灰线性加权非等距GM(1,1)形变预测模型

结合加权非等距GM(1,1)模型与线性回归理论，构建灰线性加权非等距GM(1,1)预测模型，并给出对模型预测精度起决定性作用的灰指数v和参数m的优化方法。与加权非等距GM(1,1)模型和线性回归预测模型相比，灰线性加权非等距GM(1,1)预测模型的精度更高，预测有效时间更长，模型的稳定性更好。优化v和m后，灰线性加权非等距GM(1,1)预测模型的实用性、稳定性进一步提高。

Deformation Prediction Model of Gray Line Weighted Non-Equidistance GM(1,1)

On the basis of weighted non-equidistance GM(1,1) and line regression theories, we combined a weighted non-equidistance GM(1,1) model with line regression theory organically, and propose the gray linear weighted non-equidistance GM(1,1) model. Then the optimization method of the gray index v and the value of parameter m, which are vital to the model prediction accuracy, is given. In comparison with the weighted non-equidistance GM(1,1) and line regression models, the gray linear weighted non-equidistance GM(1,1) model has advantages, such as higher prediction accuracy, more valid prediction time, and more stable prediction ability. When v and m are optimized, the applicability and stability of the gray linear weighted non-equidistance GM(1,1) model is further improved.