#br#分数阶反向累加离散灰色模型及其应用研究

为了减小离散灰色预测模型解的扰动界,增加模型的解的稳定性,并且充分利用系统的新信息,提出了分数阶反向累加离散灰色模型。通过数学推导,给出了模型具体的计算公式,并计算了其扰动界。通过比较一阶反向累加离散灰色模型和分数阶反向累加离散灰色模型扰动界的大小,证明了分数阶反向累加离散灰色模型的优越性。最后,将其应用在某型号武器系统的储存可靠性的预测中,计算结果优于传统灰色预测模型,预测精度有了大幅度提高,从而拓展了灰色预测模型的理论研究和实际应用范围。

Fractional order reverse accumulative discrete grey model and its application

In order to reduce the perturbation bounds of the solution of discrete grey forecasting model, increase the stability of the solution of the model, and make full use of new information of the system, a fractional reverse accumulative discrete grey model is put forward.Its calculation formula is deduced and its perturbation bounds are calculated.The specific calculation formula is given by mathematical deduction, and the perturbation bounds are calculated.The superiority of the fractional order reverse accumulative discrete grey model is proved by comparing the perturbation bounds of it with the first order reverse accumulative discrete grey model.Finally, it is applied in storage reliability prediction of a certain type of weapon system, and the calculation result is better than the traditional grey prediction model.The prediction accuracy has improved dramatically.〖JP2〗The proposed model expands the scope of the theoretical research and practical application of grey forecasting model.