A random simulation method and device for irregular three-dimensional terrain

Abstract

The present invention provides a random simulation method and device for irregular three-dimensional terrain, the method comprising: determining a probability model and statistical characteristic values ​​of the spatial variability of the terrain elevation of a region to be simulated, determining the dimension and scale of the three-dimensional terrain of the region to be simulated, and then obtaining the range of the three-dimensional terrain of the region to be simulated; performing grid discretization on the three-dimensional terrain of the region to be simulated, and obtaining the unit information of the three-dimensional terrain of the region to be simulated; and establishing a random field model of irregular three-dimensional terrain based on the covariance matrix decomposition method. After determining the probability model and statistical characteristics describing the spatial variability of the regional terrain elevation and the model size, the present invention performs random field modeling of the irregular characteristics of the three-dimensional terrain based on the covariance matrix decomposition method, which can more scientifically and reasonably characterize the distribution characteristics of the irregular three-dimensional terrain of the region, thereby providing a new approach and new idea for the simulation of irregular three-dimensional terrain.

Description

Technical Field

[0001] The invention relates to the technical field of geological engineering simulation, in particular to a random simulation method and device for irregular three-dimensional terrain. Background Art

[0002] Affected by various geological actions and stress history, different regions show different topography, such as plateaus, plains, mountains, etc. However, within the same region, the appearance of the terrain is often the same. For example, the Loess Plateau is full of gullies and ravines, and the terrain is undulating. It looks uneven and fragmented from a distance, but it shows similar characteristics in the entire spatial area. This feature can be called spatial variability. It is inevitable to carry out infrastructure construction on such irregular terrain. However, how to simulate irregular terrain is a technical problem. Many studies use drones or Beidou satellite photography to collect data and import them into numerical software. However, this method is costly and lacks scientific and reasonable theory as support. It is difficult to reproduce and simulate three-dimensional irregular terrain in a computer.

[0003] The inventors of this application have found through research in the process of realizing the present invention that: by carefully studying the irregular characteristics of three-dimensional terrain, it can be found that when two spatial locations on the regional surface are close to each other, there is a strong correlation between the two, and on the contrary, there is an obvious random characteristic. Therefore, the terrain elevation is taken as the research object, and the elevations of different locations show the characteristics of coexistence of randomness and correlation (such as Figure 1 As shown in Figure 2 ). Random field theory can simultaneously reflect the randomness and correlation of regional terrain position elevation. Therefore, random field simulation can be used as an effective means to reproduce and simulate regional irregular three-dimensional terrain. The random field model involves the elevation distribution characteristics of the spatial position. Generally, the covariance matrix decomposition method can be used to invert the random field model. Summary of the invention

[0004] In view of the shortcomings of the existing simulation of irregular characteristics of three-dimensional terrain, the present invention proposes a simulation method and device that can take into account the spatial variability of elevations at different locations on the regional surface. After determining the probability model and statistical characteristics that describe the spatial variability of regional terrain elevation and the model size, random field modeling of the irregular characteristics of three-dimensional terrain is performed based on the covariance matrix decomposition method, which can more scientifically and reasonably characterize the distribution characteristics of regional irregular three-dimensional terrain, thereby providing a new path and new idea for irregular three-dimensional terrain simulation.

[0005] The present invention is achieved through the following technical solutions:

[0006] A random simulation method for irregular three-dimensional terrain includes the following steps:

[0007] The first step is to determine the probability model and statistical characteristic values ​​of the spatial variability of the regional terrain elevation to be simulated. The probability model includes the probability distribution function and correlation function of the regional terrain elevation, and the statistical characteristic values ​​include the mean value μ of the regional terrain elevation H. H , standard deviation σ H , coefficient of variation δ H and related distances;

[0008] The second step is to determine the dimension and scale of the three-dimensional terrain of the area to be simulated, and then obtain the scope of the three-dimensional terrain of the area to be simulated;

[0009] Step 3: Grid discretize the three-dimensional terrain of the area to be simulated determined in Step 2 to obtain unit information of the three-dimensional terrain of the area to be simulated, wherein the unit information includes unit quantity, number and location information;

[0010] The fourth step is to establish an irregular three-dimensional terrain random field model based on the covariance matrix decomposition method: using the range and unit information of the three-dimensional terrain of the area to be simulated obtained in the second and third steps, determine the basic framework of the covariance matrix, and then use the probability model and statistical eigenvalues ​​obtained in the first step to obtain the elevation size corresponding to each unit of the covariance matrix, perform one-to-one mapping and assignment of units, and obtain the irregular three-dimensional terrain random field matrix. Use the programming platform to realize the regional terrain elevation random field matrix Z N The random field model of irregular three-dimensional terrain is obtained by constructing.

[0011] Furthermore, the probability distribution function of the regional terrain elevation is a normal distribution type:

[0012]

[0013] The mean value μ of the regional terrain elevation H H , coefficient of variation δ H and standard deviation σ H The relationship between them is:

[0014]

[0015] Furthermore, the correlation function of the regional terrain elevation is exponential, as follows:

[0016]

[0017] Among them, τ x and τ y are the relative distances between any two discrete points in the terrain in the longitude and latitude directions, ρ(τ x ,τ y ) represents τ x and τ y The correlation coefficient between x≥0,τ y ≥0,θ x and θ y are the relevant distances in longitude and latitude, respectively.

[0018] Furthermore, the third step specifically includes: selecting quadrilateral units for mesh discretization, and the coordinates of the center points of the quadrilateral units after discretization are expressed as (x i ,y j ), i=1,2,…,N x ; i, j = 1, 2, ..., N y , N x and N y are the number of units in the x and y directions respectively; the discretized grid units are numbered and represented by N, N = 1, 2, ..., N x ×N y , the grid size is between 1 / 5 and 1 / 10 of the relevant distance.

[0019] Furthermore, the fourth step specifically includes:

[0020] Let x i and x j is a discrete point in the random field, where i,j=1,2,…,n, τ ij For any two points x i and x j The relative distance between them, C is the n-order covariance matrix composed of the covariance between n points, the n-order covariance matrix is ​​a positive definite symmetric matrix, and any element of the matrix C ij Represents x i and x j The covariance between ij =C(τ ij ); the covariance matrix is ​​expressed as:

[0021]

[0022] Where ρ represents the correlation coefficient between two center points, and the correlation coefficient is calculated by formula (3);

[0023] Perform Cholesky decomposition on the covariance matrix C to obtain upper triangular and lower triangular matrices:

[0024] C=LU=LL T (5)

[0025] Where: L is the lower triangular matrix, U is the upper triangular matrix, L T is the transpose of the matrix L; Y is a column vector consisting of n independent random numbers that obey the standard normal distribution, then the n-order random field matrix Z is expressed as:

[0026] Z=LY (6)

[0027] Where: Any point Z in the random field matrix Z ij It obeys the standard normal distribution, and the covariance matrix E(ZZ T )=E(LYY T L T )=E(LL T )=C, satisfying the correlation requirement, the random field matrix Z is a realization of the standard normal random field;

[0028] The Gaussian random field that characterizes the spatial variability of regional terrain elevation is expressed as:

[0029] Z N =Z·σ H +μ H (7)

[0030] In the formula, Z N is the random field matrix of regional terrain elevation, σ H is the standard deviation, μ H is the mean value of the regional terrain elevation H; the regional terrain elevation random field matrix Z is realized on the relevant programming platform N The irregular three-dimensional terrain random field model can be obtained by constructing.

[0031] A random simulation device for irregular three-dimensional terrain, comprising:

[0032] The probability model and statistical characteristic value determination module is used to determine the probability model and statistical characteristic value of the spatial variability of the regional terrain elevation to be simulated. The probability model includes the probability distribution function and correlation function of the regional terrain elevation. The statistical characteristic value includes the mean value μ of the regional terrain elevation H. H , standard deviation σ H , coefficient of variation δ H and related distances;

[0033] A range determination module is used to determine the dimension and scale of the three-dimensional terrain of the area to be simulated, and then obtain the range of the three-dimensional terrain of the area to be simulated;

[0034] A grid discretization module is used to perform grid discretization on the determined three-dimensional terrain of the area to be simulated, and obtain the unit information of the three-dimensional terrain of the area to be simulated, and the unit information includes the number, number and position information of the unit;

[0035] The random field model establishment module is used to establish an irregular three-dimensional terrain random field model based on the covariance matrix decomposition method: using the range and unit information of the three-dimensional terrain to be simulated in the second and third steps, determine the basic framework of the covariance matrix, and then use the probability model and statistical eigenvalues ​​obtained in the first step to obtain the elevation size corresponding to each unit of the covariance matrix, perform one-to-one mapping and assignment of units, and obtain the irregular three-dimensional terrain random field matrix. Use the programming platform to realize the construction of the regional terrain elevation random field matrix and obtain the random field model of the irregular three-dimensional terrain.

[0036] Furthermore, the probability distribution function of the regional terrain elevation is a normal distribution type:

[0037]

[0038] The mean value μ of the regional terrain elevation H H , coefficient of variation δ H and standard deviation σ H The relationship between them is:

[0039]

[0040] Furthermore, the correlation function of the regional terrain elevation is exponential, as follows:

[0041]

[0042] Among them, τ x and τ y are the relative distances between any two discrete points in the terrain in the longitude and latitude directions, ρ(τ x ,τ y ) represents τ x and τ y The correlation coefficient between x ≥0,τ y ≥0,θ x and θ y are the relevant distances in longitude and latitude, respectively.

[0043] Furthermore, the mesh discretization module is specifically used to: select quadrilateral units for mesh discretization, and the coordinates of the center points of the quadrilateral units after discretization are expressed as (x i ,y j ), i=1,2,…,N x ; i, j = 1, 2, ..., N y , N x and N y are the number of units in the x and y directions respectively; the discretized grid units are numbered and represented by N, N = 1, 2, ..., N x ×Ny , the grid size is between 1 / 5 and 1 / 10 of the relevant distance.

[0044] Furthermore, the random field model building module is specifically used for:

[0045] Let x i and x j is a discrete point in the random field, where i,j=1,2,…,n, τ ij For any two points x i and x j The relative distance between them, C is the n-order covariance matrix composed of the covariance between n points, the n-order covariance matrix is ​​a positive definite symmetric matrix, and any element of the matrix C ij Represents x i and x j The covariance between ij =C(τ ij ); the covariance matrix is ​​expressed as:

[0046]

[0047] Where ρ represents the correlation coefficient between two center points, and the correlation coefficient is calculated by formula (3);

[0048] Perform Cholesky decomposition on the covariance matrix C to obtain upper triangular and lower triangular matrices:

[0049] C=LU=LL T (5)

[0050] Where: L is the lower triangular matrix, U is the upper triangular matrix, L T is the transpose of the matrix L; Y is a column vector consisting of n independent random numbers that obey the standard normal distribution, then the n-order random field matrix Z is expressed as:

[0051] Z=LY (6)

[0052] Where: Any point Z in the random field matrix Z ij It obeys the standard normal distribution, and the covariance matrix E(ZZ T )=E(LYY T L T )=E(LL T )=C, satisfying the correlation requirement, the random field matrix Z is a realization of the standard normal random field;

[0053] The Gaussian random field that characterizes the spatial variability of regional terrain elevation is expressed as:

[0054] Z N =Z·σ H +μ H(7)

[0055] In the formula, Z N is the random field matrix of regional terrain elevation, σ H is the standard deviation, μ H is the mean value of the regional terrain elevation H; the regional terrain elevation random field matrix Z is realized on the relevant programming platform N The irregular three-dimensional terrain random field model can be obtained by constructing.

[0056] The present invention has the following beneficial effects:

[0057] 1. The random simulation method and device of the present invention can be used to simulate and reproduce irregular three-dimensional terrain on a computer platform, which can significantly save costs compared to the high-cost work of drone and Beidou satellite photography;

[0058] 2. Based on the random field theory, the present invention proposes a random simulation method and device for irregular three-dimensional terrain, which is used to characterize the spatial variability of regional terrain elevation (altitude). Compared with drone and Beidou satellite photography methods, it has detailed and reasonable scientific theories as support;

[0059] 3. In the method and device for random simulation of irregular three-dimensional terrain described in the present invention, random data that can reflect the terrain distribution characteristics and attributes of the same area can be generated multiple times through the random field matrix, and then the irregular three-dimensional terrain distribution of the area can be inverted and characterized multiple times. This inversion result is not for a specific small area, but for a wide area with similar terrain distribution characteristics and attributes, and is more universal and applicable. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a typical irregular three-dimensional topographic map;

[0061] Figure 2 A schematic diagram of mesh discretization according to an embodiment of the present invention;

[0062] Figure 3 The figure is a schematic diagram of a random field model of irregular three-dimensional terrain in MATLAB according to an embodiment of the present invention. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0064] The embodiment of the present invention provides a random simulation method for irregular three-dimensional terrain, comprising the following steps:

[0065] The first step is to determine the probability model and statistical characteristic values ​​of the spatial variability of the regional terrain elevation to be simulated. The probability model includes the probability distribution function and correlation function of the regional terrain elevation, and the statistical characteristic values ​​include the mean μ H , standard deviation σ H , coefficient of variation δ H and related distances.

[0066] Specifically, for a certain terrain area to be simulated, the longitude, latitude and altitude of multiple typical locations in the area are measured as basic parameters for the subsequent simulation of the three-dimensional terrain of the area.

[0067] The random field model uses probability distribution function and correlation function to describe the randomness and correlation of the research object. Based on the acquired typical location elevation data of the region, the probability distribution function type and statistical characteristic value of the regional terrain elevation (altitude) H are calculated using probability statistics. The statistical characteristic values ​​include the mean μ H , standard deviation σ H , coefficient of variation δ H Etc. These probability statistical information reflects the random characteristics of the regional terrain elevation (altitude) H; in addition, the correlation function and correlation distance of the regional terrain elevation (altitude) H reflect the correlation characteristics, among which the correlation function type can be obtained by regression fitting of the regional terrain elevation (altitude) H, and the size of the correlation distance can be determined by the spatial recursion method.

[0068] According to literature research and statistics, combined with the intuitive understanding of terrain elevation (altitude), the probability distribution function of regional terrain elevation (altitude) H is determined to be a normal distribution type:

[0069]

[0070] The mean value μ of regional terrain elevation (altitude) H H , coefficient of variation δ H and standard deviation σ H The relationship between them is:

[0071]

[0072] An exponential correlation function is used to describe the correlation of regional terrain elevation (altitude):

[0073]

[0074] Among them, τ x and τ y are the relative distances between any two discrete points in the terrain in the longitude and latitude directions, τx ≥0,τ y ≥0,θ x and θ y are the relevant distances in two directions respectively.

[0075] According to the knowledge of geological engineering, the irregular characteristics of three-dimensional terrain can be simulated by two-dimensional random fields, and present an obvious "isotropic" correlation structure, that is, θ x =θ y .

[0076] The second step is to determine the dimension and scale of the three-dimensional terrain of the area to be simulated, and then obtain the scope of the three-dimensional terrain of the area to be simulated.

[0077] For three-dimensional irregular terrain information, the longitude and latitude of the typical location of the region can be regarded as the location in the plane space, and the elevation can be regarded as the attribute at the location. Therefore, the three-dimensional irregular terrain can be characterized by a two-dimensional random field model. For a two-dimensional random field, it is usually a rectangular or square area. The embodiment of the present invention uses a terrain of 150m×63m in a certain area to be simulated as a demonstration. After determining the dimension and size of the three-dimensional regional terrain, it is equivalent to determining the range of the covariance matrix, which provides range parameters for the subsequent construction of the covariance matrix.

[0078] The third step is to discretize the three-dimensional terrain of the area to be simulated determined in the second step into a grid, and obtain the unit information of the three-dimensional terrain of the area to be simulated, and the unit information includes the number, serial number and location information of the unit.

[0079] After determining the dimension and scale of the three-dimensional terrain of the area to be simulated, grid discretization refers to the use of regularly arranged grid cells of the same size to discretize the three-dimensional terrain area to be simulated. Quadrilateral cells are selected for grid discretization. For example, the coordinates of the center point of the quadrilateral cell after discretization can be expressed as (x i ,y j ), i=1,2,…,N x ; i, j = 1, 2, ..., N y , N x and N y are the number of units in the x and y directions respectively. The discretized grid units are numbered and represented by N, where N = 1, 2, ..., N x ×N y . The research on literature found that when the relevant distance is constant, the grid size used in the calculation has a significant impact on the calculation accuracy. Generally, the smaller the grid size, the higher the calculation accuracy, but the longer the calculation time. Taking all factors into consideration, the grid size can be between 1 / 5 and 1 / 10 of the relevant distance. Figure 2A schematic diagram of grid discretization is given. By discretizing the three-dimensional terrain of the area to be simulated, the number, serial number and location information of the cells in the area to be simulated can be obtained, providing the basic parameters of the cells for the subsequent construction of the covariance matrix.

[0080] The fourth step is to establish an irregular three-dimensional terrain random field model based on the covariance matrix decomposition method.

[0081] The covariance matrix decomposition method realizes the random field simulation of three-dimensional terrain by constructing the covariance matrix, which has high computational efficiency. According to the range and unit information of the three-dimensional terrain of the area to be simulated obtained in the second and third steps, the basic framework of the covariance matrix can be determined.

[0082] The covariance matrix construction process is: Assume x i and x j (i,j=1,2,…,n) is a discrete point in the random field, τ ij For any two points x i and x j The relative distance between them, C is the n-order covariance matrix composed of the covariance between n points, which is a positive definite symmetric matrix. Any element in the matrix C ij Represents x i and x j The covariance between ij =C(τ ij ). The covariance matrix can be expressed as:

[0083]

[0084] Wherein, ρ represents the correlation coefficient between two center points, and the correlation coefficient can be calculated by the aforementioned exponential correlation function (Formula (3)).

[0085] Perform Cholesky decomposition on the covariance matrix C to obtain upper triangular and lower triangular matrices:

[0086] C=LU=LL T (5)

[0087] Where: L is the lower triangular matrix, U is the upper triangular matrix, L T is the transpose of matrix L. Y is a column vector consisting of n independent random numbers that obey the standard normal distribution, then the n-order random field matrix Z can be expressed as:

[0088] Z=LY (6)

[0089] Where: Any point Z in the random field matrix Z ij It obeys the standard normal distribution, and the covariance matrix E(ZZ T )=E(LYY T LT )=E(LL T )=C, satisfying the correlation requirement, so the matrix Z can be used as a realization of the standard normal random field.

[0090] Therefore, the Gaussian random field that characterizes the spatial variability of regional terrain elevation can be expressed as:

[0091] Z N =Z·σ H +μ H (7)

[0092] In the formula, Z N is the random field matrix of regional terrain elevation, σ H is the standard deviation, μ H is the mean value of the regional terrain elevation H. The regional terrain elevation random field matrix Z is implemented on the relevant programming platform N The construction of the irregular three-dimensional terrain random field model in the present invention can be obtained.

[0093] Based on random field theory, the covariance matrix decomposition method is used to compile a Matlab program to implement the above process, so that a random field model of irregular three-dimensional terrain can be established.

[0094] Example:

[0095] Domestic infrastructure construction is faced with the characteristics of irregular three-dimensional terrain, which will bring huge challenges and adverse effects to engineering construction. It is very necessary to carry out irregular three-dimensional terrain simulation. This embodiment takes a typical area of ​​the Loess Plateau as the research object.

[0096] The first step is to determine the probability model and statistical characteristic values ​​of the spatial variability of the regional terrain elevation to be simulated. The probability model includes the probability distribution function and correlation function of the regional terrain elevation, and the statistical characteristic values ​​include the mean value μ of the regional terrain elevation H. H , standard deviation σ H , coefficient of variation δ H and related distances.

[0097] Taking a typical area of ​​the Loess Plateau as an example, through preliminary research, the average elevation (altitude) is determined to be 2000m, the coefficient of variation is determined to be 0.1, and the probability distribution form is normal distribution, which is used to characterize the random characteristics of regional terrain elevation (altitude); without loss of generality, the "isotropic" correlation structure is used to describe the autocorrelation of the regional three-dimensional terrain elevation, and the selected correlation function is an exponential correlation function, and the correlation distance is 100m, which is used to characterize the correlation characteristics of the regional terrain elevation (altitude). The specific relevant statistical characteristics are shown in Table 1.

[0098] Table 1 Statistical characteristics related to three-dimensional terrain elevation determined by the present invention

[0099]

[0100] According to the random parameter value and correlation parameter value of the regional terrain elevation (altitude), the random field simulation of the regional three-dimensional irregular terrain is realized through the programming platform in subsequent operations.

[0101] The second step is to determine the dimension and scale of the three-dimensional terrain of the area to be simulated, and then obtain the scope of the three-dimensional terrain of the area to be simulated.

[0102] The topographic model established in this case that reflects the spatial variability of three-dimensional terrain elevation can be used for later numerical analysis and inversion. In this case, a two-dimensional random field model is used, and the length and width of the model are 150m×63m. The determination of the size of the three-dimensional regional terrain to be simulated is equivalent to determining the size of the covariance matrix, which determines the range size for subsequent random field modeling.

[0103] The third step is to discretize the three-dimensional terrain of the area to be simulated determined in the second step to obtain the unit information of the three-dimensional terrain of the area to be simulated, which includes the number, number and location information of the unit. In this case, the discretized grid is taken as 1 / 10 of the relevant distance.

[0104] Step 4: Construct a random field model based on covariance matrix decomposition

[0105] According to formula (7), any Gaussian random field can be realized. In the present invention, the above modeling process is implemented by programming on the MATLAB platform. Figure 3 The random field simulation implementation of any irregular three-dimensional terrain is demonstrated. It can be seen that the model can present the irregular characteristics of three-dimensional terrain more intuitively, and the three-dimensional terrain elevation (altitude) shows both correlation and randomness characteristics.

[0106] The embodiment of the present invention further provides a random simulation device for irregular three-dimensional terrain, comprising:

[0107] The probability model and statistical characteristic value determination module is used to determine the probability model and statistical characteristic value of the spatial variability of the regional terrain elevation to be simulated. The probability model includes the probability distribution function and correlation function of the regional terrain elevation. The statistical characteristic value includes the mean value μ of the regional terrain elevation H. H , standard deviation σ H , coefficient of variation δ H and related distances;

[0108] A range determination module is used to determine the dimension and scale of the three-dimensional terrain of the area to be simulated, and then obtain the range of the three-dimensional terrain of the area to be simulated;

[0109] A grid discretization module is used to perform grid discretization on the determined three-dimensional terrain of the area to be simulated, and obtain the unit information of the three-dimensional terrain of the area to be simulated, and the unit information includes the number, number and position information of the unit;

[0110] The random field model establishment module is used to establish an irregular three-dimensional terrain random field model based on the covariance matrix decomposition method: using the range and unit information of the three-dimensional terrain to be simulated in the second and third steps, determine the basic framework of the covariance matrix, and then use the probability model and statistical eigenvalues ​​obtained in the first step to obtain the elevation size corresponding to each unit of the covariance matrix, perform one-to-one mapping and assignment of units, and obtain the irregular three-dimensional terrain random field matrix. Use the programming platform to realize the construction of the regional terrain elevation random field matrix and obtain the random field model of the irregular three-dimensional terrain.

[0111] The present invention utilizes the covariance matrix decomposition method to fuse different elevation data of regional terrain. By constructing a covariance matrix that can reflect the elevation distribution characteristics of spatial position, the one-to-one mapping and assignment of regional irregular terrain elevation information can be achieved. The distribution characteristics of regional irregular three-dimensional terrain can be characterized more scientifically and reasonably, thus providing a new path and new idea for irregular three-dimensional terrain simulation.

[0112] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by technicians in this technical field within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

Claims

1. A random simulation method for irregular three-dimensional terrain, characterized in that: The steps include: The first step is to determine the probability model and statistical characteristic values ​​of the spatial variability of the regional terrain elevation to be simulated. The probability model includes the probability distribution function and correlation function of the regional terrain elevation, and the statistical characteristic values ​​include the mean value μ of the regional terrain elevation H. H , standard deviation σ H , coefficient of variation δ H and related distances; The second step is to determine the dimension and scale of the three-dimensional terrain of the area to be simulated, and then obtain the scope of the three-dimensional terrain of the area to be simulated; Step 3: Grid discretize the three-dimensional terrain of the area to be simulated determined in the second step to obtain unit information of the three-dimensional terrain of the area to be simulated, and the unit information includes unit quantity, number and location information; The fourth step is to establish an irregular three-dimensional terrain random field model based on the covariance matrix decomposition method: using the range and unit information of the three-dimensional terrain of the area to be simulated obtained in the second and third steps, determine the basic framework of the covariance matrix, and then use the probability model and statistical eigenvalues ​​obtained in the first step to obtain the elevation size corresponding to each unit of the covariance matrix, perform one-to-one mapping and assignment of units, and obtain the irregular three-dimensional terrain random field matrix. Use the programming platform to realize the construction of the regional terrain elevation random field matrix and obtain the random field model of the irregular three-dimensional terrain; The fourth step specifically includes: Let x i and x j is a discrete point in the random field, where i,j=1,2,…,n, τ ij For any two points x i and x j The relative distance between them, C is the n-order covariance matrix composed of the covariance between n points, the n-order covariance matrix is ​​a positive definite symmetric matrix, and any element of the matrix C ij Represents x i and x j The covariance between ij =C(τ ij ); the covariance matrix is ​​expressed as: Where ρ represents the correlation coefficient between two center points, and the correlation coefficient is calculated by formula (3); Perform Cholesky decomposition on the covariance matrix C to obtain upper triangular and lower triangular matrices: CLULL T (5) Where: L is the lower triangular matrix, U is the upper triangular matrix, L T is the transpose of the matrix L; Y is a column vector consisting of n independent random numbers that obey the standard normal distribution, then the n-order random field matrix Z is expressed as: Z=LY (6) Where: Any point Z in the random field matrix Z ij It obeys the standard normal distribution, and the covariance matrix E(ZZ T )=E(LYY T L T )=E(LL T )=C, satisfying the correlation requirement, the random field matrix Z is a realization of the standard normal random field; The Gaussian random field that characterizes the spatial variability of regional terrain elevation is expressed as: WITH N =Z σ H +μ H (7) In the formula, Z N is the random field matrix of regional terrain elevation, σ H is the standard deviation, μ H is the mean value of the regional terrain elevation H; the regional terrain elevation random field matrix Z is realized on the relevant programming platform N The irregular three-dimensional terrain random field model can be obtained by constructing.

2. The random simulation method of irregular three-dimensional terrain according to claim 1, characterized in that: The probability distribution function of the terrain elevation of the region is a normal distribution type: The mean value μ of the regional terrain elevation H H , coefficient of variation δ H and standard deviation σ H The relationship between them is:

3. The random simulation method of irregular three-dimensional terrain according to claim 1, characterized in that: The correlation function of the regional terrain elevation is exponential, as follows: Among them, τ x and τ y are the relative distances between any two discrete points in the terrain in the longitude and latitude directions, ρ(τ x ,τ y ) represents τ x and τ y The correlation coefficient between x ≥0,τ y ≥0,θ x and θ y are the relevant distances in longitude and latitude, respectively.

4. The random simulation method of irregular three-dimensional terrain according to claim 1, characterized in that: The third step specifically includes: selecting quadrilateral elements for mesh discretization, and the coordinates of the center point of the discretized quadrilateral element are expressed as (x i ,y j ), i=1,2,…,N x ; i, j = 1, 2, ..., N y , N x and N y are the number of units in the x and y directions respectively; the discretized grid units are numbered and represented by N, N = 1, 2, ..., N x ×N y , the grid size is between 1 / 5 and 1 / 10 of the relevant distance.

5. A random simulation device for irregular three-dimensional terrain, characterized in that: include: The probability model and statistical characteristic value determination module is used to determine the probability model and statistical characteristic value of the spatial variability of the regional terrain elevation to be simulated. The probability model includes the probability distribution function and correlation function of the regional terrain elevation. The statistical characteristic value includes the mean value μ of the regional terrain elevation H. H , standard deviation σ H , coefficient of variation δ H and related distances; A range determination module is used to determine the dimension and scale of the three-dimensional terrain of the area to be simulated, and then obtain the range of the three-dimensional terrain of the area to be simulated; A grid discretization module is used to perform grid discretization on the determined three-dimensional terrain of the area to be simulated, and obtain the unit information of the three-dimensional terrain of the area to be simulated, and the unit information includes the number, number and position information of the unit; The random field model building module is used to build an irregular three-dimensional terrain random field model based on the covariance matrix decomposition method: using the range and unit information of the three-dimensional terrain of the area to be simulated obtained in the second and third steps, determine the basic framework of the covariance matrix, and then use the probability model and statistical eigenvalues ​​obtained in the first step to obtain the elevation size corresponding to each unit of the covariance matrix, perform one-to-one mapping and assignment of units, and obtain the irregular three-dimensional terrain random field matrix. Use the programming platform to realize the construction of the regional terrain elevation random field matrix and obtain the random field model of the irregular three-dimensional terrain; The random field model building module is specifically used for: Let x i and x j is a discrete point in the random field, where i,j=1,2,…,n, τ ij For any two points x i and x j The relative distance between them, C is the n-order covariance matrix composed of the covariance between n points, the n-order covariance matrix is ​​a positive definite symmetric matrix, and any element of the matrix C ij Represents x i and x j The covariance between ij =C(τ ij ); the covariance matrix is ​​expressed as: Where ρ represents the correlation coefficient between two center points, and the correlation coefficient is calculated by formula (3); Perform Cholesky decomposition on the covariance matrix C to obtain upper triangular and lower triangular matrices: CLULL T (5) Where: L is the lower triangular matrix, U is the upper triangular matrix, L T is the transpose of the matrix L; Y is a column vector consisting of n independent random numbers that obey the standard normal distribution, then the n-order random field matrix Z is expressed as: Z=LY (6) Where: Any point Z in the random field matrix Z ij It obeys the standard normal distribution, and the covariance matrix E(ZZ T )=E(LYY T L T )=E(LL T )=C, satisfying the correlation requirement, the random field matrix Z is a realization of the standard normal random field; The Gaussian random field that characterizes the spatial variability of regional terrain elevation is expressed as: WITH N =Z σ H +μ H (7) In the formula, Z N is the random field matrix of regional terrain elevation, σ H is the standard deviation, μ H is the mean value of the regional terrain elevation H; the regional terrain elevation random field matrix Z is realized on the relevant programming platform N The irregular three-dimensional terrain random field model can be obtained by constructing.

6. The random simulation device for irregular three-dimensional terrain according to claim 5, characterized in that: The probability distribution function of the terrain elevation of the region is a normal distribution type: The mean value μ of the regional terrain elevation H H , coefficient of variation δ H and standard deviation σ H The relationship between them is:

7. The random simulation device for irregular three-dimensional terrain according to claim 5, characterized in that: The correlation function of the regional terrain elevation is exponential, as follows: Among them, τ x and τ y are the relative distances between any two discrete points in the terrain in the longitude and latitude directions, ρ(τ x ,τ y ) represents τ x and τ y The correlation coefficient between x ≥0,τ y ≥0,θ x and θ y are the relevant distances in longitude and latitude, respectively.

8. The random simulation device for irregular three-dimensional terrain according to claim 5, characterized in that: The mesh discretization module is specifically used to: select quadrilateral units for mesh discretization, and the coordinates of the center points of the quadrilateral units after discretization are expressed as (x i ,y j ), i=1,2,…,N x ; i, j = 1, 2, ..., N y , N x and N y are the number of units in the x and y directions respectively; the discretized grid units are numbered and represented by N, N = 1, 2, ..., N x ×N y , the grid size is between 1 / 5 and 1 / 10 of the relevant distance.

Images