A Hybrid VMD-SVM Model for Practical Streamflow Prediction Using an Innovative Input Selection Framework

Some previous studies have proved that prediction models using traditional overall decomposition sampling (ODS) strategy are unreasonable because the subseries obtained by the ODS strategy contain future information to be predicted. It is, therefore, necessary to put forward a new sampling strategy to fix this defect and also to improve the accuracy and reliability of decomposition-based models. In this paper, a stepwise decomposition sampling (SDS) strategy according to the practical prediction process is introduced. Moreover, an innovative input selection framework is proposed to build a strong decomposition-based monthly streamflow prediction model, in which sunspots and atmospheric circulation anomaly factors are employed as candidate input variables to enhance the prediction accuracy of monthly streamflow in addition to regular inputs such as precipitation and evaporation. Meanwhile, the partial correlation algorithm is employed to select optimal input variables from candidate input variables including precipitation, evaporation, sunspots, and atmospheric circulation anomaly factors. Four basins of the U.S. MOPEX project with various climate characteristics were selected as a case study. Results indicate that: (1) adding teleconnection factors into candidate input variables helps enhance the prediction accuracy of the support vector machine (SVM) model in predicting streamflow; (2) the innovative input selection framework helps to improve the prediction capacity of models whose candidate input variables interact with each other compared with traditional selection strategy; (3) the SDS strategy can effectively prevent future information from being included into input variables, which is an appropriate substitute of the ODS strategy in developing prediction models; (4) as for monthly streamflow, the hybrid variable model decomposition-support vector machine (VMD-SVM) models, using an innovative input selection framework and the SDS strategy, perform better than those which have not adopted this framework in all study areas. Generally, the findings of this study showed that the hybrid VMD-SVM model combining the SDS strategy and innovative input selection framework is a useful and powerful tool for practical hydrological prediction work in the context of climate change.

     

Middle- and Long-Term Streamflow Forecasting and Uncertainty Analysis Using Lasso-DBN-Bootstrap Model

Middle-term and long-term streamflow forecasting is of great significance for water resources planning and management, cascade reservoirs optimal operation, agriculture and hydro-power generation. In this work, a framework was proposed which integrates least absolute shrinkage and selection operator (lasso), DBN and bootstrap to improve the performance and the stability of streamflow forecasting with the lead-time of one month. Lasso helps to screen the appropriate predictors for the DBN model, and the DBN model simulates the complex relationship between the selection predictors and streamflow, and then bootstrap with the DBN model contributes to evaluate the uncertainty. The Three-River Headwaters Region (TRHR) was taken as a case study. The results indicated that lasso-DBN-bootstrap model produced significantly more accurate forecasting results than the other three models and provides reliable information on the forecasting uncertainty, which will be valuable for water resources management and planning.

     

基于人工神经网络的日径流预测

给出了用人工神经网络(ANN)对 三峡宜昌站的日径流预测模型建模的过程，对ANN输入变量的选择和个数的确定以及隐藏层 、输出层单元数的确定等关键技术问题进行了探讨。所建立的基于ANN的预测模型可以进行 提前7 d的日径流预测，预测结果令人满意。     

Monthly Streamflow Forecasting Using Convolutional Neural Network

Monthly streamflow forecasting is vital for managing water resources. Recently, numerous studies have explored and evidenced the potential of artificial intelligence (AI) models in hydrological forecasting. In this study, the feasibility of the convolutional neural network (CNN), a deep learning method, is explored for monthly streamflow forecasting. CNN can automatically extract critical features from numerous inputs with its convolution–pooling mechanism, which is a distinct advantage compared with other AI models. Hydrological and large-scale atmospheric circulation variables, including rainfall, streamflow, and atmospheric circulation factors are used to establish models and forecast streamflow for Huanren Reservoir and Xiangjiaba Hydropower Station, China. The artificial neural network (ANN) and extreme learning machine (ELM) with inputs identified based on cross-correlation and mutual information analyses are established for comparative analyses. The performances of these models are assessed with several statistical metrics and graphical evaluation methods. The results show that CNN outperforms ANN and ELM in all statistical measures. Moreover, CNN shows better stability in forecasting accuracy.

     

An Ensemble Modeling Approach to Forecast Daily Reservoir Inflow Using Bidirectional Long- and Short-Term Memory (Bi-LSTM), Variational Mode Decomposition (VMD), and Energy Entropy Method

Daily inflow forecasts provide important decision support for the operations and management of reservoirs. Accurate and reliable forecasting plays an important role in the optimal management of water resources. Numerous studies have shown that decomposition integration models have good prediction capacity. Considering the nonlinearity and unsteady state of daily incoming flow data, a hybrid model of adaptive variational mode decomposition (VMD) and bidirectional long- and short-term memory (Bi-LSTM) based on energy entropy was developed for daily inflow forecast. The model was analyzed using the mean absolute error (MAE), the root means square error (RMSE), Nash–Sutcliffe efficiency coefficient (NSE), and correlation coefficient (r). A historical daily inflow series of the Baozhusi Hydropower Station, China, is investigated by the proposed VMD-BiLSTM with hybrid models. For comparison, BP, GRNN, ELMAN, SVR, LSTM, Bi-LSTM, EMD-LSTM, and VMD-LSTM, were adopted and analyzed for evaluation and analyzed. We found that the proposed model, with MAE?=?38.965, RMSE?=?64.783, and NSE?=?95.7%, was superior to the other models. Therefore, the hybrid model is robust and efficient for forecasting highly nonstationary and nonlinear streamflow. It can be used as the preferred data-driven tool to predict the daily inflow flow, which can ensure the safe operation of hydropower stations in reservoirs. As an interdisciplinary field spanning both machine learning and hydrology, daily inflow forecasting can become an important breakthrough in the application of deep learning to hydrology.

     

Long Term Streamflow Forecasting Using a Hybrid Entropy Model

In this paper, the development and evaluation of an entropy based hybrid data driven model coupled with input selection approach and wavelet transformation is investigated for long-term streamflow forecasting with 10 years lead time. To develop and test the models, data including 45 years of monthly streamflow time series from Taleghan basin, located in northwest of Tehran, are employed. For this purpose, first the performance of a maximum entropy forecasting model is evaluated. To boost the accuracy, an auto-correlation method with %95 confidence levels was carried out to determine the optimum order of the entropy model. Nevertheless, the basic entropy model, as expected, was only able to reach Nash-Sutcliffe efficiency (NSE) index of 0.35 during the test period. On the other hand, data driven models such as artificial neural networks (ANN) have shown to yield good accuracy in modeling complicated and nonlinear systems. Thus, to improve the performance of the maximum entropy model, an entropy-based hybrid model using evolutionary ANN (ENN) was proposed for further investigation. The proposed model with seasonality index substantially improved the test NSE to 0.51 and provided more accurate results than the basic entropy model. Moreover, when wavelet transform was applied to preprocess the input data, the model shows a slight improvement (NSE?=?0.54).     

A self-tuning ANN model for simulation and forecasting of surface flows

Artificial neural networks (ANN) are applicable for and forecasting without the need to calculate complex nonlinear functions. This paper evaluates the effectiveness of temperature, evapotranspiration, precipitation and inflow factors, and the lag time of those factors, as variables for simulating and forecasting of runoff. The genetic algorithm (GA) is coupled with ANN to determine the optimal set of variables for streamflow forecasting. The minimization of the total mean square error (MSE) is considered as the objective function of the ANN-GA method in this paper. Our results show the effectiveness of the ANN-GA for simulating and forecasting runoff with consistent accuracy compared with using pure ANN for runoff simulation and forecasting.     

A Novel Hybrid Decompose-Ensemble Strategy with a VMD-BPNN Approach for Daily Streamflow Estimating

Streamflow estimation is highly significant for water resource management. In this work, we improve the accuracy and stability of streamflow estimation through a novel hybrid decompose-ensemble model that employs variational mode decomposition (VMD) and back-propagation neural networks (BPNN). First, the latest decomposition algorithm, namely, VMD, was used to extract multiscale features that were subsequently learned and ensembled by the BPNN model to obtain the final estimate streamflow results. The historical daily streamflow series of Laoyukou and Wushan hydrological stations in China were analysed by VMD-BPNN, by a single GBRT and BPNN model, ensemble empirical mode decomposition (EEMD) models. The results confirmed that the VMD outperformed a single-estimation model without any decomposition and EEMD-based models; moreover, ensemble estimations using the BPNN model development technique were consistently better than a general summation method. The VMD-BPNN model’s estimation performance was superior to that of five other models at the Wushan station (GBRT, BPNN, EEMD-BPNN-SUM, VMD-BPNN-SUM, and EEMD-BPNN) using evaluation criteria of the root-mean-square error (RMSE?=?2.62 m³/s), the Nash–Sutcliffe efficiency coefficient (NSE?=?0. 9792) and the mean absolute error (MAE?=?1.38 m³/s). The proposed model also had a better performance in estimating higher-magnitude flows with a low criterion for MAE. Therefore, the hybrid VMD-BPNN model could be applied as a promising approach for short-term streamflow estimating.

     

Multivariable Time Series Forecasting for Urban Water Demand Based on Temporal Convolutional Network Combining Random Forest Feature Selection and Discrete Wavelet Transform

Urban water demand forecasting is crucial to reduce the waste of water resources and environmental protection. However, the non-stationarity and non-linearity of the water demand series under the influence of multivariate makes water demand prediction one of the long-standing challenges. This paper proposes a new hybrid forecasting model for urban water demand forecasting, which includes temporal convolution neural network (TCN), discrete wavelet transform (DWT) and random forest (RF). In order to improve the model’s forecasting abilities, the RF method is used to rank the factors and remove the less important factors. The dimension of raw data is reduced to improve calculating efficiency and accuracy. Then, the original water demand series is decomposed into different characteristic sub-series of multiple variables with better-behavior by DWT to weaken the fluctuation of original series. At the core of the proposed model, TCN is utilized to establish appropriate prediction models. Finally, to test and validate the proposed model, a real-world multivariate dataset from a water plant in Suzhou, China, is used for comparison experiments with the most recent state-of-the-art models. The results show that the mean absolute percentage error (MAPE) of the proposed model is 1.22% which is smaller than the other benchmark models. The proposed model indicates the only 2.2% of the prediction results have a relative error of more than 5%. It shows that the reliable results of the proposed model can be a superior tool for urban water demand forecasting.

     

Monthly Streamflow Forecasting Using ELM-IPSO Based on Phase Space Reconstruction

We have developed a hybrid model that integrates chaos theory and an extreme learning machine with optimal parameters selected using an improved particle swarm optimization (ELM-IPSO) for monthly runoff analysis and prediction. Monthly streamflow data covering a period of 55 years from Daiying hydrological station in the Chaohe River basin in northern China were used for the study. The Lyapunov exponent, the correlation dimension method, and the nonlinear prediction method were used to characterize the streamflow data. With the time series of the reconstructed phase space matrix as input variables, an improved particle swarm optimization was used to improve the performance of the extreme learning machine. Finally, the optimal chaotic ensemble learning model for monthly streamflow prediction was obtained. The accuracy of the predictions of the streamflow series (linear correlation coefficient of about 0.89 and efficiency coefficient of about 0.78) indicate the validity of our approach for predicting streamflow dynamics. The developed method had a higher prediction accuracy compared with an auto-regression method, an artificial neural network, an extreme learning machine with genetic algorithm and with PSO algorithm, suggesting that ELM-IPSO is an efficient method for monthly streamflow prediction.

     

Improving Annual Streamflow Prediction by Extracting Information from High-frequency Components of Streamflow

Annual streamflow prediction is of great significance to the sustainable utilization of water resources, and predicting it accurately is challenging due to changes in streamflow have strong nonlinearity and uncertainty. To improve the prediction accuracy of annual streamflow, this study proposes a new hybrid prediction model based on extracting information from high-frequency components of streamflow. In the proposed model, the original streamflow data is decomposed by ensemble empirical mode decomposition (EEMD) into several intrinsic mode functions (IMFs) with different frequencies. Then, the dominant component and residual component are identified from the high-frequency components IMF1 and IMF2 using singular spectrum analysis (SSA), and the residual components are accumulated as a new component. Finally, all the components, including the new component that is not noise, are modelled by support vector machine (SVM), and the SVM is optimized by grey wolf optimizer (GWO). To analyse and verify the proposed model, the annual streamflow data are collected from the Liyuan River and Taolai River in the Heihe River Basin, and six models, autoregressive integrated moving average (ARIMA), cross validation (CV)-SVM, GWO-SVM, EEMD-ARIMA, EEMD-GWO-SVM and modified EEMD-GWO-SVM are considered as comparison models. The results indicate that the prediction performance of the proposed model is obviously better than that of other reference models, and extracting valuable information from high-frequency components can effectively improve annual streamflow prediction. Thus, the high-frequency components contained in the original streamflow series have an important impact on obtaining accurate streamflow prediction, and the proposed model makes full use of the high-frequency components and provides a reliable method for streamflow prediction.

     

Daily Runoff Forecasting Using a Hybrid Model Based on Variational Mode Decomposition and Deep Neural Networks

Accurate and reliable runoff forecasting plays an increasingly important role in the optimal management of water resources. To improve the prediction accuracy, a hybrid model based on variational mode decomposition (VMD) and deep neural networks (DNN), referred to as VMD-DNN, is proposed to perform daily runoff forecasting. First, VMD is applied to decompose the original runoff series into multiple intrinsic mode functions (IMFs), each with a relatively local frequency range. Second, predicted models of decomposed IMFs are established by learning the deep feature values of the DNN. Finally, the ensemble forecasting result is formulated by summing the prediction sub-results of the modelled IMFs. The proposed model is demonstrated using daily runoff series data from the Zhangjiashan Hydrological Station in Jing River, China. To fully illustrate the feasibility and superiority of this approach, the VMD-DNN hybrid model was compared with EMD-DNN, EEMD-DNN, and multi-scale feature extraction -based VMD-DNN, EMD-DNN and EEMD-DNN. The results reveal that the proposed hybrid VMD-DNN model produces the best performance based on the Nash-Sutcliffe efficiency (NSE?=?0.95), root mean square error (RMSE?=?9.92) and mean absolute error (MAE?=?3.82) values. Thus the proposed hybrid VMD-DNN model is a promising new method for daily runoff forecasting.

     

Comparison of performance of statistical models in forecasting monthly streamflow of Kizil River,China

This paper presents the application of autoregressive integrated moving average(ARIMA),seasonal ARIMA(SARIMA),and Jordan-Elman artificial neural networks(ANN)models in forecasting the monthly streamflow of the Kizil River in Xinjiang,China.Two different types of monthly streamflow data(original and deseasonalized data)were used to develop time series and Jordan-Elman ANN models using previous flow conditions as predictors.The one-month-ahead forecasting performances of all models for the testing period(1998-2005)were compared using the average monthly flow data from the Kalabeili gaging station on the Kizil River.The Jordan-Elman ANN models,using previous flow conditions as inputs,resulted in no significant improvement over time series models in one-month-ahead forecasting.The results suggest that the simple time series models(ARIMA and SARIMA)can be used in one-month-ahead streamflow forecasting at the study site with a simple and explicit model structure and a model performance similar to the Jordan-Elman ANN models.     

Cause-driven Streamflow Forecasting Framework Based on Linear Correlation Reconstruction and Long Short-term Memory

Reasonable runoff forecasting is the foundation of water resource management. However, the impact of environmental change on streamflow was not fully revealed due to the lack of enough streamflow features in many previous studies. In contrast, too many features also could lead cause undesired problems, including unstable model, interpretation difficulty, overfitting, high computational complexity, and high memory complexity. To address the above problems, this study proposes a cause-driven runoff forecasting framework based on linear-correlated reconstruction and machine learning model and refers to this framework as CSLM. We use variance inflation factor (VIF), pairwise linear correlation (PLC) reconstruction, and long short-term memory (LSTM) to realize this framework, referred to as VIF-PLC-LSTM. Four experiments were conducted to demonstrate the accuracy and efficiency of the proposed framework and its VIF-PLC-LSTM realization. Four experiments compare 1) different filter thresholds of driving factors, 2) different combination prediction features, 3) different reconstruction methods of linear-correlated features, and 4) different CSLM models. Experimental results on daily streamflow data from the Tangnaihai station at the Yellow River source and the Yangxian station at the Han River show that 1) data filtering has the risk of feature information loss, 2) when the streamflow, ERA5L, and meteorology data are used as inputs at the same time, the performance of the model is superior to the combination of other prediction features; the prediction effect of different prediction features, 3) the reconstruction of linear-correlated features is not only better than dimension reduction but also can improve the forecasting performance for streamflow prediction, and 4) among different CSLM models, LSTM is superior to other models.

     

Prediction of flood abnormalities for improved public safety using a modified adaptive neuro-fuzzy inference system.

It is widely accepted that an efficient flood alarm system may significantly improve public safety and mitigate economical damages caused by inundations. In this paper, a modified adaptive neuro-fuzzy system is proposed to modify the traditional neuro-fuzzy model. This new method employs a rule-correction based algorithm to replace the error back propagation algorithm that is employed by the traditional neuro-fuzzy method in backward pass calculation. The final value obtained during the backward pass calculation using the rule-correction algorithm is then considered as a mapping function of the learning mechanism of the modified neuro-fuzzy system. Effectiveness of the proposed identification technique is demonstrated through a simulation study on the flood series of the Citarum River in Indonesia. The first four-year data (1987 to 1990) was used for model training/calibration, while the other remaining data (1991 to 2002) was used for testing the model. The number of antecedent flows that should be included in the input variables was determined by two statistical methods, i.e. autocorrelation and partial autocorrelation between the variables. Performance accuracy of the model was evaluated in terms of two statistical indices, i.e. mean average percentage error and root mean square error. The algorithm was developed in a decision support system environment in order to enable users to process the data. The decision support system is found to be useful due to its interactive nature, flexibility in approach, and evolving graphical features, and can be adopted for any similar situation to predict the streamflow. The main data processing includes gauging station selection, input generation, lead-time selection/generation, and length of prediction. This program enables users to process the flood data, to train/test the model using various input options, and to visualize results. The program code consists of a set of files, which can be modified as well to match other purposes. This program may also serve as a tool for real-time flood monitoring and process control. The results indicate that the modified neuro-fuzzy model applied to the flood prediction seems to have reached encouraging results for the river basin under examination. The comparison of the modified neuro-fuzzy predictions with the observed data was satisfactory, where the error resulted from the testing period was varied between 2.632% and 5.560%. Thus, this program may also serve as a tool for real-time flood monitoring and process control.     

Streamflow Forecasting Using Four Wavelet Transformation Combinations Approaches with Data-Driven Models: A Comparative Study

This study investigates the use of wavelet transformation (WT) as preprocessing tool in data-driven models (DDMs) for forecasting streamflow 7 days ahead. WT used are Continuous wavelet transformation (CWT), discrete wavelet transformation (DWT), and a new proposed combination of CWT and DWT, namely discrete continuous wavelet transformation (DCWT). In addition to these three different WTs, the single DDMs were used also to create four different schematic layouts. The DDMs applied were artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), and support vector machines (SVM). The lagged rainfall, temperature, and streamflow were incorporated as inputs into the WT-DDMs. It was found that CWT improved the forecasting accuracy of models which only included the rainfall and temperature but not the streamflow. Moreover, DWT improved the performance dramatically for the models with streamflow. Notably, DWT layout outperformed CWT layout in general while CWT layouts resulted in higher improvement to the models with rainfall and temperature only. The proposed DCWT in which CWT applied on the rainfall and temperature variables and DWT applied on the streamflow improved the forecasting ability in several models combinations when ANN was applied. Nevertheless, improvement in the forecasting accuracy was deteriorated in those with SVM while no improvement was observed with ANFIS. ANN outperformed both ANFIS and SVM while ANFIS performed better than SVM.     

Exploring the Regional Variance using ARMA-GARCH Models

Recently some generalized autoregressive conditional heteroskedasticity (GARCH) models are proposed and applied to various hydrologic variables to capture and remove the ARCH effect, which has been observed frequently in the residuals from linear autoregressive moving average (ARMA) models fitted to hydrologic time series. As a nonlinear phenomenon of variance behavior, the ARCH effect reveals partially nonstationarity and nonlinearity of hydrological processes. This paper deals with the variation of a river basin using the ARMA-GARCH error model, which combines an ARMA model for modelling the mean behavior and a GARCH model for modelling the variance behavior of the residuals from the ARMA model. Based on the heteroscedasticity of hydrological variable series, the time-varying regional variance is proposed to check the variation of a river basin for the first time. As a study case, the method is applied to four deseasonalized daily discharge series from the middle reach of Yangtze River, China. Through the analyses of the conditional variance in different streamflow series, it is concluded that: (1) The ARCH effect exists in all the studied series which means the stream processes is nonstationary in terms of the variance; (2) The variations of time-varying variances are similar for the series from adjacent hydrological stations, and the similarity degree increases from upstream to downstream; (3) The regional variance is time-varying and can be used for further regional research.     

Short-term River streamflow modeling using Ensemble-based additive learner approach

Accurate streamflow (Q_t) prediction can provide critical information for urban hydrological management strategies such as flood mitigation, long-term water resources management, land use planning and agricultural and irrigation operations. Since the mid-20th century, Artificial Intelligence (AI) models have been used in a wide range of engineering and scientific fields, and their application has increased in the last few years. In this study, the predictive capabilities of the reduced error pruning tree (REPT) model, used both as a standalone model and within five ensemble-approaches, were evaluated to predict streamflow in the Kurkursar basin in Iran. The ensemble-approaches combined the REPT model with the bootstrap aggregation (BA), random committee (RC), random subspace (RS), additive regression (AR) and disjoint aggregating (DA) (i.e. BA-REPT, RC-REPT, RS-REPT, AR-REPT and DA-REPT). The models were developed using 15 years of daily rainfall and streamflow data for the period 23 September 1997 to 22 September 2012. A set of eight different input scenarios was constructed using different combinations of the input variables to find the most effective scenario based on the linear correlation coefficient. A comprehensive suite of graphical (time-variation graph, scatter-plot, violin plot and Taylor diagram) and quantitative metrics (root mean square error (RMSE), mean absolute error (MAE), Nash-Sutcliff efficiency (NSE), Percent of BIAS (PBIAS) and the ratio of RMSE to the standard deviation of observation (RSR)) was applied to evaluate the prediction accuracy of the six models developed. The outcomes indicated that all models performed well but the AR-REPT outperformed all the other models by rendering lower errors and higher precision across a number of statistical measures. The use of the BA, RC, RS, AR and DA models enhanced the performance of the standalone REPT model by about 26.82%, 18.91%, 7.69%, 28.99% and 28.05% respectively.     

Monthly rainfall forecasting by a hybrid neural network of discrete wavelet transformation and deep learning

Rainfall forecast is critical to the management and allocation of water resources. Deep learning is used to predict rainfall time series with high temporal and spatial variability. Discrete wavelet transform (DWT), long-short term memory (LSTM) and dilated causal convolutional neural network (DCCNN) is integrated to build a hybrid model (DWT-CLSTM-DCCNN). Two methods of sample construction are used to train DWT-CLSTM-DCCNN and their effects on the model performance are analyzed. LSTM and DCCNN are built as benchmark models. The forecasting performance of DWT-CLSTM-DCCNN on monthly rainfall data from four major cities in China is evaluated. The results of DWT-CLSTM-DCCNN are compared with those of benchmark models in terms of the mean absolute error (MAE), root mean squared error (RMSE) and Nash-Sutcliffe efficiency (NSE) as well as the forecasting curves. The results show that DWT-CLSTM-DCCNN outperforms the benchmark models in model accuracy and peak and mutational rainfall capture.

     

Using Optimized Deep Learning to Predict Daily Streamflow: A Comparison to Common Machine Learning Algorithms

From a watershed management perspective, streamflow need to be predicted accurately using simple, reliable, and cost-effective tools. Present study demonstrates the first applications of a novel optimized deep-learning algorithm of a convolutional neural network (CNN) using BAT metaheuristic algorithm (i.e., CNN-BAT). Using the prediction powers of 4 well-known algorithms as benchmarks – multilayer perceptron (MLP-BAT), adaptive neuro-fuzzy inference system (ANFIS-BAT), support vector regression (SVR-BAT) and random forest (RF-BAT), the CNN-BAT model is tested for daily streamflow (Q_t) prediction in the Korkorsar catchment in northern Iran. Fifteen years of daily rainfall (R_t) and streamflow data from 1997 to 2012 were collected and used for model development and evaluation. The dataset was divided into two groups for building and testing models. The correlation coefficient (r) between rainfall and streamflow with and without antecedent events (i.e., R_t-1, R_t-2, etc.) (as the input variables) and Q_t (as the output variable) served as the basis for constructing different input scenarios. Several quantitative and visually-based evaluation metrics were used to validate and compare the model’s performance. The results indicate that R_t was the most effective input variable on Q_t prediction and the integration of R_t, R_t-1, and Q_t-1 was the optimal input combination. The evaluation metrics show that the CNN-BAT algorithm outperforms the other algorithms. The Friedman and Wilcoxon signed-rank test indicates that the prediction power of CNN-BAT algorithm is significantly/statistically different from the other developed algorithms.