初始条件自适应优化的ANGM(1,1)模型及其应用

少数据、贫信息的非等间距序列预测建模是灰色系统理论的重要内容之一，也是现实工程应用中经常遇到的难题.本文基于自适应优化的初始条件，构建了ANGM（1，1）优化模型.首先，在对已有初始条件优化的非等间距GM（1，1）模型缺陷分析基础上，设计出新型的初始条件自适应优化方法.该方法依据1-AGO序列各时点分量的实际值构建权重分配方程，既保证每个时点信息的充分利用，又自适应调整新旧信息的权重大小.然后，根据建模序列的特征，给出时间参数求解的两个准则及其推导公式，进而构建优化模型.最后，分别利用单调和波动两种特征的实际案例数据，构建4种初始条件优化模型，结果显示本文模型预测效果最好，表明本文模型的适用性和稳定性.

ANGM(1,1) model with a self-adaptive optimized initial condition and its applications

Modelling non-equidistant sequences having limited data and insufficient information is one of the important contents of the Grey System Theory, as well as one of the tough problems in engineering applications. To this end, a self-adaptive non-equidistant GM(1,1), abbreviated as ANGM(1,1), is proposed based on the optimized initial condition. Initially, the drawbacks of previous optimized initial conditions are comprehensively analyzed, and the new method of optimizing the initial condition is designed. Specifically, the optimized initial condition has a weight-function that is designed upon the real values of each data point of 1-AGO sequence. This optimized method can not only make full use of information concealed in the 1-AGO series, but also can adjust the weight values of each component based on the new information priority. Subsequently, in order to accurately estimate the time parameter in the time response function, two principles and their derived formula are put forward, which is crucial to the establishment of the ANGM(1,1) model. Lastly, to verify the efficacy of the proposed model, two empirical studies characterized by monotone decreasing and fluctuate sequences are conducted by building four competing models. Empirical results illustrate that the ANGM(1,1) model is superior to other three competitors as this model obtains the highest precision. Thus, the proposed model has good adaptability and stability.