A robust evaluation method for aero-engine turbine aero-thermal performance

Abstract

A method for evaluating the robustness of aero-engine turbine aero-thermal performance includes obtaining the number of uncertain parameters and the order of the polynomial to construct a chaotic polynomial expansion model, generating sampling points required for the chaotic polynomial expansion, obtaining result data of the sample points, calculating coefficients of the chaotic polynomial expansion method, performing sensitivity analysis calculations based on the chaotic polynomial expansion, and performing robustness and sensitivity analysis. The present invention can recommend the optimal sampling points and number of sampling points based on the actual calculation conditions, thereby significantly reducing the computational cost required for obtaining robustness analysis of aero-engine turbine aero-thermal performance. Moreover, the method is compatible with data results from multiple sources (CFD commercial software, experiments, empirical formulas, self-programming, etc.), and is more in line with the needs of aero-engine turbine design engineers.

Description

Technical Field

[0001] The present invention belongs to the technical field of aero-engine turbine aero-thermal performance system design, and in particular relates to an evaluation method for the robustness of aero-engine turbine aero-thermal performance. Background Art

[0002] With the advancement and development of aviation technology, the performance of aircraft gas turbine engines is continuously improving. Currently, the turbine inlet temperature of advanced military aircraft gas turbine engines with a thrust-to-weight ratio of 10 is approaching 2000K, and that of advanced civilian aircraft engines has reached temperatures exceeding 1700K. However, the materials used in current turbine manufacturing (such as nickel-based superalloys) can only withstand ambient operating temperatures of around 1300K. To ensure the performance and service life of aircraft gas turbine engines, researchers and turbine engineers need to develop appropriate blade cooling solutions. However, actual manufacturing and operation of gas turbine engines often do not conform to design conditions. Due to unavoidable manufacturing tolerances and extremely harsh operating conditions, the geometric parameters and operating conditions of gas turbine engines are actually characterized by random uncertainty distributions. Traditional research methods simplify parameter uncertainties into deterministic operating conditions for study. Bunker points out that turbine cooling design that considers deteriorating operating conditions, manufacturing tolerances, and machining variations is one of the most important areas for future research in gas turbine cooling. Although the uncertainty of geometric parameters and inflow conditions has attracted the attention of researchers, little research has been published, primarily due to the following reasons:

[0003] (1) The study of the aero-thermal performance of gas turbine engines is highly nonlinear and has many influencing factors. Methods such as the adjoint method are not suitable for evaluating the robustness of the aero-thermal performance of gas turbine engines because they can only evaluate the linear changes in performance within a small range.

[0004] (2) Traditionally, Monte Carlo simulations have been used to evaluate the robustness of the aero-thermal performance of gas turbine engines, but for highly nonlinear problems, tens of thousands of sampling points are often required. Although the development of CFD has saved researchers a great deal of experimental time and cost, CFD evaluation of gas turbine engine performance still requires several or even more than ten hours, making it computationally expensive for researchers to use Monte Carlo to evaluate the robustness of the aero-thermal performance of gas turbine engines.

[0005] (3) The previously developed intrusive chaotic polynomial expansion method requires researchers to manually modify the Navier-Stokes equations in combination with the intrusive chaotic polynomial theory. This undoubtedly increases the threshold for researchers to study the robustness of the aero-thermal performance of gas turbine engines. Moreover, the derivation is difficult and different robustness analyses need to be re-derived, which increases the risk of derivation errors. Therefore, the intrusive chaotic polynomial expansion method is not suitable for the robust design of gas turbine engines. Summary of the Invention

[0006] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a method for evaluating the robustness of the aero-thermal performance of an aircraft engine turbine. Based on the non-invasive generalized chaotic polynomial expansion method, the robustness of the aero-thermal performance of an aircraft engine turbine is analyzed to significantly reduce the number of samples required to obtain the robustness of the aero-thermal performance of an aircraft engine turbine, which is more in line with the needs of turbine cooling system designers.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is:

[0008] The method for evaluating the robustness of aero-engine turbine aero-thermal performance includes the following steps:

[0009] Step (1): abstracting the geometric parameters and flow parameters in the aero-engine turbine into uncertain parameters with statistical characteristics, constructing a d-dimensional hyperplane space according to the number d of uncertain parameters, taking into account the computational accuracy and computational cost required for the engineering project, and constructing a p-order non-invasive generalized chaotic polynomial as a proxy model. The proxy model approximates the original model of the d-dimensional hyperplane space. The original model is a physical model abstracted to characterize the performance of the aero-engine turbine, and its random response result is the aero-thermal performance of the aero-engine turbine;

[0010] Step (2): taking the probability density function that the uncertain parameters conform to as input and combining the polynomial order p, constructing the polynomial basis of the generalized chaotic polynomial;

[0011] Step (3): Calculate the number of sample points N required for the full tensor product and the Smolyak sparse grid method according to the dimension d and the order p of the generalized chaotic polynomial, and determine the sampling method according to the number of sample points;

[0012] Step (4): solving N groups of d-dimensional sample points according to the polynomial basis of the generalized chaotic polynomial;

[0013] Step (5): Set the calculation conditions according to the sample points, read the result information under different conditions, and calculate the generalized chaos polynomial coefficients;

[0014] Step (6): Based on the results of generalized chaos polynomial, PCE based Sobol algorithm is used to perform global sensitivity analysis calculation;

[0015] Step (7): further calculate and analyze performance characteristics, including expectation, standard deviation, probability density function and sensitivity;

[0016] Step (8): Based on the performance characteristics, analyze and evaluate the robustness of the aero-engine turbine aero-thermal performance.

[0017] Specifically, in step (1), the proxy model is expressed as follows:

[0018]

[0019] P represents the number of terms in the generalized chaotic polynomial function, and its relationship with the order p is as follows:

[0020] P=(p+1) d -1

[0021] α j represents the coefficient of the jth term in the generalized chaotic polynomial, Ψ j (ξ) represents the chaotic polynomial basis represented by the jth term in the generalized chaotic polynomial, Characterize the d-dimensional hyperplane space composed of d uncertain parameters.

[0022] Specifically, in step (2), an orthogonal polynomial basis is selected according to the probability density function conformed to each uncertain parameter, and then different uncertain parameters are combined to form a chaotic polynomial basis to achieve an exponential convergence speed, wherein when the probability density function conformed to the uncertain parameters is Gaussian distribution, gamma distribution, beta distribution, uniform distribution, Poisson distribution, binomial distribution, negative binomial distribution and hypergeometric distribution, the constructed polynomial basis are Hermite polynomial basis, Laguerre polynomial basis, Jacobi polynomial basis, Legendre polynomial basis, Charlier polynomial basis, Krawtchouk polynomial basis, Meixner polynomial basis and Hahn polynomial basis respectively.

[0023] Specifically, in step (3), the required number of sample points N is calculated. If the uncertainty parameter is not higher than three dimensions, the full tensor product solution is used; if it is higher than three dimensions, the Smolyak sparse grid method is used.

[0024] The calculation method for the number of sample points N required for the full tensor product solution is as follows:

[0025] N=P+1=(p+1) d

[0026] The calculation method of the number of sample points N required by the Smolyak sparse grid method is as follows:

[0027]

[0028] i is the summation operation parameter.

[0029] Specifically, in step (4), if the proxy model is a high-dimensional model, sparse grid technology is used to reduce the dimensionality, thereby reducing the sampling points, wherein the calculation method for each group of sample points is as follows:

[0030]

[0031] Where, Represents the numerical integration node of the d-dimensional k-order sparse grid accuracy, that is, the required d-dimensional sample point, q is a constant, q = k + d, |l| = l1 + l2 + l3 + ... + l j +…+l d , l j The ordinal number of the one-dimensional numerical integration node of the j-th expansion, j = 1, 2, 3, ..., d, Indicates the ordinal number is l j Node for one-dimensional numerical integration.

[0032] Specifically, in step (5), the coefficients of the generalized chaotic polynomial are calculated using the Galerkin projection method in the spectral method, and the formula is as follows:

[0033]

[0034] Where ρ(ξ) is the integral weight corresponding to the jth group of sampling points, Represents Ψ j (ξ) inner product with itself; <y,Ψ j (ξ)> represents the random performance response y and Ψ j The inner product of (ξ).

[0035] Specifically, the calculation formula for step (6) is as follows:

[0036]

[0037] Where S k represents the influence of the uncertain parameter combination corresponding to the kth chaotic polynomial on the random response performance, a k is the coefficient of the kth chaotic polynomial, I k For S k The corresponding k-th chaotic polynomial, Var[y(Ψ j (ξ))] represents the variance of the random response performance y corresponding to the j-th generalized chaotic polynomial, and Var[y(Ψ(ξ))] represents the variance of the random response performance y of the agent model represented by the constructed generalized chaotic polynomial.

[0038] Specifically, in step (7), the statistical characteristics of the random response result y are calculated based on the properties of the orthogonal polynomials in the generalized chaotic polynomials:

[0039] μ y =a0

[0040]

[0041] μ y represents the expectation of the random response outcome y; represents the variance of the random response result y;

[0042] Sampling and substituting the sampled data into the constructed generalized chaotic polynomial, and statistically analyzing the results of the generalized chaotic polynomial, the probability density function and skewness of the turbine aerothermal performance can be obtained.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] (1) The present invention can study and analyze the robustness of the thermal performance of various aircraft engine turbines from multiple data sources.

[0045] (2) The present invention uses a non-invasive generalized chaotic polynomial expansion method as a mathematical tool for calculating the robustness of aero-engine turbine thermal performance, which solves the drawback of the adjoint method that cannot evaluate large-scale nonlinear problems. It also greatly improves the sampling and calculation efficiency compared to the traditional Monte Carlo method, and ensures the calculation accuracy. Finally, thanks to the characteristics of the non-invasive method, there is no need to modify the Navier-Stokes equations like the invasive chaotic polynomials. It is only necessary to regard the research methods such as experiments, CFD, empirical formulas, and programming as "black box models" and use the research results as the data source of the non-invasive generalized chaotic polynomials. The present invention can not only lower the threshold for engineers to carry out robust design, but also avoid the risk of errors in the process of multiple derivation of formulas.

[0046] (3) The present invention combines full tensor product sampling and Smolyak sparse grid method in the sampling method, which can flexibly convert the sampling method to ensure the effectiveness of the sampling points for the proxy model, thereby reducing the computational cost in the robustness calculation process.

[0047] (4) The present invention can support sampling of arbitrary precision and arbitrary dimensions for robustness calculation, ensuring the flexibility of engineers when performing robustness calculation.

[0048] (5) The present invention adopts the PCE-based Sobol global sensitivity analysis method, which can analyze the sensitivity of turbine thermal performance to parameters by simply evaluating it based on chaotic polynomial calculations. Unlike the Sobol Indice method, it does not require a large number of re-sampling calculations to evaluate the performance sensitivity. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 The present invention is a flow chart of a method for robust analysis of aero-engine turbine aero-thermal performance based on a non-invasive generalized chaotic polynomial expansion method.

[0050] Figure 2 is a probability distribution diagram of the random variables in the embodiment.

[0051] Figure 3 Figure 1 shows a robust analysis of cooling performance for an aircraft engine turbine endwall with a stepped structure upstream of ΔH = 0 mm in an embodiment. (a) shows the cooling performance calculated using a conventional design (deterministic design), (b) shows the expected cooling performance when geometric deviations are considered using the present invention (robust design), and (c) shows the variance (i.e., fluctuation amplitude) of the cooling performance when geometric deviations are considered using the present invention (robust design).

[0052] Figure 4 This is a robust analysis graph of cooling performance for an aircraft engine turbine endwall with a step structure upstream of ΔH = 5 mm, as described in the embodiment. (a) is the cooling performance value calculated using a conventional design (deterministic design), (b) is the expected cooling performance value when geometric deviations are considered using the present invention (robust design), and (c) is the variance (i.e., fluctuation amplitude) of the cooling performance when geometric deviations are considered using the present invention (robust design).

[0053] Figure 5 Figure 1 shows a robust analysis of cooling performance for an aircraft engine turbine endwall with an upstream step structure of ΔH = -5 mm in the embodiment. (a) shows the cooling performance calculated using a conventional design (deterministic design), (b) shows the expected cooling performance when geometric deviations are considered using the present invention (robust design), and (c) shows the variance (i.e., fluctuation amplitude) of the cooling performance when geometric deviations are considered using the present invention (robust design). DETAILED DESCRIPTION

[0054] The embodiments of the present invention are described in detail below with reference to the accompanying drawings and examples.

[0055] The present invention is a method for evaluating the robustness of aero-engine turbine aero-thermal performance. Figure 1 As shown, the following steps are included:

[0056] Step (1): During actual processing, assembly, and operation of an aeroengine turbine, its operating conditions are subject to significant uncertainty. The present invention abstracts the geometric and flow parameters of the aeroengine turbine into uncertain parameters with statistical characteristics. A d-dimensional hyperplane space is then constructed based on the number d of uncertain parameters. Taking into account both the computational accuracy and computational cost required for the project, a p-order non-invasive generalized chaotic polynomial is constructed as a proxy model. This proxy model approximates the original model of the d-dimensional hyperplane space (i.e., the physical model abstracted to characterize the performance of the aeroengine turbine). The random response of the proxy model is the aero-thermal performance of the aeroengine turbine.

[0057] The agent model of the present invention can be adapted to the current mainstream research methods (CFD commercial software, experiments, empirical formulas, programming, etc.) Characterizing the d-dimensional hyperplane space formed by d uncertain parameters, the non-invasive generalized chaotic polynomial expansion is expressed as follows:

[0058]

[0059] Where a0 represents the coefficient of the constant term in the generalized chaotic polynomial, is the coefficient of the function term in the generalized chaotic polynomial, I0 represents the constant term basis in the generalized chaotic polynomial, Characterize the k-order composite orthogonal polynomial basis composed of uncertain parameters such as i1 and i2 (k-order chaotic polynomial, i1i2…i p Indicated by The uncertain parameter combination.

[0060] The generalized chaos polynomial can be simplified as:

[0061]

[0062] α j represents the coefficient of the jth term in the generalized chaotic polynomial, Ψ j (ξ) represents the chaotic polynomial basis represented by the jth term in the generalized chaotic polynomial.

[0063] Taking into account the calculation accuracy and calculation cost of engineering design, the generalized chaotic polynomial is truncated to a P-order polynomial:

[0064]

[0065] P represents the number of terms in the generalized chaotic polynomial function (i.e. truncated to the Pth term), and its relationship with the order p is as follows:

[0066] P=(p+1) d -1

[0067] Step (2): Taking the probability density function of the uncertain parameters as input and combining it with the polynomial order p, the polynomial basis of the generalized chaotic polynomial is constructed.

[0068] In this step, the chaotic polynomials of the Wiener scheme are not used, but the chaotic polynomials of the Wiener-Askey scheme are used. The most appropriate orthogonal polynomial basis is selected based on the probability density function of each uncertain parameter. Then, different uncertain parameters are combined to form a chaotic polynomial basis to achieve exponential convergence speed. The Wiener-Askey scheme is shown in Table 1.

[0069] Table 1 Wiener-Askey chaotic polynomials and their corresponding probability distributions

[0070] The probability distribution of the uncertain parameter (ζ) Wiener-Askey polynomial basis Gaussian distribution Hermite polynomial basis Gamma distribution Laguerre polynomial basis Beta distribution Jacobi polynomial basis Uniform distribution Legendre polynomial basis Poisson distribution Charlier polynomial basis Binomial distribution Krawtchouk polynomial basis Negative binomial distribution Meixner polynomial basis Hypergeometric distribution Hahn polynomial basis

[0071] Step (3): According to the dimension d and order p of the generalized chaotic polynomial, calculate the number of sample points N required for the full tensor product and the Smolyak sparse grid method, and determine the sampling method according to the number of sample points.

[0072] Specifically, for the calculation of the required number of sample points N, if the uncertainty parameter is not higher than three dimensions, the full tensor product solution is used; if it is higher than three dimensions, the Smolyak sparse grid method is used.

[0073] The calculation method for the number of sample points N required for the full tensor product solution is as follows:

[0074] N=P+1=(p+1) d

[0075] The calculation method of the number of sample points N required by the Smolyak sparse grid method is as follows:

[0076]

[0077] i is the summation operation parameter.

[0078] Step (4): Solve N groups of d-dimensional sample points based on the polynomial basis of the generalized chaotic polynomial.

[0079] If the proxy model is a high-dimensional model, sparse grid technology is used to reduce the dimension, thereby reducing the sampling points. The calculation method for each group of sample points is as follows:

[0080]

[0081] Where, Represents the numerical integration node of the d-dimensional k-order sparse grid accuracy, that is, the required d-dimensional sample point, q is a constant, q = k + d, |l| = l1 + l2 + l3 + ... + l j +…+l d, l j The ordinal number of the one-dimensional numerical integration node of the j-th expansion, j = 1, 2, 3, ..., d, Indicates the ordinal number is l j Node for one-dimensional numerical integration.

[0082] Step (5): Set the calculation conditions according to the sample points, read the result information under different conditions, and calculate the generalized chaos polynomial coefficients.

[0083] Specifically, the present invention uses the Galerkin projection method in the spectral method to calculate the coefficients of the generalized chaotic polynomial, and the formula is as follows:

[0084]

[0085] Where ρ(ξ) is the integral weight corresponding to the jth group of sampling points, Represents Ψ j (ξ) inner product with itself; <y,Ψ j (ξ)> represents the random performance response y and Ψ j The inner product of (ξ).

[0086] Step (6): Based on the results of generalized chaos polynomial, the PCE based Sobol algorithm is used to perform global sensitivity analysis.

[0087] Specifically, the calculation formula is as follows:

[0088]

[0089] Where S k represents the influence of the uncertain parameter combination corresponding to the kth chaotic polynomial on the random response performance, a k is the coefficient of the kth chaotic polynomial, I k For S k The corresponding k-th chaotic polynomial, Var[y(Ψ j (ξ))] represents the variance of the random response performance y corresponding to the j-th generalized chaotic polynomial, and Var[y(Ψ(ξ))] represents the variance of the random response performance y of the agent model represented by the constructed generalized chaotic polynomial.

[0090] Step (7): Based on the above calculations, further calculate and analyze the performance characteristics, including expectation, standard deviation, probability density function and sensitivity.

[0091] Specifically, based on the properties of orthogonal polynomials in generalized chaotic polynomials, the statistical characteristics of the random response result y (turbine aerothermal performance) are calculated:

[0092] μ y =a0

[0093]

[0094] μ y represents the expectation of the random response outcome y; represents the variance of the random response result y;

[0095] Sampling and substituting the sampled data into the constructed generalized chaotic polynomial, and statistically analyzing the results of the generalized chaotic polynomial, the probability density function and skewness of the turbine aerothermal performance can be obtained.

[0096] For example, the present invention can utilize traditional sampling methods such as Latin hypercube sampling and Monte Carlo sampling, substitute the sampled data into the constructed generalized chaotic polynomial, and perform statistical analysis on the results of the generalized chaotic polynomial to obtain the probability density function of the turbine's thermal performance and statistical moment information such as skewness. For example, the skewness (SK) calculation formula is as follows:

[0097]

[0098] Where n represents the number of samples; y i It represents the response value obtained by substituting the i-th sampling point into the generalized chaotic polynomial. Represents the cube of the standard deviation.

[0099] Step (8): Based on the performance characteristics, analyze and evaluate the robustness of the aero-engine turbine aero-thermal performance.

[0100] In the robust design of aircraft engine turbines, the variance of various performance characteristics must be minimized to ensure performance stability. For performance indicators such as aerodynamic performance and thermal load, these performance values ​​need to be reduced. Therefore, the expected value of performance should be minimized; while, in the probability density function, low performance values ​​should be considered high-probability events. For performance indicators such as cooling efficiency, these values ​​need to be increased. Therefore, the expected value of performance should be maximized; while, in the probability density function, high performance values ​​should be considered high-probability events.

[0101] In one embodiment of the present invention, a robust analysis of the aero-thermal performance of the endwall of a first-stage stator blade of an aircraft engine turbine is conducted. During installation and operation, factors such as thermal expansion can cause the upstream endwall of the first-stage stator blade to misalign (simplified as a step structure). Considering that the step height is uncertain during actual operation, this embodiment abstracts the height of the step structure into an uncertain parameter (ξ1). The aero-thermal cooling performance (y) of the endwall of the first-stage stator blade of the aircraft engine turbine is abstracted into a physical model with geometric parameter uncertainty. A robustness analysis of the upstream step structure design is performed for this situation. In this example, the robustness of three designed step heights is analyzed, and the corresponding parameters are shown in Table 2.

[0102] Table 2 Robustness analysis parameters for the design of the upstream end wall step structure of the first-stage stator blade of an aircraft engine turbine

[0103] <![CDATA[Parameter (ξ1)]]> Probability distribution Upstream step design height ΔH=0mm N(0,2.9) Upstream step design height ΔH=-5mm N(-5,2.9) Upstream step design height ΔH=5mm N(5,2.9)

[0104] This embodiment specifically includes the following steps:

[0105] 1. Determine the order and dimension of the chaotic polynomial

[0106] Since this embodiment only considers the impact of the step structure design on the robustness of the end wall cooling performance, the dimension is one. Taking into account the required accuracy and computational cost of the project, the non-invasive generalized chaotic polynomial adopts third-order accuracy. The random response result (i.e., the effectiveness of the thermal insulation film in this embodiment) is expanded using the non-invasive generalized chaotic polynomial method as follows:

[0107]

[0108] 2. Determine the probability density function of uncertain parameters

[0109] Since the random distribution of the step structure is assumed to be Gaussian, see Figure 2 According to the Wiener-Askey scheme, the Hermite polynomial basis is selected as the chaotic polynomial basis of the chaotic polynomial to achieve an exponential convergence speed.

[0110] 3. Calculate the number of sample points and determine the sampling method

[0111] Since the dimension of this embodiment is less than three dimensions, full tensor product sampling is used to ensure calculation accuracy and control calculation cost.

[0112] 4. Generate sampling point information

[0113] The Gaussian integral points of the determined chaotic polynomial basis of the third-order chaotic polynomial (ie, the third-order Hermite polynomial basis in this embodiment) are calculated as sampling points required for robustness analysis of the end wall cooling performance.

[0114] 5. Obtain sampling point result information and calculate chaotic polynomial coefficients

[0115] Based on the sampling points generated in the above steps, this embodiment uses CFD commercial software to obtain the performance response under the corresponding working conditions. The calculation results are used as input to calculate the coefficients of the non-invasive generalized chaotic polynomial using the Galerkin projection method.

[0116] 6. Compute statistical properties of performance (expectation, standard deviation, probability density)

[0117] According to the properties of orthogonal polynomials in chaotic polynomials, the expected value and variance of end wall cooling performance can be calculated using the calculated chaotic polynomial coefficients.

[0118] The non-intrusive generalized chaotic polynomial can be regarded as a proxy model of the original physical model to calculate the probability density function of the cooling performance.

[0119] 7. Robustness Analysis

[0120] In this example, the robustness of the end wall cooling performance of three different upstream step structures is calculated when considering the uncertainty of the upstream geometry. Figure 3 (a) to (c) Figure 4 (a) to (c) and Figure 5 From (a) to (c), it can be seen that the end wall cooling performance of the three different upstream step design structures not only has performance expectations different from the performance values ​​calculated by the traditional design (deterministic design), but also has performance fluctuations. It can also be seen that when the upstream step height is ΔH = -5mm, not only is the performance expectation higher, but more notably, its performance fluctuation range is smaller. This means that the step structure is the design scheme with the best cooling performance robustness among the three structures. Therefore, in actual production and processing, in addition to strictly ensuring the processing accuracy, attention should also be paid to the robust design of the performance, so that it has the ability to have low performance attenuation under geometric degradation or fluctuations in operating conditions. The present invention can help researchers and aero-engine design engineers to conduct robustness analysis of structural design, and then guide the robust design of aero-engine turbines, and has extremely high engineering application value.

Claims

1. A method for evaluating the robustness of aero-engine turbine aero-thermal performance, characterized in that: The following steps are involved: Step (1): abstracting the geometric parameters and flow parameters in the aero-engine turbine into uncertain parameters with statistical characteristics, constructing a d-dimensional hyperplane space according to the number d of uncertain parameters, taking into account the computational accuracy and computational cost required for the engineering project, and constructing a p-order non-invasive generalized chaotic polynomial as a proxy model. The proxy model approximates the original model of the d-dimensional hyperplane space. The original model is a physical model abstracted to characterize the performance of the aero-engine turbine, and its random response result is the aero-thermal performance of the aero-engine turbine; Step (2): taking the probability density function that the uncertain parameters conform to as input and combining the polynomial order p, constructing the polynomial basis of the generalized chaotic polynomial; Step (3): Calculate the number of sample points N required for the full tensor product and the Smolyak sparse grid method according to the dimension d and the order p of the generalized chaotic polynomial, and determine the sampling method according to the number of sample points; Step (4): solving N groups of d-dimensional sample points according to the polynomial basis of the generalized chaotic polynomial; Step (5): Set the calculation conditions according to the sample points, read the result information under different conditions, and calculate the generalized chaos polynomial coefficients; Step (6): Based on the results of generalized chaos polynomial, PCE based Sobol algorithm is used to perform global sensitivity analysis calculation; Step (7): further calculate and analyze performance characteristics, including expectation, standard deviation, probability density function and sensitivity; Step (8): Based on the performance characteristics, analyze and evaluate the robustness of the aero-engine turbine aero-thermal performance.

2. The method for evaluating the robustness of aero-engine turbine aero-thermal performance according to claim 1, characterized in that: In step (1), the proxy model is expressed as follows: P represents the number of terms in the generalized chaotic polynomial function, and its relationship with the order p is as follows: P=(p+1) d -1 α j represents the coefficient of the jth term in the generalized chaotic polynomial, Ψ j (ξ) represents the chaotic polynomial basis represented by the jth term in the generalized chaotic polynomial, Characterize the d-dimensional hyperplane space composed of d uncertain parameters.

3. The method for evaluating the robustness of aero-engine turbine aero-thermal performance according to claim 2, characterized in that: In the step (2), an orthogonal polynomial basis is selected according to the probability density function conformed to each uncertain parameter, and then different uncertain parameters are combined to form a chaotic polynomial basis to achieve an exponential convergence speed, wherein when the probability density function conformed to the uncertain parameters is Gaussian distribution, gamma distribution, beta distribution, uniform distribution, Poisson distribution, binomial distribution, negative binomial distribution and hypergeometric distribution, the constructed polynomial basis is respectively a Hermite polynomial basis, a Laguerre polynomial basis, a Jacobi polynomial basis, a Legendre polynomial basis, a Charlier polynomial basis, a Krawtchouk polynomial basis, a Meixner polynomial basis and a Hahn polynomial basis.

4. The method for evaluating the robustness of aero-engine turbine aero-thermal performance according to claim 2, characterized in that: In step (3), the required number of sample points N is calculated. If the uncertainty parameter is not higher than three dimensions, the full tensor product solution is used; if it is higher than three dimensions, the Smolyak sparse grid method is used; The calculation method for the number of sample points N required for the full tensor product solution is as follows: N=P+1=(p+1) d The calculation method of the number of sample points N required by the Smolyak sparse grid method is as follows: i is the summation operation parameter.

5. The method for evaluating the robustness of aero-engine turbine aero-thermal performance according to claim 2, characterized in that: In step (4), if the proxy model is a high-dimensional model, sparse grid technology is used to reduce the dimensionality, thereby reducing the sampling points. The calculation method for each group of sample points is as follows: Where, Represents the numerical integration node of the d-dimensional k-order sparse grid accuracy, that is, the required d-dimensional sample point, q is a constant, q = k + d, |l| = l1 + l2 + l3 + ... + l j +…+l d , l j The ordinal number of the one-dimensional numerical integration node of the j-th expansion, j = 1, 2, 3, ..., d, Indicates the ordinal number is l j Node for one-dimensional numerical integration.

6. The method for evaluating the robustness of aero-engine turbine aero-thermal performance according to claim 2, characterized in that: In step (5), the coefficients of the generalized chaotic polynomial are calculated using the Galerkin projection method in the spectral method. The formula is as follows: Where ρ(ξ) is the integral weight corresponding to the jth group of sampling points, Represents Ψ j (ξ) inner product with itself; <y,Ψ j (ξ)> represents the random performance response y and Ψ j The inner product of (ξ).

7. The method for evaluating the robustness of aero-engine turbine aero-thermal performance according to claim 1, characterized in that: The calculation formula for step (6) is as follows: Where S k represents the influence of the uncertain parameter combination corresponding to the kth chaotic polynomial on the random response performance, a k is the coefficient of the kth chaotic polynomial, I k For S k The corresponding k-th chaotic polynomial, Var[y(Ψ j (ξ))] represents the variance of the random response performance y corresponding to the j-th generalized chaotic polynomial, and Var[y(Ψ(ξ))] represents the variance of the random response performance y of the agent model represented by the constructed generalized chaotic polynomial.

8. The method for evaluating the robustness of aero-engine turbine aero-thermal performance according to claim 1, characterized in that: In step (7), the statistical characteristics of the random response result y are calculated based on the properties of the orthogonal polynomials in the generalized chaotic polynomials: m y =a0 μ y represents the expectation of the random response outcome y; represents the variance of the random response result y; Sampling and substituting the sampled data into the constructed generalized chaotic polynomial, and statistically analyzing the results of the generalized chaotic polynomial, the probability density function and skewness of the turbine aerothermal performance can be obtained.

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