灰色多变量GM(1,N)幂模型及其应用

针对多变量少数据的系统建模问题，提出了灰色多变量GM（1，N）幂模型及其派生模型GM（1，N，x^（1））幂模型，给出了其参数估计算式和近似时间响应式，在此基础上，分两种情况讨论了模型的参数优化方法，并通过数值模拟和应用实例验证了新模型的有效性. 结果表明：传统的GM（1，N）模型是GM（1，N）幂模型的特殊形式，GM（1，N）幂模型能够更好地描述系统特征行为序列与其影响因素序列的非线性关系，从而有效地提高传统灰色多变量系统建模的精度.

Grey multivariable power model GM(1,N) and its application

As to the multivariable system modeling problem with less data, the multivariable grey power model GM(1,N) and its derived model GM(1,N,x⁽¹⁾) power model are proposed. The parameters estimation algorithm and approximate time response function are then presented in the form of analytical solutions. On this basis, the parameter optimization methods are discussed in two different cases. The effectiveness of the new models is verified through numerical simulation and an application example. The results show that: the traditional GM(1,N) model is a special form of the GM(1,N) power model. The GM(1,N) power model can better describe the nonlinear relations between the system behaviors and their influencing factors, thereby effectively improve the accuracy of the multivariable grey system modeling.