基于ELM模型的浅层地下水位埋深时空分布预测

Temporal and Spatial Distribution Prediction of Shallow Groundwater Level Based on ELM Model

摘要:

选用石家庄平原区补排因子的多种组合为输入参数，利用28眼水井的实测资料作为预测目标值，首次建立基于极限学习机（Extreme learning machine，ELM）的地下水位埋深时空分布预测模型，讨论补排因子在不同缺失情况下对模型精度的影响；利用ArcGIS分析误差空间分布趋势，并与常用的三隐层BP神经网络模型进行对比。结果表明：基于水均衡理论的ELM地下水位埋深模拟模型能够准确反映人类和自然双重影响下地下水系统的非线性关系，模型输入因子中缺失降水量或开采量的模拟结果均方根误差（RMSE）比缺失其余因子的RMSE高200倍及以上，同时模型有效系数（Ens）和决定系数（R2）进一步降低；与BP模型相比，ELM模型可使RMSE减小43.6%，误差区间降低46.4%，Ens和R2提高至0.99，且RMSE在空间相同区域上均明显呈现出ELM模型小于BP模型；ELM模型在南部高误差区的移植精度（RMSE低于1.82m/a，Ens高于0.95）高于BP模型（RMSE超过3.00m/a，Ens低于0.85）；因此，影响地下水位埋深的主导因素是降水量和开采量，且ELM模型在精度、稳定性和空间均匀性上较优，移植预测效果较好，可利用已知资料推求区域空间内其余未知水井的浅层地下水位埋深；该模型可作为水文地质参数及补排资料缺乏条件下浅层地下水位埋深预测的推荐模型。

关键词:地下水位;时空分布;神经网络;极限学习机;预测

Abstract:

In order to achieve high-precision prediction of temporal and spatial distribution of the groundwater level in shallow groundwater cones region, a model was constructed firstly based on extreme learning machine (ELM). By choosing different combination factors of groundwater recharge and discharge as the input parameters of model and observing data of 28 wells as predicted target in Shijiazhuang plain, the error of spatial distribution trend was analyzed by using ArcGIS software. The results showed that the ELM model based on the water balance theory could accurately reflect the non-linear relationship of groundwater system under the influence of human and nature activity. The root mean square error (RMSE) of model under the condition without exploitation or precipitation as input factor was two times higher than that under the condition without other factors, and the coefficient of efficiency (Ens) and coefficient of determination (R2) were further reduced. Compared with the BP model, the RMSE of ELM model was reduced by 43.6%, and the scope of error was reduced by 46.4%. Ens and R2 were improved to 0.99. The tendency of error distribution showed that it was decreased from the south and southeast to the central. The RMSE of ELM model was obviously lower than that of BP model in all the regions. The accuracy of ELM model (RMSE was less than 1.82m, Ens was higher than 0.95) was higher than that of BP model (RMSE was more than 3.00m, Ens was less than 0.85) in southern high error region. Therefore, exploitation and precipitation were the main impact factors on the groundwater dynamic in the model. Meanwhile, the stability, accuracy and space uniformity of ELM model were better than those of BP model. And the transplantation results of ELM model were more satisfactory. The model could be used to forecast groundwater level of other unknown wells based on given data. Therefore, the ELM model could be used as a recommended model for predicting groundwater level under conditions of missing hydrogeological and groundwater recharge data.

Key words:groundwater level; temporal and spatial distribution; neural network; extreme learning machine; prediction