A three-dimensional random field construction method and system for simulating the mechanical properties of lunar soil bricks

Abstract

The application belongs to the field of material mechanical property analysis, and particularly discloses a three-dimensional random field construction method and system for simulating the mechanical properties of lunar soil bricks, which comprises the following steps: S1, obtaining the hardness and elastic modulus corresponding to each sampling point on the simulated lunar soil brick; S2, determining the edge distribution function F1 of the hardness based on the hardness distribution of all sampling points, and determining the edge distribution function F2 of the elastic modulus based on the elastic modulus distribution of all sampling points; S3, combining the edge distribution functions F1 and F2 into a joint distribution function based on a Copula function; S4, determining the cross-correlation coefficient between the hardness and the elastic modulus based on the joint distribution function, forming a cross-correlation coefficient covariance matrix R, and then determining the mechanical property random field of the lunar soil brick. The application realizes accurate modeling of the mechanical property random field of the simulated lunar soil brick, and provides a scientific basis for the design and selection of lunar building materials.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of material mechanical property analysis, and more particularly relates to a three-dimensional random field construction method and system for simulating the mechanical properties of lunar soil bricks. BACKGROUND

[0002] Under the current background of human exploration of the universe, lunar construction plans are gradually becoming a reality. Using in-situ resources, lunar soil, as the main material for lunar construction has become an important research direction in lunar base construction. More and more scholars use simulated lunar soil to make lunar soil bricks through sintering, melting, 3D printing and other methods to study the forming process and its mechanical properties, aiming to provide higher strength and durability building materials for lunar construction.

[0003] However, due to the randomness of the forming process parameters, the material of the simulated lunar soil brick often exhibits spatial randomness. Researchers mostly explore its macroscopic mechanical properties while ignoring its microscopic characteristics, such as nano-hardness and point domain elastic modulus. These microscopic properties may serve as weak points in lunar soil bricks, directly affecting their applicability and durability in the lunar environment. In-depth exploration of the microscopic mechanical properties of simulated lunar soil bricks and their random characteristics can not only provide material distribution basis for material simulation modeling and provide comprehensive performance analysis for lunar base building materials, but also provide a theoretical basis for improving future lunar building material manufacturing processes.

[0004] Random fields have a wide range of applications in many fields, such as meteorology, geological exploration, image segmentation, etc. They can very effectively analyze the spatial or temporal correlation present in the modeling data, helping to understand and predict the possible results of data changes. In terms of performance evaluation of material spatial distribution, the random field theory can identify possible defects and non-uniformity in the material, which often significantly affects the overall performance of the material.

[0005] Currently, there are related studies that use random field theory to model the mechanical properties of materials. However, their analysis is only based on a few independent random fields with distribution types, without fully considering the randomness and correlation characteristics between surrounding rock parameters. For example, using a Gaussian distribution to describe the hardness and elastic modulus of lunar soil bricks may not accurately reflect the actual performance changes of the material. In addition, due to the high cost of nanoindentation experiments, existing random field establishment based on nanoindentation often lacks sufficient sample coverage, resulting in data that cannot truly represent the microscopic mechanical properties of the entire material, affecting the understanding of the overall characteristics of the material. SUMMARY

[0006] In view of the above defects or improvement needs of the prior art, the present application provides a three-dimensional random field construction method and system for simulating the mechanical properties of lunar soil bricks, which aims to accurately model the random field of the mechanical properties of simulated lunar soil bricks.

[0007] To achieve the above object, according to one aspect of the present application, a three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks is provided, comprising the following steps:

[0008] S1, obtaining the hardness and elastic modulus corresponding to each sampling point on the simulated lunar soil brick;

[0009] S2, determining the edge distribution function F1 of hardness based on the hardness distribution of all sampling points, and determining the edge distribution function F2 of elastic modulus based on the elastic modulus distribution of all sampling points;

[0010] S3, combining the edge distribution functions F1 and F2 into a joint distribution function based on the Copula function;

[0011] S4, determining the cross-correlation coefficient between hardness and elastic modulus based on the joint distribution function, forming the cross-correlation coefficient covariance matrix R, and further determining the mechanical property random field of the lunar soil brick.

[0012] As a further preferred, step S4, determining the mechanical property random field of the lunar soil brick, specifically comprising:

[0013] Cholesky decomposition is performed on the cross-correlation coefficient covariance matrix R to obtain a lower triangular matrix L1;

[0014] According to the fluctuation parameter l, the autocorrelation coefficient covariance matrix C is determined, and Cholesky decomposition is performed on the autocorrelation coefficient covariance matrix C to obtain a lower triangular matrix L2; the fluctuation parameter l represents the distance range of the correlation of the lunar soil mechanical parameters;

[0015] According to the lower triangular matrices L1 and L2, the mechanical property random field Z of the lunar soil brick is obtained.

[0016] As a further preferred, the fluctuation parameter l is determined by optimization through the gazelle algorithm. When the gazelle algorithm is iterated: according to the current fluctuation parameter, the corresponding random field is determined, and then the fitness function value is determined; based on the fitness function value, the fluctuation parameter is optimized;

[0017] The fitness function Fitness calculation formula is as follows:

[0018] Fitness=(SVF h -SVF h ′) 2 +(SVF m -SVF m ′) 2

[0019] Wherein, SVF h , SVF mrespectively represent the semi-variogram values corresponding to the hardness and elastic modulus of the sampling points obtained by indentation test, SVF h ′, SVF m ′ respectively represent the semi-variogram values corresponding to the hardness and elastic modulus of the sampling points determined according to the current random field;

[0020] The above process is repeated until the termination condition is met, the iteration is stopped, and the fluctuation parameter l at this time is output; and the random field corresponding to the fluctuation parameter l is taken as the final lunar soil brick mechanical property random field Z.

[0021] As a further optimization, step S2 specifically comprises:

[0022] Based on the hardness distribution of all sampling points, the best hardness edge distribution function F1 is determined from the selected edge distribution functions by K-S test; based on the elastic modulus distribution of all sampling points, the best elastic modulus edge distribution function F2 is determined from the selected edge distribution functions by K-S test.

[0023] As a further optimization, the selected edge distribution functions include weibull distribution, Gamma distribution, Exp distribution, Normal distribution and lognormal distribution functions.

[0024] As a further optimization, step S3 specifically comprises:

[0025] Based on different Copula functions respectively, the edge distribution functions F1 and F2 are combined into joint distribution functions; and the obtained several joint distribution functions are tested by AIC or BIC to select the optimal joint distribution function.

[0026] As a further optimization, the selection of the Copula function includes Gaussian Copula function, t-Copula function, Frank Copula function, Clyton Copula function and Gumbel Copula function.

[0027] As a further optimization, the sampling points on the lunar soil brick are determined in the following manner:

[0028] The lunar soil brick is sliced into a plurality of layers with equal thickness along the height direction of the lunar soil brick to obtain a plurality of sampling surfaces;

[0029] On the first sampling surface, b sampling points are equally spaced on the sampling line along the radius direction of the lunar soil brick; and on each subsequent sampling surface, b sampling points are equally spaced on the sampling line along the radius direction of the lunar soil brick, and the sampling line of each sampling surface is rotated by 360 / a degrees in the same direction compared to the sampling line of the previous sampling surface.

[0030] As a further preferred, step S1, nanoindentation rapid lattice experiment is carried out on each sampling point on the lunar soil brick, so as to obtain the hardness and elastic modulus corresponding to each sampling point.

[0031] According to another aspect of the present application, a three-dimensional random field construction system for simulating the mechanical properties of lunar soil bricks is provided, comprising a processor configured to execute the three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks.

[0032] Overall, compared with the prior art, the above technical solutions conceived by the present application mainly have the following technical advantages:

[0033] 1. Based on the hardness and elastic modulus of a small number of sampling points on the simulated lunar soil brick, the present application uses Copula function to construct the complex distribution relationship between hardness and elastic modulus, then combines the generated Copula joint distribution function with the random field theory to determine the correlation coefficient between hardness and elastic modulus, and further obtains the mechanical property random field of the lunar soil brick, successfully fusing the micro-mechanical property distribution and spatial variation characteristics. Through this random field model, the distribution of the micro-mechanical properties of the lunar soil brick can be better understood, providing a theoretical basis and support for future micro-physical modeling.

[0034] 2. For the uncertainty of the parameter fluctuation range in the micro-mechanical property random field, the present application introduces the oryx algorithm, and combines the semi-variogram function to construct a fitness evaluation index, realizing efficient optimization of the parameter fluctuation range. Due to its superior global search capability and computational efficiency, the oryx algorithm can effectively improve the description accuracy of the micro-mechanical parameter random field, can avoid the traditional high-cost experimental parameter search process, and at the same time ensures the high credibility of the micro-mechanical property representation. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 Fig. 1 is a schematic diagram of the mechanical property sampling method of the lunar soil brick based on the embodiment of the present application;

[0036] Figure 2 Fig. 2 is a flow chart of the three-dimensional random field construction of the lunar soil brick mechanical properties according to the embodiment of the present application;

[0037] Figure 3 Fig. 3 is a flow chart of the oryx algorithm according to the embodiment of the present application. DETAILED DESCRIPTION

[0038] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0039] The embodiment of the present invention provides a three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks. Figure 2 As shown, the following steps are included:

[0040] S1. Determine the hardness and elastic modulus corresponding to each sampling point on the simulated lunar soil brick.

[0041] Specifically, such as Figure 1 As shown, simulated lunar soil bricks are made in advance by powder-abrasive hot pressing and sintering, and the lunar soil brick samples are preferably cylindrical. According to the height of the sample, equal-height layered slices are performed to determine the sampling surface, and sampling points are determined on each sampling surface to ensure the uniformity and representativeness of the sampling. Then, a nanoindentation rapid lattice experiment is performed on each sampling point: a suitable indentation spacing and indentation load are selected, and a nanoindentation rapid lattice experiment is performed at the sampling point along the radial direction using a nanoindentation testing machine to obtain the nanohardness and elastic modulus data of the material in the sampling point area, that is, each sampling point area corresponds to a lattice, and the lattice includes multiple indentation points; then, effective measurement data is screened according to the indentation depth, and the hardness and elastic modulus obtained from all indentation points in the lattice are averaged, which is the hardness and elastic modulus of the corresponding sampling point, thereby representing the mechanical properties of the sampling point.

[0042] Furthermore, the method for determining the sampling point is preferably:

[0043] The sample was sliced ​​using a linear cutting method, with the height of each slice calculated by dividing the total height by the number of slices, resulting in (a-1) slices of equal height. To maximize sampling, the sampling surfaces were defined as the upper surface of each slice and the upper and lower surfaces of the last slice, for a total of a sampling surfaces. Furthermore, to ensure that each sampling point on the sampling surface maintained spatial representativeness, the radius of each layer of sampling points was rotated by a certain angle with the height of the sampling surface, where the rotation angle was 360 degrees divided by the number of sampling surfaces. That is, for the first sampling surface, b sampling points were taken at equal intervals along the sampling line in the radial direction of the lunar soil brick. For each subsequent sampling surface, b sampling points were taken at equal intervals along the sampling line in the radial direction of the lunar soil brick, and the sampling line of each sampling surface was rotated 360 / a degrees in the same direction as the sampling line of the previous sampling surface.

[0044] For example, a 20mm high simulated lunar soil brick sample is cut into 4 pieces, each piece is 5mm high, and the sampling surface is the upper surface of the first three pieces and the upper and lower surfaces of the last piece, a total of 5 equally spaced surfaces. For the 5 sampling surfaces, the first sampling surface is at a height of 20mm, the sampling radius is set to 0 degrees, the second sampling surface is at a height of 15mm, the sampling radius is rotated 72 degrees clockwise relative to the first sampling surface, and so on.

[0045] Further, in order to obtain as much indentation information as possible and make the calculated mechanical properties more general, the indentation load of the nanoindentation rapid lattice experiment is 6000-10000 micro-newtons, preferably 8000 micro-newtons; the indentation points in the lattice are arranged in a 10*10 square, and the distance between each indentation point is 8 microns.

[0046] S2, determine the edge distribution function F1 of hardness based on the hardness distribution of all sampling points, and determine the edge distribution function F2 of elastic modulus based on the elastic modulus distribution of all sampling points.

[0047] Specifically, the edge distribution functions suitable for nano-hardness and elastic modulus are pre-selected as candidates, including but not limited to weibull distribution, Gamma distribution, Exp distribution, Normal distribution and lognormal distribution. Then, according to the sampling point hardness and elastic modulus obtained in step S1, the pre-selected edge distribution functions are determined by K-S test, and the best edge distribution functions of hardness and elastic modulus are determined respectively. The edge distribution function of nano-hardness is determined as F(x1), and the edge distribution function of elastic modulus is determined as F(x2), x1 and x2 are random variables of nano-hardness and elastic modulus.

[0048] S3, based on the Copula function, combine the edge distribution functions F1 and F2 into a joint distribution function.

[0049] Specifically, based on the determined edge distribution function, different Copula functions are selected to generate the joint distribution density of elastic modulus and hardness, and the parameters in the Copula model are solved by semi-parametric maximum likelihood estimation; the selection of Copula function includes but is not limited to Gaussian Copula function, t-Copula function, Frank Copula function, ClytonCopula function and Gumbel Copula function; finally, the AIC (Akaike information criterion) or BIC (Bayesian information criterion) is used to determine the optimal joint distribution function F(x1, x2).

[0050] Further, the Copula function is expressed as:

[0051] F(x1,x2)=C[F(x1),F(x2)]=C(F(x1),F(x2),θ)

[0052] where F(x1,x2) is the joint probability distribution function of the random variables x1 and x2, F(x1) and F(x2) are the marginal distribution functions of hardness and elastic modulus, respectively. C[F(x1),F(x2)] represents the Copula function calculation operation on the two marginal distribution functions. θ is the model parameter in the Copula function, which is obtained by the semiparametric maximum likelihood estimation method.

[0053] Furthermore, the AIC and BIC criterion formulas are:

[0054]

[0055] where u 1i with u 2i is the empirical distribution function of random variables x1 and x2, D is the probability density of the Copula function, N is the number of observations, and α is the number of model parameters.

[0056] S4. Based on the joint distribution function, the mechanical parameters of the lunar soil bricks are simulated to obtain the mutual correlation coefficient between hardness and elastic modulus, form the mutual correlation coefficient covariance matrix, and then determine the random field of the mechanical properties of the lunar soil bricks.

[0057] Specifically, a three-dimensional coordinate system is established within the random field study area. The cross-correlation matrix between nanohardness and elastic modulus is calculated based on the joint distribution function obtained in step S3. Initial parameter fluctuation ranges related to the random field and coordinates are set, and the autocorrelation matrix is ​​calculated based on the sampling point coordinate centers. Based on the cross-correlation, autocorrelation matrix, and random variable matrix, the cross-correlated standard Gaussian random field of the nanohardness and elastic modulus parameters of the simulated lunar soil brick is calculated. The standard Gaussian random field is converted into a cross-correlated uniformly distributed random field through probability integral variation. The parameter fluctuation range values ​​are continuously optimized using the Gryphon Search Algorithm (GSA) until the iteration is complete, resulting in the spatial random fields of the mechanical parameters of the simulated lunar soil brick—nanohardness and elastic modulus.

[0058] Further, the following steps are included:

[0059] Calculate the random field cross-correlation triangle matrix L1: Use the joint probability distribution function F(x1,x2) to calculate the mechanical parameters of the simulated lunar soil brick and obtain the correlation coefficient r between nanohardness and elastic modulus 12 、r 21 , and form the mutual correlation coefficient covariance matrix R 2×2 =(r 12 ) 2×2 :

[0060]

[0061] The Cholesky decomposition of the above cross-correlation coefficient matrix obtains a lower triangular matrix L1 as follows:

[0062] Satisfies,

[0063] The random field autocorrelation triangular matrix L2 is calculated: the autocorrelation coefficient p of the random field is calculated based on the fluctuation parameter l. The fluctuation parameter l is an attribute of the rock soil body, indicating the range in which the mechanical parameters (hardness, elastic modulus, etc.) of the rock soil body are correlated, for example, the compactness of the soil is correlated within a range of 2 meters in the horizontal direction, and the soil particle properties are independent outside the range of 2 meters, that is, the fluctuation parameter in the horizontal direction is 2. This parameter is generally determined by experience; and the present application proposes a fluctuation parameter l optimization method based on the gazelle algorithm for lunar soil, which will be described later.

[0064] The fluctuation parameter l includes l r , l θ , and l z , respectively representing the fluctuation ranges of the mechanical parameters in the radial direction, the azimuthal direction, and the height direction. A three-dimensional coordinate system is established in the random field research area, and column coordinate grid division is performed as needed; the autocorrelation coefficient p of the random field is calculated according to the following formula:

[0065]

[0066] Wherein, (r i , theta i , z i ) is the coordinate of the center point of the i-th column coordinate grid, (r j , theta j , z j ) is the coordinate of the center point of the j-th column coordinate grid, if the number of divided grids is k, then the covariance matrix C k×k composed of the autocorrelation coefficients corresponding between any two grid center coordinates is:

[0067]

[0068] The Cholesky decomposition of the above covariance matrix C k×k obtains a lower triangular covariance matrix L2 as follows:

[0069] Satisfies

[0070] For a matrix Y m×2, then the standard normal random field Z = L2·Y·L1 can be calculated, and the cross-correlated uniform distribution random field can be obtained by performing probability integral transformation on Z The final random field is a matrix, where each row represents a point in the random field coordinate system, the first column of each row represents the calculated value of the hardness random field, and the second column represents the calculated value of the elastic modulus random field.

[0071] Furthermore, the gazelle algorithm is selected as the parameter fluctuation range optimization algorithm, such as Figure 3 As shown, specifically including:

[0072] Initial position fitness evaluation, number of iterations, initialization based on Brownian motion random number vector and Levy distribution random number vector; global search for the fitness and optimal solution matrix of the updated position; local search for the fitness and optimal solution matrix of the updated position; output the optimal solution matrix after reaching the number of iterations.

[0073] The optimal solution matrix is ​​the fluctuation parameter l, and the fitness value is determined by the random field Z corresponding to the current fluctuation parameter l during iteration. The initial fluctuation parameter during iteration is given by the size of the study area. The fitness function, Fitness, is preferably composed of the sum of the squares of the differences between the semivariogram estimate (SVF) calculated from the experimental data at the sampling point and the semivariogram calculated from the corresponding point data in the random field. The expression is:

[0074] Fitness=(SVF h -SVF h ′) 2 +(SVF m -SVF m ′) 2

[0075] Among them, SVF h SVF m Respectively represent the semi-variance estimates of hardness and elastic modulus based on the equally spaced sampling points of the indentation test, Where m represents the sampling surface number, n represents the sampling point number, a and b represent the number of sampling surfaces and the number of sampling points in the radial direction of each sampling surface, respectively. m,n Indicates the hardness value of the nth sampling point on the mth sampling surface, e m,n Indicates the elastic modulus value of the nth sampling point on the mth sampling surface; SVF h ′、SVF m ′ is calculated in a similar way, and represents the semi-variance estimate of the hardness and elastic modulus of the corresponding sampling point obtained based on the current random field.

[0076] Those skilled in the art can easily understand that the above description is only the preferred embodiment of the present application, and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks, characterized by: The steps include: S1. Obtain the hardness and elastic modulus corresponding to each sampling point on the simulated lunar soil brick; S2, determining the edge distribution function F1 of the hardness based on the hardness distribution of all sampling points, and determining the edge distribution function F2 of the elastic modulus based on the elastic modulus distribution of all sampling points; S3, based on the Copula function, the marginal distribution functions F1 and F2 are combined into a joint distribution function; S4. Determine the correlation coefficient between hardness and elastic modulus based on the joint distribution function, form the correlation coefficient covariance matrix R, and then determine the random field of mechanical properties of lunar soil bricks, specifically including: Perform Cholesky decomposition on the cross-correlation coefficient covariance matrix R to obtain the lower triangular matrix L1; According to the fluctuation parameters l Determine the autocorrelation coefficient covariance matrix C, perform Cholesky decomposition on the autocorrelation coefficient covariance matrix C, and obtain the lower triangular matrix L2; the fluctuation parameter l The distance range indicating the correlation between lunar soil mechanical parameters; The random field of mechanical properties of lunar soil bricks is obtained based on the lower triangular matrices L1 and L2 ; Determine the volatility parameters through Gazelle algorithm optimization l ,During the iteration of the Gazelle algorithm: the corresponding random field is obtained based on the ,current fluctuation parameters, and the fitness function value is determined; ,the fluctuation parameters are optimized based on the fitness function value; The fitness function The calculation formula is as follows: in, 、 They represent the semivariogram values ​​corresponding to the hardness and elastic modulus of the sampling points obtained from the indentation test, 、 They represent the semivariogram values ​​corresponding to the hardness and elastic modulus of the sampling points determined according to the current random field; Repeat the above process until the termination condition is met, stop the iteration and output the fluctuation parameter at this time l According to the fluctuation parameter l The corresponding random field is used as the final random field of mechanical properties of lunar soil bricks .

2. The method for constructing a three-dimensional random field for simulating the mechanical properties of lunar soil bricks according to claim 1, characterized in that: Step S2 specifically includes: Based on the hardness distribution of all sampling points, the optimal hardness edge distribution function F1 is determined from the candidate edge distribution functions through the KS test; based on the elastic modulus distribution of all sampling points, the optimal elastic modulus edge distribution function F2 is determined from the candidate edge distribution functions through the KS test.

3. The method for constructing a three-dimensional random field for simulating the mechanical properties of lunar soil bricks according to claim 2, characterized in that: The marginal distribution functions to be selected include Weibull distribution, Gamma distribution, Exp distribution, Normal distribution and lognormal distribution function.

4. The method for constructing a three-dimensional random field for simulating the mechanical properties of lunar soil bricks according to claim 1, characterized in that: Step S3 specifically includes: Based on different copula functions, the marginal distribution functions F1 and F2 are combined into a joint distribution function; the obtained joint distribution functions are tested by AIC or BIC, and the optimal joint distribution function is selected.

5. The method for constructing a three-dimensional random field for simulating the mechanical properties of lunar soil bricks according to claim 4, characterized in that: The selection of the Copula function includes Gaussian Copula function, t-Copula function, Frank Copula function, Clyton Copula function and Gumbel Copula function.

6. The method for constructing a three-dimensional random field for simulating the mechanical properties of lunar soil bricks according to claim 1, characterized in that: The method for determining the sampling points on the lunar soil brick is: Slice the lunar soil brick into equal thickness slices along its height direction to obtain a sampling surface; For the first sampling surface, b sampling points were taken at equal intervals along the sampling line in the radial direction of the lunar soil brick; for each subsequent sampling surface, b sampling points were taken at equal intervals along the sampling line in the radial direction of the lunar soil brick, and the sampling line of each sampling surface was rotated 360 / a degrees in the same direction compared with the sampling line of the previous sampling surface.

7. The method for constructing a three-dimensional random field for simulating the mechanical properties of lunar soil bricks according to any one of claims 1 to 6, characterized in that: Step S1: Perform a nanoindentation rapid array experiment on each sampling point on the lunar soil brick to obtain the hardness and elastic modulus corresponding to each sampling point.

8. A three-dimensional random field construction system for simulating the mechanical properties of lunar soil bricks, characterized by: It includes a processor, which is used to execute the three-dimensional random field construction method for simulating the mechanical properties of lunar soil bricks as described in any one of claims 1-7.

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