CN113221466B - Turbine gas-thermal performance uncertainty quantification method and system based on pan-kriging model - Google Patents

Turbine gas-thermal performance uncertainty quantification method and system based on pan-kriging model Download PDF

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CN113221466B
CN113221466B CN202110599036.6A CN202110599036A CN113221466B CN 113221466 B CN113221466 B CN 113221466B CN 202110599036 A CN202110599036 A CN 202110599036A CN 113221466 B CN113221466 B CN 113221466B
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李军
黄明
李志刚
宋立明
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Abstract

A turbine gas thermal performance uncertainty quantification method based on a pan-kriging model is characterized in that a polynomial chaotic expansion to be solved is generated through a polynomial chaotic theory, and sparse/dense sample point data to be calculated is generated based on a low-order/high-order Symolyak sparse grid technology; automatically planning the calculation sequence of all sparse samples by using a genetic algorithm, and obtaining the gas-heat parameters of all samples by multimachine remote asynchronous distributed calculation; solving the coefficient of the polynomial chaotic expansion, constructing a universal kriging model by taking the obtained explicit expression as a regression function of a universal kriging model building module, and solving the expression of the universal kriging model; calculating the gas-heat parameters of each intensive sample point through an expression of a pan-kriging model; the coefficient of the polynomial chaotic expansion is solved by using a Galerkin projection method, so that the uncertainty mean value and the uncertainty deviation of the turbine gas thermal parameter can be obtained.

Description

Turbine gas-thermal performance uncertainty quantification method and system based on pan-kriging model
Technical Field
The invention belongs to the technical field of turbine uncertainty quantification design, and particularly relates to a turbine gas-thermal performance uncertainty quantification method and system based on a pan-kriging model.
Background
At present, the mainstream turbine gas-thermal performance research field at home and abroad is in a frame of deterministic research. However, there are many uncertainties in engineering practice, for example, the turbine groove depth will exhibit random distribution due to manufacturing and machining errors, and there is some uncertainty about the actual operating conditions of the turbine, such as total inlet pressure. According to studies by D 'amaro et al (D' amaro a, montomoli f. Incertation and film coating [ J ]. Computers & Fluids,2013, 71-320-326.), these geometric and operating condition deviations will significantly change the flow field configuration of the turbine and thereby affect its aerodynamic and heat transfer characteristics, deviating the true performance of the turbine from design values and significantly reducing the life and reliability of the turbine blades.
In order to study the uncertainty problem of the thermal performance of the turbine, the monte carlo method and the polynomial chaos method have been introduced by some scholars in the field of uncertainty quantification design of the turbine as mathematical tools for uncertainty quantification in recent years. However, in practice, researchers have found that the monte carlo method requires quantitative uncertainty analysis through a large number of random samples, which is very computing resource-consuming. Although the polynomial chaotic method can achieve the same calculation accuracy with less sample size compared with the monte carlo method, the polynomial chaotic method still needs a certain number of samples to perform uncertainty quantitative calculation. For example, 64 samples are needed for researching a 3-dimensional problem by using a polynomial chaos method, the time needed for computing the samples by using a mainstream Inter kernel server needs about two months, and the large computing expense is not allowed for engineering design. And as the dimension of the problem to be researched increases, the polynomial chaotic method can encounter the problem of dimension disaster, namely the sample size required by the polynomial chaotic method increases at the exponential explosion speed as the dimension of the problem to be researched increases.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a turbine gas thermal performance uncertainty quantification method and system based on a pan-kriging model so as to reduce the sample size of a polynomial chaos method in turbine gas thermal performance uncertainty quantification calculation.
In order to achieve the purpose, the invention adopts the technical scheme that:
a turbine gas thermal performance uncertainty quantification method based on a pan-kriging model comprises the following steps:
step 1, performing mathematical modeling through a polynomial chaos theory to generate a polynomial chaotic expansion to be solved, and generating sparse sample point data to be calculated based on a low-order Symolyak sparse grid technology;
step 2, automatically planning the calculation sequence of all samples by using a genetic algorithm, taking the calculation result of the last sample as the initial field of the sample to be calculated, and ensuring that the initial field iterated by each calculation is closest to the physical characteristics of the sample to be calculated, so that the calculation is not easy to diverge;
step 3, receiving the samples to be calculated and the initial field file obtained in the step 2, and dividing numerical calculation logic and result processing logic of uncertainty quantification to achieve the purpose of multi-machine different-place asynchronous distributed calculation and finally obtain gas heat parameters of all samples;
step 4, solving the coefficient of the polynomial chaotic expansion in the step 1 by using a Galerkin projection method to obtain an explicit expression of the solved polynomial chaotic expansion, and taking the explicit expression as a regression function of a universal Krigin model building module;
step 5, constructing a Pan-Critical model by combining sparse sample point distribution and a regression function;
step 6, solving an expression of a pan kriging model by using a pan kriging method;
step 7, performing mathematical modeling through a polynomial chaos theory to generate a polynomial chaos expansion to be solved, and generating dense sample point data to be calculated based on a high-order Symolylak sparse grid technology;
step 8, calculating the gas-heat parameters of each intensive sample point through an expression of a pan-kriging model;
and 9, solving the coefficient of the polynomial chaotic expansion formula in the step 7 by using a Galerkin projection method, so as to obtain the uncertainty mean value and the deviation of the turbine gas thermal parameter.
Further, in the step 3, a function under a thread method of Python is used to access the thread pool of the multi-machine different-place asynchronous distributed computing process in real time in the process of numerical value computing, so as to realize the function of monitoring the computing progress at any time.
Correspondingly, the invention also provides a turbine gas-thermal performance uncertainty quantification system based on the pan-kriging model, which comprises the following steps:
the rough polynomial chaotic model and the sparse sample point generating module are used for carrying out mathematical modeling through a polynomial chaotic theory to generate a polynomial chaotic expansion to be solved and generating sparse sample point data to be calculated based on a low-order Symolyalak sparse grid technology;
and the sparse sample point initial field distribution module is used for receiving the sparse sample point data of the rough polynomial chaotic model and the sparse sample point generation module, automatically planning the calculation sequence of all samples by using a genetic algorithm, and taking the calculation result of the last sample as the initial field of the sample to be calculated. The initial field iterated by each calculation is ensured to be closest to the physical characteristics of the sample to be calculated, so that the calculation is not easy to diverge;
the multi-machine different-place asynchronous distributed calculation module receives the calculation result of the sparse sample point initial field distribution module, and divides the numerical calculation logic and the result processing logic of uncertainty quantification to achieve the purpose of multi-machine different-place asynchronous distributed calculation and finally obtain the gas heat parameters of each sample;
the rough polynomial chaotic model solving module is used for receiving the calculation result of the multimachine allopatric asynchronous distributed calculation module, solving the polynomial chaotic expansion coefficient by using a Galerkin projection method to obtain an explicit expression of the solved polynomial chaotic expansion, and taking the explicit expression as a regression function of a subsequent universal Krigin model building module;
and the Pankriging model building module is used for receiving the calculation results of the sparse sample point initial field distribution module and the rough polynomial chaotic model solving module. Constructing a pan-kriging model by combining sparse sample point distribution and a regression function;
the Pan-Krigin model solving module is used for receiving the calculation result of the Pan-Krigin model building module and solving the expression of the Pan-Krigin model by using a Pan-Krigin method;
the high-precision polynomial chaotic model and the dense sample point generating module perform mathematical modeling through a polynomial chaotic theory to generate a polynomial chaotic expansion to be solved. Generating dense sample point data to be calculated based on a high-order Symolylak sparse grid technology;
the dense sample point gas-heat parameter solving module is used for receiving the calculation results of the Pankriging model solving module, the high-precision polynomial chaotic model and the dense sample point generating module and calculating the gas-heat parameter of each dense sample point through the expression of the Pankriging model;
the high-precision polynomial chaotic model solving module receives a calculation result of the dense sample point gas-heat parameter solving module, calculates the gas-heat parameters of the dense sample points through an expression of a universal kriging model, calculates the polynomial chaotic expansion coefficients by using a Galerkin projection method, and can calculate the uncertainty mean value and the uncertainty deviation of the turbine gas-heat parameters through the coefficients.
Compared with the prior art, the invention has the beneficial effects that:
(1) The rough polynomial chaotic model and the sparse sample point generation module introduce a polynomial chaotic expansion as a mathematical tool for describing the uncertainty of the system, and a low-order sparse grid method is used for sampling, so that the number of samples required by the uncertainty quantification of the gas-thermal performance of the turbine is greatly reduced on the basis of ensuring certain precision.
(2) The calculation order is reasonably distributed based on the angle of the global sample through the sparse sample point initial field distribution module, the calculation time of a single sample can be reduced to one third of the original calculation time, and the calculation is not easy to diverge through the reasonable setting of the initial field.
(3) Compared with the serial computing logic of the traditional research method, the invention can perform multi-machine long-distance asynchronous distributed computing, and greatly improves the use efficiency of computer computing power. And can ensure that the calculation of other samples is not influenced even after the calculation of a certain sample is diverged and interrupted.
(4) The capturing capability of the pan kriging model to local information is fully utilized by the pan kriging model building module and the pan kriging model solving module, information contained in a sample calculation result is mined to the maximum extent, and the calculation precision of the rough polynomial chaotic model is greatly improved.
(5) The acquired universal kriging model is rewritten into a high-precision polynomial chaotic model through a high-precision polynomial chaotic model, a dense sample point generating module, a dense sample point gas-thermal parameter solving module and a high-precision polynomial chaotic model solving module, and the excellent capturing capability of the polynomial chaotic method on the global uncertainty is fully utilized.
(6) Compared with the traditional polynomial chaos method, the method can obtain the uncertainty mean value and the uncertainty deviation with the same precision by one fourth of samples, and compared with the traditional Monte Carlo method, the required number of samples is reduced to one ten thousandth of the original number.
Drawings
FIG. 1 is a schematic diagram of the system of the present invention.
Fig. 2 shows the sparse sample point distribution obtained by using the Symolyak sparse grid technology in the embodiment, only 7 samples are needed for carrying out uncertainty quantification of the heat exchange quantity by using the method, and 64 samples are needed by using the traditional polynomial chaos method. In the figure D indicates the groove depth, P indicates the main inlet total pressure and a indicates the inlet flow angle.
Fig. 3 is axial distribution of the uncertainty mean value of the heat exchange amount obtained in the embodiment and axial distribution of the uncertainty mean value of the heat exchange amount obtained by the conventional polynomial chaotic method, in which Q represents the heat exchange amount, μ 1 represents the axial distribution of the uncertainty mean value of the heat exchange amount obtained in the embodiment, and μ 2 represents the axial distribution of the uncertainty mean value of the heat exchange amount obtained by the conventional polynomial chaotic method.
Fig. 4 is an axial distribution of uncertainty deviation of the heat exchange amount obtained in the embodiment and an axial distribution of uncertainty deviation of the heat exchange amount obtained by the conventional polynomial chaotic method, in which Q represents the heat exchange amount, σ 1 represents the axial distribution of uncertainty deviation of the heat exchange amount obtained in the embodiment, and σ 2 represents the axial distribution of uncertainty deviation of the heat exchange amount obtained by the conventional polynomial chaotic method.
Detailed Description
The embodiments of the present invention will be described in detail below with reference to the drawings and examples.
Example (c): uncertainty visualization analysis of gas-thermal properties was performed on the GE _ E3 leaf shapes, the geometric parameters of which are shown in Table 1.
TABLE 1 geometric parameters of the GE _E3leaf shape
Name of geometric parameter Numerical value
Mean camber line origin coordinates (40.00,13.57,-33.74)
Mean camber line end point coordinates (124.80,-60.60,-33.74)
Leaf height/mm 122.0
Referring to fig. 1, the present embodiment is based on a system for quantifying uncertainty of gas-thermal performance of a high-efficiency turbine based on a pan-kriging model, and includes:
1. and the rough polynomial chaotic model and the sparse sample point generating module input random variables needing to be researched to generate sample point distribution. The present example selects the groove depth, the main flow inlet total pressure and the inlet flow angle as random variables to be studied. The distribution of sample points obtained for the sample point space based on the Symolyak sparse grid technique is shown in fig. 2. The basic idea of the Symolyak sparse grid technique is to construct a multidimensional product formula by tensor product combination of one-dimensional product formulas. The numerical integration node of the n-dimensional k-order sparse grid precision is represented by equation (1), where n =3, k =1 in this embodiment:
Figure BDA0003092137300000061
in the formula (I), the compound is shown in the specification,
Figure BDA0003092137300000062
a numerical integral node representing the precision of the n-dimensional k-order sparse grid, q is a constant, q = k + n, | i | = i 1 +i 2 +i 3 +…+i j +…+i n ，i j Represents the ordinal number of the j term expansion one-dimensional numerical integration node, j =1,2, a.
Figure BDA0003092137300000063
The ordinal number is i j A node of the one-dimensional numerical integration of (1);
the weights w corresponding to the integration nodes are represented as follows:
Figure BDA0003092137300000064
in the formula
Figure BDA0003092137300000065
The ordinal number is i j The sparse grid numerical integral node weights of,
Figure BDA0003092137300000066
representing a vector consisting of individual components;
then high dimension integral formula- Ω yΦ j ρ (ξ) d ξ may be represented as:
Figure BDA0003092137300000067
where y is the system output and the heat exchange amount is the subject of study in this embodiment, so y is the heat exchange amount, Φ j Integral nodes of j term in continuous form, p (xi) is integral weight in continuous form, N s Representing the number of integrating nodes, y, of the sparse grid l In discrete form of y,. Phi j (ξ l ) Is phi j The discrete form of (a);
therefore, the sample point distribution data required by the polynomial chaotic expansion can be established.
For the heat exchange quantity y, the polynomial chaos method is used for expanding the heat exchange quantity y into the following steps:
Figure BDA0003092137300000068
in the formula
Figure BDA0003092137300000071
Respectively representing the orthogonal bases of each order of the polynomial
Figure BDA0003092137300000072
Figure BDA0003092137300000073
The corresponding certainty factor, i.e. the amount that needs to be solved,
Figure BDA0003092137300000074
for each projection order, theta is a random variable; the heat exchange quantity y is converted according to the finite number of random variables and the finite order of a polynomial expansion in practical operationTruncating the expression of (c):
Figure BDA0003092137300000075
where P is the order, P is set to 2 in this embodiment. a is j Is a coefficient of the quadrature basis of the j-th term, i.e.
Figure BDA0003092137300000076
Of discrete form, Ψ j And (xi) is the orthogonal base of the j term in discrete case.
2. And the sparse sample point initial field distribution module is used for receiving the sparse sample point data of the rough polynomial chaotic model and the sparse sample point generation module, automatically planning the calculation sequence of all samples by using a genetic algorithm, and taking the calculation result of the last sample as the initial field of the sample to be calculated. And the initial field iterated by each calculation is ensured to be most similar to the physical characteristics of the sample to be calculated. The implementation steps of the genetic algorithm are as follows, in this embodiment, the number of individuals is 100, the highest evolutionary algebra is 50, the cross probability is 80%, the mutation probability is 5%, and real number coding is adopted:
1) Calculating the distance between the sparse sample points in the sample point space, wherein the distance is Euclidean distance, and the calculation method comprises the following steps:
Figure BDA0003092137300000077
in the formula A 1 And A 2 The value of the first input quantity for different samples, in this example the groove depth, B 1 And B 2 For the value of the second input variable for the different samples, in this example the total main inlet pressure, C 1 And C 2 The value of the third input for a different sample, in this embodiment the inlet airflow angle;
2) Initialization: randomly generating a calculation sequence of a sample, recording the calculation sequence as an individual, repeating the calculation sequence for a plurality of times (100 times in the embodiment) to obtain an initial population containing a plurality of (namely 100) individuals, and setting an initial evolution algebra to be 0;
3) And (3) fitness evaluation: calculating the sum of the distances of all samples according to the calculation sequence represented by each sample, and taking the sum as the fitness of the individual;
4) Selecting and operating: selecting a plurality of individuals with the first fitness (80% of the individuals in the embodiment) to enter cross operation, and eliminating the last 20% of individuals;
5) And (3) cross operation: randomly exchanging the codes of the individuals obtained by the selection operation with a cross probability (i.e. 80%);
6) And (3) mutation operation: randomly replacing the codes of the individuals obtained by the cross operation with a random number according to the variation probability (namely 5 percent);
7) Randomly generating a plurality of (20 in the embodiment) individuals to be supplemented into the population subjected to the mutation operation;
8) Repeating the steps 3) -7) and adding one to the evolution algebra;
9) And when the Euclidean distance between two adjacent generations of optimal individuals is less than 0.0001 or the evolution algebra is equal to the highest evolution algebra, stopping the calculation, wherein the individual with the highest fitness of the latest generation is the optimal sample point calculation sequence, so that the difference between the sample to be calculated and the initial field is minimum.
3. The multi-machine remote asynchronous distributed computing module receives the samples to be computed and the initial field files of the sparse sample point initial field distribution module, according to the designed flow of the system, computing logic is to compute all the samples needed, and then the samples are led into a subsequent rough polynomial chaotic model solving module, so that a plurality of kernels can be called on a plurality of computers at one time to compute different samples in parallel, and the computing task of the samples can be specifically completed by calling commercial software CFX. The purpose of calculation is to obtain the gas heat parameter value of each sample, and the heat exchange amount is taken as the gas heat parameter to be researched in the embodiment.
4. And (3) a calculation progress real-time feedback module (if needed), and a function under a thread method of Python is used for accessing a thread pool of a calculation process of the multi-machine different-place asynchronous distributed calculation module in real time in the numerical calculation process, so that the function of monitoring the calculation progress at any time is realized.
5. And the rough polynomial chaotic model solving module is used for receiving the calculation result of the multi-core allopatric asynchronous distributed calculation module, solving the polynomial chaotic expansion coefficient by using a Galerkin projection method to obtain an explicit expression of the solved polynomial chaotic expansion, and taking the explicit expression as a regression function of a subsequent generic Krigin model building module. The Galerkin projection method uses the orthogonality of polynomials to project a function onto each basis function term to calculate the corresponding coefficient:
Figure BDA0003092137300000091
in the formula, psi j (ξ) represents the jth term orthogonal base,
Figure BDA0003092137300000092
is the inner product of a polynomial, J (xi) is the joint probability density function of uncertainty input variables, and each order orthogonal basis of the polynomial in the coefficient collocation formula (4) of the polynomial chaotic expansion formula
Figure BDA0003092137300000093
The expression is an explicit expression of the polynomial chaotic expansion.
6. And the Pankriging model building module is used for receiving the calculation results of the sparse sample point initial field distribution module and the rough polynomial chaotic model solving module. Constructing a Pan-Krigin model by combining sparse sample point distribution and a regression function, wherein the form of the Pan-Krigin model is as follows:
M(θ)＝f T (θ)β+z(θ) (8)
in the formula, θ represents a random variable, f T And (theta) is a regression function obtained by a solving module of the rough polynomial chaotic expansion model, beta represents a coefficient of the regression function, and z (theta) represents the approximation of local deviation.
7. And the Pan-Critical model solving module is used for receiving the calculation result of the Pan-Critical model building module and solving the expression of the Pan-Critical model. Let the covariance matrix of the local deviation z (θ) be:
E[(z(θ 1 )z(θ 2 ))]＝σ 2 R(γ，θ 1 ，θ 2 ) (9)
in the formula, theta 1 And theta 2 Representing any two sample points in sample space and gamma representing a hyper-parameter. R (gamma, theta) 1 ，θ 2 ) Denotes θ 1 And theta 2 Of (a) a spatial correlation function of (R, y, θ) 1 ，θ 2 ) The calculation method of (2) is as follows:
Figure BDA0003092137300000094
where n represents the order of the problem, and in this embodiment n is equal to 3. Gamma ray j ，θ 1j And theta 2j Gamma, theta representing j dimension 1 And theta 2 . To-be-measured point theta x The correlation with the sample point θ s is expressed as follows:
r(θ)＝R(γ，θ x ，θ s ) T (11)
the response value of each sample point obtained by the multi-machine different-place asynchronous distributed computing module is Y, and each order orthogonal basis of the polynomial in the formula (4)
Figure BDA0003092137300000095
To F, the generic kriging model can be calculated by:
M(θ)＝f T (θ)β+r T (θ)R(γ，θ x ，θ s ) -1 (Y-Fβ) (12)
8. the high-precision polynomial chaotic model and the dense sample point generating module refer to formulas of a rough polynomial chaotic model and a sparse sample point generating module, except that n is 3,k, 10 is taken, and P is 10 taken.
9. And the dense sample point gas-heat parameter solving module is used for receiving the dense sample point distribution of the high-precision polynomial chaotic model and the dense sample point generating module and the expression of the Pankriging model solving module, and calculating the heat exchange quantity of each sample point in the dense sample point distribution by using the expression of the Pankriging.
10. High-precision polynomial chaotic model solving moduleReceiving a calculation result of the dense sample point gas-thermal parameter solving module, quickly solving the statistical characteristic of the heat exchange capacity y of the system according to the orthogonality of the polynomial chaos after solving the polynomial chaos expansion coefficient by using a Galerkin projection method, wherein the mean value mu is y And variance σ y 2 Is calculated as shown in equations (18) and (19).
μ y ＝a 0 (18)
Figure BDA0003092137300000101
Fig. 3 is an axial distribution of the uncertainty mean value of the heat exchange amount obtained in the embodiment and an axial distribution of the uncertainty mean value of the heat exchange amount obtained by the conventional polynomial chaotic method, in which Q represents the heat exchange amount, μ 1 represents the axial distribution of the uncertainty mean value of the heat exchange amount obtained in the embodiment, and μ 2 represents the axial distribution of the uncertainty mean value of the heat exchange amount obtained by the conventional polynomial chaotic method. As can be seen from the figure, the uncertainty mean value of the heat exchange quantity of the blade top is maximum at 20% of the axial chord length, so that certain protective measures can be taken for the area in practical operation, such as spraying of refractory materials and the like. In addition, although the calculated sample point is only 10.93% of that of the traditional polynomial chaotic method, the calculation precision of the heat exchange uncertainty mean value is almost the same. Therefore, the method has excellent performance in saving computing resources in the research of the uncertainty quantitative mean value problem.
Fig. 4 is an axial distribution of uncertainty deviation of the heat exchange amount obtained in the embodiment and an axial distribution of uncertainty deviation of the heat exchange amount obtained by the conventional polynomial chaotic method, in which Q represents the heat exchange amount, σ 1 represents the axial distribution of uncertainty deviation of the heat exchange amount obtained in the embodiment, and σ 2 represents the axial distribution of uncertainty deviation of the heat exchange amount obtained by the conventional polynomial chaotic method. It can be seen from the figure that when uncertainty occurs in the groove depth, the main flow inlet total pressure and the inlet airflow angle, the heat exchange amount of the front area and the tail area of the blade top is most prone to large fluctuation, and in actual operation, the areas become the areas which are most prone to failure. And it can also be found that although the calculated sample point is only 10.93% of that of the traditional polynomial chaos method, the calculation accuracy of uncertainty deviation of heat exchange quantity is almost the same. The invention therefore has excellent performance in saving computational resources in the uncertainty quantification bias problem study. According to the conclusions obtained by the figures 3 and 4, the invention has important significance for guiding the actual operation work of the turbine.

Claims (10)

1. A turbine gas thermal performance uncertainty quantification method based on a pan-kriging model is characterized by comprising the following steps:
step 1, performing mathematical modeling through a polynomial chaos theory to generate a polynomial chaos expansion to be solved, and generating sparse sample point data to be calculated based on a low-order Symolyak sparse grid technology;
step 2, automatically planning the calculation sequence of all samples by using a genetic algorithm, taking the calculation result of the last sample as the initial field of the sample to be calculated, and ensuring that the initial field iterated by each calculation is closest to the physical characteristics of the sample to be calculated, so that the calculation is not easy to diverge;
step 3, receiving the samples to be calculated and the initial field file obtained in the step 2, and dividing numerical calculation logic and result processing logic of uncertainty quantification to achieve the purpose of multimachine asynchronous distributed calculation in different places and finally obtain gas heat parameters of each sample;
step 4, solving the coefficient of the polynomial chaotic expansion in the step 1 by using a Galerkin projection method to obtain an explicit expression of the solved polynomial chaotic expansion, and taking the explicit expression as a regression function of a universal Krigin model building module;
step 5, combining the sparse sample point distribution and the regression function to construct a pan-kriging model;
step 6, solving an expression of a Pankriging model by using a Pankriging method;
step 7, performing mathematical modeling through a polynomial chaos theory to generate a polynomial chaos expansion to be solved, and generating dense sample point data to be calculated based on a high-order Symolylak sparse grid technology;
step 8, calculating gas-heat parameters, namely heat exchange quantity, of each intensive sample point through an expression of the pan-kriging model and intensive sample point data to be calculated;
and 9, according to the gas thermal parameters of each dense sample point, solving the coefficient of the polynomial chaotic expansion formula in the step 7 by using a Galerkin projection method, and obtaining the uncertainty mean value and deviation of the turbine gas thermal parameters through the coefficient.
2. The turbine gas-thermal performance uncertainty quantification method based on the pan-kriging model as claimed in claim 1, wherein the gas-thermal parameter is a heat exchange amount, and in the step 1 and the step 7, a numerical integration node of n-dimensional k-order sparse grid precision is represented by the following formula:
Figure FDA0003755318380000021
in the formula (I), the compound is shown in the specification,
Figure FDA0003755318380000022
a numerical integral node representing the precision of the n-dimensional k-order sparse grid, q is a constant, q = k + n, | i | = i 1 +i 2 +i 3 +…+i j +…+i n ，i j Represents the ordinal number of the j term expansion one-dimensional numerical integration node, j =1,2, … …, n,
Figure FDA0003755318380000023
the ordinal number is i j A node of the one-dimensional numerical integration of (1);
the weights w corresponding to the integration nodes are represented as follows:
Figure FDA0003755318380000024
in the formula
Figure FDA0003755318380000025
The ordinal number is i j The sparse grid numerical integral node weights of,
Figure FDA0003755318380000026
representing a vector composed of individual components;
high dimensional integral formula- Ω yΦ j ρ (ξ) d ξ is represented as:
Figure FDA0003755318380000027
where y is the system output, i.e. the heat transfer, phi j Integral nodes of item j in continuous form, p (ξ) is integral weight in continuous form, N s Representing the number of integrating nodes, y, of the sparse grid l In discrete form of y, [ phi ] j (ξ l ) Is phi j A discrete form of (a);
therefore, the sample point distribution data required by the polynomial chaotic expansion can be established;
and expanding the system output y into the following values by using a polynomial chaos method:
Figure FDA0003755318380000028
in the formula a 0 、
Figure FDA0003755318380000029
Respectively representing various orders of orthogonal bases I of a polynomial 0 、
Figure FDA00037553183800000210
Figure FDA00037553183800000211
The corresponding certainty factor, i.e. the amount that needs to be solved,
Figure FDA00037553183800000212
for each projection order, theta is a random variable; in practical operation, the expression of the system output y is truncated according to the finite number of random variables and the finite order of the polynomial expansion as follows:
Figure FDA0003755318380000031
wherein P is the order, a j Is a coefficient of the j-th term orthogonal basis, i.e.
Figure FDA0003755318380000032
Of discrete form, Ψ j And (ξ) is the jth orthogonal base under the discrete condition, the order P of the step 7 is greater than the order P of the step 1, and the sparse grid precision order k of the step 7 is greater than the sparse grid precision order k of the step 1.
3. The method as claimed in claim 2, wherein in step 1, the order P is set to 2 and the order k =1, and in step 7, the order P is set to 2 and the order k =10.
4. The turbine gas-thermal performance uncertainty quantification method based on the pan-kriging model as claimed in claim 2 or 3, wherein in the step 2, the genetic algorithm adopts real number coding, and comprises the following steps:
step 2.1), calculating the distance between the sparse sample points in the sample point space, wherein the distance is the Euclidean distance;
step 2.2), initialization: randomly generating a calculation sequence of a sample, recording the calculation sequence as an individual, repeating the calculation sequence for a plurality of times to obtain an initial population containing a plurality of individuals, and setting an initial evolution algebra to be 0;
step 2.3), fitness evaluation: calculating the sum of the distances of all samples according to the calculation sequence represented by each sample, and taking the sum as the fitness of the individual;
step 2.4), selecting operation: selecting a plurality of individuals with the previous fitness in proportion, and performing cross operation to eliminate the rest individuals;
step 2.5), cross operation: randomly exchanging the codes of the individuals obtained by the selection operation according to the cross probability;
step 2.6), mutation operation: randomly replacing the codes of the individuals obtained by the cross operation with a random number according to the variation probability;
step 2.7), randomly generating a plurality of individuals to supplement the population subjected to the variation operation;
step 2.8), repeating the steps 2.3) to 2.7) and adding one to the evolution algebra;
and 2.9) stopping the calculation when the Euclidean distance between two adjacent generations of optimal individuals is less than 0.0001 or the evolution algebra is equal to the highest evolution algebra, wherein the individual with the highest fitness of the latest generation is the optimal sample point calculation sequence, so that the difference between the sample to be calculated and the initial field is minimum.
5. The turbine gas-thermal performance uncertainty quantification method based on the pan-kriging model according to claim 2 or 3, wherein in the step 3, all samples needed to be used are calculated, and then the samples are introduced into the step 4, so that a plurality of cores are called on a plurality of computers at one time to calculate different samples in parallel, and the calculation task of the samples is specifically completed by calling a software CFX, so that a gas-thermal parameter value of each sample is obtained.
6. A method for quantifying uncertainty in thermal performance of a turbine according to claim 2 or 3, wherein in the step 4, the Galerkin projection method uses the orthogonality of the polynomial to project a function onto each basis function term to calculate the corresponding coefficient:
Figure FDA0003755318380000041
in the formula (I), the compound is shown in the specification,
Figure FDA0003755318380000042
is the inner product of a polynomial, J (xi) is the joint probability density function of uncertainty input variables, and the coefficient of the polynomial chaotic expansion is matched with each order orthogonal base I of the polynomial 0 、
Figure FDA0003755318380000043
Figure FDA0003755318380000044
The expression is an explicit expression of the polynomial chaotic expansion.
7. The turbine gas thermal performance uncertainty quantification method based on the pan-kriging model as claimed in claim 6, wherein in the step 5, the established pan-kriging model formula is as follows:
M(θ)＝f T (θ)β+z(θ)
in the formula, θ represents a random variable, f T (theta) is a regression function obtained by a solving module of the rough polynomial chaotic expansion model, beta represents a coefficient of the regression function, and z (theta) represents the approximation of local deviation;
in step 6, let the covariance matrix of z (θ) be:
E[(z(θ 1 )z(θ 2 ))]＝σ 2 R(γ,θ 1 ,θ 2 )
in the formula, theta 1 And theta 2 Represents any two sample points in the sample space, gamma represents a hyperparameter, R (gamma, theta) 1 ,θ 2 ) Denotes theta 1 And theta 2 Of (a) a spatial correlation function of (R, y, θ) 1 ,θ 2 ) The calculation method of (2) is as follows:
Figure FDA0003755318380000045
in the formula, gamma j ，θ 1j And theta 2j Gamma, theta representing j dimension 1 And theta 2 Point to be measured theta x The correlation with the sample point θ s is expressed as follows:
r(θ)＝R(γ,θ x ,θ s ) T
the response value of each sample point obtained by the multi-machine different-place asynchronous distributed computing module is Y, and the polynomial orthogonal basis I of each order 0 、
Figure FDA0003755318380000051
For F, the pan-Critical model is calculated by:
M(θ)＝f T (θ)β+r T (θ)R(γ,θ x ,θ s ) -1 (Y-Fβ)。
8. the method as claimed in claim 7, wherein in the step 9, after the coefficients of the polynomial chaotic expansion are calculated by using the Galerkin projection method, the statistical property of the system output y is rapidly calculated according to the orthogonality of the polynomial chaos, wherein the mean value μ is y ＝a 0 And variance
Figure FDA0003755318380000052
9. The turbine gas-thermal performance uncertainty quantification method based on the pan-kriging model as claimed in claim 1, wherein in the step 3, a function under a Threadxl method of Python is used to access a thread pool of a multi-machine allopatric asynchronous distributed computation process in real time in a numerical computation process, so as to realize a function of monitoring computation progress at any time.
10. A turbine gas thermal performance uncertainty quantification system based on a pan-kriging model is characterized by comprising:
the rough polynomial chaotic model and the sparse sample point generating module are used for carrying out mathematical modeling through a polynomial chaotic theory to generate a polynomial chaotic expansion to be solved and generating sparse sample point data to be calculated based on a low-order Symolyalak sparse grid technology;
the sparse sample point initial field distribution module receives the sparse sample point data of the rough polynomial chaotic model and the sparse sample point generation module, automatically plans the calculation sequence of all samples by using a genetic algorithm, takes the calculation result of the last sample as the initial field of the sample to be calculated, and ensures that the initial field iterated by each calculation is closest to the physical characteristics of the sample to be calculated, so that the calculation is not easy to diverge;
the multi-machine different-place asynchronous distributed computing module receives the computing result of the sparse sample point initial field distribution module, and divides the numerical computing logic and the result processing logic of uncertainty quantification to achieve the purpose of multi-machine different-place asynchronous distributed computing and finally obtain the gas heat parameters of each sample;
the rough polynomial chaotic model solving module is used for receiving the calculation result of the multimachine allopatric asynchronous distributed calculation module, solving the polynomial chaotic expansion coefficient by using a Galerkin projection method to obtain an explicit expression of the solved polynomial chaotic expansion, and taking the explicit expression as a regression function of a subsequent universal Krigin model building module;
the system comprises a Pankriging model building module, a rough polynomial chaotic model solving module, a sparse sample point initial field distribution module and a Rough polynomial chaotic model initial field distribution module, wherein the Pankriging model building module is used for receiving the calculation results of the sparse sample point initial field distribution module and the Rough polynomial chaotic model solving module and combining sparse sample point distribution and a regression function to construct a Pankriging model;
the Pan-Krigin model solving module is used for receiving the calculation result of the Pan-Krigin model building module and solving the expression of the Pan-Krigin model by using a Pan-Krigin method;
the high-precision polynomial chaotic model and the dense sample point generating module are used for carrying out mathematical modeling through a polynomial chaotic theory, generating a polynomial chaotic expansion to be solved, and generating dense sample point data to be calculated based on a high-order Symolyak sparse grid technology;
the dense sample point gas-heat parameter solving module is used for receiving the calculation results of the pan kriging model solving module, the high-precision polynomial chaotic model and the dense sample point generating module and calculating the gas-heat parameter of each dense sample point through the expression of the pan kriging model;
the high-precision polynomial chaotic model solving module receives a calculation result of the dense sample point gas-heat parameter solving module, calculates the gas-heat parameters of the dense sample points through an expression of a universal kriging model, calculates the polynomial chaotic expansion coefficients by using a Galerkin projection method, and can calculate the uncertainty mean value and the uncertainty deviation of the turbine gas-heat parameters through the coefficients.
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