基于胞腔复形链的地下空间对象三维表达与分析计算统一数据模型研究
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摘要
随着科学技术的进步和社会经济的发展,地下空间作为重要的资源逐步得到开发利用,如城市地下空间设施的建设、矿产资源开发、地下能源存储库建设等。地下空间无论作何种用途,都需要对其地质环境、地质构造情况进行详细的勘察量测和模拟分析才能够进行施工作业。地下空间对象三维表达与分析计算技术可以更加便捷、精细地描述地下空间对象构造,能够对地下空间现象进行数值模拟与分析,从而使工程师们做出更加准确的决策。因此,该技术已经成为三维地理信息系统、三维地学模拟系统和岩石力学数值模拟等学科领域的研究热点。
由于没有统一的数据结构,用于地下空间对象三维表达的模型与用于分析计算的模型之间存在着本质的差异。因此,目前地下空间对象的三维表达与分析计算多被分为两个独立的过程。这样在进行地理现象模拟与分析的过程中,既不利于地下空间对象几何拓扑信息的维护,容易产生数据冲突,也降低了分析计算的效率。本文以代数拓扑为理论依据,基于胞腔复形链实现地下空间对象几何、拓扑和属性的统一表达和形式化定义,构建了能支持地下空间对象三维表达与分析计算的统一数据模型。通过本课题的研究,从理论和方法上推进地下空间对象三维表示和分析计算技术的发展,主要的研究工作和成果包括：
(1)将地下空间对象的代数拓扑描述方法从单纯同调理论扩展到胞腔同调,详细阐述了胞腔复形链及其相关操作算子的概念。在此基础上,给出了基于胞腔复形链的地下空间对象形式化定义,对其动态行为过程变化特征进行了描述与表达,为地下空间对象三维表达与分析计算统一数据模型的构建奠定了理论基础。
(2)在完成了基于胞腔复形链的地下空间对象形式化定义的基础上,从地下空间对象的抽象过程入手,结合代数拓扑学的相关理论,给出了基于胞腔复形链的地下空间对象三维表达与分析计算统一数据模型的层次结构及其实现方法；并由此实现了基于统一数据模型的复杂地下空间对象三维表达、地下空间对象属性信息空间分布特征表达及动态行为过程表达的操作。
(3)为了扩展本文提出的统一数据模型空间操作功能及增强其实用性,基于统一数据模型,实现了一系列地下空间对象三维空间分析与计算过程中的空间操作算法。基于胞腔复形链对欧拉-庞加莱公式进行了扩展,并借助于其6个拓扑不变量设计了10对欧拉算子；在此基础上,实现了基于统一数据模型的三维点集区域查询算法、三维空间相交检测算法、三维空间实体间布尔运算、三维空间网格离散及地下空间对象模型细分光滑操作等空间操作算法。
(4)采用本文构建的基于胞腔复形链的三维表达与分析计算统一数据模型及其相关空间操作方法,以盐腔围岩蠕变数值模拟与分析为例,对统一数据模型层次结构的合理性及其相关空间操作的可靠性进行了实例验证。通过对研究区基础空间数据、声纳测腔数据等数据资料的分析,构建基于统一数据模型的盐腔围岩数值分析计算模型,实现盐岩围岩空间对象几何、拓扑、属性信息的统一表达；基于胞腔复形链对常用力学元件进行表达,通过对胞腔复形链的操作运算,实现不同蠕变机理模型的重构；在此基础上,进行基于统一数据模型进行盐腔围岩蠕变数值模拟与分析。
With the progress and development of the scientific technology and socio-economic, the underground space is gradually developed and utilized as an important resource, such as the construction of urban underground spatial facilities, development of mineral resources, and construction of underground energy storage library. No matter for what purpose, it's necessary to conduct detailed survey measurements and simulations to geological environment and geological formations of the underground space before the construction work is carried out. The technology of three-dimensional representation and analysis computation of underground spatial objects can be more convenient and fine to describe the construction instance of underground spatial objects, and be able to carry out numerical simulation and analysis to underground phenomenon, which enables engineers to do more accurate decision-making. Therefore, the technology has become a research hotspot of many subject areas, such as three-dimensional geographic information system, three-dimensional geoscience modeling, rock mechanics and numerical simulation, and so on.
As the absence of a unified data structure, there are essential differences between the three-dimensional representation model of the underground space objects and computational model for the numerical analysis. Therefore, the traditional three-dimensional representation and analysis computation of underground spatial objects are divided into two separate courses, which are not conducive to the maintenance of the geometry and topology information of underground spatial objects during the simulation and analysis of geographical phenomena, but also prone to data conflicts and reduce the computational efficiency of the analysis. Taking algebraic topology as the theoretical basis, a unified representation and formal definition of the geometry, topology and properties of the underground spatial objects is achieved based on the cell complex chain, and then the unified data model of three-dimensional representation and analysis computation of underground spatial objects is constructed. Through the research of this subject, the development of three-dimensional representation and analysis computation technology of underground spatial objects will be promoted theoretically and methodology, the main research works and achievements are as follows:
(1) Expaned algebraic topologyical description method of underground spatial objects from the simplicial homology theory to cell cohomology theory, the basic concepts of the cell complex chain and its operators are described. Based on cell complex chain, the formal definition and the dynamic behavior of underground spatial objects are given and descriped, which forms the theory foundation for constructing the unified data model of the three-dimensional representation and analysis computation of underground spatial objects.
(2) On the foundation of the formal definition of underground spatial objects based on cell complex chain, starting from the abstraction processing of underground spatial objects, combining with the related theories of algebraic topology, the hierarchy structure and implementation method of the unified data model of three-dimensional representation and analysis computation of underground spatial objects are achieved based on cell complex chain. And then some operations are achieved based on the unified data model, such as the three-dimensional representation of the complex underground spatial objects, and the spatial distribution characteristics of attribute information of underground spatial objects, and the representation of dynamic behavior.
(3) In order to improve the spatial operation function of the unified data model and enhance its practicality and a series spatial operation algorithms of three-dimensional analysis and computation process of underground spatial objects based on the unified data model are developed. Euler-Poincare formula is extended based on the cell complex chain, and10Euler operators are designed by virtue of its six topological invariants; On this basis, some spatial operation algorthms are achieved, such as a3D point set range query algorithm, three-dimensional intersection detection algorithm, Boolean operations between two three-dimensional entities, three-dimensional mesh generation method and the model subdivision smoothing operation of underground spatial objects.
(4) Based on the unified data model of three-dimensional representation and analysis computation by the cell complex chain and its related spatial operation algorithms, taking the the salt cavity wall-rock creep numerical simulation and analysis for example, the rationality of hierarchy structure and the reliability of the related spatial operation of the unified data model are validated. By researching the basic spatial data of the study area and the sonar measurement data of the salt cavity, an analytical computational model of salt cavity wall-rock based on the unified data model are built. Thus, the unified representation of the geometry, topology, and attribute information of salt cavity wall-rock are achieved. The representation of mechanical components commonly used based on the cell complex chain and its operators are constructed. Through the operations on the cell complex chain, differences of creep mechanism models can be reconstructed. On this basis, the process of creep numerical simulation and analysis of salt cavity wall-rock based on the unified data model is carried out.
由于没有统一的数据结构,用于地下空间对象三维表达的模型与用于分析计算的模型之间存在着本质的差异。因此,目前地下空间对象的三维表达与分析计算多被分为两个独立的过程。这样在进行地理现象模拟与分析的过程中,既不利于地下空间对象几何拓扑信息的维护,容易产生数据冲突,也降低了分析计算的效率。本文以代数拓扑为理论依据,基于胞腔复形链实现地下空间对象几何、拓扑和属性的统一表达和形式化定义,构建了能支持地下空间对象三维表达与分析计算的统一数据模型。通过本课题的研究,从理论和方法上推进地下空间对象三维表示和分析计算技术的发展,主要的研究工作和成果包括：
(1)将地下空间对象的代数拓扑描述方法从单纯同调理论扩展到胞腔同调,详细阐述了胞腔复形链及其相关操作算子的概念。在此基础上,给出了基于胞腔复形链的地下空间对象形式化定义,对其动态行为过程变化特征进行了描述与表达,为地下空间对象三维表达与分析计算统一数据模型的构建奠定了理论基础。
(2)在完成了基于胞腔复形链的地下空间对象形式化定义的基础上,从地下空间对象的抽象过程入手,结合代数拓扑学的相关理论,给出了基于胞腔复形链的地下空间对象三维表达与分析计算统一数据模型的层次结构及其实现方法；并由此实现了基于统一数据模型的复杂地下空间对象三维表达、地下空间对象属性信息空间分布特征表达及动态行为过程表达的操作。
(3)为了扩展本文提出的统一数据模型空间操作功能及增强其实用性,基于统一数据模型,实现了一系列地下空间对象三维空间分析与计算过程中的空间操作算法。基于胞腔复形链对欧拉-庞加莱公式进行了扩展,并借助于其6个拓扑不变量设计了10对欧拉算子；在此基础上,实现了基于统一数据模型的三维点集区域查询算法、三维空间相交检测算法、三维空间实体间布尔运算、三维空间网格离散及地下空间对象模型细分光滑操作等空间操作算法。
(4)采用本文构建的基于胞腔复形链的三维表达与分析计算统一数据模型及其相关空间操作方法,以盐腔围岩蠕变数值模拟与分析为例,对统一数据模型层次结构的合理性及其相关空间操作的可靠性进行了实例验证。通过对研究区基础空间数据、声纳测腔数据等数据资料的分析,构建基于统一数据模型的盐腔围岩数值分析计算模型,实现盐岩围岩空间对象几何、拓扑、属性信息的统一表达；基于胞腔复形链对常用力学元件进行表达,通过对胞腔复形链的操作运算,实现不同蠕变机理模型的重构；在此基础上,进行基于统一数据模型进行盐腔围岩蠕变数值模拟与分析。
With the progress and development of the scientific technology and socio-economic, the underground space is gradually developed and utilized as an important resource, such as the construction of urban underground spatial facilities, development of mineral resources, and construction of underground energy storage library. No matter for what purpose, it's necessary to conduct detailed survey measurements and simulations to geological environment and geological formations of the underground space before the construction work is carried out. The technology of three-dimensional representation and analysis computation of underground spatial objects can be more convenient and fine to describe the construction instance of underground spatial objects, and be able to carry out numerical simulation and analysis to underground phenomenon, which enables engineers to do more accurate decision-making. Therefore, the technology has become a research hotspot of many subject areas, such as three-dimensional geographic information system, three-dimensional geoscience modeling, rock mechanics and numerical simulation, and so on.
As the absence of a unified data structure, there are essential differences between the three-dimensional representation model of the underground space objects and computational model for the numerical analysis. Therefore, the traditional three-dimensional representation and analysis computation of underground spatial objects are divided into two separate courses, which are not conducive to the maintenance of the geometry and topology information of underground spatial objects during the simulation and analysis of geographical phenomena, but also prone to data conflicts and reduce the computational efficiency of the analysis. Taking algebraic topology as the theoretical basis, a unified representation and formal definition of the geometry, topology and properties of the underground spatial objects is achieved based on the cell complex chain, and then the unified data model of three-dimensional representation and analysis computation of underground spatial objects is constructed. Through the research of this subject, the development of three-dimensional representation and analysis computation technology of underground spatial objects will be promoted theoretically and methodology, the main research works and achievements are as follows:
(1) Expaned algebraic topologyical description method of underground spatial objects from the simplicial homology theory to cell cohomology theory, the basic concepts of the cell complex chain and its operators are described. Based on cell complex chain, the formal definition and the dynamic behavior of underground spatial objects are given and descriped, which forms the theory foundation for constructing the unified data model of the three-dimensional representation and analysis computation of underground spatial objects.
(2) On the foundation of the formal definition of underground spatial objects based on cell complex chain, starting from the abstraction processing of underground spatial objects, combining with the related theories of algebraic topology, the hierarchy structure and implementation method of the unified data model of three-dimensional representation and analysis computation of underground spatial objects are achieved based on cell complex chain. And then some operations are achieved based on the unified data model, such as the three-dimensional representation of the complex underground spatial objects, and the spatial distribution characteristics of attribute information of underground spatial objects, and the representation of dynamic behavior.
(3) In order to improve the spatial operation function of the unified data model and enhance its practicality and a series spatial operation algorithms of three-dimensional analysis and computation process of underground spatial objects based on the unified data model are developed. Euler-Poincare formula is extended based on the cell complex chain, and10Euler operators are designed by virtue of its six topological invariants; On this basis, some spatial operation algorthms are achieved, such as a3D point set range query algorithm, three-dimensional intersection detection algorithm, Boolean operations between two three-dimensional entities, three-dimensional mesh generation method and the model subdivision smoothing operation of underground spatial objects.
(4) Based on the unified data model of three-dimensional representation and analysis computation by the cell complex chain and its related spatial operation algorithms, taking the the salt cavity wall-rock creep numerical simulation and analysis for example, the rationality of hierarchy structure and the reliability of the related spatial operation of the unified data model are validated. By researching the basic spatial data of the study area and the sonar measurement data of the salt cavity, an analytical computational model of salt cavity wall-rock based on the unified data model are built. Thus, the unified representation of the geometry, topology, and attribute information of salt cavity wall-rock are achieved. The representation of mechanical components commonly used based on the cell complex chain and its operators are constructed. Through the operations on the cell complex chain, differences of creep mechanism models can be reconstructed. On this basis, the process of creep numerical simulation and analysis of salt cavity wall-rock based on the unified data model is carried out.
引文
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