A method for solving the water depth of a trapezoidal open channel and related products

Abstract

The present application relates to the field of hydraulics calculation and hydraulic engineering design, in particular to a trapezoidal open channel hydraulics characteristic water depth solving method and related products, including a method for solving the critical water depth of a trapezoidal open channel and a method for solving the normal water depth of a trapezoidal open channel; the method obtains the section parameters and the hydraulic parameters and is dimensionless; the variable substitution is performed on the critical water depth equation, which is converted into a single variable sixth algebraic equation and the high-order iteration root finding is adopted to obtain the critical water depth; the logarithmic domain equivalent transformation is performed on the normal water depth equation to construct the root equation, and the small water depth asymptotic solution and the large water depth asymptotic solution are fused by a smoothing weight function to generate the global continuous initial value, and then the normal water depth is obtained by iteration; the residual self-checking and numerical anomaly detection are implemented in the iteration process, and when triggered, the preset low-order robust algorithm is automatically returned to correct until convergence; while ensuring the accuracy, the stability and efficiency in the difficult convergence condition are improved, and the method is suitable for the automation and batch condition calculation of water conservancy information system.

Description

Technical Field

[0001] This invention relates to the fields of hydraulic calculation and hydraulic engineering design, specifically to a method for solving the hydraulic characteristic water depth of a trapezoidal open channel and related products, and particularly to a rapid method for solving the critical water depth and normal water depth of a trapezoidal open channel under critical flow and uniform flow conditions. Background Technology

[0002] Trapezoidal open channels are a commonly used cross-sectional form in farmland irrigation, drainage, and water diversion projects, and their hydraulic calculations are a crucial part of water conservancy engineering design and verification. In steady uniform flow and critical flow analysis, determining the critical water depth and normal water depth are two fundamental and critical computational tasks. Due to the geometric relationship of the trapezoidal cross-section, the relevant governing equations are usually expressed as implicit algebraic equations or transcendental equations, often requiring iterative numerical solutions in engineering software to obtain the water depth results.

[0003] In early engineering practice, trial-and-error methods, graphical methods, or table lookup methods were often used to solve problems. However, these methods relied on manual experience, were cumbersome, and their accuracy and efficiency were greatly affected by the operation process, making it difficult to meet the requirements of modern hydraulic engineering design software for automation, high precision, and batch calculation of working conditions. With the development of computer technology, numerical iterative methods such as Newton's method and fixed-point iteration have been used for automatic solutions. However, in existing implementations, the construction of initial values ​​for iteration often adopts piecewise empirical fitting or statistical regression, that is, multiple sets of empirical initial value expressions are given for different slope coefficients or dimensionless parameter ranges. Such initial value expressions can achieve certain results within the parameter range, but when they exceed the applicable range of fitting or experience, the initial value error may increase significantly, leading to an increase in the number of iterations, a decrease in convergence speed, or even divergence or convergence to an invalid solution.

[0004] Furthermore, under extreme conditions (such as small dimensionless water depths, large roughness coefficients, or large parameter ranges), the nonlinearity of the governing equations increases, and local gradients change drastically, easily leading to rigid characteristics in numerical solutions. If the solution is directly performed within the original domain, problems such as numerical oscillations, excessively large step sizes, negative solutions, and non-numerical states (NaN / Inf) may occur during iteration, affecting the stability and usability of engineering software in batch calculations under various conditions. Meanwhile, in addition to pursuing convergence speed, practical software systems also require explicit quality control logic, such as convergence criteria based on residuals, upper bound control of the number of iterations, abnormal state detection, and automatic recovery strategies. In existing implementations, while a single high-order iterative method can achieve rapid convergence under good initial conditions, it may fail when the initial value deviates significantly or is in a difficult-to-converge region. Without residual self-checking and automatic backoff mechanisms, the system often cannot automatically switch to a more robust correction algorithm to remedy the failure of high-order iterations, leading to computational interruptions or user-side errors. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method and related products for solving the hydraulic characteristic water depth of a trapezoidal open channel, including methods for solving the critical water depth and methods for solving the normal water depth of a trapezoidal open channel. For convergence-difficult conditions, specific equivalent transformations are used to improve the numerical properties of the governing equations, and a residual self-checking and adaptive backoff mechanism are combined to improve solution stability and computational efficiency while ensuring computational accuracy.

[0006] This invention is achieved through the following technical solution:

[0007] A method for determining the hydraulic characteristic water depth of a trapezoidal open channel, used to solve for the critical water depth, includes the following steps:

[0008] Data acquisition and processing: Obtain the cross-sectional and hydraulic parameters of the trapezoidal open channel, and calculate the dimensionless parameters of the foundation;

[0009] Critical water depth solution: The dimensionless relation corresponding to the critical water depth is transformed into a single-variable algebraic polynomial root equation by variable substitution, and the critical water depth is obtained by using an iterative algorithm.

[0010] Verification and rollback control: The calculation residual is monitored in real time during the iterative solution process. When the calculation residual does not meet the preset convergence condition or the iteration shows numerical anomalies, the rollback mechanism is triggered, and the calculation is switched to the preset low-order correction algorithm until the convergence condition is met and the final critical water depth result is output.

[0011] Optionally, the steps for obtaining the basic dimensionless parameters include:

[0012] Based on the slope coefficient of the trapezoidal open channel Bottom width Gravitational acceleration Determining critical flow characteristic parameters based on flow rate-related parameters ,and Satisfy any of the following computational relationships: or or ,in, For unit bandwidth, For total flow, For equivalent width, This is a configurable coefficient.

[0013] Optionally, the critical water depth calculation step specifically includes:

[0014] Dimensionless water depth is constructed based on cross-sectional parameters. ,in, To determine the water depth, an auxiliary variable is introduced. Substitute the dimensionless relation for critical flow;

[0015] Based on the critical flow characteristic parameters Building about Single-variable algebraic polynomial root equation The current iterative solution of the equation is obtained using a numerical iterative algorithm. ;

[0016] Based on the obtained The critical water depth is obtained by reverse calculation. : .

[0017] Optionally, the numerical iteration algorithm and the verification and backoff control specifically include:

[0018] The Halley iteration method is used to solve the single-variable algebraic polynomial root equation, and its iterative update formula is as follows: ;

[0019] Calculate the current iterative solution residual value : Or its equivalent form, and with a preset convergence threshold Compare;

[0020] like If the calculation is successful, the result is output.

[0021] like If a numerical anomaly is detected during the iteration process, a rollback correction mechanism will be triggered.

[0022] The rollback correction mechanism is as follows: The current iterative solution... As the initial value, switch to the preset low-order correction algorithm to perform correction calculations until the convergence condition is met;

[0023] The low-order correction algorithm includes at least one of Newton's iteration method, fixed-point iteration method, or bisection method.

[0024] A method for determining the hydraulic characteristic water depth of a trapezoidal open channel, used to solve for the normal water depth, includes the following steps:

[0025] Data acquisition and processing: Obtain the cross-sectional and hydraulic parameters of the trapezoidal open channel, and calculate the dimensionless parameters of the foundation;

[0026] Normal water depth solution: The dimensionless relation corresponding to the normal water depth is transformed in the logarithmic field to construct the logarithmic field root equation. Continuous initial values ​​are generated based on physical asymptotic analysis, and the normal water depth is obtained by using an iterative algorithm.

[0027] Verification and rollback control: The calculation residual is monitored in real time during the iterative solution process. When the calculation residual does not meet the preset convergence condition or the iteration shows numerical abnormalities, the rollback mechanism is triggered, and the calculation is switched to the preset fixed-point iterative algorithm until the convergence condition is met and the final normal water depth result is output.

[0028] Optionally, the steps for obtaining the basic dimensionless parameters include:

[0029] According to the Manning roughness of the trapezoidal open channel bottom slope Slope coefficient Bottom width and total flow Calculate the dimensionless combination of normal water depth ,and Satisfy any of the following computational relationships: or .

[0030] Optionally, the steps for determining the normal water depth specifically include:

[0031] Dimensionless water depth is constructed based on cross-sectional parameters. ,in, To determine the water depth, the dimensionless combined quantity is introduced. ;

[0032] Constructing the characteristic root equation of the logarithmic field : ,in, This is an auxiliary constant;

[0033] The intermediate solution of the equation is obtained using a numerical iterative algorithm. And based on the obtained The normal water depth is obtained by reverse calculation. : .

[0034] Optionally, the numerical iteration algorithm and the verification and backoff control specifically include:

[0035] Calculate the initial asymptotic value of the shallow water depth asymptotically approaching the initial value of the water depth : Using a smoothing weight function right and Weighted concatenation is performed to obtain continuous initial values ​​for the entire domain. ;

[0036] The Halley iterative method is used to update and solve the logarithmic field characteristic root equation to obtain an intermediate solution. : ;

[0037] Calculate logarithmic field residuals and with preset threshold Compare;

[0038] like If the calculation is successful, the result is output.

[0039] like If a numerical anomaly occurs during calculation, a rollback mechanism is triggered, switching to a fixed-point iterative algorithm to perform corrective calculations until the iteration converges. The iterative formula for the fixed-point iterative algorithm is as follows: ,in, This is the solution before correction.

[0040] A method for solving the hydraulic characteristic water depth of a trapezoidal open channel includes:

[0041] The critical water depth of the trapezoidal open channel can be determined using the method described above.

[0042] Using the method described above, the normal water depth of the trapezoidal open channel is determined.

[0043] An electronic device includes a memory, a processor, and a computer program or instructions stored in the memory and executable on the processor, wherein the processor executes the computer program or instructions to implement the method described above.

[0044] Compared with the prior art, the present invention has the following technical features and beneficial effects:

[0045] 1) For solving the critical water depth, this invention introduces variable substitution on the basis of dimensionless transformation, which transforms the critical flow control equation into a single-variable sixth-degree algebraic polynomial root equation, and uses a high-order iterative method to find the root. Under the same accuracy requirements, the number of iteration steps can be reduced, the sensitivity to empirical initial values ​​can be reduced, and the risk of iterative oscillation, convergence failure or obtaining invalid solutions caused by initial value deviation can be reduced.

[0046] 2) For solving the problem at normal water depth, this invention performs a logarithmic domain transformation on the dimensionless relation of uniform flow, constructs a logarithmic domain characteristic root equation, and transforms the strongly nonlinear power relation in the original domain into a logarithmic domain summation form, thereby improving the numerical rigidity caused by the drastic changes in the function curve under conditions such as minimal water depth and steep slope. At the same time, based on physical asymptotic analysis, asymptotic initial values ​​for small water depth and large water depth are obtained respectively, and weighted splicing is performed through a smoothing weight function to generate continuous initial values ​​in the whole domain, so that the initial values ​​remain continuous with parameter changes, improving the convergence and stability of the iteration.

[0047] 3) In terms of iterative control, this invention introduces residual self-checking and abnormal state detection, and sets an automatic backoff mechanism: when the high-order iteration has residual over-limit, divergence, negative value or non-numerical state, it automatically switches to the preset low-order robust algorithm for correction until the convergence criterion is met, thereby improving the robustness and automation processing capability of batch working condition calculation of engineering software while taking into account the computational efficiency. Attached Figure Description

[0048] The accompanying drawings illustrate exemplary embodiments of the present invention and, together with the description thereof, serve to explain the principles of the invention. These drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, but do not constitute a limitation on the embodiments of the present invention.

[0049] Figure 1 This is a flowchart illustrating a method for solving the hydraulic characteristic water depth of a trapezoidal open channel according to the present invention, used to solve for the critical water depth.

[0050] Figure 2 This is a flowchart illustrating a method for solving the hydraulic characteristic water depth of a trapezoidal open channel according to the present invention, used to solve for the normal water depth. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0052] It should also be noted that, for ease of description, only the parts relevant to the present invention are shown in the accompanying drawings.

[0053] Where there is no conflict, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0054] Example 1

[0055] like Figure 1 As shown, this embodiment provides a method for solving the hydraulic characteristic water depth of a trapezoidal open channel, used to solve for the critical water depth. The operating logic follows a closed-loop process of "parameter dimensionlessization—equation dimensionality reduction and substitution—high-order iterative solution—intelligent residual verification". The technical solution of this embodiment will be described in detail below with specific steps:

[0056] Step 1: Data Acquisition and Processing: Acquire the cross-sectional parameters (including bottom width, slope coefficient, etc.) and hydraulic parameters (including total flow or unit width flow) of the trapezoidal open channel, and calculate the basic dimensionless parameters; dimensionless parameters refer to values ​​with physical units removed.

[0057] The steps for obtaining the basic dimensionless parameters include:

[0058] Based on the slope coefficient of the trapezoidal open channel Bottom width Gravitational acceleration Determining critical flow characteristic parameters based on flow rate-related parameters ,and Satisfy any of the following computational relationships:

[0059] If the unit width flow rate is known ,but The unit width flow rate can be calculated based on the selected diameter. or .

[0060] If the total flow rate is known and bottom width ,but

[0061] If equivalent width is used ,but ,in, This is a configurable factor (default value is 1), used to adjust the flow rate item according to actual engineering needs.

[0062] Step 2: Construction of Algebraic Equations: Substitute variables into the dimensionless relational expression corresponding to the critical water depth to transform the nonlinear equation into a single-variable algebraic polynomial root equation.

[0063] This step introduces dimensionless water depth. and auxiliary variables Dimensionality reduction is performed. A dimensionless water depth is constructed based on the cross-sectional parameters. ,in, The depth of the water is yet to be determined.

[0064] And introduce auxiliary variables Substitute the dimensionless relation for critical flow;

[0065] Based on the critical flow characteristic parameters Building about Single-variable algebraic polynomial root equation .

[0066] Step 3: Determining the critical water depth: The critical water depth is obtained by using an iterative algorithm;

[0067] For the above sixth-degree equation, this embodiment preferably uses the Halley iteration method to solve it. The Halley method is a third-order convergent algorithm, and its iterative update formula is as follows: ; For the first The value of the next iteration. and functions respectively The first and second derivatives.

[0068] When an intermediate solution that meets the required accuracy is obtained through iteration Then, by using the inverse operation of the aforementioned variable substitution relationship, the critical water depth is calculated in reverse. : .

[0069] Step 4, Verification and Rollback Control: During the iterative solution process, the computational residuals are monitored in real time. When the computational residuals do not meet the preset convergence conditions or when numerical anomalies occur during iteration (including but not limited to numerical overflow, infinity (Inf) or non-numerical (NaN)), the rollback mechanism is triggered, and the calculation is switched to the preset low-order correction algorithm until the convergence conditions are met and the final critical water depth result is output.

[0070] Calculate the current iterative solution residual value : Or its equivalent form, and with a preset convergence threshold Compare;

[0071] like If the calculation is successful, the result is output.

[0072] like If a numerical anomaly is detected during the iteration process, the current higher-order algorithm is determined to be invalid, triggering a rollback correction mechanism;

[0073] The rollback correction mechanism is as follows: The current iterative solution... As the initial value, switch to the preset low-order correction algorithm to perform correction calculations until the convergence condition is met;

[0074] The low-order correction algorithm includes at least one of Newton's iteration method, fixed-point iteration method, or bisection method. Maximum number of high-order updates. (All can be configured).

[0075] Then output the final critical water depth. And the quality flag (indicating whether a rollback was triggered).

[0076] Example 2

[0077] like Figure 2 As shown, this embodiment provides a method for solving the hydraulic characteristic water depth of a trapezoidal open channel, used to solve for the normal water depth. The operating logic follows a closed-loop process of "parameter dimensionless transformation - equation dimension reduction and substitution - high-order iterative solution - residual intelligent verification". The technical solution of this embodiment will be described in detail below with specific steps:

[0078] Step 1: Data Acquisition and Processing: Obtain the cross-sectional parameters (slope coefficient) of the trapezoidal open channel. Bottom width ) and hydraulic parameters (Manning roughness) bottom slope (Total flow rate), and calculate the basic dimensionless parameters.

[0079] Calculate the dimensionless combination of quantities for normal water depth ,and Satisfy any of the following computational relationships: or .

[0080] Step 2: Construct the logarithmic domain characteristic equation: Perform a logarithmic domain transformation on the dimensionless relation corresponding to the normal water depth to construct the logarithmic domain root equation.

[0081] Define dimensionless water depth ( (To determine the water depth), and introduce an auxiliary constant. Construct the characteristic root equation for the logarithmic field. : .

[0082] Step 3: Solving for normal water depth: Generate continuous initial values ​​based on physical asymptotic analysis, and use an iterative algorithm to solve for the normal water depth.

[0083] Based on the physical characteristics of open channel flow, the asymptotic initial values ​​for small water depths are calculated respectively. asymptotically approaching the initial value of the water depth : .

[0084] To achieve a smooth transition across the entire water depth range from the minimum to the maximum depth, a smoothing weight function is introduced. The function satisfies And follow Monotonic change:

[0085] when hour, (At this point, the initial value tends to be an asymptotic solution for shallow water depth); when hour, (At this point, the initial value is biased towards the asymptotic solution for large water depths). This embodiment preferably uses the Logistic form to construct the weight function: ,in, This is a pre-defined transition scale used to define the dominant areas of shallow and deep water; For shape parameters, satisfying (Preferred) Default value ), used to control the steepness of the transition zone.

[0086] Using smoothing weight function right and Weighted concatenation is performed to obtain continuous initial values ​​for the entire domain. .

[0087] by Starting with the Halley iteration method, the logarithmic field characteristic root equation is updated and solved to obtain intermediate solutions. : ;

[0088] The first derivative is .

[0089] The second derivative is .

[0090] The intermediate solution of the equation is obtained using a numerical iterative algorithm. And based on the obtained The normal water depth is obtained by reverse calculation. : .

[0091] Step 4, Verification and Backoff Control: During the iterative solution process, the calculation residual is monitored in real time. When the calculation residual does not meet the preset convergence condition or when numerical anomalies occur during iteration, the backoff mechanism is triggered, and the calculation is switched to the preset fixed-point iterative algorithm until the convergence condition is met and the final normal water depth result is output.

[0092] Calculate logarithmic field residuals and with preset threshold Compare;

[0093] like If the calculation is successful, then the result is determined to be converged and output; otherwise, it is directly based on... Calculate and output the normal water depth result. .

[0094] like If a numerical anomaly occurs during calculation, a rollback mechanism is triggered, switching to a fixed-point iterative algorithm to perform corrective calculations until the iteration converges. The iterative formula for the fixed-point iterative algorithm is as follows: ,in, This is the solution before correction (which can be taken from the result of the previous iteration step).

[0095] By repeatedly performing this correction calculation until the convergence condition is met, a valid normal water depth is ensured.

[0096] Then output the final normal water depth. And the quality flag (indicating whether a rollback was triggered).

[0097] Example 3

[0098] This embodiment provides a comprehensive solution method for the hydraulic characteristic water depth of a trapezoidal open channel. This method is integrated into electronic devices (such as computers and engineering design terminals) and can complete the calculation of key hydraulic elements of a trapezoidal open channel in one go.

[0099] The critical water depth of the trapezoidal open channel can be determined using the method described above.

[0100] Using the method described above, the normal water depth of the trapezoidal open channel is determined.

[0101] Step 1: Data Acquisition and Processing.

[0102] Read the foundation parameters of the trapezoidal open channel from user input or database calls, including: cross-sectional geometric parameters (bottom width) Slope coefficient ), hydraulic parameters (flow rate) Manning roughness bottom slope ) and physical constants (gravitational acceleration) ).

[0103] Step 2: Solve for the critical water depth (using the method described in Example 1). Call the critical water depth calculation module and execute the following sub-steps:

[0104] Parameter conversion: based on cross-sectional parameters , and traffic Using the formula Calculate the dimensionless characteristic parameters of the critical flow (or other equivalent methods). .

[0105] Equation Construction and Substitution: Based on Variable Substitution , build about The sixth algebraic equation .

[0106] Iteration and Verification: The Halley iterative method is used to solve the equation, and the residual self-verification and backoff control mechanism are activated to obtain a convergent solution. .

[0107] Output result: Critical water depth calculated in reverse. .

[0108] Step 3: Solve for the normal water depth (using the method described in Example 2). Call the normal water depth calculation module and execute the following sub-steps:

[0109] Parameter conversion: based on Calculate the dimensionless combination of quantities for normal water depth .

[0110] Equation Construction and Initial Value Generation: Constructing the Characteristic Equation of the Logarithmic Field Simultaneously, the Logistic weighting function is used. asymptotic values ​​for shallow water depths asymptotic value of the great water depth Perform smooth stitching to generate high-quality initial values. .

[0111] Iteration and verification: with Starting with the Halley iteration method, the logarithmic field equations are solved. If residual out-of-limit or numerical anomalies are detected, a fixed-point iteration backtracking mechanism is triggered until a convergent solution is obtained. .

[0112] Output result: Normal water depth calculated by reverse calculation .

[0113] Example 4

[0114] An electronic device includes a memory, a processor, and a computer program or instructions stored in the memory and executable on the processor, wherein the processor executes the computer program or instructions to implement the method described above.

[0115] Memory is used to store software programs and modules. The processor executes various terminal functions and data processing by running the software programs and modules stored in memory. Memory can mainly include a program storage area and a data storage area. The program storage area can store the operating system, at least one executable program required for a given function, etc.

[0116] The storage data area can store data created based on the use of the terminal. Furthermore, the memory can include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0117] In the description of this specification, the references to terms such as "one embodiment / mode," "some embodiments / modes," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment / mode or example is included in at least one embodiment / mode or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment / mode or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments / modes or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments / modes or examples described in this specification, as well as the features of different embodiments / modes or examples.

[0118] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0119] Those skilled in the art should understand that the above embodiments are merely for illustrating the present invention and are not intended to limit the scope of the invention. Those skilled in the art can make other changes or modifications based on the above invention, and these changes or modifications still fall within the scope of the present invention.

Claims

1. A method for solving the hydraulic characteristic water depth of a trapezoidal open channel, characterized in that, The method for determining the critical water depth includes the following steps: Data acquisition and processing: Obtain the cross-sectional and hydraulic parameters of the trapezoidal open channel, and calculate the dimensionless parameters of the foundation; Critical water depth solution: The dimensionless relation corresponding to the critical water depth is transformed into a single-variable algebraic polynomial root equation by variable substitution, and the critical water depth is obtained by using an iterative algorithm. Verification and rollback control: The calculation residual is monitored in real time during the iterative solution process. When the calculation residual does not meet the preset convergence condition or the iteration shows numerical anomalies, the rollback mechanism is triggered, and the calculation is switched to the preset low-order correction algorithm until the convergence condition is met and the final critical water depth result is output.

2. The method for solving the hydraulic characteristic water depth of a trapezoidal open channel according to claim 1, characterized in that, The steps for obtaining the basic dimensionless parameters include: Based on the slope coefficient of the trapezoidal open channel Bottom width Gravitational acceleration Determining critical flow characteristic parameters based on flow rate-related parameters ,and Satisfy any of the following computational relationships: or or ,in, For unit bandwidth, For total flow, For equivalent width, This is a configurable coefficient.

3. The method for solving the hydraulic characteristic water depth of a trapezoidal open channel according to claim 2, characterized in that, The steps for determining the critical water depth specifically include: Dimensionless water depth is constructed based on cross-sectional parameters. ,in, To determine the water depth, an auxiliary variable is introduced. Substitute the dimensionless relation for critical flow; Based on the critical flow characteristic parameters Building about Single-variable algebraic polynomial root equation The current iterative solution of the equation is obtained using a numerical iterative algorithm. ; Based on the obtained The critical water depth is obtained by reverse calculation. : .

4. The method for solving the hydraulic characteristic water depth of a trapezoidal open channel according to claim 3, characterized in that, The numerical iteration algorithm and the verification and rollback control specifically include: The Halley iteration method is used to solve the single-variable algebraic polynomial root equation, and its iterative update formula is as follows: ; Calculate the current iterative solution residual value : Or its equivalent form, and with a preset convergence threshold Compare; like If the calculation is successful, the result is output. like Or, if a numerical anomaly is detected during the iteration process, a rollback correction mechanism will be triggered; The rollback correction mechanism is as follows: The current iterative solution... As the initial value, switch to the preset low-order correction algorithm to perform correction calculations until the convergence condition is met; The low-order correction algorithm includes at least one of Newton's iteration method, fixed-point iteration method, or bisection method.

5. A method for solving the hydraulic characteristic water depth of a trapezoidal open channel, characterized in that, The method for determining normal water depth includes the following steps: Data acquisition and processing: Obtain the cross-sectional and hydraulic parameters of the trapezoidal open channel, and calculate the dimensionless parameters of the foundation; Normal water depth solution: The dimensionless relation corresponding to the normal water depth is transformed in the logarithmic field to construct the logarithmic field root equation. Continuous initial values ​​are generated based on physical asymptotic analysis, and the normal water depth is obtained by using an iterative algorithm. Verification and rollback control: The calculation residual is monitored in real time during the iterative solution process. When the calculation residual does not meet the preset convergence condition or the iteration shows numerical abnormalities, the rollback mechanism is triggered, and the calculation is switched to the preset fixed-point iterative algorithm until the convergence condition is met and the final normal water depth result is output.

6. The method for solving the hydraulic characteristic water depth of a trapezoidal open channel according to claim 5, characterized in that, The steps for obtaining the basic dimensionless parameters include: According to the Manning roughness of the trapezoidal open channel bottom slope Slope coefficient Bottom width and total flow Calculate the dimensionless combination of normal water depth ,and Satisfy any of the following computational relationships: or .

7. The method for solving the hydraulic characteristic water depth of a trapezoidal open channel according to claim 6, characterized in that, The steps for determining the normal water depth specifically include: Dimensionless water depth is constructed based on cross-sectional parameters. ,in, To determine the water depth, the dimensionless combined quantity is introduced. ; Constructing the characteristic root equation of the logarithmic field : ,in, This is an auxiliary constant; The intermediate solution of the equation is obtained using a numerical iterative algorithm. And based on the obtained The normal water depth is obtained by reverse calculation. : .

8. The method for solving the hydraulic characteristic water depth of a trapezoidal open channel according to claim 7, characterized in that, The numerical iteration algorithm and the verification and rollback control specifically include: Calculate the initial asymptotic value of the shallow water depth asymptotically approaching the initial value of the water depth : Using a smoothing weight function right and Weighted concatenation is performed to obtain continuous initial values ​​for the entire domain. ; The Halley iterative method is used to update and solve the logarithmic field characteristic root equation to obtain an intermediate solution. : ; Calculate logarithmic field residuals and with preset threshold Compare; like If the calculation is successful, the result is output. like If a numerical anomaly occurs during calculation, a rollback mechanism is triggered, switching to a fixed-point iterative algorithm to perform corrective calculations until the iteration converges. The iterative formula for the fixed-point iterative algorithm is as follows: ,in, This is the solution before correction.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-8.

10. An electronic device comprising a memory, a processor, and a computer program or instructions stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program or instructions, it implements the method as described in any one of claims 1-8.

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