融合自忆性原理的优化GM(1,1)幂模型构建及应用

Construction and application of optimized GM(1,1)power model incorporating self-memory principle

针对因发展变化受众多因素影响而具有饱和增长趋势或单峰特性的原始波动序列,为了提高预测精度,以灰色GM(1,1)幂模型为基础,构建了自忆性原理与优化GM(1,1)幂模型的耦合预测模型,用动力系统自忆性原理来克服传统灰色模型对初值比较敏感的弱点。结果表明,新构建模型能够充分利用系统的多个历史时次资料,模拟和预测精度都高于传统优化GM(1,1)幂模型,进一步拓展了灰色模型的应用范围。最后,以我国高中升学率的数据为例验证了所构建模型的优越性和有效性。

As for the fluctuating sequences characterized by saturated condition or single-peak,whose de-velopment and variation are subject to multi-faceted factors,the coupling prediction model combining the self-memory principle and the optimized GM（1,1 ）power model has been constructed based on the grey GM（1,1 ） power model in order to improve prediction accuracy.The traditional grey model’s weakness as being sensitive to the initial value can been overcomed by the self-memory principle of dynamic system.The results indicate that the newly-established model can take full advantage of the systematic multi-time historical data.It extends the grey model’s application span,which possesses higher accuracy of simulation and forecast than the traditional op-timized GM（1,1 ）power model.Finally,the superiority and effectiveness of this proposed model have been proved by the case of Chinese senior high school students’enrolment rate into higher education institutions.