Turbine three-dimensional blade aerodynamic parameter calculation method based on graph neural network and radial physical information embedding

Abstract

This disclosure presents an embodiment of a method for calculating the aerodynamic parameters of a three-dimensional turbine blade based on graph neural networks and radial physical information embedding. One specific implementation of this method includes: selecting multiple two-dimensional airfoil sections along a pre-created spanwise direction of the three-dimensional turbine blade; for each of the multiple two-dimensional airfoil sections, performing the following processing: splitting the airfoil line of the two-dimensional airfoil section into five continuous airfoil line segments; performing geometric feature extraction processing on the airfoil line segment information; acquiring the incoming aerodynamic operating condition parameter data of the three-dimensional turbine blade; generating aerodynamic geometric feature connection diagram data corresponding to the two-dimensional airfoil section; inputting the aerodynamic geometric feature connection diagram data into a pre-trained aerodynamic performance prediction model; and generating and displaying the turbine blade aerodynamic output performance distribution curve based on the generated aerodynamic output performance data. This implementation shortens the aerodynamic output performance prediction cycle and reduces computational resource consumption.

Description

Technical Field

[0001] The embodiments disclosed herein relate to the field of computer technology, and specifically to a method and medium for calculating aerodynamic parameters of turbine three-dimensional blades based on graph neural networks and radial physical information embedding. Background Technology

[0002] With the continuous development of aero-engines and gas turbines, higher demands are placed on the accurate prediction and rapid optimization design of turbine blade aerodynamic performance. Turbine blades are key hot-end components in engines, and their aerodynamic efficiency directly affects the overall engine performance and economy. During blade design, it is necessary to obtain aerodynamic output performance data (such as total pressure loss coefficient, exit Mach number, and exit flow angle) of the blade under different operating conditions (such as incoming flow angle of attack and inlet Mach number), and generate a performance distribution curve that continuously varies along the blade span to guide blade geometry modification and optimization. Currently, the common method for predicting the aerodynamic output performance data of turbine blades and generating turbine blade aerodynamic output performance distribution curves is to directly obtain the flow field information of the blade through high-fidelity three-dimensional computational fluid dynamics (CFD) simulation, thereby obtaining the aerodynamic performance data, i.e., the turbine blade aerodynamic output performance distribution curve.

[0003] However, when using the above method to predict the aerodynamic output performance data of turbine blades and generate a distribution curve of turbine blade aerodynamic output performance, the following technical problems often arise: A complete spanwise performance distribution curve typically requires data points at multiple spanwise locations, such as the blade root, mid-blade, and tip. High-fidelity three-dimensional computational fluid dynamics (CFD) simulations require a separate CFD solution for each data point. If multiple incoming flow conditions (such as different angles of attack) are considered, the number of required data points increases exponentially. The accumulated time and resource consumption from multiple CFD simulations is substantial, resulting in long aerodynamic output performance prediction cycles and high computational resource consumption, making it difficult to meet the demands of rapid iteration across multiple scenarios in engineering design.

[0004] The information disclosed in this background section is only intended to enhance the understanding of the background of the inventive concept, and therefore may contain information that does not form prior art known to those skilled in the art. Summary of the Invention

[0005] The summary portion of this disclosure is intended to provide a brief overview of the concepts, which will be described in detail in the detailed description portion. This summary portion is not intended to identify key or essential features of the claimed technical solutions, nor is it intended to limit the scope of the claimed technical solutions.

[0006] Some embodiments of this disclosure provide a method, apparatus, electronic device, and computer-readable medium for generating and displaying turbine blade aerodynamic output performance distribution curves to solve one or more of the technical problems mentioned in the background section above.

[0007] In a first aspect, some embodiments of this disclosure provide a method for calculating the aerodynamic parameters of a three-dimensional turbine blade based on graph neural networks and radial physical information embedding. The method includes: selecting multiple two-dimensional airfoil sections along a pre-created spanwise direction of the three-dimensional turbine blade; performing the following processing on each of the multiple two-dimensional airfoil sections: splitting the airfoil line of the two-dimensional airfoil section into five continuous airfoil segments to obtain airfoil segment information; performing geometric feature extraction processing on the airfoil segment information to obtain geometric contour feature information; acquiring incoming aerodynamic operating condition parameter data of the three-dimensional turbine blade; generating aerodynamic geometric feature connection diagram data corresponding to the two-dimensional airfoil section based on the geometric contour feature information and the incoming aerodynamic operating condition parameter data; inputting the aerodynamic geometric feature connection diagram data into a pre-trained aerodynamic performance prediction model to obtain aerodynamic output performance data; and generating and displaying a turbine blade aerodynamic output performance distribution curve based on the generated aerodynamic output performance data.

[0008] Secondly, some embodiments of this disclosure provide a turbine three-dimensional blade aerodynamic parameter calculation device based on graph neural network and radial physical information embedding. The device includes: a selection unit configured to select multiple two-dimensional airfoil sections along a pre-created spanwise direction of the three-dimensional turbine blade; a processing unit configured to perform the following processing on each of the multiple two-dimensional airfoil sections: splitting the airfoil line of the two-dimensional airfoil section into five continuous airfoil line segments to obtain airfoil line segment information; performing geometric feature extraction processing on the airfoil line segment information to obtain geometric contour feature information; acquiring the incoming flow aerodynamic operating condition parameter data of the three-dimensional turbine blade; generating aerodynamic geometric feature connection diagram data corresponding to the two-dimensional airfoil section based on the geometric contour feature information and the incoming flow aerodynamic operating condition parameter data; inputting the aerodynamic geometric feature connection diagram data into a pre-trained aerodynamic performance prediction model to obtain aerodynamic output performance data; and a generation unit configured to generate and display the turbine blade aerodynamic output performance distribution curve of the three-dimensional turbine blade based on the generated aerodynamic output performance data.

[0009] Thirdly, some embodiments of this disclosure provide an electronic device, including: one or more processors; and a storage device having one or more programs stored thereon, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method described in any implementation of the first aspect above.

[0010] Fourthly, some embodiments of this disclosure provide a computer-readable medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the method described in any of the implementations of the first aspect above.

[0011] The above-described embodiments of this disclosure have the following beneficial effects: the turbine three-dimensional blade aerodynamic parameter calculation method based on graph neural networks and radial physical information embedding in some embodiments of this disclosure shortens the aerodynamic output performance prediction cycle and reduces the consumption of computing resources. Specifically, the reason for the long aerodynamic output performance prediction cycle and high computing resource consumption is that a complete spanwise performance distribution curve usually requires data points at multiple spanwise positions such as the blade root, blade mid-section, and blade tip. Through high-fidelity three-dimensional computational fluid dynamics (CFD) simulation, each data point needs to be obtained through an independent CFD solution. If multiple incoming flow conditions (such as different angles of attack) are considered, the number of required data points increases exponentially, and the accumulated time cost and resource consumption of multiple CFD simulations are large, resulting in a long aerodynamic output performance prediction cycle and high computing resource consumption, which makes it difficult to meet the needs of rapid iteration of multiple schemes in engineering design. Based on this, the turbine three-dimensional blade aerodynamic parameter calculation method based on graph neural networks and radial physical information embedding in some embodiments of this disclosure first selects multiple two-dimensional airfoil sections along the pre-created three-dimensional turbine blade spanwise direction. Therefore, the three-dimensional blade can be decomposed into a finite number of representative two-dimensional cross-sections, avoiding the high-complexity modeling of the entire three-dimensional blade. Then, for each of the aforementioned two-dimensional airfoil cross-sections, the following processing is performed: the airfoil line of the cross-section is split into five continuous airfoil segments to obtain airfoil segment information. This simplifies the complex airfoil profile into airfoil segment information. Next, geometric feature extraction processing is performed on the airfoil segment information to obtain geometric contour feature information. This allows the extraction of key parameters (such as the coordinates of Bézier curve control points) that uniquely characterize the shape of each airfoil segment. Then, the incoming aerodynamic operating parameters of the three-dimensional turbine blade are obtained. Finally, based on the geometric contour feature information and the incoming aerodynamic operating parameters, aerodynamic geometric feature connection diagram data corresponding to the aforementioned two-dimensional airfoil cross-sections is generated. Therefore, the geometric and operating condition information of each cross-section is fused into a graph structure. Each graph node carries the geometric features of the corresponding airfoil segment and shared operating condition features. The graph edges are constructed according to the original connection order of the airfoil segments, completely preserving the spatial adjacency relationships within the cross-section. Then, the above aerodynamic geometric feature connection graph data is input into a pre-trained aerodynamic performance prediction model to obtain aerodynamic output performance data. Thus, by learning the mapping relationship from airfoil geometry and incoming flow conditions to outlet aerodynamic performance through an aerodynamic performance prediction model, the aerodynamic output performance data of this two-dimensional cross-section can be predicted without performing any CFD solution on this cross-section. Only one model forward inference (millisecond level) is required, and the model parameters are fixed after training, eliminating the need for repeated mesh generation, numerical iteration, post-processing, and other operations. Therefore, the time for predicting aerodynamic output performance data can be reduced from several days to milliseconds, while also reducing CPU / GPU resource consumption.Based on the generated aerodynamic output performance data, the aerodynamic output performance distribution curves of the aforementioned three-dimensional turbine blades are generated and displayed. Finally, the prediction results of multiple sections can be fused along the spanwise into a continuous curve and displayed. Because a multi-section decomposition strategy of representing three dimensions with two dimensions is adopted, and an aerodynamic performance prediction model that learns the mapping relationship from airfoil geometry and incoming flow conditions to outlet aerodynamic performance is used, the predicted aerodynamic output performance data of the two-dimensional section replaces the separate CFD solution for each data point. This reduces the computation time required to obtain a complete spanwise performance distribution curve from several days / weeks to milliseconds, while avoiding repetitive mesh generation, solution calculations, and post-processing operations. This significantly reduces CPU / GPU resource consumption, shortens the aerodynamic output performance prediction cycle, and reduces computational resource consumption, enabling the rapid and low-cost generation of a large number of performance curves under different blade schemes and different incoming flow conditions during the design iteration process. Attached Figure Description

[0012] The above and other features, advantages, and aspects of the embodiments of this disclosure will become more apparent from the accompanying drawings and the following detailed description. Throughout the drawings, the same or similar reference numerals denote the same or similar elements. It should be understood that the drawings are schematic, and elements are not necessarily drawn to scale.

[0013] Figure 1 This is a flowchart of some embodiments of the turbine three-dimensional blade aerodynamic parameter calculation method based on graph neural network and radial physical information embedding according to the present disclosure; Figure 2 This is a schematic diagram of the structure of some embodiments of the turbine three-dimensional blade aerodynamic parameter calculation device based on graph neural network and radial physical information embedding according to the present disclosure; Figure 3 This is a schematic diagram of the structure of an electronic device suitable for implementing some embodiments of the present disclosure. Detailed Implementation

[0014] Embodiments of this disclosure will now be described in more detail with reference to the accompanying drawings. While some embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this disclosure. It should be understood that the accompanying drawings and embodiments of this disclosure are for illustrative purposes only and are not intended to limit the scope of protection of this disclosure.

[0015] It should also be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings. Unless otherwise specified, the embodiments and features described in this disclosure can be combined with each other.

[0016] It should be noted that the concepts of "first" and "second" mentioned in this disclosure are used only to distinguish different devices, modules or units, and are not used to limit the order of functions performed by these devices, modules or units or their interdependencies.

[0017] It should be noted that the terms "a" and "a plurality of" used in this disclosure are illustrative rather than restrictive, and those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".

[0018] The names of messages or information exchanged between multiple devices in the embodiments of this disclosure are for illustrative purposes only and are not intended to limit the scope of such messages or information.

[0019] This disclosure will now be described in detail with reference to the accompanying drawings and embodiments.

[0020] Figure 1 A flowchart 100 is shown illustrating some embodiments of the turbine three-dimensional blade aerodynamic parameter calculation method based on graph neural networks and radial physical information embedding according to this disclosure. This turbine three-dimensional blade aerodynamic parameter calculation method based on graph neural networks and radial physical information embedding includes the following steps: Step 101: Select multiple two-dimensional blade sections along the pre-created three-dimensional turbine blade spanwise direction.

[0021] In some embodiments, the execution entity (e.g., a computing device) of the turbine three-dimensional blade aerodynamic parameter calculation method based on graph neural networks and radial physical information embedding can select multiple two-dimensional airfoil sections along a pre-created spanwise direction of the three-dimensional turbine blade. The three-dimensional turbine blade can be a three-dimensional model representing the complete spatial geometry of an aero-engine or gas turbine turbine blade. The spanwise direction refers to the spatial direction from the blade root (the end closer to the center of the rotor disk) to the blade tip (the end farther from the center of the rotor disk) of the three-dimensional turbine blade, and this direction is perpendicular to the plane containing the blade chord.

[0022] In some optional implementations of certain embodiments, the aforementioned execution entity can select multiple two-dimensional airfoil sections along a pre-created three-dimensional turbine blade spanwise direction through the following steps: The first step is to obtain the spanwise height range information of the aforementioned three-dimensional turbine blade. The spanwise height range refers to the total length of the three-dimensional turbine blade along the spanwise direction, from the plane containing the blade root section to the plane containing the blade tip section, typically expressed in millimeters (mm). In practice, the execution entity can directly read the spanwise height range information from the attribute data of the three-dimensional model of the three-dimensional turbine blade.

[0023] The second step involves determining the blade root position information, blade tip position information, and at least one intermediate position information located between the blade root and blade tip, based on the aforementioned spanwise height range information. The blade root position information refers to the coordinate values ​​of the three-dimensional turbine blade root section in the spanwise direction, typically taking the minimum value of the spanwise height range information (e.g., 0 mm). The blade tip position information refers to the coordinate values ​​of the three-dimensional turbine blade tip section in the spanwise direction, typically taking the maximum value of the spanwise height range information (e.g., 120 mm). The intermediate position information refers to one or more spanwise coordinate values ​​located between the coordinate values ​​represented by the blade root position information and the coordinate values ​​represented by the blade tip position information, used to characterize the intermediate section positions other than the blade root and blade tip. In practice, the executing entity can determine each intermediate position information at equal intervals based on a preset total number of sections (e.g., 5 sections). As an example, the spanwise height range can be 0mm to 120mm, the total number of preset sections can be 5, then the blade root position information can be 0mm; the first intermediate position information can be 30mm, the second intermediate position information can be 60mm, the third intermediate position information can be 90mm, and the blade tip position information can be 120mm.

[0024] The third step involves taking a two-dimensional airfoil section at each of the three-dimensional turbine blade's root, tip, and intermediate position information, resulting in multiple two-dimensional airfoil sections distributed along the spanwise direction. A two-dimensional airfoil section refers to a thin, flat outline (or curved surface) cut perpendicular to the spanwise direction (i.e., parallel to the blade's chord plane) on the three-dimensional turbine blade, where the two-dimensional geometric outline intersects the three-dimensional shape. This outline is a closed curve and can be an airfoil line. The two-dimensional airfoil section contains the two-dimensional geometric shape information of the blade at that spanwise position, such as the coordinate sequence of the leading edge, trailing edge, suction surface curve, and pressure surface curve. Two-dimensional airfoil sections distributed along the spanwise direction refer to a set of two-dimensional airfoil sections taken at different spanwise heights. For each spanwise position coordinate obtained in the first and second steps (including coordinates corresponding to the blade root position information, coordinates corresponding to each intermediate position information, and coordinates corresponding to the blade tip position information), the following interception operations are performed: First, a cutting plane perpendicular to the spanwise direction is generated in three-dimensional space. The normal direction of this cutting plane is parallel to the spanwise direction, and the plane passes through the point corresponding to the current spanwise coordinate value. Second, the intersection line between this cutting plane and the three-dimensional turbine blade surface is calculated. The intersection line can be obtained through computer geometric algorithms (e.g., finding the intersection line between a triangular mesh and a plane, or finding the intersection line between a parametric surface and a plane). Finally, all discrete points on the intersection line are stored sequentially according to their adjacency order on the closed curve, forming the two-dimensional blade section data at that spanwise position, usually saved in the form of an ordered set of points (e.g., a set of (x,y) coordinate sequences) or a parametric curve (e.g., a spline curve). The planar graphic represented by the two-dimensional blade section data is determined as the two-dimensional blade section. The executing entity has obtained the blade root position information 0mm, the intermediate position information 30mm, 60mm, 90mm, and the blade tip position information 120mm. First, a cutting plane is generated at the spanwise coordinate of 0 mm, which is perpendicular to the spanwise direction (i.e., the plane equation is z=0). The main body calculates the intersection of this plane with the triangular mesh model of the 3D turbine blade, resulting in a closed curve containing 200 ordered points as the blade root section.

[0025] Step 102: For each of the multiple two-dimensional airfoil sections, perform the following processing: Step 1021: Divide the airfoil line of the two-dimensional airfoil section into five continuous airfoil line segments to obtain airfoil line segment information.

[0026] In some embodiments, the aforementioned executing entity can split the airfoil line of the two-dimensional airfoil section into five continuous airfoil line segments to obtain airfoil line segment information. In the process of using this technical solution to solve technical problems such as turbine blade related design analysis, for the application scenario—predicting the aerodynamic output performance data of turbine blades in power plants such as aero-engines and gas turbines, and generating turbine blade aerodynamic output performance distribution curves—the following technical problems often arise: When splitting the airfoil line of the two-dimensional airfoil section, the commonly used fixed curvature threshold method is difficult to accurately adapt to the complex shape characteristics of different regions of the airfoil. Because the curvature changes of different parts of the turbine blade airfoil line (such as the leading edge, trailing edge, and throat) vary significantly, a fixed threshold cannot be simultaneously applied to airfoils of varying thickness and curvature, leading to missed or false detections in the leading / trailing edge region. This results in inaccurate positioning of the five key points (leading edge upper / lower tangent point, throat point, trailing edge upper / lower tangent point), leading to poor accuracy in the generated turbine blade aerodynamic output performance distribution curve. The following requirements are necessary for this application scenario: It should be applicable to the positioning of (leading edge upper / lower tangent point, throat point, trailing edge upper / lower tangent point) for turbine blades with various types, different curvature distributions, thicknesses, and cambers. To address these technical challenges, we have decided to adopt the following solution: In some optional implementations of certain embodiments, the execution entity can obtain airfoil segment information by dividing the airfoil line of the two-dimensional airfoil section into five continuous airfoil line segments through the following steps: The first step involves discretizing the airfoil lines of the aforementioned two-dimensional airfoil cross-section to obtain the position information of multiple contour points arranged in an orderly manner along the circumference. The execution entity first obtains the parametric representation of the airfoil lines of the aforementioned two-dimensional airfoil cross-section (e.g., a spline curve or a series of densely packed original discrete points). Then, the execution entity sets a sampling step size (e.g., an arc length step size of 0.1 mm or a total of 200 points), starting from a starting point on the airfoil line (e.g., the most convex point of the leading edge), and sequentially calculates the coordinates of each sampling point along the circumferential direction of the airfoil line until it traverses the entire closed curve and returns to the starting point. Finally, the execution entity stores the coordinates of all these sampling points in order into a list, obtaining the position information of multiple contour points arranged in an orderly manner along the circumference. The aforementioned contour point position information can be the coordinates of a single sampling point on the airfoil line.

[0027] The second step is to determine the curvature value of the profile point represented by each of the multiple profile point position information in the airfoil as the profile point curvature value. In practice, for each profile point represented by the profile point position information, take one adjacent profile point corresponding to its preceding and following profile point position information, calculate the radius of the circle determined by these three profile points, and then take the reciprocal of this radius as the curvature value of the profile point in the airfoil. It should be noted that for the first and last adjacent profile points (because the airfoil is closed), the multiple profile point position information needs to be arranged in a certain order, considered as a ring, that is, the predecessor of the first profile point position information is the last profile point position information, and the successor of the last profile point position information is the first profile point position information.

[0028] The third step involves generating a dynamic threshold for the leaf shape based on the determined curvature values ​​of each contour point. In practice, the average curvature value of each contour point can be used as the first value. Then, the standard deviation of the curvature values ​​of each contour point can be used as the second value. Next, the product of the second value and a preset coefficient (e.g., k=1.5, which can be adjusted according to the complexity of the leaf shape) can be used as the third value. Finally, the sum of the third value and the first value can be used as the dynamic threshold for the leaf shape.

[0029] The fourth step involves generating leading-edge and trailing-edge contour point region information based on the aforementioned dynamic threshold for blade shape and the curvature values ​​of each contour point. The leading-edge contour point region information refers to the coordinate set of a group of contour points in the blade profile whose curvature values ​​exceed the dynamic threshold and are continuously distributed at the front of the blade profile. The trailing-edge contour point region information refers to the coordinate set of another group of contour points in the blade profile whose curvature values ​​exceed the dynamic threshold and are continuously distributed at the rear of the blade profile. In practice, the contour points corresponding to each contour point position information in the ordered arrangement can be traversed, and the curvature values ​​of the contour points corresponding to each contour point can be compared with the dynamic threshold for blade shape. Contour points with curvature values ​​greater than the dynamic threshold are marked, resulting in the first curvature marker point set. Next, the executing entity performs connected component analysis on the first curvature marker point set. Since the blade profile is closed, adjacent marked points (with consecutive indices or intervals less than a preset gap threshold, e.g., intervals ≤ 2 points) are grouped into the same continuous region. The aforementioned execution entity can divide all marked points into several continuous regions, each region consisting of a set of indexed, continuously connected contour points. Then, the execution entity calculates the average curvature value (i.e., the arithmetic mean of the curvature values ​​of all contour points within the region) and the average x-coordinate (i.e., the arithmetic mean of the x-coordinates of all contour points within the region) of each continuous region's contour points. To distinguish which region is the leading edge and which is the trailing edge, the execution entity uses the following rule: since the leading edge radius of a turbine blade is usually smaller than the trailing edge radius, the average curvature value of the leading edge region is greater than that of the trailing edge region. The execution entity determines the region with the largest average curvature value as the leading edge candidate region and the region with the second largest average curvature value as the trailing edge candidate region. If the average curvature values ​​of two regions are very close (e.g., the difference is less than a preset threshold, which may occur in cases of symmetrical blade profiles or special designs), the execution entity can compare the average x-coordinates of the two regions: the region with the smaller average x-coordinate (closer to the left of the blade profile line) is identified as the leading edge contour point region information, and the region with the larger average x-coordinate (closer to the right of the blade profile line) is identified as the trailing edge contour point region information. Finally, the execution entity stores the coordinate set of all contour points of the identified leading edge candidate region (or its corresponding trailing edge candidate region) as leading edge contour point region information and trailing edge contour point region information, respectively.

[0030] The fifth step involves performing least-squares circular arc fitting on the aforementioned leading edge profile point region information to obtain the center and radius of the leading edge arc. The coordinates of the point of tangency between the leading edge arc and the suction surface of the blade profile are determined as the upper tangency point location information. Simultaneously, the coordinates of the point of tangency between the leading edge arc and the pressure surface of the blade profile are determined as the lower tangency point location information. Least-squares circular arc fitting refers to determining an optimal circle by minimizing the fitting error (the sum of squared distances from each profile point to the fitted circle), thereby obtaining the center coordinates and radius. The suction surface refers to the side of the blade profile line with smaller curvature that bulges outward (usually the upper surface of the blade back). The pressure surface refers to the side of the blade profile line with smaller curvature that concaves inward (usually the lower surface of the blade base). The leading edge arc is the arc fitted in the leading edge region, approximating the geometry of the blade's leading edge. The upper tangency point is the smooth connection point between the leading edge arc and the suction surface curve, where the arc and the suction surface curve share a common tangent direction. The leading-edge lower tangent point is the smooth connection point between the leading-edge arc and the pressure surface curve. In practice, the actuator searches for the point on the suction surface curve portion of the airfoil (usually the upper half of the airfoil) that is closest to the fitted circle and satisfies the tangential continuity condition; this point is the leading-edge upper tangent point. Similarly, the leading-edge lower tangent point is obtained by searching on the pressure surface curve portion (lower half). The actuator stores the coordinates of these two tangent points as the leading-edge upper tangent point position information and the leading-edge lower tangent point position information, respectively.

[0031] Step 6: Perform least-squares circular arc fitting on the aforementioned trailing edge contour point region information to obtain the center and radius of the trailing edge arc. The coordinates of the point of tangency between the trailing edge arc and the suction surface of the aforementioned blade profile are determined as the upper tangency point location information. Simultaneously, the coordinates of the point of tangency between the trailing edge arc and the pressure surface of the aforementioned blade profile are determined as the lower tangency point location information. Here, the trailing edge arc refers to the arc fitted in the trailing edge region, which approximates the geometry of the blade's trailing edge. The upper tangency point is the smooth connection point between the trailing edge arc and the suction surface curve. The lower tangency point is the smooth connection point between the trailing edge arc and the pressure surface curve.

[0032] Step 7: Obtain the pitch and installation angle of the blade cascade containing the three-dimensional turbine blade, and translate the pressure surface curve of the two-dimensional airfoil section circumferentially by one pitch to generate virtual pressure surface curves for adjacent turbine blades. The pitch refers to the circumferential distance between corresponding points (e.g., leading edge points) of two adjacent blades, usually measured in millimeters (mm). The installation angle is the angle between the blade chord and the circumferential (or axial) direction of the cascade, usually measured in degrees (°). The pressure surface curve is the segment of the curve corresponding to the pressure surface in the two-dimensional airfoil section (usually the lower half of the airfoil). Circumferential translation refers to moving the pressure surface curve along the circumferential direction (perpendicular to the axial direction) of the cascade by one pitch. The virtual pressure surface curve is the curve simulating the position of the pressure surface of adjacent blades, obtained by translating the pressure surface curve of the current blade. In practice, the execution entity reads the pitch value and installation angle from the cascade design parameter database. Then, the execution entity extracts the pressure surface curve of the current two-dimensional airfoil section (i.e., the curve segment from the leading edge incision point to the trailing edge incision point) and discretizes it into a series of ordered point coordinates. Next, the execution entity determines the circumferential translation direction: in a planar blade cascade, this is usually a horizontal direction perpendicular to the axial direction (e.g., the y-axis direction). The execution entity translates the coordinates of each point on the pressure surface curve along the circumferential direction by a distance of one grid pitch, obtaining the coordinates of the translated point (assuming the circumferential direction is the y-axis). All translated points are connected in their original order to form the virtual pressure surface curves of adjacent turbine blades. For example, the grid pitch read by the execution entity can be 12, and the installation angle can be 30°. The point (10, -5) on the current pressure surface curve is translated along the y-axis by a grid pitch of 12, resulting in (10, 7), and so on to generate virtual pressure surface curves.

[0033] Step 8 involves discretizing the suction surface curve of the airfoil in the 2D airfoil section to obtain the coordinates of each sampling point. In practice, the execution entity extracts the suction surface curve of the current 2D airfoil section (i.e., the curve segment from the leading edge tangent point to the trailing edge tangent point) and parameterizes it (e.g., a spline curve). Then, the execution entity sets the sampling step size (e.g., an arc length step of 0.2 mm) and, starting from the starting point of the suction surface curve (leading edge tangent point), calculates the coordinates of each sampling point sequentially along the curve until the ending point (tailing edge tangent point). Finally, the execution entity stores the coordinates of all sampling points in a list to obtain the coordinates of each sampling point.

[0034] The ninth step is to determine the throat width as the shortest distance from each sampling point's coordinates to the virtual pressure surface curve. This shortest distance can be the shortest Euclidean distance from the point represented by the sampling point's coordinates to the virtual pressure surface curve.

[0035] Step 10: Generate throat point location information based on the width of each throat. In practice, the coordinates of the sampling point corresponding to the throat width with the smallest value among all throat widths can be determined as the throat point location information.

[0036] Step 11: The above-mentioned leading edge upper tangent point location information, the above-mentioned leading edge lower tangent point location information, the above-mentioned throat point location information, the above-mentioned trailing edge upper tangent point location information, and the above-mentioned trailing edge lower tangent point location information are determined as five key point location information.

[0037] Step 12: Arrange the five key point location information in a clockwise direction according to the aforementioned blade profile line to obtain the key point location information sequence. The circumferential order refers to the order in which the key points are passed along the circumferential direction of the blade profile line (usually clockwise). The key point location information sequence is formed by arranging the five key points in a circumferential order, with the leading edge upper tangent point location information as the first and the trailing edge lower tangent point location information as the last (e.g., the key point location information sequence could be {leading edge lower tangent point location information, the aforementioned throat point location information, the aforementioned trailing edge upper tangent point location information, and the aforementioned trailing edge lower tangent point location information}).

[0038] Step 11: Based on the aforementioned keypoint location information sequence, connect adjacent keypoints sequentially to divide the leaf-shaped line into five connected leaf-shaped line segments, generating sub-information for each segment. The sub-information for each leaf-shaped line segment can represent a leaf-shaped line segment. Two adjacent keypoints refer to two points represented by keypoint location information that are adjacent in the keypoint location information sequence, including the location information of the last and first keypoints in the sequence. A leaf-shaped line segment refers to the leaf-shaped line arc segment located between two adjacent keypoints. The sub-information for each leaf-shaped line segment can be its geometric data. This geometric data can include the coordinates of the segment's start and end points, as well as the coordinate sequence of all contour points between the start and end points.

[0039] The twelfth step is to define the determined leaf-shaped line segment sub-information as the aforementioned leaf-shaped line segment information.

[0040] Steps 1022 to 1025, step 103, and related contents of the above technical solution constitute an inventive point of this disclosure, solving the technical problem of "poor accuracy of turbine blade aerodynamic output performance distribution curve". Factors leading to poor accuracy of turbine blade aerodynamic output performance distribution curves are often as follows: When splitting the airfoil profile in a two-dimensional airfoil section, the commonly used fixed curvature threshold is difficult to accurately adapt to the complex shape characteristics of different regions of the airfoil. Because the curvature changes of different parts of the turbine blade airfoil (such as the leading edge, trailing edge, and throat) vary significantly, a fixed threshold cannot be simultaneously applied to airfoils of varying thickness and curvature, leading to missed or false detections in the leading / tailing edge region. This results in inaccurate positioning of the five key points (leading edge upper / lower tangent point, throat point, trailing edge upper / lower tangent point), thus leading to poor accuracy of the generated turbine blade aerodynamic output performance distribution curve. Solving these factors can improve the accuracy of turbine blade aerodynamic output performance distribution curves. To achieve this effect, firstly, the airfoil lines of the aforementioned two-dimensional airfoil cross-section are discretized and sampled to obtain the position information of multiple contour points arranged in an orderly manner along the circumference. This converts the continuous airfoil lines into a discrete set of points, facilitating subsequent numerical calculations of curvature. Then, the curvature value of each contour point position information within the airfoil line is determined as the contour point curvature value. This yields the degree of curvature at each point, providing a basis for distinguishing between high-curvature regions (leading edge, trailing edge) and low-curvature regions (suction surface, pressure surface center). Next, based on the determined curvature values ​​of each contour point, a dynamic threshold for the airfoil shape is generated. This dynamic threshold is adaptively calculated based on the mean and standard deviation of the current airfoil curvature distribution, automatically adapting to the overall curvature level of different airfoils and solving the problem that a fixed threshold cannot simultaneously adapt to both thick and thin airfoils. Finally, based on the aforementioned dynamic threshold for the airfoil shape and the aforementioned curvature values ​​of each contour point, leading edge contour point region information and trailing edge contour point region information are generated. Therefore, high curvature points are selected by dynamic thresholding, and continuous regions corresponding to the leading and trailing edges are separated using connected component analysis, avoiding missed or false detections. Then, least-squares circular arc fitting is performed on the aforementioned leading edge contour point region information to obtain the center and radius of the leading edge arc. The coordinates of the tangent point between the leading edge arc and the suction surface of the aforementioned airfoil are determined as the upper tangent point position information of the leading edge, while the coordinates of the tangent point between the leading edge arc and the pressure surface of the aforementioned airfoil are determined as the lower tangent point position information of the leading edge. Similarly, circular arc fitting is performed on the trailing edge to obtain the upper / lower tangent points of the trailing edge. Thus, the smooth connection points between the leading and trailing edges and the airfoil curves on both sides are accurately calculated through circular arc fitting. These tangent point coordinates are the key boundaries for subsequent airfoil segmentation. Afterwards, the grating pitch and installation angle of the blade cascade containing the aforementioned three-dimensional turbine blade are obtained, and the pressure surface curve of the aforementioned two-dimensional airfoil section is shifted circumferentially by one grating pitch to generate virtual pressure surface curves for adjacent turbine blades.Therefore, the pressure surfaces of adjacent blades were periodically simulated using the blade cascade, providing a geometric reference for determining the throat point. Then, the suction surface curve of the airfoil in the two-dimensional airfoil section was discretized to obtain the coordinates of each sampling point. Next, the shortest distance from each sampling point's coordinates to the virtual pressure surface curve was determined as the throat width, and throat point location information was generated based on each throat width (taking the sampling point corresponding to the minimum throat width). This automatically determined the throat point at the narrowest point of the blade cascade passage, eliminating the need for manual annotation. The aforementioned leading edge upper tangent point location information, leading edge lower tangent point location information, throat point location information, trailing edge upper tangent point location information, and trailing edge lower tangent point location information were determined as five key point location information, arranged in circumferential order according to the airfoil, resulting in a key point location information sequence. Then, based on this sequence, adjacent key points were sequentially connected to divide the airfoil into five connected airfoil segments to generate sub-information of each airfoil segment, which was then determined as airfoil segment information. Thus, five relatively accurate airfoil segments (leading edge segment, pressure surface front segment, pressure surface rear segment, trailing edge segment, and suction surface segment) were obtained, each corresponding to a graph node. The aforementioned dynamic thresholding, arc fitting, and translation-generated virtual pressure surface steps work together to achieve fully automatic key point detection and airfoil segmentation for different airfoils without manual intervention. Combining steps 1022 to 1025 and step 103, geometric feature extraction processing is performed on the aforementioned airfoil segment information to obtain geometric contour feature information. The incoming aerodynamic operating parameters data of the aforementioned three-dimensional turbine blade are obtained. Based on the geometric contour feature information and the aforementioned incoming aerodynamic operating parameters data, aerodynamic geometric feature connection graph data corresponding to the aforementioned two-dimensional airfoil cross-section is generated. Thus, the precise geometric segmentation and operating parameters are fused into a graph structure. The aforementioned aerodynamic geometric feature connection graph data is input into a pre-trained aerodynamic performance prediction model to obtain aerodynamic output performance data. Because the preceding splitting step provides an accurate graph structure, the model can learn the true geometry-performance mapping, reducing output errors and thus improving the accuracy of the subsequently generated turbine blade aerodynamic output performance distribution curve. Furthermore, by employing steps such as dynamic threshold adaptive segmentation, least-squares circular arc fitting for accurate tangent point calculation, and automatic throat point detection based on grid pitch translation, high-precision blade profile splitting that adapts to different blade types without manual intervention is achieved. This ensures that the aerodynamic geometry feature connection graph truly reflects the geometric topology, improving the accuracy of the aerodynamic performance prediction model output and consequently enhancing the accuracy of the turbine blade aerodynamic output performance distribution curve.

[0041] Step 1022: Perform geometric feature extraction processing on the leaf-shaped line segment information to obtain geometric contour feature information.

[0042] In some embodiments, the execution entity may perform geometric feature extraction processing on the leaf-shaped line segment information to obtain geometric contour feature information.

[0043] In some optional implementations of certain embodiments, the aforementioned execution entity may perform geometric feature extraction processing on the aforementioned leaf-shaped line segment information through the following steps to obtain geometric contour feature information: The first step is to perform Bézier curve fitting on each of the sub-information of the blade profile line segment included in the above-mentioned blade profile line segment information to obtain Bézier curve data representing the Bézier curve. In practice, a third-order Bézier curve (i.e., a cubic Bézier curve with four control points) can be used to fit each sub-information of the blade profile line segment information to obtain the two-dimensional coordinates of the four control points as the Bézier curve data.

[0044] The second step is to determine the obtained Bézier curve data as geometric contour feature information, wherein the Bézier curve data in the above Bézier curve data corresponds one-to-one with the leaf-shaped line segments in the five continuous leaf-shaped line segments.

[0045] Step 1023: Obtain the incoming aerodynamic parameters of the three-dimensional turbine blades.

[0046] In some embodiments, the aforementioned executing entity can acquire the incoming aerodynamic operating parameters data of the three-dimensional turbine blade. These incoming aerodynamic operating parameters data can describe the aerodynamic operating parameters when the airflow enters the turbine blade. These aerodynamic operating parameters can include the incoming flow angle of attack, the inlet Mach number, and the Reynolds number. The incoming flow angle of attack refers to the angle between the airflow direction and the blade chord (it determines the angle at which the airflow impacts the blade, directly affecting the pressure distribution and loss characteristics on the blade surface).

[0047] Step 1024: Based on the geometric profile feature information and the incoming aerodynamic operating condition parameter data, generate aerodynamic geometric feature connection diagram data corresponding to the two-dimensional airfoil section.

[0048] In some embodiments, the aforementioned execution entity may generate aerodynamic geometric feature connection diagram data corresponding to the aforementioned two-dimensional airfoil section based on geometric contour feature information and the aforementioned incoming aerodynamic operating condition parameter data.

[0049] In some optional implementations of certain embodiments, the aforementioned execution entity can generate aerodynamic geometric feature connection diagram data corresponding to the aforementioned two-dimensional airfoil section by following the steps of: based on geometric profile feature information and the aforementioned incoming aerodynamic operating condition parameter data. The first step is to identify each Bézier curve data, which includes the geometric contour feature information, as a graph node in the graph structure.

[0050] The second step is to perform the following steps for each of the graph nodes mentioned above: The first sub-step is to convert the coordinates of each control point of the Bézier curve represented by the above graph nodes into vectors as geometric feature vectors.

[0051] The second sub-step involves converting the aforementioned incoming aerodynamic operating condition parameter data into a vector as the operating condition feature vector.

[0052] The third sub-step involves concatenating the aforementioned geometric feature vector and the aforementioned working condition feature vector to obtain the aerodynamic geometric feature vector corresponding to the aforementioned graph nodes.

[0053] The fourth sub-step involves binding the aerodynamic geometry feature vector to the attribute information of the aforementioned graph node. Here, attribute information can refer to data associated with the graph node that describes its characteristics.

[0054] The third step involves connecting the aforementioned graph nodes according to the connection order of their corresponding five consecutive airfoil segments, constructing an annular undirected graph corresponding to the aforementioned two-dimensional airfoil cross-section as aerodynamic geometric feature connection graph data. Each graph node carries an aerodynamic geometric feature vector. It should be noted that each Bézier curve data is mapped to a graph node, resulting in a total of five graph nodes, corresponding to the leading edge segment (the airfoil segment between the point where the leading edge upper tangent point is located and the point where the leading edge lower tangent point is located), the pressure surface segment (the airfoil segment between the point where the leading edge lower tangent point is located and the point where the throat point is located), the pressure surface trailing segment (the airfoil segment between the point where the throat point is located and the point where the trailing edge lower tangent point is located), the trailing edge segment (the airfoil segment between the point where the trailing edge lower tangent point is located and the point where the trailing edge upper tangent point is located), and the suction surface segment (the airfoil segment between the point where the trailing edge upper tangent point is located and the point where the leading edge upper tangent point is located).

[0055] Step 1025: Input the aerodynamic geometry feature connection diagram data into the pre-trained aerodynamic performance prediction model to obtain aerodynamic output performance data.

[0056] In some embodiments, the aforementioned execution entity can input the aerodynamic geometry connection graph data into a pre-trained aerodynamic performance prediction model to obtain aerodynamic output performance data. The aerodynamic performance prediction model can be a graph Transformer model that takes the aerodynamic geometry connection graph data as input and the aerodynamic output performance data as output.

[0057] In applying this technical solution to address technical issues related to turbine blade design and analysis, the following technical challenges often arise for the application scenarios: predicting the aerodynamic output performance data of turbine blades in power plants such as aero-engines and gas turbines, and generating aerodynamic output performance distribution curves of turbine blades. Obtaining blade aerodynamic performance data through high-fidelity 3D CFD simulation takes several days to weeks, which cannot meet the need for rapid iteration across multiple schemes. Therefore, this technical solution uses an aerodynamic performance prediction model to replace CFD simulation. However, in the actual construction of this model, new technical problems arise: traditional graph neural networks struggle to simultaneously consider the circumferential order of nodes when processing aerodynamic geometric feature connection graph data; the model cannot distinguish nodes at different positions, resulting in low feature representation discrimination. Furthermore, the use of full graph attention increases computational complexity, leading to wasted computational resources. Simultaneously, using a single pooling method (average pooling only or max pooling only) can result in the loss of extreme values ​​or overall distribution information, leading to incomplete graph-level global features and consequently, poor accuracy in generating turbine blade aerodynamic output performance distribution curves. To address the following requirements for this application scenario: the model should be able to perceive the circumferential order of nodes on the leaf-shaped line to distinguish nodes at different positions, such as the leading edge and trailing edge; it should capture limited long-range dependencies (such as the coupling between the leading edge and the throat) while avoiding the quadratic computational complexity of full-graph attention. To address these technical challenges, we have decided to adopt the following solution: In some optional implementations of certain embodiments, the aforementioned execution entity can input the aforementioned aerodynamic geometry feature connection diagram data into a pre-trained aerodynamic performance prediction model through the following steps to obtain aerodynamic output performance data: The first step involves inputting the geometric feature vectors of each graph node in the aforementioned aerodynamic geometry feature connection graph data, along with the aerodynamic geometry feature connection graph data itself, into the aforementioned aerodynamic performance prediction model. This aerodynamic performance prediction model includes an input layer, an input embedding layer, a multi-head self-attention module, a residual normalization module, a graph adaptive pooling layer, a global readout layer, and an aerodynamic output performance prediction layer.

[0058] The second step involves configuring the input layer to transform the received geometric feature vectors into geometric feature matrices and to perform feature extraction processing on the received aerodynamic geometry connection graph data to obtain an edge connectivity matrix. Specifically, the input layer can receive various geometric feature vectors and aerodynamic geometry connection graph data, stack the geometric feature vectors into a geometric feature matrix, and extract the edge connectivity matrix from the graph data. The geometric feature matrix can be a two-dimensional matrix formed by stacking the geometric feature vectors of all graph nodes in node order (e.g., the shape of the two-dimensional matrix can be [number of nodes, geometric feature dimension]). The edge connectivity matrix can be an adjacency matrix describing the connection relationships between graph nodes in the graph structure.

[0059] The third step involves inputting the aforementioned geometric feature matrix and edge connection matrix into the aforementioned input embedding layer to obtain the node embedding matrix. The input embedding layer can perform a linear transformation on the geometric feature matrix and generate learnable positional codes based on the circumferential order of nodes implicit in the edge connection matrix. The two are then added together to obtain the node embedding matrix.

[0060] The fourth step involves inputting the node embedding matrix into the multi-head self-attention module to obtain graph node attention aggregation feature information. This multi-head self-attention module performs multi-head self-attention calculations on the node embedding matrix, using the edge connection matrix as an attention mask (allowing only interactions between neighbors and nodes with a circumferential distance ≤ 2), and outputs graph node attention aggregation feature information. This graph node attention aggregation feature information is a vector representing the features of a graph node and its neighboring graph nodes (including connected neighbor nodes and nodes with a distance not exceeding 2) after feature aggregation through the multi-head self-attention mechanism.

[0061] The fifth step involves inputting the attention aggregation feature information of the graph nodes into the residual normalization module to obtain the feedforward nonlinear mapping feature information. Specifically, the residual normalization module can first perform layer normalization on the attention output, then pass it through the feedforward neural network, perform residual connections and a second layer normalization, and output the feedforward nonlinear mapping feature information.

[0062] The sixth step involves inputting the aforementioned feedforward nonlinear mapping feature information into the aforementioned graph adaptive pooling layer to perform soft clustering on the feedforward nonlinear mapping feature information, thereby obtaining soft clustering compressed graph feature information. The aforementioned graph adaptive pooling layer can be a graph pooling layer that performs soft clustering on the feedforward nonlinear mapping feature information, merges adjacent nodes based on node feature similarity, and outputs coarsened soft clustering compressed graph feature information.

[0063] Step 7: Input the soft clustering compressed map feature information into the global readout layer. The global readout layer includes parallel max-pooling branches, average-pooling branches, and a concatenation layer. The max-pooling branch performs a first pooling process on the soft clustering compressed map feature information to obtain a max-pooling vector. The max-pooling branch can be a max-pooling layer. The average-pooling branch can be an average-pooling layer. The max-pooling vector can be the vector obtained after max-pooling the soft clustering compressed map feature information.

[0064] Step 8: The average pooling branch performs a second pooling process on the soft clustering compressed graph feature information to obtain an average pooling vector. This average pooling vector can be the vector obtained after performing average pooling on the soft clustering compressed graph feature information.

[0065] In the ninth step, the concatenation layer concatenates the max-pooling vector and the average-pooling vector to obtain a graph-level global feature vector. This graph-level global feature vector can be the vector obtained by concatenating the max-pooling vector and the average-pooling vector.

[0066] Step 10: Input the aforementioned graph-level global feature vector into the aforementioned aerodynamic output performance prediction layer to obtain aerodynamic output performance data. The aforementioned aerodynamic output performance prediction layer can be a multilayer perceptron that takes the graph-level global feature vector as input and outputs the aerodynamic output performance data. The aforementioned aerodynamic output performance data includes the total pressure loss coefficient (Cpt, dimensionless, typically ranging from 0.01 to 0.15), the exit Mach number, and the exit airflow angle. The aforementioned exit Mach number can refer to the Mach number when the airflow leaves the turbine blade exit section. The aforementioned exit airflow angle can refer to the angle between the flow direction when the airflow leaves the turbine blade exit section and the blade chord direction (or axial direction).

[0067] The above technical solution, combined with step 103 and related content, serves as an inventive point of this disclosure, solving the technical problem of "wasting computational resources and poor accuracy of turbine blade aerodynamic output performance distribution curves." Factors leading to wasted computational resources and poor accuracy of turbine blade aerodynamic output performance distribution curves are often as follows: Traditional graph neural networks, when processing aerodynamic geometric feature connection graph data, struggle to simultaneously consider the circumferential order perception of nodes, resulting in the model's inability to distinguish nodes at different positions and low feature representation discriminability. Furthermore, the use of full graph attention increases computational complexity, leading to wasted computational resources. Simultaneously, using a single pooling method (average pooling only or max pooling only) can result in the loss of extreme values ​​or overall distribution information, leading to incomplete graph-level global features and consequently, poor accuracy of the generated turbine blade aerodynamic output performance distribution curves. Solving these factors can reduce wasted computational resources and improve the accuracy of turbine blade aerodynamic output performance distribution curves. To achieve this effect, firstly, the geometric feature vectors of each graph node in the aforementioned aerodynamic geometry feature connection graph data, along with the aerodynamic geometry feature connection graph data itself, are input into the aforementioned aerodynamic performance prediction model. This aerodynamic performance prediction model includes an input layer, an input embedding layer, a multi-head self-attention module, a residual normalization module, a graph adaptive pooling layer, a global readout layer, and an aerodynamic output performance prediction layer. Then, the input layer is configured to transform the received geometric feature vectors into geometric feature matrices and perform feature extraction processing on the received aerodynamic geometry feature connection graph data to obtain an edge connection matrix. This yields matrix-form data, namely the geometric feature matrix and the edge connection matrix, which are easily processed by neural networks. Next, the geometric feature matrix and the edge connection matrix are input into the input embedding layer to obtain a node embedding matrix. The input embedding layer then performs a linear transformation on the geometric feature matrix and generates learnable positional codes based on the circumferential order of nodes implicit in the edge connection matrix, and the two are then added together. Therefore, the embedding features of each node not only include its geometric shape information but also incorporate its circumferential position information on the airfoil (such as the leading edge segment and the pressure front segment), enabling the model to distinguish nodes at different positions and solving the problem of low feature representation discriminability. Next, the node embedding matrix is ​​input into the multi-head self-attention module to obtain graph node attention aggregation feature information. This captures non-adjacent but aerodynamically coupled node pairs (such as the leading edge and throat) while avoiding the computational complexity of full-graph attention, reducing computational resource consumption, and preserving the correlation of limited long-range dependencies. Then, the graph node attention aggregation feature information is input into the residual normalization module to obtain feedforward nonlinear mapping feature information. Finally, the feedforward nonlinear mapping feature information is input into the graph adaptive pooling layer to perform soft clustering processing, obtaining soft-clustered compressed graph feature information.Therefore, adjacent nodes can be soft-clustered and merged based on node feature similarity, reducing the number of nodes layer by layer and achieving multi-scale feature abstraction. Then, the feature information of the soft-cluster compressed graph is input to the global readout layer, which includes parallel max-pooling branches, average-pooling branches, and a concatenation layer. The max-pooling branch performs a first pooling process on the soft-cluster compressed graph feature information to obtain a max-pooling vector. The average-pooling branch performs a second pooling process on the soft-cluster compressed graph feature information to obtain an average-pooling vector. The concatenation layer concatenates the max-pooling vector and the average-pooling vector to obtain a graph-level global feature vector. Thus, the graph-level global feature vector simultaneously contains the local extrema of node features (such as peak loss) and the overall distribution (such as average loss), solving the problem of information loss in a single pooling method and making the features more comprehensive. Next, the graph-level global feature vector is input to the aerodynamic output performance prediction layer to obtain aerodynamic output performance data. Finally, combining with step 103, based on the generated aerodynamic output performance data, the aerodynamic output performance distribution curve of the aforementioned three-dimensional turbine blade is generated and displayed. Because a graph adaptive pooling layer is used to perform soft clustering on the feedforward nonlinear mapping feature information, instead of performing attention calculations on all nodes in the entire graph, similar nodes are aggregated together through soft clustering, reducing the number of node pairs that need to be processed, thereby reducing computational complexity and minimizing the waste of computational resources. Furthermore, the multi-head self-attention mechanism can simultaneously focus on information from different locations, aggregating node features from multiple perspectives, allowing the model to better capture the relationships and feature differences between nodes, thus improving the ability to distinguish nodes at different locations and enhancing the discriminative power of feature representation. Simultaneously, combining max and average pooling to obtain comprehensive graph-level global features (max pooling branches can retain the extreme value information of features, while average pooling branches can reflect the overall distribution information of features) further improves the accuracy of the aerodynamic output performance data, thereby improving the accuracy of the turbine blade aerodynamic output performance distribution curve.

[0068] Optionally, the above aerodynamic performance prediction model can be trained through the following steps: The first step is to obtain a sample set, wherein the samples in the sample set include sample aerodynamic geometry feature connection diagram data and sample aerodynamic output performance data corresponding to the sample aerodynamic geometry feature connection diagram data; The second step involves performing the following training steps based on the sample set: The first sub-step involves inputting the aerodynamic geometry feature connection graph data of at least one sample in the sample set into an initial neural network to obtain the predicted aerodynamic output performance data corresponding to each of the at least one sample. The initial neural network can be an untrained graph Transformer model.

[0069] The second sub-step involves comparing the predicted aerodynamic output performance data for each sample in the at least one set of samples with the corresponding sample aerodynamic output performance data. In practice, the execution entity can use the cross-entropy loss function to determine the difference between the predicted aerodynamic output performance data for each sample in the at least one set of samples and the corresponding sample aerodynamic output performance data.

[0070] The third sub-step involves determining whether the initial neural network has achieved a preset optimization objective based on the comparison results. This optimization objective can be that the difference between the predicted aerodynamic output performance data and the corresponding sample aerodynamic output performance data is less than a preset threshold.

[0071] The fourth sub-step is to use the initial neural network as the trained aerodynamic performance prediction model in response to the determination that the initial neural network has achieved the above optimization objective.

[0072] The fifth sub-step involves adjusting the network parameters of the initial neural network in response to the determination that the initial neural network has not achieved the above optimization objective. A sample set is then created using unused samples, and the adjusted initial neural network is used as the new initial neural network. The training steps described above are then executed again. As an example, the back propagation algorithm (BP algorithm) and gradient descent methods (such as mini-batch gradient descent) can be used to adjust the network parameters of the initial neural network.

[0073] Step 103: Based on the generated aerodynamic output performance data, generate and display the three-dimensional turbine blade aerodynamic output performance distribution curve.

[0074] In some embodiments, the aforementioned executing entity can generate and display the turbine blade aerodynamic output performance distribution curve of the three-dimensional turbine blade based on the generated aerodynamic output performance data. Each aerodynamic output performance data includes an outlet aerodynamic parameter, and each aerodynamic output performance data corresponds to one of the following positional information: blade root position information, blade tip position information, and at least one intermediate positional information located between the blade root and blade tip.

[0075] In some optional implementations of certain embodiments, the aforementioned execution entity may generate and display the turbine blade aerodynamic output performance distribution curve of the aforementioned three-dimensional turbine blade based on the generated aerodynamic output performance data through the following steps: The first step is to perform the following steps for each aerodynamic output performance data point: The first sub-step involves determining the target position information as one of the following: the blade root position information, the blade tip position information, and at least one intermediate position information located between the blade root and the blade tip, that corresponds to the aerodynamic output performance data. The target position information refers to the spanwise position coordinate corresponding to the aerodynamic output performance data (for example, for a blade root section, the target position information is the blade root position information; for a 1 / 4 blade height section, the target position information is the intermediate position information at 30mm).

[0076] The second sub-step generates spanwise position coordinates based on the aforementioned target position information. The target position information refers to the actual spanwise height value of the two-dimensional airfoil section corresponding to the current aerodynamic output performance data on the three-dimensional turbine blade. For example, the blade root position information is 0mm, a certain intermediate position is 60mm, and the blade tip position is 120mm. The spanwise position coordinates are obtained by converting the actual spanwise height values ​​into values ​​suitable for the horizontal axis of the graph. Normalization is typically used, so that the coordinates at the blade root are 0, the coordinates at the blade tip are 1, and the intermediate positions are linearly mapped to the 0-1 range. The spanwise position coordinates are used as the horizontal axis of performance data points in subsequent steps to reflect the relative positions of different sections in the blade height direction.

[0077] The third sub-step involves correlating the aerodynamic output performance data with the spanwise position coordinates to obtain performance data points. In practice, firstly, the total pressure loss coefficient included in the aerodynamic output performance data can be used as the ordinate, and the spanwise position coordinates as the abscissa to form a two-dimensional coordinate point, which is then designated as the first performance data point. Next, the exit Mach number included in the aerodynamic output performance data can be used as the ordinate, and the spanwise position coordinates as the abscissa to form a two-dimensional coordinate point, which is then designated as the second performance data point. Finally, the exit airflow angle included in the aerodynamic output performance data can be used as the ordinate, and the spanwise position coordinates as the abscissa to form a two-dimensional coordinate point, which is then designated as the third performance data point. For example, the spanwise position coordinate can be 0.5, and the aerodynamic output performance data are: total pressure loss coefficient: 0.042, exit Mach number: 0.85, exit airflow angle: 12.3 degrees. Then, the first performance data point can be (0.5, 0.042), and the second performance data point can be (0.5, 0.85). The third performance data point can be (0.5, 12.3).

[0078] The second step involves interpolating and fitting the obtained performance data points to generate at least one distribution curve showing the continuous variation of aerodynamic output performance parameters along the spanwise direction. In practice, the aforementioned execution entity can define the first performance data points included in the performance data points as the first performance data point set. It can also define the second performance data points included in the performance data points as the second performance data point set. Furthermore, it can define the third performance data points included in the performance data points as the third performance data point set. For the first performance data point set, the execution entity calls a numerical computation library (e.g., the CubicSpline function in SciPy) to input a list of horizontal and vertical axes and output an interpolation function. Then, the execution entity samples at spanwise positions 0 to 1 with a small step size (e.g., 0.01), calculates the total pressure loss coefficient value corresponding to each sampling point using the interpolation function, and connects these sampling points with smooth line segments to form a distribution curve showing the continuous variation of the total pressure loss coefficient along the spanwise direction. For the second performance data point set, the execution entity can use a cubic spline interpolation method to generate the outlet Mach number distribution curve. Similarly, for the third performance data point set, the aforementioned execution entity can use the cubic spline interpolation method to generate the outlet airflow angular distribution curve.

[0079] The third step involves rendering at least one of the aforementioned distribution curves into a turbine blade aerodynamic output performance distribution curve diagram and outputting it to a preset display device for display. In practice, firstly, for each of the aforementioned at least one distribution curve, the executing entity can use a graphics library (such as Matplotlib or Chart.js) to draw the distribution curve diagram. Then, the executing entity can stitch together at least one distribution curve diagram (e.g., stitching three diagrams vertically or horizontally) to obtain the turbine blade aerodynamic output performance distribution curve diagram. The preset display device refers to the physical display device connected to the executing entity, such as a computer monitor, industrial tablet PC, or large-screen display system. As an example, specifically, for each distribution curve, the executing entity can call a graphics library (such as Python's Matplotlib or JavaScript's Chart.js) to create a subplot. Set the horizontal axis range to [0,1] and the label to "Relative Blade Height"; set the vertical axis range (total pressure loss coefficient: 0.02~0.06, exit Mach number: 0.7~0.95, exit airflow angle: 5°~20°) and label (e.g., "Total Pressure Loss Coefficient Cpt") according to the curve type. Input the discrete points of the curve (abscissa list, ordinate list) into the plot function, specify the curve color (red, blue, green) and line width, and draw a continuous curve. Add a legend and grid lines. Next, the execution body vertically stacks the three subplots (sharing the horizontal axis), uses the subplots function of the graphics library to set nrows=3, ncols=1, sharex=True, adjusts the spacing between the subplots, and adds the overall title "Three-Dimensional Turbine Blade Aerodynamic Output Performance Distribution Curve" to obtain the complete chart. Finally, the execution body calls the show method of the graphics library (or opens after savefig) to render the canvas as an image and sends it to the frame buffer of the preset display device so that the curve is displayed on the screen. The above-described embodiments of this disclosure have the following beneficial effects: the turbine three-dimensional blade aerodynamic parameter calculation method based on graph neural networks and radial physical information embedding in some embodiments of this disclosure shortens the aerodynamic output performance prediction cycle and reduces the consumption of computing resources. Specifically, the reason for the long aerodynamic output performance prediction cycle and high computing resource consumption is that a complete spanwise performance distribution curve usually requires data points at multiple spanwise positions such as the blade root, blade mid-section, and blade tip. Through high-fidelity three-dimensional computational fluid dynamics (CFD) simulation, each data point needs to be obtained through an independent CFD solution. If multiple incoming flow conditions (such as different angles of attack) are considered, the number of required data points increases exponentially, and the accumulated time cost and resource consumption of multiple CFD simulations are large, resulting in a long aerodynamic output performance prediction cycle and high computing resource consumption, which makes it difficult to meet the needs of rapid iteration of multiple schemes in engineering design. Based on this, the turbine three-dimensional blade aerodynamic parameter calculation method based on graph neural networks and radial physical information embedding in some embodiments of this disclosure first selects multiple two-dimensional airfoil sections along the pre-created three-dimensional turbine blade spanwise direction. Therefore, the three-dimensional blade can be decomposed into a finite number of representative two-dimensional cross-sections, avoiding the high-complexity modeling of the entire three-dimensional blade. Then, for each of the aforementioned two-dimensional airfoil cross-sections, the following processing is performed: the airfoil line of the cross-section is split into five continuous airfoil segments to obtain airfoil segment information. This simplifies the complex airfoil profile into airfoil segment information. Next, geometric feature extraction processing is performed on the airfoil segment information to obtain geometric contour feature information. This allows the extraction of key parameters (such as the coordinates of Bézier curve control points) that uniquely characterize the shape of each airfoil segment. Then, the incoming aerodynamic operating parameters of the three-dimensional turbine blade are obtained. Finally, based on the geometric contour feature information and the incoming aerodynamic operating parameters, aerodynamic geometric feature connection diagram data corresponding to the aforementioned two-dimensional airfoil cross-sections is generated. Therefore, the geometric and operating condition information of each cross-section is fused into a graph structure. Each graph node carries the geometric features of the corresponding airfoil segment and shared operating condition features. The graph edges are constructed according to the original connection order of the airfoil segments, completely preserving the spatial adjacency relationships within the cross-section. Then, the above aerodynamic geometric feature connection graph data is input into a pre-trained aerodynamic performance prediction model to obtain aerodynamic output performance data. Thus, by learning the mapping relationship from airfoil geometry and incoming flow conditions to outlet aerodynamic performance through an aerodynamic performance prediction model, the aerodynamic output performance data of this two-dimensional cross-section can be predicted without performing any CFD solution on this cross-section. Only one model forward inference (millisecond level) is required, and the model parameters are fixed after training, eliminating the need for repeated mesh generation, numerical iteration, post-processing, and other operations. Therefore, the time for predicting aerodynamic output performance data can be reduced from several days to milliseconds, while also reducing CPU / GPU resource consumption.Based on the generated aerodynamic output performance data, the aerodynamic output performance distribution curves of the aforementioned three-dimensional turbine blades are generated and displayed. Finally, the prediction results of multiple sections can be fused along the spanwise into a continuous curve and displayed. Because a multi-section decomposition strategy of representing three dimensions with two dimensions is adopted, and an aerodynamic performance prediction model that learns the mapping relationship from airfoil geometry and incoming flow conditions to outlet aerodynamic performance is used, the predicted aerodynamic output performance data of the two-dimensional section replaces the separate CFD solution for each data point. This reduces the computation time required to obtain a complete spanwise performance distribution curve from several days / weeks to milliseconds, while avoiding repetitive mesh generation, solution calculations, and post-processing operations. This significantly reduces CPU / GPU resource consumption, shortens the aerodynamic output performance prediction cycle, and reduces computational resource consumption, enabling the rapid and low-cost generation of a large number of performance curves under different blade schemes and different incoming flow conditions during the design iteration process.

[0080] Further reference Figure 2 As an implementation of the methods shown in the figures, this disclosure provides some embodiments of a turbine three-dimensional blade aerodynamic parameter calculation device based on graph neural networks and radial physical information embedding. These device embodiments are similar to... Figure 1 Corresponding to the method embodiments shown, the device can be specifically applied to various electronic devices.

[0081] like Figure 2 As shown, a turbine three-dimensional blade aerodynamic parameter calculation device 200 based on graph neural network and radial physical information embedding in some embodiments includes: a selection unit 201, a processing unit 202 and a generation unit 203. The selection unit 201 is configured to select multiple two-dimensional airfoil sections along the pre-created spanwise direction of the three-dimensional turbine blade; the processing unit 202 is configured to perform the following processing on each of the multiple two-dimensional airfoil sections: splitting the airfoil line of the two-dimensional airfoil section into five continuous airfoil line segments to obtain airfoil line segment information; performing geometric feature extraction processing on the airfoil line segment information to obtain geometric contour feature information; acquiring the incoming aerodynamic operating condition parameter data of the three-dimensional turbine blade; generating aerodynamic geometric feature connection diagram data corresponding to the two-dimensional airfoil section based on the geometric contour feature information and the incoming aerodynamic operating condition parameter data; inputting the aerodynamic geometric feature connection diagram data into a pre-trained aerodynamic performance prediction model to obtain aerodynamic output performance data; and the generation unit 203 is configured to generate and display the turbine blade aerodynamic output performance distribution curve of the three-dimensional turbine blade based on the generated aerodynamic output performance data.

[0082] It is understandable that the units described in the device 200 are related to the reference. Figure 1The steps in the method described above correspond to each other. Therefore, the operations, features, and beneficial effects described above for the method also apply to the device 200 and the units contained therein, and will not be repeated here.

[0083] The following is for reference. Figure 3 It shows a schematic diagram of the structure of an electronic device 300 suitable for implementing some embodiments of the present disclosure. Figure 3 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments of this disclosure.

[0084] like Figure 3 As shown, the electronic device 300 may include a processing unit (e.g., a central processing unit, a graphics processing unit, etc.) 301, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 302 or a program loaded from a storage device 308 into a random access memory (RAM) 303. The RAM 303 also stores various programs and data required for the operation of the electronic device 300. The processing unit 301, ROM 302, and RAM 303 are interconnected via a bus 304. An input / output (I / O) interface 305 is also connected to the bus 304.

[0085] Typically, the following devices can be connected to I / O interface 305: input devices 306 including, for example, touchscreens, touchpads, keyboards, mice, cameras, microphones, accelerometers, gyroscopes, etc.; output devices 307 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; storage devices 308 including, for example, magnetic tapes, hard disks, etc.; and communication devices 309. Communication device 309 allows electronic device 300 to communicate wirelessly or wiredly with other devices to exchange data. Although Figure 3 An electronic device 300 with various devices is shown; however, it should be understood that it is not required to implement or possess all of the devices shown. More or fewer devices may be implemented or possessed alternatively. Figure 3 Each box shown can represent a device or multiple devices as needed.

[0086] In particular, according to some embodiments of this disclosure, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, some embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication device 309, or installed from storage device 308, or installed from ROM 302. When the computer program is executed by processing device 301, it performs the functions defined in the methods of some embodiments of this disclosure.

[0087] It should be noted that, in some embodiments of this disclosure, the computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium may be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In some embodiments of this disclosure, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In some embodiments of this disclosure, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wires, optical fibers, RF (radio frequency), etc., or any suitable combination thereof.

[0088] In some implementations, clients and servers can communicate using any currently known or future-developed network protocol such as HTTP (Hypertext Transfer Protocol) and can interconnect with digital data communication (e.g., communication networks) of any form or medium. Examples of communication networks include local area networks (“LANs”), wide area networks (“WANs”), the Internet (e.g., the Internet of Things), and peer-to-peer networks (e.g., ad hoc peer-to-peer networks), as well as any currently known or future-developed networks.

[0089] The computer-readable medium may be contained within an electronic device or may exist independently, not assembled into the electronic device. The computer-readable medium carries one or more programs that, when executed by the electronic device, cause the electronic device to: select multiple two-dimensional airfoil sections along a pre-created three-dimensional turbine blade spanwise direction; for each of the multiple two-dimensional airfoil sections, perform the following processing: split the airfoil line of the two-dimensional airfoil section into five continuous airfoil segments to obtain airfoil segment information; perform geometric feature extraction processing on the airfoil segment information to obtain geometric contour feature information; acquire the incoming aerodynamic operating condition parameter data of the three-dimensional turbine blade; based on the geometric contour feature information and the incoming aerodynamic operating condition parameter data, generate aerodynamic geometric feature connection diagram data corresponding to the two-dimensional airfoil sections; input the aerodynamic geometric feature connection diagram data into a pre-trained aerodynamic performance prediction model to obtain aerodynamic output performance data; and based on the generated aerodynamic output performance data, generate and display the turbine blade aerodynamic output performance distribution curve of the three-dimensional turbine blade.

[0090] Computer program code for performing operations of some embodiments of this disclosure can be written in one or more programming languages ​​or a combination thereof. Programming languages ​​include object-oriented programming languages—such as Java, Smalltalk, and C++—and conventional procedural programming languages—such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0091] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0092] The units described in some embodiments of this disclosure can be implemented in software or hardware. The described units can also be housed in a processor; for example, a processor may be described as including a selection unit, a processing unit, and a generation unit. The names of these units do not necessarily limit the unit itself; for example, a selection unit may be described as "a unit that selects multiple two-dimensional airfoil sections along a pre-created three-dimensional turbine blade spanwise direction."

[0093] The functions described above in this document can be performed at least in part by one or more hardware logic components. For example, exemplary types of hardware logic components that can be used, without limitation, include: field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), system-on-a-chip (SoCs), complex programmable logic devices (CPLDs), and so on.

[0094] The above description is merely a selection of preferred embodiments of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of this disclosure is not limited to technical solutions formed by specific combinations of technical features, but should also cover other technical solutions formed by arbitrary combinations of technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. A method for calculating the aerodynamic parameters of a turbine three-dimensional blade based on graph neural networks and radial physical information embedding, comprising: Select multiple two-dimensional airfoil sections along the pre-created three-dimensional turbine blade spanwise direction; For each of the plurality of two-dimensional airfoil sections, the following processing is performed: The airfoil line of the two-dimensional airfoil section is divided into five continuous airfoil line segments to obtain airfoil line segment information; Geometric feature extraction processing is performed on the leaf-shaped line segment information to obtain geometric contour feature information; Obtain the incoming aerodynamic parameters of the three-dimensional turbine blades; Based on the geometric profile feature information and the incoming aerodynamic operating condition parameter data, aerodynamic geometric feature connection diagram data corresponding to the two-dimensional airfoil section is generated; The aerodynamic geometry feature connection diagram data is input into a pre-trained aerodynamic performance prediction model to obtain aerodynamic output performance data; Based on the generated aerodynamic output performance data, a turbine blade aerodynamic output performance distribution curve of the three-dimensional turbine blade is generated and displayed.

2. The method according to claim 1, wherein, The selection of multiple two-dimensional blade sections along the pre-created three-dimensional turbine blade spanwise direction includes: Obtain the spanwise height range information of the three-dimensional turbine blade; Based on the spanwise height range information, determine the leaf root position information, the leaf tip position information, and at least one intermediate position information located between the leaf root and the leaf tip. A two-dimensional airfoil section is taken from the positions represented by the blade root position information, blade tip position information, and each intermediate position information of the three-dimensional turbine blade to obtain multiple two-dimensional airfoil sections distributed along the span.

3. The method according to claim 1, wherein, The leaf-shaped line segment information includes sub-information of each leaf-shaped line segment corresponding to five consecutive leaf-shaped line segments. Each sub-information of the leaf-shaped line segment represents one segment of the five consecutive leaf-shaped line segments. The geometric feature extraction processing of the leaf-shaped line segment information to obtain geometric contour feature information includes: Each leaf segment sub-information included in the leaf segment information is fitted with a Bézier curve to obtain Bézier curve data characterizing the Bézier curve. The obtained Bézier curve data are determined as geometric contour feature information, wherein the Bézier curve data in each Bézier curve data corresponds one-to-one with the leaf-shaped line segments in the five continuous leaf-shaped line segments.

4. The method according to claim 3, wherein, The generation of aerodynamic geometric feature connection diagram data corresponding to the two-dimensional airfoil section based on geometric contour feature information and the incoming flow aerodynamic operating condition parameter data includes: Each Bézier curve data included in the geometric contour feature information is determined as a graph node in the graph structure; For each of the graph nodes, perform the following steps: The coordinates of each control point of the Bézier curve represented by the graph nodes are converted into vectors as geometric feature vectors. The incoming aerodynamic operating condition parameter data is converted into a vector as an operating condition feature vector. The geometric feature vector and the working condition feature vector are concatenated to obtain the aerodynamic geometric feature vector of the graph node; The aerodynamic geometric feature vectors are bound to the attribute information of the graph nodes; Each graph node is connected by edges according to the connection order of its corresponding five consecutive blade line segments to construct an annular undirected graph corresponding to the two-dimensional blade cross section as aerodynamic geometric feature connection graph data, wherein each graph node carries an aerodynamic geometric feature vector.

5. The method according to claim 2, wherein, Each aerodynamic output performance data point includes an outlet aerodynamic parameter. Each aerodynamic output performance data point corresponds to one of the following positional information: blade root position information, blade tip position information, and at least one intermediate positional information located between the blade root and blade tip. The generation and display of the turbine blade aerodynamic output performance distribution curve based on the generated aerodynamic output performance data includes: For each pneumatic output performance data point in the various pneumatic output performance data sets, perform the following steps: The target position information is determined from the blade root position information, the blade tip position information, and at least one intermediate position information located between the blade root and the blade tip that corresponds to the aerodynamic output performance data. Based on the target location information, generate spanwise position coordinates; Correlating aerodynamic output performance data with spanwise position coordinates yields performance data points; Interpolation and fitting are performed on each performance data point to generate at least one distribution curve in which the aerodynamic output performance parameters change continuously along the spanwise direction. The at least one distribution curve is rendered into a turbine blade aerodynamic output performance distribution curve and output to a preset display device for display.

6. The method according to claim 1, wherein, The aerodynamic performance prediction model is trained through the following steps: Obtain a sample set, wherein the samples in the sample set include sample aerodynamic geometry feature connection diagram data and sample aerodynamic output performance data corresponding to the sample aerodynamic geometry feature connection diagram data; Perform the following training steps based on the sample set: The sample aerodynamic geometry feature connection map data of at least one sample in the sample set is input into the initial neural network to obtain the predicted aerodynamic output performance data corresponding to each sample in the at least one sample. The predicted aerodynamic output performance data corresponding to each of the at least one samples is compared with the corresponding sample aerodynamic output performance data; Based on the comparison results, determine whether the initial neural network has achieved the preset optimization objective; In response to determining that the initial neural network has achieved the optimization objective, the initial neural network is used as the trained aerodynamic performance prediction model; In response to the determination that the initial neural network has not achieved the optimization objective, the network parameters of the initial neural network are adjusted, and a sample set is formed using unused samples. The adjusted initial neural network is then used as the initial neural network, and the training steps are performed again.

7. A device for calculating the aerodynamic parameters of a turbine blade based on graph neural networks and radial physical information embedding, comprising: The selected element is configured to select multiple two-dimensional airfoil sections along the pre-created three-dimensional turbine blade spanwise direction; The processing unit is configured to perform the following processing on each of the plurality of two-dimensional airfoil sections: splitting the airfoil line of the two-dimensional airfoil section into five continuous airfoil line segments to obtain airfoil line segment information; Geometric feature extraction processing is performed on the leaf-shaped line segment information to obtain geometric contour feature information; Acquire the incoming aerodynamic operating parameters data of the three-dimensional turbine blade; based on the geometric profile feature information and the incoming aerodynamic operating parameters data, generate aerodynamic geometric feature connection diagram data corresponding to the two-dimensional airfoil section; input the aerodynamic geometric feature connection diagram data into a pre-trained aerodynamic performance prediction model to obtain aerodynamic output performance data; The generation unit is configured to generate and display the turbine blade aerodynamic output performance distribution curve of the three-dimensional turbine blade based on the generated aerodynamic output performance data.

8. An electronic device, comprising: One or more processors; A storage device on which one or more programs are stored; When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any one of claims 1 to 6.

9. A computer-readable medium having a computer program stored thereon, wherein, When the program is executed by the processor, it implements the method as described in any one of claims 1 to 6.

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