ABSTRACT

In this research, the mean monthly groundwater level with a range of 3.78 m in Qoşaçay plain, Iran, is forecast. Regarding three different layers of gated recurrent unit (GRU) structures and a hybrid of variational mode decomposition with gated recurrent unit (VMD-GRU), deep learning-based neural network models are developed. As the base model for performance comparison, the general single-long short-term memory-layer network model is developed. In all models, the module of sequence-to-one is used because of the lack of meteorological variables recorded in the study area. For modeling, 216 monthly datasets of the mean monthly water table depth of 33 different monitoring piezometers in the period April 2002–March 2020 are utilized. To boost the performance of the models and reduce the overfitting problem, an algorithm tuning process using different types of hyperparameter accompanied by a trial-and-error procedure is applied. Based on performance evaluation metrics, the total learnable parameters value and especially the model grading process, the new double-GRU model coupled with multiplication layer (×) (GRU2× model) is chosen as the best model. Under the optimal hyperparameters, the GRU2× model results in an R² of 0.86, a root mean square error (RMSE) of 0.18 m, a corrected Akaike’s information criterion (AICc) of −280.75, a running time for model training of 87 s and a total grade (TG) of 6.21 in the validation stage; and the hybrid VMD-GRU model yields an RMSE of 0.16 m, an R² of 0.92, an AICc of −310.52, a running time of 185 s and a TG of 3.34.

摘要

在这项研究中，预测了伊朗 Qoşaçay 平原的月平均地下水位为 3.78 m。关于三个不同层的门控循环单元（GRU）结构和变分模式分解与门控循环单元（VMD-GRU）的混合，开发了基于深度学习的神经网络模型。作为性能比较的基础模型，开发了通用的单长短期记忆层网络模型。在所有模型中，由于缺乏研究区域记录的气象变量，都使用了序列对一的模块。为了建模，使用了 2002 年 4 月至 2020 年 3 月期间 33 个不同监测压力计的月平均地下水位深度的 216 个月度数据集。为了提高模型的性能并减少过拟合问题，应用了使用不同类型的超参数并伴随试错过程的算法调整过程。基于性能评估指标、总可学习参数值，特别是模型分级过程，选择新的双GRU模型加上乘法层（×）（GRU2×模型）作为最佳模型。在最优超参数下，GRU2× 模型产生R ²为 0.86，均方根误差 (RMSE) 为 0.18 m，校正的 Akaike 信息准则 (AICc) 为 -280.75，模型训练的运行时间为 87 秒，验证中的总成绩 (TG) 为 6.21阶段; 混合 VMD-GRU 模型的 RMSE 为 0.16 m，R ²为 0.92，AICc 为 -310.52，运行时间为 185 s，TG 为 3.34。