A method for global fairing reconstruction of a periodic described blade profile

Abstract

The application discloses a periodic description blade profile global fairing reconstruction method. First, the application generates initial profile fitting curves according to curve control vertex data and node vector data, and refines the node vector of the profile fitting curve in a least square progressive iterative approximation fitting process by using a curvature guided profile subdivision method according to the discrete curvature distribution of the profile value points, so that the curve control vertex distribution is fitted to the profile shape characteristics, thereby obtaining the subdivided profile fitting curve. Finally, according to the local support of the base function, the subdivided profile fitting curve is updated and fitted in a region-by-region and successive manner by using a curvature constraint adaptive local fitting method until a global fairing periodic reconstruction curve meeting the accuracy requirement is obtained. The application finally generates a global fairing reconstruction curve which highly accurately approximates the profile value points, guarantees the reconstruction fitting efficiency, and realizes the closed characteristic by the periodic base function, and can be effectively used for subsequent T-spline blade surface modeling.

Description

Technical Field

[0001] This invention relates to the field of blade design, and more particularly to a smooth reconstruction and fitting method for blade profile curves. Background Technology

[0002] Blades are key components in turbine equipment such as gas turbines and steam turbines, enabling fluid energy conversion through high-speed rotation. Therefore, turbine equipment often has high requirements for the aerodynamic shape of its blades. In two-dimensional airfoil design, due to the complexity of the airfoil curve shape and the high requirement for geometric continuity, current methods mostly use multi-segment spliced ​​Bezier composite curves for description, and ensure the continuity at the splicing points by adding relative position constraints to the curve control vertices. However, this method suffers from poor flexibility for subsequent modifications. With the improvement of computer computing power, NURBS airfoil modeling based on a single profile curve description has become a current research trend. In his 2020 paper "Parametric model for reconstruction and representation of hydrofoils and airfoils" in Ocean Engineering, Kostas proposed an airfoil curve template method based on Bezier curve splicing. This method can directly generate closed NURBS curves with a fixed number of curve control vertices from geometric shape parameters. However, the curve control vertices also have complex geometric constraints, making them unsuitable for later modification and adjustment.

[0003] On the other hand, Progressive Iterative Approximation (PIA) is a fitting algorithm widely used in curve and surface reconstruction. It has the characteristics of clear geometric meaning, fast convergence and high fitting accuracy. In particular, the Least Square Progressive Iterative Approximation (LSPIA) method proposed in recent years can fit and describe large datasets of shape points using only a small number of curve control vertices. It is very suitable for high-precision curve reconstruction applications. However, it still does not fully utilize the geometric information such as curvature between discrete shape points.

[0004] Meanwhile, considering the characteristics of closed-loop airfoil description, although the curve-controlled vertex repetition method is mature and widely used in the NURBS modeling process for airfoils, for the currently popular T-spline surface modeling method, Li Yusha argued in his 2015 paper "Surfaceskinning using periodic T-spline in semi-NURBS form" in the Journal of Computational and Applied Mathematics that the closed-loop method relying on the first and last curves to control vertex coincidence has compatibility issues and cannot be applied to T-spline surface modeling. Therefore, closed-loop airfoil curves implemented by periodic basis functions have broad application prospects. Summary of the Invention

[0005] To address the problems mentioned in the background art, and considering the stringent requirements for continuity and design convenience of turbine blades, this invention proposes a blade profile curve reconstruction method based on the Least Square Progressive Iterative Approximation (LSPIA) method. Utilizing the set of profile points obtained from the high-density discretization of the blade cross-section profile described by the composite curve, a globally smooth and continuous periodic NURBS curve is reconstructed within minimal error requirements using a small number of curve control vertices. The distribution of its curve control vertices matches the blade curvature distribution, meeting the application requirements for T-spline blade surface geometry. This invention has the following characteristics: ① Compatible with traditional composite curve generation processes, it is correlated with geometric parameters and automatically achieves global continuity; ② The reconstruction process is combined with the blade shape characteristics, achieving curvature distribution constraints on the reconstruction process; ③ The use of periodic basis functions to achieve profile closure allows it to adapt to the T-spline blade surface generation process.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] 1) Generate the corresponding node vector data and curve control vertex data based on the blade section profile value point data;

[0008] 2) Generate an initial blade shape fitting curve based on the current curve control vertex data and node vector data. Based on the discrete curvature distribution of the shape value points, use the curvature-guided profile subdivision method to refine the node vectors of the blade shape fitting curve during the least squares asymptotic approximation fitting process, so that the distribution of the curve control vertex fits the shape characteristics of the blade, thereby obtaining the subdivided blade shape fitting curve.

[0009] 3) Based on the local support of the basis functions, the curvature constraint adaptive local fitting method is used to update the fitted curve of the subdivided leaf shape in different regions one by one until a globally smooth periodic reconstruction curve that meets the accuracy requirements is obtained.

[0010] Specifically, 2) refers to:

[0011] 2.1) Based on the current curve control vertex data and node vector data, generate an initial airfoil fitting curve using periodic NURBS basis functions. Then, divide the node intervals of the current airfoil fitting curve, calculate the deviation vector of all shape value points in each node interval, and then calculate the average fitting error and adaptive local fitting threshold of each node interval.

[0012] 2.2) For each node interval, the interval accuracy is judged. If the average fitting error of the current node interval is greater than the adaptive local fitting threshold, the node interval is refined to obtain new curve control vertices. Then, based on the current deviation vector, the adjustment vectors corresponding to the curve control vertices in the currently fitted leaf shape curve are calculated using the least squares asymptotic iterative fitting method, and the fitted leaf shape curve is updated. Then, 2.3) is executed multiple times, and then 2.4) is executed. Otherwise, the node interval is not processed, and 2.5) is executed.

[0013] 2.3) Calculate the deviation vector between all model value points and the currently fitted leaf profile curve. Based on the current deviation vector, use the least squares asymptotic iterative fitting method to calculate the adjustment vector corresponding to each curve control vertex in the currently fitted leaf profile curve, and then update the fitted leaf profile curve.

[0014] 2.4) If the average fitting error of the current node interval is still greater than the adaptive local fitting threshold, repeat step 2.2) until the average fitting error of the current node interval is less than or equal to the adaptive local fitting threshold.

[0015] 2.5) Repeat steps 2.2)-2.4) to perform accuracy checks on the remaining node intervals until all node intervals meet the accuracy requirements or the number of curve control vertices in the currently fitted leaf-shaped curve reaches the preset maximum number of curve control vertices n. max The leaf shape fitting curve after subdivision is obtained.

[0016] In step 2.1), the node intervals of the current leaf shape fitting curve are then divided, the deviation vector of all shape value points in each node interval is calculated, and then the average fitting error and adaptive local fitting threshold of each node interval are calculated, specifically as follows:

[0017] S1: Calculate the coordinates of the curve points corresponding to the parameter positions at each type value point of the current airfoil fitting curve, and calculate the deviation vector between each type value point and the fitting curve in sequence according to the following formula:

[0018]

[0019] in, Represents the j-th type value point t j The deviation vector, Q j Represents the j-th type value point t j Spatial coordinates, C 0 (t j ) represents the initial leaf shape fitting curve at the j-th shape value point t. j The spatial coordinates of the location, where m represents the total number of shape value points on the current leaf shape fitting curve;

[0020] S2: Divide the currently fitted leaf shape curve into n node intervals based on the node vector data. Calculate the average fitting error and the absolute value of the average discrete curvature for each node interval based on the deviation vector of each shape point, as shown in the following formula:

[0021]

[0022]

[0023] in, Let ε represent the interval of the i-th node. span_i This represents the average fitting error of the i-th node interval. This represents the absolute value of the average discrete curvature of the interval at the i-th node. The second norm of the deviation vector, k j Let || denote the discrete curvature of the j-th type point, || denotes taking the absolute value, and num i This represents the number of type value points within the interval of the i-th node;

[0024] S3: Calculate the adaptive local fitting threshold for each node interval based on the absolute value of the average discrete curvature of each node interval.

[0025] Specifically, S3 is:

[0026] When the difference in the absolute value of the average discrete curvature between each node interval is greater than the preset difference, the absolute value of the average discrete curvature of each node interval is smoothed to obtain the corresponding smoothed absolute value of the average discrete curvature, and the absolute value of the average discrete curvature of each node interval is updated. Then, the adaptive local fitting threshold of each node interval is calculated using the following formula based on the updated absolute value of the average discrete curvature; otherwise, the adaptive local fitting threshold of each node interval is directly calculated using the following formula:

[0027]

[0028]

[0029] Among them, hi This represents the curvature correction factor, and max() indicates the operation of taking the maximum value. This represents the absolute value of the average discrete curvature of each node interval. This represents the absolute value of the maximum average discrete curvature across all node intervals. η represents the absolute value of the maximum average discrete curvature across all intervals, and η represents the lower threshold. Indicates the basic threshold for interval refinement. This represents the adaptive local fitting threshold for the i-th node interval.

[0030] In section 2.2), for each node interval where the average fitting error is greater than the adaptive local fitting threshold, if there are two or more modulo points within the current node interval, then the bifurcation point of the average fitting error of the current node interval is determined and denoted as the error bifurcation point t. l The point t that bisects the error l The midpoint of the curve control vertex corresponding to adjacent shape value points is taken as the error bisector point t. l The initial coordinates of the corresponding curve control vertex are set; if there are fewer than two shape points within the current node interval, the interval is considered to be indivisible, and step 2.5 is executed.

[0031] In step 2.2) or 2.3), based on the current deviation vector, the adjustment vector corresponding to each control vertex in the currently fitted leaf shape curve is calculated using the least squares asymptotic iterative fitting method, and then the fitted leaf shape curve is updated. Specifically:

[0032] First, based on the local support of the B-spline basis functions, the least squares asymptotic iteration method is used to weight and superimpose the deviation vectors of the shape points within the basis function range corresponding to each control vertex in the current leaf profile fitting curve using periodic basis functions, thus obtaining the adjustment vector for each control vertex. The formula for the adjustment vector is as follows:

[0033]

[0034] Where μ represents the weight parameter, This represents the current deviation vector. This represents a periodic basis function defined on the i-th control vertex. For its corresponding local node vector, t j This represents the node value corresponding to the j-th type value point. This represents the adjustment vector at the i-th control vertex on the initial blade profile fitting curve, where n represents the total number of control vertices in the currently fitted blade profile curve.

[0035] Then, the adjustment vectors corresponding to the control vertices of each curve are used to update the control vertices of the currently fitted leaf shape curve, as shown in the following formula:

[0036]

[0037] Among them, v i (0) This represents the i-th control vertex of the initial leaf shape fitting curve. This represents the adjustment vector of the control vertex, v i (k) c represents the i-th control vertex of the fitted curve after the k-th iteration adjustment. (k+1) (t) represents the leaf shape fitting curve after the (k+1)th iteration adjustment, n k The number of control vertices for the fitted leaf-shaped curve after the k-th round of refinement, and ins_max represents the maximum number of iterations for interval refinement.

[0038] Specifically, 3) refers to:

[0039] 3.1) Calculate the regional average fitting error ε for each node interval in the node vector of each node in the subdivided leaf shape fitting curve. span_i and curvature correction factor h i Local fitting threshold and curvature correction factor h i The adaptive fitting termination threshold is obtained after multiplication. If the average fitting error ε of the current node interval span_i If the value is less than the adaptive fitting termination threshold, then the current node interval is taken as the region to be iterated, and steps 3.2)-3.4) are executed continuously until the average fitting error ε is reached. span_i If the value is greater than or equal to the adaptive fitting termination threshold, then proceed to step 3.5.

[0040] 3.2) The set of points to be iterated is composed of the shape value points in the region to be iterated. The control vertices of the subdivided leaf shape fitting curves that meet the marking conditions are added to the set of control vertices of the curves to be adjusted. The marking conditions are specifically: for the curve control vertex V in the k-th iteration process... i (k) If there exists a type value point Q in the set of points to be iterated j Its corresponding node value t j Located at the curve control vertex Within the local support range of the basis functions, the control vertex is marked;

[0041] 3.3) Based on the local support characteristics of the NURBS basis functions, the shape points that satisfy the local fitting conditions are added to the set of local fitting points. In the process, the local fitting condition is specifically: for the shape point Q in the blade section shape point data... l If a certain control vertex V exists in the set of control vertices of the curve to be adjusted i(k) Its basis functions are at the type value point Q l The corresponding node value t l If the value at point Q is non-zero, then the value of this type is point Q. l The local fitting condition is satisfied;

[0042] 3.4) Calculate the deviation vector between all the model value points in the local fitting point set and the currently subdivided leaf shape fitting curve. Based on the current deviation vector, calculate the adjustment vector of each curve control vertex in the curve control vertex set, thereby adjusting each curve control vertex in the curve control vertex set, and then subdividing the leaf shape fitting curve.

[0043] 3.5) Repeat steps 3.1)-3.4) to iterate and update the curve control vertices of all node intervals in the fitted node vectors, and finally obtain a globally smooth periodic reconstruction curve that meets the accuracy requirements.

[0044] Compared to conventional least squares asymptotic iterative approximation fitting methods, this invention transforms the global fitting strategy into local fitting in the process, and adaptively adjusts the fitting accuracy for different regions according to the richness of geometric features. In dense value point reconstruction scenarios, it can effectively balance fitting accuracy and fitting efficiency.

[0045] The beneficial effects of this invention are:

[0046] 1) The reconstruction process is compatible with the traditional compound curve generation process, can be associated with blade profile parameterization, and the generated curve has global smoothness, which facilitates subsequent adjustments and modifications.

[0047] 2) Fully utilize the curvature information between discrete value points for fitting constraints, and combine it with the characteristics of the blade shape to realize the reconstruction process, and the reconstruction accuracy is quite high.

[0048] 3) The reconstructed closed leaf profile curve is described using periodic basis functions and can be directly used for blade modeling applications expressed by T-spline surfaces.

[0049] In summary, this invention achieves the goal of reconstructing a global smooth periodic blade profile curve from a composite curve blade profile, thereby enabling convenient design adjustments and T-spline blade surface modeling. Attached Figure Description

[0050] Figure 1 This is an overall framework diagram of the present invention.

[0051] Figure 2 is Detailed process of global smooth reconstruction algorithm.

[0052] Figure 3 This is a diagram of the uniform discretization process of the composite curve.

[0053] Figure 4This is a schematic diagram of the relationships between the sets in the local fitting process.

[0054] Figure 5 This is an example of global smooth reconstruction of leaf-shaped curves.

[0055] Figure 6 This is an embodiment of the present invention for generating leaf shapes for the T-spline surface skinning process of blades. Detailed Implementation

[0056] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0057] The embodiments and processes of the present invention are as follows:

[0058] like Figure 1 and Figure 2 As shown, the present invention includes the following steps:

[0059] 1) In specific implementation, the composite curve generated by the Kostas template parameterization method is uniformly sampled to obtain the blade cross-section value point data, and the corresponding node vector data and curve control vertex data are generated based on the blade cross-section value point data;

[0060] The Kostas parametric template, proposed in the paper "Parametric model for reconstruction and representation of hydrofoils and airfoils," generates a NURBS spline curve from four Bezier curves stitched together using airfoil geometry parameters. Considering the locality of NURBS basis functions, to obtain the most uniform sampling effect possible, the resulting curve can be re-Bezierized by adding repeating nodes. Each curve segment is then discretized according to the required sampling rate, and finally, the union of the segments yields the discrete point dataset of the overall curve. The discretization process for obtaining the point dataset for a specific airfoil curve example is as follows: Figure 3 As shown.

[0061] For the initialization of the fitting process, the node values ​​corresponding to the shape points are first obtained through chord length parameterization and normalized to the range of 0 to 1 to facilitate refit reconstruction. Based on the characteristic that the least squares asymptotic iterative approximation algorithm allows for the use of curve control vertices much smaller than the number of shape points for fitting, the number of curve control vertices can be selected as 1 / 10 to 1 / 5 of the number of data points, according to the sampling density and the number of target curve control vertices. Initial curve control vertices are then uniformly selected from the shape point dataset. The initial node vectors corresponding to the curve control vertices are also selected according to the setting rules of the least squares asymptotic iterative fitting method, based on the number of curve control vertices. For the relative geometric position information between shape points on the blade section, discrete curvature values ​​are used to represent the position. The discrete curvature value k of the shape points is calculated using the following difference formula.i , where Δx i ,Δy i For the type value point Q i The first-order difference between the points and their neighbors in each direction, Δ 2 x i ,Δ 2 y i It is the second-order difference between them.

[0062] k i =Δx i Δ 2 y i -Δy i Δ 2 x i

[0063] In step 1) above, the closed curve is described using periodic basis functions, so that the connection between the beginning and end of the curve automatically satisfies C. 2 The continuity eliminates the constraint of overlapping control vertices of the first and last curves, ensuring that all generated profiles are suitable for lofting T-spline surfaces. Based on the parameterization of the chord length of the blade section profile points, the initial node vectors and corresponding curve control vertex coordinates are selected from the profile points using the least squares asymptotic iterative approximation method. This achieves an initialization effect that better fits the target shape and effectively improves the fitting efficiency.

[0064] 2) Generate an initial blade shape fitting curve based on the current curve control vertex data and node vector data. Based on the discrete curvature distribution of the shape value points, use the curvature-guided profile subdivision method to refine the node vectors of the blade shape fitting curve during the least squares asymptotic approximation fitting process, so that the distribution of the curve control vertex fits the shape characteristics of the blade, thereby obtaining the subdivided blade shape fitting curve.

[0065] 2) Specifically:

[0066] 2.1) Based on the current curve control vertex data and node vector data, generate the initial leaf shape fitting curve using periodic NURBS basis functions, as shown in the following formula:

[0067]

[0068]

[0069] Among them, C 0 (t) is the initial fitted curve, V i (0) This represents the initial spatial coordinates of the control vertices, and n represents the initial number of control vertices. Represents a t i Centered on the node, the local influence node vector range is The basis function values ​​of the third-order NURBS basis functions at node value t. This represents the basis function value of the above interval position in periodic form, where T is the period, which is a constant. For the normalized node vector, the period T = 1 is taken.

[0070] Next, the node intervals of the current leaf shape fitting curve are divided, the deviation vector of all shape value points in each node interval is calculated, and then the average fitting error and adaptive local fitting threshold of each node interval are calculated.

[0071] In section 2.1), the node intervals of the current leaf shape fitting curve are then divided, the deviation vector of all shape value points in each node interval is calculated, and then the average fitting error and adaptive local fitting threshold of each node interval are calculated, specifically as follows:

[0072] S1: Assume there are currently n+1 curve control vertices V0, V1, ..., V n The closed-loop control polygon that forms the initial airfoil fitting curve is used to calculate the curve point coordinates of the current airfoil fitting curve at each parameter value point. The deviation vector between each parameter value point and the fitting curve is calculated sequentially according to the following formula to represent the degree of deviation between the current curve shape and the desired shape:

[0073]

[0074] in, Represents the j-th type value point t j The deviation vector, Q j Represents the j-th type value point t j Spatial coordinates, C 0 (t j ) represents the initial leaf shape fitting curve at the j-th shape value point t. j The spatial coordinates of the location, where m represents the total number of shape value points on the current leaf shape fitting curve;

[0075] S2: Divide the currently fitted leaf shape curve into n node intervals based on the node vector data. Calculate the average fitting error and the absolute value of the average discrete curvature for each node interval based on the deviation vector of each shape point, as shown in the following formula:

[0076]

[0077]

[0078] in, Let ε represent the interval of the i-th node. span_i This represents the average fitting error of the i-th node interval. This represents the absolute value of the average discrete curvature of the interval at the i-th node. The second norm of the deviation vector, kj Let || denote the discrete curvature of the j-th type point, || denotes taking the absolute value, and num i This represents the number of type value points within the interval of the i-th node;

[0079] S3: Calculate the adaptive local fitting threshold for each node interval based on the absolute value of the average discrete curvature of each node interval.

[0080] S3 specifically refers to:

[0081] When the difference in the absolute value of the average discrete curvature between each node interval is greater than the preset difference, i.e., there is a large difference, the absolute value of the average discrete curvature of each node interval is smoothed. The smoothing formula is as follows: The absolute value of the average discrete curvature of the node interval. To obtain the average discrete curvature absolute value after smoothing, the corresponding average discrete curvature absolute value after smoothing is obtained and updated for each node interval. Then, the adaptive local fitting threshold for each node interval is calculated using the following formula based on the updated average discrete curvature absolute value; otherwise, the adaptive local fitting threshold for each node interval is directly calculated using the following formula:

[0082]

[0083]

[0084] Among them, h i This represents the curvature correction factor, and max() indicates the operation of taking the maximum value. This represents the absolute value of the average discrete curvature of each node interval. This represents the absolute value of the maximum average discrete curvature across all node intervals. η represents the absolute value of the maximum average discrete curvature across all intervals, and η represents the lower limit of the threshold. It is used to filter cases where the average curvature value of the airfoil section is too large. Typically, η can be set to 0.05. Indicates the basic threshold for interval refinement. This represents the adaptive local fitting threshold for the i-th node interval.

[0085] 2.2) For each node interval, the interval accuracy is judged. If the average fitting error of the current node interval is greater than the adaptive local fitting threshold, the node interval is refined to obtain new curve control vertices. Then, based on the current deviation vector, the adjustment vectors corresponding to the curve control vertices in the currently fitted leaf curve are calculated using the least squares asymptotic iterative fitting method, and the fitted leaf curve is updated. Then, 2.3) is executed multiple times (i.e., several regular LSPIA updates) before 2.4). Otherwise, the node interval is not processed, and 2.5) is executed.

[0086] In section 2.2), for each node interval where the average fitting error is greater than the adaptive local fitting threshold, if there are two or more model points within the current node interval, the bisector of the average fitting error of the current node interval is determined. That is, the fitting errors of each model point within the node interval are superimposed sequentially according to the arrangement of model points. When the superimposed error just reaches or exceeds half of the total error of the node interval, the node value corresponding to that model point is recorded as the error bisector t. l The point t that bisects the error l The midpoint of the curve control vertex corresponding to adjacent shape value points is taken as the error bisector point t. l The initial coordinates of the corresponding curve control vertex are denoted as Q. ins ,…,Q ins+a Error bisector t l Satisfy the following formula:

[0087]

[0088]

[0089] Where, ε span Q represents the average fitting error of the current node interval. h t represents the spatial coordinates of the h-th type value point. h C represents the node value corresponding to this type of value point. 0 (t h ) represents the spatial coordinates of the initial leaf shape fitting curve at the corresponding position of the shape value point, and ins+1 represents the index of the shape value point;

[0090] If there are fewer than two type value points within the current node interval, the interval is considered undivisible, and this node interval is skipped in the current interval refinement process, proceeding to step 2.5.

[0091] 2.3) Considering that the newly inserted curve control vertices after each interval refinement will cause a temporary increase in the leaf shape curve fitting error, calculate the deviation vector between all shape value points and the currently fitted leaf shape curve. Based on the current deviation vector, use the least squares asymptotic iterative fitting method to calculate the adjustment vector corresponding to each curve control vertex in the currently fitted leaf shape curve, and then update the fitted leaf shape curve.

[0092] Depending on the size of the model points, 2 to 5 regular LSPIA updates can typically be added. By inserting several regular fitting updates between refinement processes, the problem of continuous refinement caused by errors in the initial fitting stage is avoided, effectively controlling the scale of fitting iterations and ensuring the effectiveness of the reconstruction algorithm. At the same time, the distribution of vertices controlled by curves close to the leaf shape satisfies global smoothness while also facilitating subsequent design adjustments.

[0093] 2.4) If the average fitting error of the current node interval is still greater than the adaptive local fitting threshold, repeat step 2.2) until the average fitting error of the current node interval is less than or equal to the adaptive local fitting threshold.

[0094] 2.5) Repeat steps 2.2)-2.4) to perform accuracy checks on the remaining node intervals until all node intervals meet the accuracy requirements or the number of curve control vertices in the currently fitted leaf-shaped curve reaches the preset maximum number of curve control vertices n. max The leaf shape fitting curve after subdivision is obtained.

[0095] In step 2.2) or 2.3), based on the current deviation vector, the adjustment vector corresponding to each control vertex in the currently fitted leaf shape curve is calculated using the least squares asymptotic iterative fitting method, and then the fitted leaf shape curve is updated. Specifically:

[0096] First, based on the local support of the B-spline basis functions, the least squares asymptotic iteration method is used to weight and superimpose the deviation vectors of the shape points within the basis function range corresponding to each control vertex in the current leaf shape fitting curve using periodic basis functions. This yields the adjustment vector for each control vertex in this iteration. The formula for the adjustment vector is as follows:

[0097]

[0098] Where μ represents the weight parameter, This represents the current deviation vector. This represents a periodic basis function defined on the i-th control vertex. For its corresponding local node vector, t j This represents the node value corresponding to the j-th type value point. This represents the adjustment vector at the i-th control vertex on the initial leaf shape fitting curve, and n represents the total number of curve control vertices in the current fitted leaf shape curve, which can be selected by referring to the conventional LSPIA algorithm process;

[0099] Then, the adjustment vectors corresponding to the control vertices of each curve are used to update the control vertices of the currently fitted leaf shape curve, as shown in the following formula:

[0100]

[0101] in, This represents the i-th control vertex of the initial leaf shape fitting curve. This represents the adjustment vector of the control vertex, v i (k) C represents the i-th control vertex of the fitted curve after the k-th iteration adjustment. (k+1) (t) represents the leaf shape fitting curve after the (k+1)th iteration adjustment, nk The number of control vertices for the fitted leaf-shaped curve after the k-th round of refinement, and ins_max represents the maximum number of iterations for interval refinement.

[0102] By using the above curvature-guided profile subdivision method, we can obtain a curve control vertex distribution that fits the shape of the blade cross section, so that the generated curve can meet the global smoothness requirements while also facilitating subsequent adjustments and corrections.

[0103] 3) Based on the local support of the basis functions, the curvature constraint adaptive local fitting method is used to update the fitted curve of the subdivided leaf shape in different regions one by one until a globally smooth periodic reconstruction curve that meets the accuracy requirements is obtained.

[0104] 3) Specifically:

[0105] 3.1) Calculate the regional average fitting error ε for each node interval in the node vector of each node in the subdivided leaf shape fitting curve. span_i and curvature correction factor h i Preset local fitting threshold Local fitting threshold and curvature correction factor h i The adaptive fitting termination threshold is obtained after multiplication. If the average fitting error ε of the current node interval span_i If the value is less than the adaptive fitting termination threshold, then the current node interval is taken as the region to be iterated, and steps 3.2)-3.4) are executed continuously until the average fitting error ε is reached. span_i If the value is greater than or equal to the adaptive fitting termination threshold, then proceed to step 3.5.

[0106] 3.2) The set of points to be iterated is composed of the type value points in the region to be iterated. Based on the local support characteristics of NURBS basis functions, the control vertices of the subdivided leaf shape fitting curves that meet the labeling conditions are added to the set of control vertices of the curves to be adjusted, cp. (k) The specific condition to be marked is: for the curve control vertex V in the k-th iteration process i (k) If there exists a type value point Q in the set of points to be iterated j Its corresponding node value t j Located at the curve control vertex V i (k) Within the local support range of the basis functions, that is, at a given node value, the basis function value is not equal to zero. Then mark the control vertex;

[0107] 3.3) Based on the local support characteristics of the NURBS basis functions, the shape points that satisfy the local fitting conditions are added to the set of local fitting points. In the process, the local fitting condition is specifically: for the shape point Q in the blade section shape point data... l If the set of control vertices of the curve to be adjusted is cp (k) There exists a certain control vertex V. i (k) Its basis functions are at the type value point Q l The corresponding node value t l The value at point is nonzero, that is, we have Then the value point Q of this type l The local fitting condition is satisfied;

[0108] The relationships between sets in local fitting are as follows: Figure 4 As shown.

[0109]

[0110] 3.4) Calculate the deviation vector between all shape points in the local fitting point set and the currently subdivided airfoil fitting curve using the formula in S1. Based on the current deviation vector, calculate the adjustment vector of each curve control vertex in the curve control vertex set, thereby adjusting each curve control vertex in the curve control vertex set, and thus the subdivided airfoil fitting curve; the formula is as follows:

[0111]

[0112] Under this local fitting strategy, the iterative fitting accuracy is adaptively set for different regions of the blade cross-section reconstruction curve according to the richness of geometric features. At the same time, only the curve control vertex in the region that has not reached the required accuracy is adjusted, thus balancing fitting accuracy and efficiency.

[0113] 3.5) Repeat steps 3.1)-3.4) to iterate and update the curve control vertices of all node intervals in the fitted node vectors, and finally obtain a globally smooth periodic reconstruction curve that meets the accuracy requirements.

[0114] The adaptive local fitting algorithm for curvature constraints first selects the shape points that have not yet reached the required approximation accuracy, and then uses the local support property of NURBS basis functions to adjust only the curve control vertices within the local support range. Compared with the conventional least squares asymptotic iterative approximation fitting process in which all global curve control vertices participate in the fitting adjustment process in each iteration, the local fitting strategy in this method can limit the adjustment calculation to the region that has not yet reached the required accuracy, effectively reducing the iteration scale and improving the reconstruction efficiency.

[0115] For example, the implementation of the reconstructed airfoil profile. Figure 5 As shown. Among them Figure 5In (a), the result of fitting and reconstructing a blade section using traditional LPSIA is shown. It is described by 25 curve control vertices, and the total global reconstruction error is 0.2748. Figure 5 (b) shows the reconstruction result generated by this method. The refined profile is described by 31 curve control vertices, and the total reconstruction error is 0.237. It can be seen that the reconstruction accuracy of this method is improved compared with the traditional method, and the distribution of curve control vertices is more in line with the shape of the blade.

[0116] The globally smooth periodic reconstruction curve of this invention is applied to the subsequent T-spline surface lofting generation process, and the resulting T-spline surface modeling of the aerodynamic structure of the blade is implemented, for example... Figure 6 of (a), Figure 6 (b) and Figure 6 As shown in (c).

[0117] This embodiment adds a smooth reconstruction step during the blade profile design stage. First, the blade profile curve described by the composite curve is discretized with high density and uniformity. Then, a curvature-constrained profile refinement algorithm and a curvature-guided local fitting algorithm are used sequentially for reconstruction, resulting in a globally smooth and continuous periodic profile with a curve control vertex distribution that closely matches the blade shape and has high fitting accuracy. This profile can be used for subsequent adjustments and blade surface generation. An example of constructing a T-spline surface for the aerodynamic structure of a certain type of blade using the five closed blade profile curves generated by this invention is as follows: Figure 6 As shown, where Figure 6 (a) shows the generated leaf-shaped curves and their control grids. Figure 6 (b) represents the generated T-mesh topology. Figure 6 (c) represents the final generated T-spline surface of the blade aerodynamic structure. Compared with the traditional NURBS surface curve, the number of control vertices of the generated T-spline surface is reduced from 959 to 507, and its skinning process fitting error is 8.65e-6. Therefore, it can be considered that the blade profile curve generated by this method meets the generation requirements of T-spline surface.

Claims

1. A method for globally smooth reconstruction of leaf shape based on periodic description, characterized in that, Includes the following steps: 1) Generate the corresponding node vector data and curve control vertex data based on the blade section profile value point data; 2) Generate an initial blade shape fitting curve based on the current curve control vertex data and node vector data. Based on the discrete curvature distribution of the shape value points, use the curvature-guided profile subdivision method to refine the node vectors of the blade shape fitting curve during the least squares asymptotic approximation fitting process, so that the distribution of the curve control vertex fits the shape characteristics of the blade, thereby obtaining the subdivided blade shape fitting curve. Specifically, 2) refers to: 2.1) Based on the current curve control vertex data and node vector data, generate an initial airfoil fitting curve using periodic NURBS basis functions. Then, divide the node intervals of the current airfoil fitting curve, calculate the deviation vector of all shape value points in each node interval, and then calculate the average fitting error and adaptive local fitting threshold of each node interval. 2.2) For each node interval, the interval accuracy is judged. If the average fitting error of the current node interval is greater than the adaptive local fitting threshold, the node interval is refined to obtain new curve control vertices. Then, based on the current deviation vector, the adjustment vectors corresponding to the curve control vertices in the currently fitted leaf-shaped curve are calculated using the least squares asymptotic iterative fitting method, and the fitted leaf-shaped curve is updated. Then, 2.3) is executed multiple times, and then 2.4) is executed. Otherwise, the node interval is not processed, and 2.5) is executed. 2.3) Calculate the deviation vector between all model value points and the currently fitted leaf profile curve. Based on the current deviation vector, use the least squares asymptotic iterative fitting method to calculate the adjustment vector corresponding to each curve control vertex in the currently fitted leaf profile curve, and then update the fitted leaf profile curve. 2.4) If the average fitting error of the current node interval is still greater than the adaptive local fitting threshold, repeat step 2.2) until the average fitting error of the current node interval is less than or equal to the adaptive local fitting threshold. 2.5) Repeat steps 2.2)-2.4) to perform accuracy checks on the remaining node intervals until all node intervals meet the accuracy requirements or the number of curve control vertices in the currently fitted leaf-shaped curve reaches the preset maximum number of curve control vertices. , to obtain the subdivided leaf shape fitting curve; In step 2.1), the node intervals of the current leaf shape fitting curve are then divided, the deviation vector of all shape value points in each node interval is calculated, and then the average fitting error and adaptive local fitting threshold of each node interval are calculated, specifically as follows: S1: Calculate the coordinates of the curve points corresponding to the parameter positions at each type value point of the current airfoil fitting curve, and calculate the deviation vector between each type value point and the fitting curve in sequence according to the following formula: in, Indicates the first Individual value points The deviation vector, Indicates the first Individual value points spatial coordinates, This indicates that the initial leaf shape fitting curve is at the th... Individual value points Spatial coordinates of the location This indicates the total number of shape value points on the current leaf profile fitting curve; S2: Divide the currently fitted leaf curve into segments based on the node vector data. For each node interval, the average fitting error and the absolute value of the average discrete curvature are calculated based on the deviation vector of each type of value point, as shown in the following formula: in, Indicates the first Each node interval Indicates the first The average fitting error of each node interval Indicates the first The absolute value of the average discrete curvature of each node interval The L2 norm of the deviation vector. Indicates the first Discrete curvature of each type value point This indicates taking the absolute value. Indicates the first The number of type value points within each node interval; S3: Calculate the adaptive local fitting threshold for each node interval based on the absolute value of the average discrete curvature of each node interval; 3) Based on the local support of the basis functions, the curvature constraint adaptive local fitting method is used to update the fitted curve of the subdivided leaf shape region by region until a globally smooth periodic reconstruction curve that meets the accuracy requirements is obtained.

2. The method for global smooth reconstruction of leaf shape based on periodic description according to claim 1, characterized in that, Specifically, S3 is: When the difference in the absolute value of the average discrete curvature between each node interval is greater than the preset difference, the absolute value of the average discrete curvature of each node interval is smoothed to obtain the corresponding smoothed absolute value of the average discrete curvature, and the absolute value of the average discrete curvature of each node interval is updated. Then, the adaptive local fitting threshold of each node interval is calculated using the following formula based on the updated absolute value of the average discrete curvature; otherwise, the adaptive local fitting threshold of each node interval is directly calculated using the following formula: in, This represents the curvature correction factor. This indicates the operation of retrieving the maximum value. This represents the absolute value of the average discrete curvature of each node interval. This represents the absolute value of the maximum average discrete curvature across all node intervals. This represents the absolute value of the maximum average discrete curvature across all intervals. Indicates the lower limit of the threshold. Indicates the basic threshold for interval refinement. Indicates the first Adaptive local fitting threshold for each node interval.

3. The method for global smooth reconstruction of leaf shape based on periodic description according to claim 1, characterized in that, In section 2.2), for each node interval where the average fitting error is greater than the adaptive local fitting threshold, if there are two or more modulo points within the current node interval, then the bifurcation point of the average fitting error of the current node interval is determined and recorded as the error bifurcation point. The point that bisects the error The midpoint of the curve control vertex corresponding to adjacent shape value points is taken as the error bisector point. The initial coordinates of the corresponding curve control vertex; however, if there are fewer than two shape points within the current node interval, the interval is considered to be indivisible, and step 2.5 is executed.

4. The method for global smooth reconstruction of leaf shape based on periodic description according to claim 1, characterized in that, In step 2.2) or 2.3), based on the current deviation vector, the adjustment vector corresponding to each control vertex in the currently fitted leaf shape curve is calculated using the least squares asymptotic iterative fitting method, and then the fitted leaf shape curve is updated. Specifically: First, based on the local support of the B-spline basis functions, the least squares asymptotic iteration method is used to weight and superimpose the deviation vectors of the shape points within the basis function range corresponding to each control vertex in the current leaf profile fitting curve using periodic basis functions, thus obtaining the adjustment vector for each control vertex. The formula for the adjustment vector is as follows: in, Represents the weight parameters. This represents the current deviation vector. The definition is in the first place. Periodic basis functions on each control vertex Its corresponding local node vector, Indicates the first The node value corresponding to each type value point. Indicates the first step on the initial airfoil fitting curve. The adjustment vector of each control vertex at this time. This indicates the total number of control vertices in the currently fitted leaf-shaped curve; Then, the adjustment vectors corresponding to the control vertices of each curve are used to update the control vertices of the currently fitted leaf shape curve, as shown in the following formula: in, This represents the i-th control vertex of the initial leaf shape fitting curve. This represents the adjustment vector of the control vertex. This represents the i-th control vertex of the fitted curve after the k-th iteration adjustment. This represents the leaf shape fitting curve after the (k+1)th iteration adjustment. This represents the number of control vertices for the fitted leaf shape curve after the k-th round of refinement. This indicates the maximum number of iterations required for interval refinement.

5. The method for global smooth reconstruction of leaf shape based on periodic description according to claim 1, characterized in that, Specifically, 3) refers to: 3.1) Calculate the region-average fitting error for each node interval in the node vector of each node in the subdivided leaf shape fitting curve. and curvature correction factor Local fitting threshold and curvature correction factor The adaptive fitting termination threshold is obtained after multiplication. If the average fitting error of the current node interval If the value is less than the adaptive fitting termination threshold, then the current node interval is taken as the region to be iterated, and steps 3.2) to 3.4) are executed continuously until the average fitting error is reached. If the value is greater than or equal to the adaptive fitting termination threshold, then proceed to step 3.

5. 3.2) The set of points to be iterated is composed of the shape value points in the region to be iterated. The control vertices of the curves that meet the marking conditions in the subdivided leaf shape fitting curves are added to the set of control vertices of the curves to be adjusted. The marking conditions are specifically: for the control vertices of the curves in the k-th iteration process... If there exists a type value point in the set of points to be iterated Its corresponding node value Located at the curve control vertex Within the local support range of the basis functions, the control vertex is marked; 3.3) Based on the local support characteristics of NURBS basis functions, the shape points that satisfy the local fitting conditions are added to the set of local fitting points. In the process, the local fitting condition is specifically: for the shape points in the blade section shape point data... If a certain control vertex exists in the set of control vertices of the curve to be adjusted Its basis functions at the type value point Corresponding node value If the value at a point is non-zero, then the value of this type is a point. The local fitting condition is satisfied; 3.4) Calculate the deviation vector between all the model value points in the local fitting point set and the currently subdivided leaf shape fitting curve. Based on the current deviation vector, calculate the adjustment vector of each curve control vertex in the curve control vertex set, thereby adjusting each curve control vertex in the curve control vertex set, and thus the subdivided leaf shape fitting curve. 3.5) Repeat steps 3.1)-3.4), iterate through and update the curve control vertices of all node intervals in the fitted node vectors, and finally obtain a globally smooth periodic reconstruction curve that meets the accuracy requirements.

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