Unified display and calculation method, device and equipment for critical water depth of horseshoe-shaped section and medium

Abstract

The invention discloses a horseshoe-shaped section critical water depth unified display calculation method, device, equipment and medium, and the method comprises the steps: obtaining the top arch radius and the side arch or bottom arch radius of a horseshoe-shaped section, calculating parameters, obtaining the flow and the gravitational acceleration of a to-be-calculated working condition, constructing dimensionless parameters, and calculating the flow and the gravitational acceleration of the to-be-calculated working condition; and establishing a unified explicit function of the critical water depth dimensionless quantity with respect to the invariable parameter and the type parameter, thereby directly obtaining the critical water depth without iteration, and outputting the critical water depth. According to the method, complex critical flow implicit equation solution is converted into simple explicit equation substitution calculation, so that the risks of initial value sensitivity and non-convergence existing in a traditional iteration method are thoroughly avoided, rapid solution without iteration is achieved, a uniform model is constructed by introducing continuously changing type parameters, and the calculation efficiency is improved. Unified application to various standard and non-standard modified horseshoe-shaped sections is achieved.

Description

Technical Field

[0001] This invention relates to the field of hydraulic calculation and hydraulic engineering design technology, specifically to a method, device, equipment and medium for unified display and calculation of boundary water depth of horseshoe-shaped cross-sections. Background Technology

[0002] Horseshoe-shaped cross-sections are widely used in water diversion tunnels, water conveyance channels, and drainage tunnels due to their excellent stress performance and flow capacity. Critical water depth is a key hydraulic parameter for determining the flow regime (slow flow, rapid flow, critical flow) in open channels, and it is also the basis for water surface line calculations, energy verification, and energy dissipation and scour prevention design. Existing calculations typically require solving implicit equations of critical flow that include the cross-sectional area and water surface width. In engineering, trial and error or iterative methods are often used, which suffers from problems such as cumbersome calculations, sensitivity to initial values, and difficulty in guaranteeing convergence. Another approach is to transform the critical flow equations and construct an inverse function model, combined with optimization or fitting methods, to provide a direct calculation formula for the critical water depth of a standard horseshoe-shaped cross-section under specific parameter values, thereby improving computational efficiency.

[0003] However, the above direct calculation formulas are usually for a few discrete standard cross-section types (i.e., the shape parameters take certain fixed values). When the cross-section shape parameters change continuously or the cross-section is a non-standard horseshoe shape, it is still necessary to re-derive or re-fit. There is a lack of a unified explicit calculation formula and a unified coefficient construction mechanism for continuously changing shape parameters, which limits the universality and scalability of engineering applications.

[0004] Existing research has focused on typical horseshoe-shaped cross-sections such as Standard Type I and II. By performing identity transformations on the critical flow equation of open channels and constructing an inverse function model, combined with optimization or fitting methods, the true value of the critical water depth is approximated. A direct calculation formula for the critical water depth under fixed parameter values ​​has been given, thus achieving rapid calculation without iteration. Summary of the Invention

[0005] The purpose of this invention is to provide a unified display calculation method, device, equipment and medium for the boundary water depth of horseshoe-shaped cross sections, so as to solve the problems of computational dependence on iteration, poor universality and low efficiency in the prior art.

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

[0007] In a first aspect, the first embodiment of the present invention provides a method for uniformly displaying and calculating the boundary water depth of a horseshoe-shaped cross-section, comprising:

[0008] Obtain the top arch radius of the horseshoe-shaped cross section With the radius of the side arch or bottom arch And calculate type parameters , ;

[0009] Obtain the flow rate of the operating condition to be calculated With gravitational acceleration ;

[0010] Constructing dimensionless parameters The calculation formula is:

[0011] ;

[0012] Using dimensionless parameters Sum of parameters Calculate the dimensionless critical water depth using a unified explicit function for the independent variable. The unified display function is a parameter-inclusive function. The composite power function form is calculated using the following formula:

[0013] ;

[0014] in, All are about type parameters The function;

[0015] Calculate the critical water depth based on the dimensionless critical water depth x and the crown radius r. The calculation formula is:

[0016] ;

[0017] Output critical water depth.

[0018] Furthermore, the unified display function is constructed as follows:

[0019] Define normalized variables ,

[0020] ;

[0021] According to the definition of a normalized variable, a cubic polynomial is given by the following formula:

[0022] ;

[0023] Where i = 0, 1, 2, 3, 4;

[0024] Parametric constraints are used to ensure consistency between parameter notation and physical properties. The values ​​of the coefficient function are obtained based on the cubic polynomial.

[0025]

[0026] ;

[0027]

[0028]

[0029]

[0030] Furthermore, the type parameters The value range is greater than or equal to 1.5 and less than or equal to 5.0.

[0031] Furthermore, the type parameters The value range is greater than or equal to 1.8 and less than or equal to 4.0.

[0032] Furthermore, when When the method is applicable to standard Type II horseshoe cross-section, when The method is applicable to standard Type I horseshoe-shaped cross-sections.

[0033] Secondly, another embodiment of the present invention provides a unified display and calculation device for the boundary water depth of a horseshoe-shaped cross section, which is used to implement the unified display and calculation method for the boundary water depth of a horseshoe-shaped cross section described in the above embodiment. The system includes: a parameter acquisition module, a calculation module and an output module. The parameter acquisition module is used to acquire the top arch radius, side arch or bottom arch radius, flow rate and gravitational acceleration of the horseshoe-shaped cross section.

[0034] The calculation module is used to calculate the type parameters and dimensionless parameters based on the acquired data, and to calculate the dimensionless critical water depth using a unified display function with the dimensionless parameters and type parameters as independent variables. The unified display function is a composite power function that includes the type parameters. The critical water depth is calculated based on the dimensionless critical water depth and the crown radius.

[0035] The output module is used to output the critical water depth.

[0036] Furthermore, the value range of the type parameter is greater than or equal to 1.5 and less than or equal to 5.0.

[0037] Furthermore, the value range of the type parameter is greater than or equal to 1.8 and less than or equal to 4.0.

[0038] Thirdly, another embodiment of the present invention provides an electronic device comprising: a processor, an input device, an output device, and a memory, wherein the processor, the input device, the output device, and the memory are interconnected, the memory is used to store a computer program, the computer program includes program instructions, and the processor is configured to invoke the program instructions to execute the method described in the first embodiment above.

[0039] Fourthly, another embodiment of the present invention provides a computer-readable storage medium storing a computer program, the computer program including program instructions that, when executed by a processor, cause the processor to perform the method described in the first embodiment above.

[0040] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0041] This invention provides a unified method, apparatus, equipment, and medium for calculating the critical water depth of horseshoe-shaped cross-sections. It transforms the solution of complex implicit equations of critical flow into a concise explicit substitution calculation, thereby completely avoiding the initial value sensitivity and non-convergence risks inherent in traditional iterative methods and achieving rapid solutions without iteration. Furthermore, this invention overcomes the limitation of existing technologies that can only calculate specific discrete standard cross-sections. By introducing continuously varying shape parameters to construct a unified model, it achieves uniform applicability to various standard and non-standard horseshoe-shaped cross-section variations. Benefiting from its simple structure and physically consistent parameter sign constraints, this method not only ensures the numerical stability and smoothness of the calculation results when parameters change continuously, avoiding non-physical jumps, but is also easily ported to Excel spreadsheets, engineering calculation software, or embedded systems, significantly improving the efficiency of batch calculations, design verification, and automated processing in water conservancy projects. Attached Figure Description

[0042] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0043] Figure 1 A flowchart illustrating a unified display calculation method for the boundary water depth of a horseshoe-shaped cross-section provided in the first embodiment of the present invention;

[0044] Figure 2 This is a flowchart illustrating the specific methods for offline calibration and polynomial coefficient generation in the first embodiment of the present invention;

[0045] Figure 3 This is a schematic diagram of a horseshoe-shaped cross-section boundary water depth unified display and calculation device provided in another embodiment of the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0047] like Figure 1 As shown, the first embodiment of the present invention provides a method for uniformly displaying and calculating the boundary water depth of a horseshoe-shaped cross-section, comprising:

[0048] Obtain the top arch radius of the horseshoe-shaped cross section With the radius of the side arch or bottom arch , crown radius With the radius of the side arch or bottom arch The unit is m, and the type parameters are calculated. The calculation formula is:

[0049] ;

[0050] Obtain the flow rate of the operating condition to be calculated With gravitational acceleration ,flow The unit is m³ / s, gravitational acceleration. The unit is m / s², and it is usually taken as 9.81;

[0051] Constructing dimensionless parameters The calculation formula is:

[0052] ;

[0053] Using dimensionless parameters Sum of parameters Calculate the dimensionless critical water depth using a unified explicit function for the independent variable. The unified display function is a parameter containing type. The composite power function form is calculated using the following formula:

[0054] ;

[0055] in, All are about type parameters The function;

[0056] Calculate the critical water depth based on the dimensionless critical water depth and the crown radius. Critical water depth The unit is m, and the calculation formula is:

[0057] ;

[0058] Output critical water depth.

[0059] In specific implementation, the method provided in this embodiment of the invention can be implemented by means of a calculation plug-in, a calculator, etc. This embodiment takes the calculation plug-in as an example.

[0060] Define variables: : Radius of the crown (m); : Radius of side arch / bottom arch (m); : Type parameters; Flow rate (m³ / s); : Gravitational acceleration (m / s², usually taken as 9.81); : Dimensionless critical water depth; : Dimensionless parameter.

[0061] Output result: Critical water depth (m) represents the vertical distance from the lowest point of the cross-section to the water surface. The critical water depth is used to determine the flow pattern of the cross-section or to verify the design of hydraulic structures.

[0062] Users input through the calculation plugin According to the formula Calculate The calculation plugin constructs dimensionless parameters. The calculation formula is:

[0063]

[0064] The calculation plugin performs calculations using a unified explicit function:

[0065]

[0066]

[0067] Define normalized variables ,

[0068] ;

[0069] According to the definition of a normalized variable, a cubic polynomial is given by the following formula:

[0070] ;

[0071] Where i = 0, 1, 2, 3, 4. Using pre-calibrated coefficients, the coefficients of the cubic polynomial are... Calculate polynomial values ,in, , Using exponential mapping to ensure sign constraints, the values ​​of the coefficient functions obtained from the cubic polynomial are as follows:

[0072]

[0073]

[0074]

[0075]

[0076]

[0077] Thus guarantee , This enhances physical consistency and stability. (Type parameters) The range of values ​​for is: Furthermore, type parameters The range of values ​​for is: .

[0078] like Figure 2 As shown, polynomial coefficients Obtained through offline calibration. Specific methods for offline calibration include:

[0079] In preset parameters Range and dimensionless critical water depth Samples generated within the range ;

[0080] Samples are generated based on the boundary flow reference relationship of the horseshoe-shaped cross-section. dimensionless parameters ;

[0081] To minimize or To obtain the coefficients of the cubic polynomial for the objective function ;

[0082] coefficients of the cubic polynomial The parameters are stored in a parameter table or program constants for online use.

[0083] Table 1 provides a set of optimized and calibrated coefficients. Example, applicable to t∈[1.5,5.0].

[0084] Table 1. Coefficients of the cubic polynomial

[0085]

[0086] The following uses a specific engineering example to illustrate the above implementation:

[0087] Given: A horseshoe-shaped tunnel with a top arch radius r = 1.5m, a bottom arch radius R = 4.5m, and a design flow rate. Gravitational acceleration The calculation steps are as follows:

[0088] 1. .

[0089] 2. From Table 1 ( )have to

[0090]

[0091]

[0092] 3. Calculation ,

[0093]

[0094] 4. Substituting k into the unified display function yields... By calculating h using x, we obtain:

[0095]

[0096]

[0097] To verify the accuracy and stability of the unified explicit function, a comparative sample was generated using the critical flow reference relation of a horseshoe-shaped cross-section (based on the fundamental equations of critical flow and the expressions of cross-sectional geometric elements). The corresponding samples were then compared. Input the unified display function to get ,by Evaluate relative error, The calculation formula is as follows:

[0098] ;

[0099] in, The corresponding predicted value is obtained by using the unified explicit function calculation of this invention; The reference value (baseline value) refers to the dimensionless critical water depth obtained by numerically solving the implicit equation based on the basic equation of critical flow and the expression of the geometric elements of the horseshoe cross section under the same working conditions, and is used as the true value for comparison. This represents the relative error.

[0100] exist Within the range, for each Select Gridded samples (where Using the lower limit of engineering parameters (to avoid numerical sensitivity in extremely shallow water), the following statistical results were obtained: the average relative error over the entire region is approximately 0.1796%; the 95th percentile error is approximately 0.401%; the 99th percentile error is approximately 0.676%; and the maximum relative error over the entire region is approximately 1.404%, mainly occurring near the lower limit of the model parameters. Furthermore, the water depth is close to the lower limit of the sensitive area. To avoid numerical sensitivity caused by extremely shallow water depths and to conform to the lower limit commonly used in engineering, the dimensionless lower limit of water depth can be taken as:

[0101] .

[0102] Due to critical water depth The aforementioned relative error is the critical water depth relative error. For example, the maximum water depth error is on the order of approximately This meets the accuracy requirements for rapid engineering verification and batch calculation.

[0103] The horseshoe-shaped cross-section boundary water depth unified display calculation method provided in this embodiment of the invention is an explicit calculation that does not require iteration and initial value, thus avoiding the non-convergence and initial value sensitivity of the iterative method; moreover, the coefficient function adopts a continuous polynomial expression and ensures the consistency between the parameter sign and the physical condition through exponential mapping, so that the result is continuous and stable when the type parameter changes continuously, without the need to re-establish or refit a new calculation formula for different type parameters.

[0104] Suitable for automated deployment of software and spreadsheets.

[0105] This invention provides a method for uniformly displaying and calculating the boundary water depth of a horseshoe-shaped cross-section, which can be implemented in Excel using the EXP and POWER functions.

[0106] (1) Input ;

[0107] (2) Calculation , ;

[0108] (3) Calculate according to Table 1 ;

[0109] (4) Calculation , , , , ;

[0110] (5) Calculation ;

[0111] (6) Calculation Output .

[0112] Note: You should enter the following: If you need to cover a very small amount of traffic, you can choose... To avoid exist and The numerical values ​​diverge over time.

[0113] The present invention provides a unified explicit calculation method for the critical water depth of a horseshoe-shaped cross section. This method constructs dimensionless parameters and establishes a unified explicit function of the dimensionless critical water depth with respect to the dimensionless parameters and the type parameters in the form of a composite power function. At the same time, the composite power function parameters are expressed by a cubic polynomial of the type parameters, and exponential mapping is used to ensure the consistency between the parameter signs and the physical properties.

[0114] This invention transforms the solution of complex implicit equations of critical flow into a concise explicit substitution calculation, thereby completely avoiding the initial value sensitivity and non-convergence risks of traditional iterative methods and achieving rapid solutions without iteration. Simultaneously, this invention overcomes the limitation of existing technologies that can only calculate specific discrete standard cross-sections. By introducing continuously changing shape parameters to construct a unified model, it achieves uniform applicability to various standard and non-standard horseshoe-shaped cross-sections. Benefiting from its simple structure and physically consistent parameter sign constraints, this method not only ensures the numerical stability and smoothness of the calculation results when parameters change continuously, avoiding non-physical jumps, but also is easily ported to Excel spreadsheets, engineering calculation software, or embedded systems, significantly improving the efficiency of batch calculations, design verification, and automated processing in water conservancy engineering.

[0115] like Figure 3 As shown, another embodiment of the present invention provides a unified display and calculation device for the boundary water depth of a horseshoe-shaped cross section, which is used to implement the unified display and calculation method for the boundary water depth of a horseshoe-shaped cross section described in the above embodiment. The system includes: a parameter acquisition module, a calculation module and an output module. The parameter acquisition module is used to acquire the top arch radius, side arch or bottom arch radius, flow rate and gravitational acceleration of the horseshoe-shaped cross section.

[0116] The calculation module is used to calculate the type parameters and dimensionless parameters based on the acquired data, and to calculate the dimensionless critical water depth using a unified display function with the dimensionless parameters and type parameters as independent variables. The unified display function is a composite power function that includes the type parameters. The critical water depth is calculated based on the dimensionless critical water depth and the crown radius.

[0117] The output module is used to output the critical water depth.

[0118] The type parameter can take values ​​greater than or equal to 1.5 and less than or equal to 5.0. Alternatively, the type parameter can also take values ​​greater than or equal to 1.8 and less than or equal to 4.0.

[0119] The execution process of each module can be carried out according to the process steps of the unified display calculation method for the boundary water depth of a horseshoe-shaped cross section provided in the first embodiment, and will not be described in detail in this embodiment.

[0120] The horseshoe-shaped cross-section boundary water depth unified display calculation device and the horseshoe-shaped cross-section boundary water depth unified display calculation method provided in this embodiment of the invention are based on the same inventive concept and have the same beneficial effects, and will not be described again here.

[0121] Another embodiment of the present invention provides an electronic device, which includes a processor, an input device, an output device, and a memory. The processor, the input device, the output device, and the memory are interconnected. The memory is used to store a computer program, which includes program instructions. The processor is configured to call the program instructions to execute the method described in the first embodiment above.

[0122] It should be understood that, in the embodiments of the present invention, the processor may be a Central Processing Unit (CPU), but it may also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0123] Input devices may include touchpads, microphones, etc., and output devices may include displays (LCDs, etc.), speakers, etc.

[0124] The memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory may also include non-volatile random access memory. For example, the memory may also store information about the device type.

[0125] In specific implementations, the processor, input device, and output device described in the embodiments of the present invention can execute the implementation of the method embodiments described in the embodiments of the present invention, or they can execute the implementation of the system embodiments described in the embodiments of the present invention, which will not be repeated here.

[0126] The present invention also provides an embodiment of a computer-readable storage medium storing a computer program, the computer program including program instructions, which, when executed by a processor, cause the processor to perform the method described in the first embodiment above.

[0127] The computer-readable storage medium can be an internal storage unit of the terminal described in the foregoing embodiments, such as the terminal's hard drive or memory. The computer-readable storage medium can also be an external storage device of the terminal, such as a plug-in hard drive, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card equipped on the terminal. Furthermore, the computer-readable storage medium can include both internal storage units and external storage devices of the terminal. The computer-readable storage medium is used to store the computer program and other programs and data required by the terminal. The computer-readable storage medium can also be used to temporarily store data that has been output or will be output.

[0128] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0129] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the terminals and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0130] In the several embodiments provided in this application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices or units, or may be electrical, mechanical or other forms of connection.

[0131] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for uniformly displaying and calculating the boundary water depth of a horseshoe-shaped cross-section, characterized in that, include: Obtain the top arch radius of the horseshoe-shaped cross section With the radius of the side arch or bottom arch And calculate type parameters , ; Obtain the flow rate of the operating condition to be calculated With gravitational acceleration ; Constructing dimensionless parameters The calculation formula is: ； Using dimensionless parameters Sum of parameters Calculate the dimensionless critical water depth using a unified explicit function for the independent variable. The unified display function is a parameter-inclusive function. The composite power function form is calculated using the following formula: ； in, All are about type parameters The function; Calculate the critical water depth based on the dimensionless critical water depth x and the crown radius r. The calculation formula is: ； Output critical water depth.

2. The method for unified display and calculation of water depth at the boundary of a horseshoe-shaped cross-section according to claim 1, characterized in that, The constructor for the unified display function is as follows: Define normalized variables , ； According to the definition of a normalized variable, a cubic polynomial is given by the following formula: ； Where i = 0, 1, 2, 3, 4; Parametric constraints are used to ensure consistency between parameter notation and physical properties. The values ​​of the coefficient function are obtained based on the cubic polynomial. ； ； ； ； 。 3. The method for unified display and calculation of water depth at the boundary of a horseshoe-shaped cross-section according to claim 1, characterized in that, The type parameters The value range is greater than or equal to 1.5 and less than or equal to 5.

0.

4. The method for unified display and calculation of water depth at the boundary of a horseshoe-shaped cross-section according to claim 3, characterized in that, The type parameters The value range is greater than or equal to 1.8 and less than or equal to 4.

0.

5. The method for unified display and calculation of water depth at the boundary of a horseshoe-shaped cross-section according to claim 1, characterized in that, when When the method is applicable to standard Type II horseshoe cross-section, when The method is applicable to standard Type I horseshoe-shaped cross-sections.

6. A unified display and calculation device for water depth at the boundary of a horseshoe-shaped cross-section, characterized in that, The system is used to implement the unified display calculation method for the boundary water depth of a horseshoe-shaped cross section as described in any one of claims 1-5. The system includes: a parameter acquisition module, a calculation module, and an output module. The parameter acquisition module is used to acquire the top arch radius, side arch or bottom arch radius, flow rate and gravitational acceleration of the horseshoe-shaped cross section. The calculation module is used to calculate the type parameters and dimensionless parameters based on the acquired data, and to calculate the dimensionless critical water depth using a unified display function with the dimensionless parameters and type parameters as independent variables. The unified display function is a composite power function that includes the type parameters. The critical water depth is calculated based on the dimensionless critical water depth and the crown radius. The output module is used to output the critical water depth.

7. The horseshoe-shaped cross-section boundary water depth unified display and calculation device according to claim 6, characterized in that, The value range of the type parameter is greater than or equal to 1.5 and less than or equal to 5.

0.

8. The horseshoe-shaped cross-section boundary water depth unified display and calculation device according to claim 7, characterized in that, The value range of the type parameter is greater than or equal to 1.8 and less than or equal to 4.

0.

9. An electronic device, comprising: The processor, input device, output device, and memory are interconnected, the memory being used to store a computer program, the computer program including program instructions, characterized in that the processor is configured to invoke the program instructions to perform the method as described in any one of claims 1-5.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, the computer program including program instructions that, when executed by a processor, cause the processor to perform the method as described in any one of claims 1-5.

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