A method for optimizing the shape of vertical swirl flood discharge tunnel

Abstract

The present invention belongs to the technical field of water conservancy engineering, and provides a method for optimizing the shape of a vertical shaft vortex flood discharge tunnel, including: S1, determining a number of shape optimization parameters and a number of optimization indexes of a vertical shaft vortex flood discharge tunnel; S2, obtaining the value range of each shape optimization parameter and performing random sampling to form multiple groups of shape optimization parameter samples; S3, modeling the vertical shaft vortex flood discharge tunnel according to multiple groups of shape optimization parameter samples, performing numerical simulation on the obtained vertical shaft vortex flood discharge tunnel model, and obtaining the optimization index values ​​corresponding to each group of shape optimization parameter samples; S4, constructing a Kriging proxy model according to all shape optimization parameter samples and optimization index values; S5, establishing a multi-objective optimization model according to the Kriging proxy model, solving, and obtaining the optimal solution of the shape optimization parameters; S6, constructing the vertical shaft vortex flood discharge tunnel according to the optimal solution of the shape optimization parameters. The optimization method does not require multiple numerical simulations, and improves the optimization efficiency.

Description

Technical Field

[0001] The invention belongs to the technical field of water conservancy projects, and in particular relates to a method for optimizing the shape of a vertical shaft vortex flood discharge tunnel based on a Kriging proxy model. Background Art

[0002] The vertical shaft vortex spillway is an advanced water conservancy engineering structure. As a structure used by various types of water retaining dams to discharge water, its main function is to discharge water, eliminate excess energy of water flow, make the water flow smoothly, and prevent atomization and scouring of riverbed or slope in the downstream. At present, many water conservancy projects such as pumped storage projects, earth-rock dam projects and gravity dam projects have adopted the structural design of vertical shaft vortex spillway for flood discharge. The basic structure of the vertical shaft vortex spillway includes the upper flat section of the water diversion channel, the vortex chamber section, the contraction section, the vertical shaft section, the stilling well, the slope pressure section, the lower flat section of the water withdrawal tunnel, and the outlet section. In this structure, the water first enters the vortex chamber section through the upper flat section of the water diversion channel, and then begins to rotate under the action of the vortex chamber section to form a vortex. This vortex generates high-speed rotating water flow inside the shaft. The water flow rubs against the wall of the contraction section, and the gas cavity in the middle rotates downward and falls into the energy dissipation well. In this process, the potential energy and kinetic energy of the water flow are converted into heat energy, realizing the consumption of water flow energy. Since the outlet section controls the outflow through the pressure slope section, the water flow is mixed with a small amount of air before being discharged, which can effectively reduce the atomization phenomenon in the downstream. The consumption of water flow energy through the shaft vortex spillway can effectively reduce the energy of the downstream water flow, thereby protecting the stability of the downstream riverbed and riverbank. At the same time, the downstream water flow has a high oxygen content, which can promote the healthy development of the aquatic ecosystem.

[0003] The research and application of vertical shaft swirl spillway tunnels involve multiple fields such as hydraulics and fluid mechanics. For many years, the traditional vertical shaft structure design demonstration has been carried out through hydraulic model experiments. In recent years, with the development of numerical simulation technology, many researchers have used computational fluid dynamics (CFD) methods to study the hydraulic characteristics of vertical shaft swirl spillway tunnels in order to optimize their body structure design and improve their energy dissipation rate. The optimization process of the body structure of the vertical shaft swirl spillway tunnel using computational fluid dynamics methods requires repeated construction of the vertical shaft swirl spillway tunnel model and multiple numerical simulations to achieve a more ideal design discharge effect. This process is cumbersome and time-consuming, and requires very high design or optimization experience. Summary of the invention

[0004] The purpose of the present invention is to propose a method for optimizing the shape of a vertical shaft vortex flood discharge tunnel, which does not require multiple numerical simulations, reduces the number of design demonstrations, and improves the optimization efficiency.

[0005] The present invention is achieved through the following technical solutions:

[0006] The present invention provides a method for optimizing the shape of a vertical shaft swirl flood discharge tunnel, comprising the following steps:

[0007] S1. Determine several individual optimization parameters and several optimization indicators of the vertical shaft swirl spillway tunnel;

[0008] S2, obtaining the value range of each body shape optimization parameter, and performing random sampling within the value range of each body shape optimization parameter to form multiple groups of body shape optimization parameter samples;

[0009] S3. Based on multiple groups of body shape optimization parameter samples, a three-dimensional modeling software is used to perform parametric modeling of the vertical shaft vortex flood discharge tunnel, and a numerical simulation is performed on the constructed vertical shaft vortex flood discharge tunnel model to obtain the optimization index value corresponding to each group of body shape optimization parameter samples;

[0010] S4, constructing a Kriging proxy model based on all body shape optimization parameter samples and optimization index values ​​in S3;

[0011] S5. Establish a multi-objective optimization model based on the above Kriging proxy model, and solve it to obtain the optimal solution of the body shape optimization parameters;

[0012] S6. Constructing a vertical shaft swirl flood discharge tunnel according to the optimal solution of the body shape optimization parameters.

[0013] Preferably, in S1, the body shape optimization parameters include the height A of the contraction section, the ratio B of the depth of the stilling well to the diameter of the shaft section, and the ratio C of the length of the slope pressure section to the diameter of the shaft section.

[0014] Furthermore, in S5, the constraints of the multi-objective optimization model are:

[0015] a. Contraction height A constraint, A min ≤A≤A max ; A min and A max are the minimum and maximum values ​​of the height of the contraction section, respectively;

[0016] b. The ratio of the stilling well depth to the shaft section diameter is constrained by B, min ≤B≤B max ; B min and B max are the minimum and maximum values ​​of the ratio of the stilling well depth to the shaft section diameter, respectively;

[0017] c. The ratio of the length of the slope section to the diameter of the shaft section is constrained by C, min ≤C≤C max ; C min and C max They are the minimum and maximum values ​​of the ratio of the slope section length to the shaft section diameter, respectively.

[0018] Preferably, in S1, the optimization indexes include the energy dissipation rate S and the outflow velocity uniformity coefficient Z of the vertical shaft swirl flood discharge tunnel.

[0019] Furthermore, in S5, the optimization objectives of the multi-objective optimization model include: maximizing the energy dissipation rate S and minimizing the outflow velocity uniformity coefficient Z.

[0020] Preferably, in S2, the random sampling is performed within the value range of each body shape optimization parameter, specifically: a plurality of body shape optimization parameter samples are randomly selected within the value range of each body shape optimization parameter using an optimal space filling design method.

[0021] Preferably, in S3, the numerical simulation of the constructed vertical shaft vortex flood discharge tunnel model is specifically:

[0022] Numerical simulations were performed in the following areas of the shaft vortex spillway model: inlet reservoir area, air replenishment holes, upper flat section of the water diversion channel, vortex chamber section, ventilation well, contraction section, shaft section, stilling well, pressure slope section, and lower flat section of the water withdrawal tunnel.

[0023] Preferably, in S4, after the Kriging proxy model is constructed, the accuracy of the Kriging proxy model is evaluated. If the evaluation result is that the Kriging proxy model meets the accuracy requirements, S5 is performed; otherwise, return to S2 for re-sampling, and repeat steps S3 and S4 until the Kriging proxy model meets the accuracy requirements.

[0024] Furthermore, the accuracy evaluation of the Kriging proxy model is specifically as follows: within the value range of each body shape optimization parameter, several groups of verification points other than the body shape optimization parameter samples are selected, and numerical simulation is performed to calculate the optimization index value corresponding to each group of verification points to obtain a simulation value; the Kriging proxy model is used to predict the optimization index value corresponding to each group of verification points to obtain a predicted value; an error analysis is performed on the simulation value and the predicted value. If R 2 If it is greater than 0.9, the Kriging proxy model meets the accuracy requirements.

[0025] Preferably, a multi-objective genetic algorithm is used to solve the multi-objective optimization model.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] The present invention designs a shaft vortex flood discharge tunnel shape optimization method based on Kriging proxy model. Compared with the traditional optimization method, the present invention only needs to select a reasonable value range of shape optimization parameters, sample within the value range of shape optimization parameters, form multiple groups of shape optimization parameter samples, and perform modeling and numerical simulation calculation based on the shape optimization parameter samples, determine the Kriging proxy model according to the calculation results, and subsequently do not need to call the numerical simulation program for numerical simulation. According to the Kriging proxy model, the hydraulic characteristic index (i.e., optimization index) of the shaft vortex flood discharge tunnel corresponding to the shape optimization parameter can be obtained, and the optimal shape of the shaft vortex flood discharge tunnel that meets the requirements of multiple optimization indicators can be quickly obtained. The method of the present invention can find the most reasonable parameter value under many shape optimization parameter conditions, reduce the number of design demonstrations in this process, and quickly obtain the influence of each shape optimization parameter on the optimization index, thereby overcoming the defects of the traditional optimization method that multiple numerical simulations are required, the efficiency is low, and the optimization time period is long. In addition, the Kriging proxy model used in the present invention can avoid overfitting and underfitting compared with the standard response surface model, and ensure that better optimization results are obtained.

[0028] Furthermore, the present invention adopts the Optimal Space-Filling Design (OSF) technology to collect body shape optimization parameter samples, which can achieve a more uniform sample distribution in the body shape optimization parameter value range space, while maximizing the distance between sample points, ensuring the independence and diversity of sample points, thereby effectively handling extreme situations and providing comprehensive and accurate coverage of the design space.

[0029] Furthermore, the present invention can ensure the accuracy of the obtained Kriging proxy model by performing accuracy evaluation on the Kriging proxy model, thereby ensuring the accuracy of the final prediction result. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0031] Figure 1 It is a schematic diagram of a three-dimensional model of a vertical shaft swirl flood discharge tunnel of the present invention.

[0032] Figure 21 is a distribution diagram of sampling points of the body shape optimization parameters of the present invention; (a) is the height of the contraction section; (b) is the ratio B of the stilling well depth to the shaft section diameter; (c) is the ratio C of the slope pressure section length to the shaft section diameter.

[0033] Figure 3 It is the response surface diagram obtained by fitting the energy dissipation rate S with the decision variables A, B, and C; (a) is the response surface of the interaction between the height of the contraction section and the ratio B of the depth of the stilling well to the diameter of the shaft section on the energy dissipation rate; (b) is the contour map corresponding to (a); (c) is the response surface of the interaction between the height of the contraction section and the ratio C of the length of the slope section to the diameter of the shaft section on the energy dissipation rate; (d) is the contour map corresponding to (c); (e) is the response surface of the interaction between the ratio B of the depth of the stilling well to the diameter of the shaft section and the ratio C of the length of the slope section to the diameter of the shaft section on the energy dissipation rate; (f) is the contour map corresponding to (e).

[0034] Figure 4 It is the response surface diagram obtained by fitting the outflow velocity uniformity coefficient Z with the decision variables A, B, and C; (a) is the response surface of the interaction between the height of the contraction section and the ratio B of the depth of the stilling well to the diameter of the shaft section on the outflow velocity uniformity coefficient; (b) is the contour map corresponding to (a); (c) is the response surface of the interaction between the height of the contraction section and the ratio C of the length of the pressure slope section to the diameter of the shaft section on the outflow velocity uniformity coefficient; (d) is the contour map corresponding to (c); (e) is the response surface of the interaction between the ratio B of the depth of the stilling well to the diameter of the shaft section and the ratio C of the length of the pressure slope section to the diameter of the shaft section on the outflow velocity uniformity coefficient; (f) is the contour map corresponding to (e).

[0035] Figure 5 It is a Pareto frontier diagram of the multi-objective optimization model of the present invention.

[0036] Figure 6 Schematic diagram of the optimal body parameters of the vertical shaft swirl flood discharge tunnel in the embodiment of the present invention after adopting the original design scheme (a) and optimizing by the method of the present invention (b).

[0037] Figure 7 It is a flow chart of the method for optimizing the shape of a vertical shaft swirl flood discharge tunnel according to the present invention.

[0038] In the figure: entrance reservoir area 1, lock chamber section 2, air supply hole 3, upper flat section of water diversion channel 4, vortex chamber section 5, contraction section 6, vertical shaft section 7, energy dissipation well 8, pressure slope section 9, lower flat section of water withdrawal tunnel 10, outlet section 11, ventilation well 12. DETAILED DESCRIPTION

[0039] The following describes the implementation of the present invention through specific embodiments, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific implementations, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention.

[0040] It should be noted that the process equipment or devices not specifically specified in the following embodiments are all conventional equipment or devices in the art.

[0041] It should be noted that the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices. Moreover, unless otherwise specified, the numbering of each method step is only a convenient tool for identifying each method step, and is not intended to limit the order of arrangement of each method step or to define the scope of the present invention. Changes or adjustments in their relative relationships should also be regarded as the scope of the present invention without substantially changing the technical content.

[0042] The schematic diagram of the three-dimensional model of the vertical shaft swirl flood discharge tunnel of the present invention is as follows: Figure 1 As shown, it includes an inlet reservoir area 1, a lock chamber section 2, an upper flat section of a water diversion channel 4, a vortex chamber section 5, a ventilation well 12, a contraction section 6, a shaft section 7, a stilling well 8, a pressure slope section 9 and a lower flat section 10 of a water withdrawal tunnel. One end of the upper flat section 4 of the water diversion channel is connected to the inlet reservoir area 1, and the other end is connected to the vortex chamber section 5. The lock chamber section 2 and the air supplement hole 3 are arranged at the end of the upper flat section 4 of the water diversion channel close to the inlet reservoir area 1. The upper end of the vortex chamber section 5 is connected to the ventilation well 12, and the lower end is connected to the contraction section 6, the shaft section 7, and the stilling well 8 in sequence. The side wall of the stilling well 8 is connected to the pressure slope section 9 and the lower flat section 10 of the water withdrawal tunnel in sequence, and the end of the lower flat section 10 of the water withdrawal tunnel is the outlet section 11.

[0043] like Figure 7 As shown, the method for optimizing the shape of a vertical shaft swirl flood discharge tunnel according to the present invention comprises the following steps:

[0044] S1. Determine several individual optimization parameters and several optimization indicators of the vertical shaft swirl spillway tunnel;

[0045] S2, obtaining the value range of each body shape optimization parameter, and performing random sampling within the value range of each body shape optimization parameter to form multiple groups of body shape optimization parameter samples;

[0046] S3. Based on multiple groups of body shape optimization parameter samples, a three-dimensional modeling software is used to perform parametric modeling of the vertical shaft vortex flood discharge tunnel, and a numerical simulation is performed on the constructed vertical shaft vortex flood discharge tunnel model to obtain the optimization index value corresponding to each group of body shape optimization parameter samples;

[0047] S4, constructing a Kriging proxy model based on all body shape optimization parameter samples and optimization index values ​​in S3;

[0048] S5. Establish a multi-objective optimization model based on the above Kriging proxy model, and solve it to obtain the optimal solution of the body shape optimization parameters;

[0049] S6. Constructing a vertical shaft swirl flood discharge tunnel according to the optimal solution of the body shape optimization parameters.

[0050] Specifically, the method for optimizing the shape of a vertical shaft swirl flood discharge tunnel comprises the following steps:

[0051] S1. Determine several individual optimization parameters and several optimization indicators of the vertical shaft swirl flood discharge tunnel

[0052] The key body parameters affecting the energy dissipation rate and flow pattern of the vertical swirl flood discharge tunnel are selected as body optimization parameters, i.e., decision variables, and the optimization indicators are defined.

[0053] The body parameters of the vertical shaft swirl flood spillway tunnel include: the length of the upper flat section 4 of the water diversion channel, the diameter of the vortex chamber section 5, the diameter of the ventilation well 12, the height of the contraction section 6, the diameter of the vertical shaft section 7, the depth of the energy dissipation well 8, the length of the slope pressure section 9 and the length of the lower flat section 10 of the water withdrawal tunnel. Among these body parameters, the height of the contraction section 6, the diameter of the vertical shaft section 7, the depth of the energy dissipation well 8 and the length of the slope pressure section 9 have a significant impact on the energy dissipation rate and flow state of the vertical shaft swirl flood spillway tunnel. Therefore, in the embodiment of the present invention, the height of the contraction section A, the ratio of the depth of the energy dissipation well to the diameter of the vertical shaft section B, and the ratio of the length of the slope pressure section to the diameter of the vertical shaft section C are selected as decision variables (i.e., body optimization parameters), and the energy dissipation rate S and the uniform coefficient of the outflow velocity Z of the vertical shaft swirl flood spillway tunnel are used as optimization indicators.

[0054] S2. Sample point generation

[0055] Based on the experience of many engineering design schemes, the upper and lower limits of the value range of each body shape optimization parameter are selected, and the optimal space filling design method is used to generate uniformly distributed random sample points in the value range space of each body shape optimization parameter formed by the upper and lower limits to form multiple groups of body shape optimization parameter samples.

[0056] The present invention adopts the optimal space filling design method and performs optimization through multiple iterations to achieve a more uniform distribution of sample points in the value range space of the body shape optimization parameters. At the same time, the distance between sample points is maximized, ensuring the independence and diversity of sample points, thereby effectively handling extreme situations and providing comprehensive and accurate coverage of the design space.

[0057] S3. Numerical simulation

[0058] According to the generated multiple groups of shape optimization parameter samples, the vertical shaft vortex flood spillway tunnel was parametrically modeled using 3D modeling software. The obtained vertical shaft vortex flood spillway tunnel model was divided in the form of structured grids and unstructured grids, and the grids were appropriately encrypted to ensure the calculation accuracy. The turbulence model and the volume of fluid (VOF) method were used to perform numerical simulations on multiple groups of shape optimization parameter samples in turn to obtain the optimization index values, and the calculation results of all shape optimization parameter samples were recorded in the sample data set.

[0059] The simulation calculation area includes: the inlet reservoir area 1, the air replenishment hole 3, the upper flat section of the water diversion channel 4, the vortex chamber section 5, the ventilation well 12, the contraction section 6, the vertical shaft section 7, the energy dissipation well 8, the pressure slope section 9 and the lower flat section 10 of the water withdrawal tunnel.

[0060] S4. Kriging surrogate model construction and its accuracy evaluation

[0061] According to all the body shape optimization parameter samples and optimization index values ​​in S3, a Kriging proxy model is constructed to generate a response surface between the optimization index and the body shape optimization parameters (decision variables). The obtained Kriging proxy model is then evaluated for accuracy. After meeting the accuracy requirements, the final Kriging proxy model is obtained.

[0062] Among them, the basic form of the Kriging surrogate model is:

[0063] (1)

[0064] Where:

[0065] f T ( x ) is about x The polynomial function represents the global trend of the Kriging proxy model, that is, the average relationship between the input variables and the output response without considering random fluctuations. In the present invention, the input variables are decision variables, and the output response is the optimization index.

[0066] Z ( x) represents a Gaussian random process, which is used to capture random fluctuations or noise in the Kriging surrogate model that cannot be explained by the deterministic polynomial function. Z ( x ) is a Gaussian random process with zero mean and a covariance structure with parameters and related functions definition.

[0067] Z ( x ) is as follows:

[0068] (2)

[0069] Where:

[0070] x and v Any two points in the input variables

[0071] The covariance, i.e. the degree of variability of a Gaussian random process, is a key parameter used to quantify the uncertainty of the Kriging surrogate model predictions.

[0072] For about Function:

[0073] (3)

[0074] Where:

[0075] For function The dimension of , that is, the number of input variables, j =1,2,…,n.

[0076] is the anisotropic parameter, a vector used to control the correlation function In spatial statistics, these parameters can affect the smoothness and rate of change of the Gaussian random process.

[0077] is the distance between points, that is, the distance between any two points in the input space. In the Kriging proxy model, the distance between points Used to calculate the correlation function , thereby determining the correlation between the response values ​​of these points. The input space refers to the set of all input variables, the points refer to the input variables, and the response values ​​refer to the optimization index values.

[0078] The kernel function is a function used to describe the correlation between different points of a Gaussian random process. In the Kriging surrogate model, this function usually takes a specific form such as a Gaussian kernel or an exponential kernel to ensure the stability and normality of the Kriging surrogate model.

[0079] After the Kriging proxy model is constructed, the accuracy of the Kriging proxy model is evaluated. If the evaluation result shows that the Kriging proxy model meets the accuracy requirement, S5 is performed; otherwise, return to S2 for re-sampling, and repeat steps S3 and S4 until the Kriging proxy model meets the accuracy requirement.

[0080] In the embodiment of the present invention, the accuracy of the Kriging proxy model is evaluated, specifically: within the value range of each body shape optimization parameter, in addition to the body shape optimization parameter sample selected in S2, several groups of verification points are further selected to perform numerical simulation to calculate the optimization index value corresponding to each group of verification points, and obtain simulation values; the Kriging proxy model is used to predict the optimization index value corresponding to each group of verification points to obtain a predicted value; the simulation value and the predicted value are analyzed for error, if R 2 If it is greater than 0.9, the Kriging proxy model meets the accuracy requirements.

[0081] S5. Multi-objective optimization analysis

[0082] A multi-objective genetic algorithm (MOGA) is used to perform multi-objective optimization analysis on the Kriging proxy model to find the point with the best optimization index. The shape of the vertical shaft swirl flood discharge tunnel corresponding to its corresponding decision variable is the optimal shape.

[0083] The multi-objective optimization analysis model is established as follows:

[0084] (4)

[0085] Where: It is determined by the response surface (i.e. Kriging proxy model) between the optimization index energy dissipation rate and the decision variables. It is determined by the response surface (i.e., Kriging proxy model) between the optimization index outflow velocity uniformity coefficient and the decision variable. In the embodiment of the present invention, the decision variable X=[A (contraction section height), B (ratio of stilling well depth to shaft section diameter), C (ratio of slope pressure section length to shaft section diameter)].

[0086] Determine the constraints of the multi-objective optimization model. Taking the decision variable X in the embodiment of the present invention as an example, the constraints are:

[0087] a. Contraction height A constraint, A min ≤A≤A max , the minimum value of the contraction section height A of vertical swirl spillway tunnels of different designs min and the maximum value A max Different from each other, when the vertical shaft swirl flood discharge tunnel is determined, its A min , A max will also be a fixed value;

[0088] b. The ratio of the stilling well depth to the shaft section diameter is constrained by B, min ≤B≤B max , the minimum value of the ratio B for vertical swirl spillway tunnels of different designs is B min and the maximum value B max Different from each other, when the vertical shaft swirl flood discharge tunnel is determined, its B min , B max will also be a fixed value;

[0089] c. The ratio of the length of the slope section to the diameter of the shaft section is constrained by C, min ≤C≤C max , the minimum value of the ratio C of vertical swirl spillway tunnels with different designs is C min and the maximum value C max Different from each other, when the vertical shaft swirl flood discharge tunnel is determined, its C min , C max will also be a fixed value.

[0090] After the parameters of the above multi-objective optimization model are determined, the MOGA algorithm is used to set appropriate solution parameters, and finally the Pareto frontier of the multi-objective optimization model is solved and drawn. Figure 5 .

[0091] Through the optimization algorithm, a series of vertical swirl flood spillway tunnel design schemes can be obtained, and the Pareto front reflects the different trade-offs between the energy dissipation rate and the uniform coefficient of the outflow velocity. Finally, a design scheme that is most suitable for practical application can be selected from these Pareto front results, providing strong support for designers in the design and decision-making of vertical swirl flood spillway tunnel projects.

[0092] Example

[0093] This embodiment intends to optimize the shape of a vertical shaft vortex flood discharge tunnel.

[0094] Step 1: Define body shape optimization parameters and determine optimization indicators

[0095] In this embodiment, the three body optimization parameters of the vertical shaft vortex spillway tunnel are represented by the height A of the contraction section, the ratio B of the depth of the stilling well to the diameter of the vertical shaft section, and the ratio C of the length of the slope pressure section to the diameter of the vertical shaft section. S represents the energy dissipation rate of the vertical shaft vortex spillway tunnel, and Z represents the uniformity coefficient of the outflow velocity of the vertical shaft vortex spillway tunnel.

[0096] Step 2: Count the values ​​of the three body shape optimization parameters of the vertical shaft swirl flood discharge tunnels that have been built in China (Table 1), and derive the value ranges of each body shape optimization parameter according to the upper and lower limits of the values ​​(Table 2). The maximum value of the body shape optimization parameter value range actually selected in this embodiment is slightly larger than the upper limit of the value.

[0097]

[0098]

[0099] Step 2: Based on the minimum and maximum values ​​of the value range of each body shape optimization parameter, the optimal space filling design method is used to generate uniformly distributed random sample points in the value range space of each body shape optimization parameter to form multiple groups of body shape optimization parameter samples, see Table 3 and Figure 2 .

[0100]

[0101] Step 3: According to the sample data of the shape optimization parameters, the vertical shaft swirl flood spillway tunnel is parametrically modeled using 3D modeling software. The constructed vertical shaft swirl flood spillway tunnel model is divided into structured grids and unstructured grids. Numerical simulation is performed on each group of shape optimization parameter samples. The calculation results of all shape optimization parameter samples (i.e., the energy dissipation rate S and the outflow velocity uniformity coefficient Z of the vertical shaft swirl flood spillway tunnel) are recorded in the sample data set. The sample data set is shown in Table 4.

[0102]

[0103] Step 4: Fit the sample data set through the Kriging surrogate model, construct the response surface between the optimization index and the decision variable, obtain the Kriging surrogate model, and evaluate the accuracy of the obtained Kriging surrogate model. After meeting the accuracy requirements, the final Kriging surrogate model is obtained.

[0104] In order to verify whether the fitted response surface is close enough to the real response relationship, it is necessary to add a certain number of verification points for evaluating the prediction accuracy of the Kriging proxy model in the value range of each body optimization parameter, which are far away from the current sample point (i.e., the body optimization parameter sample described in step 3). The verification point set formed by the selected verification points is shown in Table 5. Numerical simulation is performed on the selected verification points to obtain the simulated values ​​of the optimization index energy dissipation rate and the outflow velocity uniformity coefficient. The Kriging proxy model is used to predict the optimization index energy dissipation rate and the outflow velocity uniformity coefficient of the verification points to obtain the predicted values. The simulated values ​​are compared with the predicted values, and the R 2 The error analysis of the Kriging surrogate model is shown in Table 6.

[0105]

[0106]

[0107] From Table 6, we can see that R 2 The Kriging surrogate model constructed in this embodiment is highly accurate. Figure 3 and Figure 4 .

[0108] Step 5: Use the MOGA algorithm to perform multi-objective optimization analysis on the Kriging proxy model to find the point with the best optimization index. The shape of the vertical shaft vortex flood discharge tunnel corresponding to its corresponding decision variable is the optimal shape.

[0109] The multi-objective optimization model is established as follows:

[0110] (4)

[0111] Where: It is determined by the response surface obtained by fitting the optimization index energy dissipation rate with the decision variables A, B, and C. It is determined by the response surface obtained by fitting the optimization index outflow velocity uniformity coefficient with the decision variables A, B, and C.

[0112] Determine the constraints of the multi-objective optimization model:

[0113] a. The contraction section height A is constrained, 12.5≤A≤20;

[0114] b. The ratio of the stilling well depth to the shaft section diameter is constrained by B, 1≤B≤1.45;

[0115] c. The ratio C of the slope pressure section length to the shaft section diameter is constrained to 2.5≤C≤4.3.

[0116] After the parameters of the above multi-objective optimization model are determined, the MOGA algorithm is used to set appropriate solution parameters, and finally the Pareto frontier of the multi-objective optimization model of the vertical shaft swirl flood discharge tunnel shape parameters is solved and drawn. Figure 5 .

[0117] After obtaining the Pareto frontier results, designers can use this result as a reference for design. By comparing and analyzing the results of various optimization target combinations, the optimal body shape with maximum energy dissipation rate and stable outflow flow pattern is obtained. Figure 6 . Figure 6 (a) is the original design of the project, and (b) is the optimal shape obtained after optimization using the method of the present invention. The height A of the contraction section of the optimal shape is 14.24m, the depth of the energy dissipation well is 13.3367m, the length of the slope section is 53.6955m, the corresponding energy dissipation rate is 81.88%, and the uniformity coefficient of the outflow velocity is 1.22%. The energy dissipation rate increased by 9.97%, and the uniformity coefficient of the outflow velocity decreased by 64.77%. Further research shows that under the optimal shape discharge condition, the water surface fluctuation in the lower flat section of the downstream retreat tunnel is significantly reduced, and the internal flow state is well adjusted.

[0118] It can be clearly seen from the above embodiments that the method of the present invention can quickly obtain the optimal body shape design scheme of the vertical shaft swirl flood discharge tunnel that simultaneously meets the energy dissipation rate and the outflow velocity uniformity coefficient, and can provide a reference basis for the vertical shaft swirl flood discharge tunnel construction project.

Claims

1. A method for optimizing the shape of a vertical shaft swirl flood discharge tunnel, characterized in that: The following steps are involved: S1. Determine several individual optimization parameters and several optimization indices of the vertical shaft vortex spillway tunnel; the body optimization parameters include the contraction section height A, the ratio B of the stilling well depth to the shaft section diameter, and the ratio C of the slope pressure section length to the shaft section diameter; the optimization indices include the energy dissipation rate S and the outflow velocity uniformity coefficient Z of the vertical shaft vortex spillway tunnel; S2, obtaining the value range of each body shape optimization parameter, and performing random sampling within the value range of each body shape optimization parameter to form multiple groups of body shape optimization parameter samples; S3. Based on multiple groups of body shape optimization parameter samples, a three-dimensional modeling software is used to perform parametric modeling of the vertical shaft vortex flood discharge tunnel, and a numerical simulation is performed on the constructed vertical shaft vortex flood discharge tunnel model to obtain the optimization index value corresponding to each group of body shape optimization parameter samples; S4, constructing a Kriging proxy model based on all body shape optimization parameter samples and optimization index values ​​in S3, and generating a response surface between the optimization index and body shape optimization parameters; S5. Establish a multi-objective optimization model according to the Kriging proxy model, and solve it to obtain the optimal solution of the body shape optimization parameters; The multi-objective optimization model is as follows: Where: Determined by the response surface between the optimization index energy dissipation rate and the decision variable X, Determined by the response surface between the optimization index outflow velocity uniformity coefficient and the decision variable X; the decision variable X=[A, B, C]; The constraints are: a. Contraction section height A constraint: A min ≤A≤A max ; A min and A max are the minimum and maximum values ​​of the height of the contraction section, respectively; b. The ratio of the depth of the stilling well to the diameter of the shaft section is constrained by B: min ≤B≤B max ; B min and B max are the minimum and maximum values ​​of the ratio of the stilling well depth to the shaft section diameter, respectively; c. The ratio of the length of the slope section to the diameter of the shaft section is constrained by C: min ≤C≤C max ; C min and C max are the minimum and maximum values ​​of the ratio of the length of the slope section to the diameter of the shaft section, respectively; S6. Constructing a vertical shaft swirl flood discharge tunnel according to the optimal solution of the body shape optimization parameters.

2. The method for optimizing the shape of a vertical shaft swirl flood discharge tunnel according to claim 1, characterized in that: In S2, random sampling is performed within the value range of each body shape optimization parameter, specifically: a plurality of groups of body shape optimization parameter samples are randomly selected within the value range of each body shape optimization parameter using an optimal space filling design method.

3. The method for optimizing the shape of a vertical shaft swirl flood discharge tunnel according to claim 1, characterized in that: In S3, the numerical simulation of the constructed vertical shaft swirl flood discharge tunnel model is specifically: The areas for numerical simulation of the vertical shaft vortex spillway model include: the inlet reservoir area, the air supply hole, the upper flat section of the water diversion channel, the vortex chamber section, the ventilation well, the contraction section, the vertical shaft section, the energy dissipation well, the pressure slope section and the lower flat section of the water withdrawal tunnel.

4. The method for optimizing the shape of a vertical shaft swirl flood discharge tunnel according to claim 1, characterized in that: In S4, after the Kriging proxy model is constructed, the accuracy of the Kriging proxy model is evaluated. If the evaluation result shows that the Kriging proxy model meets the accuracy requirements, S5 is performed; otherwise, return to S2 for re-sampling, and repeat steps S3 and S4 until the Kriging proxy model meets the accuracy requirements.

5. The method for optimizing the shape of a vertical shaft swirl flood discharge tunnel according to claim 4, characterized in that: The precision evaluation of the Kriging proxy model is specifically as follows: within the value range of each body shape optimization parameter, several groups of verification points other than the body shape optimization parameter samples are selected, and numerical simulation is performed to calculate the optimization index value corresponding to each group of verification points to obtain a simulation value; the Kriging proxy model is used to predict the optimization index value corresponding to each group of verification points to obtain a prediction value; error analysis is performed on the simulation value and the prediction value. If R 2 If it is greater than 0.9, the Kriging proxy model meets the accuracy requirements.

6. The method for optimizing the shape of a vertical shaft swirl flood discharge tunnel according to claim 1, characterized in that: A multi-objective genetic algorithm is used to solve the multi-objective optimization model.

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