基于精细积分法的无偏非齐次灰色模型构建
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作者:
作者单位:

1.上海第二工业大学;2.上海交通大学

作者简介:

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中图分类号:

N941

基金项目:

国家自然科学基金项目(面上项目,重点项目,重大项目)


An unbiased non-homogeneous grey model based on high precise direct integration method
Author:
Affiliation:

1.Shanghai Polytechnic University;2.Shanghai Jiao Tong University

Fund Project:

The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)

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    摘要:

    传统无偏灰色模型的参数估计和模拟都是通过白化方程的离散时间响应函数求相应的估计值和模拟值. 基于精细积分法,提出了一种无需求离散时间响应函数的无偏非齐次灰色模型.该模型通过引入新变量,将白化方程转化为矩阵微分方程,利用指数矩阵求得递推关系,进而推导参数无偏估计公式,并采用精细积分法直接计算灰色模型的模拟(预测)值,减少舍入误差,提高计算精度.通过严格非齐次指数序列、近似非齐次指数序列、单调序列及汽车保有量的预测等验证了该模型的有效性和实用性,提高了拟合(预测)精度.

    Abstract:

    It is a traditional way to establish parameter estimation and simulation of unbiased grey models by the discrete time response function of whiten differential equation. A novel unbiased grey model based on high precise direct integration method is proposed without using the discrete time response function. The recurrence relation can be deduced by exponential matrix of the matrix differential equation,written by introducing some new variables, and the unbiased parameters can be derived. Then the simulated value is calculated by the high precise direct integration method, that can reduce rounding errors and improve precision. The validity and utility of the proposed model is proved by rigorous non-homogenous exponential sequence, approximate non-homogenous sequence, monotone sequences and the practical example of car ownership, and it can improve the precision of simulation and prediction.

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历史
  • 收稿日期:2021-05-06
  • 最后修改日期:2021-08-31
  • 录用日期:2021-09-10
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