A method and intelligent system for synchronous assimilation of water level and flow in natural river channels

Abstract

To address the problems of high cost, difficulty in calibrating flow velocity models, and unstable relationships in natural river channel flow and water level monitoring sections, this invention discloses a method and intelligent system for synchronous assimilation of water level and flow in natural rivers. Based on the river cross-section and its evolution, a generative adversarial network is used to dynamically acquire the underwater topography of the entire river section, thereby obtaining the flow area of ​​any cross-section. Hydrodynamic equations combined with a neural network are used to achieve synchronous assimilation of water level and flow. The assimilation accuracy can be improved as needed by adding measured data from the cross-section. This invention is technologically advanced, highly operable, and of great significance for flood control, drought relief, and water resource protection.

Description

Technical Field

[0001] This invention belongs to the technical fields of flood control and disaster reduction, water resource management and smart water conservancy, and specifically relates to a method and intelligent system for synchronizing water level and flow in natural river channels. Background Technology

[0002] In recent years, affected by global climate change, floods have occurred frequently, posing a serious threat to social economy and people's lives. Meanwhile, with increasing demands for intensive water resource utilization, how to quickly and accurately obtain river water level, flow velocity, and especially flow rate has become an urgent technical problem to be solved. Traditional methods for measuring river flow include manual boat surveys, bridge surveys, cableway surveys, and wading surveys. Their basic principle is to lay out multiple vertical lines on the flow measurement cross-section, measure the water depth at each vertical line, and use a current meter to measure the average velocity at each point to obtain the average velocity along the vertical line. This leads to the cross-sectional area and the average velocity, and the flow rate is then obtained by multiplying or integrating the cross-sectional area and the average velocity.

[0003] With the continuous development of computer technology, artificial intelligence (AI) has become a hot research topic, and its application is also crucial for flood control, disaster reduction, and water resource management. In fact, with the development of embedded systems, edge-cloud collaborative architectures, and sensor technology, data assimilation between models and measured data has become a reality. This will significantly improve the reliability of data acquisition and greatly reduce investment and operating costs for equipment and facilities. Neural networks, as one of the core technologies of AI, have become a research hotspot in solving mathematical models that describe objective physical laws.

[0004] There are many equations governing river flow, commonly including the Reynolds-averaged k-ε model, shallow water equations, and the Saint-Venant equations. Solving these equations is complex. Taking the Saint-Venant equations as an example, numerical methods primarily include the method of characteristics, the direct difference method, and the finite volume method. These numerical simulation methods have high requirements for initial conditions and require grid-based storage of variables; any changes in conditions necessitate recalculation. Furthermore, these numerical methods are difficult to integrate with current mainstream artificial intelligence architectures, languages, and system hardware and software, and in particular, they are difficult to match with intelligent methods such as transfer learning, knowledge distillation, and meta-learning.

[0005] In terms of instrument monitoring, to obtain data for a certain cross section, water level and flow velocity monitoring instruments and equipment must be installed at that cross section. If all data for a certain river section is to be obtained, the existing technology requires water level gauges and flow velocity meters to be installed at each cross section. This is not only costly and results in large errors in flow calculation, but also inconvenient to operate and maintain. It also increases the difficulty of data processing and the risks to personnel and equipment.

[0006] This invention discloses a data assimilation method. Given sufficient prior topographic data for a certain cross-section, a monitoring section is set up upstream, and water level and flow velocity monitoring instruments are deployed. The assimilation method can then obtain the water level and flow rate at any cross-section throughout the entire river segment, avoiding the difficulty of converting flow velocity into cross-sectional flow rate required by conventional monitoring. Furthermore, the accuracy of the water level and flow rate at any cross-section obtained by this assimilation system continuously improves as the number of measured cross-sections increases. This invention organically combines instrument monitoring and mathematical models through an intelligent neural network, possessing advantages such as strong theoretical foundation, practical reliability, and scalability. Summary of the Invention

[0007] To address the problems of high cost, difficulty in calibrating flow velocity models, and unstable relationships in natural river channel flow and water level monitoring sections, this invention discloses a method and intelligent system for synchronous assimilation of water level and flow in natural rivers. Based on the river cross-section and its evolution, a generative adversarial network is used to dynamically acquire the underwater topography of the entire river section, thereby obtaining the flow area of ​​any cross-section. Hydrodynamic equations combined with a neural network are used to achieve synchronous assimilation of water level and flow. The assimilation accuracy can be improved as needed by adding measured data from the cross-section. This invention is technologically advanced, highly operable, and of great significance for flood control, drought relief, and water resource protection.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows:

[0009] A method for synchronizing water level and discharge in a natural river channel includes the following steps:

[0010] Step 1: Identify the river sections that need to be assimilated.

[0011] Step 2: Topographic surveying of typical cross-sections above and below water and generation of overall riverbed topography in the assimilation section.

[0012] Acquire the subsurface topography and establish the relationship between water level / depth and cross-sectional area; this is used to construct the relationship between the flow rate and depth measured by sensors and the unit width flow rate and unit width water depth.

[0013] Typical cross-sections were selected for surface and underwater topographic surveying using a combination of surface-mounted UAVs carrying lidar and underwater ultrasonic unmanned vessels. When the riverbed exhibited significant spatiotemporal variations, corresponding cross-sections were selected for measurement. The similarity metric used the cross-sections of the riverbed at the same time, oriented vertically towards the average flow velocity. The specific steps were: (1) scaling down both cross-section figures to normalize their areas; (2) finding the geometric centers of both figures and aligning them through non-rotating translation; (3) the overlapping area of ​​the two figures at this point was the similarity score.

[0014] When the similarity between the next cross section and the measured cross section is ≤0.9, the cross section shape needs to be measured again. Combine historical data to analyze riverbed stability. When the riverbed is stable, the appropriate river flow dynamics equation is selected based on empirical information on cross section shape, hydraulic gradient, and flow velocity distribution. When the riverbed is unstable, it is necessary to establish a riverbed regression model for the entire assimilated river section with the addition of sediment content, upstream soil erosion, typical cross section flow velocity, and time as inputs. This invention uses local interpolation, piecewise smooth regression, and overall stitching to reconstruct the three-dimensional topography of the entire assimilated river section. (1) The model uses the sum of Wasserstein distance and interpolation error as the loss function and introduces a three-dimensional topographic data interpolation algorithm based on Wasserstein generative adversarial network. (2) Based on the existing high-resolution DEM dataset and the previously generated 3D terrain data, a Terrain-CGANs (Conditional Encoder-Decoder Generative Adversarial Networks) was constructed and trained to generate local riverbed topography from terrain features. The generator G contains an "encoder-decoder" module consisting of 5 convolutional layers (conv) and 5 deconvolutional layers (deconv) to extract possible deep geospatial knowledge. In the discriminator D, the sampled riverbed topographic map and the corresponding complete map are first stitched together, and then the binary classification result is output through convolution.

[0015] Step 3: Selection of River Flow Model

[0016] The appropriate mathematical model is selected based on the stability, regularity, and uniformity and stability of the flow during the assimilation period of the assimilation section. For complex and unsteady non-uniform flows, simplified equations of the Navier-Stokes equations are used for assimilation. These simplified equations include four turbulence models: the standard k-ε model, the RNG k-ε model, the realizable k-ε model, and the Reynolds stress model. For straight and regular channels, the Saint-Venant equations are used for data assimilation when the flow velocity is stable.

[0017] Step four involves installing water level and flow velocity monitoring instruments upstream of the assimilation section to achieve full-time, four-dimensional variational assimilation of the assimilation section and the equations. A neural network is used for assimilation of the Saint-Venant equations. Water level and flow velocity measurements are performed using lidar for water level and a phased-array acoustic Doppler profiler for flow velocity. Water level and flow velocity sensors, embedded devices, and a computing service center are deployed at selected cross-sections (the number can be increased as needed to achieve higher accuracy) to form the assimilation system. The number of sampling cross-sections is determined based on accuracy requirements, and sensors are used to obtain water depth and flow rate at these cross-sections as boundary conditions for the model. (Sensors are needed to obtain water depth and flow rate at the upstream and downstream cross-sections as boundary conditions, and accuracy can be improved by increasing the number of sampling cross-sections).

[0018] Using flow velocity measuring instruments, and based on the idea of ​​embedding physical information into neural networks, an equivalent physical information neural network of the Saint-Venant equations was constructed. The neural network structure was optimized and network parameters were obtained by methods such as spatiotemporal scaling and adjusting equation weights. The simulation accuracy of the neural network model was verified. The neural network that met the accuracy requirements was then deployed on-site.

[0019] Step 5, the neural network-based water level-discharge assimilation method, includes the following steps:

[0020] Step 1: Construction of the neural network assimilation model. A physical information neural network is used to construct an assimilation model with the Saint-Venant equations, water level at the sampling section, and flow rate as constraints. This includes the following steps:

[0021] The one-dimensional Saint-Venant equations describing the gradually changing, unsteady flow motion in a river channel are as follows:

[0022] Continuity equation:

[0023] Dynamic equation:

[0024] In the formula, x and t represent the process flow and time, respectively; A is the cross-sectional area; Q is the flow rate through the cross-section; B T Indicates the storage width; Z is the water level; q L This is a side inflow, with inflow being positive and outflow being negative; v x For the side inflow q L The velocity component along the direction of water flow; g is the acceleration due to gravity; K is the flow modulus. R is the hydraulic radius, and n is the roughness coefficient;

[0025] Solving the Saint-Venant equation using a physical information neural network employs a single-network dual-output structure, sharing network parameters, and predicting the partial derivatives of the values ​​with respect to the independent variables. Sample the i input points at the boundary The corresponding unit width water depth h and unit width flow rate q are used to train the boundary constraints. This represents the difference between the neural network's predicted value and the theoretical value. This is the predicted value for water depth per unit width. For the predicted unit-width flow rate, the j input values ​​obtained by sampling from the Latin hypercube within the domain are... For constraints on the continuity equation and the dynamic equation, the sampling points used for boundary constraints are also subject to equation constraints. The differential terms are linearly combined according to the constraints of the continuity equation and the dynamic equation, and the loss function is constructed as follows:

[0026]

[0027] In the formula, MSE indicates that the mean squared error function is used when calculating the loss, and N f With N u The range of influence is indicated by λ, which represents the added balancing weight coefficient.

[0028] Find the neural network parameters that minimize the loss function;

[0029] Step 2: Verify the correctness of the above assimilation model using the four-point difference method. If correct, proceed to Step 4; otherwise, return to Step 3 to optimize the assimilation model.

[0030] Step 3: Deploy the qualified model on-site, update it in the embedded system, and apply it to water level and flow rate assimilation.

[0031] Step 4: Based on the water level and flow rate of the upstream section, the water level and flow rate of any downstream section are obtained in real time using a neural network assimilation model.

[0032] Furthermore, in step 1, a spatiotemporal mapping is added to the input layer of the neural network to scale the input, mapping the input to a denser region.

[0033] Furthermore, in step 1, a fully connected structure with 3 hidden layers and 200 neurons in each layer is used to construct a neural network.

[0034] Furthermore, in step 4, at least one cross-section is selected in combination with the water level and flow rate measured by the embedded device as boundary conditions.

[0035] This invention also provides an intelligent system for synchronous assimilation of water level and flow rate in natural river channels, including water level and flow velocity sensors, embedded devices, and a software system installed in the embedded devices. The software system includes a terrain measurement module, a cross-sectional data acquisition module, a neural network assimilation model construction module, a model verification module, a model deployment module, and a water level and flow rate output module. The terrain measurement module is used to coordinate with a UAV / unmanned surface vessel and a GNSS navigation system to implement step two of the river water level and flow rate assimilation method. The cross-sectional data acquisition module is used to implement step four using sensors. The neural network assimilation model construction module is used to implement step five-1. The model verification module is used to implement step five-2. The model deployment module is used to implement step five-3, deploying the model into the embedded device. The water level and flow rate output module is used to implement step five-4, ultimately outputting the water level and flow rate at any downstream cross-section.

[0036] The beneficial effects of this invention are as follows:

[0037] 1. This invention employs a neural network assimilation method, which uses a neural network to solve the Saint-Venant equations to assimilate the initial and boundary conditions of the instrument's measured data. This allows for the determination of water level and flow rate at any downstream cross-section based on the water level and flow rate at a determined upstream cross-section. Experiments have demonstrated that the output data of this invention has high accuracy.

[0038] 2. Adding weight coefficients before the loss function can effectively improve accuracy, and adding scaling to the neural network can effectively accelerate the convergence of the neural network.

[0039] 3. Using a single-network dual-output structure and sharing parameters can effectively improve the robustness of the network and reduce the number and complexity of network parameters.

[0040] 4. The method of the present invention can be used for both infinite boundary cases where upstream changes do not cause significant downstream changes within a finite time, and finite boundary cases where significant changes are caused. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the overall process of the river water level and flow assimilation method provided by the present invention.

[0042] Figure 2 This is a schematic diagram of a neural network structure.

[0043] Figure 3 This is a schematic diagram of the core network structure of PINNs.

[0044] Figure 4 A schematic diagram of the physical information neural network structure for solving the Saint-Venant equation.

[0045] Figure 5 This is a diagram comparing the training loss function with and without scaling, where dotted lines represent no scaling and solid lines represent scaling.

[0046] Figure 6 This is a visualization of the unit width water level and unit width flow rate obtained by the implicit difference method.

[0047] Figure 7 The diagrams show a comparison between the implicit difference method and the neural network method of this invention. (a) shows a diagram of the single-width depth using the implicit difference method; (b) shows a diagram of the single-width depth using the neural network method of this invention; (c) shows a diagram of the single-width flow rate using the implicit difference method; (d) shows a diagram of the single-width flow rate using the neural network method of this invention; and (c) shows a diagram of the single-width flow rate using the implicit difference method.

[0048] Figure 8The diagrams show a comparison between the implicit difference method and the neural network method of this invention. (a) shows a comparison between the unit width water depth obtained by the implicit difference method and the solution obtained by the neural network of this invention; (b) shows a comparison between the unit width flow obtained by the implicit difference method and the solution obtained by the neural network of this invention; (c) shows a comparison between the changes in unit width water depth at the cross section; and (d) shows a comparison between the changes in unit width flow at the cross section.

[0049] Figure 9 This paper presents a bounded case where changes in upstream water level and flow rate cause changes in downstream water level and flow rate within a finite time period. (a) shows a schematic diagram of unit width depth using the implicit difference method under bounded conditions; (b) shows a schematic diagram of unit width depth using the neural network method of this invention under bounded conditions; (c) shows a schematic diagram of unit width flow rate using the implicit difference method under bounded conditions; (d) shows a schematic diagram of unit width flow rate using the neural network method of this invention under bounded conditions; (e) shows the error distribution of unit width depth calculated using the implicit difference method and the neural network method under bounded conditions; and (f) shows the distribution of unit width flow rate calculated using the implicit difference method and the neural network method under bounded conditions. Detailed Implementation

[0050] The technical solutions provided by the present invention will be described in detail below with reference to specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention.

[0051] This invention provides a method for assimilating river water level and flow rate, the process of which is as follows: Figure 1 As shown, it includes the following steps:

[0052] Step 1: Identify the river sections that need to be assimilated.

[0053] Identify the river sections that need to be assimilated. Furthermore, based on the hydrological, morphological, and geological conditions of the assimilated river sections, analyze the influencing factors affecting the riverbed cross-section and their stability.

[0054] Step 2: Topographic surveying of typical cross-sections above and below water and generation of overall riverbed topography in the assimilation section.

[0055] By employing UAVs / unmanned surface vessels equipped with GNSS navigation systems, combined with shore-based dual reference systems and underwater multibeam bathymetry systems, the underwater topography is acquired, and the relationship between water level / depth and cross-sectional area is established. This information can then be used to convert water level and flow measured by sensors into unit width flow and unit width depth.

[0056] Typical cross-sections were selected for surface and underwater topographic surveying using a combination of surface drones carrying lidar and underwater ultrasonic unmanned vessels. When the riverbed changes significantly in time and space, the corresponding cross-sections were selected for measurement. A cross-section refers to the cross section of the river channel below the water surface at the same time, in the direction of the vertical average flow velocity. When the similarity between the next cross-section and the measured cross-section is ≤0.9, the cross-section shape needs to be measured again. The specific steps for similarity measurement are: (1) Scaling both cross-section figures proportionally in each direction to normalize the area; (2) Finding the geometric centers of the two figures respectively, and making several centers coincide by non-rotating translation and dragging; (3) The overlapping area of ​​the two figures at this time is the similarity.

[0057] By analyzing historical data, riverbed stability is determined. When the riverbed is stable, an appropriate river flow dynamics equation is selected based on empirical information regarding cross-sectional shape, hydraulic gradient, and flow velocity distribution. When the riverbed is unstable, a riverbed regression model for the entire assimilated river section needs to be established, incorporating additional inputs such as sediment content, upstream soil erosion, typical cross-sectional flow velocity, and time.

[0058] This invention reconstructs the 3D topography of the entire assimilated riverbed using local interpolation, piecewise smooth regression, and overall stitching. The model employs the sum of Wasserstein distance and interpolation error as the loss function and introduces a 3D topography data interpolation algorithm based on Wasserstein generative adversarial networks. Building upon the existing high-resolution DEM dataset and the 3D topography data generated in the previous step, a Terrain-CGANs (Conditional Encoder-Decoder Generative Adversarial Networks) is constructed and trained to generate local riverbed topography from topographic features. The generator G includes an "encoder-decoder" module consisting of 5 convolutional layers (conv) and 5 deconvolutional layers (deconv) to extract potential deep geospatial knowledge. In the discriminator D, the sampled riverbed topography map and the corresponding complete map are first stitched together, and then a binary classification result is output through convolution.

[0059] Step 3: Selection of River Flow Model

[0060] The appropriate mathematical model is selected based on the stability, regularity, and uniformity and stability of the flow during the assimilation period of the assimilation section. For complex and unsteady non-uniform flows, simplified equations of the Navier-Stokes equations are used for assimilation. These simplified equations include four turbulence models: the standard k-ε model, the RNG k-ε model, the realizable k-ε model, and the Reynolds stress model. For straight and regular channels, the Saint-Venant equations are used for data assimilation when the flow velocity is stable.

[0061] Step four: Install water level and flow velocity monitoring instruments in the upstream of the assimilation section to achieve full-time and spacetime four-dimensional variational assimilation of the assimilation section and the equations. For the Saint-Venant equations, a neural network is used for assimilation.

[0062] Water level and flow velocity measurement: Water level is measured using a lidar level gauge, and flow velocity is measured using a phased array acoustic Doppler profiler. Water level and flow velocity sensors, embedded devices, and a computing service center are deployed at selected cross-sections (more sampling cross-sections may be added for higher accuracy) to form an assimilation system. The number of sampling cross-sections is determined based on accuracy requirements, and the water depth and flow rate at these cross-sections are obtained from the sensors as boundary conditions for the model. More specifically, the water depth and flow rate at the upstream and downstream cross-sections are used as boundary conditions. If only the upstream cross-section data is used as the neural network boundary condition, the average absolute errors for unit width water depth and unit width flow rate in the domain are 0.294 and 0.025, respectively. If both upstream and downstream cross-sections are used, the errors are 0.136 and 0.023, respectively. If the data from the upstream and downstream cross-sections are combined with the initial full-section water level and flow rate, the errors are 0.064 and 0.013, respectively. The neural network prediction accuracy increases with the number of sampling cross-sections. An embedded system was used to develop a water level and flow sensor access, measurement, and control system. The embedded system was developed using the ARM Cortex series Cortex-A7, the Linux operating system, and the MySQL database.

[0063] A flow velocity measuring instrument was used to measure the flow rate. Based on the idea of ​​embedding physical information into a neural network, an equivalent physical information neural network of the Saint-Venant equations was constructed. The neural network structure was optimized and network parameters were obtained through methods such as spatiotemporal scaling and adjusting equation weights. The simulation accuracy of the neural network model was verified. The neural network that met the accuracy requirements was then deployed in the field. Details are described below.

[0064] Step 5, the neural network-based water level-discharge assimilation method, includes the following steps:

[0065] Step 1, Neural Network Assimilation Model Construction. A physical information neural network (PINNs) is used to construct an assimilation model constrained by the Saint-Venant equations, water level at the sampling section, and flow rate. This includes the following steps:

[0066] like Figure 2As shown, a neural network consists of several layers. The first layer is the input layer, representing the input variables of the entire network. The last layer is the output layer, representing the processing result of the network. All the layers in between are hidden layers. Each layer consists of several nodes. Each node in the hidden layer receives the output of the previous layer, processes it, and outputs the result to the next layer. Therefore, each node in the neural network in the diagram represents a processing function. Each processing function represented by a node contains several parameters to be determined. Once the parameters are determined, the entire neural network is determined. The process of determining the parameters is the optimization process of backpropagation.

[0067] This invention uses the symbol u θ Let (x) represent a neural network. We expect the function u θ The expressed neural network can handle fixed tasks. The function u θ The parameter x represents the input of the neural network. The parameter θ is the set of parameters of the function at each node of the entire neural network. The goal is to determine the parameter θ to determine the function u. θ This allows for the use of intelligent tools to determine whether a given prediction meets the objective. To achieve this, the neural network is trained given a training set with N pre-labeled sample points. Where x i This represents the i-th input, y i x represents i The corresponding output. Our goal is to get u θ (x i Approaching y i That is, the neural network for x i The nonlinear mapping with y i The results are close. Therefore, we need to solve the following optimization problem:

[0068]

[0069] The learning process is essentially the process of solving the optimization problem of the above formula. In the above formula, u... θ (x i ) represents the output of the neural network, y i This represents the accurate output label corresponding to the input. In function fitting, x... i You can y i Consider x as the input set i The analytical solution, u θ (x i ) represents the input set x i Predicted output obtained through neural network

[0070] Physics-informed neural networks (PINNs) differ from the general neural networks mentioned above in that their training set does not contain any data points related to the input x. i One-to-one corresponding label y i It is impossible to calculate the loss function by comparing the label value and the predicted value using supervised learning. Input x i Prediction is obtained through neural network. Through the Automatic differentiation can obtain Construct functions that satisfy physical constraints using the prediction and its differential. As a loss function, F is continuously optimized by adjusting the neural network parameters θ until it approaches 0. When F is sufficiently small, it can be considered that the physical law is satisfied within the domain.

[0071] We input the labeled boundary values ​​as constraints. By defining a loss function based on the boundary conditions and physical information, the problem of solving the differential equation is transformed into finding a set of parameters that minimizes the loss function, thus converting it into an optimization problem. The gradient descent algorithm can then be used to solve this problem, yielding an approximate solution that satisfies the boundary conditions to a certain extent.

[0072] The core network structure of PINNs is as follows: Figure 3 As shown, the output This represents the neural network prediction value. This represents the partial differential condition that needs to be satisfied, where N represents the combination operator, and u t＝0 and u x＝0 This represents the analytical solution at the boundary, and the loss function consists of the boundary term loss MSE. u With partial differential physical information loss (MSE) f composition. Let u represent the neural network prediction value of the i-th point sampled on the boundary u. i This indicates the corresponding accurate label; This represents the partial differential constraints at points within the domain. The summation represents the loss function constructed using the mean squared error function. Physical rules are incorporated into the loss function, and the partial derivatives are calculated using the automatic differentiation function of the neural network. By combining boundary constraints and physical constraints, the problem is transformed into an optimization problem. A set of suitable neural network parameters is found to fit the physical system, mapping the input to the corresponding output. Collecting river flow data is costly and inevitably faces the dilemma of drawing conclusions based on partial information. With limited data, such as missing data from upstream sections at a certain moment, cumulative errors can occur downstream. Neural network solutions aim to find a set of overall neural network parameters to fit the nonlinear equations, effectively avoiding this problem.

[0073] The Saint-Venant system of equations is a set of partial differential equations describing the motion of non-steady, gradually varying water flows in channels and other shallow bodies of water with free surfaces. It consists of a continuity equation reflecting the law of conservation of mass and an equation of motion reflecting the law of conservation of momentum.

[0074] The one-dimensional Saint-Venant equations describing the gradually changing, unsteady flow motion in a river channel are as follows:

[0075] Continuity equation:

[0076] Dynamic equation:

[0077] In the formula, x and t represent the flow rate (m) and time (s), respectively, and are independent variables; A is the cross-sectional area; Q is the flow rate through the cross-section; B T Z represents the water storage width (m); Z represents the water level (m); q L Side inflow (m) 2 / s), inflow is positive, outflow is negative; v x For the side inflow q L The velocity component along the direction of water flow (m / s); g is the acceleration due to gravity (m / s²). 2 K is the flow modulus. R is the hydraulic radius (m), and n is the roughness coefficient.

[0078] This invention combines a physical information neural network method to solve the Saint-Venant equation, and the process is as follows:

[0079] Solving the Saint-Venant equations using a physical information neural network, the network structure is as follows: Figure 4 A dual-output structure is adopted, sharing network parameters and automatically differentiating to obtain partial derivatives. The differential terms are linearly combined according to the constraints of the continuity equation and the dynamic equation to construct the loss function, and the neural network parameters are searched to minimize the loss function, thus transforming the equation-solving problem into an optimization problem.

[0080] like Figure 4 As shown, time t and distance x from the upstream starting section are independent variables, while unit width water depth h and unit width flow rate q are dependent variables. and Let represent the neural network predicted values, and let use automatic differentiation to obtain the partial derivatives of the predicted values ​​with respect to the independent variables. Sample the i input points at the boundary The corresponding unit width water depth h and unit width flow rate q are used for training boundary constraints, and u is used to distinguish f, where u represents the extracted boundary conditions, for a total of N. u There are 100 points, and these points are labeled. This represents the difference between the neural network's predicted value and the theoretical value. This is the predicted value for water depth per unit width. This is the predicted value for single-width flow. The input j values ​​obtained by sampling from the Latin hypercube within the domain are... For constraints on continuity and dynamic equations, the sampling points used for boundary constraints are also subject to equation constraints. f indicates sampling within the domain, with a total sampling of N. f There are several points that are unlabeled, meaning they do not have corresponding unit width depths or unit width discharges. During the analysis, it was found that the continuity equation contributes little to the loss function and cannot provide effective constraints. Therefore, a balancing weight λ is added to this term, ultimately yielding the overall expression for the loss function:

[0081]

[0082] Updating the gradient through backpropagation based on the loss function can continuously reduce the loss function. When the loss function is sufficiently small, it can be considered that the boundary constraints and physical equation constraints are satisfied. In the formula... and These represent the neural network predictions of unit width water depth and unit width flow rate, respectively. This represents the corresponding partial derivative term obtained by automatic differentiation. N is sampled from the initial and boundary points. u Each input point, along with its corresponding unit width depth h and unit width discharge q, is used to train the boundary value constraints. This represents the difference between the neural network's predicted value and the theoretical value under the constraints of boundary conditions (boundary conditions + initial conditions). N is obtained by sampling from a Latin hypercube within the domain. f Several unlabeled input points are used as constraints for the continuity and dynamic equations. It's important to note that the constraint terms in the equations are also trained on the sampled points used for boundary constraints. The triangular labels above the variables represent predicted values, MSE indicates that the mean squared error function is used when calculating the loss, and N... f With N u The range of influence is represented by λ, which represents the added balancing weight coefficient. The gradient is updated via backpropagation based on the loss function, continuously decreasing the loss function. When the loss function is sufficiently small, it is considered to satisfy the boundary value constraints and physical equation constraints. After calculating the loss of the continuous equations, the loss of the dynamic equations, and the boundary value condition loss through forward propagation of the neural network, the weight parameter λ is added to balance the contributions of each term when these three terms are summed to obtain the total loss function. Subsequently, the gradient is calculated using backpropagation of the total loss function to update the neural network parameters.

[0083] Because of the dual-output structure, more neurons are needed in the hidden layers for non-linear mapping. The more layers a neural network has, the more difficult it becomes to train; increasing depth can lead to the vanishing gradient problem and also increases computational burden. Therefore, it's crucial to minimize computation and reduce the number of network layers. In practice, a fully connected structure with 3 hidden layers and 200 neurons per layer was used to construct the neural network.

[0084] For natural river channels, the Saint-Venant equation spans a large range in both time and space. Existing literature has not considered the issue of this dimensional range, and directly using a neural network to fit the network will lead to non-convergence. The time scale is 86,400 seconds, and the spatial scale is 20,000 meters. In contrast, the unit width and water depth only increase from 4 meters to 6 meters. The dependent variable changes on a very small scale: the increment rate in the time direction is less than 2 / 86,400, the increment rate in the spatial direction is less than 2 / 20,000, and the average increment rate is less than 3 × 10⁻⁶. -5 Both the continuity equation and the dynamic equation in the Saint-Venant equations contain partial derivatives. Therefore, a scaling transformation is first added to the neural network. A spatiotemporal mapping is added to the network input layer to scale the input, mapping the input to a denser region and accelerating the convergence of the neural network. (The experiment revealed that the independent variable of the simulated river flow varied greatly, while the dependent variables, such as water depth and flow rate, varied little, resulting in a large discrepancy. Ignoring this issue would lead to poor training results. Therefore, the idea was to first scale the independent variables (input layer) to a denser space, which would not change the derivative terms. This approach also facilitated model convergence and yielded better final results. The experimental data showed that without scaling, with 10,000 points in the domain, the final evaluation index (average absolute value loss per unit width and depth) was 0.35 (almost unusable); with the same experimental conditions, the index dropped to 0.064.) The Saint-Venant equations, also known as the Saint-Venant equation system, are actually composed of continuous equations and dynamic equations. While mapping the input to a denser region can accelerate neural network convergence, it does not change the order of magnitude of the partial derivatives. Therefore, a weighting coefficient was added before the loss function to control the contribution of different equations to the loss function. Analysis of the Saint-Venant equation system revealed that the continuous equations consist entirely of partial derivative terms with extremely small magnitudes. To reflect the constraint of the continuous equations on the overall loss function, a coefficient of 1×10 was added before them. 10 The value of λ in the loss function is chosen to balance the boundary condition constraints, continuity equation constraints, and dynamic equation constraints, making them on the same order of magnitude as the boundary loss and dynamic equation. A single-network structure has fewer parameters, and both outputs are obtained from the same neural network. Using a single-network dual-output structure with parameter sharing helps improve network stability.

[0085] Step 2: Verify the correctness of the assimilation model using the four-point difference method. If correct, proceed to the next step; otherwise, return to the previous step and optimize the assimilation model by optimizing the neural network structure, iterative algorithm, loss function, etc. For example, update the neural network parameters using the gradient descent algorithm.

[0086] Specifically, using MATLAB R2016b, the simplified Saint-Venant equations were solved numerically using the Preissman four-point implicit difference method. The values ​​of h(t,x) and q(t,x) were obtained. Time t was divided into 865 time nodes at 100-second intervals, and x was divided into 201 cross-sections at 100-meter intervals. The water depth h (865*201 data points) and unit width flow rate q (865*201 data points) corresponding to each spatiotemporal node were obtained using the four-point implicit difference method.

[0087] Step 3: Deploy the validated model in the field and update it in the embedded system for water level and flow rate assimilation. After the model passes validation, deploy it and update it in the embedded system, using the cross-sectional data selected as the boundary value condition as input for data assimilation.

[0088] Step 4: Based on the water level and flow rate of the upstream determined cross-section, the water level and flow rate of any downstream cross-section are calculated in real time using a neural network assimilation model. The water level and flow rate obtained in Step 4 can be used to calculate the water level and flow rate of any downstream cross-section using only the water level and flow rate of the upstream determined cross-section, although the accuracy will be lower. The benchmark uses the unit width water level and flow rate of the two upstream and downstream cross-sections. After processing by the model, the water level and flow rate of any cross-section can be obtained. Adding sampling cross-sections to the benchmark can improve the model accuracy, while reducing constraints will reduce the model accuracy.

[0089] Based on the above method, the present invention also provides a river water level and flow rate assimilation system, including water level and flow velocity sensors, embedded devices, and a software system installed in the embedded devices. The software system includes a terrain measurement module, a cross-sectional data acquisition module, a neural network assimilation model construction module, a model verification module, a model deployment module, and a water level and flow rate output module. The terrain measurement module is used to implement step two of the method by linking a UAV / unmanned surface vessel with a GNSS navigation system. The cross-sectional data acquisition module is used to implement step four using sensors. The neural network assimilation model construction module is used to implement step five-1. The model verification module is used to implement step five-2. The model deployment module is used to implement step five-3, deploying the model into the embedded device. The water level and flow rate output module is used to implement step five-4, ultimately outputting the water level and flow rate of any downstream cross-section.

[0090] Example:

[0091] The indoor testing model used in this embodiment of the invention has the following requirements: PyTorch version 1.11, Python version 3.8, and experiments are conducted on an NVIDIA RTX 3060 GPU.

[0092] The neural network structure uses 3 hidden layers, each with 200 neurons, and the activation function is tanh. It employs the mean squared error function, the Adam optimizer, a learning rate of 0.0001, and regularization with a parameter of 0.0001.

[0093] The simulation scenario is a 20-kilometer-long rectangular unsteady flow river. Water levels and flows from the upstream and downstream sections are selected for 0-24 hours. Water levels and flows at all sections at time 0 are also selected as known. Additional sections can be added as boundary conditions based on accuracy requirements. A total of 1931 points are sampled as boundary constraints, and 100,000 points are sampled using a Latin hypercube for physical constraints in the domain space. A neural network assimilation model is trained based on these constraints, with 10,000 batches trained over approximately 20 minutes. The mean absolute error (MAE) is used to quantitatively analyze the model's performance. The absolute value of the neural network predictions minus the difference method is calculated for each point uniformly distributed within the domain, and then the average value of all points is calculated.

[0094] Ablation experiments were conducted on the network with and without scaling to observe the decreasing trend of the loss function. The aim was to verify the effectiveness of the proposed input scaling transformation through ablation experiments. A comparison was made between loss functions with and without scaling. Figure 5 As shown.

[0095] As shown in the figure, the horizontal axis represents the number of iterations, and the vertical axis represents the magnitude of the loss function during training. Adding scale scaling to the neural network results in faster training, and the loss decreases by two orders of magnitude when it stabilizes, effectively reducing the convergence speed. The experimental conclusions are consistent with the analysis results; adding scale scaling can effectively accelerate neural network convergence under large-scale input conditions.

[0096] An ablation experiment was conducted to demonstrate whether adjusting the equation weights in the network improves accuracy. Without weight adjustment, after 10,000 iterations, the relative error per unit width for water depth was 0.16, and the relative error per unit width for flow rate was 0.08. The formula for calculating the mean absolute error is: In the formula, N represents the number of verification points in the uniform sampling. Let y represent the neural network prediction output for the i-th validation point. i This represents the difference method result for the i-th validation point. Comparing the errors of 0.064 and 0.013 with the adjusted weights, the results are excellent and represent significant progress. This is because the constraint power is insufficient when the continuous equation terms are too small. By comparing the mean absolute error, it can be proven that initializing all loss terms to the same order of magnitude improves convergence.

[0097] The Saint-Venant equations were solved using the Preissman four-point implicit difference method, and the results were used to validate the neural network method.

[0098] Simulated operating conditions: A single river channel with a regular rectangular cross-section, 20 kilometers in length, roughness coefficient n = 0.025, and gravitational acceleration of 9.81 m / s². 2 The initial water depth is 4 meters, the initial flow rate is 0, the cross-sectional spacing is 100 meters, the time step is 100 seconds, and the total simulation time is 24 hours.

[0099] Boundary conditions: The upstream water depth gradually increases from 4 meters to 6 meters within 24 hours, while the downstream water depth remains constant at 4 meters. There is no lateral flow. The Saint-Venant equation is simplified based on the actual scenario:

[0100] Continuity equation:

[0101] Momentum equation:

[0102] A: Cross-sectional area; Q: Flow rate through the cross-section; u: Flow velocity at the cross-section; g: Acceleration due to gravity; Z: Water level; S f Friction ratio decrease

[0103] Consider a one-dimensional rectangular river channel and simplify further:

[0104] Continuity equation

[0105] Dynamic equations

[0106] In the formula, h is the water depth per unit width (m); q is the flow rate per unit width (m³). 2 / s), abbreviated as unit width discharge; n is the channel roughness; g is the acceleration due to gravity. Analysis of the Saint-Venant equation reveals that its independent variables are only the distance from the starting point x and time t, while the dependent variables are the unit width depth h and the unit width discharge q.

[0107] Using MATLAB R2016b programming, the simplified Saint-Venant equations were applied to the Preissman four-point implicit difference method to obtain the values ​​of h(t,x) and q(t,x). The numerical solution obtained by the difference method was regarded as the analytical solution and used to compare the physical information neural network method.

[0108] Using MATLAB, the 20km long river channel was first divided into cross-sections at 100-meter intervals, resulting in 20000 / 100+1 = 201 cross-sections. A 24-hour simulation was then performed, with each time point defined at 100-second intervals, resulting in 24*60*60 / 100+1 = 865 time points for each cross-section. Unit width depth data (865*201 data points) and unit width discharge data (865*201 data points) for all cross-sections were calculated using four-point implicit difference. Using the data obtained by the difference method as a baseline, a neural network was then used to calculate the corresponding unit width depth data (865*201 data points) and unit width discharge data (865*201 data points) for the corresponding time at each cross-section.

[0109] The final result is represented using the mean absolute error:

[0110]

[0111] In the formula, N represents the number of sampling points, which is 865*201. Let y(t) represent the output value of the neural network at the i-th sampling point. i ,x i ) represents the result of the four-point implicit difference method for the i-th sampling point.

[0112] Once the validated model is successfully deployed in the field, an embedded system will be used to collect data from selected cross-sections. The model, which has already passed indoor validation, will then be deployed to the computing service center. The field deployment must meet the following requirements: the embedded system must store historical water level and flow rates at the selected cross-sections, with a sampling interval of less than 100 seconds, a storage space greater than 1GB, and network communication capabilities. The computing service center server must have a GPU with more than 6GB of video memory. At the computing service center, in conjunction with the embedded system, the water depth and flow rates at the selected cross-sections will be measured. A neural network based on the Saint-Venant equations will be trained to construct a river water level and flow rate assimilation model. This model can then calculate the water depth and flow rates at any cross-section at any given time.

[0113] At least one cross-section needs to be selected and the water level and flow rate measured by the embedded device should be used as the boundary condition. At the same time, the accuracy of the model can be improved by increasing the number of instruments and the number of sampling cross-sections, which is in line with the general rules of assimilation models.

[0114] We verified the effectiveness of the invention under both infinite and finite boundary conditions:

[0115] Infinite boundary:

[0116] A rise in upstream water level leads to an increase in downstream flow, which in turn causes a rise in downstream cross-sectional water level. Considering a sufficiently long river, the initial rise in water level will dissipate as it propagates through the river, and will not cause a change in water level at distant cross-sections within a finite time period; this situation is called an infinite boundary. A neural network was used to simulate unsteady flow in a river with an infinite boundary, achieving an average absolute error of 0.064 per unit width for water depth and 0.013 per unit width for flow rate.

[0117] like Figure 7 As shown, the horizontal axis represents time variation, and the vertical axis represents the distance from the initial cross-section. A two-dimensional color graph is used to compare the neural network method and the differential numerical method. The left side shows the simulation results of the 4-point implicit difference method, and the right side shows the simulation results of the neural network method. The upper part represents the simulation of water depth per unit width, and the lower part represents the simulation of flow rate per unit width. The total simulation time is 24 hours, and the river section is 20 kilometers long. The initial water depth at the upstream starting point is 4 meters, which increases to 6 meters within 24 hours. The upstream water level rises, leading to an increase in water level and flow rate at the downstream cross-section at the next moment. The changes in water level and flow rate in space and time have a time delay and are not real-time changes. Considering the infinite boundary problem, the water depth at 20 kilometers does not change, and the results are consistent with expectations. The two-dimensional color graph shows that the fitting results obtained by the neural network method and the implicit difference method are consistent.

[0118] The purpose of slicing the plane is to observe the specific fitting effect at a microscopic level. The overall state of the river channel is compared at 300 seconds, 3000 seconds, 30000 seconds, 60000 seconds, and 86400 seconds. Simultaneously, the changes at three cross-sections at 500 meters, 5000 meters, and 20000 meters are compared over 24 hours.

[0119] like Figure 8 As shown, the solid line represents the result calculated by the four-point implicit difference method, and the dashed line represents the result calculated by the neural network. Microscopic observations of the fitting effect from both fixed-time and cross-sectional dimensions show a good fitting effect, fully demonstrating that the neural network of this invention can adapt to large-scale spatiotemporal variations in input.

[0120] Finite boundary:

[0121] The situation where changes in water level at an upstream section propagate to the downstream section within a finite time, causing changes in water level downstream, is called a finite boundary condition. A neural network simulates unsteady flow in a river under finite boundary conditions, with an average absolute error of 0.069 for unit width and depth, and an average absolute error of 0.043 for unit width and flow rate.

[0122] Considering the influence of boundary conditions on channel flow, a channel length of 5 kilometers is chosen to ensure that depth variations do not dissipate at an infinitely far boundary. A neural network is trained, and the error distribution is observed. Figure 9It can be seen that the error of the neural network fitting increases with time, and the error is higher than that at the boundary, which is due to the strong constraint effect imposed by the boundary conditions at the boundary.

[0123] The boundary conditions refer to the data from the downstream and upstream cross-sections. As can be seen from the above process, the solution of this invention can be used for both infinite boundary cases where upstream changes do not cause significant downstream changes within a finite time, and finite boundary cases where significant changes occur.

[0124] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A natural river water level and flow simultaneous assimilation method, characterized by, It comprises the following steps: Step 1, determining the assimilation river section Step 2, typical cross-section water and underwater topography measurement and generation of the whole riverbed topography of the assimilation section Obtain the topography below the water surface, establish the relationship between the water level / water depth and the cross-section area; Step 3, selection of river flow model According to the stability, regularity of the assimilation river section and the uniformity and smoothness of the flow during the assimilation period, the corresponding mathematical model is selected; for straight and regular river channel, when the flow velocity is stable, the Saint-Venant equation set is used for data assimilation; Step 4, setting up water level and flow velocity monitoring instruments on the upstream of the assimilation river section to collect data According to the accuracy requirement, the number of sampling sections is determined, the water level and flow velocity sensors, embedded devices and calculation service center are arranged on the selected sections to form an assimilation system; and the water depth and flow on the section are obtained by the sensor as the boundary conditions of the model; Step 5, neural network water level and flow assimilation method, comprising the following steps: Step 1, construction of neural network assimilation model, using physical information neural network to construct an assimilation model with Saint-Venant equation set, sampling section water level and flow as constraint conditions; comprising the following steps: The one-dimensional Saint-Venant equation set describing the gradual change of unsteady flow in the river channel is as follows: Continuity equation: Dynamical equations: where x, t are flow and time respectively; A is cross-sectional area; Q is flow through the cross-section; B T represents the width of the regulation storage; Z is the water level; q L is the lateral inflow, positive for inflow and negative for outflow; v x is the lateral inflow q L is the velocity component along the flow direction; g is the acceleration due to gravity; K is the discharge modulus, R is the hydraulic radius and n is the roughness. Using physical information neural network to solve Saint-Venant equations, using single network double output structure, sharing network parameters, the partial derivative of the predicted value to the independent variable Sampling i input points at the boundary And the corresponding single-width water depth h and single-width flow q are used to train the boundary constraints. The difference between the neural network predicted value and the theoretical value is represented by The single-width water depth predicted value is The single-width flow predicted value is For continuous equation and dynamic equation constraints, the sampling points for boundary constraints are also subjected to equation constraints. The differential terms are linearly combined according to the continuous equation and dynamic equation constraints, and the loss function is constructed as follows: In the formula, MSE represents using a mean square error function when calculating a loss, N f With N u represents a range of action, and λ represents a balance weight coefficient added Find the neural network parameters to minimize the loss function; Step 2, according to the four-point difference method, the correctness of the above assimilation model is verified, if correct, go to step 4, otherwise return to step 3 to optimize the assimilation model; Step 3, the tested model is deployed on site, updated in the embedded system and applied to water level and flow assimilation; Step 4, according to the water level and flow of the determined section on the upstream, the neural network assimilation model is used to obtain the water level and flow of any section on the downstream in real time.

2. The natural channel water level flow simultaneous assimilation method according to claim 1, characterized by, In the neural network of step 1, the network input layer is added with space-time mapping to scale the input scale, and the input is mapped to a more dense interval.

3. The natural channel water level flow simultaneous assimilation method according to claim 1, characterized by, In step 1, a neural network is constructed using a full connection structure with 3 layers of hidden layers and 200 neurons in each layer.

4. The natural channel water level flow simultaneous assimilation method according to claim 1, characterized by, In step 4, at least one section is selected to combine the water level and flow measured by the embedded device as the boundary condition.

5. The natural channel water level flow synchronization assimilation method of claim 1, wherein, The step 2 comprises the following process: Typical cross-section is selected to measure the water surface and underwater topography by using the combination of water surface unmanned aerial vehicle carrying laser radar and underwater unmanned ship; when the riverbed space-time change is large, the corresponding section is selected for measurement; when the similarity of the next section to the measured section is ≤0.9, the section shape measurement needs to be performed again; the reconstruction of the three-dimensional topography of the whole assimilation riverbed is realized.

6. The natural channel water level flow simultaneous assimilation method according to claim 5, characterized by, The similarity is calculated by the following steps: (1) normalize the area by scaling each direction of the two cross-section figures proportionally; (2) find the geometric centers of the two figures respectively, and make the centers coincide by non-rotating translation dragging; (3) the coincidence area of the two figures is the similarity.

7. The natural channel water level flow simultaneous assimilation method according to claim 5, characterized by, The reconstruction of the three-dimensional topography of the assimilation riverbed is performed by the following steps: A three-dimensional terrain data interpolation algorithm based on Wasserstein generative adversarial network is introduced by using the sum of Wasserstein distance and interpolation error as the loss function; based on the generated terrain three-dimensional data on the existing high-resolution DEM data set, starting from the terrain features, the Terrain-CGANs for generating local riverbed terrain from terrain features is constructed and trained, which contains an "encoding-decoding" module composed of 5 layers of convolutional layers and 5 layers of inverse convolutional layers in the generator G to extract deep geographic spatial knowledge; in the discriminator D, the sampled riverbed terrain map and the corresponding complete map are first spliced, and then the convolution is performed to output the binary classification judgment result.

8. A natural river water level and flow rate synchronous assimilation intelligent system, comprising a water level and flow rate sensor, an embedded device, and a software system arranged in the embedded device, characterized in that: The natural river water level and flow simultaneous assimilation method of any one of claims 1-7 is implemented, wherein the software system comprises a terrain measurement module, a cross-section data acquisition module, a neural network assimilation model construction module, a model verification module, a model deployment module, and a water level and flow output module; the terrain measurement module is used to realize the content in step two by linking the unmanned aerial vehicle / unmanned ship with the GNSS navigation system, the cross-section data acquisition module is used to realize the content in step four by using sensors, the neural network assimilation model construction module is used to realize the content in step 1 of step five, the model verification module is used to realize the content in step 2 of step five, the model deployment module is used to realize the content in step 3 of step five, and the model is deployed into an embedded device; and the water level and flow output module is used to realize the content in step 4 of step five, and finally outputs the water level and flow of any cross-section in the downstream.

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