A method for accelerating the life test of a gas turbine blade

Abstract

A method for accelerating the life test of a gas turbine blade, generating a chaotic polynomial expansion and sample point coordinates to be solved according to the distribution of uncertain input quantities; obtaining the wall temperature of the gas turbine blade at each sample point; calculating the coefficients of the chaotic polynomial expansion to obtain an explicit equation of the chaotic polynomial expansion; constructing a universal Kriging model to be solved; solving the response surface equation of the universal Kriging model, i.e., the calculation equation of the wall temperature of the gas turbine blade; receiving the distribution of uncertain input quantities and generating the coordinates of a corresponding number of sampling points according to the calculation requirements; calculating the wall temperature of the gas turbine blade at the working condition corresponding to each sampling point, and then calculating the failure time of the gas turbine blade at the working condition corresponding to each sampling point from the wall temperature-life diagram of the gas turbine blade; calculating the probability density function of the three-parameter Weibull distribution of the gas turbine blade life; and testing the gas turbine blade life using the life acceleration test theory.

Description

Technical Field

[0001] The present invention belongs to the technical field of reliability analysis, and particularly relates to a method for accelerating the life test of gas turbine blades. Background Art

[0002] Gas turbines are widely used in the fields of power generation and aviation. The research and development of advanced gas turbines is of great significance. However, due to the lack of relevant experience and technical accumulation, the life prediction of gas turbine blades under harsh working conditions has always been a weak link in the field of gas turbine design and manufacturing. The life acceleration test in the industrial field was first proposed by the Rome Air Development Center of the US Air Force. Its goal is to predict the life characteristics of products under normal stress based on the life characteristics under an accelerated environment beyond the normal stress level using physical equations and statistical models related to failure on the basis of reasonable engineering assumptions, so as to shorten the test time. However, there are the following problems when this accelerated life test is applied to the reliability analysis field of gas turbine blades: 1. For expensive industrial components such as gas turbine blades, using traditional experiment-based life acceleration tests is extremely costly. 2. The methods of traditional life acceleration tests require a large number of test samples to obtain statistically reliable conclusions. 3. Traditional life acceleration tests need to wait until the blades break to obtain data, making it difficult to obtain failure data and resulting in a long experimental cycle. Summary of the Invention

[0003] In order to overcome the above-mentioned disadvantages of the prior art, the purpose of the present invention is to provide a method for accelerating the life test of gas turbine blades to save the time of the life acceleration test of gas turbine blades. The invention is mainly based on the polynomial chaos method and the Kriging surrogate model method, without the need for experiments, uses mathematical theory to model the life model of gas turbines, can predict the life of gas turbine blades at any wall temperature of the gas turbine blades, and is of great significance for the research and development of advanced gas turbines.

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

[0005] A method for accelerating the life test of gas turbine blades, comprising the following steps:

[0006] S1, based on the distribution of uncertain input quantities, generate the chaotic polynomial expansion formula to be solved and the sample point coordinates based on the chaotic polynomial theory;

[0007] S2, according to the sample point coordinates, obtain the wall temperature of the gas turbine blades at each sample point;

[0008] S3, according to the chaotic polynomial expansion formula and the wall temperature of the gas turbine blades at each sample point, calculate the coefficients of the chaotic polynomial expansion formula, so as to obtain the explicit equation of the chaotic polynomial expansion formula;

[0009] S4. Construct a universal Kriging model to be solved according to the explicit equation of the chaotic polynomial expansion.

[0010] S5. Solve the response surface equation of the universal Kriging model, i.e., the calculation equation of the gas turbine blade wall temperature, according to the universal Kriging model to be solved and the gas turbine blade wall temperatures at each sample point.

[0011] S6. Receive the distribution of uncertain input variables and generate the coordinates of a corresponding number of sampling points according to the calculation requirements.

[0012] S7. Calculate the gas turbine blade wall temperature under the working conditions corresponding to each sampling point according to the calculation equation of the gas turbine blade wall temperature and the coordinates of the sampling points, and then calculate the failure time of the gas turbine blade under the working conditions corresponding to each sampling point from the wall temperature - life diagram of the gas turbine blade.

[0013] S8. Calculate the probability density function of the three - parameter Weibull distribution of the gas turbine blade life according to the coordinates of the sampling points and the failure time of the gas turbine blade under the working conditions corresponding to each sampling point.

[0014] S9. Test the gas turbine blade life using the life acceleration test theory according to the probability density function.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0016] (1) Introduce the uncertainty theory to conduct the accelerated life test of the gas turbine blade instead of using experiments for calculation as in the traditional method, and replace the experiment with a mathematical model, so the cost can be greatly reduced.

[0017] (2) The present invention greatly reduces the number of test samples by introducing the polynomial chaos method based on the universal Kriging model.

[0018] (3) The results of each test sample are calculated by a computer, and there is no need to wait for the blade to break for a long time as in the traditional method.

[0019] (4) This method can predict the life of the gas turbine blade at any gas turbine blade wall temperature using a limited number of test samples. Description of the Drawings

[0020] Figure 1 It is a schematic diagram of the geometric parameters of the GE - E3 gas turbine blade profile.

[0021] Figure 2 It is a schematic diagram of the system of the present invention.

[0022] Figure 3It is a wall temperature-life diagram of a gas turbine blade.

[0023] Figure 4 It is the life acceleration test result of the blade life of a GE-E3 gas turbine. Specific implementation manner

[0024] The following combines the drawings and embodiments to detail the implementation manner of the present invention.

[0025] Example: The calculation model comes from the widely used GE_E3 blade profile (Kwak J S, 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 GE_E3 blade profile are shown in Table 1, and the meanings of each geometric parameter are shown in Figure 1 .

[0026] Table 1 Geometric parameters of the GE_E3 blade profile

[0027] Geometric 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] Reference Figure 2 , this embodiment is based on a gas turbine blade life acceleration test method, including:

[0029] 1. Chaos polynomial model construction and sample point coordinate generation module, which receives the distribution of uncertain input quantities, and based on the chaos polynomial theory, generates the chaos polynomial expansion to be solved and the sample point coordinates. In this embodiment, the tip clearance (S), the mainstream inlet total temperature (T0), the mainstream inlet total pressure (P0), and the inlet flow angle (A) are selected as uncertain variables, and they respectively satisfy the Gaussian distribution in Table 2. In the chaos polynomial theory, the coordinates of the numerical integration nodes are the sample point coordinates to be calculated, which are calculated by formula (1):

[0030]

[0031] In the formula, n represents the dimension of the problem, that is, the number of types of uncertain input quantities, and k represents the calculation accuracy. In this embodiment, n = 4 and k = 4. represents the n-dimensional k-order numerical integration node, 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 numerical integration node of the j-th expansion, j = 1, 2, ……, n, represents the ordinal number as ij Nodes for one-dimensional numerical integration; the coordinates of each numerical integration node contain n parameters, i.e., the uncertain input variables of the operating conditions represented by the numerical integration node.

[0032] To solve the chaotic polynomial, the weights w corresponding to each numerical integration node also need to be given, and w can be calculated by formula (2):

[0033]

[0034] In the formula, represents the component of the weight of the numerical integration node with ordinal number i j and represents the vector composed of each component.

[0035] Table 2 Distribution of Uncertainty Variables

[0036] Geometric parameter name Mean value Standard deviation Tip clearance (S) 0.4 mm 0.08 mm Total temperature at the mainstream inlet (D) 709.0K 17.24K Total pressure at the mainstream inlet (G) 126900 Pa 7480 Pa Inlet flow 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, that is, the chaotic polynomial expansion formula to be solved in the present invention, namely formula (3). In this embodiment, y is the system output, that is, the wall temperature of the gas turbine blade, n = 4, k = 4.

[0038]

[0039] In the formula, a0, respectively represent the coefficients corresponding to the orthogonal bases I0, ... of each order of the chaotic polynomial expansion formula, that is, the quantities to be solved, are the projections of each order, θ is the uncertain input variable; in actual operation, according to the dimension n of the problem and the calculation accuracy k, the expression of the wall temperature y of the gas turbine blade can be expressed as:

[0040]

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

[0042] 2. Sample Point Wall Temperature Solving Module, which accepts the coordinates of the numerical integration nodes of n dimensions and k orders, that is, the coordinates of the sample points The coordinates of each sample point contain n parameters, which are, in sequence, the tip clearance (S), the mainstream inlet total temperature (T0), the mainstream inlet total pressure (P0), and the inlet flow angle (A) of the working condition represented by this numerical integration node. Inputting these n parameters into the open-source computational fluid dynamics library OpenFOAM can calculate the gas turbine blade wall temperature of the working condition represented by this numerical integration node; inputting the parameters included in the coordinates of all numerical integration nodes into the open-source computational fluid dynamics library OpenFOAM can obtain the gas turbine blade wall temperature of the working condition represented by each sample point.

[0043] 3. The chaotic polynomial solving module receives the chaotic polynomial expansion and the gas turbine blade wall temperatures of each sample point calculated by the chaotic polynomial model building and sample point coordinate generation module. It uses the Galerkin projection method to calculate the coefficients of the chaotic polynomial expansion to obtain the explicit equation of the chaotic polynomial expansion. The coefficients of the chaotic polynomial expansion are the coefficients of each order of orthogonal basis in the chaotic polynomial expansion, and are solved using the Galerkin projection method. The formula is as follows:

[0044]

[0045] In the formula, Ψ j (ξ) represents the jth orthogonal basis, is the polynomial inner product, J(ξ) is the joint probability density function of the uncertain input variables, and the coefficients of the chaotic polynomial expansion are combined with the polynomial orthogonal bases I0 of each order in the chaotic polynomial expansion That is the explicit equation of the required chaotic polynomial expansion. The input of this explicit equation is the tip clearance (S), the mainstream inlet total temperature (T0), the mainstream inlet total pressure (P0), and the inlet flow angle (A) of a certain working condition, and the output is the gas turbine blade wall temperature of the GE-E3 under this working condition.

[0046] 4. The universal Kriging model building module receives the explicit equation of the chaotic polynomial generated by the chaotic polynomial solving module and constructs the universal Kriging model to be solved. The form of the universal Kriging model is as follows:

[0047] M(θ) = f T (θ)β + z(θ) (6)

[0048] In the formula, f T (θ) is the explicit equation of the chaotic polynomial expansion, which serves as the regression function of the universal Kriging model, β represents the coefficient of the regression function, and z(θ) represents the approximation of the local deviation.

[0049] 5. Universal Kriging model solving module, which receives the Universal Kriging model to be solved generated by the Universal Kriging model building module and the gas turbine blade wall temperatures of each sample point generated by the sample point wall temperature solving module, obtains and solves the response surface equation of the Universal Kriging model, and this response surface equation is also the calculation equation of the gas turbine blade wall temperature. Let the covariance matrix of the local deviation z(θ) be:

[0050] E[(z(θ1)z(θ2))] = σ 2 R(γ,θ1,θ2) (7)

[0051] In the formula, θ1 and θ2 represent any two sample points in the sample space, and γ represents the hyperparameter. R(γ,θ1,θ2) represents the spatial correlation function of θ1 and θ2, and the calculation method of R(γ,θ1,θ2) is as follows:

[0052]

[0053] In the formula, n represents the dimension of the problem, and in this embodiment, n is equal to 4. γ j , θ 1j and θ 2j represent γ, θ1 and θ2 in the j-th dimension. The correlation between the point to be measured θ x and the sample point θs is expressed as follows:

[0054] r(θ) = R(γ,θ x ,θ s ) T (9)

[0055] Record the gas turbine blade wall temperatures of each sample point obtained by the sample point wall temperature solving module into the matrix Y. The orthogonal bases I0 of each order of the polynomial in formula (3) are represented as F, then the response surface equation of the Universal Kriging model is calculated by the following formula:

[0056] M(θ) = f T (θ)β + r T (θ)R(γ,θ x ,θ s ) -1 (Y - Fβ) (10)

[0057] 6. Monte Carlo sampling module, which receives the distribution of the uncertain input quantity and generates the coordinates of the corresponding number of sampling points according to the calculation requirements. Each coordinate contains four parameters, namely the tip clearance (S), the total temperature at the mainstream inlet (T0), the total pressure at the mainstream inlet (P0), and the inlet flow angle (A) of the sampling point. In order to fit the Weibull distribution with high precision, it is necessary to set the number of sampling points N point , and the larger this value is, the better. In this embodiment, the number of sampling points Npoint Set it to 80000. Calculate the coordinates of N point sampling points using Monte Carlo sampling as follows:

[0058] 1) First, use the random function of the open-source library in Python to randomly generate N point values distributed between (0, 1), and put them into the array Z point in turn.

[0059] 2) Let the coordinates of the m-th sampling point be (m1, m2, m3, m4), then according to the Monte Carlo principle:

[0060] (11)

[0061] (12)

[0062] (13)

[0063] (14)

[0064] In the formula, Z point [m i is the m-th point value of the array Z i , ν is a variable for auxiliary calculation. According to the above formula, the coordinates of the m-th sampling point can be calculated, that is, the tip clearance (S), the total temperature at the mainstream inlet (T0), the total pressure at the mainstream inlet (P0), and the inlet flow angle (A) of the m-th sampling point.

[0065] 3) Perform the operations in step 2) on all N point sampling points, and the coordinates of these N point sampling points can be obtained.

[0066] 7. Sampling point failure time solving module, which receives the coordinates of the sampling points generated by the Monte Carlo sampling module and the calculation equation of the gas turbine blade wall temperature generated by the universal Kriging model solving module, calculates the gas turbine blade wall temperature of each sampling point corresponding to the working condition, and then calculates the failure time of the gas turbine blade of each sampling point corresponding to the working condition from the wall temperature-life diagram of the gas turbine blade. The failure time of the gas turbine blade is its life. The wall temperature-life diagram of the gas turbine blade is as Figure 3As shown, the data is from the literature (Rowe J P, Freeman J W, Voorhees H R. Final report to the General Electric Company Aircraft Gas Turbine Division on effect of overheating on the creep - rupture properties of Udimet 500 alloy at 16000F and 28,500 PSI[R]. 1957.).

[0067] 7. Three - parameter Weibull distribution fitting module, which receives the failure time of the gas turbine blade under the working condition corresponding to each sampling point generated by the sampling point failure time solving module and the coordinates of the sampling points generated by the Monte Carlo sampling module, and calculates the probability density function of the three - parameter Weibull distribution of the gas turbine blade life; the probability density function of the three - parameter Weibull distribution satisfies formula (15):

[0068]

[0069] where τ is the failure time of the gas turbine blade, a w is the location parameter of the Weibull distribution, b w is the scale parameter of the Weibull distribution, c w is the shape parameter of the Weibull. It can be found that after solving a w and b w and c w the probability density function of the Weibull distribution of the gas turbine blade life can be transformed into an explicit calculation formula. The present invention uses the maximum likelihood method to calculate a w and b w and c w of the Weibull distribution of the gas turbine blade life. The formula is as follows:

[0070] a w =τ min (16)

[0071]

[0072]

[0073] where τ min is the minimum value of the failure times of all sampling points. λ i is a variable for auxiliary calculation, λ i =τ i -τ min and τ i is the failure time of the i - th sampling point. nw is the set number of iteration steps, n w The larger it is set, the higher the calculation accuracy. In this embodiment, n w is set to 10,000. Calculate a w and c w using formula (16) and formula (17), and then substitute them into formula (18) to calculate b w .

[0074] 8. Life acceleration test module, which receives the probability density function of the Weibull distribution of the life of the gas turbine blade generated by the three-parameter Weibull distribution fitting module, and tests the life of the gas turbine blade using the life acceleration theory test. The life acceleration test formula is as follows:

[0075]

[0076] The input of the accelerated life formula is the failure time τ and the wall temperature S of the gas turbine blade, and the output is the probability of the failure time being τ at the wall temperature of the gas turbine blade.

[0077] Figure 4 is the relationship diagram of the wall temperature and the failure time of the GE-E3 gas turbine blade obtained in the embodiment. It can be found from the figure that as the wall temperature increases, the failure time of the GE-E3 gas turbine blade decreases rapidly, that is, the life of the GE-E3 gas turbine blade decreases rapidly. When the wall temperature increases by 40K, the life of the GE-E3 gas turbine blade will be reduced by about 6,000 hours. The present invention can also output the prediction of the life of the gas turbine blade at a custom wall temperature. For example, when the custom temperature is 725K, it can be found from the figure that the life of the gas turbine blade is 13,205 hours. The present invention models the life test of the gas turbine based on the uncertainty theory, eliminating the expensive and time-consuming experiments, but predicting the life of the gas turbine blade based on mathematical theory, which is of great significance to the research and development of advanced gas turbines.

Claims

1. A method for accelerating the life test of a gas turbine blade, characterized in that, It includes the following steps: S1. Based on the distribution of the uncertain input quantity and the chaos polynomial theory, generate the chaos polynomial expansion to be solved and the sample point coordinates. S2. According to the sample point coordinates, obtain the gas turbine blade wall temperature of each sample point. S3. According to the chaos polynomial expansion and the gas turbine blade wall temperature of each sample point, calculate the coefficients of the chaos polynomial expansion, so as to obtain the explicit equation of the chaos polynomial expansion. S4. According to the explicit equation of the chaos polynomial expansion, construct the universal Kriging model to be solved. S5. According to the universal Kriging model to be solved and the gas turbine blade wall temperature of each sample point, solve the response surface equation of the universal Kriging model, that is, the calculation equation of the gas turbine blade wall temperature. S6. Receive the distribution of the uncertain input quantity, and generate the coordinates of the corresponding number of sampling points according to the calculation requirements. S7. According to the calculation equation of the gas turbine blade wall temperature and the coordinates of the sampling points, calculate the gas turbine blade wall temperature of each sampling point corresponding to the working condition, and then calculate the failure time of the gas turbine blade of each sampling point corresponding to the working condition from the wall temperature - life diagram of the gas turbine blade. S8. According to the coordinates of the sampling points and the failure time of the gas turbine blade of each sampling point corresponding to the working condition, calculate the probability density function of the three-parameter Weibull distribution of the gas turbine blade life. S9. According to the probability density function, test the gas turbine blade life using the life acceleration test theory.

2. The gas turbine blade life acceleration test method according to claim 1, wherein For the above S1, the uncertain input variables are tip clearance S , total temperature at the mainstream inlet T 0, total pressure at the mainstream inlet P 0 and inlet flow angle A , which respectively satisfy the Gaussian distribution; the sample point coordinates are calculated by the following formula: In the formula, n represents the dimension of the problem, that is, the number of types of uncertain input variables, k represents the calculation accuracy, represents n dimension k order numerical integration nodes, q is a constant, q = k + n , , i j represents the ordinal number of the one-dimensional numerical integration nodes of the j th term expansion, j = 1, 2, ……, n , represents that the ordinal number is i j of the one-dimensional numerical integration nodes; The coordinates of each numerical integration node contain n parameters, i.e., the uncertain input variables of the working conditions represented by the numerical integration node; The chaos polynomial expansion to be solved is expressed as follows: In the formula, y is the system output, i.e., the wall temperature of the gas turbine blade, , , , respectively represent the orthogonal bases of each order of the chaotic polynomial expansion , , , The corresponding coefficients, that is, the quantities to be solved, are the projections of each order, θ is the uncertainty input quantity; In actual calculations, according to the dimension of the problem n and the calculation accuracy k the expression of the wall temperature of the gas turbine blade can be expressed as: In the formula, P is the order of the chaotic polynomial expansion, P The larger the value, the more accurate the calculation. is the coefficient of the -th orthogonal basis, that is, the discrete form of the coefficients of the orthogonal bases of each order of the chaotic polynomial. is the -th orthogonal basis in the discrete case.

3. The gas turbine blade life acceleration test method according to claim 2, characterized in that Calculate the weights corresponding to the numerical integration nodes using the following formula w :[[]]END]] wherein, represents the component of the numerical integration node weight with the ordinal number of i j and represents a vector composed of each component.

4. The method for accelerating the life test of a gas turbine blade according to claim 3, wherein S2 uses the open-source computational fluid dynamics library OpenFOAM to obtain the wall temperature of the gas turbine blade at the sample points to be calculated. The method is as follows: input the n parameters into the open-source computational fluid dynamics library OpenFOAM to calculate the wall temperature of the gas turbine blade under the conditions represented by the numerical integration nodes; input the parameters included in the coordinates of all numerical integration nodes into the open-source computational fluid dynamics library OpenFOAM to obtain the wall temperature of the gas turbine blade under the conditions represented by each sample point.

5. The gas turbine blade life acceleration test method according to claim 4, characterized in that In step S3, the coefficients of the chaos polynomial expansion, that is, the coefficients of each order of orthogonal basis of the chaos polynomial expansion, are solved using the Galerkin projection method, and the formula is as follows: In the formula, is the polynomial inner product, is the joint probability density function of the uncertain input variables, and the coefficients of the chaotic polynomial expansion are paired with the orthogonal bases of each order of the polynomials in the chaotic polynomial expansion , , is the explicit equation of the required chaotic polynomial expansion. The input of this explicit equation is the tip clearance at a certain working condition S , the total temperature at the mainstream inlet T 0, the total pressure at the mainstream inlet P 0 and the inlet flow angle A , and the output is the blade wall temperature of the gas turbine under this working condition.

6. The gas turbine blade life acceleration test method according to claim 5, wherein In step S4, the form of the universal Kriging model is as follows: In the formula, is the explicit equation of the chaotic polynomial expansion, which serves as the regression function of the universal Kriging model. β represents the coefficient of the regression function. represents the approximation of the local deviation.

7. The gas turbine blade life acceleration test method according to claim 6, characterized in that The S5 makes the covariance matrix of the local deviation be as follows: wherein, θ 1 and θ 2 represent any two sample points in the sample space, γ represents a hyperparameter, represents θ 1 and θ the spatial correlation function of 2, The calculation method of is as follows: In the formula, γ j , θ 1j and θ 2j represent the j -dimensional γ, θ 1 and θ 2. The relevance between the point to be measured θ x and the sample point θs is expressed as follows: Record the gas turbine blade wall temperatures of each sample point into a matrix Y Among them, the orthogonal bases of each order of the polynomial , , Are expressed as F Then the response surface equation of the universal Kriging model is calculated by the following formula: (10)。 8. The gas turbine blade life acceleration test method according to claim 7, wherein S6, setting the number of sampling points N point , and calculating the coordinates of N point sampling points using Monte Carlo sampling is as follows: 1) First, use the random function of the open-source library in Python to randomly generate N point numerical values distributed between (0, 1), and place them into the array Z point in sequence; 2) Suppose the coordinates of the mth sampling point are (m1, m2, m3, m4), then according to the Monte Carlo principle: where Z point [m i is an array Z point of the m i -th value, ν is a variable for auxiliary calculation. According to the above formula, the coordinates of the m-th sampling point, that is, the tip clearance of the m-th sampling point S , the total temperature at the mainstream inlet T 0, the total pressure at the mainstream inlet P 0 and the inlet flow angle A ; 3) For N point each sampling point, perform the operation in step 2), and the coordinates of these N point sampling points can be obtained.

9. The gas turbine blade life acceleration test method according to claim 8, wherein In step S8, the probability density function of the three-parameter Weibull distribution satisfies the following formula: where τ is the failure time of the gas turbine blade, a w is the location parameter of the Weibull distribution, b w is the scale parameter of the Weibull distribution, c w is the shape parameter of the Weibull; Calculate using the maximum likelihood method a w , b w and c w , the formula is as follows: a w = τ min where τ min is the minimum value among the failure times of all sampling points, λ i is a variable for auxiliary calculation, λ i = τ i - τ min , τ i is the failure time of the i th sampling point, n w is the set number of iteration steps, n w The larger it is set, the higher the calculation accuracy.

10. The gas turbine blade life acceleration test method according to claim 9, characterized in that, In step S9, the life acceleration test formula is as follows: The input of the accelerated life formula is the failure time τ and the wall temperature of the gas turbine blade S , and the output is the probability that the failure time is τ at the wall temperature of the gas turbine blade.

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