基于最小化m阶中心矩的优化方法在测量工程问题中的应用

IF 0.2 Q4 ENGINEERING, GEOLOGICAL Archives for Technical Sciences Pub Date : 2021-05-31 DOI:10.31648/TS.6555
S. Cellmer
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引用次数: 0

摘要

本文提出了一种新的优化方法——最小m阶中心矩法,它是对最小二乘法的推广。它允许将一个几何对象拟合成一组点,这样拟合后对象与点之间的最大位移比最小二乘法要小。这一特性在某些工程任务中非常有用,例如在铁路轨道或龙门轨道的重新排列中。分析了该优化方法的理论性质。讨论了计算问题。提出了适当的计算技术来克服这些问题。推导了迭代过程的详细计算算法和公式。为了说明所提出的技术的操作,给出了数值试验。对结果进行了分析,并得出了结论。
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Optimization method based on minimization m-Order central moments used in surveying engineering problems
A new optimization method presented in this work – the Least m-Order Central Moments method, is a generalization of the Least Squares method. It allows fitting a geometric object into a set of points in such a way that the maximum shift between the object and the points after fitting is smaller than in the Least Squares method. This property can be very useful in some engineering tasks, e.g. in the realignment of a railway track or gantry rails. The theoretical properties of the proposed optimization method are analyzed. The computational problems are discussed. The appropriate computational techniques are proposed to overcome these problems. The detailed computational algorithm and formulas of iterative processes have been derived. The numerical tests are presented, in order to illustrate the operation of proposed techniques. The results have been analyzed, and the conclusions were then formulated.
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来源期刊
Archives for Technical Sciences
Archives for Technical Sciences ENGINEERING, GEOLOGICAL-
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