A data mining method for uncertainty quantification of gas turbines based on cubic convolution

Abstract

The present invention discloses a data mining method for uncertainty quantification of gas turbines based on cubic convolution. Raw dense grid vertex data is generated using the geometric parameters of the gas turbine and the gas-thermal parameters to be studied. An initial Delaunay triangular grid is constructed on the grid vertices, and after data sparsification, a sparse Delaunay triangular grid is constructed. Then, a sparse regular rectangular grid is generated, and the gas-thermal parameters and their uncertainty indices of each grid vertex of the sparse regular rectangular grid are calculated. Subsequently, a dense regular rectangular grid is generated, and using the double BiCubic function cubic convolution method, the uncertainty indices of the gas-thermal parameters of each grid vertex of the dense regular rectangular grid are obtained. Finally, the spatial coordinates of each grid vertex of the dense regular rectangular grid and the uncertainty indices of the gas-thermal parameters are input into the open-source computing library matplotlib to generate a distribution cloud map of the uncertainty indices of the gas-thermal parameters.

Description

Technical Field

[0001] The present invention belongs to the technical field of turbine design, and particularly relates to a data mining method for gas turbine uncertainty quantification based on cubic convolution. Background Art

[0002] There are many inherent uncertainties in gas turbine manufacturing. For example, machining and assembly errors in the tip clearance of turbine blades and geometric profile degradation caused by thermal ablation. Traditional gas turbine research simplifies these uncertainty parameters into deterministic values for research. Therefore, the performance prediction of traditional research often does not match the actual operation of gas turbines, resulting in premature failure of turbine blades. Uncertainty quantification algorithms have been introduced into the turbine design field in the past decade. However, current mainstream domestic and foreign uncertainty quantification research focuses on improving algorithm efficiency while ignoring the mining of data obtained by the algorithms. The rich data obtained from uncertainty quantification calculations still uses processing methods under a deterministic framework, thus losing a large amount of effective information. Since the field of gas turbine uncertainty quantification is at the forefront of current domestic and foreign research, there are few studies on data mining algorithms for uncertainty quantification data in the current public literature. Compared with the processing methods under a deterministic framework, there are the following problems in the mining of uncertainty quantification data:

[0003] (1) The data involved in gas turbine uncertainty quantification contains millions of grid vertices. With such a large amount of data, even using parallel algorithms requires a large amount of time cost, not to mention the huge computing resources and memory resources occupied.

[0004] (2) Uncertainty quantification research requires calculating samples of different geometries. The spatial coordinates of grid vertices representing the same position in space for different geometric samples cannot coincide, so subsequent uncertainty quantification calculations for the same spatial position cannot be performed. Currently, some researchers have proposed using clustering methods to solve this problem. However, clustering methods can only be applied to data mining of grid vertices near the wall of structured grids. For grid vertices far from the wall or unstructured grids, due to strong distortion of grid spatial coordinates, clustering methods fail.

[0005] (3) Currently, the visualization of gas turbine calculation data mainly used in China relies on commercial software under a deterministic framework, such as Fluent or ANSYS CFX, etc. Using these commercial software not only requires high costs, but also the drawing calculation process is completely closed. Researchers cannot customize the calculation data processing images that meet the requirements of uncertainty quantification. Summary of the Invention

[0006] To overcome the disadvantages of the above-mentioned existing technologies, the purpose of the present invention is to provide a data mining method for uncertainty quantification of gas turbines based on cubic convolution. Based on cubic convolution and Delaunay triangulation interpolation technology, it can support the processing of uncertainty quantification calculation data for both structured grids and unstructured grids, and the image calculation process is completely independent of any commercial software. The uncertainty quantity distribution cloud map of the three-dimensional model obtained is not yet available in the currently published literature, and it has great engineering value for revealing the uncertainty phenomena in the processing and operation of gas turbines and guiding the robust optimization design of turbine blades.

[0007] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0008] A data mining method for uncertainty quantification of gas turbines based on cubic convolution, comprising the following steps:

[0009] Step 1: Generate original dense grid vertex data using the geometric parameters of the gas turbine and the gas-thermal parameters to be studied, and construct an initial Delaunay triangular grid on the grid vertices;

[0010] Step 2: Use methods such as the Visvalingam-Whyatt sparse algorithm to sparsify the data of the initial Delaunay triangular grid to greatly reduce the number of grid vertices that need to be calculated in subsequent steps;

[0011] Step 3: Construct a sparse Delaunay triangular grid on the grid vertices after data sparsification;

[0012] Step 4: Generate a sparse regular rectangular grid at equal intervals according to a preset precision parameter 1, and obtain the spatial coordinates of each grid vertex of the sparse regular rectangular grid;

[0013] Step 5: According to the spatial coordinates of each grid vertex of the sparse Delaunay triangular grid and the sparse regular rectangular grid, use methods such as Delaunay triangulation interpolation to calculate the gas-thermal parameters of each grid vertex of the sparse regular rectangular grid;

[0014] Step 6: For all working conditions that need to be calculated for uncertainty quantification, perform the operations of Step 1 to Step 5 to obtain the spatial coordinates and gas-thermal parameters of each grid vertex of each sparse regular rectangular grid for each working condition; use the polynomial chaos method to calculate the uncertainty indicators, namely the mean and standard deviation, of the gas-thermal parameters of each grid vertex of each sparse regular rectangular grid;

[0015] Step 7: Generate a dense regular rectangular grid at equal intervals according to the preset precision parameter, and obtain the spatial coordinates of each grid vertex of the dense regular rectangular grid;

[0016] Step 8: According to the spatial coordinates of each grid vertex of the sparse regular rectangular grid and the uncertainty index of the gas thermal parameters, as well as the spatial coordinates of each grid vertex of the dense regular rectangular grid, use the bicubic function cubic convolution method for encryption to obtain the uncertainty index of the gas thermal parameters of each grid vertex of the dense regular rectangular grid;

[0017] Step 9: Input the spatial coordinates and the uncertainty index of the gas thermal parameters of each grid vertex of the dense regular rectangular grid into the open-source computing library matplotlib to generate a distribution cloud map of the uncertainty index of the gas thermal parameters.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0019] (1) By introducing the Visvalingam-Whyatt sparse algorithm, the number of grid vertices to be processed in the subsequent time-consuming uncertainty quantification calculation is greatly reduced. In one embodiment, the number of grid vertices to be processed in the uncertainty quantification calculation is reduced to 33.2% of the original.

[0020] (2) The grid vertex data of all samples are mined for information by the Delaunay triangulation interpolation algorithm and mapped onto the same sparse regular rectangular grid, fundamentally solving the problem that the spatial coordinates of the grid vertices at the same position in the representation space of different geometric samples cannot coincide. Compared with the clustering method, the method proposed by the present invention can be applied to both structured or unstructured grids, and data mining of grid vertices near the wall surface or far from the wall surface.

[0021] (3) The present invention combines the bicubic function cubic convolution method to perform high-fidelity encryption on the sparse regular rectangular grid, and greatly improves the image calculation accuracy of the distribution cloud map of the uncertainty index of the gas thermal parameters at extremely low cost.

[0022] (4) Since the present invention greatly reduces the computational amount in the uncertainty quantification data mining process, it can even realize the calculation of the distribution cloud map of the uncertainty index of the gas thermal parameters of a three-dimensional gas turbine model. Such distribution cloud maps have not been reported in the currently published literature. The rich information that can be expressed is of great significance for turbine designers to understand the flow mechanism of the uncertainty behavior in the actual operation process of gas turbines.

[0023] (5) Only by skipping step six, the present invention can calculate the distribution cloud map of the gas thermal parameters under the deterministic framework. Therefore, the present invention can not only adapt to the forefront uncertainty quantification research, but also be applied to the traditional deterministic quantification research.

[0024] (6) The present invention is completely based on self-developed algorithms and a small number of publicly available libraries, and does not rely on any domestic or foreign commercial software. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a schematic diagram of the system of the present invention.

[0026] Figure 2 It is a schematic diagram of the implementation of the double BiCubic function cubic convolution method.

[0027] Figure 3 It is the standard deviation distribution cloud map of the heat transfer amount generated by the present invention, where Q in the figure represents the standard deviation of the heat transfer amount. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0028] The following will describe in detail the implementation manner of the present invention with reference to the drawings and embodiments.

[0029] In a specific embodiment of the present invention, the calculation model comes from the grooved blade tip of the GE-E3 gas turbine blade widely used in the industry. Its specific geometric parameters are shown in Table 1. In the embodiment of the present invention, the heat transfer amount is used as the gas thermal parameter to be studied.

[0030] Table 1 Geometric parameters of the GE_E3 blade shape

[0031] Geometric parameter name Value (mm) Axial chord length 86.1 Groove depth 5.08 Tip clearance 1.97 Pitch 122 Shoulder wall thickness 2.29

[0032] On this basis, referring to Figure 1 , the specific process of an uncertainty quantification data mining algorithm based on the cubic convolution method of the present invention is as follows:

[0033] Step 1, generate the initial Delaunay triangular mesh.

[0034] Receive the original dense grid vertex data, and use the Lawson algorithm to quickly construct the initial Delaunay triangular mesh on the dense grid vertices.

[0035] In one embodiment, by inputting the geometric parameters of the gas turbine and the gas thermal parameters to be studied into the publicly available computational fluid dynamics library OPENFOAM, the original dense grid vertex data can be obtained. The original dense grid vertex data output by OPENFORM is a matrix M with L rows and 4 columns DensenThe number of L is the number of the original dense grid vertex data. Each row represents the spatial coordinates and gas-thermal parameters of a grid vertex, where the first three columns represent the x-coordinate, y-coordinate, and z-coordinate of the grid vertex, and the fourth column represents the gas-thermal parameter of the grid vertex. The generation of the initial Delaunay triangular mesh is to establish the topological relationship of all the original dense grid vertices. In this embodiment, L takes the value of 3497810, and the gas-thermal parameter is the heat transfer amount.

[0036] The present invention uses the Lawson algorithm to construct an initial Delaunay triangular mesh on the original dense grid vertices, and the method is as follows:

[0037] 1) Denote the grid vertex represented by the first row of the matrix M Densen as the base point P Base , traverse all the grid vertices of the matrix M Densen and find the grid vertex with the maximum Euclidean distance from the base point P Base , denote it as P Tail , connect P Base and P Tail , to obtain the line segment P Base P Tail , denote it as the base line; for any grid vertex P Densen in the matrix M Any to the Euclidean distance d Base from the base point P Any , the calculation formula is as follows:

[0038]

[0039] where (x Any , y Any, , z Any ) are the spatial coordinates of P Any , and (x base , y base, , z base ) are the spatial coordinates of the base point P Base .

[0040] 2) Traverse all the grid vertices of the matrix M Densen , calculate the Euclidean distances from all the grid vertices with x coordinates greater than the base point P Base to the line segment P Base P Tail , and find the point P Base P Tail with the minimum Euclidean distance to the line segment P Min . For any grid vertex P Densen in the matrix M Any to the Euclidean distance d Base P Tail from the base line P AnylineThe calculation formula is as follows:

[0041]

[0042] In the formula, (x Any , y Any , z Any ) are the spatial coordinates of P Any , (x Stroke , y Stroke , z Stroke ) are the spatial coordinates of the foot of the perpendicular from point P Any to the line segment P Base P Tail . Solving the following system of equations can obtain its spatial coordinates:

[0043]

[0044] x Stroke = (x a - x b )·t + x a (4)

[0045] y Stroke = (y a - y b )·t + y a (5)

[0046] z Stroke = (z a - z b )·t + z a (6)

[0047] In the formula, t is an auxiliary variable required to solve the equation. (x a , y a , z a ) and (x b , y b , z b ) are the spatial coordinates of any two points on the line segment P Base P Tail . In this step, these two points are P Base and P Tail .

[0048] 3) Connect point P Min and P Base to obtain the line segment P Min P Base , connect point P Min and P Tail to obtain the line segment P Min P Tail . The line segment P Base P Tail , the line segment P MinP Base and line segment P Min P Tail form a triangle P Base P Tail P Min This triangle is a Delaunay triangle. Then, using line segment P Min P Base and line segment P Min P Tail as the new base lines, point P Min as the base point of line segment P Min P Base and point P Tail as the base point of line segment P Min P Tail .

[0049] 4) Repeat 2) and 3) until all grid vertices of matrix M Densen are in a certain Delaunay triangle, and all Delaunay triangles form the initial Delaunay triangular mesh. At this time, the topological relationships of all grid vertices can be represented by the initial Delaunay triangular mesh.

[0050] Step 2: Data sparsification.

[0051] Receive the initial Delaunay triangular mesh, and use the Visvalingam-Whyatt sparsification algorithm to sparsify the initial Delaunay triangular mesh to greatly reduce the number of grid vertices to be calculated in subsequent steps. The implementation steps of the Visvalingam-Whyatt sparsification algorithm are as follows:

[0052] 1) Receive the initial Delaunay triangular mesh, and delete the vertex that is not on the longest side of the Delaunay triangle with the smallest area. The area S Delaunay of any Delaunay triangle is calculated as follows:

[0053]

[0054] s1 = (x2 - x1) 2 + (y2 - y1) 2 + (z2 - z1) 2 (8)

[0055] s2 = (x3 - x1) 2 + (y3 - y1) 2 + (z3 - z1) 2 (9)

[0056] Wherein, s1 and s2 are auxiliary variables required for solving the equation. (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) are the spatial coordinates of the three vertices of the Delaunay triangle whose area is to be calculated.

[0057] 2) Use the method in step 1 to generate a Delaunay triangular mesh again for the remaining grid vertices.

[0058] 3) Perform the operation in 1) on the newly generated Delaunay triangular mesh, and delete one grid vertex again until the ratio of the number of remaining grid vertices to the number of grid vertices in the original matrix M Densen reaches the preset value N res . N res The larger the value, the higher the drawing accuracy, but the slower the calculation speed. In this embodiment, N res is set to 30%.

[0059] 4) Put the spatial coordinates of the thinned grid vertices and the corresponding heat transfer amounts into a new matrix M Sparse , and the data stored in this matrix is the data of the thinned grid vertices.

[0060] Step three, generate a sparse Delaunay triangular mesh.

[0061] Receive the matrix M of the data of the thinned grid vertices Sparse , and quickly construct a sparse Delaunay triangular mesh on the thinned grid vertices. The construction method is exactly the same as that in step 1.

[0062] Step four, generate a sparse regular rectangular mesh.

[0063] Receive the matrix M of the data of the thinned grid vertices Sparse , traverse the matrix M Sparse , record the x coordinate of the grid vertex with the largest x coordinate as x max , record the x coordinate of the grid vertex with the smallest x coordinate as x min , x max and the difference between x min is d x . Record the y coordinate of the grid vertex with the largest y coordinate as y max , record the y coordinate of the grid vertex with the smallest y coordinate as y min , y max and the difference between y min is d y . Record the z coordinate of the grid vertex with the largest z coordinate as z max , record the z coordinate of the grid vertex with the smallest z coordinate as z min , z max and the difference between z min is d z。Divide d x equidistantly into N x parts, then the length of each part is d x / N x 。Divide d y equidistantly into N y parts, then the length of each part is d y / N y 。Divide d z equidistantly into N z parts, then the length of each part is d z / N z 。Among them, N x , N y and N z are all preset precision parameters, that is, the precision parameter one defined in the present invention includes N x , N y and N z ; the larger N x , N y and N z are, the higher the image calculation precision is, but the longer the calculation time is. In this embodiment, N x is set to 400, N y is set to 400, and N z is set to 400. Then a sparse regular rectangular grid with 400 rows, 400 columns and 400 pages, which altogether contains 64,000,000 grid vertices, is generated, that is, the number of grid vertices of the generated sparse regular rectangular grid is N x ×N y ×N z . The calculation method of the spatial coordinates of the grid vertex in the i-th row, j-th column and k-th page is as follows:

[0064]

[0065]

[0066]

[0067] In the formula, i is an integer ranging from 1 to N x , j is an integer ranging from 1 to N y , and k is an integer ranging from 1 to N z . Since the three-dimensional model is surrounded by a two-dimensional plane, the sparse regular rectangular grid is a two-dimensional grid. This means that one of d x , d y and d z must be 0. In this embodiment, the subsequent operations in the case where d z is 0 are given, while for d x or d yIn the case where it is 0, it can be replaced by d by setting the x-axis or y-axis as the z-axis. z In the case where it is 0 (that is, swapping the z-coordinate and x-coordinate of all grid vertices or swapping the z-coordinate and y-coordinate of all grid vertices). Therefore, the subsequent operations of this embodiment can be applied to d. x , d y and d z In the case where any one of them is 0. Since d z is 0, the sparse regular rectangular grid is a sparse regular rectangular grid with 400 rows and 400 columns, containing a total of 160,000 grid vertices.

[0068] Step Five, Delaunay triangulation interpolation.

[0069] Receive the spatial coordinates of each grid vertex of the sparse Delaunay triangular grid and the sparse regular rectangular grid, and calculate the heat transfer amount of each grid vertex of the sparse regular rectangular grid. For each grid vertex of any sparse regular rectangular grid, the method of calculating its heat transfer amount according to the sparse Delaunay triangular grid first needs to traverse the sparse Delaunay triangular grid to determine which Delaunay triangle each grid vertex of the sparse regular rectangular grid to be calculated for heat transfer amount falls into. To determine whether a grid vertex is in a certain Delaunay triangle, a ray along the positive x-axis needs to be drawn from the grid vertex. If the number of intersections of this ray with the three sides of the Delaunay triangle is even, the grid vertex is outside the Delaunay triangle. If the number of intersections of the three sides of the Delaunay triangle is odd, the grid vertex is inside the Delaunay triangle. The calculation method of the heat transfer amount of the grid vertex at the i-th row and j-th column of the sparse regular rectangular grid by Delaunay triangulation interpolation is as follows:

[0070]

[0071]

[0072]

[0073]

[0074] In the formula, (x O , y O ), (x P , y P ), (x Q , y Q ) are respectively the spatial coordinates of the three vertices of the Delaunay triangle where the grid vertex at the i-th row and j-th column is located, Q O, Q P , Q Q They are the gas thermal parameters corresponding to the three vertices of the Delaunay triangle where the drawing node in the i-th row and j-th column is located. After calculating the gas thermal parameters of the grid vertices of all sparse regular rectangular grids, the spatial coordinates of the corresponding grid vertices are put into a new matrix M together. Qsparse In this embodiment, M Qsparse is a matrix with 160,000 rows and 3 columns. Each row represents the grid vertex of a sparse regular rectangular grid. The first two columns are the x-coordinate and y-coordinate of the grid vertex respectively, and the third column is the gas thermal parameter of the corresponding grid vertex, that is, the heat transfer quantity.

[0075] Step Six, uncertainty quantification calculation.

[0076] For all samples, that is, the working conditions required for uncertainty quantification calculation, the operations from Step One to Step Five are performed, and the spatial coordinates and gas thermal parameters of each grid vertex of each sparse regular rectangular grid of each sample are obtained. Input them into the publicly available uncertainty quantification calculation library aPC_Matlab, and the uncertainty indices (mean and standard deviation) of the gas thermal parameters of each grid vertex of each sparse regular rectangular grid can be calculated. In this embodiment, the standard deviation of the heat transfer quantity is studied. After calculating the standard deviation of the heat transfer quantity of the grid vertices of all sparse regular rectangular grids, the spatial coordinates of the corresponding grid vertices are put into a new matrix M together. Usparse M Usparse is a matrix with 160,000 rows and 3 columns. Each row represents the grid vertex of a sparse regular rectangular grid. The first two columns are the x-coordinate and y-coordinate of the grid vertex respectively, and the third column is the standard deviation of the heat transfer quantity of the corresponding grid vertex.

[0077] Step Seven, generate a dense regular rectangular grid.

[0078] Receive matrix M Usparse , traverse matrix M Usparse , denote the x-coordinate of the grid vertex with the largest x-coordinate as x Umax , denote the x-coordinate of the grid vertex with the smallest x-coordinate as x Umin , x Umax minus x Umin is d Ux . Denote the y-coordinate of the grid vertex with the largest y-coordinate as y Umax , denote the y-coordinate of the grid vertex with the smallest y-coordinate as y Umin , y Umax minus y Umin is d Uy . Take d Ux and equally divide it into N Ux parts, then the length of each part is d Ux / N Ux . Take dUy Equally divided into N Uy parts, and the length of each part is d Uy / N Uy . Among them, N Ux , N Uy and N Uz are all preset precision parameters, that is, the precision parameter two of the present invention includes N Ux , N Uy and N Uz . The larger N Ux and N Uy are, the higher the image calculation accuracy is, but the calculation time is longer. In this embodiment, N Ux is set to 2000, and N Uy is set to 2000. Then a sparse regular rectangular grid with 2000 rows and 2000 columns, a total of 4000000 grid vertices, is generated, that is, the number of grid vertices of the generated dense regular rectangular grid is N Ux ×N Uy . Among them, the calculation method of the spatial coordinates of the grid vertex in the i U -th row and j U -th column is as follows:

[0079]

[0080]

[0081] In the formula, i U is an integer with a value ranging from 1 to N Ux , and j U is an integer with a value ranging from 1 to N Uy .

[0082] Step Eight, double BiCubic function cubic convolution encryption.

[0083] Receive matrix M Usparse , and the spatial coordinates of each grid vertex of the dense regular rectangular grid, and use the double BiCubic function cubic convolution method for encryption to obtain the standard deviation of the heat transfer amount of each grid vertex of the dense regular rectangular grid. The steps of using the BiCubic function cubic convolution method to solve the uncertainty index of the gas thermal parameter (in this embodiment, that is, the standard deviation of the heat transfer amount) for the grid vertex P U in the i U -th row and j U -th column of the dense regular rectangular grid are as follows:

[0084] 1) Traverse matrix M Usparse , and find four grid vertices that meet the following requirements: the x coordinate and P UThe difference in the x - coordinate is negative, and the absolute value of the difference is the smallest and the second - smallest among all the grid vertices, and the y - coordinate and P U The difference in the y - coordinate is negative, and the absolute value of the difference is the smallest and the second - smallest among all the grid vertices; the x - coordinate and P U The difference in the x - coordinate is positive, and the absolute value of the difference is the smallest and the second - smallest among all the grid vertices, and the y - coordinate and P U The difference in the y - coordinate is negative, and the absolute value of the difference is the smallest and the second - smallest among all the grid vertices; the x - coordinate and P U The difference in the x - coordinate is negative, and the absolute value of the difference is the smallest and the second - smallest among all the grid vertices, and the y - coordinate and P U The difference in the y - coordinate is positive, and the absolute value of the difference is the smallest and the second - smallest among all the grid vertices; the x - coordinate and P U The difference in the x - coordinate is positive, and the absolute value of the difference is the smallest and the second - smallest among all the grid vertices, and the y - coordinate and P U The difference in the y - coordinate is positive, and the absolute value of the difference is the smallest and the second - smallest among all the grid vertices. Finally, the sixteen points as shown in Figure 2 are found: a 11 、a 12 、a 13 、a 14 、a 21 、a 22 、a 23 、a 24 、a 31 、a 32 、a 33 、a 34 、a 41 、a 42 、a 43 、a 44 .

[0085] 2) Construct the BiCubic function as follows:

[0086]

[0087] In the formula, a is 0.5. x Bi is a parameter for auxiliary calculation.

[0088] 3) Then the uncertainty index of the gas - heat parameter of P U can be calculated as follows:

[0089]

[0090] In the formula, i PU is an integer with a value range from 1 to 4, jPU is an integer with a value range from 1 to 4. is the grid vertex of the heat transfer deviation, that is, the uncertainty index of the gas thermal parameters calculated here.

[0091] and are parameters for auxiliary calculation. For For For For For For For For where u PU and v PU are variables for auxiliary calculation, and their calculation methods are as follows:

[0092]

[0093]

[0094] In the formula, floor() means rounding down in mathematics.

[0095] When the grid vertex P U in the i U th row and j U th column of the dense regular rectangular grid is located on the boundary of the dense regular rectangular grid, the number of grid vertices around it is less than 16. At this time, it is necessary to traverse the matrix M Usparse . Use the nearest principle to assign the heat transfer deviation of the grid vertex with the smallest Euclidean distance to P U , and the calculation method of the Euclidean distance is as follows: U

[0096]

[0097] In the formula, (x close , y close ) are the spatial coordinates of the grid vertex whose Euclidean distance from P U is to be solved, and (x PU , y PU ) are the spatial coordinates of P U .

[0098] After calculating the uncertainty index of the gas thermal parameters of each grid vertex of the dense regular rectangular grid, put it together with the spatial coordinates of each grid vertex of the dense regular rectangular grid into a new matrix M Udense . M Udense ​It is a matrix of 4,000,000 rows and 3 columns, where each row represents the grid vertices of a dense regular rectangular grid. The first two columns are the x and y coordinates of the grid vertices respectively, and the third column is the uncertainty index of the gas thermal parameters of the corresponding grid vertices, that is, the standard deviation of the heat transfer amount in this embodiment.

[0099] Step Nine, generate the distribution cloud map of the uncertainty index of the gas thermal parameters.

[0100] Receiving the spatial coordinates of each grid vertex of the dense regular rectangular grid and the standard deviation of the heat transfer amount and inputting them into the open-source computing library matplotlib can generate the distribution cloud map of the standard deviation of the heat transfer amount as shown in Figure 3 Figure.

[0101] Figure 3 It is the distribution cloud map of the standard deviation of the heat transfer amount obtained in the embodiment of the present invention. In the figure, Q represents the standard deviation of the heat transfer amount. It can be intuitively found from the figure that there are two high heat transfer deviation regions (Region I and Region II) in the grooved blade tip. Among them, Region I is near the leading edge impact point, and Region II is near the fin. Therefore, in the design and manufacture of gas turbine blades, the film cooling structure should be designed mainly in Region I and Region II to strengthen the cooling to protect the wall surface at that place. In the spraying of the thermal barrier coating, the coating thickness in Region I and Region II needs to be significantly greater than that in other regions. In fact, according to Figure 3 the distribution cloud map of the standard deviation of the heat transfer amount given, the spraying scheme of the thermal barrier coating can be directly determined. The darker the color in the figure, the thicker the thermal barrier coating required. It is impossible to obtain the distribution cloud map of the standard deviation of the heat transfer amount as shown in Figure 3 Figure by using the traditional uncertainty data mining method. Therefore, the spraying of the thermal barrier coating is often carried out according to the over-interference strategy based on experience. Therefore, the actual thermal barrier coating is often too thick, which not only affects the aerodynamic performance but also wastes expensive thermal barrier coating materials. However, the distribution cloud map of the standard deviation of the heat transfer amount calculated according to the present invention can design the thermal barrier coating according to the precise wall protection requirements. Therefore, the present invention is of great significance for turbine designers to understand the uncertainty phenomenon during the operation of the gas turbine tip and to guide the turbine design.

Claims

1. A data mining method for uncertainty quantification of gas turbines based on cubic convolution, characterized in that It includes the following steps: Step 1: Generate the original dense grid vertex data using the geometric parameters of the gas turbine and the gas thermal parameters to be studied, and construct an initial Delaunay triangular grid on the grid vertices; Step 2: Sparsify the data of the initial Delaunay triangular grid; Step 3: Construct a sparse Delaunay triangular grid on the grid vertices after data sparsification; Step 4: Generate a sparse regular rectangular grid at equal intervals according to a preset accuracy parameter one; Step 5: Calculate the gas thermal parameters of each grid vertex of the sparse regular rectangular grid according to the spatial coordinates of each grid vertex of the sparse Delaunay triangular grid and the sparse regular rectangular grid; Step 6: For all working conditions that need to be calculated for uncertainty quantification, perform operations from Step 1 to Step 5 to obtain the spatial coordinates and gas thermal parameters of each grid vertex of each sparse regular rectangular grid for each working condition; use the polynomial chaos method to calculate the uncertainty indicators, namely the mean and standard deviation, of the gas thermal parameters of each grid vertex of each sparse regular rectangular grid; Step 7: Generate a dense regular rectangular grid at equal intervals according to a preset accuracy parameter two; Step 8: According to the spatial coordinates and uncertainty indicators of the gas thermal parameters of each grid vertex of the sparse regular rectangular grid, and the spatial coordinates of each grid vertex of the dense regular rectangular grid, use the bicubic function cubic convolution method for encryption to obtain the uncertainty indicators of the gas thermal parameters of each grid vertex of the dense regular rectangular grid; Step 9: Input the spatial coordinates and uncertainty indicators of the gas thermal parameters of each grid vertex of the dense regular rectangular grid into the open-source computing library matplotlib to generate a distribution cloud map of the uncertainty indicators of the gas thermal parameters.

2. The method for gas turbine uncertainty quantification data mining based on cubic convolution according to claim 1, wherein The geometric parameters of the gas turbine are the axial chord length, groove depth, tip clearance, pitch, and shoulder wall thickness of the grooved tip of the gas turbine blade; the gas thermal parameters to be studied are the heat transfer amount.

3. The method for gas turbine uncertainty quantification data mining based on cubic convolution according to claim 1 or 2, characterized in that, In the first step, the geometric parameters of the gas turbine and the gas thermal parameters to be studied are input into the open-source computational fluid dynamics library OPENFOAM to obtain the original dense grid vertex data; the original dense grid vertex data is a matrix M with L rows and 4 columns. Densen , where the number of L is the number of the original dense grid vertex data, and each row represents the spatial coordinates and gas thermal parameters of a grid vertex. Among them, the first three columns represent the x coordinate, y coordinate, and z coordinate of the grid vertex, and the fourth column represents the gas thermal parameter of the grid vertex.

4. The method for gas turbine uncertainty quantification data mining based on cubic convolution according to claim 3, wherein In Step 1, the Lawson algorithm is used to construct an initial Delaunay triangular grid on the original dense grid vertices, and the method is as follows: 1) Denote the matrix M Densen The grid vertex represented by the first row of Base as the base point P Densen Traverse all the grid vertices of the matrix M Base and find the grid vertex with the largest Euclidean distance from the base point P Tail Denote it as P Base Connect P Tail and P Base to obtain the line segment P Tail P Tail Denote it as the base line; For any grid vertex P Densen of the matrix M Any The Euclidean distance d Base from the base point P Any is calculated as follows: wherein, (x Any , y Any , z Any ) are the spatial coordinates of P Any , and (x base , y base , z base ) are the spatial coordinates of the base point P Base ; 2) Traverse the matrix M Densen for all grid vertices, calculate the Euclidean distances from all grid vertices with x - coordinates greater than the base point P Base to the line segment P Base P Tail ; find the point P Base P Tail with the minimum Euclidean distance to the line segment P Min ; for any grid vertex P Densen in the matrix M Any to the line segment P Base P Tail the Euclidean distance d Anyline is calculated as follows: Wherein, (x Stroke , y Stroke , z Stroke ) is the space coordinate of the foot of the perpendicular from P Any to the line segment P Base P Tail . Solve the following simultaneous equations to obtain its space coordinates: x Stroke = (x a - x b ) · t + x a (4) y Stroke = (y a - y b ) · t + y a (5) z Stroke = (z a - z b )·t + z a (6) where t is an auxiliary variable required to solve the equation, (x a , y a , z a ) and (x b , y b , z b ) are the spatial coordinates of any two points on the line segment P Base P Tail . In this step, these two points are P Base and P Tail ; 3) Connect point P Min and P Base to obtain line segment P Min P Base ; connect point P Min and P Tail to obtain line segment P Min P Tail ; line segment P Base P Tail , line segment P Min P Base and line segment P Min P Tail form a triangle P Base P Tail P Min , and this triangle is a Delaunay triangle; then using line segment P Min P Base and line segment P Min P Tail as the new base lines, point P Min as the base point of line segment P Min P Base , and point P Tail as the base point of line segment P Min P Tail ; 4) Repeat steps 2) and 3) until all grid vertices of matrix M Densen are within one of the Delaunay triangles, and all the Delaunay triangles form the initial Delaunay triangular grid; at this time, the topological relationships of all grid vertices are represented by the initial Delaunay triangular grid.

5. The gas turbine uncertainty quantification data mining method based on cubic convolution according to claim 4, characterized in that In Step 2, the Visvalingam-Whyatt sparse algorithm is used to sparsify the data of the initial Delaunay triangular grid, and the steps are as follows: 1) Receive the initial Delaunay triangular mesh, delete the vertex that is not on the longest side of the Delaunay triangle with the smallest area, and the area S of any Delaunay triangle Delaunay is calculated as follows: s1 = (x2 - x1) 2 + (y2 - y1) 2 + (z2 - z1) 2 (8) s2 = (x3 - x1) 2 + (y3 - y1) 2 + (z3 - z1) 2 (9) In the formula, s1 and s2 are auxiliary variables required for solving the equation, and (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) are the spatial coordinates of the three vertices of the Delaunay triangle whose area is to be calculated; 2) Use the method of Step 1 to generate a Delaunay triangular grid again on the remaining grid vertices; 3) Perform operation 1) on the regenerated Delaunay triangular mesh, and delete one mesh vertex again until the ratio of the number of remaining mesh vertices to the number of mesh vertices of the original matrix M Densen reaches the preset value N res ; 3) Put the spatial coordinates of the thinned grid vertices and the corresponding gas thermal parameters to be studied into a new matrix M Sparse , and the data stored in this matrix are the thinned grid vertex data.

6. The method for gas turbine uncertainty quantification data mining based on cubic convolution according to claim 5, characterized in that In the fourth step, traverse the matrix M Sparse , denote the x - coordinate of the grid vertex with the largest x - coordinate as x max , denote the x - coordinate of the grid vertex with the smallest x - coordinate as x min , x max and the difference between x min is d x ; denote the y - coordinate of the grid vertex with the largest y - coordinate as y max , denote the y - coordinate of the grid vertex with the smallest y - coordinate as y min , y max and the difference between y min is d y ; denote the z - coordinate of the grid vertex with the largest z - coordinate as z max , denote the z - coordinate of the grid vertex with the smallest z - coordinate as z min , z max and the difference between z min is d z ; equally divide d x into N x parts, then the length of each part is d x / N x ; equally divide d y into N y parts, then the length of each part is d y / N y ; equally divide d z into N z parts, then the length of each part is d z / N z ; the first precision parameter includes N x , N y and N z , and the number of grid vertices of the generated sparse regular rectangular grid is N x ×N y ×N z ; the calculation method of the spatial coordinates of the grid vertex in the i - th row, j - th column and k - th page is as follows: where i is an integer ranging from 1 to N x and j is an integer ranging from 1 to N y and k is an integer ranging from 1 to N z .

7. The method for gas turbine uncertainty quantification data mining based on cubic convolution according to claim 6, characterized in that In Step 5, the Delaunay triangulation interpolation calculation method for the gas thermal parameters of the grid vertex in the i-th row and j-th column of the sparse regular rectangular grid is as follows: where (x O , y O ), (x P , y P ), and (x Q , y Q ) are the spatial coordinates of the three vertices of the Delaunay triangle where the grid vertex in the i-th row and j-th column is located, and Q O , Q P , and Q Q are the gas thermal parameters corresponding to the three vertices of the Delaunay triangle where the drawing node in the i-th row and j-th column is located. After calculating the gas thermal parameters to be studied for the grid vertices of all sparse regular rectangular grids, the spatial coordinates of the corresponding grid vertices are put into a new matrix M Qsparse ; each row of the matrix M Qsparse represents a grid vertex of a sparse regular rectangular grid, the first two columns are the x coordinate and y coordinate of the grid vertex respectively, and the third column is the gas thermal parameter of the corresponding grid vertex.

8. The method for gas turbine uncertainty quantification data mining based on cubic convolution according to claim 7, characterized in that In Step 6, after calculating the uncertainty indices of the gas thermal parameters of the grid vertices of all sparse regular rectangular grids, the spatial coordinates of the corresponding grid vertices are put into a new matrix M Usparse ; In Step 7, traverse matrix M Usparse , denote the x - coordinate of the grid vertex with the largest x - coordinate as x Umax , denote the x - coordinate of the grid vertex with the smallest x - coordinate as x Umin , the difference between x Umax and x Umin is d Ux ; Denote the y - coordinate of the grid vertex with the largest y - coordinate as y Umax , denote the y - coordinate of the grid vertex with the smallest y - coordinate as y Umin , the difference between y Umax and y Umin is d Uy ; Divide d Ux into N Ux equal - spaced parts, then the length of each part is d Ux / N Ux ; Divide d Uy into N Uy equal - spaced parts, then the length of each part is d Uy / N Uy ; The precision parameter two includes N Ux , N Uy and N Uz , the number of grid vertices of the generated dense regular rectangular grid is N Ux ×N Uy pieces, and the calculation method of the spatial coordinates of the grid vertex in the i U - th row and j U - th column is as follows: where \(i\) U is an integer ranging from 1 to N Ux and \(j\) U is an integer ranging from 1 to N Uy .

9. The method for gas turbine uncertainty quantification data mining based on cubic convolution according to claim 8, wherein In the eighth step, for the grid vertex P at the i-th U row and j-th U column of the dense regular rectangular grid, U the steps for solving the uncertainty index of the gas thermal parameters using the bicubic function cubic convolution method are as follows: 1) Traverse matrix M Usparse , and find four grid vertices that meet the following requirements: the difference between the x - coordinate and the x - coordinate of P U is negative, and the absolute value of the difference is the smallest and the second - smallest among all grid vertices, and the difference between the y - coordinate and the y - coordinate of P U is negative, and the absolute value of the difference is the smallest and the second - smallest among all grid vertices; the difference between the x - coordinate and the x - coordinate of P U is positive, and the absolute value of the difference is the smallest and the second - smallest among all grid vertices, and the difference between the y - coordinate and the y - coordinate of P U is negative, and the absolute value of the difference is the smallest and the second - smallest among all grid vertices; the difference between the x - coordinate and the x - coordinate of P U is negative, and the absolute value of the difference is the smallest and the second - smallest among all grid vertices, and the difference between the y - coordinate and the y - coordinate of P U is positive, and the absolute value of the difference is the smallest and the second - smallest among all grid vertices; the difference between the x - coordinate and the x - coordinate of P U is positive, and the absolute value of the difference is the smallest and the second - smallest among all grid vertices, and the difference between the y - coordinate and the y - coordinate of P U is positive, and the absolute value of the difference is the smallest and the second - smallest among all grid vertices; 2) Construct a bicubic function as follows: where a is 0.5 and x Bi is a parameter for auxiliary calculation; 3) P U The uncertainty index of the gas thermal parameters is calculated as follows: where i PU is an integer with a value range from 1 to 4, and j PU is an integer with a value range from 1 to 4, is the uncertainty index of the gas thermal parameter of the grid vertex , and and are parameters for auxiliary calculation; for for for for for for for for where u PU and v PU are variables for auxiliary calculation, and their calculation methods are as follows: In the formula, floor() represents rounding down mathematically; When the grid vertex P at the i-th U row and j-th U column of the dense regular rectangular grid U is located on the boundary of the dense regular rectangular grid, the number of surrounding grid vertices is less than 16. At this time, traverse the matrix M Usparse ; Use the nearest principle to assign the uncertainty index of the gas thermal parameter of the grid vertex with the smallest Euclidean distance to P U , and the calculation method of the Euclidean distance is as follows: U ​ wherein, (x close , y close ) are the spatial coordinates of the grid vertex for which the Euclidean distance from P U is to be solved, and (x PU , y PU ) are the spatial coordinates of P U ; After calculating the uncertainty index of the gas thermal parameters at each grid vertex of the computationally intensive regular rectangular grid, it is placed together with the spatial coordinates of each grid vertex of the regular rectangular grid into a new matrix M Udense , where each row represents a grid vertex of the regular rectangular grid, the first two columns are the x and y coordinates of the grid vertex respectively, and the third column is the uncertainty index of the gas thermal parameters corresponding to the grid vertex.

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