非线性趋势模型参数的外点最速下降算法  

An algorithm of the outer point fastest drop for the parameter of nonlinear trend model

作　　者：刘翠芝[1] 吴桐[1] 杨恒赞 LIUCuizhi;WU Tong;YANG Hengzan(School of Resources and Civil Engineering,Northeastern University,Shenyang 110819,China;College of Electrical and Electronic Engineering, Nanyang Technological University,Singapore 639798,Singapore)

机构地区：[1]东北大学资源与土木工程学院,沈阳110819 [2]南洋理工大学电机与电子工程学院,新加坡639798

出　　处：《测绘科学》2019年第1期16-20,25,共6页Science of Surveying and Mapping

摘　　要：针对非线性趋势模型参数求解问题,该文提出一种全新通用算法:外点最速下降算法。该算法依据约束最优化方法理论,使用外点法和最速下降法,将参数求解问题转化为有约束非线性规划问题。以沉降预测为例,通过对3种典型非线性趋势模型的试算,说明使用该算法所得参数建立模型预测精度普遍较高;同时选用预测平均绝对误差作为衡量精度指标,在此算法下,能在事先计算出此数值,从而可大致估计预测精度;之后分情况给出获得精度较高参数的公式,并通过分析,进一步优化选点方法。Aiming to the problem of solving nonlinear trend models,this paper proposed a new generalpurpose algorithm:an algorithm of the outer point fastest drop,this algorithm is based on the theory of constrained optimization method,using the outer point method and the fastest descent method,transformed the problem of parameter solution into constrained nonlinear programming problem.Taking the settlement prediction as an example,through the trial calculation of 3 typical nonlinear trend models,shown that the prediction accuracy of this algorithm is generally high.At the same time,the prediction mean absolute error is used as the precision index,the value can be calculated beforehand under this algorithm,and then the prediction accuracy can be estimated roughly.After that,the formula of obtaining higher precision parameters is given,and the method of selecting points is further optimized through analysis.

关 键 词：非线性趋势模型 参数求解 约束最优化问题 沉降预测 精度控制 

分 类 号：TP22[自动化与计算机技术—检测技术与自动化装置]