基于改进的变权缓冲灰色模型在沉降预测中的应用

针对灰色模型在中后期沉降预测中的精度问题，提出了单、双权幂函数弱化缓冲算子，并结合变权背景值建立改进的变权缓冲GM(1,1)模型。证明了新算子能提高光滑性、缩小级比偏差，实现对原始沉降数据的预处理。对于模型中的权值采用以还原值与原始值平均相对误差最小为目标的粒子群优化算法确定。最后，以高填方机场地表沉降数据预测为例，验证所提改进模型的有效性。结果表明：新算子能够有效弱化沉降序列受到的冲击扰动影响，结合变权背景值能显著提高灰色模型在中后期沉降预测中的精度。此外，对新算子的权值进行限定后，可得到两种不同的变权弱化缓冲算子。

Application of Improved Variable Weight Buffer Grey Model in Settlement Prediction

Aiming at the accuracy of the grey model in the middle and late subsidence prediction, a dual-weight power function weakened buffer operator is proposed, and an improved variable-weight buffer GM(1,1) model is established combined with the variable-weight background value. It is proved that the new operator can improve the smoothness, reduce the scale deviation, realize the preprocessing of the original sedimentation data, and give the condition that the reduction error does not expand. The weights in the model are determined by the particle swarm optimization algorithm with the objective of minimizing the average relative error between the restored value and the original value. Finally, an airport high-fill foundation settlement data prediction is used as an example to verify the effectiveness of the proposed improved model. The results show that the new operator can effectively weaken the impact of the subsidence sequence, and the combination of the variable weight background value can significantly improve the accuracy of the gray model in the middle and late subsidence prediction. In addition, after the weight of the new operator is limited, two different variable weight weakening buffer operators can be obtained.