最大熵模型结合遗传算法解算DEM插值权系数
发布时间：2019-01-01 07:34
【摘要】：针对传统格网DEM插值数学模型在解算权系数时存在负权现象的问题,提出了解算DEM插值权系数的最大熵模型算法。首先,以熵函数作为目标函数,以参考点数据的0、1、2阶统计矩作为约束条件,并增设非负约束条件,通过最大化熵值来求解格网DEM插值的非负权系数;其次,利用罚函数法,将有约束问题转化为无约束问题,并结合遗传算法的全局最优化特性进行优化解算。在MATLAB平台编程验证算法的正确性、准确性,并与杨赤中法、二次规划法进行了比较。对比显示:最大熵法解得权系数大小比例与点位关系相适应,且其估值精度优于杨赤中法、二次规划法。
[Abstract]:In order to solve the problem of negative weight in the traditional DEM interpolation model of grid, a maximum entropy model algorithm is proposed to solve the weight coefficient of DEM interpolation. Firstly, the entropy function is taken as the objective function, the statistical moment of order 0 / 1 / 2 of the reference point data is taken as the constraint condition, and the non-negative constraint condition is added to solve the non-negative weight coefficient of the DEM interpolation in grid by maximizing the entropy value. Secondly, the penalty function method is used to transform the constrained problem into an unconstrained problem, and the global optimization characteristic of genetic algorithm is used to solve the optimization problem. The correctness and accuracy of the algorithm are verified by programming on MATLAB platform, and are compared with Yang Chi's method and quadratic programming method. The comparison shows that the maximum entropy method adapts to the relation of point position and the ratio of solving weight coefficient, and its estimation accuracy is better than that of Yang Chi's method and quadratic programming method.
【作者单位】： 桂林理工大学广西空间信息与测绘重点实验室;
【基金】：国家自然科学基金项目(41161072) 广西空间信息与测绘重点实验室资助课题(桂科能1207115-08)
【分类号】：P208
本文编号：2397205
[Abstract]:In order to solve the problem of negative weight in the traditional DEM interpolation model of grid, a maximum entropy model algorithm is proposed to solve the weight coefficient of DEM interpolation. Firstly, the entropy function is taken as the objective function, the statistical moment of order 0 / 1 / 2 of the reference point data is taken as the constraint condition, and the non-negative constraint condition is added to solve the non-negative weight coefficient of the DEM interpolation in grid by maximizing the entropy value. Secondly, the penalty function method is used to transform the constrained problem into an unconstrained problem, and the global optimization characteristic of genetic algorithm is used to solve the optimization problem. The correctness and accuracy of the algorithm are verified by programming on MATLAB platform, and are compared with Yang Chi's method and quadratic programming method. The comparison shows that the maximum entropy method adapts to the relation of point position and the ratio of solving weight coefficient, and its estimation accuracy is better than that of Yang Chi's method and quadratic programming method.
【作者单位】： 桂林理工大学广西空间信息与测绘重点实验室;
【基金】：国家自然科学基金项目(41161072) 广西空间信息与测绘重点实验室资助课题(桂科能1207115-08)
【分类号】：P208
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