高速铁路CPⅢ高程控制网条件方程的建立

Establishment of condition equations for vertical control network in high-speed railway

针对高速铁路CPⅢ高程控制网条件方程列立时易出现的多样性、冗余性和效率低等问题,提出了一种建立条件方程的方法:基于图论将控制网视为连通图,采用广度优先搜索(BFS)获取生成树、余树和父节点矩阵,根据余树枝节点、联测水准点至根点的路径分别构建闭合环、附合路线,并建立对应的条件方程,通过有限次相加或相减运算,即可得到最简形条件方程。实例分析结果表明:该方法列立的条件方程具有唯一性、最简形,且耗时少,有着较高的实用价值。

Aiming at the shortcomings of the multiformity,redundancy and inefficiency in establishing conditional equations of high-speed railway CPⅢ vertical control network,a novel method is proposed in this paper.Firstly,the control network was regarded as a connected graph,the spanning tree,cotree and predecessor matrix were obtained via BFS;Secondly,all of the closed loops and annexed leveling lines were found according to the paths from the cotree vertexes and known elevation points to the root,and the corresponding condition equations were respectively established;Finally,the simplest form of conditional equations could be obtained by finite addition or subtraction among the equations.A case study was given and the results show that：the method mentioned above could establish the unique and the simplest conditional equations in less time,and has more practical value.