Unified optimization method for stilling well-turning section body type of flood discharge vertical well

Abstract

The invention discloses a flood discharge vertical shaft stilling well-turning section body type unified optimization method. The method comprises the steps that multi-working-condition physical constraints describing body type parameters of a flood discharge vertical shaft, a stilling well and a turning section are obtained, and a combined feasible region is constructed; obtaining a typical flood working condition set; an active sampling strategy is adopted, body type sample data are obtained through iteration aiming at the typical flood working condition set in the joint feasible region, and a flow regime partition model and a hydraulic index agent model are constructed through iteration; according to the active sampling strategy, multi-working-condition uncertainty and flow regime partition boundary information are fused; in the joint feasible region, the flow regime partition model and the hydraulic index agent model are applied, a robust optimization model considering the cross-working-condition flow regime stability is constructed and solved, and a unified optimization body type scheme is obtained. According to the method, by introducing the flow state middle layer and combining the sampling strategy of flow state boundary driving, the capturing capacity and optimization efficiency of nonlinear flow state sudden change are improved.

Description

Technical Field

[0001] This invention belongs to the field of hydraulic structure design and data-driven optimization, and in particular, it is a method for unified optimization of the shape of flood discharge shaft stilling well-turning section. Background Technology

[0002] A spillway shaft is a typical high-head water discharge structure and a core component of high-dam, large-reservoir hydropower projects. The stilling well and bend at the bottom of the shaft are crucial for energy dissipation and the transition from vertical to horizontal flow patterns. The flow here is characterized by strong turbulence, shearing, and mixing, with significant air incorporation accompanied by spiral vortices and violent swirling. The flow structure is far more complex than in other areas, and its extreme three-dimensionality can cause erosion and impact. The design of this section directly affects the smooth dissipation of massive water flow energy during flood discharge, the structural safety against cavitation and vibration, and the protection against scouring in downstream river channels. While the stilling well and bend are spatially connected, and due to the continuous medium nature of water, they share overall geometric and hydraulic uniformity, numerous past engineering cases and experiments have shown a seesaw effect between energy dissipation requirements and engineering economics. In summary, it is necessary to design the stilling well and turning section as a whole system, and to perform refined shape optimization on this complex three-dimensional hydraulic system to ensure its safe, stable, and efficient operation under multiple typical flood conditions throughout its entire life cycle. This approach balances the fluid-structure interaction within the structure, achieving a synergistic effect greater than the sum of its parts in terms of energy dissipation and flow rectification, effectively improving the overall safety margin and engineering economy. This method has significant engineering implications and is urgently needed in practice.

[0003] Currently, in the design of stilling well-turning sections of spillway shafts, three-dimensional computational fluid dynamics (CFD) numerical simulation has become the mainstream analytical method. Researchers typically rely on CFD combined with physical model experiments to evaluate the hydraulic characteristics of a limited number of pre-set design schemes. Building on this, some studies have begun to explore combining surrogate models with multi-objective optimization algorithms. These methods usually employ radial basis function (RBF) or Kriging models to fit the functional relationship between the geometric parameters of the shaft and several key hydraulic indicators (such as energy dissipation rate, bottom impact pressure, and outflow uniformity), and then perform optimization solutions to obtain relatively optimal shaft parameters.

[0004] However, existing surrogate model-based optimization methods still suffer from technical bottlenecks when dealing with such complex, high-dimensional nonlinear hydraulic problems, including insufficient characterization of the physical mechanisms of high-speed water flow and a lack of understanding of key regions. Existing methods generally construct a single-layer black-box mapping between volume and hydraulic indices, ignoring the fundamental cause of nonlinear abrupt changes in hydraulic indices—namely, the transitions in flow morphology (flow regime) under changes in water level and flow rate. For example, a small adjustment in volume or change in operating conditions can cause a sudden transition from a stable annular hydraulic jump to an unstable vortex flow within a stilling well. This qualitative change in flow regime cannot be adequately characterized by a single, continuous energy dissipation rate or pressure index, resulting in severely insufficient accuracy of surrogate models near the boundaries of flow regime transitions. Furthermore, due to the lack of understanding of flow regime boundaries, existing active sampling strategies (such as sampling based on prediction variance) are also blind, failing to actively identify and densely sample these flow regime transition regions crucial to optimization results and structural safety. This leads to valuable computational resources being wasted on smooth regions with low information content, while critical nonlinear boundaries cannot be accurately captured by the model due to sparse samples. Summary of the Invention

[0005] The purpose of this invention is to provide a method for optimizing the shape of the stilling well-turning section of a flood discharge shaft, so as to solve the above-mentioned problems existing in the prior art.

[0006] Technical solution: A method for unified optimization of the shape of flood discharge shaft stilling well-turning section, including:

[0007] Obtain multi-condition physical constraints describing the shape parameters of the flood discharge shaft, stilling well, and turning section, and construct a joint feasible domain; at the same time, obtain a set of typical flood conditions;

[0008] An active sampling strategy is adopted to iteratively obtain volume sample data for a set of typical flood conditions within the joint feasible domain; based on this, a flow regime partitioning model and a hydraulic index proxy model are iteratively constructed; the active sampling strategy integrates multi-condition uncertainty and flow regime partitioning boundary information.

[0009] Within the joint feasible domain, a robust optimization model considering cross-condition flow stability is constructed and solved by applying the flow regime partitioning model and the hydraulic index proxy model, resulting in a unified optimized body shape scheme.

[0010] Beneficial effects: By introducing a flow intermediate layer into the flood discharge shaft stilling well-turning section coupling system and combining it with a flow boundary-driven sampling strategy, this invention improves the ability to capture nonlinear flow changes and optimize efficiency. Attached Figure Description

[0011] Figure 1 A flowchart illustrating the steps of a method for uniformly optimizing the shape of a flood discharge shaft stilling well-turning section, as provided in this application embodiment.

[0012] Figure 2 A flowchart illustrating the steps for constructing a flow partitioning model as provided in this application embodiment.

[0013] Figure 3 A flowchart illustrating the steps for obtaining a unified optimized body shape scheme as provided in the embodiments of this application.

[0014] Figure 4 A flowchart illustrating the steps for constructing a cross-condition flow stability evaluation function, as provided in this application embodiment.

[0015] Figure 5 This is a schematic diagram of a first modified scheme for the flood discharge shaft stilling well-turning section structure provided in the embodiments of this application.

[0016] Figure 6 This is a schematic diagram of a second modified scheme for the flood discharge shaft stilling well-turning section structure provided in the embodiments of this application.

[0017] The attached diagram is labeled as follows: 1. Vertical shaft spillway; 2. Center of vertical shaft; 3. Ventilation hole; 4. Upper edge elliptical curve; 5. Slope section outlet; 6. End of slope section; 7. Lower edge elliptical curve; 8. Stilling well section. Detailed Implementation

[0018] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0019] It should be noted that the terms include and have, and any variations thereof, are intended to cover non-exclusive inclusion. 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 that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product, or device.

[0020] The study also found that existing methods, without considering differences in flow rate or operating conditions, simply feed the body shape parameters of different samples into the model for training and iteration, obtaining a relatively optimal solution from a mathematical perspective. This ignores the engineering and hydrological background of these engineering samples, as well as hydraulic conditions such as flow rate and flow regime. The results obtained may not match the actual flood scenarios of the engineering projects, meaning the adaptability is unknown. It is also possible that the body shape may be numerically optimal, but it is only applicable to a certain extreme condition and does not match real common floods, resulting in unreasonable applicability of the body shape.

[0021] like Figure 1 As shown, a method for unified optimization of the shape of the stilling well and turning section of the flood discharge shaft is proposed, including the following steps:

[0022] Obtain multi-condition physical constraints describing the shape parameters of the flood discharge shaft, stilling well, and turning section, and construct a joint feasible domain; at the same time, obtain a set of typical flood conditions.

[0023] In this embodiment, shape parameters refer to key dimensionless parameters used to describe the geometry of the spillway shaft, stilling basin, and turning section, such as the relative diameter-to-depth ratio and relative length ratio of the stilling basin, and the curvature coefficient (turning angle) of the turning section. Multi-condition physical constraints refer to the fundamental physical restrictions that the structure must satisfy under different flood flows, such as constraints derived from energy equations, momentum equations, cavitation safety conditions, or inundation limitations. The typical flood condition set refers to several representative flood scenarios selected from the design flood process, such as 100-year flood and 1000-year flood check conditions. Each condition corresponds to a set of hydraulic input parameters, such as inflow rate and downstream water level. Specifically, for each typical flood condition, single-condition physical constraint inequalities regarding shape parameters are derived based on physical principles. By performing a mathematical intersection operation on the set of inequalities for all conditions, a parameter subspace that simultaneously satisfies the requirements of all conditions is obtained, i.e., the joint feasible region, denoted as Ω. joint The joint feasible region constitutes a hard boundary for subsequent optimization, making any candidate size physically feasible.

[0024] In some alternative implementations, the determination of the typical flood case set can also be based on flood frequency and severity, assigning different weights to each representative case, and this weight information can be used for subsequent robust optimization.

[0025] An active sampling strategy is adopted to iteratively obtain volume sample data for a set of typical flood conditions within the joint feasible domain. Based on the volume sample data, a flow regime zoning model and a hydraulic index proxy model are iteratively constructed. The active sampling strategy integrates the uncertainty of multiple conditions and the boundary information of flow regime zoning to obtain a converged flow regime zoning model and a hydraulic index proxy model.

[0026] In this embodiment, the flow regime partitioning model differs from traditional hydraulic indices, such as the dimensionless number Fr (Froude number) which broadly distinguishes between rapid and slow flow, and Re (Reynolds number) which broadly distinguishes between laminar and turbulent flow. Instead, it divides continuous flow field characteristics, such as vortices, negative pressure zones, backflow zones, hydraulic jumps, water drops, and alternating open and full flows, into discrete flow regime categories with clear engineering significance, such as stable, metastable, or unstable flow regimes, through clustering and other methods. The hydraulic index surrogate model is a mathematical model used to predict specific performance indicators, including energy dissipation rate, impact pressure, and turbulence intensity. The body shape sample data includes body shape parameters, operating conditions, corresponding flow regime categories, and hydraulic indices. This embodiment abandons the traditional single-layer body shape-index surrogate model and instead constructs a three-layer mapping architecture of body shape-flow regime-index. Specifically, the flow regime partitioning model maps body shape parameters and operating conditions to flow regime categories, i.e., R = f(X, C); while the hydraulic index surrogate model uses body shape parameters, operating conditions, and the flow regime category R determined by the flow regime partitioning model as inputs to predict the hydraulic index I = g(X, C, R). The flow regime category R, ​​as an intermediate physical layer, can more accurately reflect nonlinear abrupt changes in flow, thereby improving the prediction accuracy of the hydraulic index surrogate model g. To efficiently construct the above models, an active sampling strategy is used to guide the addition of new numerical calculation samples, avoiding wasting computational resources in regions with low information content. For example, the active sampling strategy evaluates the value of candidate body shape x through a fused sampling value function V(x). V(x) integrates information from multiple dimensions, especially multi-operating condition uncertainties and flow regime partitioning boundary information, i.e., regions where the hydraulic index surrogate model g cannot predict accurately and regions where the flow regime partitioning model f has difficulty distinguishing flow regimes, i.e., flow regime abrupt change regions. The iterative process is as follows: initial models f and g are obtained based on a small amount of initial body shape sample data. Using V(x), the highest-value body shape point is selected within the joint feasible region, and high-precision numerical calculations are performed on it to obtain new body shape sample data. This new data is then incorporated into the dataset, and the flow regime partitioning model f and the hydraulic index surrogate model g are retrained. This process is repeated until the model accuracy reaches the preset convergence criterion, ultimately yielding a converged flow regime partitioning model and a converged hydraulic index surrogate model.

[0027] Within the joint feasible domain, a robust optimization model considering cross-condition flow stability is constructed and solved by applying the flow regime partitioning model and the hydraulic index proxy model, resulting in a unified optimized body shape scheme.

[0028] In this embodiment, the robust optimization model refers to an optimization model that not only pursues optimal average performance but also seeks stable and safe performance under all operating conditions, especially the most unfavorable conditions. A convergent flow regime partitioning model f and a hydraulic index surrogate model g are used as rapid evaluation tools, replacing time-consuming high-precision calculations. Simultaneously, cross-condition flow regime stability is taken as the core constraint or objective of optimization. Specifically, using the convergent flow regime partitioning model f, any body shape X can be evaluated under all typical operating conditions c. j Can all of these remain in a stable flow state? For example, a constraint S(X) ≥ S can be constructed. min Where S(X) is the flow stability index calculated based on the classification confidence score predicted by model f. The optimization solution process is as follows: in the joint feasible region Ω joint Internally, using the body shape parameter X as the decision variable, the multi-condition weighted fitness and worst-case performance predicted by the hydraulic index model g are used as optimization objectives, and the cross-condition flow stability predicted by the flow regime partitioning model f is used as a constraint. A multi-objective optimization algorithm is employed to solve the problem. The final result is one or more body shape parameter combinations that exhibit excellent performance and flow regime stability, i.e., a unified optimized body shape scheme. This scheme can be further supplemented with high-fidelity verification and engineering validation, and the specific structural geometric dimensions can be calculated as the final output.

[0029] In a specific embodiment, several structural parameters of the stilling well and the turning section are defined as subsequent optimization objects. Design parameters that significantly affect the energy dissipation, rectification, and flow regime transition effects of the stilling well and the turning section are selected as optimization parameters. Specifically, the stilling well is a caisson-shaped energy dissipation structure protruding downwards from the bottom plate of a vertical shaft, including the upstream wall, downstream wall, side walls, and bottom plate. Before optimization, the cross-section of the stilling well is the same as the upper vertical shaft, a circle with equal diameter. The main structural parameters include: the stilling well depth h, generally taken as 1.5D ~ 2.5D, where D is the diameter of the circular cross-section of the flood discharge vertical shaft (the vertical shaft parameters are known engineering data), and the stilling well depth is calculated from the top of the lower wall of the turning section to the bottom plate of the stilling well. Furthermore, to facilitate comparison of different structural types and parameter generalization, the dimensionless ratio of the stilling well depth to the vertical shaft diameter (depth-to-diameter ratio d = h / D) is used to characterize the required stilling well depth, where d is between 1.5 and 3. The upstream width d1 of the stilling basin cross-section is determined by the fact that during flood discharge, the incoming flow recedes downstream through the stilling basin and turning section, resulting in relatively low water pressure on the upstream wall. Considering energy dissipation requirements and excavation volume, the upstream shape of the stilling basin can be consistent with the upper vertical shaft section, i.e., a semicircle with a radius equal to the vertical shaft radius R', where d1 = R'. The downstream width d2 of the stilling basin cross-section can be defined in three ways based on the relationship between d2 and the vertical shaft diameter D: the section modulus of the stilling basin bottom plate is defined as S = d2 / D. When d2 = D (S = 1), it is defined as a gate-shaped section; when d2 > D (S > 1), it is defined as a tunnel-shaped section; and when d2 < D (S < 1), it is defined as a horseshoe-shaped section. The downstream length l of the stilling basin center is measured from the center of the vertical shaft to the downstream endpoint of the stilling basin; the total length of the stilling basin = R' + l. Therefore, the dimensionless extension coefficient of the stilling well section, i.e., the downstream extension, is defined as: T = l / R', where T is generally between 1.2 and 2.0. It should be noted that, unless necessary, such as when hydraulic parameters like wall pressure are within a reasonable range, expanding the stilling well upstream to increase the water volume will not be considered; if water volume expansion is required, the stilling well is usually expanded downstream to increase the water volume.

[0030] The turning section includes the connecting curves of the upper and lower walls, and the slope section. Upstream, it connects to the vertical shaft and the lower stilling well; downstream, it connects to the drainage tunnel. Key structural parameters include: the horizontal radius a1, vertical radius b1, and turning angle α1 of the upper wall of the turning section. It should be noted that the starting point of the upper wall of the turning section is the bottom endpoint of the vertical shaft section, and the ending point is the end point of the top plate of the slope section. Similarly, the horizontal radius a2, vertical radius b2, and turning angle α2 of the lower wall of the turning section should be noted. Again, the starting point of the lower wall of the turning section is the top endpoint of the stilling well, and the ending point is the end point of the bottom plate of the slope section. Slope section: The length of the top plate of the slope section is L1, the slope ratio is i, and the length of the bottom plate is L2, which is the same as the horizontal projection length of the top plate. Further, the turning ratio R* of the upper and lower walls of the turning section is defined as: R* = vertical radius (b) / horizontal radius (a). The closer this ratio is to 1, the closer the turning section curve is to a quarter circle. The greater the ratio deviates from 1, whether greater or less, the closer the arc is to a quarter-ellipse; the further the ratio is from 1, the flatter the ellipse is horizontally or the more slender it is vertically. When R* = 1, the turning segment is a quarter of a perfect circle, with the vertical radius equal to the horizontal radius; when R* < 1, the turning segment is a flat elliptical arc, with the vertical radius smaller than the horizontal radius; when R* > 1, the turning segment is a slender elliptical arc, with the vertical radius larger than the horizontal radius. Preferably, the turning angle α is 90°, meaning the starting and ending points of the turning segment are tangent to the vertical shaft wall and the horizontal slope or bottom plate, respectively.

[0031] In one possible embodiment, constructing a joint feasible domain includes:

[0032] For each case in the typical flood case set, we derive the single-case physical constraint inequalities related to the shape parameters.

[0033] In other words, the shape parameter X is defined as a dimensionless geometric parameter vector; for the typical flood condition set C={c1, ..., c m Each working condition c in} j The single-condition physical constraint inequalities describing the physical constraints of this working condition are derived. The set of single-condition physical constraint inequalities defines the single-condition physical feasible region Ω corresponding to this working condition. j .

[0034] In a preferred implementation, the single-condition physical constraint inequality is derived based on at least two of the energy equation, momentum equation, cavitation safety condition, and flooding constraint.

[0035] In other words, deriving the physical constraint inequalities for a single operating condition includes: establishing the shape parameter X under operating condition c based on the energy equation, momentum equation, or cavitation safety condition. jThe hydraulic response calculation function is used; the standard control parameters, including the allowable cavitation index and the allowable maximum impact pressure, are read; by comparing the hydraulic response calculation function with the standard control parameters, a single-condition physical constraint inequality is established, which includes at least: σ(X, c j )≥σ allowed ;P(X,c j )≤P max ;where σ(X, c j ) is based on X and c j The calculated cavitation number, σ allowed To standardize the allowable cavitation index in the control parameters; P(X, c j ) is based on X and c j The calculated impact pressure, P max To standardize the maximum allowable impact pressure in the control parameters.

[0036] In this embodiment, it is necessary to organize the basic engineering data and standard control parameters. The basic engineering data includes topographic data of the dam site and downstream river channel, the initial layout of the spillway shafts, and structural reference dimensions; among which, the structural reference dimensions include the shaft diameter D. Standard control parameters define the design red lines, i.e., the boundary values ​​allowed by design specifications or engineering requirements, such as the maximum impact pressure P allowed by the specifications. max Or the allowable cavitation number σ required by engineering specifications. allowed The typical flood case set C = {c1, ..., c2} m} represents scenarios selected from design flood process data. For example, c1 could be a 100-year design scenario, and c2 could be a 1000-year check scenario. Each scenario c j This corresponds to a specific set of hydraulic parameters, such as the inflow rate Q under this operating condition. j and downstream control water level Z j The body size parameters are defined as a dimensionless geometric parameter vector X = [x1, x2, ..., x...]. n The term x1 is used to uniformly describe the shape of the energy dissipation well and the turning section. For example, x1 can be the depth-to-diameter ratio of the energy dissipation well, x2 can be the curvature coefficient of the turning section, and x3 can be the relative length of the bottom of the well.

[0037] The derivation process is for each working condition c. j This embodiment establishes a functional relationship between fundamental hydraulic principles and the parameter vector X. It abandons the traditional experience-based design approach and instead uses physical equations to define feasibility. For example, regarding cavitation safety conditions, a calculation function σ can be established based on the energy equation. calc (X, c) j ), used to calculate the size X and working condition c j The actual cavitation number under the given condition. This constraint is then expressed as σ.calc (X, c) j )≥σ allowed For example, regarding the impact pressure limitation, a calculation function P can be established based on the momentum equation. calc (X, c) j This constraint is used to calculate the maximum impact pressure on the base plate. It is represented by P. calc (X, c) j )≤P max Similarly, for the flooding constraint, a function H can be established. calc (X, c) j )≥H min This is to prevent unwanted flow patterns from occurring during the turning section. Summarizing all the above inequalities forms the operating condition c. j The set of single-condition physical constraint inequalities, which defines the single-condition physical feasible region Ω in the n-dimensional parameter space. j .

[0038] In some alternative implementations, the above calculation function σ calc and P calc It can be obtained through simplified hydraulic formulas, or it can be quickly evaluated through high-precision three-dimensional numerical simulation (CFD) or a trained surrogate model.

[0039] Perform intersection operations on the single-condition physical constraint inequalities for all operating conditions to form a joint feasible region.

[0040] In other words, the joint feasible region Ω is determined by performing an intersection operation on all single-case physical feasible regions. joint =∩ j=1 m Ω j Where j is the operating condition index, m is the total number of typical flood operating conditions, and Ω j Let Ω be the single-condition physical feasible region corresponding to the j-th working condition. joint A joint feasible region that satisfies all operating condition constraints.

[0041] In this embodiment, multiple single-condition physical feasible domains Ω are considered. j Perform a mathematical intersection operation on (j=1, 2, ..., m). The resulting joint feasible region Ω joint It is a subset in the shape parameter space X that simultaneously satisfies the physical constraints of all m typical flood conditions. Its mathematical expression can be written as: Ω joint =∩ j=1 m Ω jThis ensures that any subsequent sampling or optimization within this feasible region has physically safe and feasible candidate sizes. It reduces the search space and improves the efficiency and reliability of subsequent data-driven optimization. In some embodiments, if conflicts exist between constraints of different operating conditions leading to Ω... joint For an empty set, a feedback step may also be included, namely, adjusting the specification control parameters or engineering basic data, and re-executing this embodiment until a non-empty joint feasible region is obtained.

[0042] In an optional embodiment, before iteratively acquiring body size sample data, an initial multi-condition flow regime and hydraulic index dataset is constructed, specifically as follows:

[0043] Generate an initial set of body shape parameter samples within the joint feasible region.

[0044] In this embodiment, in a high-dimensional (n-dimensional) and possibly irregularly shaped joint feasible region Ω joint Internally, a set of sample points with good space-filling and representativeness is selected. Preferably, the Latin hypercube sampling (LHS) method can be used, ensuring that the projection is uniformly distributed in each dimension of the body size parameter X, resulting in high sampling efficiency. Alternatively, in other embodiments, methods such as uniform design, orthogonal experimental design, or low-discrepancy sequence sampling based on Hammersley sequences can also be used. It should be noted that, due to the joint feasible region Ω... joint It is defined by the intersection of inequalities and may have a complex form. Therefore, the sampling process can be combined with constraint handling techniques, for example, in the case of a joint feasible region Ω. joint Sampling is performed within the hyperrectangle, and sample points that do not satisfy all constraints are removed, i.e., points not within the joint feasible region Ω are removed. joint Sample points within the range. Output the initial body shape parameter sample set {X1, X2, ..., X...} N}, where N is the number of initial samples, for example, N=50 or 100.

[0045] High-precision three-dimensional numerical calculations are performed on an initial set of body shape parameters under typical flood conditions.

[0046] Specifically, the input sample set {X} i} and working condition set {c j}, perform the full combination calculation process, that is, for each body shape parameter X i In each typical operating condition c j Under these conditions, high-precision three-dimensional numerical calculations are performed. Preferably, this high-precision calculation employs computational fluid dynamics (CFD) simulation. For example, a k-ε turbulence model based on the Reynolds-averaged flow (RANS) method is used, combined with the VOF (volume of fluid) method to capture the free surface morphology. The boundary conditions of the computational model are determined according to the operating condition c.j Settings, for example, the ingress is set to traffic Q. j The outlet is set to water level Z. j Output N×m high-fidelity raw flow field datasets, where N is the number of samples and m is the number of operating conditions; each dataset contains detailed velocity field, pressure field, and free surface position field data.

[0047] Extract raw data of flow patterns and hydraulic indices under multiple operating conditions to construct an initial dataset of flow patterns and hydraulic indices under multiple operating conditions.

[0048] In this embodiment, N×m raw flow field datasets are input. The unstructured flow field data is transformed into structured features and labels that can be used for subsequent machine learning. Specifically, the raw hydraulic index data are calculated, which serve as the training labels for the subsequent hydraulic index surrogate model g(). For example, for each flow field, its total energy dissipation rate η and maximum impact pressure P on the bottom plate are calculated. max_calc The outflow velocity non-uniformity coefficient, etc., are used to extract the original flow data under multiple operating conditions, which are the training features for the subsequent flow zoning model f(). This process includes calculating vortex intensity, negative pressure zone volume, recirculation zone geometric boundary, hydraulic jump morphology parameters, water drop location, and whether open full flow occurs. The volume parameter X is then used to... i Operating condition c j The corresponding raw flow data and raw hydraulic index data are correlated and organized to form an initial multi-condition flow data and hydraulic index dataset.

[0049] In an exemplary embodiment, the iterative construction of the flow regime partitioning model and the hydraulic index proxy model includes:

[0050] Construct a flow regime partitioning model R=f(X, C) to map body shape parameters and working conditions to discrete flow regime categories; where X represents the input body shape parameters; C represents the working conditions; f() represents the flow regime partitioning model; and R is the discrete flow regime category.

[0051] like Figure 2 As shown, in a preferred implementation, the flow partitioning model is constructed, including:

[0052] Flow pattern features that characterize the flow morphology are extracted from the multi-condition flow field data contained in the body sample data to form a flow pattern feature dataset.

[0053] In this embodiment, physical features capable of quantitatively describing the flow pattern, i.e., flow regime features, are extracted from N×m high-fidelity flow field raw data sets as the basis for subsequent flow regime partitioning. The high-fidelity flow field raw data includes velocity fields, pressure fields, and free surface position fields. Preferably, the flow regime features include, but are not limited to, the following: First, negative pressure region features, used to characterize the cavitation risk and potential instability of the flow. Specifically, a pressure threshold can be set, such as the absolute pressure P.threshold = 10000 Pa, traversing all grid cells in the computational domain, the statistical stress is lower than P. threshold Total unit volume V neg V neg The first characteristic is the flow regime. The second characteristic is the vortex intensity, used to characterize the vortex intensity within a vertical shaft or the vortex structure within a stilling well. Specifically, the spatial average or maximum value of the vorticity ω can be calculated at key sections of the vertical shaft or stilling well, or the statistical measure of streamline curvature can be calculated as the vortex intensity characteristic. The third characteristic is the annular hydraulic jump morphology, used to characterize the energy dissipation morphology within the stilling well. Preferably, using the VOF method to determine the free water surface position Y(x) with α=0.5, the starting and ending points of the hydraulic jump are automatically located by analyzing the gradient ΨY / Ψx or curvature of the water surface line Y(x), thereby calculating the relative length L of the hydraulic jump. jump Or relative thickness H jump As a flow regime characteristic, Ψ is the partial derivative, and x is the horizontal coordinate along the mainstream direction. Fourth, the impact point drift characteristic is used to characterize the stability of the mainstream impact point. Specifically, the spatial coordinates (x, z) of the point of maximum pressure (impact point) are located on the bottom plate of the stilling well, and its spatial standard deviation (drift range) over time is statistically analyzed as a characterization feature of flow regime stability. The multiple flow regime characteristics (V) calculated above are then used to characterize the stability of the flow regime. neg ,max(|ω|),L jump The spatial standard deviation is combined to form an n-dimensional flow eigenvector V. f For each body type-working condition combination (X) i c j All of these operations are performed on V. f The various dimensions are normalized to form the final flow feature dataset.

[0054] Cluster analysis is performed on the flow characteristic dataset to define flow categories and generate flow category labels for body size samples. The flow zoning model is trained by taking the body size parameters and working conditions in the body size sample data as inputs and the flow category labels as outputs.

[0055] In this embodiment, using a flow regime feature dataset, unsupervised learning is employed to automatically classify the flow regime into several categories with clear engineering significance, and a supervised classification model f is trained based on these categories. Specifically, unsupervised clustering analysis is performed. Preferably, the K-means clustering algorithm is used. The input to the clustering algorithm is the normalized flow regime feature vector V of all samples. fThe distance metric preferably uses Euclidean distance. Preferably, the Elbow Method or Silhouette Score can be used to evaluate the clustering effect at different values ​​of the number of clusters K. For example, when K=3, the Silhouette Score is the highest, thus classifying the flow regime into 3 categories. The clustering results undergo engineering review and naming. Those skilled in the art can analyze the K=3 clusters based on the visualization results of the flow field and name them as flow regime category labels R with engineering significance. For example: R1 = stable flow regime, corresponding to low V neg Stable L jump R2 = metastable flow state, R3 = unstable flow state, corresponding to high V neg Or, the hydraulic jump morphology may break. A flow regime partitioning model f is trained; this is a supervised classification task. The model's input is the body shape parameter X and the working condition C, and its output is the flow regime category label R. Preferably, a Support Vector Machine (SVM), Random Forest, or Deep Neural Network can be used as the classifier. After training, the flow regime partitioning model R = f(X, C) is obtained. This model f can predict the flow regime category R for any unknown body shape-working condition combination. In some preferred embodiments, the flow regime partitioning model f not only outputs the predicted category R... k It also outputs the classification confidence p of the prediction, i.e., p(R = R). k | X, C).

[0056] A hydraulic index proxy model I=g(X, C, R) is constructed to map the body shape parameters, operating conditions, and flow regime categories determined by the flow regime partitioning model into hydraulic indices; where g() is the hydraulic index proxy model; and I is the hydraulic index.

[0057] In this embodiment, a surrogate model g is constructed to predict hydraulic index I; where hydraulic index I includes energy dissipation rate η and impact pressure P. The input to model g is not only the body shape parameter X and the operating condition C, but also the flow regime category R as an independent input feature. In other words, the mathematical form of this model is: I = g(X, C, R). Since the physical laws governing the response of hydraulic index I differ under different flow regimes R, i.e., the function g has different functional forms under different R, the traditional single-layer model I = g(X, C) attempts to fit this highly nonlinear and abrupt physical process with a continuous function, thus limiting its accuracy. This embodiment introduces an intermediate layer R, decomposing the complex fitting task into first classifying f and then piecewise regressing g, which is physically more reasonable and has higher prediction accuracy. Specifically, the surrogate model g preferably uses a multi-output Gaussian process regression (GPR) or radial basis function (RBF) network. Its training dataset input is (X, C) i c j R i The output is (I1, I2, ..., I).m ), where R i This is the sample (X) i c j ) Determined flow state category label, I m Let m represent the m-th hydraulic index. Ultimately, two models are obtained: the flow regime partitioning model R = f(X, C) and the hydraulic index surrogate model I = g(X, C, R).

[0058] In an exemplary embodiment, hydraulic evaluation indicators, i.e., hydraulic indices, are defined for stilling wells and bend sections. Specifically, the following five main evaluation indicators are defined to evaluate the rationality of the shape of stilling wells and bend sections from the perspectives of energy dissipation effect, rectification effect, and drainage effect, including: the overall energy dissipation rate of the stilling well and bend section η = (E1-E2) / E1; where E1 is the total head of the reservoir area in meters; E2 is the total head of the outlet section of the bend section in meters; the energy dissipation rate is preferably at least greater than 35%, which is considered to be basically reasonable; greater than 50% is preferable. The maximum impact pressure P of the stilling well bottom plate: P = (F max -F min ) / F avg ;where F max F min F avg These represent the maximum, minimum, and average hydrostatic pressure on the bottom plate, respectively. Preferably, the impact pressure on the bottom plate should be less than 10m pressure head. The coefficient of non-uniformity of pulsating pressure distribution δ on the walls of the stilling well and turning section should preferably be less than 0.5 to prevent stress concentration along the path. The calculation formula is: μ Cp =1 / n ∑ i=1 n C pi ;σ Cp =sqrt(1 / n ∑ i=1 n (C pi -μ Cp ) 2 ); δ=σ Cp / μ Cp Where n represents the total number of measuring points; C pi The root mean square value of the pulsating pressure at each measuring point is expressed in units of ×9.81 kPa; μ Cp The average pulsating pressure represents the average level of pulsation intensity across the entire wall surface; σ Cp This reflects the degree of dispersion between the pulsation intensity value at each measuring point and the average level. σ CpThe larger the value, the greater the difference in pulsation intensity at each point, and the more uneven the distribution. The non-uniformity coefficient δ is the ratio of the standard deviation to the mean; a dimensionless number can more accurately reflect the relative dispersion of the data. The relative height Hr of the annular hydraulic jump in the shaft needs to be sufficient to raise the inlet water level into the shaft through the stilling well and the turning section, maintaining a certain submerged water depth. This means the water level needs to be able to rise above the turning section without affecting the discharge capacity or the shaft's discharge capacity. Preferably, the water level should exceed the top of the upper wall of the turning section without affecting the discharge flow rate of the upper funnel section of the shaft. The value range of the annular hydraulic jump height Hc is generally greater than twice the stilling well depth h and less than the difference between the height of the shaft's circular pipe section and the stilling well depth. The calculation formula is: 2h < Hc < H / 2; where H is the total drop of the shaft, in meters, from the shaft inlet to the bottom plate of the stilling well; and h is the stilling well depth, in meters. Preferably, H > 7h~9h, and Hr = Hc / h, then the range of the relative height of the annular hydraulic jump is: 2 < Hr < 3.5. The outflow non-uniformity coefficient U at the end of the bend: the maximum flow velocity V at the outlet section at the end of the bend. max With average flow velocity V avg The ratio of the velocity distribution to the velocity distribution at the cross-section can characterize the uniformity of the flow, revealing whether the flow pattern is uniform and stable, and whether unfavorable phenomena such as water fins are prone to occur. Preferably, the velocity distribution at the inlet of the drainage tunnel should meet the following requirement: the velocity non-uniformity coefficient does not exceed 2.

[0059] According to one aspect of this application, since initial sampling is blind and high-precision 3D numerical computation resources are extremely valuable, it is necessary to concentrate limited computational resources on the parameter regions most valuable for model convergence. Specifically, an active sampling strategy is adopted to iteratively obtain body shape sample data, including:

[0060] Generate candidate body shape parameter points that have not yet been calculated within the joint feasible region.

[0061] Specifically, in the joint feasible region Ω joint Within this process, a dense set of candidate body shape parameter points {x} is generated, which is much larger than the initial sample size; for example, the number of candidate points N. candidate = 10000. Using the currently converged f and g models, these 10000 candidate points x are analyzed across all m typical operating conditions c. j The following prediction is performed. For each (x, c) j Combining these methods, we obtain the predicted flow regime category R. j = f(x, c) j ) and its classification confidence level p j = p(R = R j | x, c j Predicted hydraulic parameters I j = g(x, c)j R j ).

[0062] An active sampling value function is constructed to evaluate candidate body shape parameter points.

[0063] In other words, an active sampling value function is constructed to evaluate the candidate body shape parameter points.

[0064] In a preferred implementation, an active sampling value function is constructed, including:

[0065] The prediction uncertainty of the multi-condition comprehensive fitness of candidate body shape parameter points is evaluated using a hydraulic index surrogate model; the distance of candidate body shape parameter points to the flow regime boundary is evaluated using a flow regime zoning model; and the prediction consistency of candidate body shape parameter points across flow regime categories in a typical flood condition set is evaluated using a flow regime zoning model.

[0066] By integrating the multi-condition comprehensive fitness prediction uncertainty, the distance to the flow regime partition boundary, and the consistency with the cross-condition flow regime category prediction, the active sampling value function is determined as V(x) = w1·U(x) + w2·D(x) + w3·C(x); where V(x) is the active sampling value score of the candidate body shape parameter point x; U(x) is the multi-condition comprehensive fitness prediction uncertainty; D(x) is the flow regime partition boundary distance; C(x) is the cross-condition flow regime category prediction consistency; and w1, w2, and w3 are preset weight coefficients used to integrate the three dimensions.

[0067] Specifically, a comprehensive active sampling value score V(x) is calculated for each candidate body shape x. A higher V(x) indicates that performing CFD calculations at point x is more valuable for improving model accuracy. V(x) is preferably constructed as a weighted fusion of three sub-items: V(x) = w1·U(x) + w2·D(x) + w3·C(x); where w1, w2, and w3 are preset weight coefficients used to balance the preferences of different sampling strategies. The multi-condition integrated fitness prediction uncertainty U(x) is used to quantify the degree of uncertainty of the hydraulic index surrogate model g regarding its prediction results. If model g uses Gaussian process regression (GPR), U(x) can preferably be defined as the posterior variance var(I(x)) of the prediction by model g at point x, where I(x) is the predicted value of the hydraulic index at point x. If other models are used, U(x) can be estimated by calculating the standard deviation of the prediction results of multiple models using ensemble learning or bootstrap methods. The region with high U(x) represents the knowledge blind spot of model g.

[0068] The distance D(x) to the flow regime boundary quantifies the degree of uncertainty in the flow regime partitioning model f, i.e., the distance of candidate point x from the flow regime abrupt change boundary. Model f faces the greatest difficulty and is most prone to error in predictions near the partition boundaries, representing the region where the model most needs strengthening. In an exemplary embodiment, evaluating the flow regime boundary distance includes: using the flow regime partitioning model to predict the flow regime category and corresponding classification confidence of candidate body shape parameter points under each condition in a typical flood condition set; comparing the classification confidence with a preset flow regime boundary determination threshold to quantify the proximity of candidate body shape parameter points to the flow regime partition boundary; and using the proximity to the flow regime partition boundary as the flow regime boundary distance D(x) = max j∈{1，2，…，m} {D j (x)};D j (x)=1- max k {p(R k | x, c j )};where D(x) is the distance of the flow regime partition boundary for candidate body size x; D j (x) represents the candidate body shape x under a single working condition c. j The degree of proximity of the flow boundary; j is the working condition index; m is the total number of typical flood working conditions; p(R k | x, c j ) is x in c j The classification confidence score of a class belonging to category k; max k {} represents taking the maximum classification confidence among all flow state categories k; max k {p k} represents the classifier's confidence in its most likely prediction. 1 - max k {p k}, that is, D j (x) represents the uncertainty or entropy of the classifier. A high value of this value means that the classifier cannot clearly distinguish which class x belongs to, i.e., x is located near the boundary of the flow regime partition. max j {} represents taking the value closest to the flow boundary among all operating conditions. Preferably, D(x) is calculated based on the classification confidence level p. j For a single operating condition c j Its boundary distance D j (x) can be defined as: D j (x)=1- max k {p(R k | x, c j )}; where k iterates through all flow state categories. D j (x) means: if model f is highly certain, for example, p = 0.99, then D j =0.01, far from the boundary; if the model f is extremely perplexing, for example, p=0.5 between two classes, then Dj =0.5, located on the boundary. For multiple operating conditions, D(x) preferably takes the most unfavorable case among all operating conditions, i.e., D(x) = max j {D j (x)}.

[0069] Some flow types x may exhibit R1 (stable) under flow condition c1, but jump to R3 (instability) under flow condition c2. This inconsistency between flow types across different flow conditions is a key obstacle to robust optimization and a region that the model needs to focus on characterizing. The consistency of flow type predictions across different flow conditions, C(x), can be defined as a score, for example, the statistical analysis of the predicted R values ​​of flow type x under m flow conditions. j The total number of categories; the more categories, the higher the C(x) score.

[0070] Based on the evaluation results, new body type samples are selected, and body type sample data is obtained iteratively.

[0071] Alternatively, one could say that new body shape samples are selected based on the active sampling value function to iteratively obtain body shape sample data.

[0072] In this embodiment, 10,000 candidate points are sorted according to their V(x) scores, and the K body shape parameter points with the highest V(x) scores are selected as the newly added body shape samples for this round. For these K newly added body shape samples, high-precision three-dimensional numerical calculations are performed on them under all m working conditions, and flow regime features and hydraulic indices are extracted to form an incremental dataset. Further, the incremental dataset is merged into the initial multi-working-condition flow regime and hydraulic index dataset to form a larger and more information-rich updated dataset. Based on this, the steps including feature extraction, cluster analysis, and training of models f and g are repeated to obtain the updated flow regime partitioning model f. update Hydraulic index proxy model g update Perform a convergence check. For example, evaluate f on an independent validation set. update and g update The accuracy is determined by the threshold. If the improvement in accuracy compared to the previous iteration is less than a preset threshold (e.g., 1%), or if the total number of iterations reaches the upper limit, the model is considered to have converged. If it has not converged, then f... update and g update As the new current model, return to begin a new round of active sampling. If convergence has been achieved, the iterative process terminates. The final obtained f update and g update This refers to the convergent flow regime partitioning model and the convergent hydraulic index proxy model.

[0073] like Figure 3 As shown, in one embodiment of this application, a unified optimized body shape scheme is obtained, including:

[0074] Using a hydraulic index proxy model, a multi-condition weighted fitness function and a worst-case performance function are constructed.

[0075] In this embodiment, a convergent surrogate model is used to construct the various components of the robust optimization mathematical model. Specifically, the objective function for optimization is constructed using the convergent hydraulic index surrogate model I = g(X, C, R) and R provided by the f model. Preferably, two objective functions are constructed: a multi-condition weighted fitness function J. weighted (X) is used to measure the average performance level of body type X under all m typical operating conditions. For example, the hydraulic indicators I such as energy dissipation rate and impact pressure predicted by g are normalized and weighted, and then weighted and averaged according to the operating condition weights to obtain J. weighted (X). Performance function J under the most unfavorable operating condition. worst (X) is used to measure the worst performance of body size X across all m operating conditions, ensuring the robustness of the optimization. For example, J worst (X) = max j {P calc (X, c) j )}, that is, take the maximum value of the predicted impact pressure among all working conditions.

[0076] A cross-condition flow stability evaluation function is constructed using a flow regime partitioning model.

[0077] like Figure 4 As shown, in a preferred implementation, a cross-condition flow stability evaluation function is constructed, including:

[0078] By applying the flow regime partitioning model, the flow regime category and classification confidence of any body shape parameter under each condition in the typical flood condition set are predicted;

[0079] Based on the degree of consistency of the predicted flow regime category across different operating conditions, or based on the minimum classification confidence of the predicted stable flow regime, the cross-operating condition flow regime stability evaluation function S(X) = min j∈{1，2，…，m} {p(R=R stable |X, c j )}; where j is the working condition index; m is the total number of typical flood working conditions; c j For the j-th typical flood condition; R stable Let R be the target stable flow regime category; R be the discrete flow regime category; p(| ) be the classification confidence score; p(R=R stable |X, c j () indicates that body size X is under working condition c j The classification confidence level of the flow that is predicted to be a stable flow state.

[0080] Specifically, using the convergent flow regime partitioning model R = f(X, C), the key constraints for optimization are constructed, namely, the cross-condition flow regime stability evaluation function S(X). S(X) is preferably defined as: the body shape X in all m typical flood conditions c j The following is predicted by model f to be a steady flow state (denoted as R). stable The minimum classification confidence score of X is calculated as follows: S(X) = min j∈{1，2，…，m} {p(R=R stable |X, c j )};where X is the body shape parameter vector, c j Let be the j-th typical working condition, and p(| ) be the classification confidence score output by the flow regime partitioning model f. The cross-working condition flow regime stability evaluation function S(X) represents the degree to which the body shape X is closest to the flow regime change boundary among all the working conditions it faces. By constraining S(X) in the optimization, the final body shape scheme can be made to have sufficient safety margin under all working conditions and always maintain a stable flow pattern.

[0081] Using body shape parameters as decision variables, within the joint feasible region, the optimization objective is to minimize the weighted fitness function under multiple operating conditions and the performance function under the worst operating condition. X∈Ωjoint {J weighted (X), J worst (X)}, and with the cross-condition flow stability evaluation function as the constraint condition S(X)≥S min The solution yields a unified optimized body shape scheme; where X is the optimization decision variable, i.e., the body shape parameter; Ω joint The joint feasible region; min indicates taking the minimum value; J weighted (X) is the multi-condition weighted fitness function; J worst S(X) is the performance function under the most unfavorable operating condition; S(X) is the flow stability evaluation function across operating conditions; S min This is the preset minimum allowable flow stability threshold.

[0082] In this embodiment, the constructed functions are assembled to form a complete multi-objective constrained optimization model. The preferred mathematical form of this robust optimization model is: min X∈Ωjoint {J weighted (X), J worst (X)},st S(X)≥S min Where min indicates that the optimization objective is to minimize J weighted and J worst The smaller the value, the better; X is the decision variable, i.e., the body shape parameter vector; Ω joint It represents the joint feasible region, serving as the boundary constraint for the decision variable; st represents the constraint condition; S min It is a preset minimum allowable flow stability threshold, such as S.min = 0.75, indicating that the confidence level of the body shape in predicting a steady flow state under any operating condition must not be lower than 75%. A multi-objective optimization algorithm is used to solve this mathematical model. In each step of the optimization iteration, the algorithm generates a new candidate body shape X and calculates its J by calling models f and g. weighted J worst The fitness and feasibility of the optimization are evaluated using S(X). The final output of the optimization is the Pareto front solution set of this multi-objective problem, i.e., the candidate set of multi-condition optimization body shapes. Each body shape in this set is a candidate body shape that, under the premise of satisfying the flow stability constraint S(X), achieves a good average performance J. weighted And worst performance J worst The optimal solution that achieves non-dominated equilibrium between them.

[0083] In a further embodiment, it also includes:

[0084] High-precision three-dimensional numerical calculations are performed on the candidate set of multi-condition optimized body shapes obtained by solving the robust optimization model to obtain a dataset of hydraulic indexes for multi-condition optimized body shape verification.

[0085] In this embodiment, a candidate set of optimized flow fields under multiple operating conditions is input, such as 20 preferred flow fields on the Pareto front. Although the surrogate models f and g have converged, prediction biases may still exist, requiring physical verification of the final candidate solutions through high-precision computation. Specifically, representative flow fields are selected from the candidate set, for example, five are selected uniformly, and high-precision three-dimensional numerical calculations (CFD) are re-executed for these five flow fields under all m typical flood conditions. The output is a physically realistic multi-condition optimized flow field verification dataset and a multi-condition optimized flow field verification hydraulic index dataset for these five candidate flow fields.

[0086] The multi-condition optimized body shape verification hydraulic index dataset is compared with the prediction results of the surrogate model of the hydraulic index surrogate model. When the deviation between the verification data and the prediction results is large, the multi-condition optimized body shape verification hydraulic index dataset is merged into the multi-condition flow regime and hydraulic index dataset to correct the surrogate model.

[0087] In this embodiment, the high-fidelity verification results are cross-validated with the prediction results of the surrogate model. Specifically, the verification hydraulic index dataset (CFD true values) is compared with the surrogate model prediction results predicted by model g. If the deviation between the two is within an acceptable engineering accuracy range, such as 5%, it proves that the surrogate models f and g are accurate in the critical solution space region, and can proceed to the next screening step. If a large deviation is found, such as exceeding 15%, the model correction mechanism is triggered. The specific operation is as follows: the verification flow field dataset and the verification hydraulic index dataset are merged into the updated dataset, which is equivalent to forced, high-value active sampling for the optimal solution region. The expanded dataset is used to perform an additional round of iterative training on f and g to correct the model's deviation near the optimal solution. After correcting the model, the optimization solution can be re-executed.

[0088] Furthermore, it also includes: using the multi-condition optimized body shape verification hydraulic index dataset to correct the performance of each candidate body shape in the multi-condition optimized body shape candidate set; calculating the multi-condition comprehensive fitness score for each candidate body shape in the multi-condition optimized body shape candidate set, and extracting its most unfavorable working condition performance and flow stability; sorting based on the multi-condition comprehensive fitness score, and selecting a unified optimized body shape scheme from the multi-condition optimized body shape candidate set in combination with the engineering safety margin requirements.

[0089] Specifically, input is a validated or revised and re-optimized set of reliable multi-condition optimized body models and their corresponding high-fidelity or high-precision prediction performance data. For each candidate body model, calculate its multi-condition comprehensive fitness score. This score can be a comprehensive index, for example, based on the weights of the operating conditions, for J... weighted (X), J worst We perform a weighted summation or multi-attribute decision ranking on (X) and S(X). Simultaneously, we extract the worst-case performance J for each candidate body type. worst And the flow stability degree S(X). Based on the comprehensive fitness score for multiple operating conditions, the models were ranked, while their performance under the most unfavorable operating conditions and the degree of flow stability were rigorously reviewed to ensure they met the engineering safety margin requirements. For example, among the body types with the highest scores, J was selected. worst The body shape with the smallest S(X) margin is selected. This selected body shape is the final output unified optimized body shape scheme, which is the dimensionless geometric parameter vector X. optimal .

[0090] In one possible embodiment, after obtaining the unified optimized body shape scheme, the method further includes:

[0091] The dimensionless parameters of the unified and optimized body shape are back-calculated into structural geometric design parameters.

[0092] In this embodiment, the input is a unified optimized body shape scheme, i.e., the optimal dimensionless geometric parameter vector X.optimal This includes the engineering foundation dataset, particularly structural reference dimensions, such as the reference diameter D of the spillway shaft. During the inverse transformation, the shape parameters are defined as dimensionless vectors X, such as x1 = H / D (relative depth of the stilling well), x2 = L / D (relative length of the stilling well), where L is the specific length of the stilling well. Based on X... optimal = [x 1，optimal x 2，optimal , ..., x m，optimal ], and calculate the specific geometric dimensions with engineering scale. For example, if X optimal Chinese x 1，optimal = 1.5, and the reference diameter D = 10 meters, then the calculated depth H of the stilling well is H = x 1， optimal ·D = 1.5·10 = 15 meters. By analyzing X... optimal Performing this inverse calculation on all components yields a complete set of structural geometric design parameters, including specific stilling well lengths, widths, base plate elevations, turning radius, etc. (in meters or degrees). These parameters are used to guide subsequent engineering drawing.

[0093] Perform multi-condition engineering-level verification of the unified and optimized body shape.

[0094] In this embodiment, a set of structural geometric design parameters and a set of typical flood conditions are input. At a real engineering scale, the final selected design scheme undergoes a final high-precision verification to validate its performance. Specifically, based on the parameter set, a full-scale 3D geometric model and numerical calculation model are reconstructed. On this full-scale model, engineering-level fluid dynamics calculations are performed for the set of typical flood conditions and necessary verification conditions, such as other flow conditions between the typical conditions. This calculation accuracy is typically the highest and is used for final confirmation. The output is an engineering verification flow field and index dataset containing the flow field distribution, water level morphology, and key hydraulic parameters for each condition.

[0095] The engineering verification results were compared with the physical constraints under multiple operating conditions.

[0096] Specifically, the input includes the engineering verification flow field and index dataset, as well as the original set of multi-condition physical constraints, namely P. max , σ allowed The standard red line is then defined. This step is a verification process involving item-by-item comparison. For example, the maximum impact pressure P under the verification condition is extracted from the dataset. check and compare it with the maximum allowable impact pressure P max Compare and determine whether P is satisfied. check ≤P maxBy verifying all key indicators under all operating conditions, an engineering verification conclusion dataset is generated; key indicators include energy dissipation rate, cavitation risk, water surface oscillation, and outflow uniformity. In some optional implementations, if certain indicators, such as P... check Slightly exceeding the constraints, but still within the acceptable range for the project or can be resolved by fine-tuning the structure, may also include making small adjustments to the set of structural geometric design parameters to obtain a modified set of structural geometric design parameters, and recording the impact of the modified parameters on the hydraulic indices and flow regimes under each working condition, in order to evaluate the safety margin and stability of the final design.

[0097] Output structural design parameters and verification report.

[0098] In this embodiment, the key results of all the preceding steps are summarized. Specifically, the set of structural geometric design parameters or the modified set of structural geometric design parameters is summarized with the engineering verification conclusion dataset to form a complete structural design parameter and verification report. This report preferably includes: design basis, source of joint feasible domain, description of flow regime partitioning and active sampling methods, dimensionless parameters of unified optimized body shape and final structural geometric parameters, and multi-condition engineering verification results. This report provides complete and traceable technical support for engineering design decisions.

[0099] In one possible embodiment, constructing the flow regime partitioning model and the hydraulic index proxy model can also be as follows: read the initial multi-condition flow regime and hydraulic index dataset, extract the three-dimensional velocity field, pressure field, and free water surface position field corresponding to each body shape parameter and each typical flood condition combination, forming an original subset of multi-condition flow field raw data; for this subset of multi-condition flow field raw data, perform unified processing on the coordinate system, time step, and grid topology, map the flow field results under different body shapes and different conditions to a unified reference coordinate system and a unified cross-sectional position, and remove obvious numerical outliers and convergence failure conditions to obtain a multi-condition flow field preprocessing dataset for subsequent feature calculations. This dataset continues to correspond one-to-one with the original dimensionless geometric parameters of the body shape and the condition parameters. By reading the preprocessed data set of multi-condition flow field and combining the engineering experience of flow control in vertical shaft stilling wells and turning sections, the types of features used to characterize the flow state are determined, including the vortex intensity distribution characteristics of vertical shafts, the statistical characteristics of vorticity near the bottom plate of stilling wells, the volume and spatial location of negative pressure regions, the length and relative height of annular hydraulic jumps, the spatial coordinates and drift range of the main impact point on the bottom plate, and the velocity uniformity index of the velocity field of the outflow section. For each type of feature, specific calculation methods and value locations are given, forming a set of flow state feature definition rules that describe feature names, calculation formulas, cross-sectional locations, and statistical methods. Read the flow characteristic definition rule set and the multi-condition flow field preprocessing dataset. For each body shape and condition combination, calculate the flow characteristics such as vortex intensity statistics, negative pressure region volume, annular hydraulic jump length and relative height, impact point coordinates and drift range, and outflow cross-sectional velocity non-uniformity index according to the flow characteristic definition rule set. Arrange the obtained multiple feature values ​​in a fixed order to form a feature vector. Bind the feature vector to the corresponding body shape dimensionless geometric parameters and condition parameters to form a multi-condition flow characteristic original dataset containing multiple sets of body shape-condition-feature vectors. Read the original dataset of multi-condition flow characteristics, and normalize each feature dimension according to its physical dimensions and typical value range. For example, use linear normalization based on empirical upper and lower limits or standardization based on statistical standard deviation to map features of different dimensions and orders of magnitude to a unified numerical range, thereby eliminating the dimensional differences between features. After normalization, maintain a one-to-one correspondence between the normalized feature vectors and the corresponding dimensionless geometric parameters and operating condition parameters to form a structurally complete multi-condition flow characteristic dataset.The multi-condition flow regime feature dataset and the initial multi-condition flow regime and hydraulic index dataset are read and matched according to the combination key of the dimensionless geometric parameters of the body shape and the condition parameters. The normalized feature vector is merged with the calculated hydraulic indices such as energy dissipation rate, maximum impact pressure of the bottom plate, non-uniformity coefficient of wall pulsating pressure, relative height of the annular hydraulic jump and non-uniformity coefficient of outflow velocity to form a complete multi-condition flow regime and hydraulic index feature dataset. This dataset contains both feature information describing the flow regime morphology and hydraulic performance indicators, and serves as the common basic data for subsequent flow regime partitioning and training of multi-condition hydraulic index surrogate models.

[0100] Read the multi-condition flow regime and hydraulic index feature dataset, select the normalized flow regime feature vector as the clustering input, and perform unsupervised clustering analysis on all samples of body size and working condition combination using distance or density metric methods. The samples are naturally divided into several flow regime clusters, each cluster corresponding to a typical flow regime pattern. The clustering results are recorded as the cluster number of each sample, and on this basis, a flow regime clustering result dataset containing the correspondence between sample index and cluster number is formed. The flow pattern clustering result dataset and the corresponding multi-condition flow pattern and hydraulic index feature dataset are read. Engineering technicians combine the mean flow pattern features, hydraulic index levels and typical flow field images of each cluster in the clustering results to manually review the clusters. According to the engineering significance of stable flow, metastable flow, and unstable flow, the clusters are merged or split to determine the engineering flow pattern category corresponding to each cluster. After the review and adjustment are completed, a final flow pattern category label is assigned to each sample to form a flow pattern category label set. This flow pattern category label set records the engineering flow pattern category corresponding to each combination of body size and working condition. The system reads dimensionless geometric parameters of body shape and operating condition parameters, as well as the flow state category label set, from the multi-condition flow state and hydraulic index feature dataset. The samples are divided into training subsets and validation subsets according to a preset ratio. The system constructs a flow state classification dataset using the dimensionless geometric parameters of body shape and operating condition parameters as inputs and the flow state category labels as outputs. Based on this, an initial flow state partitioning model is constructed by selecting an appropriate classification algorithm. The parameters are trained through the training subset so that the model can predict the corresponding flow state category based on the dimensionless geometric parameters of body shape and operating condition parameters. After training, an initial flow state partitioning model that can be used to predict flow state category and its probability information is obtained. The initial flow regime partitioning model and validation subset data are read. Flow regime categories are predicted on the validation subset, and the prediction results are compared with the true flow regime category labels. Evaluation metrics such as classification accuracy, confusion matrix, and recall for each class are calculated. Simultaneously, the class probabilities output by the model are extracted as flow regime classification confidence scores, and the confidence score distribution is statistically analyzed. Based on these evaluation metrics, it is determined whether the initial flow regime partitioning model meets the accuracy requirements. When the model performance meets the preset standards, the initial flow regime partitioning model is determined as a convergence candidate multi-condition flow regime partitioning model, and a flow regime partitioning model performance evaluation result containing classification accuracy data and confidence score statistics is generated. This provides a basis for measuring the flow regime boundary distance using classification confidence scores during subsequent active sampling.

[0101] A multi-condition flow regime and hydraulic index feature dataset and flow regime category label set are read. Dimensionless geometric parameters of the body shape, operating parameters, and corresponding flow regime category information are used as inputs. Hydraulic indices such as energy dissipation rate, maximum impact pressure on the floor, wall pulsating pressure non-uniformity coefficient, annular hydraulic jump relative height, and outflow velocity non-uniformity coefficient are used as outputs. A multi-condition hydraulic index training dataset containing input-output mapping relationships is constructed, and this dataset is divided into training and validation subsets according to a preset ratio. The multi-condition hydraulic index training dataset is read, and based on the number of input variables, the number of output indices, and the expected fitting accuracy, one or more surrogate model forms suitable for multi-output regression are selected, such as a multi-output surrogate model based on radial basis functions. Its structural parameters, including the number of basis function centers, basis function width, and regularization coefficient, are configured to form the initial structural parameter configuration set of the surrogate model. This configuration set determines the specific form and complexity of the initial multi-condition hydraulic index surrogate model. The training dataset and initial structural parameter configuration set for multi-condition hydraulic indices are read. A surrogate model for multi-condition hydraulic indices is trained on the training subset. The least squares method or regularization method is used to fit the input-output mapping relationship, resulting in an initial surrogate model for predicting multi-condition hydraulic indices. During training, the change in training error with iterations is recorded, forming a training error sequence for the hydraulic index surrogate model. The initial surrogate model and validation subset data are read. The dimensionless geometric parameters of the body shape, operating parameters, and flow regime categories from the validation subset are input into the surrogate model to obtain the corresponding predicted hydraulic indices. These predicted indices are compared with the actual hydraulic indices in the validation subset, and the fitting accuracy indices for each hydraulic index are calculated, such as the coefficient of determination, mean square error, and maximum relative error. These accuracy indices are then summarized to form the accuracy evaluation result of the initial surrogate model.

[0102] Read the joint feasible region parameter range and the currently calculated body shape sample set, including the initial body shape parameter sample set and the body shapes that have completed numerical calculation in the newly added body shape parameter sample set. Use the space filling method to generate body shape parameter points that have not yet been calculated in three dimensions within the joint feasible region parameter range, and ensure that these candidate body shapes maintain a certain distance from existing samples in the dimensionless parameter space to avoid over-concentration of sampling, so as to obtain a candidate body shape parameter set covering the blank area of ​​the joint feasible region. The system reads the candidate body shape parameter set, the typical flood condition set, the converged candidate multi-condition flow regime partitioning model, and the initial multi-condition hydraulic index surrogate model. For each body shape parameter point in the candidate body shape parameter set, under each typical flood condition, the converged candidate flow regime partitioning model is called to predict the flow regime category and its classification confidence. At the same time, the initial multi-condition hydraulic index surrogate model is called to predict the corresponding multi-condition hydraulic indices such as energy dissipation rate, maximum impact pressure on the bottom plate, wall pulsating pressure non-uniformity coefficient, annular hydraulic jump relative height, and outflow velocity non-uniformity coefficient. The predicted flow regime categories, classification confidence, and hydraulic indices under all conditions are organized according to the combination of body shape and conditions to form a candidate body shape multi-condition prediction performance dataset. The multi-condition prediction performance dataset of candidate body types is read using the accuracy evaluation results of the initial surrogate model. The error information of each hydraulic index in the initial surrogate model accuracy evaluation results is used to map the error level to the prediction uncertainty estimate of the corresponding hydraulic index. Based on this, the predicted hydraulic indices of each candidate body type under all typical flood conditions are summarized, and the overall uncertainty of its multi-condition weighted fitness prediction is calculated. Using the classification confidence score output by the flow regime partitioning model, the classification confidence score of each candidate body type under each condition is compared with the preset flow regime boundary judgment threshold to obtain the degree of proximity of the candidate body type to the flow regime partition boundary. The flow regime category of the candidate body type changes between different conditions, thereby calculating the cross-condition flow regime consistency index. Through the above calculations, an actively sampled feature index dataset describing the multi-condition prediction uncertainty, flow regime boundary distance, and flow regime consistency degree of each candidate body type is obtained. The system reads the working condition weight information from the active sampling feature index dataset and the typical flood working condition set. According to the preset weight rules, it weights and fuses the multi-working condition prediction uncertainty, cross-working condition flow consistency, and proximity to the relative flow boundary for each candidate body type. For example, it assigns a higher weight to the multi-working condition prediction uncertainty, assigns a higher value to samples close to the flow zone boundary, and gives an additional importance score to samples with large cross-working condition flow changes. Finally, it calculates a comprehensive active sampling value score for each candidate body type and organizes all candidate body types and their value scores to form an active sampling value index set.

[0103] The active sampling value index set is read, and several candidate body shape parameter points are selected in descending order of active sampling value scores. This ensures that the selected body shapes have good distribution in the dimensionless parameter space and take into account both high uncertainty regions and regions near the flow regime boundaries. This constitutes the new body shape parameter sample set for this round of high-precision three-dimensional numerical calculations. The new body shape parameter sample set, typical flood conditions set, and three-dimensional body shape geometric model construction methods and boundary condition configuration rules are read. For each new body shape parameter sample, a corresponding three-dimensional body shape geometric model and numerical calculation model are constructed under each typical flood condition. The inlet flow boundary, outlet water level boundary, and wall conditions are set to be consistent with the original samples. Three-dimensional numerical calculations are performed to obtain the corresponding velocity field, pressure field, and free surface morphology. These results are organized into an incremental multi-condition flow field raw dataset. Multiple hydraulic indices of the new samples under each condition are calculated, and the resulting data are organized into an incremental multi-condition hydraulic index raw dataset. The process involves reading the initial multi-condition flow regime and hydraulic index dataset, or the converged multi-condition flow regime and hydraulic index dataset from the previous iteration, as well as the original incremental multi-condition flow field dataset and the original incremental multi-condition hydraulic index dataset. Indexing is performed according to body shape parameters and operating condition parameters. Incremental flow field data and incremental hydraulic index data are appended to the original dataset. Feature preprocessing and feature merging operations are repeated for the new samples, incorporating the flow regime features and hydraulic indices of the incremental samples into a unified data structure, forming an updated multi-condition flow regime and hydraulic index dataset containing both original and new samples. The updated multi-condition flow regime and hydraulic index dataset is then used to re-execute the feature extraction and flow regime partitioning model training process, resulting in a new updated multi-condition flow regime partitioning model and its corresponding performance evaluation results. Simultaneously, the updated multi-condition flow regime and hydraulic index surrogate model is retrained using the updated dataset, yielding a new updated multi-condition hydraulic index surrogate model and its corresponding accuracy evaluation results, reflecting the improvement in flow regime partitioning and hydraulic index prediction accuracy brought about by the new samples.The system reads the performance evaluation results of the updated flow regime partitioning model and the accuracy evaluation results of the updated surrogate model. Based on the preset convergence criteria, it comprehensively evaluates the accuracy of flow regime classification, the accuracy of multi-condition hydraulic index prediction, and the number of active sampling rounds. When the accuracy indicators of the two models change less than the preset threshold in the most recent iterations, and the impact of the new samples brought by active sampling on the overall multi-condition adaptability evaluation results has been reduced to an acceptable level, the current updated multi-condition flow regime partitioning model and the updated multi-condition hydraulic index surrogate model are determined as convergent multi-condition flow regime partitioning model and convergent multi-condition hydraulic index surrogate model. At the same time, the updated multi-condition flow regime and hydraulic index dataset is determined as the convergent multi-condition flow regime and hydraulic index dataset, and all newly added body shape parameter samples in this round and previous rounds are uniformly organized into an updated body shape sample set. If the convergence condition is not yet met, the updated multi-condition flow regime and hydraulic index dataset and the updated model are used as the new initial state, and the loop is executed again until the convergence condition is met.

[0104] According to one aspect of this application, a method for unified optimization of the shape of a flood discharge shaft, stilling well, and turning section can further include: performing a preliminary numerical simulation of the entire flood discharge shaft, calculating the flow field and water phase distribution, determining the impact weights of N typical floods experienced by the stilling well and turning section, and extracting the corresponding flow characteristics, including the inflow rate Q and the outlet water level H of the turning section. t The initial range of body shape parameters was determined based on comprehensive engineering experience and specifications. Preliminary numerical simulations were performed using the upper, average, and lower limits of each parameter, and compared with the original flow pattern to further narrow down the sampling range of the body shape parameter set. Within this range, M design parameter samples were generated using Latin hypercube sampling or orthogonal experimental design. Local models of the stilling wells and bends for each sample were constructed, and the flow characteristics obtained in the preceding steps were input as control conditions to simplify the calculations. For the N determined typical flood conditions, CFD modeling calculations were performed on M samples (total computation time M×N), and key hydraulic indices were extracted.

[0105] Based on the correlation between the shape parameters and hydraulic indices of stilling wells and turning sections, a high-precision RBF surrogate model is fitted to map the laws governing shape parameters and hydraulic performance. Based on the RBF model, multi-objective optimization models are established for N typical flood conditions. The Pareto front is solved using the NSGA-II multi-objective algorithm to obtain the set of optimal solutions for shape parameters corresponding to hydraulic indices under each typical flood condition. For the parameter sets of the optimal shape for each of the above N conditions, the hydraulic indices under the remaining (N-1) typical flood conditions are calculated for each shape. A weighted total score is calculated based on the previously determined flood frequency influence weights to obtain the comprehensive flow adaptability score for each shape to floods of each frequency. The shape with the optimal comprehensive flow adaptability is selected as the final optimized scheme.

[0106] In a specific embodiment, the stilling well-turning section of the flood discharge shaft is adjusted using the unified optimization method for the shape of the stilling well-turning section of the flood discharge shaft described in this application. Specifically, as follows... Figure 5 and Figure 6 As shown, for the spillway shaft of a pumped storage power station project, two modification schemes are proposed for the overall structure of the stilling well and the L-shaped bend section connecting the lower part of the spillway shaft with the drainage tunnel: the first modification scheme and the second modification scheme. The black line in the base diagram represents the original scheme, and the position of the stilling well-behaved section structure in the spillway of the entire spillway shaft is shown by the purple schematic line in the figure. First modification scheme: The short circular arc curves on the upper and lower walls of the L-shaped bend section are changed to elliptical curves, with the equation of the upper edge elliptical curve being x. 2 / 6.3 2 +(2.5-y) 2 / 2.5 2 =1, the equation of the lower edge elliptic curve is x 2 / 6.0 2 +(3.5-y) 2 / 3.5 2 =1; The slope section is appropriately extended, with a total length of 19.3m from the center of the vertical shaft to the end of the slope section, and an outlet height of 2m; the stilling well has a circular cross-section with a diameter of 5m, and the depth of the stilling well is approximately 10.5m calculated from the elevation of the first end of the bottom plate of the slope section, with the bottom plate lowered to an elevation of 683.64m. Second modification: The elliptical curves of the upper and lower walls are adjusted, with the equation of the upper edge elliptical curve being x 2 / 6.0 2 +(3.5-y) 2 / 3.5 2 =1, the equation of the lower edge elliptic curve is x 2 / 6.2 2 +(3-y) 2 / 3 2 =1; The slope section is further extended, with a total length of 30.65m from the center of the vertical shaft to the end of the slope section, and the exit height of the slope section is 2m; The stilling well is extended 2m downstream, and the cross-section is expanded from a circle to a horseshoe shape, with a distance of 7m between the first and last ends of the horseshoe shape; Calculated from the elevation of the first end of the bottom plate of the slope section, the depth of the stilling well is 12.0m, and the elevation of the bottom plate of the well is reduced to 682.77m.

[0107] In summary, the unified optimization method for the shape of the flood discharge shaft, stilling well, and turning section in this application is based on multi-condition physical constraints, deriving and constructing a joint feasible region as the hard boundary for optimization. A three-layer mapping proxy model of shape, flow regime, and index is constructed: a flow regime partitioning model is built through flow regime feature extraction and cluster analysis to map the shape and conditions to discrete flow regime categories; a high-precision hydraulic index proxy model is constructed by taking the shape, conditions, and flow regime categories as inputs. An active sampling strategy that integrates multi-condition uncertainty, flow regime partition boundary distance, and cross-condition flow regime consistency is adopted to iteratively update the model. Within the joint feasible region, a robust optimization model considering cross-condition flow regime stability is solved to obtain a unified optimized shape scheme.

[0108] This invention proposes a three-layer mapping architecture of body shape, flow regime, and hydraulic index. Through flow regime feature extraction and unsupervised clustering, complex continuous flow fields are divided into discrete flow regime categories with clear engineering significance. Based on this, two cascaded models are constructed: a flow regime partitioning model R and a hydraulic index model I with flow regime category R as explicit input. The complex nonlinear fitting task is decomposed into classification and conditional regression, enabling the model to physically and accurately capture and express flow regime transition boundaries, overcoming the bottleneck of insufficient accuracy of traditional models near flow regime transition points. Furthermore, a flow regime boundary-driven active sampling strategy is proposed. This strategy no longer relies solely on the prediction variance of hydraulic indices to guide sampling, but instead constructs a fusion sampling value function V(x). This function introduces two key terms: the flow regime partitioning boundary distance D(x) and the cross-condition flow regime category prediction consistency C(x). This allows the sampling strategy to proactively and intelligently identify and intensively sample the flow regime boundary regions most perplexing to the model f and the regions where the flow regime jumps between conditions. This allows computational resources to be precisely allocated to the parameter space locations most critical for capturing fluid dynamics changes and ensuring robustness, solving the problem of blind sampling and improving optimization efficiency.

[0109] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for optimizing the shape of a flood discharge shaft, energy dissipation shaft, and turning section, characterized in that... include: Obtain multi-condition physical constraints describing the shape parameters of the flood discharge shaft, stilling well, and turning section, and construct a joint feasible domain; at the same time, obtain a set of typical flood conditions; An active sampling strategy is adopted to iteratively obtain volume sample data for a set of typical flood conditions within the joint feasible domain; based on this, a flow regime partitioning model and a hydraulic index proxy model are iteratively constructed; the active sampling strategy integrates multi-condition uncertainty and flow regime partitioning boundary information. Within the joint feasible domain, a robust optimization model considering cross-condition flow stability is constructed and solved by applying the flow regime partitioning model and the hydraulic index proxy model, resulting in a unified optimized body shape scheme.

2. The method according to claim 1, characterized in that, Iteratively constructing flow regime partitioning models and hydraulic index proxy models, including: Construct a flow regime partitioning model R=f(X, C) to map body shape parameters and working conditions to discrete flow regime categories; where X represents the input body shape parameters; C represents the working conditions; f() represents the flow regime partitioning model; and R is the discrete flow regime category. A hydraulic index proxy model I=g(X, C, R) is constructed to map the body shape parameters, operating conditions, and flow regime categories determined by the flow regime partitioning model into hydraulic indices; where g() is the hydraulic index proxy model; and I is the hydraulic index.

3. The method according to claim 2, characterized in that, Constructing a flow partitioning model includes: From the multi-condition flow field data contained in the body sample data, flow pattern features that characterize the flow morphology are extracted to form a flow pattern feature dataset; Perform cluster analysis on the flow regime feature dataset to define flow regime categories and generate flow regime category labels for body size samples; Using body shape parameters and working conditions from body shape sample data as input and flow regime category labels as output, a flow regime partitioning model is trained.

4. The method according to claim 1, characterized in that, A unified body shape optimization plan was obtained, including: Using a hydraulic index proxy model, a multi-condition weighted fitness function and a worst-case performance function are constructed. A cross-condition flow stability evaluation function is constructed using a flow regime partitioning model. Using body shape parameters as decision variables, within the joint feasible region, the optimization objective is to minimize the weighted fitness function under multiple operating conditions and the performance function under the worst operating condition. X∈Ωjoint {J weighted (X), J worst (X)}, and with the cross-condition flow stability evaluation function as the constraint condition S(X)≥S min The solution yields a unified optimized body shape scheme; where X is the optimization decision variable, i.e., the body shape parameter; Ω joint The joint feasible region; min indicates taking the minimum value; J weighted (X) is the multi-condition weighted fitness function; J worst S(X) is the performance function under the most unfavorable operating condition; S(X) is the flow stability evaluation function across operating conditions; S min This is the preset minimum allowable flow stability threshold.

5. The method according to claim 4, characterized in that, Construct a cross-condition flow stability evaluation function, including: By applying the flow regime partitioning model, the flow regime category and classification confidence of any body shape parameter under each condition in the typical flood condition set are predicted; Based on the degree of consistency of the predicted flow regime category across different operating conditions, or based on the minimum classification confidence of the predicted stable flow regime, the cross-operating condition flow regime stability evaluation function S(X) = min j∈{1，2，…，m} {p(R=R stable |X, c j )}; where j is the working condition index; m is the total number of typical flood working conditions; c j For the j-th typical flood condition; R stable Let R be the target stable flow regime category; R be the discrete flow regime category; p(| ) be the classification confidence score; p(R=R stable |X, c j () indicates that body size X is under working condition c j The classification confidence level of the flow that is predicted to be a stable flow state.

6. The method according to claim 1, characterized in that, Iteratively obtain body shape sample data, including: Generate candidate body shape parameter points that have not yet been calculated within the joint feasible region; Construct an active sampling value function to evaluate candidate body shape parameter points; Based on the evaluation results, new body type samples are selected, and body type sample data is obtained iteratively.

7. The method according to claim 6, characterized in that, Constructing an active sampling value function includes: The uncertainty of multi-condition comprehensive fitness prediction for candidate body shape parameter points is evaluated using a hydraulic index surrogate model. The distances between the flow regime partitions and the boundary of candidate body shape parameter points are evaluated using a flow regime partitioning model. The consistency of cross-condition flow regime predictions for candidate body shape parameter points in a typical flood condition set is evaluated using a flow regime partitioning model. By integrating the multi-condition comprehensive fitness prediction uncertainty, the distance to the flow regime partition boundary, and the consistency with the cross-condition flow regime category prediction, the active sampling value function is determined as V(x) = w1·U(x) + w2·D(x) + w3·C(x); where V(x) is the active sampling value score of the candidate body shape parameter point x; U(x) is the multi-condition comprehensive fitness prediction uncertainty; D(x) is the flow regime partition boundary distance; C(x) is the cross-condition flow regime category prediction consistency; and w1, w2, and w3 are preset weight coefficients used to integrate the three dimensions.

8. The method according to claim 7, characterized in that, Evaluate the distance to the flow regime partition boundary, including: Using a flow regime partitioning model, the flow regime category and corresponding classification confidence of candidate body shape parameter points under each typical flood condition set are predicted; The classification confidence score is compared with the preset flow regime boundary determination threshold to quantify the proximity of candidate body shape parameter points to the flow regime partition boundary; The proximity of the flow regime partition boundaries is used as the flow regime partition boundary distance D(x) = max j∈{1，2，…，m} {D j (x)};D j (x)=1- max k {p(R k | x, c j )};where D(x) is the distance of the flow regime partition boundary for candidate body size x; D j (x) represents the candidate body shape x under a single working condition c. j The degree of proximity of the flow boundary; j is the working condition index; m is the total number of typical flood working conditions; p(R k | x, c j ) is x in c j The classification confidence score of a class belonging to category k; max k {} represents taking the maximum classification confidence among all flow state categories k; max j {} indicates that the value closest to the flow boundary is taken among all operating conditions.

9. The method according to claim 1, characterized in that, Constructing a joint feasible domain includes: The shape parameter X is defined as a dimensionless geometric parameter vector; for the typical flood condition set C={c1,…,c…} m Each working condition c in} j The single-condition physical constraint inequalities describing the physical constraints of this working condition are derived. The set of single-condition physical constraint inequalities defines the single-condition physical feasible region Ω corresponding to this working condition. j ; The joint feasible region Ω is determined by performing an intersection operation on all single-case physical feasible regions. joint =∩ j=1 m Ω j Where j is the operating condition index, m is the total number of typical flood operating conditions, and Ω j Let Ω be the single-condition physical feasible region corresponding to the j-th working condition. joint A joint feasible region that satisfies all operating condition constraints.

10. The method according to claim 9, characterized in that, Derive the physical constraint inequalities for a single operating condition, including: Based on the energy equation, momentum equation, or cavitation safety conditions, establish the shape parameter X under operating condition c. j Hydraulic response calculation function; Read the standard control parameters, including the allowable cavitation index and the allowable maximum impact pressure; By comparing the hydraulic response calculation function with the standard control parameters, a single-condition physical constraint inequality is established. This single-condition physical constraint inequality includes at least: σ(X, c) j )≥σ allowed ;P(X,c j )≤P max ;where σ(X, c j ) is based on X and c j The calculated cavitation number, σ allowed To standardize the allowable cavitation index in the control parameters; P(X, c j ) is based on X and c j The calculated impact pressure, P max To standardize the maximum allowable impact pressure in the control parameters.

Images