高精度工程控制网的二类优化设计研究

本文探讨适合于工程控制网的二类优化设计方法。文章通过对准则矩阵合理设计的讨论,构造了适合于工程控制网的二类优化设计的模型,并讨论了相应数值解算方法。     

形变监测网的二类优化设计

本文提出了一种根据灵敏度要求直接构造变形参数准则矩阵的方法。并以准则矩阵为基础,顾及可靠性、精度及费用要求,用二次规划求解形变监测网的最优观测权。最后通过一个算例说明形变监测网二类优化设计的方法。     

边角网二类优化设计

本文首先根据控制网的可靠性理论,讨论了它的设计方法;其次,在综合考虑精度、可靠性和费用准则的基础上,应用线性规划法,推导出边角网二类优化设计的通用模型;最后,通过测边网、方向网和边角同测网二类优化设计的例子,详细说明了边角网二类优化设计的一般方法。     

构造准则矩阵的逆特征值法

当用准则矩阵进行控制网二类优化设计时，主要问题之一就是如何给定合理的准则矩阵，近年来发展起来的矩阵逆特征值理论给我们提供了新的解决办法。考虑到从优化的目的出发能够事先确定部分特征信息（特征值和特征向量等等）。本文提出应用逆特征理论构造准则矩阵的新方法，并通过算例说明了整个构造过程，最后给了应用实例。     

控制网可靠性研究中若干问题的探讨

本文主要讨论了控制网的可靠性指标及与精度的相互关系。通过理论分析和数值计算,证明了目前普遍使用的观测值的多余观测分量不宜用作控制网二类设计的可靠性指标,并建议直接采用控制网可发现粗差的下界值作为可靠性指标。文中通过分析控制网二类设计中可靠性与精度准则的相互关系,获得了一些有益的结论。     

测量控制网优化设计的可靠性准则法

测量控制网优化设计与网的精度、可靠性、灵敏度以及费用等准则有关,但这些准则之间的关系又十分密切,本文提出了一种基于观测值内部可靠性指标的测量控制网模拟法优化设计新方法,介绍了其原理和特点,并用实例说明了用该方法的计算步骤和优化效益。     

测量控制网顾及多种约束条件的二类设计问题

测量控制网的二类设计(Second order Design)问题(以下简称SOD问题),在不同的目标函数和约束条件下就会导致不同的优化结果。为了更好地和实际测量工作密切结合,本文顾及了准则矩阵Q,网中部分元素之精度要求,测量作业实际需要和费用等因素,提出了在综合考虑多种因素情况下控制网的二类设计,最后给出了一算例。     

同时顾及精度和可靠性准则的控制网优化设计

本文通过对精度和可靠性两种准则在控制网优化设计中的作用特点的分析，探讨了同时顾及精度和可靠性准则的优化设计方法，并用实例对该方法进行了具体数值研究。     

工程控制网观测纲要的最优设计

讨论了工程控制网观测纲要的最优化设计,同时,还把网的可靠性作为一个重要的设计指标,用以限制观测粗差对控制网的影响。     

GPS工程控制网最优化设计的研究

本文讨论了GPS工程控制网的最优化设计问题;通过对GPS工程控制网的精度和可靠性分析,建立了应用点位精度矩阵相关性优化GPS网的数学模型;针对解算中存在的问题,提出了最短路径法寻找整数变量线性规划问题的最优解。     

大地网的二类优化设计

本文首先分析了当前大地网二类优化设计的各种解算方法,并在此基础上,利用矩阵的谱分解理论以及组成和解算法方程的思想,给出了一种新的解算方法。     

Comparison of reliability and geometrical strength criteria in geodetic networks

 The proper and optimal design and subsequent assessment of geodetic networks is an integral part of most surveying engineering projects. Optimization and design are carried out before the measurements are actually made. A geodetic network is designed and optimized in terms of high reliability and the results are compared with those obtained by the robustness analysis technique. The purpose of an optimal design is to solve for both the network configuration (first-order design) and observations accuracy (second-order design) in order to meet the desired criteria. For this purpose, an analytical method is presented for performing the first-order design, second-order design, and/or the combined design. In order to evaluate the geometrical strength of a geodetic network, the results of robustness analysis are displayed in terms of robustness in rotation, robustness in shear, and robustness in scale. Results showed that the robustness parameters were affected by redundancy numbers. The largest robustness parameters were due to the observations with minimum redundancy numbers. Received: 14 August 2000 / Accepted: 2 January 2001     

连续网模拟优化方法研究

本文根据连续网精度数字化分析的结数,建立了适用于大规模连续网优化的快速选择最优附加观测量的方法。借此,成功地将解析模拟法应用到较大规模连续网的优化设计和改进中。     

The parallel sum of matrices and its application in geodetic adjustments

Summary . It is well known that for the comparison and combination of geodetic networks their heterogeneous datum definitions are well to be considered. Various algorithms have been developed for this purpose. As an alternative concept to deal with hybrid datum problems, the operator parallel sum of matrices is introduced in this paper. To begin with, a definition is given and some basic properties are explained. To demonstrate the usefulness of the operator, two practical applications are given. The first deals with the estimation of parameters describing the deformation of two networks which are to be compared to each other. The second one treats the estimation of parameters representing the heterogeneous datum definitions of two networks which are to be merged into a hybrid network. It will be shown that – regardless of the datum definitions of the preadjusted individual networks – the parallel sum of matrices can be used to simplify the algorithms applied for the estimation of those parameters. Received 15 December 1995; Accepted 24 September 1996     

大地网三类设计的功效函数法

本文首先阐述了大地网三类设计的意义和研究进展,分析了传统三类设计理论的弊端;针对大地网三类设计中评定网的改进质量的标准问题,引入了功效函数法,并指出了这一方法从总体上给出新增观涮值对原网改进的实际贡献,为改进大地网的累积误差和总体系统误差提供了依据,而且计算十分简单。为了证明本理论的正确性,文中作了大量模拟计算。     

Second-order design of combined linear-angular geodetic networks

The paper deals with the solution of the weight problem for linear-angular networks on the base of criterion matrices. The observation plan of combined linear-angular networks consists of distances as well as of directions in any form. In particular the role of criterion matrices of completely isotropic structure for this type of two-dimensional network is discussed. Starting from an extreme network design, the results of a least-squares approximation are described analytically. In this case, the observation plan contains all geometrical point connections. Finally, the considerations are completed by giving as an example the second-order design of a control network for a dam of a water reservoir.     

控制网连接点坐标值粗差的可定位性研究

在原有测量控制网(称旧网)的基础上建立同级扩大网或低级加密网(称新网)时,新旧网之间的重合点(称连接点)坐标值粗差的检验是平差前的一个重要环节。本文将连接点坐标视为带协方差阵的观测值,采用数据探测法定位其粗差。借助于 Gauss-Markov模型下两个备选假设检验的理论,推导了连接点相关坐标观测值粗差可定位性基本公式,讨论了各类平面网中连接点坐标观测值粗差的可发现性和可区分性。