Feedback Correction Method for Implicit Discharge Reconstruction in River Cross-Sections under Sparse Water Levels

Abstract

This application discloses a feedback correction method for reconstructing implicit flow in river cross-sections under sparse water levels. The method includes: performing spatiotemporal global correction of the initial reconstructed complete water level field using a water level observation field; evaluating the initial reconstructed flow state from three dimensions—physical equilibrium consistency, flow propagation consistency, and equivalent resistance stability—based on the corrected reconstructed complete water level field; using a water level-flow decoupling condition factor as a flow reliability correction factor to obtain a comprehensive reliability score for each initial reconstructed flow; setting a low-reliability criterion to identify low-reliability initial reconstructed flows; employing a diagnostic contribution-driven loss correction model to obtain the comprehensive flow physical loss of the low-reliability initial reconstructed flow field; and feeding this loss function back to the loss function of the hydrodynamic state reconstruction model for feedback correction. This application improves the accuracy of the flow field derived from the model under sparse water level observation conditions.

Description

Technical Field

[0001] This invention belongs to the field of river hydrodynamic simulation technology, specifically relating to a method for reconstructing and correcting the implicit flow of a river cross-section under sparse water levels. Background Technology

[0002] In natural river channels, reservoir backwater areas, and long-distance regulated river sections, flow processes are crucial fundamental variables for water resource allocation, flood forecasting, ecological flow assurance, digital twin water system operation, and hydrodynamic model calibration. Compared to water level, actual flow measurements at internal cross-sections typically require specialized equipment and specific on-site conditions, and are significantly affected by navigation safety, river cross-sectional morphology, flow turbulence, regulated processes, and measurement costs, making continuous observation across all cross-sections and time periods difficult. Therefore, in engineering practice, there is often a situation where water level observations are relatively sufficient, while internal flow observations are significantly insufficient, especially in reservoir sections, mountainous river channels, and river sections significantly affected by regulated flows.

[0003] To address the aforementioned issues, traditional methods typically employ level-discharge curves, empirical hydraulic formulas, or one-dimensional hydrodynamic models to estimate river flow. Level-discharge curves are simple and suitable for river sections with stable cross-sectional morphology, weak backwater influence, and available long-term measured data. However, in reservoir areas with fluctuating backwater, river sections affected by dam operations, or sections with significant scouring and deposition, a stable single-value relationship between level and flow is often lacking, making fixed curves prone to significant errors. One-dimensional hydrodynamic models can describe river flow motion based on continuity and momentum equations, considering factors such as cross-sectional geometry, boundary conditions, and roughness. However, their accuracy is highly dependent on boundary conditions, initial conditions, roughness parameters, and cross-sectional data. When internal flow measurements are insufficient, model parameters may exhibit multiple solutions; that is, different roughness or resistance configurations may yield similar level errors, but the corresponding internal flow processes may differ significantly.

[0004] In recent years, machine learning and deep learning methods have been widely used for water level prediction, flow prediction, and hydrodynamic state reconstruction. For example, Long Short-Term Memory (LSTM) networks, convolutional neural networks, graph neural networks, and Transformer-type models can learn nonlinear mapping relationships from historical hydrological and meteorological data, exhibiting good fitting capabilities in scenarios with sufficient data. However, purely data-driven methods often lack explicit hydrodynamic constraints, making them prone to physically inconsistent results in sparsely observed water level regions, such as local flow abrupt changes, abnormal upstream-downstream propagation relationships, or failure to satisfy mass conservation laws. Even if the model exhibits small errors at observed water levels, it cannot directly prove that the reconstructed internal flow field satisfies hydrodynamic laws. Especially under conditions of few water level observation sections, lack of supervision of internal flow, and adjustable equivalent drag parameters, the model may improve water level fitting by adjusting drag distribution or internal state, while the flow field still exhibits propagation anomalies or local physical imbalances.

[0005] Therefore, how to improve the accuracy of the flow field derived from the model under sparse water level observation conditions, and make the flow field satisfy various physical constraints, is an urgent problem to be solved. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a feedback correction method for reconstructing implicit flow in river cross-sections under sparse water levels, which can effectively solve the above-mentioned problems.

[0007] The technical solution adopted in this invention is as follows:

[0008] This invention provides a method for reconstructing and correcting the implicit flow in a river cross-section under sparse water levels, comprising the following steps:

[0009] Step S1: Select multiple cross sections along the flow direction of the target river section; The hydrodynamic state reconstruction model takes the cross section location, boundary conditions, initial conditions, and scheduling operation information at each moment of the simulation period as input. Under the action of the loss function with physical constraints, it performs hydrodynamic state simulation on all cross sections of the target river section during the simulation period and outputs the initial reconstructed water level field and the initial reconstructed flow field in the entire spatiotemporal domain.

[0010] Step S2: Obtain the water level observation field formed by sparse water level observation data of the target river section during the simulation period; use the spatiotemporal neighborhood water level correction coupled with the spatiotemporal propagation effect algorithm of water level to perform spatiotemporal global correction on the initial reconstructed complete water level field through the water level observation field to obtain the corrected reconstructed complete water level field.

[0011] Step S3: Construct a water level-flow reliability relationship model that includes the unsteady flow propagation factor, backwater backwater influence factor, and hysteresis loop strength. Using the corrected reconstructed water level complete field as a benchmark, perform reliability analysis on the initial reconstructed flow complete field to obtain the water level-flow decoupling condition factor for each initial reconstructed flow.

[0012] Step S4: Construct a flow state evaluation model; the flow state evaluation model uses the corrected reconstructed water level complete field as a benchmark, and evaluates the state of each initial reconstructed flow from three flow state dimensions: physical equilibrium consistency, flow propagation consistency, and equivalent resistance stability, to obtain its flow state score and physical loss in each flow state dimension.

[0013] The flow status scores of various flow status dimensions are weighted and fused, and the water level-flow decoupling condition factor is used as the flow reliability correction factor to obtain the comprehensive reliability score of each initial reconstructed flow.

[0014] Step S5: Set low reliability criteria. Based on the water level-flow decoupling condition factor and comprehensive reliability score of each initial reconstructed flow in the complete field of initial reconstructed flow, identify the low reliability initial reconstructed flow and form a low reliability initial reconstructed flow field.

[0015] Step S6: Construct a diagnostic contribution-driven loss correction model; the diagnostic contribution-driven loss correction model performs low reliability diagnosis on each low reliability initial reconstruction traffic from different traffic state dimensions, obtains the reliability reduction contribution of each traffic state dimension, the reliability reduction contribution corrects the physical loss in the corresponding traffic state dimension obtained by calling the traffic state evaluation model, obtains the physical loss correction amount, integrates the physical loss correction amount of each low reliability initial reconstruction traffic, and introduces a smoothing constraint term to obtain the comprehensive traffic physical loss corresponding to the low reliability initial reconstruction traffic field;

[0016] Step S7: Feedback the integrated flow physical loss to the loss function of the hydrodynamic state reconstruction model to perform feedback correction on the hydrodynamic state reconstruction model.

[0017] The beneficial effects of this invention are as follows:

[0018] This invention independently evaluates the initial reconstructed flow rate output by the hydrodynamic state reconstruction model based on sparse water level observation data. It diagnoses the reliability of the initial reconstructed flow rate, i.e., the implicit flow rate, from three flow state dimensions: physical equilibrium consistency, flow propagation consistency, and equivalent resistance stability. The physical loss is corrected by using the contribution of the low-reliability initial reconstructed flow rate to the reliability reduction in each flow state dimension, resulting in a comprehensive flow physical loss. The loss function of the hydrodynamic state reconstruction model is then fed back and corrected, thereby improving the accuracy of the flow field derived by the model under sparse water level observation conditions. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 A flowchart of the feedback correction method for reconstructing implicit flow in river cross-sections under sparse water levels provided by the present invention;

[0021] Figure 2 This is a distribution diagram along the path of the comprehensive reliability score of each section before and after correction, obtained from an embodiment of the present invention.

[0022] Figure 3 This is a spatiotemporal distribution diagram of the comprehensive reliability score before and after correction obtained in an embodiment of the present invention. Detailed Implementation

[0023] To make the technical problems solved, the technical solutions, and the beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the invention.

[0024] This invention proposes a feedback correction method for reconstructing implicit flow in river cross-sections under sparse water levels. Based on sparse water level observation data, the initial reconstructed flow output by the hydrodynamic state reconstruction model is independently evaluated. The reliability of the initial reconstructed flow, i.e., the implicit flow, is diagnosed from three flow state dimensions: physical equilibrium consistency, flow propagation consistency, and equivalent resistance stability. The contribution of the diagnosed low-reliability initial reconstructed flow to the reliability reduction in each flow state dimension is used to correct the physical loss, resulting in a comprehensive flow physical loss. The loss function of the hydrodynamic state reconstruction model is then fed back and corrected, thereby improving the accuracy of the flow field derived by the model under sparse water level observation conditions.

[0025] The method of this invention is to take any hydrodynamic state reconstruction model that can output water level field and implicit flow field as the object, construct a multi-physics consistency diagnosis process after the model output, and further transform the reliability score and the contribution of diagnosis causes into a feedback correction strategy for model loss.

[0026] It should be noted that this invention does not limit the specific type of hydrodynamic state reconstruction model. The hydrodynamic state reconstruction model can be a data-driven neural network model, a physically constrained neural network model, a data assimilation model, or a combination thereof; as long as it can output the initial reconstructed water level and initial reconstructed flow at each cross section and at each time point in the studied river section, it can be used as the correction object of this invention.

[0027] See Figure 1 This invention provides a method for reconstructing and correcting the implicit flow of a river cross-section under sparse water levels, comprising the following steps S1 to S7:

[0028] Step S1: Select multiple cross sections along the flow direction of the target river section; The hydrodynamic state reconstruction model takes the cross section location, boundary conditions, initial conditions, and scheduling operation information at each moment of the simulation period as input. Under the action of the loss function with physical constraints, it performs hydrodynamic state simulation on all cross sections of the target river section during the simulation period and outputs the initial reconstructed water level field and the initial reconstructed flow field in the entire spatiotemporal domain.

[0029] As one implementation method, multiple cross-sections are selected along the direction of water flow in the target river section. The cross-sections are numbered from upstream to downstream and denoted as cross-sections. , section In spatial direction The cross-sectional location is Each moment in the simulation period is represented as Therefore, each spatiotemporal location within the entire spatiotemporal domain is represented as For ease of formula expression, Simplified representation as Within the entire spatiotemporal domain, each initial reconstructed water level is represented as: Each initial reconstruction flow is represented as .

[0030] Step S2: Obtain the water level observation field formed by sparse water level observation data of the target river section during the simulation period; use the spatiotemporal neighborhood water level correction coupled with the spatiotemporal propagation effect algorithm of water level to perform spatiotemporal global correction on the initial reconstructed complete water level field through the water level observation field to obtain the corrected reconstructed complete water level field.

[0031] This step can be achieved through steps S21 to S24:

[0032] Step S21: Obtain the water level observation field formed by sparse water level observation data of the target river section during the simulation period; extract the initial reconstructed local water level field with water level observation data from the initial reconstructed complete water level field; use formula (1) to calculate the deviation between each initial reconstructed water level in the initial reconstructed local water level field and the corresponding water level observation data in the water level observation field, and obtain the water level reconstruction deviation:

[0033] (1)

[0034] in: Indicates the spatiotemporal location with available water level observation data; Indicates cross-section At any moment Water level reconstruction deviation; Indicates cross-section At any moment The initial reconstructed water level; Indicates cross-section At any moment Water level observation data; Indicates cross-section Characteristic water depth; This indicates a stable parameter that avoids having an excessively small denominator when correcting for water level.

[0035] Step S22: Locate the target initial reconstructed water level with water level observation data constraints in the spatiotemporal neighborhood of the initial reconstructed water level complete field. Using formulas (2) and (3), based on the deviation between the observed water level data in the spatiotemporal neighborhood and the initial reconstructed water level of the target, a spatiotemporal influence scale factor is introduced to adjust the initial reconstructed water level of the target. Priority correction is performed to obtain the water level correction change. :

[0036] (2)

[0037] (3)

[0038] in: Indicates the initial reconstructed water level of the target. The target spatiotemporal location, Indicates the target cross section. Indicates the target time; Indicates the spatiotemporal location of the target The spatiotemporal neighborhood range; Represents the spatiotemporal neighborhood. Inside, various water level observation data Relative target initial reconstruction water level Spatial-temporal joint weights; Indicates the target cross section and cross-section The distance along the route between them; Indicates the scale of spatial influence; This indicates that time affects the scale;

[0039] Step S23: Using formula (4), the initial reconstructed water level of the target is obtained. Corrected reconstructed water level :

[0040] (4)

[0041] in: This is the water level correction intensity coefficient, with a value ranging from 0 to 1, based on the spatiotemporal location within the spatiotemporal neighborhood. Water level reconstruction deviation Confirmed, if the water level reconstruction deviation... If the overall value is low within the spatiotemporal neighborhood, then decrease. Conversely, increase ;

[0042] Step S24: Based on each corrected reconstructed water level, the water level correction change is smoothly extended along the cross-sectional direction and the time direction to correct the initial reconstructed water level that does not have water level observation data constraints in the spatiotemporal neighborhood, so as to obtain the complete field of corrected reconstructed water level.

[0043] The proposed spatiotemporal neighborhood water level correction coupled with the spatiotemporal propagation effect algorithm of water level is used to perform spatiotemporal global correction on the initial reconstructed complete water level field through the water level observation field, resulting in a corrected reconstructed complete water level field. This method has the advantage of being more accurate than the corrected reconstructed complete water level field. In subsequent steps, the initial reconstructed flow rate is analyzed for reliability based on the corrected reconstructed complete water level field, which improves the accuracy of the reliability analysis of the initial reconstructed flow rate.

[0044] Step S3: Construct a water level-flow reliability relationship model that includes the unsteady flow propagation factor, backwater backwater influence factor, and hysteresis loop strength. Using the corrected reconstructed water level complete field as a benchmark, perform reliability analysis on the initial reconstructed flow complete field to obtain the water level-flow decoupling condition factor for each initial reconstructed flow.

[0045] This step can be achieved through steps S31 to S34:

[0046] Step S31: Calculate the propagation factor of unsteady flow based on the propagation mode of water level and flow rate changes over time.

[0047] (5)

[0048] in: Represents each spatiotemporal location within the entire spatiotemporal domain; Indicates cross-section At any moment The non-steady flow propagation factor; Indicates the fault surface of the reconstructed complete water level field after correction. At any moment The corrected and reconstructed water level; Indicates cross-section At any moment The initial reconstruction traffic; and These represent the weights of the water level change term and the flow rate change term, respectively. and These represent the normalized scales for the water level change term and the flow rate change term, respectively.

[0049] Step S32: Calculate the backwater backwater influence factor based on the degree of reduction in water surface slope and the intensity of downstream boundary water level change.

[0050] (6)

[0051] in: Indicates cross-section At any moment Factors affecting the backwater backflow; Indicates cross-section At any moment Water surface slope; Indicates the normalized scale of water surface slope; Indicates at time The downstream boundary water level; Indicates the normalized scale of downstream boundary water level changes;

[0052] Step S33: Calculate the hysteresis loop strength formed by the water level-flow process using a sliding time window.

[0053] (7)

[0054] in: Indicates cross-section At any moment hysteresis loop strength; Indicated by time A sliding time window centered on the subject; Indicates cross-section The magnitude of change in the initial reconstructed flow within the sliding time window; Indicates cross-section The magnitude of water level change is reconstructed after correction within the sliding time window; This refers to a stability parameter used to avoid having an excessively small denominator when calculating the strength of a hysteresis loop. Indicates cross-section Reconstruct the water level after correction at the next adjacent time step; Indicates time Step size;

[0055] Step S34, the non-steady flow propagation factor Factors affecting backwater jacking Hysteresis loop strength By merging the data, the water level-flow rate decoupling condition factor is obtained. :

[0056] (8)

[0057] in: These represent the fusion weights of the unsteady flow propagation factor, the backwater backwater influence factor, and the hysteresis loop intensity, respectively. , .

[0058] Step S4: Construct a flow state evaluation model; the flow state evaluation model uses the corrected reconstructed water level complete field as a benchmark, and evaluates the state of each initial reconstructed flow from three flow state dimensions: physical equilibrium consistency, flow propagation consistency, and equivalent resistance stability, to obtain its flow state score and physical loss in each flow state dimension.

[0059] The flow status scores of various flow status dimensions are weighted and fused, and the water level-flow decoupling condition factor is used as the flow reliability correction factor to obtain the comprehensive reliability score of each initial reconstructed flow.

[0060] This step can be achieved through steps S41 to S42:

[0061] Step S41, for each initial reconstruction flow By using the traffic state evaluation model, its performance in each traffic state dimension is obtained. Traffic status score and physical loss ;in, , These represent the physical equilibrium consistency dimension, the flow propagation consistency dimension, and the equivalent resistance stability dimension, respectively.

[0062] Step S42, using formula (9), obtain the initial reconstruction flow. Overall reliability score :

[0063] (9)

[0064] in: A comprehensive reliability score ranging from 0 to 100. These represent the weights of the physical equilibrium consistency dimension, the flow propagation consistency dimension, and the equivalent resistance stability dimension, respectively. , ; , and These represent the flow state scores for the physical equilibrium consistency dimension, the flow propagation consistency dimension, and the equivalent resistance stability dimension, respectively. This indicates the water level-flow rate decoupling factor. This represents the reduction factor for the water level-flow decoupling condition.

[0065] For step S41 above, each traffic state dimension Traffic status score and physical losses The calculation method is as follows:

[0066] Step S411: Using hydraulic geometry mapping elements, based on the cross-sectional hydraulic geometry data, a learnable mapping function is used to map each cross-section... At any moment Corrected reconstructed water level Mapped to cross-sectional hydraulic geometry, including the water flow area Hydraulic radius and water surface slope ;

[0067] As one implementation method, mapping is performed using the water surface area mapping function, the hydraulic radius mapping function, and the water surface slope mapping function, respectively. Each mapping function can be determined from measured cross-sectional data, cross-sectional interpolation relationships, hydraulic geometric empirical relationships, or hydraulic geometric mapping networks.

[0068] Step S412: Using the equivalent resistance parameter back-calculation unit, based on the initial reconstructed flow rate... The equivalent drag parameters of the cross-section can be derived from the hydraulic geometry of the cross-section:

[0069] (10)

[0070] in: Indicates cross-section At any moment The equivalent resistance parameters; This represents a stable parameter to avoid an excessively small denominator when performing flow correction.

[0071] Step S413: Based on the hydraulic geometry of the cross section and the equivalent resistance parameters, calculate the flow state score and physical loss for the physical equilibrium consistency dimension and the equivalent resistance stability dimension, respectively; perform feature analysis on the initial reconstructed flow of adjacent cross sections, and calculate the flow state score and physical loss for the flow propagation consistency dimension.

[0072] The calculation methods for the flow state score and physical loss in the physical balance consistency dimension are as follows:

[0073] Step A1, Residuals of the Continuity Equation:

[0074] (11)

[0075] in: Indicates cross-section At any moment The residuals of the continuity equation; Indicates the spatial direction of the cross-section from upstream to downstream; Indicates cross-section At any moment Lateral inflow term; when measured data for lateral inflow is lacking, it can be estimated based on tributary inflow, inter-regional confluence, or scheduling data, or in embodiments where there is no significant lateral inflow. Take 0.

[0076] Step A2, Momentum Equation Residual:

[0077] (12)

[0078] in: Indicates cross-section At any moment The momentum equation residual; g represents gravitational acceleration; This represents external sources or sinks or modifications. When external sources or sinks are not considered, it can be set as follows: =0;

[0079] Step A3: Normalize the residuals of the continuity equation and the momentum equation, and construct a flow state score based on the physical equilibrium consistency dimension. :

[0080] (13)

[0081] (14)

[0082] (15)

[0083] in: and These represent the normalized scales of the residuals of the continuity equation and the momentum equation, respectively. and These represent the normalized scores of the residuals of the continuity equation and the momentum equation, respectively. and Let the weights of the residuals of the continuity equation and the momentum equation be respectively, satisfying... ;

[0084] Step A4: Calculate the physical loss in the physical equilibrium consistency dimension. :

[0085] (16)

[0086] in: and These represent the physical loss weights of the residuals of the continuity equation and the momentum equation, respectively.

[0087] The calculation methods for the flow state score and physical loss in the equivalent resistance stability dimension are as follows:

[0088] Step B1, Equivalent resistance anomaly:

[0089] (17)

[0090] in: Indicates cross-section At any moment The equivalent resistance anomaly; , and These represent the weighting coefficients for the spatial variation term, the temporal variation term, and the out-of-bounds anomaly term, respectively. and These represent the normalized scales of the spatial variation term and the temporal variation term, respectively; This indicates that the equivalent resistance parameter is preset within a reasonable range. These represent the lower and upper limits of a preset reasonable range, respectively. Indicates the indicator function, in The indicator function takes the value 1 when the internal condition is true, and 0 otherwise.

[0091] Step B2 converts the equivalent resistance anomaly degree into a flow state score based on the equivalent resistance stability dimension. :

[0092] (18)

[0093] The closer it is to 1, the more stable the equivalent resistance parameter is in space and time, and the higher the coordination between the initial reconstructed flow and the water level gradient.

[0094] Step B3: Calculate the physical loss in the equivalent resistance stability dimension. :

[0095] (19)

[0096] in: This indicates that the equivalent resistance parameter exceeds the preset reasonable range. The penalty items.

[0097] The calculation methods for the traffic state score and physical loss in the traffic propagation consistency dimension are as follows:

[0098] Step C1: Calculate and estimate the propagation time delay based on the initial reconstructed flow process at adjacent cross sections:

[0099] (20)

[0100] (twenty one)

[0101] in: Indicates cross-section To the cross-section The estimated propagation time delay; Indicates cross-section and cross-section Candidate propagation lag The correlation coefficient of the flow process under the following conditions; Indicates to make Largest candidate propagation delay ; Indicates cross-section At any moment The initial reconstruction traffic; Indicates cross-section At any moment The initial reconstructed flow, specifically referring to the cross-section At any moment Through candidate propagation time lag Initial reconstructed traffic after translation; Indicates the candidate propagation time lag Down and Both have overlapping time sets of data; Indicates cross-section In overlapping time sets Average initial reconstruction flow within; Indicates cross-section Through candidate propagation time lag Translation in overlapping time sets Average initial reconstruction flow within;

[0102] Step C2, after considering the estimated propagation delay and lateral inflow, calculate the flow propagation anomaly degree:

[0103] (twenty two)

[0104] in: Indicates cross-section At any moment The degree of traffic propagation anomaly; Indicates cross-section To the cross-section Lateral inflow rate; Indicates cross-section At any moment The initial reconstruction traffic;

[0105] Step C3: Convert the traffic propagation anomaly degree into a traffic state score based on the traffic propagation consistency dimension. :

[0106] (twenty three)

[0107] in: It represents the attenuation scale of traffic propagation anomaly, and its value range can be 0.05-0.50, preferably 0.10-0.30. The closer it is to 1, the more coordinated the upstream and downstream flow propagation relationship is.

[0108] Step C4, Physical loss in the consistency dimension of traffic propagation :

[0109] (twenty four)

[0110] This step is now complete.

[0111] Step S5: Set low reliability criteria. Based on the water level-flow decoupling condition factor and comprehensive reliability score of each initial reconstructed flow in the complete field of initial reconstructed flow, identify the low reliability initial reconstructed flow and form a low reliability initial reconstructed flow field.

[0112] The low reliability criterion is:

[0113] (25)

[0114] in: This indicates the identified low-reliability spatiotemporal locations. This indicates a low reliability flag operation. This represents the identified and flagged low-reliability initial reconstruction traffic, specifically representing the cross-section. At any moment The initial reconstruction traffic is low-reliability initial reconstruction traffic; Indicates the overall reliability threshold; This indicates the threshold value for water level-flow rate decoupling. Indicates the indicator function, in When the internal condition is true, the indicator function takes the value 1; otherwise, it takes the value 0. Specifically, when... When the internal condition is met, it indicates that the initial reconstruction traffic corresponding to that spatiotemporal location is low-reliability initial reconstruction traffic. A low-reliability marking operation is then performed on that spatiotemporal location, i.e., [the following is omitted as the text is incomplete and requires further context]. Marked as Otherwise, the low reliability marking operation will not be performed.

[0115] Step S6: Construct a diagnostic contribution-driven loss correction model; the diagnostic contribution-driven loss correction model performs low reliability diagnosis on each low reliability initial reconstruction traffic from different traffic state dimensions, obtains the reliability reduction contribution of each traffic state dimension, the reliability reduction contribution corrects the physical loss in the corresponding traffic state dimension obtained by calling the traffic state evaluation model, obtains the physical loss correction amount, integrates the physical loss correction amount of each low reliability initial reconstruction traffic, and introduces a smoothing constraint term to obtain the comprehensive traffic physical loss corresponding to the low reliability initial reconstruction traffic field;

[0116] This step can be achieved through steps S61 to S63:

[0117] Step S61, construct the contribution model of diagnostic causes:

[0118] (26)

[0119] in: Representing the traffic state dimension The flow state for the initial reconstructed flow The reliability of the contribution is reduced; Representing the traffic state dimension The weights;

[0120] Step S62, for the identified low-reliability initial reconstruction traffic The diagnostic cause contribution model is invoked to obtain each traffic state dimension. Reliability reduction contribution And convert it into adaptive correction weights. :

[0121] (27)

[0122] in: Representing the traffic state dimension The basic weights; Representing the traffic state dimension Diagnostic contribution amplification factor;

[0123] Step S63: Calculate the comprehensive flow physical loss corresponding to the low-reliability initial reconstructed flow field. :

[0124] (28)

[0125] in: Represents a set of spatiotemporal locations with low reliability; , and These represent the adaptive correction weights for the physical equilibrium consistency dimension, the flow propagation consistency dimension, and the equivalent resistance stability dimension, respectively. , and These represent the spatial and temporal positions of the physical equilibrium consistency dimension, the flow propagation consistency dimension, and the equivalent resistance stability dimension, respectively, in low-reliability environments. The physical loss is read from the flow state evaluation model; Indicates the smoothing constraint weights; The smoothing constraint term representing the correction result is calculated using the following formula:

[0126] (29)

[0127] in: This indicates the number of spatiotemporal locations with low reliability. and These represent the spatiotemporal locations of low reliability. The corrected reconstructed water level and initial reconstructed flow rate;

[0128] Step S7: Feedback the integrated flow physical loss to the loss function of the hydrodynamic state reconstruction model to perform feedback correction on the hydrodynamic state reconstruction model.

[0129] As one implementation method, a formula is used. Update the model parameters to achieve feedback correction; among which, To correct the number of iterations, For model parameters, Update the step size for the parameters. For model parameters The gradient operator.

[0130] The following example uses a section of the main stream in the Three Gorges Reservoir area with fluctuating backwater as an illustration:

[0131] This embodiment selects the same research river section, the same simulation period, and the same set of boundary conditions. The cross-section numbers are 1, 2, ..., 25 from upstream to downstream. The simulation period for this embodiment is from 19:00 on August 17, 2020 to 19:00 on August 23, 2020. The overall execution process is as follows: Figure 1 As shown.

[0132] By employing the methods described in steps S1 to S7 of this invention, the initial reconstructed flow field output by the hydrodynamic state reconstruction model is iteratively corrected multiple times. When the iteration termination condition is met, the corrected hydrodynamic state reconstruction model is obtained. The iteration termination condition can be that the increase in the overall reliability score before and after correction is less than a set threshold, or the number of low-reliability reconstructed flows no longer decreases, or the maximum number of correction iterations is reached.

[0133] When the hydrodynamic state reconstruction model is not corrected, the cross section At any moment Initial reconstruction traffic The overall reliability score is The reconstructed flow rate output by the hydrodynamic state reconstruction model corrected by this invention is expressed as follows: Its overall reliability score is expressed as . and For example Figure 2 As shown, from Figure 2 It can be seen that after multiple rounds of correction, the overall reliability score of the reconstructed traffic improved, and some initial reconstructed traffic that was below the low reliability threshold before correction recovered to a higher reliability range after correction. Figure 3 As shown, the spatiotemporal distribution of the overall reliability score of the reconstructed flow becomes shallower overall, and the continuous distribution range of low reliability periods and low reliability sections is significantly reduced.

[0134] As can be seen from the above embodiments, the present invention does not only output a single error index, but can perform multi-source consistency diagnosis on implicit reconstructed traffic and transform the causes of low reliability into the basis for model parameter correction, thereby improving the accuracy of the reconstructed traffic output by the model.

[0135] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for reconstructing and correcting the implicit flow of a river cross-section under sparse water levels, characterized in that, Includes the following steps: Step S1: Select multiple cross sections along the flow direction of the target river section; The hydrodynamic state reconstruction model takes the cross section location, boundary conditions, initial conditions, and scheduling operation information at each moment of the simulation period as input. Under the action of the loss function with physical constraints, it performs hydrodynamic state simulation on all cross sections of the target river section during the simulation period and outputs the initial reconstructed water level field and the initial reconstructed flow field in the entire spatiotemporal domain. Step S2: Obtain the water level observation field formed by sparse water level observation data of the target river section during the simulation period; use the spatiotemporal neighborhood water level correction coupled with the spatiotemporal propagation effect algorithm of water level to perform spatiotemporal global correction on the initial reconstructed complete water level field through the water level observation field to obtain the corrected reconstructed complete water level field. Step S3: Construct a water level-flow reliability relationship model that includes the unsteady flow propagation factor, backwater backwater influence factor, and hysteresis loop strength. Using the corrected reconstructed water level complete field as a benchmark, perform reliability analysis on the initial reconstructed flow complete field to obtain the water level-flow decoupling condition factor for each initial reconstructed flow. Step S4: Construct a flow state evaluation model; the flow state evaluation model uses the corrected reconstructed water level complete field as a benchmark, and evaluates the state of each initial reconstructed flow from three flow state dimensions: physical equilibrium consistency, flow propagation consistency, and equivalent resistance stability, to obtain its flow state score and physical loss in each flow state dimension. The flow status scores of various flow status dimensions are weighted and fused, and the water level-flow decoupling condition factor is used as the flow reliability correction factor to obtain the comprehensive reliability score of each initial reconstructed flow. Step S5: Set low reliability criteria. Based on the water level-flow decoupling condition factor and comprehensive reliability score of each initial reconstructed flow in the complete field of initial reconstructed flow, identify the low reliability initial reconstructed flow and form a low reliability initial reconstructed flow field. Step S6: Construct a diagnostic contribution-driven loss correction model; the diagnostic contribution-driven loss correction model performs low reliability diagnosis on each low reliability initial reconstruction traffic from different traffic state dimensions, obtains the reliability reduction contribution of each traffic state dimension, the reliability reduction contribution corrects the physical loss in the corresponding traffic state dimension obtained by calling the traffic state evaluation model, obtains the physical loss correction amount, integrates the physical loss correction amount of each low reliability initial reconstruction traffic, and introduces a smoothing constraint term to obtain the comprehensive traffic physical loss corresponding to the low reliability initial reconstruction traffic field; Step S7: Feedback the integrated flow physical loss to the loss function of the hydrodynamic state reconstruction model to perform feedback correction on the hydrodynamic state reconstruction model.

2. The method for reconstructing and correcting the implicit flow of a river cross-section under sparse water levels according to claim 1, characterized in that, Step S2 specifically includes: Step S21: Obtain the water level observation field formed by sparse water level observation data of the target river section during the simulation period; extract the initial reconstructed local water level field with water level observation data from the initial reconstructed complete water level field; use formula (1) to calculate the deviation between each initial reconstructed water level in the initial reconstructed local water level field and the corresponding water level observation data in the water level observation field, and obtain the water level reconstruction deviation: （1） in: Indicates the spatiotemporal location with available water level observation data; Indicates cross-section At any moment Water level reconstruction deviation; Indicates cross-section At any moment The initial reconstructed water level; Indicates cross-section At any moment Water level observation data; Indicates cross-section Characteristic water depth; This indicates a stable parameter that avoids having an excessively small denominator when correcting for water level. Step S22: Locate the target initial reconstructed water level with water level observation data constraints in the spatiotemporal neighborhood of the initial reconstructed water level complete field. Using formulas (2) and (3), based on the deviation between the observed water level data in the spatiotemporal neighborhood and the initial reconstructed water level of the target, a spatiotemporal influence scale factor is introduced to adjust the initial reconstructed water level of the target. Priority correction is performed to obtain the water level correction change. : （2） （3） in: Indicates the initial reconstructed water level of the target. The target spatiotemporal location, Indicates the target cross section. Indicates the target time; Indicates the spatiotemporal location of the target The spatiotemporal neighborhood range; Represents the spatiotemporal neighborhood. Inside, various water level observation data Relative target initial reconstruction water level Spatial-temporal joint weights; Indicates the target cross section and cross-section The distance along the route between them; Indicates the scale of spatial influence; This indicates that time affects the scale; Step S23: Using formula (4), the target initial reconstructed water level is obtained. Corrected reconstructed water level : （4） in: This is the water level correction intensity coefficient, with a value ranging from 0 to 1, based on the spatiotemporal location within the spatiotemporal neighborhood. Water level reconstruction deviation Confirmed, if the water level reconstruction deviation... If the overall value is low within the spatiotemporal neighborhood, then decrease. Conversely, increase ; Step S24: Based on each corrected reconstructed water level, the water level correction change is smoothly extended along the cross-sectional direction and the time direction to correct the initial reconstructed water level that does not have water level observation data constraints in the spatiotemporal neighborhood, so as to obtain the complete field of corrected reconstructed water level.

3. The method for reconstructing and correcting the implicit flow of a river cross-section under sparse water levels according to claim 1, characterized in that, Step S3 specifically includes: Step S31: Calculate the propagation factor of unsteady flow based on the propagation mode of water level and flow rate changes over time. （5） in: Represents each spatiotemporal location within the entire spatiotemporal domain; Indicates cross-section At any moment The non-steady flow propagation factor; Indicates the fault surface of the reconstructed complete water level field after correction. At any moment The corrected and reconstructed water level; Indicates cross-section At any moment The initial reconstruction traffic; and These represent the weights of the water level change term and the flow rate change term, respectively. and These represent the normalized scales for the water level change term and the flow rate change term, respectively. Step S32: Calculate the backwater backwater influence factor based on the degree of reduction in water surface slope and the intensity of downstream boundary water level change. （6） in: Indicates cross-section At any moment Factors affecting the backwater backflow; Indicates cross-section At any moment Water surface slope; Indicates the normalized scale of water surface slope; Indicates at time The downstream boundary water level; Indicates the normalized scale of downstream boundary water level changes; Step S33: Calculate the hysteresis loop strength formed by the water level-flow process using a sliding time window. （7） in: Indicates cross-section At any moment hysteresis loop strength; Indicated by time A sliding time window centered on the subject; Indicates cross-section The magnitude of change in the initial reconstructed flow within the sliding time window; Indicates cross-section The magnitude of water level change is reconstructed after correction within the sliding time window; This refers to a stability parameter used to avoid having an excessively small denominator when calculating the strength of a hysteresis loop. Indicates cross-section Reconstruct the water level after correction at the next adjacent time step; Indicates time Step size; Step S34, the non-steady flow propagation factor Factors affecting backwater support Hysteresis loop strength By merging the data, the water level-flow rate decoupling condition factor is obtained. : （8） in: These represent the fusion weights of the unsteady flow propagation factor, the backwater backwater influence factor, and the hysteresis loop intensity, respectively. , .

4. The method for reconstructing and correcting the implicit flow of a river cross-section under sparse water levels according to claim 1, characterized in that, Step S4 specifically includes: Step S41, for each initial reconstruction flow By using the traffic state evaluation model, its performance in each traffic state dimension is obtained. Traffic status score and physical losses ;in, , These represent the physical equilibrium consistency dimension, the flow propagation consistency dimension, and the equivalent resistance stability dimension, respectively. Step S42, using formula (9), obtain the initial reconstruction flow. Overall reliability score : （9） in: These represent the weights of the physical equilibrium consistency dimension, the flow propagation consistency dimension, and the equivalent resistance stability dimension, respectively. , ; , and These represent the flow state scores for the physical equilibrium consistency dimension, the flow propagation consistency dimension, and the equivalent resistance stability dimension, respectively. This indicates the water level-flow rate decoupling factor. This represents the reduction factor for the water level-flow decoupling condition.

5. The method for reconstructing and correcting the implicit flow of a river cross-section under sparse water levels according to claim 4, characterized in that, Step S41 includes: Step S411: Using hydraulic geometry mapping elements, based on the cross-sectional hydraulic geometry data, a learnable mapping function is used to map each cross-section... At any moment Corrected reconstructed water level Mapped to cross-sectional hydraulic geometry, including the water flow area Hydraulic radius and water surface slope ; Step S412: Using the equivalent resistance parameter back-calculation unit, based on the initial reconstructed flow rate... The equivalent drag parameters of the cross-section can be derived from the hydraulic geometry of the cross-section: （10） in: Indicates cross-section At any moment The equivalent resistance parameters; This represents a stable parameter to avoid an excessively small denominator when performing flow correction. Step S413: Based on the hydraulic geometry of the cross section and the equivalent resistance parameters, calculate the flow state score and physical loss for the physical equilibrium consistency dimension and the equivalent resistance stability dimension, respectively; perform feature analysis on the initial reconstructed flow of adjacent cross sections, and calculate the flow state score and physical loss for the flow propagation consistency dimension.

6. The method for reconstructing and correcting the implicit flow of a river cross-section under sparse water levels according to claim 5, characterized in that, The calculation methods for the flow state score and physical loss in the physical balance consistency dimension are as follows: Step A1, Residuals of the Continuity Equation: （11） in: Indicates cross-section At any moment The residuals of the continuity equation; Indicates cross-section At any moment Lateral inflow term; Indicates the spatial direction of the cross-section from upstream to downstream; Step A2, Momentum Equation Residual: （12） in: Indicates cross-section At any moment The momentum equation residual; g represents gravitational acceleration; Indicates external sources or sinks or modifications; Step A3: Normalize the residuals of the continuity equation and the momentum equation, and construct a flow state score based on the physical equilibrium consistency dimension. : （13） （14） （15） in: and These represent the normalized scales of the residuals of the continuity equation and the momentum equation, respectively. and These represent the normalized scores of the residuals of the continuity equation and the momentum equation, respectively. and Let the weights of the residuals of the continuity equation and the momentum equation be respectively, satisfying... ; Step A4: Calculate the physical loss in the physical equilibrium consistency dimension. : （16） in: and These represent the physical loss weights of the residuals of the continuity equation and the momentum equation, respectively.

7. The method for reconstructing and correcting the implicit flow of a river cross-section under sparse water levels according to claim 5, characterized in that, The calculation methods for the flow state score and physical loss in the equivalent resistance stability dimension are as follows: Step B1, Equivalent resistance anomaly: (17) in: Indicates cross-section At any moment The equivalent resistance anomaly; , and These represent the weighting coefficients for the spatial variation term, the temporal variation term, and the out-of-bounds anomaly term, respectively. and These represent the normalized scales of the spatial variation term and the temporal variation term, respectively; This indicates that the equivalent resistance parameter is preset within a reasonable range. These represent the lower and upper limits of a preset reasonable range, respectively. Indicates the indicator function, in The indicator function takes the value 1 when the internal condition is true, and 0 otherwise. Step B2 converts the equivalent resistance anomaly into a flow state score based on the equivalent resistance stability dimension. : (18) Step B3: Calculate the physical loss in the equivalent resistance stability dimension. : (19) in: This indicates that the equivalent resistance parameter exceeds the preset reasonable range. The penalty items.

8. The method for reconstructing and correcting the implicit flow of a river cross-section under sparse water levels according to claim 5, characterized in that, The calculation methods for the traffic state score and physical loss in the traffic propagation consistency dimension are as follows: Step C1: Calculate and estimate the propagation time delay based on the initial reconstructed flow process at adjacent cross sections: （20） （21） in: Indicates cross-section To the cross-section The estimated propagation time delay; Indicates cross-section and cross-section Candidate propagation lag The correlation coefficient of the flow process under the following conditions; Indicates to make Largest candidate propagation delay ; Indicates cross-section At any moment The initial reconstruction traffic; Indicates cross-section At any moment The initial reconstructed flow, specifically referring to the cross-section At any moment Through candidate propagation time lag Initial reconstructed traffic after translation; Indicates the candidate propagation time lag Down and Both have overlapping time sets of data; Indicates cross-section In overlapping time sets Average initial reconstruction flow within; Indicates cross-section Through candidate propagation time lag Translation in overlapping time sets Average initial reconstruction flow within; Step C2, after considering the estimated propagation delay and lateral inflow, calculate the flow propagation anomaly degree: (22) in: Indicates cross-section At any moment The anomaly of traffic propagation; Indicates cross-section To the cross-section Lateral inflow rate; Indicates cross-section At any moment The initial reconstruction traffic; Step C3: Convert the traffic propagation anomaly degree into a traffic state score based on the traffic propagation consistency dimension. : (23) in: This indicates the attenuation scale of traffic propagation anomaly. Step C4, Physical loss in the consistency dimension of traffic propagation : (24) This step is now complete.

9. The method for reconstructing and correcting the implicit flow of a river cross-section under sparse water levels according to claim 4, characterized in that, The low reliability criterion is: （25） in: This indicates the identified low-reliability spatiotemporal locations. This indicates a low reliability flag operation. This represents the identified and flagged low-reliability initial reconstruction traffic, specifically representing the cross-section. At any moment The initial reconstruction traffic is low-reliability initial reconstruction traffic; Indicates the overall reliability threshold; This indicates the threshold value for water level-flow rate decoupling. Indicates the indicator function, in The indicator function takes the value 1 when the internal condition is met, and 0 otherwise.

10. The method for reconstructing and correcting the implicit flow of a river cross-section under sparse water levels according to claim 9, characterized in that, Step S6 includes: Step S61, construct the contribution model of diagnostic causes: （26） in: Representing the traffic state dimension The flow state for the initial reconstructed flow The reliability of the contribution is reduced; Representing the traffic state dimension The weights; Step S62, for the identified low-reliability initial reconstruction traffic The diagnostic cause contribution model is invoked to obtain each traffic state dimension. Reliability reduction contribution And convert it into adaptive correction weights. : （27） in: Representing the traffic state dimension The basic weights; Representing the traffic state dimension Diagnostic contribution amplification factor; Step S63: Calculate the comprehensive flow physical loss corresponding to the low-reliability initial reconstructed flow field. : （28） in: Represents a set of spatiotemporal locations with low reliability; , and These represent the adaptive correction weights for the physical equilibrium consistency dimension, the flow propagation consistency dimension, and the equivalent resistance stability dimension, respectively. , and These represent the spatial and temporal positions of the physical equilibrium consistency dimension, the flow propagation consistency dimension, and the equivalent resistance stability dimension, respectively, in low-reliability environments. The physical loss is read from the flow state evaluation model; Indicates the smoothing constraint weights; The smoothing constraint term representing the correction result is calculated using the following formula: （29） in: This indicates the number of spatiotemporal locations with low reliability. and These represent the spatiotemporal locations of low reliability. The corrected reconstructed water level and initial reconstructed flow rate.

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