改进的灰色预测模型及其在测绘数据处理中的应用

发布时间：2018-04-03 12:39

本文选题：GM(1　切入点：1)　出处：《东华理工大学》2017年硕士论文

【摘要】：科学的预测是指在分析过去资料的基础上对未来发展变化趋势形成较为客观反映,科学的预测是预测的根本目的和主要任务。在现有的众多预测方法中,灰色预测模型以它建模需要的样本少、计算量小且适应性强等特点,已被广泛应用到各个领域。尽管灰色预测建模技术经过30多年的发展已取得了一些可喜的研究成果,但作为一门学科,其理论体系还有待于进一步丰富和完善,本文通过深入分析影响灰色预测模型精度的因素,对模型进行了改进和优化,其主要工作包括以下几个方面:(1)针对GM(1,1)模型初始条件的最优化问题,推导得出了一种新的最优初始条件求解算法,即把对最优初始条件选择问题转化为求最优的C值,经过两次运用最小二乘法求出满足误差平方和最小的C值,通过算例分析表明,文中的算法不仅有较高的精度,而且简单直观,运行效率高,更有利于程序实现。(2)针对灰色GM(1,1)模型参数估计采用最小二乘法抗差能力不强,以及原始数据含少量粗差时影响到累加生成的数据进而可能导致参数估计偏差较大,提出对原始数据直接应用具有较强稳健性的最小一乘来估计参数,将非线性的还原函数进行线性化后通过利用线性规划的思想来估计参数。实验结果表明,本文提出的算法具有较强的稳健性,更适合本身呈指数变化规律序列混入粗差时的参数估计。(3)通过分析GM(1,1)和PGM(1,1)模型在参数求解过程中构造的背景值的缺陷,对不同的时刻引入不同的加权背景值参数,同时结合灰色非线性模型和粒子权算法以进一步提高模型的预测精度,从而建立了基于粒子群算法和加权灰色组合的PSO-GM模型,通过理论分析和实例验证了新模型的可靠性和实用性。(4)构建了基于双变权缓冲算子的GM(1,1)模型,将变权弱化缓冲算子和基于加权的背景值相结合同时优化传统GM(1,1)模型,并将其应用到北斗卫星钟差短期预报,有效改善了传统GM(1,1)模型的预报精度,拓展了模型的适用范围。(5)针对传统多变量MGM(1,n)模型在参数求解中取累加值的紧邻均值作为背景值的缺陷,对相关联的每个点赋不同的权值构造背景值,并通过遗传算法寻优满足误差平方和最小的一组权值,算例结果表明优化的模型相比传统模型精度有较大的提高。
[Abstract]:Scientific prediction refers to the objective reflection of the trend of future development and change based on the analysis of past data. Scientific prediction is the basic purpose and main task of prediction.Among the existing prediction methods, the grey prediction model has been widely used in various fields because of its characteristics of less samples, less computation and better adaptability.Although more than 30 years of development of grey prediction modeling technology has made some gratifying research results, but as a discipline, its theoretical system needs to be further enriched and improved.In this paper, the factors influencing the precision of the grey prediction model are analyzed, and the model is improved and optimized. The main work includes the following aspects: 1) the optimization of the initial conditions of the model.A new algorithm for solving the optimal initial conditions is derived, that is, the problem of selecting the optimal initial conditions is transformed into the optimal C value, and the least square method is used twice to find out the C value which satisfies the minimum sum of the square error.The example analysis shows that the proposed algorithm not only has high precision, but also has simple and intuitive operation efficiency, which is more favorable to the realization of the program. (2) the least square method is not strong in the estimation of grey GM1 / 1) model parameters.And when the raw data contains a small amount of gross error, the accumulated data may lead to a large deviation in parameter estimation.The nonlinear reduction function is linearized and the parameters are estimated by using the idea of linear programming.The experimental results show that the proposed algorithm is more robust and is more suitable for parameter estimation when the exponential variation sequence is mixed with gross error. By analyzing the background values of the GM-1 and PGM1) models, the background values constructed in the process of parameter solving are analyzed.In order to improve the prediction accuracy of the model, the PSO-GM model based on particle swarm optimization and weighted grey combination is established by introducing different parameters of weighted background value at different times and combining the grey nonlinear model and particle weight algorithm.The reliability and practicability of the new model are verified by theoretical analysis and practical examples. (4) A new model based on double variable weight buffer operator is constructed, which combines the variable weight weakening buffer operator with the weighted background value and optimizes the traditional GMN 1 / 1) model at the same time.It has been applied to the short-term prediction of Beidou satellite clock difference, which has effectively improved the prediction accuracy of the traditional GM1 / 1) model.The applicability of the model is extended. (5) aiming at the defect of the traditional multivariable MGM1 / n) model taking the adjoining mean of the accumulated value as the background value in the parameter solving, we assign different weights to each associated point to construct the background value.The genetic algorithm is used to find a set of weights which satisfy the minimum sum of square error. The example shows that the precision of the optimized model is much higher than that of the traditional model.
【学位授予单位】：东华理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P20;N941.5

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