Gharehbaghi Amin, Ghasemlounia Redvan, Ahmadi Farshad, Mirabbasi Rasoul, Torabi Haghighi Ali
Department of Civil Engineering, Faculty of Engineering, Hasan Kalyoncu University, Şahinbey, Gaziantep, 27110, Turkey.
Department of Civil Engineering, Faculty of Engineering, Istanbul Gedik University, Istanbul, 34876, Turkey.
Sci Rep. 2025 Jun 3;15(1):19436. doi: 10.1038/s41598-025-03185-3.
Streamflow contemplates a fundamental criterion to evaluate the impact of human activities and climate changes on the hydrological cycle. In this study, a novel innovative deep neural network (DNN) structure by integrating a double Gated Recurrent Units (GRU) neural network model with a multiplication layer and meta-heuristic whale optimization algorithm (WOA) (i.e., hybrid 2GRU×-WOA model) is developed to improve the prediction accuracy and performance of mean monthly Chehel-Chai River's streamflow (CCRSF) in Iran. The Pearson's correlation coefficient (PCC) and Cosine Amplitude Sensitivity (CAS) as feature (input) selection process determine the only precipitation (P) as the most effective input variable among a list of on-site potential climate time series parameters recorded in the study area. Thanks to a well-proportioned layer network structural framework in the suggested hybrid 2GRU×-WOA model, it leads to an appropriate total learnable parameter (TLP) compared to standard individual GRU and Bi-GRU as the benchmark models developed in the comparable meta-parameters. This hybrid model under the optimal meant meta-parameters tuned i.e., coupling a state activation functions (SAF) of tanh-softsign, dropout rate (P-rate) of 0.5, numbers of hidden neurons (NHN) of 70, outperforms with an R of 0.79, NSE of 0.76, MAE of 0.21 (m/s), MBE of -0.11(m/s), and RMSE of 0.36 (m/s). Hybridizing the 2GRU× model with WOA algorithm causes to increase in the value of R by 6.8% and reduce in the value of RMSE by 20.4%. Comparatively, standard individual GRU and Bi-GRU models result in an R of 0.59 and 0.66, NSE of 0.55 and 0.6, MAE of 0.91 and 0.53 (m/s), MBE of 0.047 and - 0.06 (m/s), RMSE of 1.29 and 0.83 (m/s), respectively.
流量是评估人类活动和气候变化对水文循环影响的一个基本标准。在本研究中，通过将双门控循环单元（GRU）神经网络模型与乘法层和元启发式鲸鱼优化算法（WOA）相结合，开发了一种新颖的创新深度神经网络（DNN）结构（即混合2GRU×-WOA模型），以提高伊朗切赫勒-柴河月平均流量（CCRSF）的预测精度和性能。皮尔逊相关系数（PCC）和余弦振幅敏感性（CAS）作为特征（输入）选择过程，在研究区域记录的一系列现场潜在气候时间序列参数中，确定唯一的降水量（P）为最有效的输入变量。由于所建议的混合2GRU×-WOA模型中具有比例恰当的层网络结构框架，与作为可比元参数中开发的基准模型的标准单个GRU和双向GRU相比，它导致了合适的总可学习参数（TLP）。该混合模型在调谐的最优均值元参数下，即耦合双曲正切-软信号的状态激活函数（SAF）、0.5的辍学率（P-rate）、70个隐藏神经元（NHN），其表现优于其他模型，相关系数R为0.79，纳什效率系数NSE为0.76，平均绝对误差MAE为0.21（m/s），平均偏差误差MBE为-0.11（m/s），均方根误差RMSE为0.36（m/s）。将2GRU×模型与WOA算法杂交导致相关系数R的值增加6.8%，均方根误差RMSE的值降低20.4%。相比之下，标准单个GRU和双向GRU模型的相关系数R分别为0.59和0.66，纳什效率系数NSE分别为0.55和0.6，平均绝对误差MAE分别为0.91和0.53（m/s），平均偏差误差MBE分别为0.047和-0.06（m/s），均方根误差RMSE分别为1.29和0.83（m/s）。
