CN111080783A - A patch-type 3D modeling method for engineering geology kriging fitting - Google Patents
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Abstract
Description
技术领域technical field
本发明属于工程建模技术领域,尤其涉及一种工程地质克里金拟合贴片式三维建模方法。The invention belongs to the technical field of engineering modeling, and in particular relates to a three-dimensional modeling method of engineering geological kriging fitting patch type.
背景技术Background technique
三维模型是物体的多边形表示,通常用计算机或者其它视频设备进行显示。显示的物体可以是现实世界的实体,也可以是虚构的物体。任何物理自然界存在的东西都可以用三维模型表示,三维模型经常用三维建模工具这种专门的软件生成,但是也可以用其它方法生成。作为点和其它信息集合的数据,三维模型可以手工生成,也可以按照一定的算法生成。尽管通常按照虚拟的方式存在于计算机或者计算机文件中,但是在纸上描述的类似模型也可以认为是三维模型。三维模型广泛用任何使用三维图形的地方。A 3D model is a polygonal representation of an object, usually displayed on a computer or other video device. The displayed objects can be real-world entities or fictitious objects. Anything that exists in physical nature can be represented by a 3D model. 3D models are often generated by specialized software such as 3D modeling tools, but can also be generated by other methods. As the data of points and other information sets, the 3D model can be generated manually or according to a certain algorithm. Similar models described on paper can also be considered three-dimensional models, although they usually exist virtually in a computer or computer file. 3D models are widely used anywhere 3D graphics are used.
目前,铁路工程三维地质建模过程中主要有以下几种方式:一、利用拉伸体元构建线性工程三维地质模型;二、利用三棱柱体做基本体元构建三维地质体模型;三、利用克里金拟合三维地层面后,通过逐层剖切的方法获得体元。At present, there are mainly the following methods in the process of 3D geological modeling of railway engineering: 1. Constructing linear engineering 3D geological model by using stretched voxels; 2. Using triangular prisms as basic voxels to construct 3D geological model; After kriging fits the 3D stratigraphic plane, voxels are obtained by layer-by-layer sectioning.
在上述的第三种方法中,采用逐层剖切的方法受布尔运算影响较大,极易出现错误导致剖切失败,且速度较慢。In the third method mentioned above, the method of layer-by-layer sectioning is greatly affected by Boolean operations, which is prone to errors and causes sectioning failure, and the speed is slow.
发明内容SUMMARY OF THE INVENTION
本发明提供一种工程地质克里金拟合贴片式三维建模方法,旨在解决采用逐层剖切的方法受布尔运算影响较大,极易出现错误导致剖切失败,且速度较慢问题。The invention provides a patch-type three-dimensional modeling method for engineering geological kriging, which aims to solve the problem that the layer-by-layer sectioning method is greatly affected by Boolean operations, is prone to errors and causes sectioning failure, and has a slow speed. question.
本发明是这样实现的,一种工程地质克里金拟合贴片式三维建模方法,包括如下步骤:The present invention is realized in this way, a kind of engineering geological kriging fitting patch type three-dimensional modeling method, comprising the following steps:
步骤S10:确定已知点并形成已知的顶面;Step S10: determine a known point and form a known top surface;
步骤S20:采用克里金插值拟合方法,根据已知点,计算范围内未知点到参考面的高;Step S20: using the kriging interpolation fitting method, according to the known points, calculate the height from the unknown point within the range to the reference surface;
步骤S30:将未知点的高加上原坐标的Z值,即可得到未知点拟合后的坐标值;Step S30: adding the height of the unknown point to the Z value of the original coordinate to obtain the fitted coordinate value of the unknown point;
步骤S40:利用已知点坐标和未知点拟合后的坐标形成地质体底面和三棱柱;Step S40: forming the bottom surface of the geological body and the triangular prism by using the coordinates of the known point and the coordinates after fitting of the unknown point;
步骤S50:将所有得到的三棱柱合并,得到该层完整的地质体。Step S50: Combine all the obtained triangular prisms to obtain a complete geological body of this layer.
优选的,所述步骤S10中包括获取需要建立地质体的勘探孔位层底坐标,并计算层底节点到参考面的高,并利用层底坐标的X、Y值和层底坐标到参考面的高组成已知点。Preferably, the step S10 includes acquiring the bottom coordinates of the exploration holes where the geological body needs to be established, and calculating the height of the bottom node to the reference plane, and using the X and Y values of the bottom coordinates and the bottom coordinates to the reference plane The high composition of known points.
优选的,所述步骤S20还包括如下步骤:Preferably, the step S20 further includes the following steps:
步骤S1、根据已知散列点线特征自动拟合原始三维地形和地质曲面;Step S1, automatically fitting the original three-dimensional terrain and geological surface according to the known hash point and line features;
步骤S2、利用高精度特征线对所述原始三维地形和地质曲面进行修正;Step S2, using high-precision feature lines to correct the original three-dimensional terrain and geological surface;
步骤S3、根据高斯过程回归模型预测格网点三维坐标,并在修正后的原始三维地形和地质曲面中内插格网点,以获得未知点的高。Step S3, predicting the three-dimensional coordinates of the grid points according to the Gaussian process regression model, and interpolating the grid points in the modified original three-dimensional terrain and geological surface to obtain the height of the unknown point.
优选的,所述步骤S30中计算出的未知点的坐标设有多个,并分别对应多个三棱柱。Preferably, there are multiple coordinates of the unknown point calculated in the step S30, which correspond to multiple triangular prisms respectively.
优选的,所述步骤S40中的三棱柱是将地质体底面的每一个三角面与地质体顶面的对应三角面而形成的。Preferably, the triangular prism in the step S40 is formed by combining each triangular surface of the bottom surface of the geological body with the corresponding triangular surface of the top surface of the geological body.
优选的,步骤S50中,将多个三棱柱中,相邻的三棱柱稳定侧面进行合并。Preferably, in step S50, among the plurality of triangular prisms, the stable sides of adjacent triangular prisms are merged.
优选的,多个三棱柱合并之后,多个三棱柱的底层和顶层合并形成地面和底面。Preferably, after the multiple triangular prisms are combined, the bottom layer and the top layer of the multiple triangular prisms are combined to form the ground and the bottom surface.
与现有技术相比,本发明的有益效果是:本发明的一种工程地质克里金拟合贴片式三维建模方法,利用克里金插值拟合方法进行对未知点坐标进行计算,并根据未知点的坐标和顶面形成三棱柱,随后对多个三棱柱进行合并,从而得到完整的工程地质体,利用三棱柱的合并使用,能有效降低剪切过程中产生的错误和剪切失败的风险,从而提高建模效率,且该方法更适用实现自动化三维建模,具有明显的社会经济效益。Compared with the prior art, the beneficial effects of the present invention are: the Kriging fitting patch type three-dimensional modeling method for engineering geology of the present invention utilizes the kriging interpolation fitting method to calculate the coordinates of unknown points, And form triangular prisms according to the coordinates and top surfaces of unknown points, and then merge multiple triangular prisms to obtain a complete engineering geological body. The combined use of triangular prisms can effectively reduce errors and shearing generated in the shearing process. The risk of failure is improved, and the modeling efficiency is improved, and the method is more suitable for automatic 3D modeling, which has obvious social and economic benefits.
附图说明Description of drawings
图1为本发明的方法流程示意图;Fig. 1 is the method flow schematic diagram of the present invention;
具体实施方式Detailed ways
为了使本发明的目的、技术方案及优点更加清楚明白,以下结合附图及实施例,对本发明进行进一步详细说明。应当理解,此处所描述的具体实施例仅仅用以解释本发明,并不用于限定本发明。In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.
请参阅图1,本发明提供一种技术方案:一种工程地质克里金拟合贴片式三维建模方法,包括如下步骤:Referring to Fig. 1, the present invention provides a technical solution: a method for engineering geology kriging fitting patch type three-dimensional modeling, comprising the following steps:
步骤S10:确定已知点并形成已知的顶面;Step S10: determine a known point and form a known top surface;
步骤S20:采用克里金插值拟合方法,根据已知点,计算范围内未知点到参考面的高;Step S20: using the kriging interpolation fitting method, according to the known points, calculate the height from the unknown point within the range to the reference surface;
步骤S30:将未知点的高加上原坐标的Z值,即可得到未知点拟合后的坐标值;Step S30: adding the height of the unknown point to the Z value of the original coordinate to obtain the fitted coordinate value of the unknown point;
步骤S40:利用已知点坐标和未知点拟合后的坐标形成地质体底面和三棱柱;Step S40: forming the bottom surface of the geological body and the triangular prism by using the coordinates of the known point and the coordinates after fitting of the unknown point;
步骤S50:将所有得到的三棱柱合并,得到该层完整的地质体。Step S50: Combine all the obtained triangular prisms to obtain a complete geological body of this layer.
在本实施方式中,首先根据地质体边界范围确定范围内地质体的顶面,随后获取需要建立地质体的勘探孔位层底坐标,并计算层底节点到参考面的高,并利用层底坐标的X、Y值和层底坐标到参考面的高组成已知点,并采用克里金插值拟合方法,根据已知点,计算范围内未知点到参考面的高;在上述的公式计算中已获得未知点的高,将未知点的高加上原坐标的Z值,即可得到未知点拟合后的坐标值,并利用已知点坐标和未知点拟合后的坐标形成地质体底面,随后将地质体底面的每一个三角面与地质体顶面的对应三角面形成三棱柱,将所有得到的三棱柱合并,得到该层完整的地质体,在三棱柱合并的过程中,每个相邻三棱柱之间的侧面相互合并,当所有三棱柱进行合并之后,并形成一个多面体,该多面体便为工程地质体,其次,在多个三棱柱合并中,多个三棱柱的底层合并形成工程地质体的底面,多个三棱柱的顶层相互合并形成工程地质体的顶面。In this embodiment, the top surface of the geological body within the range is first determined according to the boundary range of the geological body, and then the bottom coordinates of the exploration holes where the geological body needs to be established are obtained, and the height from the bottom node to the reference plane is calculated, and the bottom layer is used. The X and Y values of the coordinates and the height of the bottom coordinate to the reference surface form a known point, and the Kriging interpolation fitting method is used to calculate the height from the unknown point within the range to the reference surface according to the known point; in the above formula The height of the unknown point has been obtained in the calculation. Add the height of the unknown point to the Z value of the original coordinate to obtain the coordinate value of the unknown point after fitting, and use the coordinates of the known point and the fitted coordinates of the unknown point to form a geological body The bottom surface, then each triangular surface of the bottom surface of the geological body and the corresponding triangular surface of the top surface of the geological body form a triangular prism, and all the obtained triangular prisms are merged to obtain the complete geological body of this layer. In the process of merging the triangular prisms, each The sides between two adjacent triangular prisms are merged with each other. When all the triangular prisms are merged, a polyhedron is formed, and the polyhedron is an engineering geological body. Secondly, in the merging of multiple triangular prisms, the bottom layers of multiple triangular prisms are merged. The bottom surface of the engineering geological body is formed, and the top layers of the plurality of triangular prisms are merged with each other to form the top surface of the engineering geological body.
进一步的,步骤S10中包括获取需要建立地质体的勘探孔位层底坐标,并计算层底节点到参考面的高,并利用层底坐标的X、Y值和层底坐标到参考面的高组成已知点。Further, step S10 includes acquiring the bottom coordinates of the exploration hole location where the geological body needs to be established, and calculating the height of the bottom node to the reference plane, and using the X and Y values of the bottom coordinates and the height of the bottom coordinates to the reference plane. Form known points.
本实施方式中,在其中,利用底层坐标中的X和Y值,并配合参看面的高,其三个数值的相互结合,便能够顺利的做成已知点的坐标,并利用多个已知点稳的坐标便能够顺利的支持顶面二得形成。In this embodiment, the X and Y values in the bottom layer coordinates are used in combination with the height of the reference plane, and the three values of the three values can be combined with each other, so that the coordinates of the known points can be smoothly made, and the coordinates of the known points can be formed by using a number of known points. Knowing the stable coordinates of the point can smoothly support the formation of the top surface.
进一步的,步骤S20还包括如下步骤:Further, step S20 also includes the following steps:
步骤S1、根据已知散列点线特征自动拟合原始三维地形和地质曲面;Step S1, automatically fitting the original three-dimensional terrain and geological surface according to the known hash point and line features;
步骤S2、利用高精度特征线对原始三维地形和地质曲面进行修正;Step S2, using high-precision feature lines to correct the original three-dimensional terrain and geological surface;
步骤S3、根据高斯过程回归模型预测格网点三维坐标,并在修正后的原始三维地形和地质曲面中内插格网点,以获得未知点的高。Step S3, predicting the three-dimensional coordinates of the grid points according to the Gaussian process regression model, and interpolating the grid points in the modified original three-dimensional terrain and geological surface to obtain the height of the unknown point.
在本实施方式中,已知散列点线特征包括已知散列点线的三维坐标集合(xi,yi,zi),i=1...m。In this embodiment, the known hash point line feature includes a three-dimensional coordinate set (x i , y i , z i ) of the known hash point line, i=1...m.
优选的,步骤S2中,根据修正点线的三维坐标集合(xi,yi,Δzi),i=1...m对原始三维地形和/或地质曲面进行修正,且ΔZ值为修正点线到既有面的高差。Preferably, in step S2, the original three-dimensional terrain and/or geological surface is corrected according to the three-dimensional coordinate set (x i , y i , Δzi ) of the corrected point line, i =1...m, and the value of ΔZ is corrected The height difference between the dotted line and the existing surface.
优选的,步骤S3包括:Preferably, step S3 includes:
S31、引入回归模型F和随机函数Z,且回归模型F和随机函数Z满足下述公式(1)、(2)所示条件:S31. Introduce regression model F and random function Z, and regression model F and random function Z satisfy the conditions shown in the following formulas (1) and (2):
F(β:,l,x)=β1f1(x)+...+βnfn(x)F(β :,l ,x)=β 1 f 1 (x)+...+β n f n (x)
=[f1(x)+...+fn(x)]β: =[f 1 (x)+...+f n (x)]β :
=f(x)Tβ: (2);=f(x) T β : (2);
其中,为利用回归模型F计算结果;fn(x)为第n个变量函数值;f(x)T为[f1(x)+...+fn(x)]变成列向量的数学表示;{βk}为回归参数;随机函数Z均值为0,且协方差满足下述公式(3)所示条件:in, In order to use the regression model F to calculate the result; f n (x) is the nth variable function value; f(x) T is the mathematics of [f 1 (x)+...+f n (x)] into a column vector represents; {β k } is the regression parameter; the mean value of the random function Z is 0, and the covariance satisfies the conditions shown in the following formula (3):
E[Z(w)Z(x)]=σ2R(θ,w,x) (3);E[Z(w)Z(x)]=σ 2 R(θ,w,x) (3);
其中,Var[Z(x)]=σ2;R(θ,w,x)为高斯核函数,且w,x表示两个不同的变量,θ为高斯核函数的自定义参数;Wherein, Var[Z(x)]=σ 2 ; R(θ, w, x) is a Gaussian kernel function, and w, x represent two different variables, and θ is a self-defined parameter of the Gaussian kernel function;
S32、建立预测模型且获得下述公式(4)所示误差方程:S32. Establish a prediction model And the error equation shown in the following formula (4) is obtained:
且F=[f(s1)...f(sm)]T;Z=[z1...zm]T,是行向量[Z1(x)...Zn(x)]的数学表示;f(x)=FTc(x);c(x)T表示函数c(x)的多个结果;Y=Fβ+Z,为回归模型F的计算结果;and F=[f(s 1 )...f(s m )] T ; Z=[z 1 ...z m ] T , is the row vector [Z 1 (x)...Z n (x) ] mathematical representation; f(x)=F T c(x); c(x) T represents multiple results of the function c(x); Y=Fβ+Z, which is the calculation result of the regression model F;
S33、计算获得公式(4)的方差,且方差满足下述公式(5)所示条件:S33, calculate and obtain the variance of formula (4), and the variance satisfies the conditions shown in the following formula (5):
其中,Rij=R(θ,si,sj),i,j=1...m,r(x)=[R(θ,s1,x)...R(θ,sm,x)]T,si,sj分别是第i个变量和第j个变量;y(x)为样本变量x对应的真实值,为预测值;where R ij =R(θ,s i ,s j ),i,j=1...m,r(x)=[R(θ,s 1 ,x)...R(θ,s m ,x)] T , s i , s j are the ith variable and the jth variable respectively; y(x) is the true value corresponding to the sample variable x, is the predicted value;
S34、根据预测方差最小原则,将c(x)的求解问题化为f(x)=FTc(x)约束条件下求公式(5)的极值,以获得拉格朗日乘子且满足下述公式(6)所示条件; (6);S34. According to the principle of minimum prediction variance, the solution problem of c(x) is transformed into the extreme value of formula (5) under the constraint condition of f(x)=F T c(x) to obtain the Lagrange multiplier and Meet the conditions shown in the following formula (6); (6);
且得到如下述公式(7)所示的预测期望方差:And the expected variance of prediction is obtained as shown in the following formula (7):
S35、根据下述公式(8)计算获得c(x),且根据c(x)在修正后的原始三维地形和/或地质曲面中内插格网点坐标值,以获得未知点的高:S35, calculate and obtain c(x) according to the following formula (8), and interpolate the coordinate values of grid points in the modified original three-dimensional terrain and/or geological surface according to c(x) to obtain the height of the unknown point:
(8)。 (8).
c(x)=R-1(r(x)-Fλ)c(x)=R -1 (r(x)-Fλ)
优选的,步骤S31实施前还包括:Preferably, before step S31 is implemented, it further includes:
S30a、将m个样本点线数据分解成平面坐标集合S=[s1...si...sm]T,si∈IRn和高程集合Y=[y1...yi...ym]T,yi∈IR;S30a, decompose the m sample point line data into a plane coordinate set S=[s 1 ... s i ... s m ] T , s i ∈IR n and an elevation set Y=[y 1 ... y i ...y m ] T , y i ∈ IR;
S30b、按照下述公式(9)、(10)对S和Y进行标准化处理,使其符合标准正态分布;S30b, standardize S and Y according to the following formulas (9) and (10) to make them conform to the standard normal distribution;
u[S:,j]=0;V[S:,j,S:,j]=1;j=1,...,n; (9);u[S :,j ]=0; V[S :,j ,S :,j ]=1; j=1,...,n; (9);
u[Y:]=0;V[Y:,Y:]=1; (10);u[Y : ]=0; V[Y : , Y : ]=1; (10);
其中,u[.]和V[.,.]分别代表均值和协方差。where u[.] and V[.,.] represent the mean and covariance, respectively.
进一步的,步骤S30中计算出的未知点的坐标设有多个,并分别对应多个三棱柱。Further, there are multiple coordinates of the unknown point calculated in step S30, which correspond to multiple triangular prisms respectively.
在本实施方式中,在使用的过程中,利用克里金插值拟合方法便可计算出多个未知点的左边,而根据多个未知点的坐标便可形成多个间接的三棱柱,并将多个三棱柱进行合并,从而得出一个完成的地质体。In this embodiment, in the process of use, the kriging interpolation fitting method can be used to calculate the left side of a plurality of unknown points, and a plurality of indirect triangular prisms can be formed according to the coordinates of the plurality of unknown points, and Merge multiple triangular prisms to produce a finished geobody.
进一步的,步骤S50中,将多个三棱柱中,相邻的三棱柱稳定侧面进行合并;多个三棱柱合并之后,多个三棱柱的底层和顶层合并形成地面和底面。Further, in step S50, among the plurality of triangular prisms, the stable sides of adjacent triangular prisms are merged; after the multiple triangular prisms are merged, the bottom and top layers of the multiple triangular prisms are merged to form the ground and the bottom surface.
在本实施方式中,每个相邻三棱柱之间的侧面相互合并,当所有三棱柱进行合并之后,并形成一个多面体,该多面体便为工程地质体,其次,在多个三棱柱合并中,多个三棱柱的底层合并形成工程地质体的底面,多个三棱柱的顶层相互合并形成工程地质体的顶面。In this embodiment, the sides between each adjacent triangular prisms are merged with each other. After all the triangular prisms are merged, a polyhedron is formed, and the polyhedron is an engineering geological body. Secondly, in the merging of multiple triangular prisms, The bottom surfaces of the plurality of triangular prisms are combined to form the bottom surface of the engineering geological body, and the top layers of the plurality of triangular prisms are combined with each other to form the top surface of the engineering geological body.
以上仅为本发明的较佳实施例而已,并不用以限制本发明,凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等,均应包含在本发明的保护范围之内。The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the present invention. Inside.
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