Multivariate Drought Forecasting in Short- and Long-Term Horizons Using MSPI and Data-Driven Approaches

Summary Many methods have been developed to determine the solution gas/oil ratio (Rs), starting with experiments, followed by empirical correlations establishments, and recently with machine learning applications receiving much interest due to their ability to produce precise results compared with empirical correlations. In this paper, the group method of data handling (GMDH) and the enhanced GMDH based on discrete differential evolution (GMDH-DDE) are used for the first time to estimate the Rs and to provide a correlation to the laboratory measured Rs from bubblepoint pressure (Pb), oil API gravity (API), gas-specific gravity (γg), and reservoir temperature (T) without crude oil properties. These two methods are compared with backpropagation neural networks (BPNN). The reason for using the hybrid GMDH (GMDH-DDE) is to overcome the drawbacks of the GMDH, such as the method used to calculate neuron weights (i.e., quadratic polynomial transfer function), which seems to have inaccuracies. Also, in selecting model inputs, the GMDH tends to choose the most appropriate inputs for the model; however, the selection criteria are not straightforward and may affect the final results. Furthermore, the GMDH has a multicollinearity problem, affecting model coefficient stability and overfitting problems, etc. A total of 420 data sets from the Mpyo oil field were used, with 70% used for training and 30% used for testing. According to the findings, the GMDH-DDE outperformed both the GMDH and BPNN. In comparison with the GMDH and BPNN, the GMDH-DDE has a higher correlation coefficient (R), lower root-mean-square error (RMSE), and lower mean absolute error (MAE). During training, R, RMSE, and MAE were 0.9849, 0.090, and 0.010, respectively, and during testing, R = 0.9603, RMSE = 0.290, and MAE = 0.017. The second-best technique (GMDH) produces R, RMSE, and MAE values of 0.9611, 0.122, and 0.032 in training, and R = 0.9438, RMSE = 0.349, and MAE = 0.055 in testing. Furthermore, the GMDH-DDE used less computational time (1.32 seconds) compared with the GMDH (2.01 seconds) and BPNN (4.96 seconds), proving that the GMDH-DDE has accurate and fast convergence compared with the GMDH and BPNN. These findings show that the GMDH-DDE and GMDH can be adopted as alternative methods for predicting the Rs.

Drought is a complex and frequently occurring natural hazard in many parts of the world. Therefore, accurate drought forecasting is essential to mitigate its adverse impacts. This research has inferred the implication and the appropriateness of the extreme learning machine (ELM) algorithm for drought forecasting. For numerical evaluation, time series data of the Standardized Precipitating Temperature Index (SPTI) are used for nine meteorological stations located in various climatological zones of Pakistan. To assess the performance of ELM, this research includes parallel inferences of multilayer perceptron (MLP) and autoregressive integrated moving average (ARIMA) models. The performance of each model is assessed using root mean square error (RMSE), mean absolute error (MAE), mean absolute percent error (MAPE), Kling‐Gupta efficiency (KGE), Willmott index (WI), and Karl Pearson’s correlation coefficient. Generally, graphical results illustrated an excellent performance of the ELM algorithm over MLP and ARIMA models. For training data of SPTI‐1, ELM’s best performance has observed at Chitral station (RMSE = 0.374, KGE = 0.838, WI = 0.960, MAE = 0.272, MAPE = 259.59, R = 0.93). For SPTI‐1 at Astore station, the numerical results are (RMSE = 0.688, KGE = 0.988, WI = 0.997, MAE = 0.798, MAPE = 247.35). The overall results indicate that the ELM outperformed by producing the smallest RMSE, MAE, and MAPE values and maximum values for KGE, WI, and correlation coefficient values at almost all the selected meteorological stations for (1, 3, 6, 9, and 12) month time scales. In summary, this research endorses the use of ELM for accurate drought forecasting.

Drought is considered one of the costliest natural disasters that result in water scarcity and crop damage almost every year. Drought monitoring and forecasting are essential for the efficient management of water resources and sustainability in agriculture. However, the design of a consistent drought prediction model based on the dynamic relationship of the drought index with its antecedent values remains a challenging task. In the present research, the SVR (support vector regression) model was hybridized with two different optimization algorithms namely; Particle Swarm Optimization (PSO) and Harris Hawks Optimization (HHO) for reliable prediction of effective drought index (EDI) 1 month ahead, at different locations of Uttarakhand State of India. The inputs of the models were selected through partial autocorrelation function (PACF) analysis. The output produced by the SVR-HHO and SVR-PSO models was compared with the EDI estimated from observed data using five statistical indicators, i.e., RMSE (Root Mean Square Error), MAE (Mean Absolute Error), COC (Coefficient of Correlation), NSE (Nash-Sutcliffe Efficiency), WI (Willmott Index), and graphical inspection of radar-chart, time-variation plot, box-whisker plot, and Taylor diagram. Appraisal of results indicates that the SVR-HHO model (RMSE = 0.535-0.965, MAE = 0.363-0.622, NSE = 0.558-0.860, COC = 0.760-0.930, and WI = 0.862-0.959) outperformed the SVR-PSO model (RMSE = 0.546-0.967, MAE = 0.372-0.625, NSE = 0.556-0.855, COC = 0.758-0.929, and WI = 0.861-0.956) in predicting EDI. Visual inspection of model performances also showed a better performance of SVR-HHO compared to SVR-PSO in replicating the median, inter-quartile range, spread, and pattern of the EDI estimated from observed rainfall. The results indicate that the hybrid SVR-HHO approach can be utilized for reliable EDI predictions in the study area.

In this study, a new hybrid model integrated adaptive neuro fuzzy inference system with Firefly Optimization algorithm (ANFIS-FFA), is proposed for forecasting monthly rainfall with one-month lead time. The proposed ANFIS-FFA model is compared with standard ANFIS model, achieved using predictor-predictand data from the Pahang river catchment located in the Malaysian Peninsular. To develop the predictive models, a total of fifteen years of data were selected, split into nine years for training and six years for testing the accuracy of the proposed ANFIS-FFA model. To attain optimal models, several input combinations of antecedents’ rainfall data were used as predictor variables with sixteen different model combination considered for rainfall prediction. The performances of ANFIS-FFA models were evaluated using five statistical indices: the coefficient of determination (R 2 ), Nash-Sutcliffe efficiency (NSE), Willmott’s Index (WI), root mean square error (RMSE) and mean absolute error (MAE). The results attained show that, the ANFIS-FFA model performed better than the standard ANFIS model, with high values of R 2 , NSE and WI and low values of RMSE and MAE. In test phase, the monthly rainfall predictions using ANFIS-FFA yielded R 2 , NSE and WI of about 0.999, 0.998 and 0.999, respectively, while the RMSE and MAE values were found to be about 0.272 mm and 0.133 mm, respectively. It was also evident that the performances of the ANFIS-FFA and ANFIS models were very much governed by the input data size where the ANFIS-FFA model resulted in an increase in the value of R 2 , NSE and WI from 0.463, 0.207 and 0.548, using only one antecedent month of data as an input (t-1), to almost 0.999, 0.998 and 0.999, respectively, using five antecedent months of predictor data (t-1, t-2, t-3, t-6, t-12, t-24). We ascertain that the ANFIS-FFA is a prudent modelling approach that could be adopted for the simulation of monthly rainfall in the present study region.

With the in-depth implementation of China’s “National Strategy for Building a Strong Transportation Network,” the scale of expressway construction has continued to expand. As a result, the number of high-fill and deep-cut subgrade projects under complex geological conditions has increased significantly, leading to a surge in landslide-related issues. Consequently, accurate prediction of slope displacement is of critical importance for early warning and prevention of landslide disasters. This study proposes a hybrid prediction model, VMD-MPA-LSSVM-LSTM (VMLL), which integrates Variational Mode Decomposition (VMD), Marine Predators Algorithm (MPA), Least Squares Support Vector Machine (LSSVM), and Long Short-Term Memory (LSTM) networks. Using monitoring data from the high-fill embankment slope at Hongtuyao as the research subject, the VMLL model is employed to predict slope displacement based on small-sample data. The objective is to provide a more accurate method for early warning of slope displacement. Firstly, the original monitoring data are decomposed into trend displacement components and fluctuation displacement components using Variational Mode Decomposition (VMD). Subsequently, the trend component and the fluctuation component are predicted using Least Squares Support Vector Machine (LSSVM) and Long Short-Term Memory (LSTM) networks, respectively. Finally, the Marine Predators Algorithm (MPA) is employed to optimize the hyperparameters of the predictive models. Based on this framework, a VMLL-based slope displacement prediction model is constructed. To verify the superiority of the VMLL model, a comparative analysis was conducted against LSSVM, LSTM, and the VMD-LSSVM-LSTM models. The results demonstrate that the VMLL model achieves the highest prediction accuracy, with a Mean Absolute Percentage Error (MAPE) of 0.4022%, a Mean Absolute Error (MAE) of 0.016 mm, a Root Mean Square Error (RMSE) of 0.0206 mm, a coefficient of determination (R²) of 94.08%, and a Variance Accounted For (VAF) of 96.5%. Compared with the other three models, the VMLL model reduces the MAPE, MAE, and RMSE by 30.41–67.62%, 30.38–67.40%, and 27.32–71.00%, respectively. Meanwhile, it improves the R² and VAF by 5.95–217.51% and 0.38–11.48%, respectively. These improvements clearly demonstrate that the VMLL model outperforms the other models, indicating its significant advantage over single prediction models. Furthermore, three additional datasets were used to evaluate the model’s performance. The average values of the performance evaluation metrics for these datasets were 0.6207% (MAPE), 0.0238 mm(MAE), 0.0273 mm(RMSE), 90.33%(R²), and 96.81%(VAF), respectively. These results demonstrate the high accuracy and strong robustness of the proposed model in predicting both horizontal displacement and vertical settlement of slopes, providing a reliable methodological framework for slope stability assessment and landslide disaster early warning.

The study uses the comparison of Group Method of Data Handling (GMDH)-type neural network algorithm with Vector error correction model to predict the value of FDI on the basis of accuracy of prediction and to model the determinants of FDI in Pakistan. It was estimated in the times series data during the time period 1971-2013 and the time period 2014-2018 has been utilized to predict FDI. The Augmented Dickey-Fuller (ADF) test suggests that all variables data are of I (1) and Johansen co-integration test proved nexus of the variables FDI and its determinants in the long run. Nonetheless, the error correction-term of the vector error correction model (VECM) indicates that around 3 % of cumulative disequilibrium was expunged in every year in Pakistan. This paper compares two new methods Group Method of Data Handling (GMDH) Neural Network Algorithm and Vector Error Correction Model (VECM) in an attempt to obtain the more useful one based on accuracy of analysis when making predictions. Whereas, the effectiveness of VECM is then compared with a non parametric GMDH-like type neural network. An evaluation of forecasting model accuracies in terms of FDI was done using Root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and Diebold Mariano (DM) test. The empirical outcomes are a clear indication that Group Method of Data Handling GMDH-type of neural network algorithm did very well in comparison with the vector error correction model based on forecasting.

Literature review revealed that scour modeling using artificial intelligence (AI) lacks majorly in two aspects - one is the Input variable selection (IVS) and secondly, the relative ranking of scour models based on their performance. In this study, state-of-the-art AI algorithms, including artificial neural network (ANN), artificial neuro-fuzzy interface system (ANFIS), support vector machine (SVM), model tree (M5P), gene expression programming (GEP), and group method of data handling (GMDH) were employed to compute the Local Scour Depth (LSD) and to address identified lacunas. A total of 378 data set consisting of laboratory and field data was used for modeling. Evaluation criteria such as the index of agreement (IOA), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Skill Score (SS), Correlation (Correl), and Taylor diagram were employed to check the goodness-of-fit of the proposed models. IVS was performed using partial mutual information (PMI). The findings of the study showed that velocity (V), the diameter of the pier (b), Reynolds pier number (Rp), and particle densimetric Froude number (Frd) were highly sensitive parameters to the scour. Quantitative and qualitative results indicated that SVM performed better with RMSE (0.06), MAPE (0.04) and SS (0.9). Tayler diagram also confirmed the above findings.

Oilseeds have been the backbone of India’s agricultural economy since long. Oilseed crops play the second most important role in Indian agricultural economy, next to food grains, in terms of area and production. Oilseeds production in India has increased with time, however, the increasing demand for edible oils necessitated the imports in large quantities, leading to a substantial drain of foreign exchange. The need for addressing this deficit motivated a systematic study of the oilseeds economy to formulate appropriate strategies to bridge the demand-supply gap. In this study, an effort is made to forecast oilseeds production by using Autoregressive Integrated Moving Average (ARIMA) model, which is the most widely used model for forecasting time series. One of the main drawbacks of this model is the presumption of linearity. The Group Method of Data Handling (GMDH) model has also been applied for forecasting the oilseeds production because it contains nonlinear patterns. Both ARIMA and GMDH are mathematical models well-known for time series forecasting. The results obtained by the GMDH are compared with the results of ARIMA model. The comparison of modeling results shows that the GMDH model perform better than the ARIMA model in terms of mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). The experimental results of both models indicate that the GMDH model is a powerful tool to handle the time series data and it provides a promising technique in time series forecasting methods.

PurposeThe purpose of this paper is to use Group Method of Data Handling (GMDH)-type artificial neural network to model the affecting factors of housing price in Isfahan city housing market.Design/methodology/approachThis paper presents an accurate model based on GMDH approach to describing connection between housing price and considered affecting factors in case study of Isfahan city based on trusted data that have been collected from 1995 to 2017 for every six months. The accuracy of the model has been evaluated by mean absolute percentage error (MAPE), root mean square error (RMSE) and mean absolute error (MAE) in this case.FindingsDue to the obtained value of MAPE, RMSE and MAE and also their interpretation, accuracy of modelling the factors affecting housing price in Isfahan city housing market using GMDH-type artificial neural network that has been conducted in this paper, is acceptable.Research limitations/implicationsDue to limitation of reliable data availability about affecting factors, selected period is from 1995 to 2017. Accessing to longer periods of reliable data can improve the accuracy of the model.Originality/valueThe key point of this research is reaching to a mathematical formula that accurately shows the relationships between housing price in Isfahan city and effective factors. The simplified formula can help users to use it easily for analysing and describing the status of housing market in Isfahan city of Iran.

This article uses machine learning techniques as fuzzy and neuro-fuzzy ANFISs, to develop and compare prediction models capable of relating pregnant women’s exposure to air pollutants, such as Nitrogen Dioxide and Particulate Matter, the mother’s age, and the number of prenatal consultations to the incidence of premature birth. In the current literature, studies can be found that relate prematurity to the exposure of pregnant women to NO2, O3, and PM10; to Toluene and benzene, mainly in the window 5 to 10 days before birth; and to PM10 in the week before birth. Both models used logistic regression to quantify the effects of pollutants as a result of premature birth. Datasets from Brazil—Departamento de Informatica do Sistema Único de Saúde (DATASUS) and Companhia Ambiental do Estado de São Paulo (CETESB)—were used, covering the period from 2016 to 2018 and comprising women living in the city of São José dos Campos (SP), Brazil. In order to evaluate and compare the different techniques used, evaluation metrics were calculated, such as correlation (r), coefficient of determination (R2), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Mean Square Error (MSE), and Mean Absolute Error (MAE). These metrics are widely used in the literature due to their ability to evaluate the robustness and efficiency of prediction models. For the RMSE, MAPE, MSE, and MAE metrics, lower values indicate that prediction errors are smaller, demonstrating better model accuracy and confidence. In the case of (r) and R2, a positive and strong result indicates alignment and better performance between the real and predicted data. The neuro-fuzzy ANFIS model showed superior performance, with a correlation (r) of 0.59, R2 = 0.35, RMSE = 2.83, MAPE = 5.35%, MSE = 8.00, and MAE = 1.70, while the fuzzy model returned results of r = 0.20, R2 = 0.04, RMSE = 3.29, MSE = 10.81, MAPE = 6.67%, and MAE = 2.01. Therefore, the results from the ANFIS neuro-fuzzy system indicate greater prediction capacity and precision in relation to the fuzzy system. This superiority can be explained by integration with neural networks, allowing data learning and, consequently, more efficient modeling. In addition, the findings obtained in this study have potential for the formulation of public health policies aimed at reducing the number of premature births and promoting improvements in maternal and neonatal health.

A hybrid air quality early-warning framework: An hourly forecasting model with online sequential extreme learning machines and empirical mode decomposition algorithms

In this paper, we compare and analyze the prediction performance of existing ANFIS (Adaptive Neuro Fuzzy Inference System) models. The ANFIS model is a fusion of neural networks with learning ability, adaptability, and computational ability, and a fuzzy system with human-like thinking ability and reasoning ability. In this paper, we analyze the prediction performance of ANFIS models using different input space partitioning methods. ANFIS 1 uses SC (Subtractive Clustering), a clustering method based on the density of data, to calculate the center of the cluster by calculating potential values inversely proportional to the distances of the different inputs. ANFIS 2 uses Fuzzy C-Means (FCM) clustering, which is a clustering method based on degree of belonging to data, and classifies each data belonging to each cluster according to degree of affiliation. ANFIS 3 is a method of using Context based Fuzzy C-Means (CFCM) clustering, which is a clustering method considering characteristics of input and output space based on FCM clustering. It creates clusters for each context generated according to characteristics of output space, to classify the data. To evaluate these ANFIS models, we use short term electricity price forecasting data and Boston housing data. The prediction performance is based on the Root Mean Squared Error (RMSE) method. Experimental results show that the prediction performance of the ANFIS model is different depending on the characteristics of each data. Furthermore, we confirmed that the prediction performance of ANFIS model using CFCM clustering method is constant.

Stream-flow forecasting using extreme learning machines: A case study in a semi-arid region in Iraq

Mapping of groundwater salinization and modelling using meta-heuristic algorithms for the coastal aquifer of eastern Saudi Arabia

Assessing the accuracy of ANFIS, EEMD-GRNN, PCR, and MLR models in predicting PM2.5