本文選題：GM(1　切入點：1)　出處：《東華理工大學(xué)》2017年碩士論文

【摘要】：科學(xué)的預(yù)測是指在分析過去資料的基礎(chǔ)上對未來發(fā)展變化趨勢形成較為客觀反映,科學(xué)的預(yù)測是預(yù)測的根本目的和主要任務(wù)。在現(xiàn)有的眾多預(yù)測方法中,灰色預(yù)測模型以它建模需要的樣本少、計算量小且適應(yīng)性強等特點,已被廣泛應(yīng)用到各個領(lǐng)域。盡管灰色預(yù)測建模技術(shù)經(jīng)過30多年的發(fā)展已取得了一些可喜的研究成果,但作為一門學(xué)科,其理論體系還有待于進一步豐富和完善,本文通過深入分析影響灰色預(yù)測模型精度的因素,對模型進行了改進和優(yōu)化,其主要工作包括以下幾個方面:(1)針對GM(1,1)模型初始條件的最優(yōu)化問題,推導(dǎo)得出了一種新的最優(yōu)初始條件求解算法,即把對最優(yōu)初始條件選擇問題轉(zhuǎn)化為求最優(yōu)的C值,經(jīng)過兩次運用最小二乘法求出滿足誤差平方和最小的C值,通過算例分析表明,文中的算法不僅有較高的精度,而且簡單直觀,運行效率高,更有利于程序?qū)崿F(xiàn)。(2)針對灰色GM(1,1)模型參數(shù)估計采用最小二乘法抗差能力不強,以及原始數(shù)據(jù)含少量粗差時影響到累加生成的數(shù)據(jù)進而可能導(dǎo)致參數(shù)估計偏差較大,提出對原始數(shù)據(jù)直接應(yīng)用具有較強穩(wěn)健性的最小一乘來估計參數(shù),將非線性的還原函數(shù)進行線性化后通過利用線性規(guī)劃的思想來估計參數(shù)。實驗結(jié)果表明,本文提出的算法具有較強的穩(wěn)健性,更適合本身呈指數(shù)變化規(guī)律序列混入粗差時的參數(shù)估計。(3)通過分析GM(1,1)和PGM(1,1)模型在參數(shù)求解過程中構(gòu)造的背景值的缺陷,對不同的時刻引入不同的加權(quán)背景值參數(shù),同時結(jié)合灰色非線性模型和粒子權(quán)算法以進一步提高模型的預(yù)測精度,從而建立了基于粒子群算法和加權(quán)灰色組合的PSO-GM模型,通過理論分析和實例驗證了新模型的可靠性和實用性。(4)構(gòu)建了基于雙變權(quán)緩沖算子的GM(1,1)模型,將變權(quán)弱化緩沖算子和基于加權(quán)的背景值相結(jié)合同時優(yōu)化傳統(tǒng)GM(1,1)模型,并將其應(yīng)用到北斗衛(wèi)星鐘差短期預(yù)報,有效改善了傳統(tǒng)GM(1,1)模型的預(yù)報精度,拓展了模型的適用范圍。(5)針對傳統(tǒng)多變量MGM(1,n)模型在參數(shù)求解中取累加值的緊鄰均值作為背景值的缺陷,對相關(guān)聯(lián)的每個點賦不同的權(quán)值構(gòu)造背景值,并通過遺傳算法尋優(yōu)滿足誤差平方和最小的一組權(quán)值,算例結(jié)果表明優(yōu)化的模型相比傳統(tǒng)模型精度有較大的提高。
[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.
【學(xué)位授予單位】：東華理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：P20;N941.5

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