基于几何代数的时空统一数据模型构建理论与方法

Even the research of GIS data model has undergone rapid development, to date, existing GIS data models are still limited by the multi-source data intergration, the efficiency and ability of supporting complex geographical model analysis are still weak. The spatial and temporal dimension are usually separated in exiting data models. In this project, the theory of geometric algebra is introduced to develop a new type of spatio-temporal data model, which is unified in both spatial and temporal dimension, multi-level and connected with the geometrical expression and algebra computation, with integration of the description of spatio-temporal elements, relations, semetics and attributes. The proposal starts from the unified expresssion, description and computation of geographic space and time, and develops the spatio-temporal data model that can directly supports geographical model's construction and computation. The unified spacification of spatio-temporal description and expression will first be constructed under the geometric algebra framework. The unified expression of geographic space and time, and the mapping and transformation mechanism from the geographical space & time to the unified geometric algebra space & time will be studied. .Based on the geometric algebra multivector structures, the data modeling, organization, storage and multi-information integration approaches will be proposed with the integration of the geometric, stemetic, relations and attribute information. On the basis of grammar and lexical rules, existing geographic model will be parsed and reconstructed under the geometric algebra framework and the mechanism of model analysis and reconstruction. The coupled parrelized model running strategies will also be proposed, in order to effectively support the analysis of complex geographical scenarios and the implementation of the geographical models. This project will provide future GIS researches in the sensor network and cloud computing era with innovative theories and methods, which have characteristics of temporal and spatial integration and supporting complex geological analysis, and are expected to promote the development of geographic information science.

针对现有GIS数据模型对多源数据集成困难、时空分离、时空-语义-属性分割、分析效率低下，以及对地理分析模型支撑不足等问题。本项目引入几何代数理论，从地理时空的统一表达、描述与计算的基础理论与方法为切入点，发展以时空统一、多源信息集成表达、可支撑地理模型运算与分析为特征的新型GIS时空数据模型- - 基于几何代数的时空统一数据模型。通过研究地理时空的统一表达模式及其向几何代数空间的映射与转化模式，建立几何、时间、语义、关系及属性数据的几何代数整体表示方法，实现对复杂地理对象及动态地理过程的有效表达与建模。建立基于几何代数的时空统一数据模型与现有GIS数据模型转换方法，并建立该数据模型与现有GIS和地理分析模型的集成模式，实现数据模型与地理模型在表达、计算与分析上的有效统一。本项目研究可为地理时空数据的表达、建模、计算与模型分析提供新的思路，为云计算与物联网时代的新型GIS发展奠定理论和方法基础。

本项目针对以欧氏几何和计算几何为基础的传统GIS空间数据模型时空、多维表达不统一，缺乏代数化结构支撑地理计算等问题，从地理信息科学研究的整体脉络出发，原创性地引入统一时空观与几何代数理论进行时空统一数据模型构建理论与方法研究。项目研究获得了如下成果：1）研究了地理时空与几何代数时空间的映射转换机制，形成了适用于地理对象及动态地理过程时空表达的概念模型；2）构建了“六要素”（地理语义、时空定位、几何形态、演化过程、要素关系、属性特征）几何代数时空数据模型；3）设计了表达-组织-存储-检索-计算结构一致的多重向量树（MVTree）数据结构；4）开发了可用于几何代数GIS算法快速开发与并行优化的计算引擎；5）从数据耦合、模型集成和模型改造三个不同的视角探讨了几何代数在模型构建、模型改造和模型耦合运行方面对地理分析模型的支撑；6)最后将本项目方法推广应用于应急疏散、南极冰盖模拟、传感器数据解析等领域。项目研究成果在国内外权威刊物上发表研究论文59篇，其中SCI/SSCI检索论文41篇、EI检索论文11篇，申请国家发明专利15项，其中授权3项，培养博士研究生7名，硕士研究生18名。项目研究成果在地理环境演化过程重建、模拟与预估得到应用，并获2017年教育部自然科学一等奖。研究显示，从维度统一与多重信息表达与集成的视角进行时空数据模型构建，探索几何、时间、语义、关系、属性的统一表达模式，打破现有GIS数据模型对坐标高度依赖的表达与计算模式，从数据模型层面实现对地理计算与地理分析模型构建与运算的直接支撑，有望从计算理论与方法上直接对各类地理计算进行统一与简化，有效提高GIS和地理分析模型的运行效率，实现GIS理论、方法与应用模式的跨越发展。