A method for calculating the failure probability of gas turbine blades

Abstract

A method for calculating the failure probability of a gas turbine blade, based on the probability density distribution function of the uncertainty input variable of the gas turbine blade, generates the coordinates of the integral nodes required for solving the chaotic polynomial, generates the spatial coordinates of the mesh vertices for the physical model to be studied, obtains the physical quantity of each mesh vertex of the working condition represented by each integral node, that is, the wall temperature of the gas turbine blade; calculates the coefficients of the chaotic polynomial of each physical quantity, obtains the explicit equation of the chaotic polynomial; calculates the failure probability of each mesh vertex; generates a Delaunay triangulation according to the spatial coordinates of the mesh vertex, calculates the failure probability of the refined node; generates a gas turbine blade failure probability distribution cloud map according to the failure probabilities at two locations. The present invention is based on polynomial chaos theory, carries out the calculation of the failure probability of gas turbine blades from an uncertainty framework, does not rely on engineering experience, and is of great significance to the research and development, manufacturing, operation and maintenance of gas turbine blades.

Description

Technical Field

[0001] The invention belongs to the technical field of turbine reliability analysis, and in particular relates to a method for calculating the failure probability of a gas turbine blade. Background Art

[0002] Gas turbines play an irreplaceable role in national defense construction and national economic development. As an important power output device, they are widely used in aircraft, ships and power generation industries. Gas turbines are mainly composed of three parts: compressor, combustion chamber and gas turbine. The compressor continuously inhales air and compresses it. The combustion chamber receives the compressed air and mixes it with fuel and ignites it, eventually generating high-temperature combustion gas. Finally, the high-temperature combustion gas flows into the gas turbine to expand and do work. Among the three core components, the operating environment of the gas turbine as a power output component is the worst. Under extremely high operating temperatures, the gas turbine blades are very likely to fail due to defects such as wear, thermal corrosion, and thermal fatigue. At present, both domestic and foreign countries use regular maintenance to detect the failure of gas turbine blades. However, this method has the following problems: 1. Regular maintenance requires a lot of time and money. 2. The choice of maintenance time depends entirely on experience, without theoretical calculations, and there are hidden dangers for newly designed gas turbines. 3. Regular maintenance is only a protective measure, and it cannot guide the design from the design stage of gas turbine blades. Frequent overhaul and unpredictable failure of gas turbine blades have become one of the biggest obstacles to the manufacture and application of advanced gas turbines. Summary of the invention

[0003] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a method for calculating the failure probability of gas turbine blades to predict the failure of gas turbine blades. The invention is mainly based on polynomial chaos theory, and calculates the failure probability of gas turbine blades from an uncertainty framework without relying on engineering experience. It is of great significance to the research, development, manufacturing, operation and maintenance of gas turbine blades.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is:

[0005] A method for calculating the failure probability of a gas turbine blade comprises the following steps:

[0006] Step 1, according to the probability density distribution function of the uncertainty input variable of the gas turbine blade, based on the polynomial chaos theory, the coordinates of the integral nodes required for solving the chaos polynomial are generated;

[0007] Step 2, combining the geometric parameters of the gas turbine blades, and using the open source computational fluid dynamics library OpenFOAM to generate the spatial coordinates of the mesh vertices;

[0008] Step 3, according to the coordinates of the integration nodes and the spatial coordinates of the mesh vertices, using the open source computational fluid dynamics library OpenFOAM to obtain the physical quantity of each mesh vertex of the working condition represented by each integration node, the physical quantity being the wall temperature of the gas turbine blade;

[0009] Step 4, according to the coordinates of the integration node and the physical quantity of each mesh vertex, based on the Galerkin projection method, calculate the coefficients of the chaotic polynomial of the physical quantity of each mesh vertex, thereby calculating the explicit equation of the chaotic polynomial of the physical quantity of each mesh vertex;

[0010] Step 5, calculating the failure probability of each grid vertex according to the explicit equation of the chaotic polynomial combined with the Monte Carlo sampling method;

[0011] Step 6, generating a Delaunay triangulation network according to the spatial coordinates of the mesh vertices;

[0012] Step 7, taking the midpoint of each edge of each Delaunay triangle in the Delaunay triangulation as a refinement node, and calculating the spatial coordinates of the refinement node;

[0013] Step 8, calculating the failure probability of the refined node using an inverse distance interpolation method;

[0014] Step 9: Generate a gas turbine blade failure probability distribution cloud map according to the failure probability of each mesh vertex and the failure probability of the refined node.

[0015] Compared with the prior art, the present invention has the following beneficial effects:

[0016] (1) The present invention is based on numerical calculations and does not rely on experiments at all. It also does not require stopping the running gas turbine like traditional maintenance methods, which can save a lot of time and cost.

[0017] (2) Uncertainty theory is introduced into the failure calculation of gas turbine blades, and prediction is carried out from the perspective of mathematical theory, which reduces the empirical nature of failure prediction of gas turbine blades.

[0018] (3) The gas turbine blade failure probability distribution cloud map provided by the present invention can not only predict the failure of the gas turbine being operated, but also provide guidance for the gas turbine blades being designed.

[0019] (4) The use of polynomial chaos method as a mathematical tool for uncertainty quantification can significantly reduce the number of calculation samples and greatly accelerate the iteration speed of gas turbine failure prediction and optimization design.

[0020] (5) The present invention allows the customization of the physical quantities that need to be calculated in the physical quantity solving module. Therefore, failures caused by different reasons can be flexibly calculated. For example, when the physical quantity that needs to be solved in the physical quantity solving module is set to the wall temperature, the present invention can be used to predict the failure of gas turbine blades caused by high temperature. When the physical quantity that needs to be solved in the physical quantity solving module is set to stress, the present invention can be used to predict the failure of gas turbine blades caused by high load. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Schematic diagram of the blade geometry parameters of the GE_E3 gas turbine.

[0022] Figure 2 Schematic diagram of the system of the present invention.

[0023] Figure 3 This is the failure probability distribution cloud diagram of GE_E3 gas turbine blades. DETAILED DESCRIPTION

[0024] The embodiments of the present invention are described in detail below with reference to the accompanying drawings and examples.

[0025] Example: The calculation model is derived from the widely used blade shape of the GE_E3 gas turbine (Kwak JS, Han J C. Heat-transfer coefficients of a turbine blade-tip and near-tip regions [J]. Journal of thermophysics and heat transfer, 2003, 17 (3): 297-303.). The geometric parameters of the blade shape of the GE_E3 gas turbine are shown in Table 1. The meaning of each geometric parameter is shown in Figure 1 .

[0026] Table 1 Geometric parameters of the blade shape of the GE_E3 gas turbine

[0027] Geometry parameter name Value(mm) Tip clearance(S) 0.4 Groove Depth (D) 5.08 Shoulder wall thickness (G) 2.29 Blade height (H) 122

[0028] refer to Figure 2 This embodiment is based on a method for calculating the failure probability of a gas turbine blade and is implemented based on the following functional modules:

[0029] 1. An integration node coordinate generation module receives the probability density distribution of the uncertainty input variables of the gas turbine blades, and uses the polynomial chaos theory to generate the coordinates of the integration nodes required to solve the chaos polynomial according to the dimension n and calculation accuracy k of the problem. In this embodiment, the blade tip clearance (S), the mainstream inlet total temperature (T0), the mainstream inlet total pressure (P0) and the inlet airflow angle (A) are selected as uncertainty variables, which respectively satisfy the Gaussian distribution in Table 2. In this embodiment, the coordinates of the integration node include four variables, namely the blade tip clearance, the mainstream inlet total temperature, the mainstream inlet total pressure and the inlet airflow angle of the working condition represented by this integration node. In the chaos polynomial theory, the coordinates of the integration node are calculated by formula (1). In this embodiment, n=4, k=4:

[0030]

[0031] In the formula, Represents an n-dimensional k-order integration node n represents the dimension of the problem, that is, the number of types of uncertain input quantities, k represents the calculation accuracy, q is a constant, q=k+n, |i|=i1+i2+i3+…+i j +…+i n , i j represents the ordinal number of the one-dimensional integration node of the j-th chaotic polynomial, j = 1, 2, ..., n, Indicates the ordinal number is i j The coordinates of each integration node contain n parameters, i.e., the uncertainty input of the working condition represented by the integration node.

[0032] In order to solve the coefficients of the chaotic polynomial, it is also necessary to give the weight w corresponding to each integral node, which can be calculated by formula (2):

[0033]

[0034] In the formula Indicates the ordinal number is i j The component of the integration node weight, Represents a vector consisting of its components.

[0035] Table 2 Probability density distribution of uncertainty input

[0036] Geometry parameter name Mean Standard Deviation Tip clearance(S) 0.4mm 0.08mm Main stream inlet total temperature (D) 709.0K 17.24K Main flow inlet total pressure (G) 126900Pa 7480Pa Inlet airflow angle (H) 0.0° 0.67°

[0037] According to the dimension n of the problem and the calculation accuracy k, a chaotic polynomial of the system output y can also be established. In this embodiment, y is the wall temperature of the gas turbine blade.

[0038]

[0039] Where a0, Respectively represent the orthogonal basis I0, The corresponding coefficient, that is, the quantity that needs to be solved, is the projection of each order, θ is a random variable; in actual operation, according to the dimension n of the problem and the calculation accuracy k, the expression of the wall temperature y is truncated to:

[0040]

[0041] Wherein, P is the order of the chaotic polynomial. The larger the value of P, the more accurate the calculation. In this embodiment, P is set to 4. j is the coefficient of the jth orthogonal basis, that is, the discrete form of the coefficient of the orthogonal basis of each order of the chaotic polynomial, Ψ j (ξ) is the jth orthogonal basis in the discrete case.

[0042] 2. A mesh vertex spatial coordinate generation module is used to input the physical model to be studied. In this embodiment, the physical model to be studied is the blade shape of the GE_E3 gas turbine. The geometric parameters of the blade shape of the GE_E3 gas turbine are input into the open source computational fluid dynamics library OpenFOAM to generate the spatial coordinates of the mesh vertices. In this embodiment, a total of 5.6 million mesh vertices are generated.

[0043] 3. A physical quantity solving module receives the coordinates of the integration nodes calculated by the integration node coordinate generating module and the spatial coordinates of each mesh vertex calculated by the mesh vertex spatial coordinate generating module, and inputs them into the open source computational fluid dynamics library OpenFOAM, so as to obtain the physical quantity of each mesh vertex of the working condition represented by each integration node. In this embodiment, the physical quantity is the wall temperature of the gas turbine blade.

[0044] 4. A chaotic polynomial explicit equation solving module receives the integral node coordinates calculated by the integral node coordinate generating module and the wall temperature of each mesh vertex of the working condition represented by each integral node generated by the physical quantity solving module. The coefficients of the multi-chaotic polynomial of the wall temperature of each mesh vertex are calculated based on the Galerkin projection method, thereby calculating the explicit equation of the chaotic polynomial of the wall temperature of each mesh vertex.

[0045] Among them, the calculation formula of the coefficient of the multi-chaos polynomial is as follows:

[0046]

[0047] In the formula, Ψ j (ξ) represents the jth orthogonal basis, is the inner product of the polynomial, J(ξ) is the joint probability density function of the uncertain input variables, the coefficients of the chaotic polynomial are matched with the orthogonal bases I0, I1 and I2 of the polynomials in formula (4). This is the explicit equation of the desired chaotic polynomial.

[0048] The input of the explicit equation is the tip clearance, mainstream inlet total temperature, mainstream inlet total pressure and inlet airflow angle of a certain grid vertex under a certain working condition, and the output is the wall temperature of the grid vertex of the GE_E3 gas turbine blade under the working condition. In this embodiment, a total of 5.6 million explicit equations of chaotic polynomials of the wall temperature of the grid vertices are generated.

[0049] 5. A mesh vertex failure probability solving module receives the explicit equation of the chaotic polynomial of the wall temperature of each mesh vertex generated by the chaotic polynomial explicit equation solving module, and calculates the failure probability of each mesh vertex in combination with the Monte Carlo sampling method.

[0050] The method of using the Monte Carlo method to calculate the failure probability of a certain mesh vertex is as follows:

[0051] 1) Set the number of sampling points N Sum , N Sum The larger the value, the more accurate the calculation. In this embodiment, N Sum Set to 1000000. The coordinates of each sampling point include the uncertain input variables. That is, in this embodiment, four variables are included, namely, the blade tip clearance, the mainstream inlet total temperature, the mainstream inlet total pressure and the inlet airflow angle of the working condition represented by the sampling point.

[0052] 2) Use Python's open source library random function to randomly generate N Sum values ​​distributed between (0,1) and put them into the array P in sequence point middle;

[0053] 3) Let the coordinates of the nth sampling point be (η1, η2, ..., η i ,……,η n ), then according to the Monte Carlo principle:

[0054]

[0055] In this embodiment, n=4, then:

[0056]

[0057]

[0058]

[0059]

[0060] Where P point [η] is the array P pointThe ηth value of . ν is a variable for auxiliary calculation. According to formulas (7, 8, 9, 10), the coordinates of the ηth sampling point can be calculated, that is, the blade tip clearance, mainstream inlet total temperature, mainstream inlet total pressure and inlet airflow angle of the working condition represented by the ηth sampling point.

[0061] 4) According to the explicit equation of the chaotic polynomial, calculate the wall temperature of the grid vertex under the working condition represented by each sampling point, and put the calculation results into the array T all middle.

[0062] 5) Receive the wall temperature of the grid vertex of the first integral node solved by the physical quantity solving module. According to the polynomial chaos theory, the working condition represented by the first integral node is the design working condition, that is, the wall temperature of the gas turbine blade when it is assumed that there is no uncertainty.

[0063] 6) According to the literature (Cherry DG, Gay CH, Lenahan D T. Energy efficient engine. Low pressure turbine test hardware detailed design report [R]. 1982.), when the temperature of the gas turbine blade exceeds the design wall temperature by 70 degrees Celsius, the blade is considered to have failed. Set an auxiliary variable V sum , V sum The initial value of is set to 0. all Subtract the wall temperature of all the walls in from the wall temperature of the mesh vertex at the first integration node. When the difference is greater than 70 degrees Celsius, V sum Plus one. Finally, V sum Divide by N Sum The quotient obtained is the failure probability of the mesh vertex.

[0064] Repeating process 1) to 6) for all mesh vertices can calculate the failure probability of all mesh vertices.

[0065] 6. A Delaunay triangulation generation module receives the mesh vertex spatial coordinates calculated by the mesh vertex spatial coordinate generation module and generates a Delaunay triangulation. Drawing a gas turbine blade failure probability distribution cloud map requires the positional relationship between each mesh vertex. The present invention introduces the Delaunay triangulation technology in geographical science to generate the mutual positional relationship between each mesh vertex. The generation process of the Delaunay triangulation is as follows:

[0066] 1) The mesh vertex with ordinal number 1 is recorded as the initial base point, denoted by P O , calculate the distance from all other mesh vertices to this point. The mesh vertex farthest from the initial base point is denoted as P F , connecting point PO and point P F is the baseline, denoted as P O P F The distance is calculated as follows:

[0067]

[0068] Where (x0, y0, z0) is the spatial coordinate of the mesh vertex to be calculated, (x base ,y base ,z base ) is the spatial coordinate of the initial base point;

[0069] 2) Traverse all mesh vertices, find all mesh vertices with x coordinates greater than the initial base point, and calculate the distance from these mesh vertices to the baseline P O P F distance, find the distance from the baseline P O P F The smallest point, as P Q , the distance from a point to a straight line is calculated using the following formula;

[0070]

[0071] In the formula, (x point ,y point ,z point ) is the spatial coordinate of any point in space, (x tem ,y tem ,z tem ) is the spatial coordinate of the perpendicular point from this point to the straight line, (x tem ,y tem ,z tem ) is calculated as follows:

[0072]

[0073] x tem =(x1-x2)·t+x1 (14)

[0074] y tem =(y1-y2)·t+y1 (15)

[0075] z tem =(z1-z2)·t+z1 (16)

[0076] Where, the spatial coordinates of any two points on the straight line (x1, y1, z1) and (x2, y2, z2) are P in step 2. O and P F ;

[0077] 3) Connect point P Oand point P Q The straight line P O P Q , connecting point P F and point P Q The straight line P F P Q ; At this time, triangle P O P F P Q is a Delaunay triangle, and then the straight line P O P Q and straight line P F P Q As a new baseline;

[0078] 4) Repeat steps 2) and 3) until all mesh vertices are contained in a Delaunay triangle. At this point, all Delaunay triangles form a Delaunay triangulation network, and the positional relationship between all mesh vertices can be represented by the Delaunay triangles in which they are located.

[0079] 7. A refinement node spatial coordinate generation module receives the Delaunay triangulation calculated by the Delaunay triangulation generation module, and calculates the spatial coordinates of the midpoints of each edge of each Delaunay triangle in the Delaunay triangulation. In order to make the distribution of the gas turbine blade failure probability distribution cloud map accurate enough, it is necessary to add the refinement node information. The midpoint of each edge of each Delaunay triangle is used as a refinement node in the present invention. The two vertices P of a certain edge of a certain Delaunay triangle are recorded as follows: A , P B The spatial coordinates of A ,y A ,z A )、(x B ,y B ,z B ). Then the edge P A P B The midpoint P AB The spatial coordinates (x AB , y AB ,z AB ) is calculated as follows:

[0080]

[0081]

[0082]

[0083] Formulas (17, 18, 19) can be used to calculate the spatial coordinates of the midpoints of the three sides of all Delaunay triangles in the Delaunay triangulation.

[0084] 8. The failure probability calculation module of the refined node calculates the failure probability of the midpoint (i.e., the refined node) of each edge of each Delaunay triangle in the Delaunay triangulation network according to the inverse distance interpolation method. A , P B The failure probabilities are L A With L B . Then the edge P A P B The midpoint P AB That is, the failure probability L of the corresponding refined node AB , the calculation formula is as follows:

[0085]

[0086] 9. The gas turbine blade failure probability distribution cloud map generation module receives the spatial coordinates and failure probability of each mesh vertex and the spatial coordinates and failure probability of the midpoint of each edge of each Delaunay triangle in the Delaunay triangulation, and inputs them into the plot_surface function of the drawing open source library matplotlib to generate the gas turbine blade failure probability distribution cloud map.

[0087] Figure 3 The GE_E3 gas turbine blade failure probability distribution cloud diagram obtained in the embodiment is based on Figure 3 It can guide the spraying of thermal barrier coatings on gas turbine blades. The darker the location in the figure, the greater the failure probability there is. Therefore, a thicker thermal barrier coating should be sprayed in this area to prevent blade failure. Moreover, for a running gas turbine, the present invention can be used to calculate the failure probability distribution cloud map of its blades in real time. When the failure probability of a certain area is too high (more than 80%), it needs to be shut down and replaced immediately. In addition, Figure 3 The GE_E3 gas turbine blade failure probability distribution cloud diagram can also guide the optimization design of new gas turbines. Figure 3 It can be found that for gas turbines, the leading edge area at the top of the blade and the trailing edge near the pressure side area have a very high probability of failure. Therefore, in the newly developed gas turbine, dense film cooling holes can be set in these two areas to help cool the wall surface there. It can be found that the present invention is of great significance both for the operation, maintenance and monitoring of the gas turbine in operation and for the research and development guidance of the gas turbine being designed.

Claims

1. A method for calculating the failure probability of a gas turbine blade, characterized in that: The steps include: Step 1, according to the probability density distribution function of the uncertainty input variable of the gas turbine blade, based on the polynomial chaos theory, the coordinates of the integral nodes required for solving the chaos polynomial are generated; Step 2, combining the geometric parameters of the gas turbine blades, and using the open source computational fluid dynamics library OpenFOAM to generate the spatial coordinates of the mesh vertices; Step 3, according to the coordinates of the integration nodes and the spatial coordinates of the mesh vertices, using the open source computational fluid dynamics library OpenFOAM to obtain the physical quantity of each mesh vertex of the working condition represented by each integration node, the physical quantity being the wall temperature of the gas turbine blade; Step 4, according to the coordinates of the integration node and the physical quantity of each mesh vertex, based on the Galerkin projection method, calculate the coefficients of the chaotic polynomial of the physical quantity of each mesh vertex, thereby calculating the explicit equation of the chaotic polynomial of the physical quantity of each mesh vertex; Step 5, calculating the failure probability of each grid vertex according to the explicit equation of the chaotic polynomial combined with the Monte Carlo sampling method; Step 6, generating a Delaunay triangulation network according to the spatial coordinates of the mesh vertices; Step 7, taking the midpoint of each edge of each Delaunay triangle in the Delaunay triangulation as a refinement node, and calculating the spatial coordinates of the refinement node; Step 8, calculating the failure probability of the refined node using an inverse distance interpolation method; Step 9: Generate a gas turbine blade failure probability distribution cloud map according to the failure probability of each mesh vertex and the failure probability of the refined node.

2. The method for calculating the failure probability of a gas turbine blade according to claim 1, characterized in that: In step 1, the uncertain input variables satisfy the Gaussian distribution, which are the blade tip clearance, the mainstream inlet total temperature, the mainstream inlet total pressure and the inlet airflow angle. In the chaotic polynomial theory, the coordinates of the integration nodes are calculated by formula (1): In the formula, represents an n-dimensional k-order integration node, n represents the dimension of the problem, that is, the number of types of uncertain input quantities, k represents the calculation accuracy, q is a constant, q=k+n, |i|=i1+i2+i3+…+i j +…+i n ,i j represents the ordinal number of the one-dimensional integration node of the j-th chaotic polynomial, j = 1, 2, ..., n, Indicates the ordinal number is i j The coordinates of each integration node contain n parameters, i.e., the uncertainty input of the working condition represented by the integration node; The weight w corresponding to each integration node is calculated by formula (2): In the formula Indicates the ordinal number is i j The component of the integration node weight, represents a vector composed of its components; The gas turbine blade wall temperature y is calculated by formula (3): Where a0, Respectively represent the orthogonal basis I0, The corresponding coefficient, that is, the quantity that needs to be solved, is the projection of each order, θ is a random variable; in actual operation, according to the dimension n of the problem and the calculation accuracy k, the expression of the wall temperature y is truncated to: In the formula, P is the order of the chaotic polynomial. The larger the value of P, the more accurate the calculation. j is the coefficient of the jth orthogonal basis, that is, the discrete form of the coefficient of the orthogonal basis of each order of the chaotic polynomial, Ψ j (ξ) is the jth orthogonal basis in the discrete case.

3. The method for calculating the failure probability of a gas turbine blade according to claim 2, characterized in that: The method of calculating the coefficients of the chaotic polynomial of the physical quantity of each mesh vertex based on the Galerkin projection method is as shown in formula (5): In the formula, Ψ j (ξ) represents the jth orthogonal basis, is the inner product of the polynomial, J(ξ) is the joint probability density function of the uncertain input variables, the coefficients of the chaotic polynomial are matched with the orthogonal bases I0, I1 and I2 of the polynomials in formula (4). This is the explicit equation of the desired chaotic polynomial.

4. The method for calculating the failure probability of a gas turbine blade according to claim 1, characterized in that: The method of calculating the failure probability of a mesh vertex using the Monte Carlo method in step 5 is as follows: 1) Set the number of sampling points N Sum , N Sum The larger the value, the more accurate the calculation. The coordinates of each sampling point contain the uncertainty input variable. 2) Use Python's open source library random function to randomly generate N Sum values ​​distributed between (0,1) and put them into the array P in sequence point middle; 3) Let the coordinates of the nth sampling point be (η1, η2, ..., η i ,……,η n ), then according to the Monte Carlo principle: Where P point [η] is the array P point The nth value of , ν is a variable for auxiliary calculation; 4) According to the explicit equation of the chaotic polynomial, calculate the wall temperature of the grid vertex under the working conditions represented by each sampling point, and put the calculation results into the array T all middle; 5) obtaining the wall temperature of the grid vertex of the first integration node calculated in step 3, the operating condition represented by the first integration node being the design operating condition, that is, the wall temperature of the gas turbine blade assuming that there is no uncertainty; 6) Set an auxiliary variable V sum , V sum The initial value of T is set to 0. all Subtract the wall temperature of all the walls in from the wall temperature of the mesh vertex at the first integration node. When the difference is greater than 70 degrees Celsius, V sum Plus one, finally, V sum Divide by N Sum The quotient obtained is the failure probability of the mesh vertex; Repeating process 1) to 6) for all mesh vertices can calculate the failure probability of all mesh vertices.

5. The method for calculating the failure probability of a gas turbine blade according to claim 1, characterized in that: In step 6, the generation process of the Delaunay triangulation is as follows: 1) The mesh vertex with ordinal number 1 is recorded as the initial base point, denoted by P O , calculate the distances from all other mesh vertices to the initial base point, and the mesh vertex farthest from the initial base point is denoted as P F , connecting point P O and point P F is the baseline, denoted as P O P F ; 2) Traverse all mesh vertices, find all mesh vertices with x coordinates greater than the initial base point, and calculate the distance from these mesh vertices to the baseline P O P F distance, find the distance from the baseline P O P F The smallest point, as P Q ; 3) Connect point P O and point P Q The straight line P O P Q , connecting point P F and point P Q The straight line P F P Q ; At this time, triangle P O P F P Q is a Delaunay triangle, and then the straight line P O P Q and straight line P F P Q As a new baseline; 4) Repeat steps 2) and 3) until all mesh vertices are contained in a Delaunay triangle. At this time, all Delaunay triangles form a Delaunay triangulation network, and the positional relationship between all mesh vertices is represented by the Delaunay triangles in which they are located.

6. The method for calculating the failure probability of a gas turbine blade according to claim 1, characterized in that: In step 8, record the two vertices P of a certain edge of a Delaunay triangle A , P B The failure probabilities are L A With L B , then edge P A P B The midpoint P AB That is, the failure probability L of the corresponding refined node AB The calculation formula is as follows:

Images