灰色Verhulst拓展模型的病态性问题

Morbid property of grey extended Verhulst model

有效判定灰色模型的病态性是进行灰预测建模的关键.为了揭示灰色Verhulst拓展模型建模参数在原始序列存在微小扰动下的变化规律,以矩阵谱条件数为工具对该模型灰导数的背景值进行分类证明.结果表明,灰色Verhulst拓展模型不存在严重病态性.采用灰色Verhulst拓展模型进行预测建模,模型的解不会因系统原始数据在收集过程中存在微小误差而产生显著漂移现象.

It is essential to effectively judge the morbidity of grey model in constructing grey predictive models. Aiming to reveal the change law of modeling parameters of grey Verhulst extended model resulted from a small perturbation of primitive sequence, the spectrum condition number of matrix is taken as a tool of measuring the morbidity of this model, and the values of condition of coefficient matrix with the background value of this model in different case are analyzed. Research result shows that grey Verhulst extended model has no unusually severe morbidity. The research conclusion suggests that, in the grey prediction modeling process, while using the grey extended Verhulst model, the solution of this model will not occur significant drift for the original data series of systems exist minor errors in collecting process.