Space cabin uncertainty heat conduction analysis method based on generalized low-deviation point set

Abstract

The invention provides a space cabin uncertainty heat conduction analysis method based on a generalized low-deviation point set, and belongs to the field of space cabin uncertainty heat conduction analysis. Firstly, a finite element calculation model of a space cabin is established; secondly, constructing a generalized low-deviation point set for heat conduction analysis of the space cabin and a corresponding point set weight; thirdly, constructing a thermal parameter random field through a Karhunen-Loeve expansion method in combination with sample points based on generalized deviation, and performing finite element thermal analysis to obtain a temperature field of the space cabin; and finally, calculating the statistical information of the temperature field of the space cabin by using a generalized Monte Carlo method. According to the method, conditions can be provided for uncertainty analysis of heat conduction of the space cabin, and uncertainty analysis of heat conduction of the space cabin is completed; the precision is high, and the calculation amount required for analyzing the uncertainty of the space cabin is reduced; the device is high in universality, suitable for space cabins of any model and also suitable for any complex structure.

Description

Technical Field

[0001] The invention belongs to the field of uncertainty heat conduction analysis of space cabins, and relates to an uncertainty heat conduction analysis method of space cabins based on a generalized low-deviation point set. Background Art

[0002] In the field of aerospace, structural design and analysis are increasingly focusing on thermal issues, especially under the action of thermal loads, the heat transfer and heat dissipation of structures has become a widely concerned research issue. The Chinese invention patent "A design method for unified thermal management in the cabin of a high-speed aircraft" (application number: 201910855437.6) made a detailed study on the cabin environment, the heat resistance limit of cabin components, the influencing factors and laws of temperature and cooling measures, and completed the optimization of the thickness of the cabin thermal layer / insulation layer. The Chinese invention patent "A fine calculation of the coupled thermal environment in the cabin of a hypersonic aircraft" (application number 201910159395.2) provides a fine calculation method for the coupled thermal environment in a space cabin. The calculation method considers multiple heat sources, radiation, convection, and three-dimensional heat transfer phenomena. However, none of the above patents considers uncertainty factors. Considering the widely used composite materials in aerospace engineering, there are uncertainties in the physical parameters of these materials, such as density and thermal conductivity. Due to these uncertainties, the output response is also uncertain, resulting in the loss of effectiveness of the deterministic calculation method. Therefore, it is necessary to establish an efficient and accurate uncertainty analysis method for the problem of heat conduction in the space cabin.

[0003] At present, the uncertainty analysis methods applied in the aerospace field include chaotic polynomial method, Monte Carlo method, quasi-Monte Carlo method and random perturbation method. Among them, Monte Carlo method and quasi-Monte Carlo method have been widely used because of their simple calculation format and easy implementation. The Monte Carlo series of algorithms have an important common step: an important common step of these methods is to select certain sample points in the probability space based on a certain criterion, and then calculate the response values ​​corresponding to these sample points, and combine these response values ​​according to a certain rule to obtain the final statistical information. On the other hand, the calculation of the statistical information of the uncertainty response (such as mean, variance, etc.) often involves high-dimensional integration. Therefore, the calculation process of the non-embedded method can be approximately regarded as a numerical approximation of the high-dimensional integral, and the arrangement of the sample points and the weight of each sample point are very important. How to determine the optimal arrangement of the sample points and the weight of each sample point is a problem that needs further study.

[0004] The commonly used principle for determining the distribution and weight of sample points is that the distribution and weight of sample points should be set to minimize the error of statistical information. For the Monte Carlo method, the law of large numbers can be used to evaluate the upper limit of the error of its calculation results; and for the quasi-Monte Carlo method, the KH inequality can be used to evaluate the upper limit of the error of its calculation results. According to the KH inequality, the quality of sample point arrangement can be determined based on the deviation of the point set. The smaller the deviation, the better the arrangement of sample points. At present, many different types of point set deviations have been developed, such as mean-centered center deviation, convolution deviation, L2 deviation, etc. However, these point set deviations are only applicable to the case where the weights of sample points (matching points) are equal, while the weights of sample points in many algorithms are not equal, and how to estimate the upper limit of their errors is a problem. Recently, the literature [JB Chen and SH Zhang, "Improving point selection in cubature by a new discrepancy," SIAM J. Sci. Comput., vol. 35, no. 5, pp. A2121-A2149, 2013, doi: 10.1137 / 12089377X.] proposed a generalized deviation to measure the error of the calculation results for the uncertainty quantification algorithm with unequal weights. The literature [Song Pengyan and Chen Jianbing, "Point set optimization and multidimensional numerical integration based on generalized L2 deviation," Scientia Sinica (Technical Sciences), vol. 45, no. 5, pp. 547-558, 2015, doi: 10.1360 / N092014-00200.] further studied the optimization of sample point arrangement and weights based on the generalized L2 deviation with non-uniform weights. Although the L2 deviation has the advantage of being simple and easy to calculate compared to the star deviation, the deviation is centered on the origin. According to the KH inequality, if the function value (or its derivative value) at the origin is very large, it may cause the integral error to be still large even if the L2 deviation is very small. If the central deviation can be combined with the non-weighted generalized deviation theory to develop a non-equal-weighted deviation with better symmetry, and the layout of the sample points is optimized accordingly, it will obviously be of great benefit to improving the accuracy of the uncertainty quantification calculation results. In particular, considering many complex aerospace engineering problems with uncertain parameters, the amount of computation for deterministic calculations is already very large, and the amount of computation for analysis under the condition of uncertain parameters is even greater. If the layout of sample points can be optimized and statistical results with good accuracy can be given using as few sample points as possible, it will be of significant significance for the uncertainty quantification analysis of complex aerospace engineering problems and is worthy of study. The present invention is dedicated to this work. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides a method for uncertainty heat conduction analysis of a space cabin based on a generalized low-deviation point set. The present invention is used to perform uncertainty analysis of heat conduction, with fast calculation speed, high calculation accuracy and high algorithm stability.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A method for analyzing uncertainty heat conduction of a space cabin based on a generalized low-deviation point set. The method first establishes a finite element model of the space cabin; secondly, constructs a generalized low-deviation point set and corresponding point set weights for heat conduction analysis of the space cabin; then, a thermal parameter random field is constructed by combining the sample points based on generalized deviations through the Karhunen-Loeve expansion method, and a finite element thermal analysis is performed to obtain the temperature field corresponding to all samples; finally, the statistical information of the temperature field of the space cabin is calculated using the generalized Monte Carlo method. The method includes the following steps:

[0008] The first step is to establish a finite element calculation model of the space capsule, specifically:

[0009] Step 1.1, build a three-dimensional model of the space capsule according to the engineering drawing.

[0010] Step 1.2, import the three-dimensional model of the space capsule modeled in step 1.1 into the finite element analysis software, divide the mesh and export the node information at the mesh nodes.

[0011] Step 1.3, according to the actual situation, select the material properties of the space capsule, and determine the thermal load and boundary conditions of the space capsule according to the actual working conditions of the space capsule.

[0012] Step 1.4, based on the known three-dimensional model of the space capsule and the node information of the grid, finite element software is used to perform deterministic heat conduction calculations on the space capsule to obtain the temperature field information of the space capsule.

[0013] The second step is to construct a generalized low-deviation point set and corresponding point set weights for space cabin heat conduction analysis. Specifically:

[0014] Step 2.1, based on the extended Koksma-Hlawka inequality and the existing L2 deviation method, consider uniformly distributed random variables and obtain the generalized L2 deviation of the new generalized quasi-Monte Carlo integration format for random variables For the convenience of writing, the present invention uses the generalized low deviation as a proxy. Where ξ=(ξ1,ξ2,…,ξ s ) is the probability space [0,1] s Any point in the space, where s is the dimension of the sample space, ξ irepresents the spatial coordinate of the sample point in the i-th dimension, i = 1, 2, ..., s. sn represents a point set of n sample points in s dimension, and X sn ={x1,…,x n}(x i =(x i,1 ,…,x i,s ) T ). P=[P1,P2,…,P n ], P i Represents the point set X sn The weight corresponding to the i-th sample point in , i = 1, 2, ..., n. This step is based on the extended Koksma-Hlawka inequality, and the existing L2 deviation is extended to obtain the generalized low deviation As the low deviation point set X sn And the quality assessment standard with its corresponding weight P.

[0015] Step 2.2, construct the generalized low deviation in step 2.1 The minimum point set weight P. Specifically:

[0016] To select step 2.1 point set X sn For each point x i The corresponding weight P i Satisfies the following formula, i = 1, 2, ..., n:

[0017]

[0018] According to formula (1), we can get:

[0019] P=G -1 b(2)

[0020] Where P represents the optimal point set weight determined according to formula (1); b is a sequence consisting of n elements; G is an abbreviation symbol given for convenience of writing; the complete forms of b and G are shown in the following formula:

[0021]

[0022] Among them, b j represents the j-th element in sequence b, j = 1, 2, ..., n; Indicates the selection of a point ξ i After x j,i The function value of Indicates the selection of a point ξ i After x j,i and x m,i The relevant function value of g jm Represents element x j,i and x m,iThe relevant function value of x j,i and x m,i They respectively represent the value of the element of the j-th sample point at the i-th dimension and the value of the element of the m-th sample point at the i-th dimension, where j=1, 2, …, n, m=1, 2, …, n, and i=1, 2, …, s.

[0023] The expression is as follows:

[0024]

[0025] Where sign(·) represents the sign function; ξ i Represented as probability space [0,1] s The spatial coordinates of any point in the i-th dimension, i = 1, 2, ..., s; when x j,i -ξ i >0, sign(x j,i -ξ i )=1; when x j,i -ξ i =0, sign(x j,i -ξ i )=0; when x j,i -ξ i When <0, sign(x j,i -ξ i )=-1.

[0026] The expression is as follows:

[0027]

[0028] The min(·) function returns the minimum value in the brackets, and the max(·) function returns the maximum value in the brackets.

[0029] Step 2.3, select sample point X sn Make the random variable uniformly distributed Minimum. Specific:

[0030] The present invention constructs sample point X based on Halton sequence sn , the Halton sequence is based on a series of special vectors π to generate sample points X sn (π), since the size of the vector π is small, the Halton sequence construction method can efficiently construct the sample point X sn . This step is in the space [0,1] s Select sample point X sn Make Minimum, this is essentially an optimization problem, which needs to satisfy The present invention uses a heterogeneous comprehensive learning particle swarm optimization algorithm to As the objective function, the vector π in the Halton sequence is optimized to obtain the optimal distribution Further, through the construction method of Halton sequence, we can obtain The smallest point set

[0031] In the third step, the Karhunen-Loeve expansion method is used to construct a random field of thermal parameters in combination with sample points based on generalized deviations, and finite element thermal analysis is performed to obtain the temperature field of the space cabin. Specifically:

[0032] Step 3.1, considering the influence of different material parameters on the temperature field of the space cabin, the thermal conductivity is set as a uniformly distributed random variable.

[0033] Step 3.2, use the Karhunen-Loeve (KL) expansion method to generate the thermal conductivity random field k(η)=k0[1+σk1(η)], where k0 is the mean of the thermal conductivity; η is the spatial coordinate of a point in the space cabin; σ is the uncertainty coefficient of variation, which is the ratio of the mean to the variance; k1(η) is a zero-mean random field constructed by KL expansion.

[0034] Then the correlation function C(η1,η2) between different spatial positions η1,η2 of the zero-mean random field is defined as:

[0035]

[0036] Where L is the correlation length of the KL expansion method and ||·||1 is the 1-norm of the vector.

[0037] Finally, using the KL expansion method, the thermal conductivity random field k(η) is constructed as follows:

[0038]

[0039] Among them, x i represents an independent random variable that follows a uniform distribution, obtained by sampling in the second step; M represents the number of expansion terms of the KL expansion; λ i represents the i-th eigenvalue of the correlation function C(η1,η2), i = 1, 2, ..., M; f i (η) represents the i-th characteristic function of the correlation function C(η1,η2), i = 1, 2, …, M; σ represents the coefficient of variation of the thermal conductivity; k0 is the mean value of the thermal conductivity.

[0040] Step 3.3, each sample point x i The corresponding generated random field k(η) is substituted into the heat conduction finite element analysis software to calculate each sample point xi The corresponding space cabin temperature value T(x i ).

[0041] The fourth step is to use the generalized Monte Carlo method to calculate the statistical information of the temperature field of the space cabin, specifically:

[0042] Step 4.1, using the generalized quasi-Monte Carlo method, combining the temperature values ​​at all sample points {T(x1), T(x2), …, T(x n )}, and the mean temperature at each node is obtained. The formula for the generalized quasi-Monte Carlo mean is as follows:

[0043]

[0044] Where T(X) represents the mean value of the temperature field calculated when the adiabatic coefficient is a random variable, X represents the random variable of the adiabatic coefficient; Ω represents the probability space; ρ(X) represents the probability density function of the random variable X; P i represents the point set X obtained in step 2.2 sn For each point x i The corresponding weight P i ; i=1, 2,…, n.

[0045] Step 4.2, using the generalized quasi-Monte Carlo method, combining the temperature values ​​at all sample points {T(x1), T(x2), …, T(x n )}, and the variance of the temperature at each node is obtained. The formula for the generalized quasi-Monte Carlo variance is as follows:

[0046]

[0047] At this point, the uncertainty analysis of heat conduction in the space cabin is completed.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] (1) The present invention provides a new deviation through the generalized quasi-Monte Carlo method. The sample points constructed based on the generalized L2 deviation based on arbitrary points proposed by the present invention have better point set performance, which provides conditions for the uncertainty analysis of heat conduction in space cabins.

[0050] (2) The present invention completes the uncertainty analysis of heat conduction in space cabins based on the generalized quasi-Monte Carlo method combined with the sample points constructed based on the generalized L2 deviation of arbitrary points, providing a new perspective and method for the uncertainty analysis of heat conduction in space cabins.

[0051] (3) Compared with the traditional Monte Carlo method and the quasi-Monte Carlo method, the calculation method provided by the present invention requires fewer sample points and has higher accuracy, which greatly reduces the amount of calculation required for the analysis of the uncertainty of the space cabin.

[0052] (4) The calculation method provided by the present invention is highly versatile and applicable to any type of space capsule and any complex structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flow chart of the uncertainty heat conduction analysis method of space cabin based on generalized low deviation point set. DETAILED DESCRIPTION

[0054] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0055] The first step is to establish a finite element calculation model of the space capsule, specifically:

[0056] Step 1.1, build a three-dimensional model of the space capsule according to the engineering drawing.

[0057] Step 1.2, import the completed three-dimensional model of the space capsule into the finite element analysis software, divide the mesh and export the node information at the mesh nodes.

[0058] Step 1.3, according to the actual situation, select the material properties of the space cabin, the cabin density is 4510kg / m 3 The average thermal conductivity is 400 W / (m·℃). The temperature of the bottom surface of the inner wall of the capsule structure is determined to be 300 K, the surface of the outer wall of the capsule structure is subjected to a heat flux load of 100,000, and the other walls are assumed to be insulated.

[0059] Step 1.4, based on the known three-dimensional model of the space capsule and the node information of the grid, that is, 45773 linear four-node units, finite element software is used to perform deterministic heat conduction calculations on the space capsule to obtain the temperature field information of the space capsule.

[0060] The second step is to construct a generalized low-deviation point set and corresponding point set weights for space cabin heat conduction analysis. Specifically:

[0061] Step 2.1, first based on the extended Koksma-Hlawka inequality and the existing L2 deviation method, consider the uniformly distributed random variables, and obtain the generalized L2 deviation of the generalized quasi-Monte Carlo integration format for a new random variable For the convenience of writing, the present invention uses the generalized low deviation as a proxy. Where ξ=(ξ1,ξ2,…,ξ s ) is the probability space [0,1] s Any point in the space, where s is the dimension of the sample space, ξ i represents the spatial coordinate of the sample point in the i-th dimension, i = 1, 2, ..., s. sn represents a point set of n sample points in s dimension, and X sn ={x1,…,x n}(x i =(x i,1 ,…,x i,s ) T ). P=[P1,P2,…,P n ], P i Represents the point set X sn The weight corresponding to the i-th sample point in , i = 1, 2, ..., n. This step is based on the extended Koksma-Hlawka inequality, and the existing L2 deviation is extended to obtain the generalized low deviation Can be used as a low deviation point set X sn And the quality assessment standard with its corresponding weight P.

[0062] Step 2.2, construct the generalized low deviation in step 2.1 The minimum point set weight P. Specifically:

[0063] To select step 2.1 point set X sn For each point x i The corresponding weight P i Satisfies the following formula, i = 1, 2, ..., n:

[0064]

[0065] According to formula (1), we can get:

[0066] P=G -1 b(2)

[0067] Where P represents the optimal point set weight determined according to formula (1); b is a sequence consisting of n elements; G is an abbreviation symbol given for convenience of writing; the complete form is shown as follows:

[0068]

[0069] Among them, b j represents the j-th element in sequence b, j = 1, 2, ..., n; Indicates the selection of a point ξ i After x j,i The function value of Indicates the selection of a point ξ i After x j,i and x m,i The relevant function value of g jm Represents element x j,i and x m,i The relevant function value of j,i and x m,i They respectively represent the value of the element of the j-th sample point at the i-th dimension and the value of the element of the m-th sample point at the i-th dimension, where j=1, 2, …, n, m=1, 2, …, n, and i=1, 2, …, s.

[0070] The expression is as follows:

[0071]

[0072] Where sign(·) represents the sign function; ξ i Represented as probability space [0,1] s The spatial coordinates of any point in the i-th dimension, i = 1, 2, ..., s; when x j,i -ξ i >0, sign(x j,i -ξ i )=1; when x j, i-ξ i =0, sign(x j,i -ξ i )=0; when x j,i -ξ i When <0, sign(x j,i -ξ i )=-1.

[0073] The expression is as follows:

[0074]

[0075] The min(·) function returns the minimum value in the brackets, and the max(·) function returns the maximum value in the brackets.

[0076] Step 2.3, select sample point X sn Make the random variable uniformly distributed Minimum. Specific:

[0077] The present invention constructs sample point X based on Halton sequence sn , which generates sample points X based on a series of special vectors π sn (π), since the size of the vector π is small, the Halton sequence construction method can be used to efficiently construct the sample point Xsn . This step is in the space [0,1] s Select sample point X sn Make Minimum, this is essentially an optimization problem, which needs to satisfy The present invention uses a heterogeneous comprehensive learning particle swarm optimization algorithm to As the objective function, the vector π in the Halton sequence is optimized to obtain the optimal distribution Further, through the construction method of Halton sequence, we can obtain The smallest point set

[0078] The third step is to construct a random field of thermal parameters by combining the sample points based on generalized deviations through the Karhunen-Loeve expansion method, and perform finite element thermal analysis to obtain the temperature field of the space cabin. Specifically:

[0079] Step 3.1, considering the influence of different material parameters on the temperature field of the space cabin, the thermal conductivity is set as a uniformly distributed random variable.

[0080] Step 3.2, use the Karhunen-Loeve (KL) expansion method to generate the thermal conductivity random field k(η)=k0[1+σk1(η)], where k0 is the mean of the thermal conductivity; η is the spatial coordinate of a point in the space cabin; σ is the uncertainty coefficient of variation, which is the ratio of the mean to the variance; k1(η) is a zero-mean random field constructed by KL expansion.

[0081] Then the correlation function C(η1,η2) between different spatial positions η1,η2 of the zero-mean random field is defined as:

[0082]

[0083] Where L is the correlation length of the KL expansion method and ||·||1 is the 1-norm of the vector.

[0084] Finally, using the KL expansion method, the thermal conductivity random field k(η) is constructed as follows:

[0085]

[0086] Among them, x i represents an independent random variable that follows a uniform distribution, which can be obtained by sampling in the second step; M represents the number of expansion items of the KL expansion; λ i represents the i-th eigenvalue of the correlation function C(η1,η2), i = 1, 2, ..., M; f i(η) represents the i-th characteristic function of the correlation function C(η1,η2), i = 1, 2, …, M; σ represents the coefficient of variation of the thermal conductivity; k0 is the mean value of the thermal conductivity.

[0087] Step 3.3, each sample point x i The corresponding generated random field k(η) is substituted into the heat conduction finite element analysis software to calculate each sample point x i The corresponding space cabin temperature value T(x i ).

[0088] The fourth step is to use the generalized Monte Carlo method to calculate the statistical information of the temperature field of the space cabin, specifically:

[0089] Step 4.1, using the generalized quasi-Monte Carlo method, combining the temperature values ​​at all sample points {T(x1), T(x2), …, T(x n )}, and the mean temperature at each node is obtained. The formula for the generalized quasi-Monte Carlo mean is as follows:

[0090]

[0091] Where T(X) represents the mean value of the temperature field calculated when the adiabatic coefficient is a random variable, X represents the random variable of the adiabatic coefficient; Ω represents the probability space; ρ(X) represents the probability density function of the random variable X; P i represents the point set X obtained in step 2.2 sn For each point x i The corresponding weight P i ; i=1, 2,…, n.

[0092] Step 4.2, using the generalized quasi-Monte Carlo method, combining the temperature values ​​at all sample points {T(x1), T(x2), …, T(x n )}, and the variance of the temperature at each node is obtained. The formula for the generalized quasi-Monte Carlo variance is as follows:

[0093]

[0094] At this point, the uncertainty analysis of heat conduction in the space cabin is completed.

[0095] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for analyzing uncertainty heat conduction of a space cabin based on a generalized low-deviation point set, characterized in that: The uncertain heat conduction analysis method for a space cabin comprises the following steps: The first step is to establish a finite element calculation model of the space capsule; The second step is to construct a generalized low-deviation point set and corresponding point set weights for space cabin heat conduction analysis; The third step is to construct the random field of thermal parameters by combining the sample points based on generalized deviation through the Karhunen-Loeve expansion method, and then perform finite element thermal analysis to obtain the temperature field of the space cabin. The fourth step is to use the generalized Monte Carlo method to calculate the statistical information of the temperature field of the space cabin.

2. The method for analyzing uncertainty heat conduction of a space cabin based on a generalized low deviation point set according to claim 1 is characterized in that: The first step comprises the following steps: Step 1.1, modeling a three-dimensional model of the space capsule; Step 1.2, importing the three-dimensional model of the space capsule modeled in step 1.1 into the finite element analysis software, dividing the mesh and exporting the node information at the mesh nodes; Step 1.3, according to the actual situation, select the material properties of the space capsule, and determine the heat load and boundary conditions of the space capsule according to the actual working conditions of the space capsule; Step 1.4, based on the known three-dimensional model of the space capsule and the node information of the grid, finite element software is used to perform deterministic heat conduction calculations on the space capsule to obtain the temperature field information of the space capsule.

3. The method for analyzing uncertainty heat conduction of a space cabin based on a generalized low deviation point set according to claim 1 is characterized in that: The second step comprises the following steps: Step 2.1, based on the extended Koksma-Hlawka inequality and L2 deviation method, consider uniformly distributed random variables and obtain the generalized L2 deviation of the generalized quasi-Monte Carlo integration format for new random variables and define it as generalized low deviation, As the low deviation point set X sn and its corresponding weight P quality assessment standard; where ξ=(ξ1,ξ2,…,ξ s ) is the probability space [0,1] s Any point in the space, where s is the dimension of the sample space, ξ i represents the spatial coordinates of the sample point in the i-th dimension, i = 1, 2, ..., s; X sn represents a point set of n sample points in s dimension, and X sn ={x1,…,x n }(x i =(x i,1 ,…,x i,s ) T ); P = [P1, P2, ..., P n ], P i Represents the point set X sn The weight corresponding to the i-th sample point in , i = 1, 2, ..., n; Step 2.2, construct the generalized low deviation in step 2.1 The minimum point set weight P; specifically: To select step 2.1 point set X sn For each point x i The corresponding weight P i Satisfies the following formula, i = 1, 2, ..., n: According to formula (1), we can get: P=G -1 b (2) Wherein, P represents the optimal point set weight determined according to formula (1); b is a sequence consisting of n elements; G is an abbreviation symbol given for convenience of writing; Step 2.3, select sample point X sn Make the random variable uniformly distributed Minimal; specific: Constructing sample points X based on Halton sequence sn The Halton sequence is based on a series of special vectors π to generate sample points X sn (π); in the space [0,1] s Select sample point X sn Make Minimum, satisfactory Using heterogeneous comprehensive learning particle swarm optimization algorithm, As the objective function, the vector π in the Halton sequence is optimized to obtain the optimal distribution Then, through the construction method of Halton sequence, we can get The smallest point set 4. The method for analyzing uncertainty heat conduction of a space cabin based on a generalized low deviation point set according to claim 3 is characterized in that: In step 2.2, the complete forms of b and G are as follows: Among them, b j represents the j-th element in sequence b, j = 1, 2, ..., n; Indicates the selection of a point ξ i After x j,i The function value of ; Indicates the selection of a point ξ i After x j,i and x m,i The relevant function value of g jm Represents element x j,i and x m,i The relevant function value of x j,i and x m,i They respectively represent the value of the element of the j-th sample point at the i-th dimension and the value of the element of the m-th sample point at the i-th dimension, where j=1, 2, …, n, m=1, 2, …, n, and i=1, 2, …, s.

5. The method for analyzing uncertainty heat conduction of a space cabin based on a generalized low deviation point set according to claim 4 is characterized in that: Said The expression is as follows: Where sign(·) represents the sign function; ξ i Represented as probability space [0,1] s The spatial coordinates of any point in the i-th dimension, i = 1, 2, ..., s; when x j,i -ξ i >0, sign(x j,i -ξ i )=1; when x j,i -ξ i =0, sign(x j,i -ξ i )=0; when x j,i -ξ i When <0, sign(x j,i -ξ i )=-1.

6. The method for analyzing uncertainty heat conduction of a space cabin based on a generalized low deviation point set according to claim 4 is characterized in that: Said The expression is as follows: The min(·) function returns the minimum value in the brackets, and the max(·) function returns the maximum value in the brackets.

7. The method for analyzing uncertainty heat conduction of a space cabin based on a generalized low deviation point set according to claim 1 is characterized in that: The third step comprises the following steps: Step 3.1, considering the influence of different material parameters on the temperature field of the space cabin, the thermal conductivity is set as a uniformly distributed random variable; Step 3.2, using the Karhunen-Loeve expansion method to generate the thermal conductivity random field k(η)=k0[1+σk1(η)], where k0 is the mean of the thermal conductivity; η is the spatial coordinate of a point in the space cabin; σ is the uncertainty coefficient of variation, which is the ratio of the mean to the variance; k1(η) is a zero-mean random field constructed by KL expansion; Finally, using the KL expansion method, the thermal conductivity random field k(η) is constructed as follows: Among them, x i represents independent random variables that follow uniform distribution; M represents the number of expansion items of KL expansion; λ i represents the i-th eigenvalue of the correlation function C(η1,η2) between different spatial positions η1,η2 of the zero-mean random field, i = 1, 2, ..., M; f i (η) represents the i-th characteristic function of the correlation function C(η1,η2), i = 1, 2, ..., M; σ represents the coefficient of variation of thermal conductivity; k0 is the mean value of thermal conductivity; Step 3.3, each sample point x i The corresponding generated random field k(η) is substituted into the heat conduction finite element analysis software to calculate each sample point x i The corresponding space cabin temperature value T(x i ).

8. The method for analyzing uncertainty heat conduction of a space cabin based on a generalized low deviation point set according to claim 7 is characterized in that: In step 3.2, the correlation function C(η1,η2) is: Where L is the correlation length of the KL expansion method and ||·||1 is the 1-norm of the vector.

9. The method for analyzing uncertainty heat conduction of a space cabin based on a generalized low deviation point set according to claim 1 is characterized in that: The fourth step comprises the following steps: Step 4.1, using the generalized quasi-Monte Carlo method, combining the temperature values ​​at all sample points {T(x1), T(x2), …, T(x n )}, find the mean temperature at each node; Step 4.2, using the generalized quasi-Monte Carlo method, combining the temperature values ​​at all sample points {T(x1), T(x2), …, T(x n )}, find the variance of the temperature at each node; At this point, the uncertainty analysis of heat conduction in the space cabin is completed.

10. The method for analyzing uncertainty heat conduction of a space cabin based on a generalized low deviation point set according to claim 9, characterized in that: In the fourth step: In step 4.1, the formula for generalized quasi-Monte Carlo mean is as follows: Where T(X) represents the mean value of the temperature field calculated when the adiabatic coefficient is a random variable, X represents the adiabatic coefficient random variable; Ω represents the probability space; ρ(X) represents the probability density function of the random variable X; P i represents the point set X obtained in step 2.2 sn For each point x i The corresponding weight P i ; i = 1, 2, ..., n; In step 4.2, the formula for calculating the variance using the generalized quasi-Monte Carlo method is as follows:

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