CN115471679A - Method and intelligent system for synchronously assimilating water level and flow of natural river - Google Patents

Method and intelligent system for synchronously assimilating water level and flow of natural river Download PDF

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CN115471679A
CN115471679A CN202210610006.5A CN202210610006A CN115471679A CN 115471679 A CN115471679 A CN 115471679A CN 202210610006 A CN202210610006 A CN 202210610006A CN 115471679 A CN115471679 A CN 115471679A
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方卫华
钟华
徐孟启
肖城
戴佳琦
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Nanjing Hydraulic Research Institute of National Energy Administration Ministry of Transport Ministry of Water Resources
Nanjing Water Conservancy and Hydrology Automatization Institute Ministry of Water Resources
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Abstract

The invention discloses a method and an intelligent system for synchronously assimilating water level and flow of a natural river channel, aiming at the problems of high automation cost of the flow and water level monitoring section of the natural river channel, difficulty in calibration of a flow velocity model, unstable relational expression and the like. The method has advanced technology and strong operability, and has very important significance for flood control, drought resistance and water resource protection.

Description

Method and intelligent system for synchronously assimilating water level and flow of natural river
Technical Field
The invention belongs to the technical field of flood prevention and disaster reduction, water resource management and intelligent water conservancy crossing, and particularly relates to a method and an intelligent system for synchronously assimilating water level and flow of a natural river channel.
Background
In recent years, under the influence of global climate change, flood disasters frequently occur, which brings serious threats to social economy and life safety of people, and meanwhile, along with the improvement of intensive utilization requirements on water resources, how to quickly and accurately obtain the water level, the flow speed and especially the flow of a river becomes a technical problem which needs to be solved urgently. Traditional river flow methods include manual shipborne surveying, bridge surveying, cableway, and wading surveying, among others. The basic principle is that a plurality of vertical lines are arranged on a flow measurement section, the water depth is measured at each vertical line, the water depth is measured point by a current meter, so that the average flow velocity of the vertical lines is obtained, the area of the section and the average flow velocity of the section are further obtained, and the flow is obtained by the product or integral of the area of the section and the average flow velocity of the section.
With the continuous development of computer technology, artificial intelligence technology has become a focus of research of people, and artificial intelligence energization is also needed for flood prevention and disaster reduction and water resource management. In fact, with the development of embedded systems, end edge cloud cooperative architectures and sensor technologies, it has become practical to implement data assimilation of model-measured data, which will significantly improve the reliability of data acquisition and greatly save investment and operating costs of equipment and facilities. Neural networks, one of the core technologies of artificial intelligence, have been the research focus of artificial intelligence in solving mathematical models describing objective physical laws.
River water flow equations are many, and a k-epsilon model based on Reynolds average, a shallow water equation, a Saint-Wein equation set and the like are common. The solution of the equations is complex, taking the numerical solution of the saint-wien equation set as an example, the solution mainly comprises a characteristic line method, a direct difference method, a finite volume method and the like. These numerical simulation methods have high requirements for initial conditions and require partitioning of grid storage variables, and once conditions change, recalculation is required. The numerical method is difficult to be compatible with the current mainstream artificial intelligence architecture, language and system hardware and software equipment, and is particularly difficult to be matched with intelligent methods such as transfer learning, knowledge distillation, meta-learning and the like.
In the aspect of instrument monitoring, water level and flow velocity monitoring instrument equipment must be arranged on a certain section to obtain data of the section, and if all data of a certain river reach are to be obtained, the prior art requires that a water level meter and a flow velocity meter are arranged on each section, so that the cost is high, the error of calculated flow is large, the operation and maintenance are inconvenient, and the data processing difficulty and the risk of personnel and equipment are increased.
The invention discloses a data assimilation method, which is characterized in that on the premise of obtaining topographic data of a certain section in the early stage, a monitoring section is arranged at the upstream, and a water level and flow rate monitoring instrument is arranged, so that the water level and flow rate of any section of the whole river reach can be obtained through the assimilation method, and the difficulty that the flow rate needs to be converted into the flow rate of the section in conventional monitoring is avoided. And along with the increase of increase actual measurement section quantity, the water level and the flow precision of arbitrary section that this assimilation system obtained also can constantly improve. The invention realizes the organic combination of instrument monitoring and mathematical models through an intelligent neural network, and has the advantages of strong theoretical basis, practicality, reliability, popularization and the like.
Disclosure of Invention
The invention discloses a method and an intelligent system for synchronously assimilating water level and flow of a natural river channel, aiming at the problems of high automation cost of the flow and water level monitoring section of the natural river channel, difficulty in calibration of a flow velocity model, unstable relational expression and the like. The method has advanced technology and strong operability, and has very important significance for flood control, drought resistance and water resource protection.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a method for synchronously assimilating water level and flow of a natural river comprises the following steps:
step one, determining river reach needing assimilation
Step two, measuring the water and underwater topography of the typical section and generating the integral riverbed topography of the assimilation section
Acquiring a terrain below a water surface, and establishing a relation between a water level/water depth and a section area; the single-wide-flow single-wide water depth measuring device is used for constructing a sensor to measure the relation between the flow water depth and the single-wide-flow single-wide water depth;
the method is characterized in that a typical section is selected, a mode that an overwater unmanned aerial vehicle carries a laser radar and an ultrasonic unmanned ship is combined is adopted for overwater and underwater topographic survey, and when the space-time change of a riverbed is large, a corresponding section is selected for surveying. The similarity measurement adopts the cross section of the river channel in the vertical average flow velocity direction under the water surface at the same moment. The method comprises the following specific steps: (1) Scaling the two water cross section graphs for area normalization; (2) Respectively finding out the geometric centers of the two figures, and enabling the centers to coincide by non-rotating translation dragging; and (3) at the moment, the overlapping area of the two graphs is the similarity.
When the similarity between the next section and the measured section is less than or equal to 0.9, the section shape measurement needs to be performed again. And analyzing the stability of the riverbed by combining historical data, and selecting an adaptive riverway water flow dynamics equation by combining empirical information of the section shape, hydraulic slope drop and flow velocity distribution when the riverbed is stable. When the riverbed is unstable, a regression model of the riverbed of the whole assimilation river reach is required to be established, wherein the regression model is additionally provided with the sediment content, the upstream water and soil loss, the typical section flow rate and the time as input. The method realizes the reconstruction of the three-dimensional topography of the riverbed of the whole assimilation river reach by adopting the modes of local interpolation, segmental smooth regression and integral splicing. (1) The model adopts the sum of Wasserstein distance and interpolation error as a loss function, and introduces a three-dimensional terrain data interpolation algorithm for generating a confrontation network based on Wasserstein. (2) Based on the Terrain three-dimensional data generated by the prior high-resolution DEM data set in one step, tertain-CGANs (Conditional Encoder-Decoder general adaptive Networks) for generating local riverbed Terrain by the Terrain features are constructed and trained starting from the Terrain features, and a generator G comprises an encoding-decoding module consisting of 5 convolutional layers (conv) and 5 reverse convolutional layers (deconv) and is used for extracting possible depth geospatial knowledge. In the discriminator D, the sampled riverbed topographic map and the corresponding complete map are spliced, and the judgment result of the second classification is output through convolution.
Thirdly, selecting river water flow models
And selecting a corresponding mathematical model according to the stability and regularity of the assimilation river reach and the uniformity and stationarity of the water flow in the assimilation period. Simplified equations of Navier-Stokes equations are selected for assimilation of complex flow state and non-constant non-uniform flow, and the simplified equations comprise 4 turbulence models including a standard k-epsilon model, an RNG k-epsilon model, a realizable k-epsilon model and a Reynolds stress model. For a straight and regular river channel, data assimilation is carried out by adopting an Saint-Venn equation set when the flow velocity is stable.
And step four, arranging a water level and flow rate monitoring instrument at the upstream of the assimilation river reach to realize full-time-space 4-dimensional variational assimilation of the assimilation section and the equation, and adopting a neural network to assimilate the Saint-Venen equation set. Measuring the water level flow rate: the water level adopts a laser radar, and the flow velocity adopts a phased array acoustic Doppler profiler. Arranging a water level sensor, a flow velocity sensor, embedded equipment and a calculation service center on a selected section (which can be increased according to the precision requirement) to form an assimilation system; determining the number of sampling sections according to the precision requirement, and acquiring the water depth and the flow on the sections by adopting a sensor as boundary conditions of a model; (the water depth and flow on the two sections of the most upstream and the most downstream need to be acquired by adopting a sensor as boundary conditions, and the accuracy can be improved by increasing the sampling sections).
Constructing an equivalent physical information neural network of the Saint-Venn equation set by adopting a flow velocity measuring instrument according to the idea of embedding physical information into the neural network; optimizing a neural network structure and acquiring network parameters by methods of time-space scaling, equation weight adjustment and the like; testing the simulation precision of the neural network model; and deploying the neural network meeting the precision requirement on site.
Step five, the water level flow assimilation method of the neural network comprises the following steps:
step 1, establishing a neural network assimilation model, namely establishing an assimilation model by adopting a physical information neural network, wherein the assimilation model takes the Saint-Venen equation set and the water level and the flow of a sampling section as constraint conditions; the method comprises the following steps:
the one-dimensional saint-wien equation system for describing the river channel gradual change non-constant water flow motion is as follows:
the continuous equation:
Figure BDA0003672894890000031
the equation of power:
Figure BDA0003672894890000032
in the formula, x and t are respectively a flow and time; a is the area of the cross section; q is the flow through the cross section; b is T Indicating a regulation width; z is water level; q. q.s L The side inflow is positive, and the outflow is negative; v. of x For side inflow q L A velocity component in the direction of water flow; g is the acceleration of gravity; k is the flow modulus,
Figure BDA0003672894890000033
r is hydraulic radius, and n is roughness;
solving the Saint Vietnam equation by using a physical information neural network, sharing network parameters by adopting a single-network double-output structure, and predicting partial derivatives of values to independent variables
Figure BDA0003672894890000034
I input points to be sampled at the boundary
Figure BDA0003672894890000035
And corresponding single wide water depth h, singleThe wide traffic q is used to train the boundary constraints,
Figure BDA0003672894890000036
represents the difference between the predicted value and the theoretical value of the neural network,
Figure BDA0003672894890000037
the predicted value of the single-wide water depth is,
Figure BDA0003672894890000038
for single wide flow prediction, we will define the input j sampled by Latin hypercube in the domain
Figure BDA0003672894890000041
The sampling points for continuous equation and dynamic equation constraint and boundary constraint are also subjected to equation constraint, differential terms are linearly combined according to the continuous equation and the dynamic equation constraint respectively, and a loss function is constructed as follows:
Figure BDA0003672894890000042
where MSE denotes the use of a mean square error function in calculating the loss, N f And N u Representing the action range, and lambda represents the added balance weight coefficient;
searching neural network parameters to minimize a loss function;
step 2, checking the correctness of the assimilation model according to a four-point difference method, if the correctness is correct, entering step 4, and if the correctness is not correct, returning to step 3 to optimize the assimilation model;
step 3, completing field deployment of the qualified model, updating the qualified model in an embedded system, and applying the qualified model to water level flow assimilation;
and 4, determining the water level and the flow of the cross section according to the upstream, and obtaining the water level and the flow of any downstream cross section in real time based on a neural network assimilation model.
Further, the network input layer in the neural network of step 1 adds space-time mapping scaling input scale, and maps the input to a denser interval.
Further, in the step 1, a neural network is constructed by using 3 hidden layers and a full-connection structure of 200 neurons in each layer.
Further, at least one section is selected in the step 4 to be combined with the water level and the flow rate measured by the embedded device to be used as boundary conditions.
The invention also provides a synchronous assimilation intelligent system for the water level and the flow of the natural river channel, which comprises a water level sensor, a flow velocity sensor, embedded equipment and a software system arranged in the embedded equipment, wherein the software system comprises a terrain measurement module, a 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 for linking the unmanned aerial vehicle/unmanned ship to configure a GNSS navigation system to realize the content in the second step in the river water level flow assimilation method, the section data acquisition module is used for realizing the content in the fourth step by adopting a sensor, the neural network assimilation model construction module is used for realizing the content in the fifth step-1, the model verification module is used for realizing the content in the fifth step-2, the model deployment module is used for realizing the content in the fifth step-3, and the model is deployed into embedded equipment; and the water level flow output module is used for realizing the content in the step five-4 and finally outputting the water level and the flow of any downstream section.
The beneficial effects of the invention are as follows:
1. the invention adopts a neural network assimilation method, namely, the instrument measures the initial condition and the boundary condition of data actually, the neural network is used for solving the Saint-Venn equation set to realize data assimilation, and the water level and the flow of any downstream section can be obtained based on the water level and the flow of the upstream determined section. Experiments prove that the method has high accuracy of output data.
2. The accuracy can be effectively improved by adding the weight coefficient before the loss function, and the convergence of the neural network can be effectively accelerated by adding the scale scaling in the neural network.
3. The single-network double-output structure is used, the robustness of the network can be effectively improved through a parameter sharing method, and the network parameter quantity and complexity are reduced.
4. The method of the invention can be used for both the infinite boundary condition that the upstream change does not cause the downstream significant change within the limited time and the finite boundary condition that causes the significant change.
Drawings
Fig. 1 is a schematic overall flow diagram of a river water level flow assimilation method provided by the invention.
Fig. 2 is a schematic diagram of a neural network structure.
Fig. 3 is a schematic diagram of a core network structure of the PINNs.
Fig. 4 is a schematic diagram of the structure of the physical information neural network of the plaintenna equation.
FIG. 5 is a graph showing a comparison of training loss functions with and without scaling, wherein the dotted line shows no scaling and the solid line shows scaling.
Fig. 6 is a diagram illustrating the visualization effect of the single wide water level and the single wide flow obtained by the implicit difference method.
Fig. 7 is a schematic diagram comparing an implicit difference method with a neural network method of the present invention, wherein (a) is a schematic diagram of a single wide water depth under the implicit difference method, (b) is a schematic diagram of a single wide water depth under the neural network of the present invention, (a) is a schematic diagram of a single wide flow under the implicit difference method, and (d) is a schematic diagram of a single wide flow under the neural network of the present invention. And (c) is a schematic diagram of single wide flow under an implicit difference method.
Fig. 8 is a schematic diagram showing a fitting comparison between an implicit difference method and a neural network method of the present invention, wherein (a) is a schematic diagram showing a comparison between an implicit difference method and a single wide water depth obtained by a solution of the neural network of the present invention, (b) is a schematic diagram showing a comparison between an implicit difference method and a single wide flow obtained by a solution of the neural network of the present invention, (c) is a schematic diagram showing a comparison between a single wide water depth change of a cross section, and (d) is a schematic diagram showing a comparison between a single wide flow change of a cross section.
Fig. 9 is a bounded condition in which upstream water level flow changes cause downstream water level flow changes within a limited time, where (a) is a single-wide water depth schematic diagram under a bounded condition in an implicit difference method, (b) is a single-wide water depth schematic diagram under a bounded condition in a neural network of the present invention, (c) is a single-wide flow schematic diagram under an implicit difference method under a bounded condition, and (d) is a single-wide flow schematic diagram under a bounded condition in a neural network of the present invention. (e) Calculating single-wide water depth error distribution by using an implicit difference method and a neural network method under a bounded condition, and (f) calculating single-wide flow distribution by using the implicit difference method and the neural network method under the bounded condition.
Detailed Description
The technical solutions provided by the present invention will be described in detail with reference to specific examples, which should be understood that the following specific embodiments are only illustrative and not limiting the scope of the present invention.
The invention provides a river water level flow assimilation method, the flow of which is shown in figure 1, and the method comprises the following steps:
step one, determining river reach needing assimilation
And determining river reach needing assimilation. And influence factors influencing the cross section of the riverbed and the stability of the cross section can be analyzed according to hydrological, river vigor and geological conditions of the assimilation river reach.
Step two, measuring the water and underwater topography of the typical section and generating the integral riverbed topography of the assimilation section
An unmanned aerial vehicle/unmanned ship is adopted to configure a GNSS navigation system, a shore-based double-datum underwater multi-beam sounding system is combined to obtain the terrain below the water surface, and the relation between the water level/water depth and the section area is established; and the water level flow which can be used for being measured by the sensor in the subsequent process is converted into single-wide-flow single-wide water depth.
The method is characterized in that a typical section is selected, a mode that an overwater unmanned aerial vehicle carries a laser radar and an ultrasonic unmanned ship is combined is adopted for measuring the overwater and underwater topography, and when the space-time change of a riverbed is large, the corresponding section is selected for measuring. The cross section refers to the cross section of the river channel passing through water in the vertical average flow velocity direction under the water surface at the same moment. When the similarity between the next section and the measured section is less than or equal to 0.9, the section shape measurement needs to be performed again. The similarity measurement adopts the following specific steps: (1) Carrying out all-directional equal-proportion scaling on the two water-passing section graphs for area normalization; (2) Respectively finding out the geometric centers of the two figures, and enabling the centers to coincide by non-rotating translation dragging; and (3) at the moment, the overlapping area of the two graphs is the similarity.
And analyzing the stability of the riverbed by combining historical data, and selecting an adaptive riverway water flow dynamics equation by combining empirical information of the section shape, hydraulic slope drop and flow velocity distribution when the riverbed is stable. When the riverbed is unstable, a regression model of the riverbed of the whole assimilation river reach is required to be established, wherein the regression model is additionally provided with the sediment content, the upstream water and soil loss, the typical section flow rate and the time as input.
The method realizes the reconstruction of the three-dimensional topography of the riverbed of the whole assimilation river reach by adopting the modes of local interpolation, segmental smooth regression and integral splicing. The model adopts the sum of Wasserstein distance and interpolation error as a loss function, and introduces a three-dimensional terrain data interpolation algorithm for generating a confrontation network based on Wasserstein. Based on the Terrain three-dimensional data generated by the prior high-resolution DEM data set in one step, terrain-CGANs (Conditional Encoder-Decoder generic adaptive Networks) for generating local riverbed Terrain by Terrain features are constructed and trained from the Terrain features, and a generator G comprises a coding-decoding module consisting of 5 convolutional layers (conv) and 5 inverse convolutional layers (deconv) for extracting possible depth geospatial knowledge. In the discriminator D, the sampled riverbed topographic map and the corresponding complete map are spliced, and the judgment result of the second classification is output through convolution.
Thirdly, selecting river water flow models
And selecting a corresponding mathematical model according to the stability and regularity of the assimilation river reach and the uniformity and stationarity of the water flow in the assimilation period. Simplified equations of Navier-Stokes equations are selected for assimilation of complex flow state and non-constant non-uniform flow, and the simplified equations comprise 4 turbulence models including a standard k-epsilon model, an RNG k-epsilon model, a realizable k-epsilon model and a Reynolds stress model. For a straight and regular river channel, data assimilation is carried out by adopting an Saint-Venn equation set when the flow velocity is stable.
And step four, arranging a water level and flow velocity monitoring instrument at the upstream of the assimilation river reach to realize full-time-space 4-dimensional variational assimilation of the assimilation section and the equation, and adopting a neural network to assimilate the Saint-Venn equation set.
Measuring the water level flow velocity: the water level is measured by a laser radar water level gauge, and the flow velocity is measured by a phased array acoustic Doppler profiler. Arranging a water level, a flow velocity sensor, embedded equipment and a calculation service center on a selected section (when the precision is required to be improved, the sampling section is required to be increased) to form an assimilation system; and determining the number of the sampling sections according to the precision requirement, and acquiring the water depth and the flow on the sections by adopting a sensor as boundary conditions of the model. More specifically, the sensor is required to acquire the water depth and the flow rate on the two sections of the most upstream and the most downstream as boundary conditions. If only the most upstream section data is used as the boundary condition of the neural network, the average absolute value errors of the single wide water depth and the single wide flow in the defined area are respectively 0.294,0.025; if the two sections at the most upstream and the most downstream are used, the error is 0.136,0.023; if the data of the most upstream and the most downstream fracture surfaces are used and the full fracture surface water level flow at the initial moment is added, the error is 0.064,0.013; the neural network prediction accuracy increases as the number of sampling sections increases. An embedded system is adopted to develop a water level and flow sensor access, measurement and control system. The embedded system is developed by adopting ARM Cortex series Cortex-A7, a Linux operating system and a MySQL database.
Constructing an equivalent physical information neural network of the Saint-Venn equation set by adopting a flow velocity measuring instrument according to the idea of embedding physical information into the neural network; optimizing a neural network structure and acquiring network parameters by methods of time-space scaling, equation weight adjustment and the like; testing the simulation precision of the neural network model; and deploying the neural network meeting the precision requirement on site. As will be described later
Step five, the water level flow assimilation method of the neural network comprises the following steps:
step 1, constructing a neural network assimilation model. And (3) constructing an assimilation model with the Saint-Venn equation set, the sampling section water level and the flow as constraint conditions by adopting Physical Information Neural Networks (PINNs). The method specifically comprises the following steps:
as shown in fig. 2, the neural network is composed of several layers. The first layer is the input layer, representing the input variables of the entire network. The last layer is an output layer and represents the processing result of the network. All layers in the middle are hidden layers. Each layer in turn is composed of several nodes. And each node of the hidden layer receives the output of the previous layer and outputs the result to the next layer after processing. Thus, each node of the neural network in the graph represents a processing function. The processing function represented by each node contains several parameters to be determined, and once the parameters are determined, the whole neural network is determined. The process of determining the parameters is the back propagation optimization process.
The invention uses the symbol u θ (x) To represent a neural network. We expect a function u θ The expressed neural network can handle fixed tasks. Function u θ Expresses the input of the neural network. The parameter θ is a set of parameters of the function of each node of the entire neural network. The goal is to determine the parameter θ and thus the function u θ This allows for an intelligent tool to determine whether a given prediction meets a target. To this end, the neural network is trained, given a number of training sets that have been identified with N sample points,
Figure BDA0003672894890000071
wherein x is i Represents the ith input, y i Denotes x i And outputting correspondingly. Our goal is to want u θ (x i ) Approximation y i I.e. neural network pair x i Non-linear mapping of (a) and (b) i The results of (a) are close. To do this, we need to solve the following optimization problem:
Figure BDA0003672894890000072
the learning process is the process of solving the optimization problem of the above formula. In the above formula u θ (x i ) Representing the neural network output, y i Indicating the exact output label corresponding to the input. In function fitting, x i Can be combined with y i Viewed as a set of inputs x i Analytic solution of (a), u θ (x i ) Representing a set of inputs x i Prediction output by neural network
Figure BDA0003672894890000081
Unlike the general neural networks described above, physical information neural networks (PINNs for short) are not used in the training set of the domain with the input x i One-to-one correspondence of labels y i And the difference value between the label value and the predicted value cannot be calculated in a supervised learning mode to obtain a loss function. Input x i Obtaining predictions via neural networks
Figure BDA0003672894890000082
By making a pair
Figure BDA0003672894890000083
By automatic differentiation, can be obtained
Figure BDA0003672894890000084
Construction of functions satisfying physical constraints using predictions and predicted differentials
Figure BDA0003672894890000085
As a loss function, F is made to approach 0 by constantly optimizing the neural network parameter θ. When F is sufficiently small, the physical laws can be considered satisfied within the domain of definition.
Some labeled boundary values are brought in as constraints. The problem of solving the differential equation is converted into an optimization problem by finding a set of parameters that minimize the loss function through the loss function defined by the boundary conditions and the physical information. And then, the solution can be completed by using a gradient descent algorithm, so that an approximate solution meeting the boundary condition to a certain extent is obtained.
The core network structure of PINNs is shown in FIG. 3, with outputs
Figure BDA0003672894890000086
The neural network is represented as a predicted value of the neural network,
Figure BDA0003672894890000087
representing partial differential conditions to be satisfied, where N represents a combining operator, u t=0 And u x=0 Representing an analytical solution at the boundary, the loss function being lost by the boundary termMSE u With partial differential physical information loss MSE f And (4) forming.
Figure BDA0003672894890000088
Neural network prediction value representing the ith point sampled on boundary u, u i Representing the corresponding exact label;
Figure BDA0003672894890000089
representing a partial differential constraint defining a point within the domain. Summing represents the construction of a loss function using a mean square error function. And (4) compiling the physical rule into a loss function, and calculating partial derivatives by utilizing the automatic derivation function of the neural network. Combining boundary constraints and physical constraints, converting a solving problem into an optimization problem, finding a group of adaptive neural network parameters, fitting a physical system, and mapping input to corresponding output. The collection cost of the river water flow data is high, the problem that a conclusion is obtained under partial information is inevitably needed, in the case of a small amount of data, the data of an upstream section at a certain moment is lost, and downstream accumulated errors can be caused, and the neural network solution is a set of nonlinear equation for fitting the parameters of the whole neural network, and can be well avoided.
The Saint-Venant system of equations is a system of partial differential equations that describes the law of motion of non-constant, gradual water currents in waterways and other shallow bodies of water having free surfaces. The system consists of a continuous equation reflecting the conservation of mass and a motion equation reflecting the conservation of momentum.
The one-dimensional holy-vican equation system for describing the movement of the gradually-changed non-constant water flow of the river channel is as follows:
the continuous equation:
Figure BDA00036728948900000810
the equation of power:
Figure BDA00036728948900000811
wherein x, t-scheme (m) and time(s) are independent variables; a is the area of the cross section; q is the flow through the cross section; b is T Indicating the regulated storage widthDegree (m); z is water level (m); q. q.s L Is a side inflow (m) 2 S), influent is positive and effluent is negative; v. of x For side inflow q L A velocity component (m/s) in the direction of water flow; g is gravity acceleration (m/s) 2 ) (ii) a K is the flow modulus and K is the flow modulus,
Figure BDA0003672894890000091
r is the hydraulic radius (m), and n is the roughness.
The invention combines a physical information neural network method to solve the Saint-Vietnam equation, and the process is as follows:
the network structure is shown in figure 4 by using the St.Vietnam equation of the physical information neural network. And a double-output structure is adopted, network parameters are shared, and partial derivatives are obtained through automatic differentiation. And constructing a loss function according to the constraint linear combination of the continuous equation and the dynamic equation, respectively, searching neural network parameters to minimize the loss function, and converting the equation solving problem into an optimization problem.
As shown in fig. 4, the time t and the distance x from the most upstream starting section are independent variables, and the single wide water depth h and the single wide flow q are dependent variables.
Figure BDA0003672894890000092
And
Figure BDA0003672894890000093
respectively representing the predicted values of the neural network, and obtaining partial derivatives of the predicted values to the independent variables by using automatic differentiation
Figure BDA0003672894890000094
Figure BDA0003672894890000095
I input points to be sampled at the boundary
Figure BDA0003672894890000096
And corresponding single wide water depth h and single wide flow q are used for training boundary constraint, u is used for distinguishing f, u represents the definite solution condition of extraction, and N is total u Points, which are labeled.
Figure BDA0003672894890000097
Represents the difference between the predicted value and the theoretical value of the neural network,
Figure BDA0003672894890000098
the predicted value of the single-wide water depth is,
Figure BDA0003672894890000099
and predicting the single-width flow. Sampling the input j of Latin hypercube in the definition domain
Figure BDA00036728948900000910
The sampling points for continuous equation and kinetic equation constraint, which are bound by the boundary, are also bound by the equation. f denotes sampling within the domain of definition, co-sampling N f Points that are unlabeled, i.e., have no corresponding single wide water depth and single wide flow. During analysis, the continuous equation is found to have small contribution to the loss function, effective constraint cannot be provided, a balance weight lambda is added to the term, and finally, the overall expression of the loss function can be obtained:
Figure BDA00036728948900000911
and updating the gradient according to the back propagation of the loss function to continuously reduce the loss function, and considering that the boundary constraint and the physical equation constraint are met when the loss function is small enough. In the formula
Figure BDA00036728948900000912
And with
Figure BDA00036728948900000913
The method respectively represents the single-wide water depth and the single-wide flow predicted by the neural network.
Figure BDA00036728948900000914
Representing the corresponding partial derivative term obtained by automatic derivation. N sampled at the initial and boundary u An input point and correspondingThe single wide water depth h and the single wide flow q are used for training the fixed solution constraint,
Figure BDA00036728948900000915
and (4) representing the difference between the predicted value and the theoretical value of the neural network under the constraint of definite solution conditions (boundary conditions + initial conditions). N sampled from Latin hypercube within the domain of definition f And (4) using the unlabeled input points as constraints for the continuity equations and the dynamic equations. It should be noted that the equation constraint terms are also trained on the sampling points for which the boundary constraint is performed. The triangular mark above the variable represents the predicted value, MSE represents the use of the mean square error function when calculating the loss, N f And N u Denotes the action range and lambda denotes the added balance weight factor. And continuously reducing the loss function according to the back propagation updating gradient of the loss function, and considering that the definite solution constraint and the physical equation constraint are met when the loss function is small enough. After continuous equation term loss, dynamic equation term loss and solution condition loss are obtained through forward propagation calculation of the neural network, a weight parameter lambda is added to balance contributions when the three terms are accumulated to obtain a total loss function. The neural network parameters are then updated by the total loss function back-propagation computation gradient.
Due to the use of a dual output structure, more neurons are needed in the hidden layer for non-linear mapping. The training is more difficult as the number of the neural network layers is more, the gradient disappearance problem exists when the depth is increased, and meanwhile, the calculation burden is brought, so that the calculation amount is reduced as much as possible, and the number of the network layers is reduced. In practice, 3 hidden layers are used, and a neural network is constructed by a full-connection structure of 200 neurons in each layer.
For a natural river channel, the Saint-Vietnam equation has large span in time and space, the span problem in unit dimension is not considered in the prior literature work, the non-convergence is caused by directly using a neural network fitting network, the time scale is 86400 seconds, and the space scale is 20000 meters. Compared with the water depth of a single wide, which is increased from 4 meters to 6 meters. The variation scale of the dependent variable is too small, the increment speed in the time direction is less than 2/86400, the increment in the space direction is less than 2/20000, and the average increment speed is less than 3 multiplied by 10 -5 . Partial derivatives exist in both continuous equations and dynamic equations in the holy-vitamin equation setAn item. Therefore, scale transformation is added in the neural network firstly, space-time mapping is added in a network input layer to scale an input scale, and an input is mapped to a denser interval, so that convergence of the neural network is accelerated. The experimental data is that if the scaling is not carried out, 10000 points are taken in a defined domain, the evaluation index evaluation is finally carried out (the average absolute value loss of single wide water depth is 0.35 (almost unusable)), the index is reduced to 0.064 after the addition of the same experimental condition, namely a Saint Vinan equation set is also called as a Saint Vinan equation set, the Saint Vinan equation set actually consists of a continuous equation and a dynamic equation, and the dynamic equation is also called a motion equation, although the input is mapped to a dense interval, the neural convergence network can be accelerated, but the order of partial derivative is not changed, a weight coefficient is added before the loss function, and the contribution degree of different equations to the loss function is controlled 10 And taking the value of lambda in the loss function, and balancing the constraint of the definite condition, the constraint of the continuous equation and the constraint of the dynamic equation so as to enable the value to be in the same order of magnitude as the boundary loss and the dynamic equation. The single-network structure has few parameters, two outputs are obtained by the same neural network, and the single-network double-output structure is used to improve the stability of the network by a parameter sharing method.
And 2, checking the correctness of the assimilation model according to a four-point difference method, entering the next step if the assimilation model is correct, and returning to the previous step to optimize the assimilation model through optimizing a neural network structure, an iterative algorithm, a loss function and the like if the assimilation model is not correct. For example, the neural network parameters are updated by a gradient descent algorithm.
Specifically, the simplified saint-venin equation is subjected to a Preissman four-point implicit differential numerical solution by using MATLAB R2016b programming. Values for h (t, x) and q (t, x) are obtained. Dividing the time t into one time node every 100 seconds, wherein 865 time nodes are provided, and 201 sections are drawn by taking 100 meters as the time section space of x. And obtaining water depth h (865 × 201 data) and single width flow q (865 × 201 data) by a 4-point implicit difference method, wherein the water depth h and the single width flow q correspond to each space-time node.
And 3, completing field deployment of the qualified model, updating the qualified model in an embedded system, and applying the qualified model to water level flow assimilation. And after the model is qualified, deploying and updating the model in the embedded system, and carrying out data assimilation by taking the section data selected as the definite solution condition as input.
And 4, determining the water level and the flow of the cross section according to the upstream, and obtaining the water level and the flow of any downstream cross section in real time based on a neural network assimilation model. The water level and the flow rate obtained in the step four can be obtained by only calculating the downstream arbitrary section water level flow rate by the section water level flow meter determined at the upstream, and the accuracy is lower. The standard uses the single-wide water level flow of two sections at the most upstream and the most downstream, and the water level flow of any section can be obtained after passing through the model; the accuracy of the model can be improved by increasing the sampling section on the basis of the reference, and the accuracy of the model can be reduced by reducing the constraint.
Based on the method, the invention also provides a river water level flow assimilation system, which comprises a water level and flow velocity sensor, embedded equipment and a software system arranged in the embedded equipment, wherein the software system comprises a terrain measurement module, a section data acquisition module, a neural network assimilation model construction module, a model verification module, a model deployment module and a water level flow output module; the terrain measurement module is used for linking the content in the second step in the implementation method of the GNSS navigation system configured by the unmanned aerial vehicle/unmanned ship, the section data acquisition module is used for realizing the content in the fourth step by adopting a sensor, the neural network assimilation model construction module is used for realizing the content in the fifth step-1, the model verification module is used for realizing the content in the fifth step-2, and the model deployment module is used for realizing the content in the fifth step-3 and deploying the model into embedded equipment; and the water level flow output module is used for realizing the content in the step five-4 and finally outputting the water level and the flow of any downstream section.
Example (b):
the indoor inspection model adopted by the embodiment of the invention is not lower than the following requirements: experiments were performed on NVIDIA RTX 3060 GPU using pytorech version 1.11, python version 3.8.
The neural network structure uses a total of 3 hidden layers, 200 neurons per layer, and the activation function uses tanh. Using the mean square error function, adam optimizer, learning rate was set to 0.0001 and regularization with a parameter of 0.0001 was added.
The simulation scene is a rectangular non-constant flow river channel with the length of 20 kilometers. The water level and the flow of the two cross sections of the most upstream and the most downstream are selected from 0 to 24 hours, and the water levels and the flows of all the cross sections at the time of 0 are selected as known, so that the cross sections can be increased according to the precision requirement to serve as boundary conditions. 1931 points of boundary total sampling are used as boundary constraints, and 100000 points of Latin hypercube sampling are used for physical constraints in a defined domain space. 10000 batches of the neural network assimilation model are trained for about 20 minutes based on the constraint training. And (3) calculating the absolute value of the neural network predicted value subtraction difference method result of each point uniformly distributed in the defined domain by using the average absolute value error quantitative analysis model effect, and then calculating to obtain the average value of all the points.
And carrying out an ablation experiment on whether the network is scaled or not, and observing the descending trend of the loss function, so as to verify the effect of the proposed input scale transformation through the ablation experiment. A comparison of the loss functions with and without scaling is shown in figure 5.
As shown, the abscissa represents the number of iterations and the ordinate represents the magnitude of the loss function in the training. The neural network training is faster after the scaling of the neural network addition, 2 orders of magnitude is reduced when the loss tends to be stable, and the convergence speed is effectively reduced. The experimental conclusion is consistent with the analysis result, and the convergence of the neural network can be effectively accelerated by adding scale scaling under the condition of large-scale input.
And carrying out an ablation experiment on whether the network adjusts the equation weight or not, and aiming at proving that the adjustment of the weight is beneficial to improving the precision through the ablation experiment. The relative error of the single wide water depth after 10000 iterations without weight adjustment is 0.16, singleThe wide flow relative error is 0.08. The average absolute value error is calculated by the formula:
Figure BDA0003672894890000121
where N represents the number of uniformly sampled verify points,
Figure BDA0003672894890000122
representing the predicted output of the neural network for the ith verification point, y i The difference method result of the ith verification point is shown. The error of weight adjustment is compared with 0.064 and 0.013, so that the effect is good and the progress is great. The reason is that the constraint capability is insufficient due to the continuous equation term being too small. The better convergence effect of all the loss terms initially in the same order of magnitude can be demonstrated by comparing the mean absolute value errors.
And solving the Saint-Vietnam equation set by using a Preissman four-point implicit difference method, and using the result for verifying the neural network method.
Simulating the working condition: a single river channel with a regular rectangular cross section of 20km long, a roughness n =0.025, and a gravity acceleration of 9.81m/s 2 The initial water depth is 4 meters, the initial flow is 0, the section spacing is 100 meters, the time step length is 100 seconds, and the total simulation time is 24 hours.
Boundary conditions are as follows: the water depth upstream was increased gradually from 4 meters to 6 meters over 24 hours, and the water depth downstream was constant at 4 meters. Without side streams. Simplifying the Saint Vietnam equation according to the actual scene:
the continuous equation:
Figure BDA0003672894890000123
the momentum equation:
Figure BDA0003672894890000124
a is the area of the cross section; q is the flow passing through the cross section; u is the flow velocity of the cross section; g, gravity acceleration; z water level; s f The friction-drag ratio is reduced, and the friction-drag ratio is reduced,
Figure BDA0003672894890000125
and simplifying the one-dimensional single-width rectangular river channel:
equation of continuity
Figure BDA0003672894890000126
Equation of force
Figure BDA0003672894890000127
Wherein h is the single width water depth (m); q is the flow rate per unit width (m) 2 (s), referred to as single wide flow; n is the roughness of the river channel; g is the acceleration of gravity. Analysis of the Saint-Venn equation can find that independent variables only have a distance x and a time t from a starting point, and dependent variables are single-width water depth h and single-width flow q.
And programming by using MATLAB R2016b, obtaining values of h (t, x) and q (t, x) by applying a Preissman four-point implicit difference method to the simplified Saint-Venn equation set, and taking a numerical solution obtained by the difference method as an analytic solution for comparing the physical information neural network method.
By applying matlab, the 20km long river channel is divided into sections at intervals of 100 meters, and 20000/100+1=201 sections are obtained. A24-hour simulation is carried out, a time node is divided every 100 seconds, and each section can obtain 24 × 60/100+1=865 time nodes. And (3) obtaining single wide water depth data (865 × 201) and single wide flow data (865 × 201) of all the sections by four-point implicit differential calculation. And calculating single wide water depth data (865 × 201) and single wide flow data (865 × 201) of corresponding sections at corresponding time by using the data obtained by the difference method as a reference.
The final effect is embodied by using the average absolute value error:
Figure BDA0003672894890000131
wherein N represents the number of sampling points, 865 x 201,
Figure BDA0003672894890000132
the neural network output value, y (t), representing the ith sample point i ,x i ) Represents the ithAnd (5) four-point implicit difference method results of sampling points.
And completing field deployment of the qualified model, acquiring selected section data by adopting an embedded system, and deploying the model subjected to indoor inspection to a computing service center. The field deployment is not lower than the following requirements: the embedded system equipment stores the historical water level flow of the selected section, the sampling time interval is less than 100 seconds, the storage space is greater than 1GB, and the embedded system equipment has network communication capacity. And the GPU video memory of the server of the computing service center is larger than 6GB, the depth flow of the selected section is measured in the computing service center by combining with embedded equipment, and the neural network of the Saint-Venn equation set is trained to construct a river water level flow assimilation model. The water depth and flow of any section at any moment can be calculated through the model.
At least one section is required to be selected to be combined with embedded equipment to measure water level flow to serve as boundary conditions, meanwhile, the number of sampling sections can be increased by increasing the number of instruments, model accuracy is improved, a better effect is achieved, and the general rule of assimilation models is met.
We verify the effect of the invention in both infinite and finite boundary cases:
infinite boundary:
the upstream water level in the river channel rises to cause the downstream flow to increase, thereby causing the downstream cross-sectional water level to rise. Considering the situation that the river channel is long enough, dissipation phenomenon can occur when the initial section water level rises and propagates through the river channel, and the remote section water level change can not be caused in a limited time, which is called as an infinite boundary. The neural network simulates the unsteady stream of the riverway with infinite boundaries, the average absolute value error of the single wide water depth is 0.064, and the average absolute value error of the single wide flow is 0.013.
As shown in fig. 7, the abscissa represents the temporal change, and the ordinate represents the distance from the starting cross-section, comparing the neural network method with the differential numerical method by a two-dimensional color chart. The left side is the simulation result of the 4-point implicit difference method, and the right side is the simulation result of the neural network. The upper part represents the simulation of single-wide water depth, and the lower part represents the simulation of single-wide flow, wherein the total simulation time is 24 hours, and the river reach is 20 kilometers. The initial water depth of 4 meters at the upstream starting point is increased to 6 meters in 24 hours, the upstream water level rises, and the rising flow of the downstream section water level at the next moment is increased. The water level and the flow change in time and space with a certain time delay and non-real-time change, and the water depth does not change at the position of 20 kilometers by considering infinite boundary problems, so that the result accords with the expected effect. The fitting result obtained by the neural network method and the implicit difference method is consistent through the two-dimensional color images.
And (4) carrying out section observation on the plane, and aiming at microcosmically observing the specific effect of fitting. The overall state of the river was compared at 300 seconds, 3000 seconds, 30000 seconds, 60000 seconds, and 86400 seconds. Meanwhile, the changes of the sections of 500 m, 5000 m and 20000 m within 24 hours are compared.
As shown in fig. 8, the solid line indicates the result of the four-point implicit difference method calculation, and the dotted line indicates the result of the neural network calculation. The fitting effect is observed microscopically from two dimensions of fixed time and a section, the fitting effect is good, and the neural network can be suitable for large-scale time-space change input.
A finite boundary:
the situation that the upstream cross-sectional water level changes to the downstream within a limited time and causes the downstream water level changes is called a limited boundary situation. The neural network simulates the non-constant stream of the river channel under the limited boundary condition, the single-width water depth average absolute value error is 0.069, and the single-width flow average absolute value error is 0.043.
Considering that the boundary influences the water flow of the channel, the length of the river channel is taken as 5 kilometers, so that the water depth change cannot be dissipated due to the infinite boundary. The neural network is trained and the error distribution is observed, and it can be seen from fig. 9 that the error for the neural network fit increases over time, and that the error is higher at the far edge than at the edge due to the strong constraint imposed by the boundary condition at the edge.
The boundary conditions refer to the downstream-most section data and the upstream-most section data. From the above process, it can be seen that the scheme of the present invention can be used for both the infinite boundary condition where the upstream change does not cause the downstream significant change in a limited time and the limited boundary condition where the upstream change causes the significant change.
It should be noted that the above-mentioned contents only illustrate the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and it is obvious to those skilled in the art that several modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations fall within the protection scope of the claims of the present invention.

Claims (8)

1. A method for synchronously assimilating water level and flow of a natural river is characterized by comprising the following steps:
step one, determining river reach needing assimilation
Step two, measuring the water and underwater topography of the typical section and generating the integral riverbed topography of the assimilation section
Acquiring the terrain below the water surface, and establishing the relation between the water level/water depth and the section area;
thirdly, selecting river water flow models
Selecting a corresponding mathematical model according to the stability and regularity of the assimilation river reach and the uniformity and stationarity of water flow in the assimilation period; for a straight and regular river channel, when the flow velocity is stable, data assimilation is carried out by adopting an Saint-Vietnam equation set;
setting a water level and flow rate monitoring instrument at the upstream of the assimilation river reach to collect data
Determining the number of sampling sections according to the precision requirement, arranging a water level sensor, a flow velocity sensor, an embedded device and a calculation service center on the selected sections, and forming an assimilation system; acquiring water depth and flow on a section by using a sensor as boundary conditions of a model;
step five, the water level flow assimilation method of the neural network comprises the following steps:
step 1, establishing a neural network assimilation model, namely establishing an assimilation model with a Saint-Venn equation set, a sampling section water level and flow as constraint conditions by adopting a physical information neural network; the method comprises the following steps:
the one-dimensional holy-vican equation system for describing the movement of the gradually-changed non-constant water flow of the river channel is as follows:
the continuous equation:
Figure FDA0003672894880000011
the equation of power:
Figure FDA0003672894880000012
in the formula, x and t are respectively a flow and time; a is the area of the cross section; q is the flow through the cross section; b is T Indicating the regulation width; z is water level; q. q.s L The side inflow is positive, and the outflow is negative; v. of x For side inflow q L A velocity component in the direction of water flow; g is gravity acceleration; k is the flow modulus,
Figure FDA0003672894880000013
r is hydraulic radius, and n is roughness;
solving the Saint Vietnam equation by using a physical information neural network, sharing network parameters by adopting a single-network double-output structure, and predicting partial derivatives of values to independent variables
Figure FDA0003672894880000014
I input points to be sampled at the boundary
Figure FDA0003672894880000015
And the corresponding single wide water depth h and single wide flow q are used for training boundary constraint,
Figure FDA0003672894880000016
representing the difference between the predicted value and the theoretical value of the neural network,
Figure FDA0003672894880000017
the predicted value of the single-wide water depth is,
Figure FDA0003672894880000018
for single wide flow prediction, we will define the input j sampled by Latin hypercube in the domain
Figure FDA0003672894880000019
For connectingContinuous equations and dynamic equations are constrained, the sampling points for boundary constraint are also constrained, differential terms are linearly combined according to continuous equations and dynamic equations respectively, and the loss function is constructed as follows:
Figure FDA0003672894880000021
where MSE denotes the use of a mean square error function in calculating the loss, N f And N u Representing the action range, and lambda represents the added balance weight coefficient;
searching neural network parameters to minimize a loss function;
step 2, checking the correctness of the assimilation model according to a four-point difference method, if the assimilation model is correct, entering step 4, and if the assimilation model is not correct, returning to step 3 to optimize the assimilation model;
step 3, completing field deployment of the qualified model, updating the qualified model in an embedded system, and applying the qualified model to water level flow assimilation;
and 4, determining the water level and the flow of the cross section according to the upstream, and obtaining the water level and the flow of any downstream cross section in real time based on a neural network assimilation model.
2. The method for synchronously assimilating water level and flow of natural river of claim 1, wherein the network input layer in the neural network of step 1 is added with a space-time mapping scaling input scale to map the input to a denser interval.
3. The method for synchronously assimilating water level and flow in natural river according to claim 1, wherein 3 hidden layers are used in step 1, and a neural network is constructed in a full-connection structure with 200 neurons in each layer.
4. The method for synchronously assimilating water level and flow in natural river according to claim 1, wherein at least one section in step 4 is selected as a boundary condition in combination with the water level and flow measured by an embedded device.
5. The method for synchronously assimilating water level and flow rate of a natural river according to claim 1, wherein the second step comprises the following processes:
selecting a typical section, carrying a laser radar by an overwater unmanned aerial vehicle, and carrying out overwater and underwater topography measurement by combining an ultrasonic unmanned ship, and selecting a corresponding section for measurement when the space-time change of a riverbed is large; when the similarity between the next section and the measured section is less than or equal to 0.9, the section shape needs to be measured again; and realizing the reconstruction of the three-dimensional topography of the riverbed of the whole assimilation river reach.
6. The method for synchronously assimilating water level and flow of natural river according to claim 5, wherein the similarity is calculated by adopting the following steps:
(1) Carrying out all-directional equal-proportion scaling on the two water-passing section graphs for area normalization;
(2) Respectively finding out the geometric centers of the two figures, and enabling the centers to coincide by non-rotating translation dragging;
(3) At this time, the overlapping area of the two graphs is the similarity.
7. The method for synchronously assimilating the water level and the flow of the natural river according to claim 5, wherein the three-dimensional topography of the riverbed of the assimilation river reach is reconstructed by the following steps:
the sum of Wasserstein distance and interpolation error is used as a loss function, and a three-dimensional terrain data interpolation algorithm for generating a confrontation network based on Wasserstein is introduced; on the basis of generating Terrain three-dimensional data on one step by using the existing high-resolution DEM data set, terrain-CGANs for generating local riverbed Terrain by Terrain features are constructed and trained, and a generator G comprises a coding-decoding module consisting of 5 convolutional layers and 5 inverse convolutional layers and is used for extracting possible depth geospatial knowledge; in the discriminator D, the sampled riverbed topographic map and the corresponding complete map are spliced, and the judgment result of the second classification is output through convolution.
8. The utility model provides a synchronous assimilation intelligent system of natural river water level flow, includes water level, velocity of flow sensor, embedded equipment and sets up the software system in embedded equipment, its characterized in that: the software system comprises a terrain measurement module, a section data acquisition module, a neural network assimilation model construction module, a model verification module, a model deployment module and a water level flow output module; the terrain measurement module is used for linking an unmanned aerial vehicle/unmanned ship configuration GNSS navigation system to achieve the content in the second step of the natural river water level flow synchronization assimilation method in any one of claims 1-7, the section data acquisition module is used for achieving the content in the fourth step by adopting a sensor, the neural network assimilation model construction module is used for achieving the content in the fifth step-1, the model verification module is used for achieving the content in the fifth step-2, the model deployment module is used for achieving the content in the fifth step-3, and a model is deployed into embedded equipment; and the water level flow output module is used for realizing the content in the step five-4 and finally outputting the water level and the flow of any downstream section.
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Publication number Priority date Publication date Assignee Title
CN116502775A (en) * 2023-06-27 2023-07-28 江西省水利科学院(江西省大坝安全管理中心、江西省水资源管理中心) Hydrologic sequence enhancement and prediction method
CN116502775B (en) * 2023-06-27 2023-09-19 江西省水利科学院(江西省大坝安全管理中心、江西省水资源管理中心) Hydrologic sequence enhancement and prediction method
CN116956588A (en) * 2023-07-21 2023-10-27 武汉大学 River channel water depth inversion method based on water depth-water surface area mathematical model and remote sensing
CN116956588B (en) * 2023-07-21 2024-01-09 武汉大学 River channel water depth inversion method based on water depth-water surface area mathematical model and remote sensing
CN117077571A (en) * 2023-10-13 2023-11-17 长江三峡集团实业发展(北京)有限公司 Water surface line simulation method and device, computer equipment and storage medium
CN117077571B (en) * 2023-10-13 2024-01-26 长江三峡集团实业发展(北京)有限公司 Water surface line simulation method and device, computer equipment and storage medium

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