针对工程中大量存在的非等间距序列的建模问题，提出了非等间距GM(1, 1)幂模型。以平均相对误差绝对值最小化为目标，以模型参数之间的关系为约束，构建了一个非线性优化模型实现非等间距GM(1, 1)幂模型的参数估计。结果表明，非等间距GM(1, 1)幂模型的形式较为灵活，非等间距GM(1, 1)模型和灰色Verhulst模型均是非等间距GM(1, 1)幂模型的特殊情形，幂指数的优化有利于提高建模精度。最后通过一个工程实例验证了非等间距GM(1, 1)幂模型的有效性与实用性。

Aiming at the problem of modeling for non-equidistant sequence, the non-equidistant GM(1,1) power model was proposed. A non-linear optimization model is constructed with the objective of minimum average relative error, the constraints of relationships between parameters in order to optimize the power exponent and the background value. The results showed that the form of non equidistant GM(1,1) power model was more flexible than the traditional ones. Both non equidistant GM(1,1) model and Grey Verhulst model were the special cases of non equidistant GM(1,1) power model. Optimization of power exponent helped to improve modeling accuracy. Finally, an engineering example of non-equidistant sequence shows modeling accuracy in traditional modeling, which was significantly improved by non equidistant GM(1,1) power model.

王正新（1981—），男，江苏高邮市人，浙江财经学院讲师，博士，研究方向为灰色系统理论、优化与决策