Applications of graph theory to gross error detection for GPS geodetic control networks

This paper describes a broad perspective of the application of graph theory to establishment of GPS control networks whereby the GPS network is considered as a connected and directed graph with three components. In this algorithm the gross error detection is undertaken through loops of different spanning trees using the “Loop Law” in which the individual components ΔX, ΔY and ΔZ sum up to zero. If the sum of the respective vector components ΩX, ΩY and ΩZ in a loop is not zero and if the error is beyond the tolerable limit (ε>ω), it indicates the existence of gross errors in one of the baselines in the loop and therefore the baseline must be removed or re-observed. After successful screening of errors by graph theory, network adjustment can be carried out. In this paper, the GPS data from the control network established as refence system for the HP Dam at Baishan county in Liaoning province is presented to illustrate the algorithm.     

Double-epoch algorithm in rapid positioning using single frequency GPS receivers

A new algorithm, called as Double-Epoch Algorithm (DEA) is proposed in GPS rapid positioning using two epoch single frequency phase data in this paper. Firstly, the structure characteristic of the normal matrix in GPS rapid positioning is analyzed. Then, in the light of the characteristic, based on TIK-HONOV regularization theorem, a new regularizer is designed to mitigate the ill-condition of the normal matrix. The accurate float ambiguity solutions and their MSEM (Mean Squared Error Matrix) are obtained, using two epoch single frequency phase data. Combined with LAMBDA method, DEA can fix the integer ambiguities correctly and quickly using MSEM instead of the covariance matrix of the ambiguities. Compared with the traditional methods, DEA can improve the efficiency obviously in rapid positioning. So, the new algorithm has an extensive application outlook in deformation monitoring, pseudokinematic relative positioning and attitude determination, etc.     

Applications of Lodrigues matrix in 3D coordinate transformation

Three transformation models (Bursa-Wolf, Molodensky, and WTUSM) are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms: the traditional ? rotation angles θ, φ, ψ are substituted with a,b,c which are three respective values in the anti-symmetrical or Lodrigues matrix; ? directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ? a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.     

On the relation between excess hydraulic head and flow in a conduit imbedded within a porous matrix

This article provides a partial answer to the question “What is the relation between excess hydraulic head and volume flux of water in a conduit within a porous matrix?”, focusing on the case that the forcing is steady. The conduit is modelled as a horizontal circular cylinder, imbedded within a porous matrix of rectangular cross section, having constant head prescribed on the sidewalls and being confined top and bottom. Laminar flow in the matrix is assumed to obey Darcy's law, while turbulent flow in the conduit is quantified using the Darcy–Weisbach equation. Analysis of the latter equation shows that the length scale of variations in the direction of the conduit is large compared with the scale of lateral and vertical variations. This permits separation of the full three-dimensional non-linear problem into a two-dimensional linear problem for head within the matrix and a one-dimensional non-linear problem for head within the conduit. Analytic solutions are obtained for the distribution of head in the matrix and in a conduit of either infinite or finite length. In both cases, the volume flux of water is proportional to the excess head to the 2/3 power, the conduit radius to the 5/3 power, the matrix permeability to the 1/3 power and gravity to the 1/3 power. The scale of variation of head along the conduit is proportional to the excess head to the ?1/3 power, the conduit radius to the 5/3 power, the matrix permeability to the ?2/3 power and gravity to the 1/3 power.     

加速遗传算法在预应力连续箱梁桥有限元模型修正中的应用

针对预应力混凝土连续箱梁桥的通扬运河大桥,建立其有限元模型.基于评价模型修正效果的频率指标与振型相关系数指标、柔度矩阵指标和挠度指标,定义三个目标函数,利用环境激励的试验模态参数,通过实数编码加速遗传算法对有限元模型进行了修正.相对于基于频率指标与振型相关系数指标定义的目标函数,基于柔度矩阵指标或挠度指标定义的目标函数修正的有限元模型,能同时较准确地反映其动态和静态特性,也能实现其试验模态振型较精确的质量归一化.     

水环境规划中的层次分析模型研究

水环境规划是现代环境规划的重要内容,而层析分析法是水环境规划的有效手段之一。根据层次分析法的原理,建立层次分析决策模型,并结合实际,确定出环境治理指标的优先原则。     

首钢京唐公司基坑护坡及降水问题研究

在对位于曹妃甸地区的首钢京唐公司深基坑护坡工程进行全面总结的基础上,进行了多因素矩阵法基坑史护方法分类,对该地区护坡降水提出了几点建议,对于指导下一步曹妃甸地区护坡降水工作具有重要的意义。     

一种基于加权非负矩阵分解的矿产预测方法

提出了一种新颖的基于加权非负矩阵分解的矿产预测方法,运用非负矩阵分解的非负性、降维性及稀疏性对多维矿产数据进行处理。通过R型聚类分析,按照变量相似度将变量聚合成群,对相关性高的元素的聚类结果进行加权非负矩阵分解得到基向量,进行回归分析验证基向量用于矿产预测的有效性。最后,以广东省新寮岽铜多金属矿区数据为例,通过基向量预测圈定异常,绘制矿产预测分布图,得到明显的异常区域,取得了好的预测结果。     

模糊数学在地下水水质评价中的应用——以盘锦曙光地区为例

采用模糊数学的方法对盘锦市曙光地区2011年的地下水环境进行综合评价,建立包括总硬度,总矿化度,铁离子,锰离子等多个污染因子的因子集,评价集,隶属函数和权重集等模糊集合。结果表明,曙光地区地下水污染在近几年表现出一定程度降低,主要污染物来源于石油污染、海水入侵和农业灌溉,所得结果基本符合当地实际情况,说明了模糊综合评价的合理性和可靠性,对于曙光地区地下水环境综合评价具有实际意义。     

全国农村人均住房面积的空间自相关分析

利用2006年全国各省农村居民人均住房面积统计数据,基于空间自相关方法从空间尺度分析其空间分布特征。首先建立空间邻近网络和邻接矩阵,通过Moran′I自相关指数分析空间关联性,为确定农村人均住房面积的分布存在空间相关性而非随机性,采用蒙特卡罗方法进行多次模拟证明,并利用2011年统计数据进行实际验证。实验分析,2006与2011年农村人均住房面积Moran′I指数分别为0．5566和0．5983,表明空间聚集特点明显,基本可以分为东部发达地区、中部和西部三种聚类,并且两年之间聚集现象有显著变化。