拉格朗日插值法在预测建筑离散沉降中的应用

Application of Lagrange Interpolation Method in Prediction of Discrete Settlement of Buildings

建筑沉降预测中,灰色模型是一种比较常见的预测模型,实际应用中通常需要根据较少的数据做出长期的预测,而较少的原始序列会导致灰色模型在预测中期出现比较强烈的指数增长偏差。本文针对此问题,提出使用拉格朗日插值法外插原始序列,增长原始序列的长度,以获得更好的灰色模型预测效果。实例验证表明,使用拉格朗日插值法优化后的模型平均相对误差为21.20%,优于常规外插方法的60.15%,优于灰色模型的40.25%。

In the prediction of building settlement,the grey model is a common prediction model.In practical application,it is usually necessary to make a long-term prediction based on less data and less original series will lead to strong exponential growth deviation in the medium-term prediction of the grey model.In order to solve this problem,this paper proposes to use Lagrange interpolation method to extrapolate the original sequence,so as to increase the length of the original sequence,so as to obtain better prediction effect of grey model.The results show that the average relative error of the optimized model is 21.20%,which is better than 60.15%of the conventional extrapolation method and 40.25%of the grey model.