existing within a specific scale range can be effectively highlighted, while features at other scales are suppressed.

[0052] Subsequently, the difference sequences at each scale are aggregated to form the multi-scale turbulence pattern sequence. Aggregating the difference sequences at different scales aims to create a comprehensive data structure that fully reflects the multi-scale characteristics of water turbulence. This aggregation process allows subsequent feature extraction (such as the construction of temporal features of turbulence intensity) to simultaneously utilize information from different scale levels, thereby capturing the dynamics of water movement more accurately and robustly. This aggregation process can be achieved by stacking or stitching the difference sequences at different scales along a certain dimension. For example, if each difference sequence is a two-dimensional image sequence, they can be stacked along the channel dimension to form a multi-channel image sequence, where each channel represents turbulence pattern information at a specific scale. Alternatively, they can be managed as independent sequences and used in parallel in subsequent processing.

[0053] Furthermore, temporal features of turbulence intensity are constructed based on multi-scale turbulence pattern sequences, including: For the turbulent pattern images corresponding to each target scale in the multi-scale turbulent pattern sequence, the spatial gradient is calculated in the pixel neighborhood and the structure tensor is constructed accordingly. The maximum eigenvalue of the structure tensor is determined as the texture intensity; Temporal difference processing is performed on the texture intensity of adjacent frames to obtain a characterization of turbulence intensity variation; The turbulence intensity variation characteristics corresponding to each target scale are stacked along the feature channel dimension to form a temporal feature of turbulence intensity.

[0054] Specifically, spatial gradients are calculated within the pixel neighborhood and used to construct a structure tensor. The spatial gradient is the rate of change of image pixel intensity in space, typically obtained by calculating the partial derivatives of the image in the horizontal and vertical directions. These gradients effectively capture edge and texture information in the image, reflecting the trend of local pixel intensity changes. Within the pixel neighborhood, such as a 3x3 or 5x5 window, a structure tensor can be constructed by combining these spatial gradients. The structure tensor is a symmetric matrix that comprehensively describes the texture orientation, intensity, and anisotropy of a local image region, providing a mathematical foundation for subsequent texture intensity extraction.

[0055] Subsequently, the maximum eigenvalue of the structure tensor is determined as the texture intensity. The eigenvalues ​​of the structure tensor represent the intensity of changes in local image structure along different principal directions. The maximum eigenvalue corresponds to the direction of the most drastic pixel intensity change within a local region, thus directly quantifying the texture intensity or edge intensity of that region. By selecting the maximum eigenvalue as the texture intensity, the salient features of turbulent patterns in the image can be effectively highlighted, while minor or noise-induced intensity changes are filtered out, resulting in a value with good characterization of turbulence intensity.

[0056] Based on this, temporal difference processing is performed on the texture intensity of adjacent frames to obtain a representation of turbulence intensity changes. Temporal difference processing refers to subtracting the texture intensity at the same spatial location in consecutive video frames. For example, the texture intensity of the current frame is subtracted from the texture intensity of the previous frame. This processing method can effectively remove static background or slowly changing texture information in a video sequence, thereby highlighting the rapid and dynamic texture intensity changes caused by water turbulence. Through temporal difference, a dynamic representation that directly reflects the change of turbulence intensity over time can be obtained, which is crucial for capturing the instantaneous characteristics of water flow.

[0057] Finally, the turbulence intensity variation representations corresponding to each target scale are stacked along the feature channel dimension to form a temporal feature of turbulence intensity. Since water turbulence has multi-scale characteristics, turbulence pattern sequences at different scales will generate their own turbulence intensity variation representations. To comprehensively capture this information, these turbulence intensity variation representations obtained at different scales are stacked along the feature channel dimension. This means that if there are N target scales, the final turbulence intensity temporal feature will be a feature map with N channels, each channel corresponding to a specific scale of turbulence intensity variation. This stacking method provides a rich and multi-dimensional input for subsequent deep learning models, enabling them to comprehensively consider turbulence dynamics at different scales, thereby more accurately inferring the surface velocity of the water body.

[0058] Example 3 This embodiment proposes a method for training a deep learning model and a specific construction method for the deep learning model.

[0059] It should be noted that the method also includes: Training monocular video sequences under different flow velocities and hydrological conditions were collected, and the reference surface flow velocity field corresponding to each training monocular video sequence was collected simultaneously to form a training dataset. A deep learning model is trained using a training dataset.

[0060] Specifically, firstly, training monocular video sequences are collected under different flow velocities and hydrological conditions. These training monocular video sequences are specifically used as visual input data for training deep learning models. To ensure the model has good generalization ability and robustness, video data covering various flow velocity states (e.g., slow flow, fast flow, turbulent flow) and different hydrological conditions (e.g., different water depths, riverbed morphology, water surface texture, illumination changes, etc.) needs to be collected. Through diverse data collection, the model can learn the complex mapping relationship between the visual features of the water surface and the flow velocity in various real-world scenarios. The acquisition of video sequences is usually accomplished using camera equipment mounted above the water area to be measured, ensuring that the video footage clearly reflects the movement characteristics of the water surface.

[0061] Secondly, reference surface velocity fields corresponding to each of the training monocular video sequences are simultaneously acquired. The reference surface velocity field is real water surface velocity data that precisely corresponds to the training monocular video sequences in time and space, serving as the "correct answer" or supervision signal during model training. Subsequently, a training dataset is constructed. The training dataset is a collection of the acquired training monocular video sequences and their corresponding reference surface velocity fields. Each data sample contains a pair of inputs (video sequence) and outputs (reference velocity field). This dataset forms the basis for supervised learning of the deep learning model. By analyzing a large number of samples in the dataset, the model gradually adjusts its internal parameters to minimize the difference between the predicted velocity and the reference velocity. The size and quality of the dataset directly affect the training effect of the model and the final measurement accuracy.

[0062] Finally, the deep learning model is trained using the training dataset. The training process involves adjusting the weights and bias parameters within the deep learning model using an iterative optimization algorithm on the constructed training dataset. In each iteration, the model receives a monocular video sequence as input, generates a preliminary surface velocity field and an auxiliary pressure field, and calculates the mass conservation residual and momentum conservation residual through a physical constraint layer. Combining the data consistency loss (the difference between the preliminary velocity field and the baseline velocity field) and the physical constraint loss, the total loss function is calculated, and the model parameters are updated via backpropagation based on the gradient of the loss function. This process continues until the model's performance on the training dataset reaches a preset standard or converges, enabling the model to accurately infer the surface velocity field of the water body from the video sequence and ensuring that the inference results conform to the fundamental laws of fluid mechanics.

[0063] In practice, the model in this application is trained end-to-end using the Adam optimizer, with an initial learning rate set to 1×10⁻⁶. 4. And a learning rate decay strategy is adopted.

[0064] It should be noted that the feature extraction network adopts an encoder and decoder structure; The encoder contains a multi-stage downsampling structure. Each stage of the encoder includes two consecutive convolutional processing units, and the kernel size of each convolutional processing unit is 3. 3. Each convolutional processing unit sequentially includes convolution processing, batch normalization processing, and linear rectified activation processing; a max-pooling downsampling unit is set after two consecutive convolutional processing units, with a pooling window of 2. 2. The downsampling step size is 2; the number of encoder channels is doubled after each downsampling stage. The decoder contains a multi-stage upsampling structure. Each stage of the decoder includes a transposed convolutional upsampling unit, and the kernel size of the transposed convolutional upsampling unit is 2. 2; The upsampled features of the transposed convolutional upsampling unit and the corresponding level features of the encoder are concatenated through skip connections, and then sequentially passed through two identical convolutional processing units for feature recovery; the kernel size of the convolutional processing unit used for feature recovery is 3. 3, and includes convolution processing, batch normalization processing and linear rectified activation processing in sequence; The decoder ends with a convolution kernel size of 1. A 1-mapped convolutional layer is used to output the initial surface velocity field and the corresponding auxiliary pressure field.

[0065] The multi-level downsampling structure in the encoder aims to progressively reduce the spatial size of the feature map while increasing the number of feature channels, thereby extracting more abstract and semantic features. Each level of downsampling typically includes two steps: feature extraction and spatial size reduction. Two consecutive convolutional processing units are used for sufficient feature learning before downsampling. Each convolutional processing unit employs 3... A 3x3 convolutional kernel can capture local spatial information. Batch normalization after convolution helps stabilize the training process, accelerates model convergence, and improves the model's generalization ability. Rectified linear activation (ReLU) introduces non-linearity, enabling the network to learn more complex feature representations. After two consecutive convolutional units, a max-pooling downsampling unit with a pooling window of 2 is set. 2. The downsampling step size of 2 effectively halves the spatial size of the feature map while retaining the most important feature information and increasing the receptive field of the features. The initial number of channels of the encoder is set to a preset value (usually 64), providing a rich initial feature space for subsequent feature extraction. After each downsampling stage, the number of channels doubles, which allows the network to learn richer and more abstract feature representations while reducing spatial resolution.

[0066] The multi-level upsampling structure in the decoder corresponds to the encoder. Its purpose is to progressively restore the spatial resolution of the feature maps and utilize the deep features extracted from the encoder to generate the final output. Each level of upsampling includes a transposed convolutional upsampling unit with a kernel size of 2. 2. It can double the spatial size of the feature map to achieve upsampling. To compensate for the details that may be lost during encoder downsampling, the upsampled features of the transposed convolutional upsampling unit are concatenated with the corresponding level features of the encoder through skip connections. This skip connection mechanism allows the decoder to directly access the fine-grained spatial information retained in the encoder, thereby helping to generate a more accurate and detailed output. After concatenation, feature recovery is performed sequentially through two identical convolutional processing units with a kernel size of 3. 3. It also includes convolution processing, batch normalization processing, and linear rectified activation processing for further fusion and refinement of features from the encoder and decoder.

[0067] At the end of the decoder, a convolutional kernel with a size of 1 is set. A 1-channel mapping convolutional layer. The main function of this layer is to adjust the number of channels in the feature map, mapping it to 3. These three channels correspond to the two components of the initial surface velocity field (e.g., the horizontal and vertical velocity components) and the auxiliary pressure field. A convolutional layer can efficiently project a high-dimensional feature space onto the desired output dimension without changing the spatial size of the feature map.

[0068] The physical constraint layer is used to construct the physical constraint loss during the training phase. The physical constraint layer is a network layer without trainable parameters and includes a spatial derivative approximation module and a temporal derivative approximation module. The spatial derivative approximation module uses a preset and fixed differentiable convolution operator to calculate the first-order spatial variation of the initial surface velocity field and the auxiliary pressure field, and to calculate the second-order spatial diffusion characterization of the initial surface velocity field, so as to obtain the divergence characterization of the initial surface velocity field, the pressure gradient characterization of the auxiliary pressure field, and the viscous diffusion characterization of the initial surface velocity field. The time derivative approximation module performs inter-frame difference processing on the initial surface velocity field and the auxiliary pressure field corresponding to adjacent time points to obtain the time variation characteristics of the initial surface velocity field and the auxiliary pressure field.

[0069] The physical constraint layer is designed as a network layer without any trainable parameters. This means that its internal computational logic and weights are pre-set and fixed, and will not be updated during model training through methods such as gradient descent. Its main function is, during the training phase, to calculate the deviation between the model output (initial surface velocity field and auxiliary pressure field) and the physical conservation equations based on physical laws, and to convert these deviations into physical constraint losses, thereby guiding the parameter updates of the feature extraction network. This design ensures the rigor and invariance of physical laws, avoiding the possibility of the physical rules themselves being "learned" or "distorted" by the model.

[0070] The physical constraint layer contains a spatial derivative approximation module and a temporal derivative approximation module. The spatial derivative approximation module is responsible for calculating the rate of change of the flow field in the spatial dimension, such as gradient and divergence; the temporal derivative approximation module is responsible for calculating the rate of change of the flow field in the time dimension. These two modules work together to provide the basic data for constructing the terms in the fluid dynamics governing equations.

[0071] Based on the construction of the deep learning model described above, the method also includes: Construct mass-conserving residuals based on the divergence characterization of the initial surface velocity field; Based on the temporal variation of the initial surface velocity field, the first-order spatial variation of the initial surface velocity field, the pressure gradient of the auxiliary pressure field, and the viscous diffusion of the initial surface velocity field, and combined with the water density and the water kinematic viscosity coefficient, a momentum conservation residual is constructed. Based on the mass conservation residual and momentum conservation residual, a physical constraint loss is constructed according to the preset aggregation rules, and the model parameters of the constraint feature extraction network are updated.

[0072] The construction of the mass conservation residual aims to quantify whether the "inflow" and "outflow" of the initial surface velocity field are in spatial equilibrium. For incompressible fluids, the divergence of their velocity field should be zero. Therefore, by directly using the divergence of the initial surface velocity field as the mass conservation residual, we can intuitively reflect whether the mass of the fluid is conserved in a local region. If the divergence deviates from zero, it indicates that mass is not conserved. This residual value will be used for subsequent loss calculations to guide the model in adjusting its parameters to satisfy the law of mass conservation.

[0073] The construction of the momentum conservation residual aims to evaluate whether the initial surface velocity field and the auxiliary pressure field satisfy the momentum conservation law of fluid mechanics. This residual comprehensively considers multiple physical factors of fluid motion: the time variation of the initial surface velocity field reflects the local acceleration of the fluid; the first-order spatial variation of the initial surface velocity field (usually used to calculate convection terms) describes the transfer of momentum with fluid motion; the pressure gradient of the auxiliary pressure field reflects the driving effect of pressure on fluid motion; and the viscous diffusion of the initial surface velocity field characterizes the dissipation of momentum by viscous forces within the fluid. By combining these physical quantities with water density and kinematic viscosity (as physical parameters) according to the governing equations of incompressible fluids, the momentum conservation residual can be obtained. This residual quantifies the deviation between the model-predicted flow field and the actual physical laws; the closer its value is to zero, the more the model-predicted flow field conforms to the physical laws.

[0074] The physical constraint loss is constructed by integrating the calculated mass conservation residuals and momentum conservation residuals into a single scalar loss value using a pre-defined aggregation rule. This aggregation rule can take various forms, such as a weighted sum of the L1 or L2 norms of the two residuals, or a statistical measure like mean squared error (MSE). Through this aggregation, the physical constraint loss can comprehensively reflect the overall deviation of the model-predicted flow field from the conservation of mass and momentum. During training, this physical constraint loss is used as part of the training objective function, guiding the update of the model parameters of the feature extraction network through backpropagation. This ensures that the output preliminary surface velocity field and auxiliary pressure field better satisfy the fundamental laws of fluid mechanics, thereby improving the physical rationality and accuracy of the velocity measurement results.

[0075] It should be noted that the training of deep learning models uses a training objective function consisting of data consistency loss and physical constraint loss; Data consistency loss is used to characterize the difference between the initial surface velocity field and the baseline surface velocity field acquired synchronously with the training samples; Physical constraint loss is used to characterize the overall deviation between the mass conservation residual and the momentum conservation residual; The training objective function is obtained by weighting the data consistency loss and the physical constraint loss according to preset weights.

[0076] The training of deep learning models no longer relies solely on a single dimension of data fitting or physical constraints, but rather organically combines both. Specifically, the training objective function is obtained by weighting the data consistency loss and the physical constraint loss according to preset weights. The data consistency loss ensures that the initial surface velocity field output by the model can accurately fit the benchmark surface velocity field collected synchronously with the training samples, thereby guaranteeing the model's learning ability and prediction accuracy based on actual observation data. Simultaneously, the physical constraint loss, by characterizing the overall deviation between the mass conservation residual and the momentum conservation residual, forces the velocity field and auxiliary pressure field output by the model to satisfy basic fluid dynamics principles, effectively preventing the model from producing physically unreasonable predictions. This dual constraint mechanism allows the model to maintain physical rationality while learning data features, thus outputting a more accurate and physically interpretable water surface velocity field. By adjusting the preset weights, the data-driven and physical-driven learning processes can be flexibly balanced to adapt to the needs of different data qualities and application scenarios, ultimately improving the robustness and reliability of water surface velocity measurement.

[0077] Example 4 A water surface velocity measurement system, comprising: Processor and memory; The processor and memory are connected via a communication bus: The processor is used to call and execute programs stored in memory. A memory for storing a program, which is at least used to execute a method for measuring surface flow velocity of a water body as described in the above embodiments.

[0078] It is understood that the same or similar parts in the above embodiments can be referred to each other, and the contents not described in detail in some embodiments can be referred to the same or similar contents in other embodiments.

[0079] It should be noted that in the description of this application, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Furthermore, in the description of this application, unless otherwise stated, "a plurality of" means at least two.

[0080] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing a particular logical function or process, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the function involved, as will be understood by those skilled in the art to which embodiments of this application pertain.

[0081] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0082] Those skilled in the art will understand that all or part of the steps of the methods described in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it includes one or a combination of the steps of the method embodiments.

[0083] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0084] The storage media mentioned above can be read-only memory, disk, or optical disk, etc.

[0085] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0086] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of this application.

Claims

1. A method for measuring surface velocity of water, characterized in that, include: Acquire monocular video sequences of the water area to be measured; Flat field correction is performed on the monocular video sequence, and contrast-limited adaptive histogram equalization is performed to obtain a preprocessed video sequence. Multi-scale Gaussian difference filtering is performed on the preprocessed video sequence to obtain a multi-scale turbulence pattern sequence characterizing underwater turbulence patterns at different scales; Based on the multi-scale turbulence pattern sequence, temporal features of turbulence intensity are constructed. The temporal features of the turbulence intensity are input into a pre-trained deep learning model with physical constraints; the deep learning model includes a feature extraction network and a physical constraint layer. The feature extraction network outputs a preliminary surface velocity field and an auxiliary pressure field corresponding to the preliminary surface velocity field. The physical constraint layer calculates the mass conservation residual and momentum conservation residual based on the initial surface velocity field and the auxiliary pressure field; including: performing spatial derivative approximation and time derivative approximation on the initial surface velocity field and the auxiliary pressure field, and using water density and water kinematic viscosity as physical parameter inputs to obtain the mass conservation residual and momentum conservation residual of the corresponding incompressible fluid control equation; The preliminary surface velocity field is constrained based on the mass conservation residual and the momentum conservation residual to output the surface velocity field of the water body to be measured.

2. The method for measuring surface velocity of water according to claim 1, characterized in that, The preprocessed video sequence is subjected to multi-scale Gaussian difference filtering to obtain a multi-scale turbulence pattern sequence characterizing underwater turbulence patterns at different scales, including: The preprocessed video sequence is smoothed using multiple sets of Gaussian kernels of different scales to obtain multiple smoothed sequences of corresponding scales. Perform a difference operation on two sets of smoothed sequences at adjacent scales to obtain the difference sequences at the corresponding scales; The difference sequences at each scale are aggregated to form the multi-scale turbulent pattern sequence; wherein the multi-scale turbulent pattern sequence includes at least four difference sequences corresponding to the scales, and the scale ratio between adjacent scales is a preset constant.

3. The method for measuring surface velocity of water according to claim 1, characterized in that, Based on the multi-scale turbulent pattern sequence, temporal features of turbulence intensity are constructed, including: For the turbulent pattern images corresponding to each target scale in the multi-scale turbulent pattern sequence, the spatial gradient is calculated in the pixel neighborhood and the structure tensor is constructed accordingly. The maximum eigenvalue of the structure tensor is determined as the texture intensity; Temporal difference processing is performed on the texture intensity of adjacent frames to obtain a characterization of turbulence intensity variation; The turbulence intensity variation characteristics corresponding to each target scale are stacked along the feature channel dimension to form a temporal feature of turbulence intensity.

4. The method for measuring surface velocity of water according to claim 1, characterized in that, The method further includes: Training monocular video sequences under different flow velocities and hydrological conditions are collected, and the reference surface flow velocity field corresponding to each training monocular video sequence is collected simultaneously to form a training dataset. The deep learning model is trained using the training dataset.

5. The method for measuring surface velocity of water according to claim 4, characterized in that, The feature extraction network adopts an encoder-decoder structure; The encoder comprises a multi-stage downsampling structure, each stage of which includes two consecutive convolutional processing units, and the kernel size of each convolutional processing unit is 3.

3. Each convolutional processing unit sequentially includes convolution processing, batch normalization processing, and linear rectified activation processing; a max-pooling downsampling unit is set after the two consecutive convolutional processing units, and the pooling window of the max-pooling downsampling unit is 2.

2. The downsampling step size is 2; the number of channels of the encoder is doubled after each downsampling stage; The decoder comprises a multi-level upsampling structure, each level of which includes a transposed convolutional upsampling unit with a kernel size of 2. 2; The upsampled features of the transposed convolutional upsampling unit and the features of the corresponding level of the encoder are concatenated through a skip connection, and the features are restored sequentially through two identical convolutional processing units; The kernel size of the convolutional processing unit used for feature recovery is 3. 3, and includes convolution processing, batch normalization processing and linear rectified activation processing in sequence; The decoder end is configured with a convolution kernel size of 1. A 1-mapped convolutional layer is used to output the initial surface velocity field and the auxiliary pressure field corresponding to the initial surface velocity field.

6. The method for measuring surface velocity of water according to claim 4, characterized in that, The physical constraint layer is used to construct the physical constraint loss during the training phase, and the physical constraint layer is a network layer without trainable parameters. The physical constraint layer includes a spatial derivative approximation module and a temporal derivative approximation module. The spatial derivative approximation module uses a preset and fixed differentiable convolution operator to calculate the first-order spatial variation of the initial surface velocity field and the auxiliary pressure field, and to calculate the second-order spatial diffusion characterization of the initial surface velocity field, so as to obtain the divergence characterization of the initial surface velocity field, the pressure gradient characterization of the auxiliary pressure field, and the viscous diffusion characterization of the initial surface velocity field. The time derivative approximation module performs inter-frame difference processing on the initial surface velocity field and the auxiliary pressure field corresponding to adjacent time points to obtain the time variation characteristics of the initial surface velocity field and the time variation characteristics of the auxiliary pressure field.

7. The method for measuring surface velocity of water according to claim 6, characterized in that, The method further includes: The mass-conserving residual is constructed based on the divergence characterization of the preliminary surface velocity field; The momentum conservation residual is constructed based on the time variation characterization of the initial surface velocity field, the first-order spatial variation of the initial surface velocity field, the pressure gradient characterization of the auxiliary pressure field, and the viscous diffusion characterization of the initial surface velocity field, combined with the water density and the water kinematic viscosity coefficient. The mass conservation residual and the momentum conservation residual are combined according to a preset aggregation rule to construct a physical constraint loss, thereby constraining the model parameter updates of the feature extraction network.

8. The method for measuring surface velocity of water according to claim 7, characterized in that, The deep learning model is trained using a training objective function consisting of data consistency loss and physical constraint loss. The data consistency loss is used to characterize the difference between the preliminary surface velocity field and the reference surface velocity field acquired synchronously with the training samples; The physical constraint loss is used to characterize the overall deviation between the mass conservation residual and the momentum conservation residual; The training objective function is obtained by weighting the data consistency loss and the physical constraint loss according to preset weights.

9. The method for measuring surface velocity of water according to claim 1, characterized in that, The monocular video sequence was acquired by an optical acquisition device deployed above the water area to be measured; The optical acquisition device is equipped with a polarization filter in the imaging optical path to suppress water surface reflection and enhance the contrast of underwater turbulent structures. In addition, an auxiliary lighting device is used to supplement the water area under test when the ambient light is insufficient.

10. A water surface velocity measurement system, characterized in that, include: Processor and memory; The processor and memory are connected via a communication bus: The processor is used to call and execute the program stored in the memory; The memory is used to store a program, which is at least used to execute the water surface flow velocity measurement method according to any one of claims 1-9.

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