基于模糊理论的可能性线性规划数据处理研究

Research on data processing based on possible linear programming of fuzzy sets

针对现实中测量数据的不确定性不完全满足概率论中的“随机变量”定义,不一定服从随机分布,用经典平差方法处理数据显得不够严密的问题,本文基于模糊理论,以模糊数为研究对象,选取常见的三角、余弦及抛物线模糊数,分别构建基于高斯-马尔柯夫模型(G-Mmodel)的可能性线性规划模型。运用MATLAB优化工具箱里linprog函数进行编程,以水准网测量数据为例进行模糊解算,并与经典最小二乘估计结果进行比较、分析。结果表明:可能性线性规划的结果与经典平差理论结果基本一致,模糊数选取的不同对参数估值、观测值估值的影响不大,Δx最大均不超过2.2mm,Δh最大均不超过3.0mm。该方法经过实例验证是可行、合理的,并且利用抛物线模糊数的可能性线性规划模型解算时效果最佳。

Aimed at the problems that the uncertainty of the surveying data in reality does not completely match the definition of "random variable"in probability theory and does not necessarily follow the random distribution and is not strict by using classical data adjustment,this paper takes the fuzzy number as the research object based on the fuzzy theory and chooses the common fuzzy numbers such as triangle,cosine and parabola. The possible linear programming models based on G-M model are established individually. Then programming based on the linprog function in MATLAB tool box is used for fuzzy calculation to leveling net data,and results are compared and analyzed with classical least squares estimation. The results show that the results of possible linear programming are basically consistent with those of classical adjustment theory,and the fuzzy numbers selected differently have little effect on parameters estimation and observation estimation. The maximum Δx is not greater than 2.2 mm and that of Δh is not greater than 3.0 mm. The method is feasible and rational through case verification,and the possible linear programming model with parabolic fuzzy numbers is the best solution.