线性时变参数非等间距GM(1,1)幂模型及其应用  

Linear Time-varying Parameter Non-equidistant GM(1,1) Power Model and Its Application

作　　者：罗友洪 陈友军[1] LUO You-hong;CHEN You-jun(School of Mathematics and Information,China West Normal University,Nanchong 637002,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637002

出　　处：《系统工程》2021年第5期152-158,共7页Systems Engineering

基　　金：西华师范大学英才科研基金资助项目(17YC370);西华师范大学教学改革与研究重点项目(jgxmzd1824)。

摘　　要：针对非线性系统内小样本非等间距数据序列建模、以及建模最后需要对时间响应式还原的问题,建立线性时变参数非等间距GM(1,1)幂模型,推导模型时间响应式,并基于积分原理,使用原始数据序列的1-γ次幂生成序列与其对应的一次累减生成序列构建与模型白化方程参数相匹配的灰色微分方程,研究了模型最优初始条件与非线性参数γ的求解方法。案例分析结果验证了线性时变参数非等间距GM(1,1)幂模型的可行性与有效性。Aiming at the modeling of small sample non-linear spaced data sequences in nonlinear systems, and the problem of time response restoration at the end of modeling, a linear time-varying parameter non-equal spaced GM(1,1) power model is constructed, derive the model time response, based on the principle of integration, using the power generation sequence of the original data sequence and its corresponding one-time accumulative generation sequence to construct a gray differential equation matching the parameters of the model whitening equation, and the optimal initial conditions of the model and the non-linear parameters γ solution method are studied. The results of the case analysis verifies the feasibility and validity of the GM(1,1) power model with linear time-varying parameters.

关 键 词：非等间距GM(1 1)幂模型 线性时变参数 初始条件 

分 类 号：N941[自然科学总论—系统科学]