Hydrodynamic model parameter calibration method and device based on improved Monte Carlo, computer equipment and readable storage medium

Abstract

The invention discloses a hydrodynamic model parameter calibration method and device based on improved Monte Carlo, computer equipment and a readable storage medium, provides a random multiple increase and decrease convergence strategy based on water level error feedback, and improves a traditional Monte Carlo method. The defects that an original Monte Carlo method cannot achieve rapid convergence, cannot effectively utilize existing information and depends on a large amount of unnecessary repeated calculation are overcome, and the parameter calibration efficiency and precision of the hydrodynamic model are effectively improved. According to the method, historical water level flow data of a hydrometric station is actually measured through the river section, the upper boundary, the lower boundary and the initial condition of each section of the model are determined, the one-dimensional hydrodynamic model is established, the roughness of each river reach is calibrated in combination with the improved Monte Carlo method, and a new thought and method are provided for multi-dimensional parameter calibration of the hydrodynamic model.

Description

Technical Field

[0001] The invention belongs to the field of hydraulics and river dynamics, and in particular relates to a method, device, computer equipment and readable storage medium for calibrating parameters of a hydrodynamic model based on improved Monte Carlo. Background Art

[0002] The hydrodynamic model is a mathematical model that studies the laws of water flow movement and is widely used in water resources management, river management, flood forecasting and other aspects in the field of hydrology. Roughness is an important parameter that describes the roughness of the river surface. It directly affects important hydrological characteristics such as water flow resistance, velocity distribution and water level. Therefore, accurately determining the roughness parameter is crucial to the accuracy and reliability of the model. However, in practical applications, determining the roughness parameter is often a challenging problem. The study of the optimization problem of the roughness parameter has important theoretical significance and practical application value. By proposing effective parameter optimization algorithms and methods, the accuracy and reliability of the hydrodynamic model can be improved, providing more reliable support for water resources management and hydrological disaster prediction.

[0003] The existing roughness parameter calibration methods for hydrodynamic models mainly include trial and error, random simulation, gradient search and heuristic algorithms. However, the trial and error method relies on expert experience and cannot guarantee the optimal value; the random simulation algorithm relies on randomness and cannot effectively use existing information, and often requires a large number of iterations to find a satisfactory result, resulting in low algorithm efficiency; the gradient search method is sensitive to the initial value and is not suitable for discontinuous optimization problems; the heuristic algorithm is more sensitive to parameter settings, and cannot guarantee the global optimal solution, and often falls into the local optimal solution and is difficult to escape.

[0004] In summary, the traditional trial and error method relies too much on empirical knowledge, the random search algorithm cannot effectively utilize existing information, and the heuristic algorithm has low computational efficiency, resulting in the problem of low efficiency in high-dimensional parameter calibration of hydrodynamic models.

[0005] Therefore, it is necessary to design a hydrodynamic model parameter calibration method, device, computer equipment and readable storage medium based on improved Monte Carlo to solve the above problems. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a method, device, computer equipment and readable storage medium for calibrating the parameters of a hydrodynamic model based on an improved Monte Carlo. The method aims to solve the problems that the trial and error method in the prior art is too dependent on empirical knowledge, the random search algorithm cannot effectively utilize existing information, and the heuristic algorithm has low calculation efficiency, resulting in low efficiency in high-dimensional parameter calibration of the hydrodynamic model.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is: The hydrodynamic model parameter calibration method based on improved Monte Carlo includes the following steps: S1, obtain the measured water level and flow data of each hydrological station in the river section, as well as the cross-sectional data of each section; S2, determine the upper and lower boundaries of the one-dimensional hydrodynamic model and the initial conditions of each section based on the acquired data, use the finite volume method to discretize and solve the Saint-Venant equations, and use the Euler-Lagrange method to solve the convection term in the momentum equation; S3, taking the minimum total root mean square error between the simulated values ​​and the measured values ​​of all hydrological stations in the river section as the calculation target, the improved Monte Carlo method is used to solve the optimal roughness parameter combination for each river section.

[0008] Preferably, the Saint-Venant equations are: ; ; In the formula, B The width of the water surface, is the water level, Q For flow, q For lateral inflow, t For time, x is the distance along the river, A is the cross-sectional area of ​​water flow, g is the acceleration due to gravity, R is the hydraulic radius, C It is Xie Cai coefficient.

[0009] Preferably, the finite volume method is used to discretely solve the Saint-Venant equations: ; In the formula, the subscript i Indicates i Control volume interface, superscript t Indicates t a moment, Indicates the section spacing; ; In the formula, n is the roughness, is the length of the control body, is the result of the Euler-Lagrange method, that is, t At the moment i The flow particle of the interface is found t -1 Moment of motion and position; Combined to get: ; in,D , F , G for t The value is known at all times, and the specific expression is: ; ; ; In the formula, the subscript i Indicates i Control volume interface, superscript t Indicates t a moment, Indicates the time difference.

[0010] Preferably, the improved Monte Carlo method of the random multiplication and reduction convergence strategy based on water level error feedback is: ; ; In the formula, , and Respectively represent k The first and second t Second and t + Roughness value generated in 1 iteration; Indicates k The average value of the average relative error of adjacent measured stations in a river section; express Random numbers within and conform to uniform distribution; Indicates k The adjacent measured stations in the river section are t The simulated value is relative to the measured value. R The average value of the square; Indicates the ideal setting R 2 Threshold value; is the range of random multiples in decimal places; the range of roughness is: .

[0011] The hydrodynamic model parameter calibration device based on improved Monte Carlo includes: The raw data acquisition module is used to obtain the raw data of each hydrological station in the river section, including the measured water level, flow data, and cross-sectional data of each section; The Saint-Venant equations construction module is used to determine the upper and lower boundaries of the one-dimensional hydrodynamic model and the initial conditions of each section based on the acquired original data to construct the Saint-Venant equations; Saint-Venant equations solving module, used to discretely solve Saint-Venant equations using finite volume method; The module for solving the optimal roughness parameter of a river section is used to solve the optimal roughness parameter of a river section through an improved Monte Carlo method with a random multiplication and reduction convergence strategy based on water level error feedback.

[0012] Furthermore, a computer device includes a memory and a processor, the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the improved Monte Carlo-based hydrodynamic model parameter calibration method by executing the computer instructions.

[0013] Furthermore, a computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a computer to execute the hydrodynamic model parameter calibration method based on improved Monte Carlo.

[0014] The beneficial effects of the present invention are as follows: The present invention makes full use of the error information between the simulated value and the measured value of the last iterative optimization result, proposes a convergence strategy based on the error direction, effectively improves the convergence of the original Monte Carlo method, and greatly improves the calculation efficiency of parameter calibration of the hydrodynamic model. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of a method for calibrating parameters of a hydrodynamic model based on an improved Monte Carlo method of the present invention; Figure 2 is a study area map provided by an embodiment of the present invention; Figure 3 It is the average convergence process of the improved method provided by the embodiment of the present invention and the traditional method iterating 50 times and running independently 30 times; Figure 4 It is a comparison diagram of the simulated water level and the measured water level process of the Xiantao station at a regular rate according to an embodiment of the present invention; Figure 5 It is a comparison diagram of the simulated water level and the measured water level process of Hanchuan Station during the rate period provided by an embodiment of the present invention; Figure 6 It is a comparison diagram of the simulated water level and the measured water level process of Xiantao Station during the verification period 1 provided by an embodiment of the present invention; Figure 7 It is a comparison diagram of the simulated water level and the measured water level process of Hanchuan Station in the verification period 1 provided by an embodiment of the present invention; Figure 8 It is a comparison diagram of the simulated water level and the measured water level process of Xiantao Station during the verification period 2 provided by an embodiment of the present invention; Fig. 9 It is a comparison diagram of the simulated water level and the measured water level process of Hanchuan Station in the verification period 2 provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0016] Embodiment 1: like Figure 1 As shown, the hydrodynamic model parameter calibration method based on improved Monte Carlo includes the following steps: S1, obtain the measured water level and flow data of each hydrological station in the river section, as well as the cross-sectional data of each section; S2, determine the upper and lower boundaries of the one-dimensional hydrodynamic model and the initial conditions of each section based on the acquired data, use the finite volume method to discretize and solve the Saint-Venant equations, and use the Euler-Lagrange method to solve the convection term in the momentum equation; S3, taking the minimum total root mean square error between the simulated values ​​and the measured values ​​of all hydrological stations in the river section as the calculation target, the improved Monte Carlo method is used to solve the optimal roughness parameter combination for each river section.

[0017] Preferably, the Saint-Venant equations are: ; ; In the formula, B The width of the water surface, is the water level, Q For flow, q For lateral inflow, t For time, x is the distance along the river, A is the cross-sectional area of ​​water flow, g is the acceleration due to gravity, R is the hydraulic radius, C It is Xie Cai coefficient.

[0018] Preferably, the finite volume method is used to discretely solve the Saint-Venant equations: ; In the formula, the subscript i Indicates i Control volume interface, superscript t Indicates t a moment, Indicates the section spacing; ; In the formula, n is the roughness, is the length of the control body, is the result of the Euler-Lagrange method, that is, t At the moment i The flow particle of the interface is found t -1 Moment of motion and position; Combined to get: ; in, D , F , G for t The value is known at all times, and the specific expression is: ; ; ; In the formula, the subscript i Indicates i Control volume interface, superscript t Indicates t a moment, Indicates the time difference.

[0019] Preferably, the improved Monte Carlo method of the random multiplication and reduction convergence strategy based on water level error feedback is: ; ; In the formula, , and Respectively represent k The first and second t Second and t + Roughness value generated in 1 iteration; Indicates k The average value of the average relative error of adjacent measured stations in a river section; express Random numbers within and conform to uniform distribution; Indicates k The adjacent measured stations in the river section are t The simulated value is relative to the measured value. R The average value of the square; Indicates the ideal setting R 2 Threshold value; is the range of random multiples in decimal places; the range of roughness is: .

[0020] The hydrodynamic model parameter calibration device based on improved Monte Carlo includes: The raw data acquisition module is used to obtain the raw data of each hydrological station in the river section, including the measured water level, flow data, and cross-sectional data of each section; The Saint-Venant equations construction module is used to determine the upper and lower boundaries of the one-dimensional hydrodynamic model and the initial conditions of each section based on the acquired original data to construct the Saint-Venant equations; Saint-Venant equations solving module, used to discretely solve Saint-Venant equations using finite volume method; The module for solving the optimal roughness parameter of a river section is used to solve the optimal roughness parameter of a river section through an improved Monte Carlo method with a random multiplication and reduction convergence strategy based on water level error feedback.

[0021] Furthermore, a computer device includes a memory and a processor, the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the improved Monte Carlo-based hydrodynamic model parameter calibration method by executing the computer instructions.

[0022] Furthermore, a computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a computer to execute the hydrodynamic model parameter calibration method based on improved Monte Carlo.

[0023] Embodiment 2: The present invention provides a method for calibrating parameters of a hydrodynamic model based on improved Monte Carlo, comprising the following steps: 1. The middle and lower reaches of the Han River Basin are taken as the research object. The schematic diagram of the basin is as follows Figure 2 , the Saint-Venant equations are: ; (1) ; (2) In the formula, B The width of the water surface, is the water level, Q For flow, q For lateral inflow, t For time, x is the distance along the river, A is the cross-sectional area of ​​water flow, g is the acceleration due to gravity, R is the hydraulic radius, C It is Xie Cai coefficient.

[0024] 2. Discrete equation (1) by forward difference in time and backward difference in space to obtain: ; (3) In the formula, the subscript i Indicates i Control volume interface, superscript t Indicates t a moment, Indicates the section spacing.

[0025] 3. Forward difference of time term and space term in equation (2) is performed, and Euler-Lagrange method is used to solve the convection term. The momentum equation can be discretized as: ; (4) In the formula, n is the roughness, is the length of the control body, is the result of the Euler-Lagrange method, that is, t At the moment i The flow particle of the interface is found t -1 Moment of motion and position; Combined to get: ; (5) in, D , F , G for t The value is known at all times, and the specific expression is: ; (5-a) ; (5-b) ; (5-c) Fourth, assuming that the river sections between adjacent measured sites share a common roughness value and each river section adopts the same convergence strategy, then k The improved Monte Carlo method convergence strategy formula for each river section is as follows: ; (6) ; (7) In the formula, , and Respectively represent k The first and second t Second and t + Roughness value generated in 1 iteration; Indicates k The average value of the average relative error of adjacent measured stations in a river section; express Random numbers within and conform to uniform distribution; Indicates k The adjacent measured stations in the river section are t The simulated value is relative to the measured value. R The average value of the square; Indicates the ideal setting R 2 Threshold value; is the range of random multiples in decimal places; the range of roughness is: .

[0026] In order to more clearly reflect the purpose of the present invention, the methods and overall logic adopted, the content of the present invention is further explained by taking the Shayang-Hankou section of the middle and lower reaches of the Han River as the research object, wherein Shayang County is located in the middle and lower reaches of the Han River, and the river section to Hankou is about 264.3km long, and the river section includes two hydrological stations, Xiantao Station and Hanchuan Station; the river section from Shayang County to Hankou is divided into 249 sections in total, and the section spacing varies from about 0.4 to 2.7km, with an average spacing of about 1.06km. Xiantao Station and Hanchuan Station are located at the 96th section and the 140th section respectively.

[0027] The roughness was calibrated from January 1, 2008 to February 29, 2008 (rate period), and the verification was conducted from March 1, 2008 to April 31, 2008 (verification period 1) and 2010 (verification period 2). The flow process of Shayang Station was used as the upper boundary condition of the model, the water level process of Hankou Station was used as the lower boundary condition of the model, and it was assumed that the Shayang-Xiantao River section shared a common roughness value. n 1 , Xiantao-Hanchuan river section shares a common roughness value n 1 , the Hanchuan-Hankou section shares a common roughness value n 1 The initial water level data of Xiantao, Hanchuan and Hankou stations were used for linear interpolation to obtain the initial water surface line of the river section, which is the initial condition for model calculation. The measured hydrological stations Xiantao and Hanchuan in the Shayang-Hankou river section were selected for simulation and comparative analysis. The coefficient of determination ( DC ), Root Mean Square Error ( RMSE ), the sum of the root mean square error ( sum-RMSE ) and the mean relative error ( MRE ) to comprehensively evaluate the performance of the improved method.

[0028] The specific parameter settings of the improved method are shown in Table 1:

[0029] Table 1: Parameter settings of the improved Monte Carlo method; Depend on Figure 3 It can be seen that the traditional Monte Carlo method performs poorly when there are only 50 iterations. Its basic characteristics determine that it is difficult for Monte Carlo to obtain the ideal value of the objective function with a limited number of iterations. Especially for high-dimensional complex problems, it can only rely on a large number of repeated random simulation calculations, which will lead to excessive time costs and extremely low efficiency. In contrast, the improved Monte Carlo method has a convergence strategy that can more effectively utilize the limited number of iterations and quickly approach the optimal solution. It can be seen that it only takes 20 times to converge to a relatively ideal result.

[0030] Table 2 shows the parameter optimization results for the middle and lower reaches of the Han River from January 1, 2008 to February 29, 2008, a total of 60 days. The parameter optimization results of the Monte Carlo method are the parameter combination corresponding to the minimum fitness function value in 50 iterations and 30 independent runs (equivalent to the parameters corresponding to the optimal fitness function in 1500 iterations). The parameter optimization results of the improved Monte Carlo method are all the parameter combinations corresponding to the average convergence curve in the last iteration. Table 3 shows the performance index results of the two improved and unimproved methods.

[0031]

[0032] Table 2: Parameter calibration results of the method with and without regular rate improvement;

[0033] Table 3: Performance indicators of the method with regular rate improvement and no improvement; From Table 3, Figure 4 and Figure 5 It can be seen that for Hanchuan Station, the RMSE of the improved Monte Carlo method dropped from 0.116 to 0.100, the MRE dropped from 0.067 to -0.011, and the DC increased from 0.809 to 0.857; but for Xiantao Station, the three indicators of the two algorithms are similar; sum-RMSE dropped from 0.197 to 0.183. This shows that the last roughness combination of the improved Monte Carlo method after 50 iterations is better than the best roughness combination of the original Monte Carlo method after 1500 iterations, and is closer to the measured results.

[0034]

[0035] Table 4: Performance indicators of improved and unimproved methods in validation period 1;

[0036] Table 5: Performance indicators of improved and unimproved methods in validation period 2 From Table 4, Table 5 and Figure 6-9 It can be seen that the two verification periods with different time spans have proved that the optimization and improvement effect of the improved method is more significant.

[0037] In general, the invented improved Monte Carlo method can calculate a better roughness combination with fewer iterations, which not only greatly improves the calculation efficiency but also further improves the calculation accuracy.

[0038] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. The hydrodynamic model parameter calibration method based on improved Monte Carlo is characterized by: The following steps are involved: S1, obtain the original data of each hydrological station in the river section; S2, construct and solve the Saint-Venant equations and solve the convection term in the momentum equation using the Euler-Lagrange method; S3, taking the minimum total root mean square error between the simulated values ​​and the measured values ​​of all hydrological stations in the river section as the calculation target, the improved Monte Carlo method is used to solve the optimal roughness parameter combination for each river section.

2. The method for calibrating hydrodynamic model parameters based on improved Monte Carlo according to claim 1, characterized in that: The original data include measured water level, flow data, and cross-sectional data of each section.

3. The method for calibrating hydrodynamic model parameters based on improved Monte Carlo according to claim 1, characterized in that: In step S2, the upper and lower boundaries of the one-dimensional hydrodynamic model and the initial conditions of each section are determined according to the acquired original data, and the Saint-Venant equations are discretely solved using the finite volume method.

4. The method for calibrating hydrodynamic model parameters based on improved Monte Carlo according to claim 3, characterized in that: The Saint-Venant equations are: ； ； In the formula, B The width of the water surface, is the water level, Q For flow, q For lateral inflow, t For time, x is the distance along the river, A is the cross-sectional area of ​​water flow, g is the acceleration due to gravity, R is the hydraulic radius, C It is Xie Cai coefficient.

5. The method for calibrating hydrodynamic model parameters based on improved Monte Carlo according to claim 4, characterized in that: The finite volume method is used to discretize the Saint-Venant equations: ； In the formula, the subscript i Indicates i Control volume interface, superscript t Indicates t a moment, Indicates the section spacing; ； In the formula, n is the roughness, is the length of the control body, is the result of the Euler-Lagrange method, that is, t At the moment i The flow particle of the interface is found t -1 The motion state and position at the moment.

6. The method for calibrating hydrodynamic model parameters based on improved Monte Carlo according to claim 5, characterized in that: Combining the two equations of the Saint-Venant equations gives: ； in, D , F , G for t The value is known at all times, and the specific expression is: ； ； ； In the formula, the subscript i Indicates i Control volume interface, superscript t Indicates t a moment, Indicates the time difference.

7. The method for calibrating hydrodynamic model parameters based on improved Monte Carlo according to claim 1, characterized in that: The improved Monte Carlo method based on the random multiplication and reduction convergence strategy of water level error feedback is: ； ； In the formula, , and Respectively represent k The first and second t Second and t + Roughness value generated in 1 iteration; Indicates k The average value of the average relative error of adjacent measured stations in a river section; express Random numbers within and conform to uniform distribution; Indicates k The adjacent measured stations in the river section are t The simulated value is relative to the measured value. R The average value of the square; Indicates the ideal setting R 2 Threshold value; is the range of random multiples in decimal places; the range of roughness is: .

8. A hydrodynamic model parameter calibration device based on improved Monte Carlo for use in any one of claims 1 to 7, characterized in that: The device includes: The raw data acquisition module is used to obtain the raw data of each hydrological station in the river section, including the measured water level, flow data, and cross-sectional data of each section; The Saint-Venant equations construction module is used to determine the upper and lower boundaries of the one-dimensional hydrodynamic model and the initial conditions of each section based on the acquired original data to construct the Saint-Venant equations; Saint-Venant equations solving module, used to discretely solve Saint-Venant equations using finite volume method; The module for solving the optimal roughness parameter of a river section is used to solve the optimal roughness parameter of a river section through an improved Monte Carlo method with a random multiplication and reduction convergence strategy based on water level error feedback.

9. A computer device, characterized in that: The invention comprises a memory and a processor, the memory and the processor are communicatively connected with each other, the memory stores computer instructions, and the processor executes a hydrodynamic model parameter calibration method based on improved Monte Carlo as described in any one of claims 1 to 7 by executing the computer instructions.

10. A computer-readable storage medium, characterized in that: Computer instructions are stored on the computer-readable storage medium, and the computer instructions are used to enable a computer to execute a hydrodynamic model parameter calibration method based on improved Monte Carlo as described in any one of claims 1 to 7.

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