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Existing artificial neural networks (ANNs) have attempted to efficiently identify underlying patterns in environmental series, but their structure optimization needs a trial-and-error process or an external optimization effort. This makes ANNs time consuming and more complex to be applied in practice. To alleviate these issues, we propose a stabilized ANNs, called SANN. The SANN efficiently optimizes ANN structure via incorporation of an additional numeric parameter into every layer of the ANN. To exemplify the efficacy and efficiency of the proposed approach, we provided two practical case studies involving meteorological drought forecasting at cities of Burdur and Isparta, Türkiye. To enhance SANN forecasting accuracy, we further suggested the hybrid VMD-SANN that integrated variation mode decomposition (VMD) with SANN. To validate the new hybrid model, we compared its results with those obtained from hybrid VMD-ANN and VMD-Radial Base Function (VMD-RBF) models. The results showed superiority of the VMD-SANN to its counterparts. Regarding Nash Sutcliffe Efficiency measure, the VMD-SANN achieves accurate forecasts as high as 0.945 and 0.980 in Burdur and Isparta cities, respectively.

Accurate estimation of the longitudinal dispersion coefficient (LDC) is essential for modeling the pollution status in rivers. This research investigates the capabilities of machine-learning methods such as multi-layer perceptron (MLP), multi-layer perceptron trained with particle swarm optimization (MLP-PSO), multi-layer perceptron trained with Stochastic gradient descent deep learning (MLP-SGD) and different regressions including linear and non-linear regressions (LR and NLR) methods for determining the LDC of pollution in natural rivers and evaluates the accuracy of these methods in comparison with real measured data. Furthermore, the correlation coefficient (CC), root mean squared error (RMSE) and Willmott’s Index (WI) were implemented to evaluate the accuracies of the mentioned methods. Comparison of the results showed the superiority of the MLP-SGD model with CC of 0.923, RMSE of 281.4 and WI of 0.954, which indicates the undeniable accuracy and quality of the deep-learning model that can be used as a powerful model for LDC simulation. Also due to the acceptable performance of the PSO algorithm in the hybridization of the MLP model, the use of PSO algorithms is recommended to train machine-learning techniques for LDC estimation.

Inflatable dams are flexible hydraulic structures that are constructed on rivers and are inflated by fluids such as air or water. This research investigates the effects of influential dimensionless factors on estimating one of the critical hydraulic characteristics of inflatable dams, namely the discharge capacity. Various parameters such as the proportion of total upstream head to dam height (H1/Dh), the ratio of overflowing head to dam height (h/Dh), the ratio of discharge per unit width to its maximum value (q/qmax), the ratio of the internal pressure of the tube to its maximum value (p/pmax) and the ratio of the longitudinal coordinate placement of each element to xmax are used. A hybrid model based on the Particle Swarm Optimization (PSO) and the Genetic Algorithm (GA), PSO-GA, is proposed to improve the accuracy of the estimation by combining the advantages of both algorithms. Moreover, the performance of the model is compared with available hybrid models, including the Artificial Neural Networks (ANNs) optimized by Stochastic Gradient Descent (SGD) model (ANN-SGD) and the ANN-PSO and ANN-GA models. Finally, the performance of the algorithms is evaluated using statistical indicators such as the coefficient of determination (R2), root mean square error (RMSE), mean absolute percentage error (MAPE) and the scatter index (SI). The results show that the internal pressure plays a vital role with respect to forecasting the discharge coefficient, and omitting it degrades the accuracy by 2.12%. In comparison with other models, the proposed PSO-GA hybrid model provides the most accurate results (R2 = 0.999, MAPE = 0.04). Finally, comparing the results of the proposed PSO-GA with the benchmarked ANN-GA, ANN-PSO and ANN-SGD methods proves the superiority of the hybrid PSO-GA method.

Hydrological droughts are characterized based on their duration, severity, and magnitude. Among the most critical factors, precipitation, evapotranspiration, and runoff are essential in modeling the droughts. In this study, three indices of drought, i.e., Standardized Precipitation Index (SPI), Standardized Streamflow Index (SSI), and Standardized Precipitation Evapotranspiration Index (SPEI), are modeled using Support Vector Regression (SVR), Gene Expression Programming (GEP), and M5 model trees (MT). The results indicate that SPI delivered higher accuracy. Moreover, MT model performed better in predicting SSI by a CC of 0.8195 and a RMSE of 0.8186. Abbreviations: ANFIS: adaptive neuro-fuzzy inference system; ANN: artificial neural network; ANN: artificial neural network; BS-SVR: boosted-support Vector Regression; CC: correlation coefficient; ELM: extreme learning machine; GEP: gene Expression Programming; GP: genetic Programming; GPR: Gaussian process regression; KNN: k-nearest neighbor; LSSVM: least squares Support Vector Machine; LSSVR: least support vector regression; MAE: mean absolute error; MARS: multivariate adaptive regression splines; MLP: multilayer perceptron; MLR: multiple linear regression; MT: M5 model tree; P: precipitation; PDSI: palmer drought severity index; PET: potential evapotranspiration; RAE: relative absolute error; RMSE: root mean square error; RVM: relevance vector machine; SAR: sodium absorption index; SDR: standard deviation reduction; SPEI: standardized precipitation evapotranspiration index; SPI: standardized precipitation index; SSI: standardized streamflow index; SVM: support vector machine; SVR: support vector regression; WAANN: Wavelet-ARIMA-ANN; WANFIS: Wavelet-Adaptive Neuro-Fuzzy Inference System; WN: wavelet network