Successive approximation method-based water flow sediment carrying force coefficient and index inversion method

Abstract

The invention discloses a water flow sediment carrying force coefficient and index inversion method based on a successive approximation method, and relates to the technical field of river water and sediment transport simulation, and the method comprises the following steps: 1, taking a water flow sediment carrying force coefficient k and an index m of each section as piecewise linear functions of water and sediment comprehensive parameters, constructing a water flow sediment carrying force parameter inversion model based on a one-dimensional river network water sediment mathematical model by taking the minimum sum of squares of sediment content errors of each observation station as an objective function and taking the value ranges of the water flow sediment carrying force coefficient k and the index m and the maximum sediment content error as constraints; 2, parameter values such as grouping sediment carrying capacity grading, recovery saturation coefficient and roughness in the one-dimensional river network water-sediment mathematical model are determined; 3, adopting a successive approximation method to carry out parallel solving on the water flow sediment carrying force parameter inversion model; according to the method provided by the invention, automatic calibration of the water flow sand-carrying force coefficient k and the index m can be realized, so that the calibration difficulty of the water flow sand-carrying force parameter is reduced, and the simulation precision of a water-sand mathematical model is improved.

Description

Technical Field

[0001] The invention relates to the technical field of river water and sediment transport simulation, and in particular to a method for inverting a water flow sediment entrainment coefficient and an index based on a successive approximation method. Background Art

[0002] The sediment carrying capacity of water flow is a comprehensive indicator reflecting the ability of water flow to carry sediment when the riverbed is in a state of erosion and deposition balance. Whether its value is reasonable directly affects the accuracy of water and sediment transport simulation. At present, the Zhang Ruijin formula is usually used to calculate the sediment carrying capacity of water flow. The coefficient k and exponent m in the formula vary with the comprehensive parameters of water and sediment. In actual rivers, the sediment-carrying force of water flow is difficult to measure directly. Generally, manual debugging methods are used to determine the values ​​of coefficient k and exponent m in the formula. By continuously debugging the coefficient k and exponent m, the calculated sediment content process is in good agreement with the measured data. This method is not only time-consuming and labor-intensive, but also has a large degree of empiricism and arbitrariness. Especially when the scale of river network calculation is large, it is difficult to ensure the accuracy of water and sediment transport simulation by simply taking the coefficient k and exponent m as constants. Therefore, it is necessary to propose an inversion method for the sediment-carrying force coefficient k and exponent m of water flow, and realize the automatic calibration of the sediment-carrying force coefficient k and exponent m of water flow through iterative optimization, thereby reducing the difficulty of calibrating the sediment-carrying force parameters of water flow and improving the simulation accuracy of the water-sediment mathematical model. Summary of the invention

[0003] The purpose of the present invention is to provide a method for inverting the water flow sediment entrainment coefficient and exponent based on the successive approximation method, so as to solve the problems of large empiricism and arbitrariness of manual debugging and time-consuming and labor-intensive in the prior art when determining the water flow sediment entrainment coefficient k and the exponent m, thereby improving the simulation accuracy of the water-sediment mathematical model.

[0004] To achieve the above object, the present invention provides a method for inverting the water flow sediment entrainment coefficient and index based on the successive approximation method, comprising the following steps: Step 1: The water flow sediment entrainment coefficient k and index m of each section are regarded as piecewise linear functions of the water and sediment comprehensive parameters. The minimum sum of squares of sediment content errors at each measuring station is taken as the objective function. The value range of the water flow sediment entrainment coefficient k and index m and the maximum sediment content error are taken as constraints. An inversion model of water flow sediment entrainment parameters based on a one-dimensional river network water and sediment mathematical model is constructed. The one-dimensional river network water and sediment mathematical model includes a single river channel water and sediment movement control equation and a river network branch point connection equation. Step 2, determine the values ​​of parameters such as grouped sediment entrainment gradation, recovery saturation coefficient and roughness in the one-dimensional river network water-sediment mathematical model; Step 3: Use the successive approximation method to solve the inversion model of water flow sediment entrainment force parameters in parallel.

[0005] Preferably, the water flow sediment entrainment force parameter inversion model based on the one-dimensional river network water-sediment mathematical model constructed in step 1 is as follows: Objective function: (1) In the formula, and are the water flow sediment entrainment coefficient k and index m of the i-th section under different water and sediment comprehensive parameter levels, expressed as and , is the total number of levels of comprehensive water and sediment parameters; is the total number of river sections; is the number of observation sections for sediment content; and are the calculated value and measured value of the sediment content of the i-th sediment content observation section at the t-th moment, respectively; The value range constraints of water flow sediment entrainment coefficient k and index m are as follows: (2) (3) In the formula, and are the lower and upper limits of the sediment entrainment coefficient of the i-th section respectively; and are the lower and upper limits of the sediment entrainment index of the i-th section respectively; Maximum sediment content error constraint: (4) In the formula, is the maximum sediment content error allowed in the ith river section.

[0006] Preferably, the single river channel water and sediment movement control equation includes a water flow movement control equation and a sediment movement control equation; The expression of the water flow motion control equation is as follows: (5) (6) In the formula, Z is the water level; Q is the flow rate; is the longitudinal distance along the water flow direction; t is the time; B is the width of the channel; n is the roughness; is the lateral inflow per unit length of the corresponding river section; V is the average flow velocity of the section; is the component of the lateral inflow velocity in the x direction; A is the cross-sectional area; R is the hydraulic radius; g is the gravitational acceleration; The sediment movement control equation is expressed as follows: (7) Where S is the average sediment content of the section; is the water flow sediment entrainment force, and its calculation expression is: ,in , is an empirical parameter, is the average water depth of the section, is the average settling velocity of sediment; is the sediment content of lateral inflow; is the recovery saturation coefficient; Considering that the deformation of the riverbed is affected by the combined effects of bedload and suspended load, the deformation equation is constructed and the expression is as follows: (8) In the formula, is the riverbed erosion and siltation area; is the dry bulk density of sediment.

[0007] Preferably, the river network branch point connection equation satisfies the flow connection condition, the dynamic connection condition and the sediment transport balance condition, which are as follows: Flow connection condition: The amount of water entering and leaving the branch point is equal to the increase or decrease in the amount of water in the branch point. The expression is as follows: (9) In the formula, is the flow entering the fork through the i-th river section, and N is the number of river sections flowing into the fork; is the water storage capacity of the branch point. When the branch point is generalized as a point, =0; Dynamic connection condition: When the branch point is generalized as a point, there is no hydrological mutation in the water flow and sediment conditions at this point, so the water level at each branch point of the river meets the condition of equalization, and the expression is as follows: (10) In the formula, is the water level of each river section at the fork; is the average water level at the branch point; Sediment transport balance condition: The amount of sediment entering and leaving the branch point must be equal to the increase or decrease rate of actual scouring and silting in the branch point, and the expression is as follows: (11) In the formula, is the sediment content of the water entering the branch point through the i river section; is the flow rate outflowing from the fork through river segment j; is the sediment content of the water flowing out of the fork through the jth river section; M is the number of river sections flowing out of the fork, It is the thickness of riverbed erosion and siltation.

[0008] Preferably, the specific contents of determining the values ​​of parameters such as grouped sediment entrainment gradation, recovery saturation coefficient and roughness in the one-dimensional river network water-sediment mathematical model in step 2 are as follows: The calculation expression of grouped sand holding capacity gradation is as follows: (12) In the formula, , They are the sediment entrainment capacity gradation and bed sand gradation of the kth particle size group; is the sediment settling velocity of the kth particle size group, is the muddy water Karman constant, is the friction velocity, is a parameter related to the turbulence intensity and the normal distribution function, and the calculation expression is as follows: (13) In the formula, is the vertical turbulence intensity, ; is the normal distribution function, calculated by looking up the standard normal distribution table; Under the condition of known bed sand gradation, the group sand entrainment gradation is calculated by formula (12), and the non-uniform group sand entrainment gradation is further obtained. , the expression is as follows: (14) The recovery saturation coefficient is taken as 0.25 when siltation occurs, and the recovery saturation coefficient is taken as 1 when scour occurs; Roughness is a comprehensive coefficient that reflects water flow conditions and riverbed morphology. It is affected by the roughness of the riverbed, the geometry of the cross-section, and the hydraulic elements of the water flow characteristics. Based on the measured water level and flow data, the roughness values ​​at different flow rates in different river sections are taken separately.

[0009] Preferably, the process of solving the water flow sediment entrainment force parameter inversion model using the successive approximation method in step 3 is as follows: S31. According to the distribution of sediment measurement stations, the river is divided into sub-sections; then, according to the changes of the water and sediment comprehensive parameters along the course of each sub-section, each sub-section is divided into two parts, and the sub-sections after the second division are numbered 1, 2, ..., from upstream to downstream. According to the possible value range of the comprehensive parameters of water and sediment in each sub-river section, it is divided into The water flow sediment entrainment coefficient k and index m of each optimization stage are set in the value range of each sub-river section. , ( ) to obtain different combinations of k and m values; S32. Give the initial values ​​of the water flow sediment entrainment coefficient k and index m for each sub-river section at each stage to meet the constraint conditions. , ; S33, fixing the water flow sediment entrainment coefficient k and index m of other sub-river sections, combining the discrete values ​​of the water flow sediment entrainment coefficient k and index m of the first sub-river section in the first stage one by one, and obtaining different value schemes; substituting each value scheme into the one-dimensional non-constant water-sediment mathematical model, using OpenMP parallel technology to simultaneously calculate the objective function value corresponding to each value scheme, taking the water flow sediment entrainment coefficient k and index m value scheme with the smallest objective function value as the optimal scheme, and updating the water flow sediment entrainment coefficient k and index m of the first sub-river section in the first stage accordingly; S34, according to the optimization method of S33, the second to the first sub-river section are sequentially The water flow sediment entrainment coefficient k and index m of each stage are optimized until the optimization calculation of all stages is completed; S35, repeat S33-S34, and perform multiple iterative calculations on the sub-river section until the change of the objective function after two iterations meets the accuracy requirement or the number of iterations is reached; S36, repeat S33~S35, and perform the following operations on the second to the third The water flow sediment entrainment coefficient k and index m of each sub-river section are optimized until the optimization calculation of all sub-river sections is completed; S37, repeat S33~S36, and perform multiple iterative calculations until the objective function after two iterations meets the accuracy requirement or the number of iterations is reached; the last iterative optimization calculation result is used as the optimal value solution for the required water flow sediment entrainment coefficient k and index m.

[0010] Therefore, the present invention adopts the above-mentioned water flow sediment entrainment coefficient and exponential inversion method based on the successive approximation method, which has the following beneficial effects: (1) The present invention regards the water flow sediment entrainment coefficient k and index m of each section as piecewise linear functions of the water-sediment comprehensive parameters, takes the minimum sum of square errors of the sediment content at each measuring station as the objective function, constructs a water flow sediment entrainment parameter inversion model based on a one-dimensional river network water-sediment mathematical model, and proposes a parallel solution method based on the successive approximation method to achieve automatic calibration of the water flow sediment entrainment coefficient k and index m. Compared with the manual debugging method, it saves more time and effort and has higher accuracy; (2) When dividing the sub-sections, the present invention not only considers the distribution of sediment measurement stations, but also fully considers the variation of water-sediment comprehensive parameters along the river, and divides the continuous sections with the same magnitude of variation of water-sediment comprehensive parameters along the river into a sub-section, thereby further improving the inversion accuracy of the sediment entrainment coefficient k and the exponent m of each section.

[0011] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is an overall flow chart of a method for inverting the water flow sediment entrainment coefficient and index based on the successive approximation method of the present invention; Figure 2 It is a flow chart of solving the inversion model of water flow sediment entrainment force parameters by using the successive approximation method according to an embodiment of the present invention; Figure 3 1 is a diagram of the inlet and outlet boundary conditions of a water-sediment model of a reservoir according to an embodiment of the present invention; wherein (a) is a flow process diagram of the main stream hydrological station 1, the tributary hydrological station 1 and the tributary hydrological station 2; (b) is a sediment content process diagram of the main stream hydrological station 1, the tributary hydrological station 1 and the tributary hydrological station 2; (c) is a water level process diagram of the dam front water level station 1; Figure 4 1 is a graph showing the inversion results of the water flow sand entrainment coefficient k and index m according to an embodiment of the present invention; wherein (a) is a graph showing the inversion results of the water flow sand entrainment coefficient k; (b) is a graph showing the inversion results of the water flow sand entrainment index m; Figure 5 1 is a comparison diagram of the simulated value and the measured value of the sediment content at different stations in the reservoir area of ​​a certain reservoir according to an embodiment of the present invention; wherein, (a) is a comparison diagram of the simulated value and the measured value of the sediment content of the main stream hydrological station 2; (b) is a comparison diagram of the simulated value and the measured value of the sediment content of the main stream hydrological station 3; (c) is a comparison diagram of the simulated value and the measured value of the sediment content of the main stream hydrological station 4; (d) is a comparison diagram of the simulated value and the measured value of the sediment content of the main stream hydrological station 5. DETAILED DESCRIPTION

[0013] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0014] See also Figure 1-Figure 5 , a method for inverting the water flow sediment entrainment coefficient and index based on the successive approximation method, comprising the following steps: Step 1: The water flow sediment entrainment coefficient k and index m of each section are regarded as piecewise linear functions of the water-sediment comprehensive parameters. The minimum sum of squares of sediment content errors at each measuring station is taken as the objective function. The value range of the water flow sediment entrainment coefficient k and index m and the maximum sediment content error are taken as constraints. The water flow sediment entrainment parameter inversion model based on the one-dimensional river network water-sediment mathematical model is constructed. The details are as follows: Objective function: (1) In the formula, and are the water flow sediment entrainment coefficient k and index m of the i-th section under different water and sediment comprehensive parameter levels, expressed as and , is the total number of levels of comprehensive water and sediment parameters; is the total number of river sections; is the number of observation sections for sediment content; and are the calculated value and measured value of the sediment content of the i-th sediment content observation section at the t-th moment, respectively; The values ​​of the water flow sediment entrainment coefficient k and index m should be within a reasonable range that conforms to the actual situation. The value range constraints of the water flow sediment entrainment coefficient k and index m are: (2) (3) In the formula, and are the lower and upper limits of the sediment entrainment coefficient of the i-th section respectively; and are the lower and upper limits of the sediment entrainment index of the i-th section respectively; The purpose of the model is to find the values ​​of the water flow sediment entrainment coefficient k and index m that can minimize the sum of square errors of sediment content in the calculated river section within the calculation period. It is a comprehensive consideration of the values ​​of the water flow sediment entrainment coefficient k and index m. In order to avoid excessive errors in sediment content in individual time periods or sections, a maximum sediment content error constraint is given; the maximum sediment content error constraint is: (4) In the formula, is the maximum sediment content error allowed in the ith river section.

[0015] In formula (1), It is calculated based on the one-dimensional river network water and sediment mathematical model. In the one-dimensional river network water and sediment mathematical model, the main and tributary rivers can be decomposed into a series of single river channels through the branch points (i.e., intersection points). The one-dimensional river network water and sediment mathematical model includes the single river channel water and sediment movement control equation and the river network branch point connection equation; among them, the single river channel water and sediment movement control equation includes the water flow movement control equation and the sediment movement control equation; The expression of the water flow motion control equation is as follows: (5) (6) In the formula, Z is the water level; Q is the flow rate; is the longitudinal distance along the water flow direction; t is the time; B is the width of the channel storage river; is the momentum correction coefficient; n is the roughness; is the lateral inflow per unit length of the corresponding river section; V is the average flow velocity of the section; is the component of the lateral inflow velocity in the x direction; A is the cross-sectional area; R is the hydraulic radius; g is the gravitational acceleration; The sediment movement control equation is expressed as follows: (7) Where S is the average sediment content of the section; is the water flow sediment entrainment force, and its calculation expression is: ,in , is an empirical parameter, is the average water depth of the section, is the average settling velocity of sediment; is the sediment content of lateral inflow; is the recovery saturation coefficient; Considering that the deformation of the riverbed is affected by the combined effects of bedload and suspended load, the deformation equation is constructed and the expression is as follows: (8) In the formula, is the riverbed erosion and siltation area; is the dry bulk density of sediment.

[0016] The key to river network calculation is the calculation of water flow and sediment movement at the branch point. Although the water and sediment conditions of different branch points are different, under normal circumstances, the branch points will meet the following conditions. The connection equation of the river network branch points meets the flow connection conditions, dynamic connection conditions and sediment transport balance conditions, as follows: Flow connection condition: The amount of water entering and leaving the branch point is equal to the increase or decrease in the amount of water in the branch point. The expression is as follows: (9) In the formula, is the flow entering the fork through the i-th river section, and N is the number of river sections flowing into the fork; is the water storage capacity of the branch point. When the branch point is generalized as a point, =0; Dynamic connection condition: When the branch point is generalized as a point, there is no hydrological mutation in the water flow and sediment conditions at this point, so the water level at each branch point of the river meets the condition of equalization, and the expression is as follows: (10) In the formula, is the water level of each river section at the fork; is the average water level at the branch point; Sediment transport balance condition: The amount of sediment entering and leaving the branch point must be equal to the increase or decrease rate of actual scouring and silting in the branch point, and the expression is as follows: (11) In the formula, is the sediment content of the water entering the branch point through the i river section; is the flow rate outflowing from the fork through river segment j; is the sediment content of the water flowing out of the fork through the jth river section; M is the number of river sections flowing out of the fork, It is the thickness of riverbed erosion and siltation.

[0017] Step 2: Determine the values ​​of parameters such as grouped sediment entrainment gradation, recovery saturation coefficient and roughness in the one-dimensional river network water-sediment mathematical model; the specific contents are as follows: The calculation expression of grouped sand holding capacity gradation is as follows: (12) In the formula, , They are the sediment entrainment capacity gradation and bed sand gradation of the kth particle size group; is the sediment settling velocity of the kth particle size group, is the muddy water Karman constant, is the friction velocity, is a parameter related to the turbulence intensity and the normal distribution function, and the calculation expression is as follows: (13) In the formula, is the vertical turbulence intensity, ; is the normal distribution function, calculated by looking up the standard normal distribution table; Under the condition of known bed sand gradation, the group sand entrainment gradation is calculated by formula (12), and the non-uniform group sand entrainment gradation is further obtained. , the expression is as follows: (14) The recovery saturation coefficient reflects the recovery speed of the sediment content to the saturated sediment content, that is, the sediment-carrying capacity of the water flow, when the suspended load is unbalanced. It is an important parameter in the calculation of sediment mathematical models and has a significant impact on the calculation of riverbed scouring and deposition deformation and sediment concentration distribution.

[0018] The recovery saturation coefficient is taken as 0.25 when siltation occurs, and the recovery saturation coefficient is taken as 1 when scour occurs; Roughness is a comprehensive coefficient that reflects water flow conditions and riverbed morphology. It is affected by hydraulic factors such as riverbed roughness, cross-sectional geometry, and water flow characteristics. Its value varies not only along the course, but also with flow or water level. Therefore, the roughness values ​​of different river sections at different flow rates should be determined based on measured water level and flow data.

[0019] Step 3, using the successive approximation method to solve the inversion model of the water flow sediment entrainment force parameters in parallel; specifically: the inversion problem of the water flow sediment entrainment force coefficient k and the exponent m is a complex multi-dimensional, multi-parameter, nonlinear optimization problem, and it involves the calculation of non-steady flow water and sand in a one-dimensional river network, and the amount of calculation and the difficulty of solving it are both large. For this reason, this application uses the successive approximation method to solve the inversion model. The basic solution idea is: according to the changes in the comprehensive parameters of river water and sand along the river channel and the distribution of sediment measurement stations, the inversion problem of the water flow sediment entrainment force coefficient k and the exponent m is decomposed into a multi-river section and multi-stage optimization problem. In the optimization process, only the current sub-river section and the current water-sediment comprehensive parameter level of the water flow entrainment coefficient k and index m value scheme are optimized each time, while the water flow entrainment coefficient k and index m values ​​of other sub-river sections remain unchanged. This method can not only reduce the dimension and reduce the amount of calculation, but also realize parallel calculation based on the mutual independence of different water flow entrainment coefficient k and index m value schemes, combined with OpenMP parallel technology, so as to further improve the calculation efficiency and shorten the calculation time. The specific process is as follows: S31. According to the distribution of sediment measurement stations, the river is divided into sub-sections; then, according to the changes of the water and sediment comprehensive parameters along the course of each sub-section, each sub-section is divided into two parts, and the sub-sections after the second division are numbered 1, 2, ..., from upstream to downstream. According to the possible value range of the comprehensive parameters of water and sediment in each sub-river section, it is divided into The water flow sediment entrainment coefficient k and index m of each optimization stage are set in the value range of each sub-river section. , ( ) to obtain different combinations of k and m values; S32. Give the initial values ​​of the water flow sediment entrainment coefficient k and index m for each sub-river section at each stage to meet the constraint conditions. , ; S33, fixing the water flow sediment entrainment coefficient k and index m of other sub-river sections, combining the discrete values ​​of the water flow sediment entrainment coefficient k and index m of the first sub-river section in the first stage one by one, and obtaining different value schemes; substituting each value scheme into the one-dimensional non-constant water-sediment mathematical model, using OpenMP parallel technology to simultaneously calculate the objective function value corresponding to each value scheme, taking the water flow sediment entrainment coefficient k and index m value scheme with the smallest objective function value as the optimal scheme, and updating the water flow sediment entrainment coefficient k and index m of the first sub-river section in the first stage accordingly; S34, according to the optimization method of S33, the second to the first sub-river section are sequentially The water flow sediment entrainment coefficient k and index m of each stage are optimized until the optimization calculation of all stages is completed; S35, repeat S33-S34, and perform multiple iterative calculations on the sub-river section until the change of the objective function after two iterations meets the accuracy requirement or the number of iterations is reached; S36, repeat S33~S35, and perform the following operations on the second to the third The water flow sediment entrainment coefficient k and index m of each sub-river section are optimized until the optimization calculation of all sub-river sections is completed; S37, repeat S33~S36, and perform multiple iterative calculations until the objective function after two iterations meets the accuracy requirement or the number of iterations is reached; the last iterative optimization calculation result is used as the optimal value solution for the required water flow sediment entrainment coefficient k and index m.

[0020] Example The established model and method are applied to a one-dimensional water-sediment mathematical model of a reservoir. The model calculation range is from the upstream main stream hydrological station 1 to the water level station 1 in front of a reservoir dam, of which the main stream has a total of 393 sections, and the two tributaries have 65 and 71 sections respectively. The measured flow and sediment content processes of the main stream hydrological station 1, tributary hydrological station 1 and tributary hydrological station 2 from May 1 to October 31, 2018 are selected as the upstream boundary conditions of the model, such as Figure 3 As shown in (a) and (b) in Figure 2, the measured water level process at the dam water level station 1 is used as the downstream boundary condition of the model, as shown in Figure 3 As shown in (c) in the figure. The measured sediment content process of mainstream hydrological stations 2, 3, 4 and 5 is used to invert the water flow sediment entrainment coefficient k and index m in the model. According to the distribution of hydrological stations, that is, the variation of water and sediment comprehensive parameters along the river, the river channel is divided into 10 sub-river sections, and the water and sediment comprehensive parameters of each sub-river section are divided into 9 levels. The value ranges of water flow sediment entrainment coefficient k and index m are [0.01, 2] and [0.1, 2], respectively. The successive approximation method based on OpenMP is used to invert the water flow sediment entrainment coefficient k and index m.

[0021] The inversion model of the water flow sediment entrainment coefficient k and index m established in this application is used to calculate the water flow sediment entrainment coefficient k and index m values ​​under different water and sediment comprehensive parameter levels in different sub-river sections, such as Figure 4 As shown. Figure 4 As can be seen from (a) in the figure, the values ​​of the river flow sediment entrainment coefficient k are mostly between 0.12 and 0.30, with an average value of 0.45. Figure 4 As can be seen from (b) in the figure, the value range of the index m is [0.35, 1.17], and the average value is 0.84.

[0022] The average absolute errors of simulated and measured sediment concentrations at four stations along the main stream of a reservoir are shown in Table 1. As can be seen from the table, the average absolute errors of simulated and measured sediment concentrations at main stream hydrological stations 2, 3, 4 and 5 range from 0.033 to 0.068 kg / m 3 The average absolute error of the overall sediment content is 0.052 kg / m 3 , the error in calculating the sand content is very small.

[0023] Table 1 Average absolute error of sediment content of hydrological stations along the one-dimensional river network water-sediment mathematical model of a reservoir ;

[0024] The simulation and measurement process of sediment content at mainstream hydrological stations 2, 3, 4 and 5 are as follows: Figure 5 As shown. Figure 5 It can be seen that the simulation process of sediment content at various stations along a reservoir is in good agreement with the actual situation, indicating that based on the inversion results of the water flow sediment entrainment coefficient and index, the water-sediment mathematical model can better simulate the changes in sediment content along the river channel.

[0025] This application regards the water flow sediment entrainment coefficient k and index m of each section as piecewise linear functions of the water and sediment comprehensive parameters, takes the minimum sum of square errors of sediment content at each measuring station as the objective function, and constructs an inversion model for water flow sediment entrainment parameters. The established model and method are applied to the calculation of a one-dimensional river network water and sediment mathematical model of a reservoir. The results show that the error between the simulated value of sediment content calculated by the inversion model of the water flow sediment entrainment coefficient k and index m established by this application is small, which can provide technical support for the accuracy determination of the water flow sediment entrainment coefficient k and index m and the improvement of the simulation accuracy of the one-dimensional water and sediment mathematical model.

[0026] Therefore, the present invention adopts the above-mentioned water flow sediment entrainment coefficient and exponent inversion method based on the successive approximation method, regards the water flow sediment entrainment coefficient k and exponent m of each section as piecewise linear functions of the water and sediment comprehensive parameters, takes the minimum sum of square errors of sediment content at each measuring station as the objective function, constructs a water flow sediment entrainment parameter inversion model based on the one-dimensional river network water and sediment mathematical model, and proposes a parallel solution method based on the idea of ​​successive approximation to realize automatic calibration of the water flow sediment entrainment coefficient k and exponent m, thereby reducing the difficulty of calibrating the water flow sediment entrainment parameters and improving the simulation accuracy of the water and sediment mathematical model.

[0027] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for inverting the water flow sediment entrainment coefficient and index based on the successive approximation method, characterized in that: The following steps are involved: Step 1: The water flow sediment entrainment coefficient k and index m of each section are regarded as piecewise linear functions of the water and sediment comprehensive parameters. The minimum sum of squares of sediment content errors at each measuring station is taken as the objective function. The value range of the water flow sediment entrainment coefficient k and index m and the maximum sediment content error are taken as constraints. An inversion model of water flow sediment entrainment parameters based on a one-dimensional river network water and sediment mathematical model is constructed. The one-dimensional river network water and sediment mathematical model includes a single river channel water and sediment movement control equation and a river network branch point connection equation. Step 2, determine the parameter values ​​of grouped sediment entrainment gradation, recovery saturation coefficient and roughness in the one-dimensional river network water-sediment mathematical model; Step 3: Use the successive approximation method to solve the inversion model of water flow sediment entrainment force parameters in parallel.

2. The method for inverting the water flow sediment entrainment coefficient and index based on the successive approximation method according to claim 1, characterized in that: The inversion model of water flow sediment entrainment parameters based on the one-dimensional river network water-sediment mathematical model constructed in step 1 is as follows: Objective function: (1) In the formula, and are the water flow sediment entrainment coefficient k and index m of the i-th section under different water and sediment comprehensive parameter levels, expressed as and , is the total number of levels of comprehensive water and sediment parameters; is the total number of river sections; is the number of observation sections for sediment content; and are the calculated value and measured value of the sediment content of the i-th sediment content observation section at the t-th moment, respectively; The value range constraints of water flow sediment entrainment coefficient k and index m are as follows: (2) (3) In the formula, and are the lower and upper limits of the sediment entrainment coefficient of the i-th section respectively; and are the lower and upper limits of the sediment entrainment index of the i-th section respectively; Maximum sediment content error constraint: (4) In the formula, is the maximum sediment content error allowed in the ith river section.

3. The method for inverting the water flow sediment entrainment coefficient and index based on the successive approximation method according to claim 2, characterized in that: The governing equations of water and sediment movement in a single river channel include the governing equations of water flow movement and sediment movement; The expression of the water flow motion control equation is as follows: (5) (6) In the formula, Z is the water level; Q is the flow rate; is the longitudinal distance along the water flow direction; t is the time; B is the width of the channel; n is the roughness; is the lateral inflow per unit length of the corresponding river section; V is the average flow velocity of the section; is the component of the lateral inflow velocity in the x direction; A is the cross-sectional area; R is the hydraulic radius; g is the gravitational acceleration; The sediment movement control equation is expressed as follows: (7) Where S is the average sediment content of the section; is the water flow sediment entrainment force, and its calculation expression is: ,in , is an empirical parameter, is the average water depth of the section, is the average settling velocity of sediment; is the sediment content of lateral inflow; is the recovery saturation coefficient; Considering that the deformation of the riverbed is affected by the combined effects of bedload and suspended load, the deformation equation is constructed and the expression is as follows: (8) In the formula, is the riverbed erosion and siltation area; is the dry bulk density of sediment.

4. The method for inverting the water flow sediment entrainment coefficient and index based on the successive approximation method according to claim 3, characterized in that: The connection equation of the river network branches meets the flow connection conditions, dynamic connection conditions and sediment transport balance conditions, as follows: Flow connection condition: The amount of water entering and leaving the branch point is equal to the increase or decrease in the amount of water in the branch point. The expression is as follows: (9) In the formula, is the flow entering the fork through the i-th river section, and N is the number of river sections flowing into the fork; is the water storage capacity of the branch point. When the branch point is generalized as a point, =0; Dynamic connection condition: When the branch point is generalized as a point, there is no hydrological mutation in the water flow and sediment conditions at this point, so the water level at each branch point of the river meets the condition of equalization, and the expression is as follows: (10) In the formula, is the water level of each river section at the fork; is the average water level at the branch point; Sediment transport balance condition: The amount of sediment entering and leaving the branch point must be equal to the increase or decrease rate of actual scouring and silting in the branch point, and the expression is as follows: (11) In the formula, is the sediment content of the water entering the branch point through the i river section; is the flow rate outflowing from the fork through river segment j; is the sediment content of the water flowing out of the fork through the jth river section; M is the number of river sections flowing out of the fork, It is the thickness of riverbed erosion and siltation.

5. The method for inverting the water flow sediment entrainment coefficient and index based on the successive approximation method according to claim 4, characterized in that: The specific contents of determining the parameter values ​​of grouped sediment entrainment gradation, recovery saturation coefficient and roughness in the one-dimensional river network water-sediment mathematical model in step 2 are as follows: The calculation expression of grouped sand holding capacity gradation is as follows: (12) In the formula, , They are the sediment entrainment capacity gradation and bed sand gradation of the kth particle size group; is the sediment settling velocity of the kth particle size group, is the muddy water Karman constant, is the friction velocity, is a parameter related to the turbulence intensity and the normal distribution function, and the calculation expression is as follows: (13) In the formula, is the vertical turbulence intensity, ; is the normal distribution function, calculated by looking up the standard normal distribution table; Under the condition of known bed sand gradation, the group sand entrainment gradation is calculated by formula (12), and the non-uniform group sand entrainment gradation is further obtained. , the expression is as follows: (14) The recovery saturation coefficient is taken as 0.25 when siltation occurs, and the recovery saturation coefficient is taken as 1 when scour occurs; Roughness is a comprehensive coefficient that reflects water flow conditions and riverbed morphology. It is affected by the roughness of the riverbed, the geometry of the cross-section, and the hydraulic elements of the water flow characteristics. Based on the measured water level and flow data, the roughness values ​​at different flow rates in different river sections are taken separately.

6. The method for inverting the water flow sediment entrainment coefficient and index based on the successive approximation method according to claim 5, characterized in that: The process of parallel solution of the inversion model of water flow sediment entrainment force parameters using the successive approximation method in step 3 is as follows: S31. According to the distribution of sediment measurement stations, the river is divided into sub-sections; then, according to the changes of the water and sediment comprehensive parameters along the course of each sub-section, each sub-section is divided into two parts, and the sub-sections after the second division are numbered 1, 2, ..., from upstream to downstream. According to the possible value range of the comprehensive parameters of water and sediment in each sub-river section, it is divided into The water flow sediment entrainment coefficient k and index m of each optimization stage are set in the value range of each sub-river section. , ( ) to obtain different combinations of k and m values; S32. Give the initial values ​​of the water flow sediment entrainment coefficient k and index m for each sub-river section at each stage to meet the constraint conditions. , ; S33, fixing the water flow sediment entrainment coefficient k and index m of other sub-river sections, combining the discrete values ​​of the water flow sediment entrainment coefficient k and index m of the first sub-river section in the first stage one by one, and obtaining different value schemes; substituting each value scheme into the one-dimensional non-constant water-sediment mathematical model, using OpenMP parallel technology to simultaneously calculate the objective function value corresponding to each value scheme, taking the water flow sediment entrainment coefficient k and index m value scheme with the smallest objective function value as the optimal scheme, and updating the water flow sediment entrainment coefficient k and index m of the first sub-river section in the first stage accordingly; S34, according to the optimization method of S33, the second to the first sub-river section are sequentially The water flow sediment entrainment coefficient k and index m of each stage are optimized until the optimization calculation of all stages is completed; S35, repeat S33-S34, and perform multiple iterative calculations on the sub-river section until the change of the objective function after two iterations meets the accuracy requirement or the number of iterations is reached; S36, repeat S33~S35, and perform the following operations on the second to the third The water flow sediment entrainment coefficient k and index m of each sub-river section are optimized until the optimization calculation of all sub-river sections is completed; S37, repeat S33~S36, and perform multiple iterative calculations until the objective function after two iterations meets the accuracy requirement or the number of iterations is reached; the last iterative optimization calculation result is used as the optimal value solution for the required water flow sediment entrainment coefficient k and index m.

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