River course roughness optimization method based on unbiased estimation of water level mean values of different flow levels
By dividing the river section and flow rate in the one-dimensional hydrodynamic model, the unbiased estimation method is used to optimize the roughness rate, which solves the problem of high difficulty and low efficiency in determining the roughness rate of the river channel, and achieves more refined roughness optimization, which improves the accuracy and efficiency of reservoir water level prediction.
Patent Information
- Application Number
- CN202510257009.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-05
- Publication Date
- 2025-07-18
AI Technical Summary
The refinement automatic rate determination of the river channel roughness in the existing one-dimensional hydrodynamic model is difficult and the optimization efficiency is low, resulting in the calculation accuracy of the hydrodynamic model in engineering practice.
By dividing the river section and flow rate, the roughness is optimized by unbiased estimation method, and the one-dimensional hydrodynamic model is discretely solved using the four-point eccentric hidden format of Preissmann. The iterative step length is adaptively adjusted according to the changes in the prediction error of the water level station before and after the roughness optimization, and iterative optimization is obtained to obtain the roughness of the river channel of different flow rates.
It improves the degree of refinement and efficiency of the rough rate determination, reduces uncertainty, simplifies the optimization method, and is suitable for the precise level prediction of reservoir flood control scheduling in engineering practice.
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Figure CN120336664A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the field of reservoir operation control, and particularly relates to a method for optimizing channel roughness based on unbiased estimation of water level means at different flow levels. Background Art
[0002] The prediction and calculation of the water level at the key section of a reservoir play an important role in reservoir flood control scheduling. The commonly used method is to calculate by solving the one-dimensional hydrodynamic equations (Saint-Venant equations). This model has a complete mathematical theory support and good interpretability. However, the calibration of the sensitivity parameter channel roughness in the model is a difficult problem. Whether the roughness value is reasonable directly affects the accuracy of channel hydrodynamic calculation, and there is currently no general method for calculating roughness.
[0003] In actual engineering, the channel roughness is generally determined by the look-up table method or manual debugging method, which has great subjectivity and arbitrariness. When the scale of channel calculation is large, the manual debugging workload is large and the accuracy is difficult to guarantee. Some scholars have proposed roughness inversion methods, generally taking the sum of squares of water level prediction errors at all water level stations in the channel or its variants as the optimization objective, and using optimization methods such as the simplex method, improved Newton-Raphson method, singular value decomposition method, composite shape method, undetermined Lagrange multiplier variational method, genetic algorithm, particle swarm optimization algorithm, simulated annealing algorithm and machine learning to automatically calibrate the roughness. However, the current roughness inversion research generally only considers the variation of roughness along the channel, and rarely considers the variation of roughness at different flow levels; for individual calibration methods considering the variation of roughness with flow or water level, their optimization methods are complex, and in addition, the one-dimensional hydrodynamic model itself is complex to solve, and the combination of the two leads to low optimization efficiency and high calculation cost, which is restricted more in engineering practice.
[0004] Therefore, it is very necessary to calibrate the roughness finely and quickly at different flow levels according to the measured data such as water level and flow. Summary of the Invention
[0005] The technical problem of the invention is that the fine automatic calibration of the channel roughness in the existing one-dimensional hydrodynamic model is difficult, the roughness optimization method with the sum of squares of water level prediction errors at all water level stations in the channel or its variants as the optimization objective function is complex, and the optimization efficiency is low, resulting in the inability to guarantee the calculation accuracy of the hydrodynamic model in engineering practice.
[0006] The object of the present invention is to solve the above problems and provide a method for optimizing the roughness coefficient of a river channel based on the unbiased estimation of the water level mean of different flow levels. The present invention divides river reaches and flow levels, groups the simulated water level errors of the one-dimensional hydrodynamic model according to different flow levels, takes the unbiased estimation of the true water level mean of each group at each water level station as the optimization objective, and determines the roughness coefficient optimization direction for each flow level; according to the change of the predicted mean absolute error of each water level station before and after the roughness coefficient optimization, the iteration step size is reduced, and the roughness coefficient of the river channel corresponding to different flow levels is obtained through iterative optimization. Compared with the manual trial-and-error method, it greatly improves the parameter calibration efficiency and reduces the uncertainty; compared with the previous roughness coefficient inversion methods, it simplifies the optimization method. This method takes the mean of the predicted water level errors of each water level station under different flow levels approaching 0 as the optimization objective, adaptively optimizes the roughness coefficient of each river reach respectively, and is easy to implement. This method can obtain a more refined roughness coefficient, taking into account both the changes along the way and the changes brought by the flow rate, improving the usability and facilitating its application in engineering practice.
[0007] In order to achieve the above technical features, the object of the present invention is achieved as follows: A method for optimizing the roughness coefficient of a river channel based on the unbiased estimation of the water level mean of different flow levels, comprising the following steps:
[0008] Step 1, collect the hydrological data and topographic data of the main and tributary rivers in the reservoir area to form the initial conditions, boundary conditions and topographic data required for the one-dimensional hydrodynamic model;
[0009] Step 2, collect the historical measured water level data of the water level stations in the reservoir area to form a measured water level data set;
[0010] Step 3, divide the river reaches and flow levels according to the spatial distribution of the water level stations, give the initial empirical roughness coefficient values of each river reach under different flow levels, and give the roughness coefficient search interval;
[0011] Step 4, set the maximum number of algorithm iterations and the initial update step size Δn of the roughness coefficient of each river reach i , where i represents the river reach index, the acceptable interval [-ε, ε] of the mean of the water level prediction errors of each group at each water level station, and the expected mean absolute water level error e;
[0012] Step 5, use the Preissmann four-point eccentric implicit format to discretely solve the one-dimensional hydrodynamic model, and calculate the water surface profile and flow process of the river channel under the current roughness coefficient;
[0013] Step 6, group the corresponding water level prediction errors according to different flow levels, judge whether the mean of the predicted water levels of each group is an unbiased estimate of the true water level mean, and determine the roughness coefficient optimization direction for each flow level;
[0014] Step 7: Execute Step 5. If, after updating the roughness coefficient, the mean absolute error of the water levels at some gauging stations increases, then reduce the roughness coefficient update step size for the corresponding river reach. It is recommended to reduce the roughness coefficient update step size to half of the original step size, and then execute Step 6.
[0015] Step 8: If the maximum number of iterations is reached, or the water level errors at all gauging stations are less than the set value e, the algorithm ends, and the output of the model, i.e., the corresponding channel roughness coefficient values at different flow levels, is obtained.
[0016] Preferably, in Step 1, it specifically includes:
[0017] Collect or specify the initial water levels and flows at each cross-section of the main stream and tributaries to form the initial conditions of the one-dimensional hydrodynamic model.
[0018] Collect the reservoir inflow, water level in front of the dam, and upstream main stream and tributary inlet flow sequences to form the boundary conditions of the one-dimensional hydrodynamic model.
[0019] Collect the topographic data of each cross-section of the main stream and tributaries.
[0020] Preferably, when solving the one-dimensional hydrodynamic model in Step 5, the Preissmann four-point eccentric implicit scheme is used to discretize the Saint-Venant equations.
[0021] Preferably, Step 5 specifically includes:
[0022] Intercept several cross-sections on the river to discretize the river length, and use k to represent the cross-section number; then discretize the calculation time, with the time interval denoted as Δt, use s to represent the time sequence number, and use θ to represent the time weight factor.
[0023] Under this discretization scheme, the function value and each first-order partial derivative at the point (x, t) are calculated as follows:
[0024]
[0025] In the formula: Δx k represents the distance from the k-th cross-section to the (k + 1)-th cross-section; Δt represents the time step; since the water flow motion equation contains non-linear terms, a discrete non-linear equation set can be obtained.
[0026] Preferably, in Step 5, in the numerical calculation method, when solving the non-linear equation set, and when the river topography is relatively complex, the iterative method is not easily convergent. Based on this, a linearization method is adopted to linearize the non-linear terms therein and transform them into a linear equation set.
[0027] Preferably, in Step 6, it specifically includes:
[0028] If the mean value of the water level errors at a certain set of corresponding flow levels is greater than the right boundary ε of the acceptable interval, update the roughness coefficient downward in the search space, i.e., ni,j = n i,j -Δn i , n i,j represents the roughness coefficient corresponding to the j-th flow level of the i-th river reach;
[0029] If the mean value of the water level error at the corresponding flow level is less than the left boundary -ε of the acceptable interval, update the roughness coefficient of the corresponding river reach upward in the search space, that is, n i,j = n i,j +Δn i ;
[0030] If the mean value of the water level prediction errors at all stations is within the set acceptable interval, the algorithm ends and outputs the current roughness coefficient value.
[0031] Preferably, in step 6, considering that there is a lack of measured flow data at some key cross-sections, the flow is calculated using a hydrodynamic model when counting different flow levels.
[0032] Preferably, in step 6, when grouping according to different flow levels, for the j-th flow level Q j , count the water level errors corresponding to the flows falling within the interval as a group.
[0033] The present invention has the following beneficial effects:
[0034] 1. By dividing different flow levels and adopting an adaptive iterative optimization method for the roughness coefficients of each river reach, the present invention can quickly obtain more refined roughness coefficients along the river course, further saving the time and labor costs for roughness coefficient calibration, effectively improving the efficiency of roughness coefficient calibration in engineering practice, improving the calculation accuracy of the hydrodynamic model, and then accurately predicting the water levels at key cross-sections, providing technical support for flood control and beneficial operation decision-making of large reservoirs or cascade reservoirs. BRIEF DESCRIPTION OF THE DRAWINGS
[0035] The present invention will be further described below in conjunction with the drawings and embodiments.
[0036] Figure 1 is a schematic flow chart of the method for inverse calculation of river roughness coefficient of the present invention.
[0037] Figure 2 (a)(b)(c)(d) are the comparison effect diagrams of the predicted water levels and measured water levels at the Miaohe, Zigui, Badong, and Wushan stations of the Three Gorges Reservoir after roughness coefficient calibration from July 1, 2023 to July 31, 2023 in the embodiment.
[0038] Figure 3 (a)(b)(c)(d) are the comparison effect diagrams of the predicted water levels and measured water levels at the Fengjie, Wanxian, Zhongxian, and Baishatuo stations of the Three Gorges Reservoir after roughness coefficient calibration from July 1, 2023 to July 31, 2023 in the embodiment.
[0039] Figure 4 (a)(b)(c)(d) are the comparison effect diagrams of the predicted water levels and the measured water levels at Qingxichang, Beigong, Changshou, and Taihonggang stations of the Three Gorges Reservoir after the roughness coefficient calibration from July 1 to July 31, 2023 in the embodiment.
[0040] Figure 5 (a)(b)(c)(d) are the comparison effect diagrams of the predicted water levels and the measured water levels at Yuzui, Tongluoxia, Luozhongzi, and Xiaonanhai stations of the Three Gorges Reservoir after the roughness coefficient calibration from July 1 to July 31, 2023 in the embodiment.
[0041] Figure 6 (a)(b) are the comparison effect diagrams of the predicted water levels and the measured water levels at Jingangtuo and Zhutuo stations of the Three Gorges Reservoir after the roughness coefficient calibration from July 1 to July 31, 2023 in the embodiment.
[0042] Figure 7 It shows the change of the average absolute error of the water levels at each station during the roughness coefficient inversion process by using the data of the Three Gorges Reservoir from July 1 to July 31, 2023 in the embodiment.
[0043] Figure 8 (a)(b)(c)(d) are the comparison effect diagrams of the predicted water levels and the measured water levels at Miaohe, Zigui, Badong, and Wushan stations of the Three Gorges Reservoir after the roughness coefficient calibration from October 1 to October 31, 2023 in the embodiment.
[0044] Figure 9 (a)(b)(c)(d) are the comparison effect diagrams of the predicted water levels and the measured water levels at Fengjie, Wanxian, Zhongxian, and Baishatuo stations of the Three Gorges Reservoir after the roughness coefficient calibration from October 1 to October 31, 2023 in the embodiment.
[0045] Figure 10 (a)(b)(c)(d) are the comparison effect diagrams of the predicted water levels and the measured water levels at Qingxichang, Beigong, Changshou, and Shantuo stations of the Three Gorges Reservoir after the roughness coefficient calibration from October 1 to October 31, 2023 in the embodiment.
[0046] Figure 11 (a)(b)(c)(d) are the comparison effect diagrams of the predicted water levels and the measured water levels at Taihonggang, Tongluoxia, Cuntan, and Xiaonanhai stations of the Three Gorges Reservoir after the roughness coefficient calibration from October 1 to October 31, 2023 in the embodiment.
[0047] Figure 12 (a)(b) are the comparison effect diagrams of the predicted water levels and the measured water levels at Jingangtuo and Zhutuo stations of the Three Gorges Reservoir after the roughness coefficient calibration from October 1 to October 31, 2023 in the embodiment.
[0048] Figure 13 (a)(b)(c)(d) are the comparison effect diagrams of the predicted water levels and the measured water levels at the Miahe, Zigui, Badong, and Wushan stations of the Three Gorges Reservoir after the roughness calibration from July 1 to July 31, 2024, in the embodiments.
[0049] Figure 14 (a)(b)(c)(d) are the comparison effect diagrams of the predicted water levels and the measured water levels at the Fengjie, Baisha, Changshou, and Taihonggang stations of the Three Gorges Reservoir after the roughness calibration from July 1 to July 31, 2024, in the embodiments.
[0050] Figure 15 (a)(b)(c)(d) are the comparison effect diagrams of the predicted water levels and the measured water levels at the Yuzui, Tongluoxia, Cuntan, and Xiaonanhai stations of the Three Gorges Reservoir after the roughness calibration from July 1 to July 31, 2024, in the embodiments.
[0051] Figure 16 (a)(b) are the comparison effect diagrams of the predicted water levels and the measured water levels at the Jingangtuo and Zhutuo stations of the Three Gorges Reservoir after the roughness calibration from July 1 to July 31, 2024, in the embodiments. Detailed implementation manners
[0052] The following further describes the implementation manners of the present invention with reference to the accompanying drawings.
[0053] Embodiment 1:
[0054] Please refer to Figure 1 , the present invention provides a technical solution: a channel roughness optimization method based on unbiased estimation of water level means at different flow levels, including the following steps:
[0055] Step 1, collect the hydrological data and topographic data of the main and tributary rivers in the reservoir area to form the initial conditions, boundary conditions, and topographic data required for the one-dimensional hydrodynamic model; specifically including:
[0056] Collect or specify the initial water levels and flows at each cross-section of the main and tributary rivers to form the initial conditions of the one-dimensional hydrodynamic model;
[0057] Collect the reservoir inflow, water level in front of the dam, and upstream main and tributary inlet flow sequences to form the boundary conditions of the one-dimensional hydrodynamic model;
[0058] Collect the topographic data of each cross-section of the main and tributary rivers.
[0059] Step 2, collect the historical measured water level data of the water level stations in the reservoir area to form a measured water level data set;
[0060] Step 3, divide the river reaches and flow levels according to the spatial distribution of the water level stations, specify the initial empirical roughness values of each river reach under different flow levels, and specify the roughness search interval;
[0061] Step 4, set the maximum number of algorithm iterations and the initial update step Δn of the roughness coefficient for each river reach i , where i represents the river reach index, the acceptable interval [-ε, ε] of the mean of the water level prediction errors for each group of water level stations, and the expected mean absolute water level error e;
[0062] Step 5, use the Preissmann four-point eccentric implicit scheme to discretely solve the one-dimensional hydrodynamic model, and calculate the water surface profile and flow process under the current roughness coefficient;
[0063] When solving the one-dimensional hydrodynamic model, the Preissmann four-point eccentric implicit scheme is used to discretize the Saint-Venant equations;
[0064] Intercept several cross-sections on the river to discretize the river length, and use k to represent the cross-section number; then discretize the calculation time, the time interval is denoted as Δt, use s to represent the time sequence number, and use θ to represent the time weight factor;
[0065] Under this discretization scheme, the function value and the first-order partial derivatives at the point (x, t) are calculated as follows:
[0066]
[0067] In the formula: Δx k represents the distance from the k-th cross-section to the (k + 1)-th cross-section; Δt represents the time step. Since the flow motion equation contains non-linear terms, a discrete non-linear equation system can be obtained. Since the flow motion equation contains non-linear terms, a discrete non-linear equation system can be obtained.
[0068] In numerical calculation methods, solving non-linear equation systems is costly, and when the river terrain is complex, the iteration method is not easy to converge. Therefore, the linearization method proposed by Yang Guolu in the book "River Mathematical Model" is adopted to linearize the non-linear terms and transform them into a linear equation system.
[0069] Step 6, group the corresponding water level prediction errors according to different flow levels, judge whether the mean of the predicted water levels in each group is an unbiased estimate of the true water level mean, and determine the roughness coefficient optimization direction for each flow level. Specifically, if the mean of the water level errors under a certain corresponding flow level is greater than the right boundary ε of the acceptable interval, update the roughness coefficient downward in the search space, that is, n i,j = n i,j -Δn i , n i,j represents the roughness coefficient corresponding to the j-th flow level of the i-th river reach;
[0070] If the mean of the water level errors under the corresponding flow level is less than the left boundary -ε of the acceptable interval, update the roughness coefficient of the corresponding river reach upward in the search space, that is, ni,j = n i,j + Δn i ;
[0071] If the mean of the water level prediction errors at all stations is within the set acceptable range, the algorithm ends and outputs the current roughness coefficient value.
[0072] Step 7, execute Step 5. If, after updating the roughness coefficient, the mean absolute error of the water levels at some water level stations increases, then reduce the roughness coefficient update step size for the corresponding river reach. It is recommended to reduce the roughness coefficient update step size to half of the original step size, and execute Step 6;
[0073] Step 8: If the maximum number of iterations is reached, or the water level errors at all water level stations are less than the set value e, the algorithm ends and the output of the model, that is, the corresponding channel roughness coefficient values at different flow levels, is obtained.
[0074] Furthermore, in Step 6, considering that there is a lack of measured flow data at some key cross-sections, the flow is calculated using a hydrodynamic model when statistically analyzing different flow levels.
[0075] Furthermore, in Step 6, when grouping by different flow levels, for the j-th flow level Q j , the water level errors corresponding to the flows falling within the interval are statistically analyzed as a group.
[0076] Example 2:
[0077] The method for adaptive iterative inversion of channel roughness coefficient at different flow levels proposed by the present invention can be applied to the calibration of the roughness coefficient of the river reach in the large reservoir area.
[0078] The Three Gorges Reservoir is the reservoir with the largest storage capacity in the Yangtze River Basin of our country. The reservoir area is large and the river channel is complex and changeable. The distance from Zhutuo in its upper reaches to the dam is about 757 km. During the flood season and the water storage period when there is a large inflow at the reservoir tail, flooding is likely to occur. Therefore, the accurate prediction of the water surface line in the Three Gorges Reservoir area under different dispatching schemes is crucial. At present, the most reliable method in practice is to construct a one-dimensional hydrodynamic model, and the calibration of the roughness coefficient is a difficult and key task. The Three Gorges Reservoir area is selected in the example to invert the roughness coefficient of the river channel in the Three Gorges Reservoir area.
[0079] As Figure 1 shown, the method for adaptive iterative inversion of channel roughness coefficient at different flow levels includes the following steps,
[0080] Step 1: Collect the initial water levels and flows of each cross-section of the main and tributary rivers to form the initial conditions of the one-dimensional hydrodynamic model; collect the reservoir inflow, the water level in front of the dam, and the upstream main and tributary inlet flow sequences to form the boundary conditions of the one-dimensional hydrodynamic model; collect the topographic data of each cross-section of the main and tributary rivers.
[0081] The embodiment takes Zhutuo as the upper boundary and the front of the dam as the lower boundary, and considers 14 relatively large tributaries including the Jialing River, Yulin River, Longxi River, Wujiang River, Quxi River, Long River, Xiaojiang River, Tangxi River, Modao River, Meixi River, Daning River, Yanduhe River, Qinggang River and Xiangxi River as lateral inflows. The inflow discharges of Zhutuo, Beibei and Wulong are collected as the inlet discharges of the main stream of the Yangtze River, the Jialing River and the Wujiang River respectively, and the excess reservoir inflow of the Three Gorges is evenly distributed to the other twelve tributaries. The embodiment collects the flow data of the Zhutuo Station, Beibei Station, Wulong Station, the reservoir inflow of the Three Gorges and the water level data in front of the Three Gorges Dam from July 1 to July 31, 2023, from October 1 to October 31, 2023, and from July 1 to July 31, 2024; the embodiment collects the topographic data of 417 sections from Zhutuo to the front of the dam on the main stream of the Yangtze River.
[0082] Step 2: The embodiment collects the measured water level data of 20 important stations in the reservoir area, namely Miaohe, Zigui, Badong, Wushan, Fengjie, Wanxian, Zhongxian, Baishatuo, Qingxichang, Beigong, Changshou, Fantuo, Taihonggang, Yuzui, Tongluoxia, Cuntan, Luozhongzi, Xiaonanhai, Jingangtuo, Zhutuo, from July 1 to July 31, 2023, from October 1 to October 31, 2023, and from July 1 to July 31, 2024, to form a measured water level data set.
[0083] Step 3: According to the spatial distribution of important stations, river reaches are divided. The embodiment divides into 20 river reaches in total, and according to the flow levels of 2500, 3000, 5000, 8000, 10000, 15000, 20000, 30000, 40000, 50000, 60000, 80000 m 3 / s, the initial roughness coefficient value n i,j is given for each river reach, i = 1, 2,..., 20, j = 1, 2,... 10, n i,j represents the roughness coefficient value at the j-th flow level in the i-th river reach.
[0084] In order to test the roughness inversion effect, when calibrating the roughness coefficient for the water level data from July 1 to July 31, 2023, the initial roughness coefficients of the river reaches upstream of Wushan are all set to 0.04, and the initial roughness coefficient from Wushan to the front of the dam is 0.07. For the roughness inversion from October 1 to October 31, 2023, the results finally calibrated using the data from July 1 to July 31, 2023 are taken as the initial values. For the roughness inversion from July 1 to July 31, 2024, adopting a scenario closer to the actual application, the embodiment takes the empirical values in engineering practice as the initial values.
[0085] Step 4: The acceptable interval for the mean of the water level prediction errors at each station in the embodiment is [-0.1 m, 0.1 m], and the desired mean absolute error of the water level is 0.3 m. For the calibration of the roughness coefficient from July 1, 2023 to July 31, 2023, the maximum number of algorithm iterations in the embodiment is set to 20, and the initial update step size Δn of the roughness coefficient for each river reach i = 0.005; For the inversion of the roughness coefficient from October 1, 2023 to October 31, 2023, on the basis of the former with fine-tuning, the maximum number of algorithm iterations in the embodiment is set to 10, and the initial update step size of the roughness coefficient for the river reaches between Shantuo, Taihonggang, Yuzui, Tongluoxia, Cuntan, and Luozhongzi is set to Δn i = 0.002, and the initial update step size of the roughness coefficient for the remaining river reaches is Δn i = 0.001; For the inversion of the roughness coefficient from July 1, 2024 to July 31, 2024, the empirical values in engineering practice are taken as the initial values, the maximum number of algorithm iterations is set to 10, and the initial update step size of the roughness coefficient for each river reach is Δn i = 0.001.
[0086] For each time period, Steps 5 to 8 are executed separately.
[0087] Step 5: Calculate the water surface profile and flow process of the river channel under the current roughness coefficient, and discretize the Saint-Venant equation using the Preissmann four-point eccentric implicit scheme;
[0088] Step 6: Statistically calculate the mean of the water level prediction errors at each station under different flow levels. Among them, for the j-th flow level Q j , statistically calculate the water level errors corresponding to the flows falling within the interval . If the mean of the water level errors under the corresponding flow level is greater than 0.1 m, the roughness coefficient of the corresponding river reach at this flow level is equal to the original roughness coefficient minus the corresponding update step size, that is, n i,j = n i,j -Δn i ; If the mean of the water level errors under the corresponding flow level is less than -0.1 m, update the roughness coefficient of the corresponding river reach upward, that is, n i,j = n i,j +Δn i ; If the mean value is within the interval [-0.1 m, 0.1 m], the roughness coefficient remains unchanged.
[0089] Step 7: Execute Step 5. If, after updating the roughness coefficient, the mean absolute error of the water level prediction at some stations becomes larger, the optimization step size of the roughness coefficient of the corresponding river reach is reduced to half of the original step size, that is, Δn i = Δn i / 2, and then execute Step 6;
[0090] Step 8: If the maximum number of iterations is reached, or the water level errors of all water level stations are less than the set value, the process ends, and the corresponding channel roughness values at different flow levels are obtained.
[0091] Table 1 shows the roughness inversion values obtained by the embodiment based on the water level data from July 1, 2023 to July 31, 2023. Since the flow rates of each river section in July cannot cover all flow levels, the roughness corresponding to the flow levels not covered by the data (when the flow rate is relatively large or small) is the original roughness without adjustment.
[0092] Table 1 Roughness calibrated in July 2023 in the embodiment
[0093]
[0094]
[0095] Figures 2 - 6 It shows the fitting situation of the water levels at Miaohe, Zigui, Badong, Wushan, Fengjie, Wanxian, Zhongxian, Baishatuo, Qingxichang, Beigong, Changshou, Taihonggang, Yuzui, Tongluoxia, Luozhongzi, Xiaonanhai, Jingangtuo, and Zhutuo from July 1, 2023 to July 31, 2023 after roughness calibration. It can be seen that the predicted water level and the actual water level are in good agreement, verifying the rationality of roughness calibration.
[0096] Table 2 shows the mean absolute error of the predicted water levels at each station in July 2023 after roughness calibration in the embodiment. It can be seen that the calibration effect is good.
[0097] Table 2 Mean absolute error of the predicted water levels at each station in July 2023 in the embodiment
[0098]
[0099]
[0100] Figure 7 It shows the change process of the mean absolute error of the water levels at each station with the progress of iteration for the data from July 1, 2023 to July 31, 2023. It can be seen that the algorithm converges quickly, and the results tend to be stable after about eight iterations.
[0101] Table 3 shows the roughness inversion values obtained by the embodiment based on the water level data from October 1, 2023 to October 31, 2023. Since it is a fine-tuning based on the roughness values in July 2023, it can be seen that only the roughness of individual river sections has changed slightly (the bold part) at some flow levels.
[0102] Table 3 Roughness calibrated in October 2023 in the embodiment
[0103]
[0104]
[0105] Figures 8 - 12 After the roughness coefficient calibration, the water level fitting conditions of Miaohe, Zigui, Badong, Wushan, Fengjie, Wanxian, Zhongxian, Baishatuo, Qingxichang, Beigong, Changshou, Shantuotuo, Taihonggang, Tongluoxia, Cuntan, Xiaonanhai, Jingangtuo, and Zhutuo from October 1, 2023 to October 31, 2023 are shown. It can be seen that the predicted water level and the actual water level are in good agreement, verifying the rationality of the roughness coefficient calibration.
[0106] Table 4 shows the mean absolute error of the predicted water levels at each station in October 2023 after the roughness coefficient calibration of the embodiment. Compared with July, the error during the water storage period in October is generally smaller.
[0107] Table 4 Mean absolute error of the predicted water levels at each station in October 2023 of the embodiment
[0108] Station Name Miaohe Zigui Badong Wushan Fengjie Mean Absolute Error (m) 0.065 0.065 0.060 0.134 0.067 Station Name Wanxian Zhongxian Baishatuo Qingxichang Beigong Mean Absolute Error (m) 0.066 0.056 0.110 0.056 0.084 Station Name Changshou Shantuo Taihonggang Yuzui Tongluoxia Mean Absolute Error (m) 0.081 0.076 0.085 0.138 0.134 Station Name Cuntan Luozhongzi Xiaonanhai Jingangtuo Zhutuo Mean Absolute Error (m) 0.105 0.880 0.124 0.101 0.117
[0109] Table 5 shows the roughness coefficient inversion values obtained by the embodiment based on the water level data from July 1, 2024 to July 31, 2024. For the roughness coefficient inversion in July 2024, the embodiment adopts a scenario closer to the actual application and takes the empirical value in engineering practice as the initial value.
[0110] Table 5 Roughness coefficient calibrated in July 2024 of the embodiment
[0111]
[0112]
[0113] Figures 13 - 16 After the roughness coefficient calibration, the water level fitting conditions of each station in the Three Gorges Reservoir from July 1, 2024 to July 31, 2024 are shown. It can be seen that the predicted water level and the actual water level are in good agreement, verifying the rationality of the roughness coefficient calibration.
[0114] Table 6 shows the comparison results of the mean absolute error of the predicted water levels at each station in July 2024 after applying the empirical roughness coefficient and the refined roughness coefficient calibration. It can be seen that except for a slight increase in the mean absolute error at the Wanxian, Zhongxian, and Qingxichang stations, the mean absolute error of the water levels at the other stations has decreased significantly, indicating the effectiveness of the refined roughness coefficient automatic calibration method.
[0115] Table 6 Mean absolute error of the predicted water levels at each station before and after the roughness coefficient update in July 2024 of the embodiment
[0116]
[0117] The above are only optional embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.
Claims
1. An optimized method for channel roughness based on unbiased estimation of water level mean of different flow levels, characterized in that, It includes the following steps: Step 1: Collect the hydrological data and topographic data of the main and tributary rivers in the reservoir area to form the initial conditions, boundary conditions, and topographic data required for the one-dimensional hydrodynamic model; Step 2: Collect the historical measured water level data of the water level stations in the reservoir area to form a measured water level data set; Step 3: According to the spatial distribution of the water level stations, divide the river reaches and flow levels, give the initial empirical roughness coefficient values of each river reach under different flow levels, and give the roughness coefficient search interval; Step 4, set the maximum number of algorithm iterations and the initial update step Δn of the roughness coefficient for each river reach i , where i represents the river reach index, the acceptable interval [-ε, ε] of the mean of the water level prediction errors for each group of water level stations, and the expected mean absolute error e of the water level; Step 5: Use the Preissmann four-point eccentric implicit scheme to discretely solve the one-dimensional hydrodynamic model, and calculate the water surface profile and flow process of the river channel under the current roughness coefficient; Step 6: Group the corresponding water level prediction errors according to different flow levels, judge whether the mean value of the predicted water levels in each group is an unbiased estimate of the true water level mean value, and determine the roughness coefficient optimization direction for each flow level; Step 7: Execute Step 5. If, after updating the roughness coefficient, the mean absolute error of the water levels of some water level stations increases, then reduce the roughness coefficient update step size of the corresponding river reach. It is recommended to reduce the roughness coefficient update step size to half of the original step size, and execute Step 6; Step 8: If the maximum number of iterations is reached, or the water level errors of all water level stations are less than the set value e, the algorithm ends, and the output of the model, that is, the corresponding river channel roughness coefficient values under different flow levels, is obtained.
2. The channel roughness optimization method based on unbiased estimation of water level mean value at different flow rates according to claim 1, wherein Specifically included in Step 1 are: Collect or give the initial water levels and flows of each cross-section of the main and tributary rivers to form the initial conditions of the one-dimensional hydrodynamic model; Collect the reservoir inflow, water level in front of the dam, and upstream main and tributary inlet flow sequences to form the boundary conditions of the one-dimensional hydrodynamic model; Collect the topographic data of each cross-section of the main and tributary rivers.
3. The channel roughness optimization method based on unbiased estimation of water level mean value at different flow rates according to claim 1, wherein, When solving the one-dimensional hydrodynamic model in Step 5, the Preissmann four-point eccentric implicit scheme is used to discretize the Saint-Venant equation.
4. The channel roughness optimization method based on unbiased estimation of water level mean value at different flow rates according to claim 3, characterized in that, Step 5 specifically includes: Intercept several cross-sections on the river to discretize the river length, and use k to represent the cross-section number; then discretize the calculation time, the time interval is denoted as Δt, use s to represent the time serial number, and use θ to represent the time weight factor; Under this discretization scheme, the function value and each first-order partial derivative at the point (x, t) are calculated as follows: where: Δx k represents the distance from the k-th cross section to the (k + 1)-th cross section; Δt represents the time step; since the water flow motion equation contains non-linear terms, a discrete non-linear equation set can be obtained.
5. The channel roughness optimization method based on unbiased estimation of water level mean value at different flow rates according to claim 4, characterized in that, In Step 5, in the numerical calculation method, when solving the nonlinear equations, and when the river topography is relatively complex, the iterative method is not easy to converge. Based on this, a linearization method is adopted to linearize the nonlinear terms therein and transform them into linear equations.
6. The channel roughness optimization method based on unbiased estimation of water level mean value at different flow rates according to claim 5, characterized in that, Specifically included in Step 6 are: If the mean water level error under a certain corresponding flow rate level is greater than the right boundary ε of the acceptable interval, update the roughness coefficient downward in the search space, i.e., n i,j = n i,j - Δn i , n i,j represents the roughness coefficient corresponding to the j-th flow rate level of the i-th river reach; If the mean water level error at the corresponding flow rate is less than the left boundary of the acceptable interval - ε, update the roughness coefficient of the corresponding river reach upward in the search space, i.e., n i,j = n i,j + Δn i ; If the mean value of the water level prediction errors of all stations is within the set acceptable interval, the algorithm ends, and the current roughness coefficient value is output.
7. The channel roughness optimization method based on unbiased estimation of water level mean value at different flow rates according to claim 6, wherein In Step 6, considering that there is a lack of measured flow data for some key cross-sections, the flow is calculated using the hydrodynamic model when counting different flow levels.
8. The channel roughness optimization method based on unbiased estimation of water level mean value for different flow rates according to claim 7, characterized in that, In step 6, when grouping by different flow levels, for the j-th flow level Q j , the water level errors corresponding to the flows falling within the interval are counted as a group.