Group Method Of Data Handling Model Research Articles

Chlorophyll-a Estimation in 149 Tropical Semi-Arid Reservoirs Using Remote Sensing Data and Six Machine Learning Methods

It is crucial to monitor algal blooms in freshwater reservoirs through an examination of chlorophyll-a (Chla) concentrations, as they indicate the trophic condition of these waterbodies. Traditional monitoring methods, however, are expensive and time-consuming. Addressing this hindrance, we conducted a comprehensive investigation using several machine learning models for Chla modeling. To this end, we used in situ collected water sample data and remote sensing data from the Sentinel-2 satellite, including spectral bands and indices, for large-scale coverage. This approach allowed us to conduct a comprehensive analysis and characterization of the Chla concentrations across 149 freshwater reservoirs in Ceará, a semi-arid region of Brazil. The implemented machine learning models included k-nearest neighbors, random forest, extreme gradient boosting, the least absolute shrinkage, and the group method of data handling (GMDH); in particular, the GMDH approach has not been previously explored in this context. The forward stepwise approach was used to determine the best subset of input parameters. Using a 70/30 split for the training and testing datasets, the best-performing model was the GMDH model, achieving an R2 of 0.91, an MAPE of 102.34%, and an RMSE of 20.4 μg/L, which were values consistent with the ones found in the literature. Nevertheless, the predicted Chla concentration values were most sensitive to the red, green, and near-infrared bands.

Modeling of ionic liquids viscosity via advanced white-box machine learning.

Ionic liquids (ILs) are more widely used within the industry than ever before, and accurate models of their physicochemical characteristics are becoming increasingly important during the process optimization. It is especially challenging to simulate the viscosity of ILs since there is no widely agreed explanation of how viscosity is determined in liquids. In this research, genetic programming (GP) and group method of data handling (GMDH) models were used as white-box machine learning approaches to predict the viscosity of pure ILs. These methods were developed based on a large open literature database of 2813 experimental viscosity values from 45 various ILs at different pressures (0.06-298.9MPa) and temperatures (253.15-573K). The models were developed based on five, six, and seven inputs, and it was found that all the models with seven inputs provided more accurate results, while the models with five and six inputs had acceptable accuracy and simpler formulas. Based on GMDH and GP proposed approaches, the suggested GMDHmodel with seven inputs gave the most exact results with an average absolute relative deviation (AARD) of 8.14% and a coefficient of determination (R2) of 0.98. The proposed techniques were compared with theoretical and empirical models available in the literature, and it was displayed that the GMDH model with seven inputs strongly outperforms the existing approaches. The leverage statistical analysis revealed that most of the experimental data were located within the applicability domains of both GMDH and GP models and were of high quality. Trend analysis also illustrated that the GMDH and GP models could follow the expected trends of viscosity with variations in pressure and temperature. In addition, the relevancy factor portrayed that the temperature had the greatest impact on the ILs viscosity. The findings of this study illustrated that the proposed models represented strong alternatives to time-consuming and costly experimental methods of ILs viscosity measurement.

Application of group method of data handling and gene expression programming to modeling molecular diffusivity of CO2 in heavy crudes

Successful enhancement of heavy oil and bitumen production using CO2-based enhanced oil recovery (EOR) techniques requires extensive knowledge about the diffusivity of CO2 in heavy crudes. In this work, two advanced correlative approaches, namely group method of data handling (GMDH) and gene expression programming (GEP), were utilized to establish simple-to-use mathematical correlations by applying a comprehensive dataset including 260 laboratory data of CO2 diffusion coefficient (DC) in heavy crudes and taking into account all the parameters affecting the accuracy of the models. Moreover, the response surface and contour plots were analyzed to obtain the desired response values and operating conditions. The GMDH correlation represented more reliable results with better statistical criteria including average absolute percentage error (AAPRE) values of 7.47%, 7.83%, and 7.54% for training, testing, and the total sets, respectively. Also, the results showed that the increase in pressure and/or temperature caused an increment in the amount of diffusivity of CO2 in heavy crudes; and the maximum amount of CO2 DC was obtained at the upper limit of these operational parameters. At a given temperature and pressure, it appears that the highest CO2 DC in heavy crudes was obtained when the CO2 mass fraction was less than 0.02. Furthermore, the Pearson and Spearman correlation coefficients were used to investigate linear and non-linear relationships between input variables and the responses of GMDH and GEP correlations. The mass fraction of CO2, temperature, pressure, and temperature_PVT had a direct relationship, and on the other hand, the viscosity and density of crudes had a reverse relationship with CO2 DC. Finally, the reliability of the data bank of CO2 DC in heavy crudes along with the high validity of GMDH and GEP correlations was verified by the leverage technique. Notably, no out-of-leverage data were identified, with only seven and five data points considered as suspected for GMDH and GEP models, respectively.

State-of-Health Estimation of Lithium-ion Batteries Based on Singular Value Decomposition and an Improved Group Method of Data Handling

Lithium-ion batteries are complex electrochemical systems, and the degradation of their state of health (SOH) is a nonlinear process. Accurate SOH estimation is critical to lithium-ion battery life and safety. This paper uses a data-driven approach to study SOH estimation of lithium-ion batteries. Firstly, this paper uses the singular value decomposition (SVD) method to extract features from the battery charging history data. Secondly, the particle swarm optimization (PSO) algorithm is used to optimize the parameter configuration of the group method of data handling (GMDH). Finally, the SOH estimation is completed using the optimized GMDH. The results show that the proposed PSO-GMDH estimation model maintains an error within 0.89% for estimating its subsequent SOH using historical data of a certain battery, and maintains an error within 0.5% for estimating the SOH of another battery of the same model using historical data of multiple batteries. At the same time, the results also show that the PSO-GMDH estimation model has higher estimation accuracy than the GMDH model without parameter optimization.

Application of the Group Method of Data Handling Network in Intermittent Time Series Data Forecasting

Intermittent data, characterized by sporadic and irregular occurrences, have successive zero values in time series, had present unique challenges for modeling and analysis. Forecasting using intermittent data is not easy to do. This paper presents an application of the Group Method of Data Handling (GMDH) in modeling and forecasting intermittent data. GMDH models excel in capturing non-linear patterns, handling missing or sparse data, and adapting to changing dynamics. By iteratively selecting the most informative variables and estimating their coefficients, GMDH constructs a hierarchical network of interconnected models that can effectively handle intermittent data. The forecasting results show that GMDH is able to follow the pattern of actual data. The mean deviation accuracy analysis shows a value of 72.22%. The findings showcase the potential of GMDH as a valuable tool in addressing the challenges associated with intermittent data and offer insights into its application across various domains.

Coefficient of permeability prediction of soils using gene expression programming

The coefficient of permeability is the most important parameter for characterizing the permeability characteristics of soil. In this study, a database of the coefficient of permeability (k) for soils was compiled firstly, including effective size (d10), mean grain size (d50), the particle diameters at the cumulative percent content of 60% (d60) and void ratio (e), which can reflect the impact of the particle size distribution characteristics. Gene expression programming (GEP), was employed to develop a predictive equation of k, which is convenient for engineering application. The GEP model was compared with eight empirical models and other artificial intelligence models (i.e., random forest (RF) and group method of data handling (GMDH)). The results show that the GEP model and RF model have the highest accuracy, followed by GMDH model and empirical models. Then, the sensitivity analysis was conducted. According to the results, k increases with increasing d10, d50 and e; the effective size d10 has the largest influence on k, followed by d50 and e, which indicates that fine particle content has the control effect on seepage and the effect of soil gradation parameters on k is greater than that of void ratio. Additionally, the SHAP and PDP analysis were conducted to investigate the feature importance and conditional expectation of each feature. The feature importance order is d10 > d50 > e > d60, and the SHAP values of d10, d50 and e increase with the increase of them, while the SHAP value of d60 is basically unchanged.

Predicting default risk bancassurance using GMDH and dce-GMDH neural network models

Purpose This study aims to develop a novel approach for predicting default risk in bancassurance, which plays a crucial role in the relationship between interest rates in banks and premium rates in insurance companies. The proposed method aims to improve default risk predictions and assist with client segmentation in the banking system. Design/methodology/approach This research introduces the group method of data handling (GMDH) technique and a diversified classifier ensemble based on GMDH (dce-GMDH) for predicting default risk. The data set comprises information from 30,000 credit card clients of a large bank in Taiwan, with the output variable being a dummy variable distinguishing between default risk (0) and non-default risk (1), whereas the input variables comprise 23 distinct features characterizing each customer. Findings The results of this study show promising outcomes, highlighting the usefulness of the proposed technique for bancassurance and client segmentation. Remarkably, the dce-GMDH model consistently outperforms the conventional GMDH model, demonstrating its superiority in predicting default risk based on various error criteria. Originality/value This study presents a unique approach to predicting default risk in bancassurance by using the GMDH and dce-GMDH neural network models. The proposed method offers a valuable contribution to the field by showcasing improved accuracy and enhanced applicability within the banking sector, offering valuable insights and potential avenues for further exploration.

Presentation of machine learning methods and multi-objective optimization of fracture indices for asphalt rubber mixtures containing wax-based warm mix additives modified by nano calcium carbonate

Warm mix asphalt (WMA) additives have been proposed to overcome the high viscosity problem of crumb rubber modified asphalt (CRMA) binders. Various additives have been used to improve the low-temperature cracking performance of asphalt mixtures, but no study has been conducted to present the optimum additive content in CRMA binders in different loading modes. Therefore, this research aims to present the optimum content of nano calcium carbonate (NCC) to improve the fracture toughness and energy of asphalt rubber mixtures containing WMA additives (slack wax (SW) and polypropylene wax (PPW)). The semi-circular bend (SCB) fracture test was applied under pure mode I, mixed mode I-II, mixed mode II-I and pure mode II loadings at subzero temperature. Machine learning methods, including multivariate regression (MVR) and artificial neural network (ANN) models of group method of data handling (GMDH) and multilayer perceptron (MLP), were used to provide the prediction models of effective stress intensity factor (Keff) and fracture energy (Gf). Finally, the multi-objective optimization of Keff and Gf was performed to obtain optimum NCC content. The results indicated that in MVR model, the outputs had a small correlation with laboratory values, so that R value of MVR was 0.8406 and 0.8011 for Keff and Gf, respectively. Also, it was revealed in MVR that NCC had the highest impact on Keff and Gf significantly. GMDH model results showed that the relationships between predicted and laboratory values of Keff and Gf are appropriately described with R value of 0.9546 and 0.9229 for Keff and Gf models, respectively. In MLP model, different layer structures of the feed-forward neural network were developed to obtain the most accurate structure. It was indicated that MLP with 4–22–1 and 3–19–1 structures had a higher accuracy for Keff and Gf prediction models with R value of 0.9951 and 0.9978, respectively. Finally, by the use of the best model relationships, the results of the multi-objective optimization indicated that 4.91% and 6.37% NCC were the design optimum contents resulting in a maximum of Keff and Gf simultaneously for SW and PPW-modified CRMA mixtures. Moreover, the optimum NCC contents in loading modes of mode mixity Me of 1, 0.8, 0.4 and 0 were 3.62%, 5.12%, 4.08% and 3.42% for SW-modified CRMA mixtures and 4.35%, 6.51%, 7.19% and 2.84% for PPW-modified CRMA mixtures, respectively.

Prediction of the thermal conductivity of rocks using group method of data handling (GMDH)

The effective thermal conductivity of rock (ETCR) is widely used in the field of geology engineering. However, the ETCR is influenced by various factors, and the determination of ETCR is difficult. This paper presents a group method of data handling (GMDH) technique to predict the ETCR. Totally 270 measurements containing four input variables (i.e., temperature T, pressure P, porosity n and density ρ) were collected. A GMDH model of rock thermal conductivity was proposed based on this database, with R2 and RMSE values of 0.940 and 0.126. In addition, several existing models are employed to compare with the GMDH model. According to the results, these models have similar change tendency. However, these existing models can only reflect the effect of temperature on the ETCR, while the GMDH model can reflect the effects of more parameters. Moreover, a sensitivity analysis was performed. The results indicate that this model can well characterize the coupling relationship between the ETCR and two main parameters, i.e., temperature and pressure. The predicted ETCR increases with the increase of pressure, while it decreases with the increase of temperature. Finally, a graphical user interface (GUI) was established for practical application.

Terrestrial water storage anomaly estimating using machine learning techniques and satellite‐based data (a case study of Lake Urmia Basin)

AbstractIn this study, the Terrestrial Water Storage Anomaly (TWSA) in the Lake Urmia Basin (LUB) was obtained by using the GRACE satellites. The whole study area was covered by 10 GRACE/GFO pixels, and the TWSA value was calculated for these 10 pixels. Examining the changing trend showed that the value of TWSA in the LUB has a decreasing trend and fluctuates from approximately −200 to +200 compared to the average value. The TWSA was modelled using the group method of data handling (GMDH) by considering six different parameters obtained from the European Centre for Medium‐Range Weather Forecasts (ECMWF) Reanalysis V5 (ERA5) and the Global Land Data Assimilation System version 2.0 (GLDAS V2.0). Finally, the best models with two to six input variables were selected. Among the models with different inputs, the GMDH Model 2, with three inputs, had the best performance compared to the other models. After choosing the best inputs in calculating the TWSA value by the GMDH, the TWSA value was also modelled by using the Adaptive Neuro‐Fuzzy Inference System (ANFIS), the Extreme Learning Machine (ELM) and the Artificial Neural Network (ANN). The results showed that GMDH not only outperformed other models but also provided some simple equations to apply in practical tasks.

A GMDH model and parametric investigation of geopolymeric recycled concrete FRP-spiral-confined members

For the sustainability of the environment, minimization of the carbon dioxide (CO2) emissions from the production of cement and resolving the issues related to the dumping of construction and demolition waste have become the most important measures. Furthermore, deep learning and numerical models have been required for the accurate predictions of the axial structural efficiency of glass fiber reinforced polymer (GFRP) reinforced geopolymeric recycled aggregate concrete (GRC) columns with synthetic fibers (GGRC columns). The present study investigated the behavior of novel GGRC columns under concentric and eccentric loads. A set of 9 circular spirals confined concrete columns (300 mm x 1200 mm) was produced. A new three-dimensional (3-D) finite element model (FEM) for capturing the mechanical efficacy of GGRC columns was put forward. A parametric study was carried out using the projected FEM to examine the impact of reinforcement of longitudinal FRP rebars (ρl), compression stress of concrete (fco′), the diameter of GGRC columns (D), Young’s modulus of FRP rebars (Ef), the height of GGRC members (H), and the ultimate tensile stress of FRP rebars (fy). The results indicated that the GGRC members presented better structural efficiency in terms of axial stress and ductility under concentric and eccentric loads. The increment in axial stress for GGRC concentric members was noticed to be 9% at a reduction of spiral spacing from 100 mm to 50 mm. The suggested FEM portrayed 1.66% and 9.13% divergence of results for axial stress and relative axial strain of the samples, correspondingly. An artificial neural network (ANN) model was projected using the Group Method of Data Handling (GMDH) based on the previous experimental database for predicting the stress of GGRC members. The advised GMDH model performed well over the dataset by involving the axial contribution of GFRP bars and the confinement efficiency of spirals and reported the highest accuracy with MAE = 195.67, RMSE = 255.41, and R2 = 0.94 as compared with the previous models.

Enhancing predictive ability of optimized group method of data handling (GMDH) method for wildfire susceptibility mapping

Wildfire is one of the most significant environmental challenges and causing damage to ecosystems, habitats, infrastructure and especially human lives. Thus, spatial assessment of fire risk is vital to reduce the impacts of wildfires. This paper introduces an effective wildfire susceptibility mapping framework by applying a group method of data handling (GMDH) with three metaheuristic methods of biogeography-based optimization (BBO), imperialist competitive algorithm (ICA), and teacher-learning-based optimization (TLBO). A total of 13 wildfire influencing factors, including elevation, slope, aspect, plan curvature, profile curvature, topographic wetness index, valley depth, wind speed, normalized difference vegetation index, rainfall, temperature, distance to roads, and distance to rivers were used in the proposed models for wildfire susceptibility mapping of Oahu Island in Hawaii, USA. The predictive performance of models was evaluated by the root mean square error (RMSE), mean squared error (MSE), and area under the receiver operating characteristic curve (AUC). The findings demonstrated that the three hybrid models outperformed the standalone GMHD in the study area. For example, in the validation phase, the models of GMDH-TLBO, GMDH-ICA, GMDH-BBO, and GMDH produced AUC values of 0.81, 0.80, 0.79, and 0.75, respectively. The MSE values for the GMDH, GMDH-ICA, GMDH-BBO, and GMDH-TLBO models were 0.048, 0.026, 0.030, and 0.020 and the RMSE values were 0.2119, 0.162, 0.17, and 0.142, respectively. Thus, the GMDH-TLBO and GMDH were the most and least effective algorithms because they had the highest and lowest predictive accuracy. Moreover, distance to road is the most effective factor for detecting wildfire-prone areas. It is followed by temperature, slope, and elevation. By localizing the input data, the methodology can be applied to other regions for wildfire susceptibility mapping, facilitating wildfire mitigation and prevention.

Development of novel optimized deep learning algorithms for wildfire modeling: A case study of Maui, Hawai‘i

To address the growing global concern regarding increased wildfire occurrences and their widespread socio-ecological impacts, cost-effective and practical approaches must be urgently identified to accurately predict the probability of wildfire incidents. The objective of this study was to develop deep learning models to estimate the likelihood of wildfire incidents and compare the predictive capability of the methods. To this end, the group method of data handling (GMDH) and convolutional neural network (CNN) algorithms were coupled with the biogeography-based optimization (BBO) and ant colony optimization (ACO) algorithms to enhance the predictive performance of the models. Overall, 1745 historical wildfires were identified in the island of Maui, Hawai‘i. Among them, 1221 events (70%) were randomly selected to generate the models, and the remaining 524 (30%) were used for validation. The frequency ratio, information gain ratio (IGR), and variance inflation factor methods were used to select the optimal number of predictor variables for model development. 13 influencing factors: elevation, aspect, slope, plan curvature, slope length, valley depth, topographic wetness index, mean annual wind speed, mean annual air temperature, mean monthly rainfall, distance to the road, distance to the river, and normalized difference vegetation index were selected to generate the proposed models and detect fire-prone areas. The IGR values indicated that the key parameters for predicting wildfire susceptibility were the distance to the road, mean annual air temperature, elevation, and slope. Finally, the area under the receiver operating characteristic curve (AUROC) was computed to verify the reliability and accuracy of the wildfire susceptibility maps. Both the optimization algorithms enhanced the performances of the GMDH and CNN models. The ACO most notably enhanced the CNN performance compared with the models (AUROCTraining=0.889 and AUROCTesting=0.885). The findings demonstrated the potential of coupled models in overcoming the limitations of individual models for mapping fire-susceptible areas and analyzing the multifactorial aspects that lead to wildfire occurrence. Overall, the proposed frameworks can be used to predict the spatio-temporal patterns of wildfire occurrence, which are of significance for land management, wildfire prevention, and mitigation of wildfire consequences.

Predicting the returns of the US real estate investment trust market: evidence from the group method of data handling neural network

PurposeThe Group Method of Data Handling (GMDH) neural network has demonstrated good performance in data mining, prediction, and optimization. Scholars have used it to forecast stock and real estate investment trust (REIT) returns in some countries and region, but not in the United States (US) REIT market. The primary goal of this study is to predict the US REIT market using GMDH and then compare its accuracy with that derived from the traditional prediction method.Design/methodology/approachTo forecast the return on the US REIT index, this study used the GMDH neural network and the generalized autoregressive conditional heteroscedasticity (GARCH) model. In this test, the training samples, testing samples, and kernel functions of the GMDH model are controlled to investigate their impact on the accuracy of the machine learning approach. Corresponding experiments were performed using the GARCH model, and the accuracies of these two approaches were compared.FindingsCompared with GARCH, GMDH’s accuracy is much higher, indicating that the machine learning approach can provide a highly accurate prediction of REIT prices. The size of the training samples and the kernel functions in the GMDH model affect the accuracy of the prediction results. In particular, the kernel function has a significant impact on prediction accuracy. The linear and linear covariance kernel functions are simple to train and yield accurate predictions, whereas the quadratic function is difficult to train. Even with small training samples, GMDH can outperform GARCH in prediction accuracy.Research limitations/implicationsAlthough GMDH shows good performance in predicting the US REIT return, it is still a black-box model, and the algorithm is difficult for financial analysts to develop and customize. The data used in this study come from the US REIT market, which is the world’s largest and most liquid market.Social implicationsThis research shows that the GMDH model outperforms the GARCH model in forecasting REIT returns. Hence, investors can use the machine learning approach to make more accurate predictions of the target REITs’ returns and thus better investment decisions. Future investors and researchers may use GMDH to forecast the performance of REITs in other markets.Originality/valueThis is the first study to apply the GMDH neural network to the US REIT market and determine the impact of the two factors on its performance. For example, this research first discusses the impact of kernel functions on the US REIT market using the GMDH neural network. It also includes short-term daily prediction returns that were not previously considered, making it a valuable reference for financial industry analysts.

A novel hybrid model based on grey wolf optimizer and group method of data handling for the prediction of monthly mean significant wave heights

Significant wave height prediction is challenging owing to the nonlinear and nonsmooth attributes of wave heights. This study presents a hybrid model coupling group method of data handling (GMDH) with grey wolf optimizer (GWO) for the prediction of significant wave heights. The datasets were assembled from three different observations, Stations 41001, 41002 and 44004 in the Atlantic; the datasets of Stations 41001 and 41002 were used for training, and those of Station 44004 were used for testing. The performance of the GWO-GMDH model was compared with four artificial intelligence models, the GMDH, gene expression programming (GEP), adaptive neuro-fuzzy inference system (ANFIS) and back propagation (BP) neural network models, and one empirical equation derived by Buckingham π-theorem. Both regression plots and statistical indices (e.g., correlation coefficient (R), root mean squared error (RMSE), mean squared error (MSE) and mean absolute percentage error (MAPE)) were adopted to evaluate the performance of the hybrid GWO-GMDH model. The MSE, RMSE, MAPE and R values were 0.041, 0.202, 7.353% and 0.953, respectively, for the training datasets and 0.031, 0.175, 7.598% and 0.941, respectively, for the testing datasets. Compared with the single GMDH model, the statistical indices of the training datasets of the hybrid GWO-GMDH model were almost the same; however, the MSE, RMSE and MAE values decreased by 24.39%, 13.37% and 7.95%, respectively, and the R value increased by 2.28% in the testing datasets. Compared with the GEP, BP, and ANFIS models and empirical equation models, the GWO-GMDH model also shows high accuracy and robustness, especially compared with empirical formulations. In addition, a graphical user interface (GUI) was developed to facilitate the application of practical engineering use.

Estimating the energy dissipation of flow passing over triangular and trapezoidal plan weirs using the GMDH model

Abstract Weirs are one of the most common hydraulic structures used in water engineering projects. In this research, a group method of data handling (GMDH) was developed to estimate the energy dissipation of the flow passing over the labyrinth weirs with triangular and trapezoidal plans. To compare the performance of this model with other types of soft computing models, a multilayer perceptron neural network (MLPNN) was developed. The dimensionless parameters derived from dimensional analysis, including the relative upstream head (ho/P), the number of cycles (Ncy), the Froude number ( Fr), and the magnification ratio (Mr) were used as input variables. The error statistical indicators of the GMDH model in the training phase were R2 = 0.913, RMSE = 0.010, and in the testing phase were R2 = 0.829, RMSE = 0.015. The error statistical indicators of the MLPNN in the training phase were R2 = 0.957, RMSE = 0.007, and in the testing phase were R2 = 0.945, RMSE = 0.009. Examining the structure of the GMDH network shows that ho/P, Ncy, and Mr play more meaningful roles in the development network.

Air Kerma Calculation in Diagnostic Medical Imaging Devices Using Group Method of Data Handling Network

The air kerma, which is the amount of energy given off by a radioactive substance, is essential for medical specialists who use radiation to diagnose cancer problems. The amount of energy that a photon has when it hits something can be described as the air kerma (the amount of energy that was deposited in the air when the photon passed through it). Radiation beam intensity is represented by this value. Hospital X-ray equipment has to account for the heel effect, which means that the borders of the picture obtain a lesser radiation dosage than the center, and that air kerma is not symmetrical. The voltage of the X-ray machine can also affect the uniformity of the radiation. This work presents a model-based approach to predict air kerma at various locations inside the radiation field of medical imaging instruments, making use of just a small number of measurements. Group Method of Data Handling (GMDH) neural networks are suggested for this purpose. Firstly, a medical X-ray tube was modeled using Monte Carlo N Particle (MCNP) code simulation algorithm. X-ray tubes and detectors make up medical X-ray CT imaging systems. An X-ray tube's electron filament, thin wire, and metal target produce a picture of the electrons' target. A small rectangular electron source modeled electron filaments. An electron source target was a thin, 19,290 kg/m3 tungsten cube in a tubular hoover chamber. The electron source-object axis of the simulation object is 20° from the vertical. For most medical X-ray imaging applications, the kerma of the air was calculated at a variety of discrete locations within the conical X-ray beam, providing an accurate data set for network training. Various locations were taken into account in the aforementioned voltages inside the radiation field as the input of the GMDH network. For diagnostic radiology applications, the trained GMDH model could determine the air kerma at any location in the X-ray field of view and for a wide range of X-ray tube voltages with a Mean Relative Error (MRE) of less than 0.25%. This study yielded the following results: (1) The heel effect is included when calculating air kerma. (2) Computing the air kerma using an artificial neural network trained with minimal data. (3) An artificial neural network quickly and reliably calculated air kerma. (4) Figuring out the air kerma for the operating voltage of medical tubes. The high accuracy of the trained neural network in determining air kerma guarantees the usability of the presented method in operational conditions.

Estimation of water's surface elevation in compound channels with converging and diverging floodplains using soft computing techniques

Abstract In this research, water's surface elevation in compound channels with converging and diverging floodplains using soft computing models including the Multi-Layer Perceptron Neural Network (MLPNN), Group Method of Data Handling (GMDH), Neuro-Fuzzy Group Method of Data Handling (NF-GMDH) and Support Vector Machine (SVM) was modeled and predicted. For this purpose, laboratory data published in this field were used. Parameters including convergence angle (with a positive sign) and divergence angle (with a negative sign), relative depth, and relative distance were used as input variables. The results showed that all the used models have appropriate performance. However, the best performance was related to the SVM model with statistical indicators R2 = 0.998 and RMSE = 0.008 in the testing stage. The use of the adaptive fuzzy approach in developing the GMDH model led to a remarkable increase in accuracy so that its statistical indicators in the testing stage reached R2 = 0.985 and RMSE = 0.203. It was found that the best performance of the activation and kernel functions in the development of the MLPNN model and the SVM is related to the sigmoid and radial tangent functions.

Evaluation of phase equilibrium conditions of clathrate hydrates in natural gas binary mixtures: Machine learning approach

Hydrate formation temperature (T) is an important parameter for any industrial process that deals with natural gas hydrates. In this study, the Group Method of Data Handling (GMDH) approach is used to predict hydrate formation T in natural gas binary mixtures. A comprehensive database containing 728 data samples is compiled from 46 published experimental works. To find the best combination of input variables, different sets of input variables were assessed. A total of seven models were developed using different sets of input variables. Compared to the correlations proposed in the literature, the developed models in this study performed better and the model developed based on input Set #7 was the most accurate: RMSE values of 1.6381 and 1.5499 for the training and testing datasets, respectively. All models also were evaluated using a blind dataset-that was not included in testing or training-to check model applicability to wider data. Similarly, all GMDH models performed excellently for the external dataset, where the developed model based on input Set #5 showed the best performance: RMSE values of 1.3482. The findings of this study contribute to our understanding of hydrate formation conditions in natural gas binary mixtures. As pure and binary mixtures of natural gas main constituents are studied, the results can be especially useful for purification and energy transport applications.

Application of advanced correlative approaches to modeling hydrogen solubility in hydrocarbon fuels

In petroleum and petrochemical refineries, having precise knowledge regarding H2 solubility in hydrocarbon fuels and feedstocks is critical. In this study, the hydrogen solubility in hydrocarbon fuels was estimated using genetic programming (GP) and group method of data handling (GMDH), two exemplary robust advanced models for generating correlation. To do this, 445 observations derived from labratory findings on hydrogen solubility in 17 different hydrocarbon fuels such as bitumen, atmospheric residue, heavy coking gas oil, heavy virgin gas oil, light virgin gas oil, straight run gas oil, shale fuel oil, dephenolated shale fuel oil, diesel, hydrogenated coal liquid, coal liquid, and coal oil, over a large interval of P- operating pressures and T-temperatures were collected. Temperature, pressure, as well as density at 20 °C, molecular weight, and weight percentage of carbon (C) and hydrogen (H) in hydrocarbon fuels, were used as input parameters in developing robust correlations. The outcomes showed the GMDH approach is more precise compared to the GP, with a root mean square error (RMSE) of 0.053302 and a determination coefficient (R2) of 0.9641. Additionally, sensitivity analysis showed that pressure, followed by temperature and H (wt%) of hydrocarbon fuels, has the greatest impact on hydrogen solubility in hydrocarbon fuels. Ultimately, the Leverage method's results suggested that the GMDH model could be relied on to predict hydrogen solubility in hydrocarbon fuels.