Radial Basis Function Artificial Neural Network Model Research Articles

Using radial basis artificial neural networks to predict radiation hazard indices in geological materials.

The estimation of exposures to humans from the various sources of radiation is important. Radiation hazard indices are computed using procedures described in the literature for evaluating the combined effects of the activity concentrations of primordial radionuclides, namely, 238U, 232Th, and 40K. The computed indices are then compared to the allowed limits defined by International Radiation Protection Organizations to determine any radiation hazard associated with the geological materials. In this paper, four distinct radial basis function artificial neural network (RBF-ANN) models were developed to predict radiation hazard indices, namely, external gamma dose rates, annual effective dose, radium equivalent activity, and external hazard index. To make RBF-ANN models, 348 different geological materials' gamma spectrometry data were acquired from the literature. Radiation hazards indices predicted from each RBF-ANN model were compared to the radiation hazards calculated using gamma spectrum analysis. The predicted hazard indices values of each RBF-ANN model were found to precisely align with the calculated values. To validate the accuracy and the adaptability of each RBF-ANN model, statistical tests (determination coefficient (R2), relative absolute error (RAE), root mean square error (RMSE), Nash-Sutcliffe Efficiency (NSE)), and significance tests (F-test and Student's t-test) were performed to analyze the relationship between calculated and predicted hazard indices. Low RAE and RMSE values as well as high R2, NSE, and p-values greater than 0.95, 0.71, and 0.05, respectively, were found for RBF-ANN models. The statistical tests' results show that all RBF-ANN models created exhibit precise performance, indicating their applicability and efficiency in forecasting the radiation hazard indices of geological materials. All the RBF-ANN models can be used to predict radiation hazard indices of geological materials quite efficiently, according to the performance level attained.

Comparison and error evaluation of Arrhenius model and typical machine learning algorithms for high-temperature flow stress prediction of GH3536 superalloy

In this work, the Arrhenius model and four typical machine learning (ML) algorithms including random forest (RF), support vector machine (SVM), back propagation artificial neural network (BP-ANN) and radial basis function artificial neural network (RBF-ANN) were used to forecast the high-temperature flow stress of GH3536 superalloy. The prediction accuracy order is RBF＞ BP＞SVM＞Arrhenius model＞RF. The accuracy of SVM, BP and RBF algorithms is significantly higher than that of Arrhenius model, and the error distribution range is much smaller than that of Arrhenius model and RF. For all ML algorithms, the error distributions of test and training set are basically similar. The RBF-ANN model presents extremely excellent prediction performance, the correlation coefficient R2/ root mean square error (RMSE)/ average absolute relative error (AARE) of reaches 0.9998/0.63 MPa/0.3%. Except RF, the prediction performance of test set is basically equivalent to that of training set.

Machine Learning Approaches to Estimate Flow Rate of Drip Irrigation Emitter Based on Structure Parameters and Pressure

The agricultural water-saving irrigation systems need to be adapted to local conditions, and irrigation emitters with different flow rates need to be designed to meet actual needs. In this study, machine learning approaches were used to predict the flow rate of the labyrinth emitters. The structural parameters of the emitter [number of channel units (N), channel unit length (L), channel width (W), tooth height (H) and channel depth (D)] and working pressure (P) were considered as independent variables. The applied machine learning models included k-nearest neighbor (KNN), multi-layer perceptron (MLP), support vector machine (SVM) and radial basis function artificial neural network (RBF-ANN). The accuracy of the machine learning model was evaluated by the mean square error (MSE) and coefficient of determination (R 2). The results show that the MSE and R2 of the RBF-ANN model were higher than the corresponding parameters of the other three models, indicating the RBF-ANN model can predict the flow rate of the labyrinth emitter more accurately. The research provides a reference for the rapid design of emitters with different flow rate. It is helpful to realize the automation of agricultural irrigation, and then realize the construction of a smart agricultural irrigation system.

Predicting the mortality risk of acute respiratory distress syndrome: radial basis function artificial neural network model versus logistic regression model.

To predict the mortality of acute respiratory distress syndrome (ARDS) by using a radial basis function (RBF) artificial neural network (ANN) model. This study included 217 patients who were admitted between June 2013 and November 2019. The RBF ANN model and logistic regression (LR) model were based on twelve factors related to ARDS. Statistical indexes were used to determine the value of the prediction in the two models. The sensitivity, specificity and accuracy of the RBF ANN model to predict mortality were 83.6%, 88.5% and 82.5%, respectively. Significant differences were found between the RBF ANN and LR models (P < 0.05). When the RBF ANN model was used to identify ARDS, the area under the ROC curve was 0.854 ± 0.029. LDH, organ failure, SP-D and PaO2/FiO2 were the most important independent variables. The RBF ANN model was more likely to predict the mortality of ARDS than the LR model. In addition, it can extract informative risk factors for ARDS.

An artificial neural network modeling approach for short and long fatigue crack propagation

Fatigue crack growth-based damage modeling approaches have received great interest due to its critical importance in the industry. However, a substantial deficiency of an explicit fatigue damage model to quantify the accurate fatigue crack growth behavior remains due to the complex fatigue crack growth behavior in different length scales. This complexity arises from the fact that fatigue crack growth (FCG) in different length scales depends on many damage controlling parameters. Machine learning-based fatigue damage modeling approaches have received noticeable attention for fatigue crack growth analysis due to their abilities to account for numerous damage parameters simultaneously. In the presented paper, a radial basis function artificial neural network (RBF-ANN) model has been developed to predict the FCG behavior, including the short and long crack regimes. The presented RBF-ANN model has been trained and verified by experimental data sets of Ti-6Al-4V titanium alloy, 2024-T3 and 7075-T6 aluminium alloys. The predictions showed that the RBF-ANN model has a good interpolation capability to predict the nonlinearity of both short and long crack growth behavior. However, the model shows poor extrapolation capability for accurate short crack growth predictions for cases that there are limited data sets in hand. The model effectiveness greatly depends on sufficient available input data.

Application of RBF-ANN in prediction of natural gas density in different operational conditions

The degree of accuracy in prediction of different processes of gas engineering is extensively dependent on gas properties. One of the dominant properties which has straight effects on calculation and performance of different parts of gas industries is natural gas density. Due to this fact, in this paper, radial basis function artificial neural network (RBF-ANN) was used as novel approach to estimate gas density in terms of molecular weight, critical pressure and critical temperature of gas, pressure and temperature. To prepare and validate RBF-ANN model, a large and reliable experimental data bank was gathered from literature. A comprehensive analysis which include statistical and different graphical analysis were done to evaluate the performance. The coefficients of determination (R2) were determined as 0.99995 and 0.99993 for training and testing phases respectively. The comparisons illustrate that the RBF-ANN has great potential in prediction of natural gas density at different operational conditions.

Thermoelectric Transport Modeling Based on Neural Computation

Analytical and neural network models for the thermoelectric transport in Bi2Te3 are presented with non-parabolic band effects’ consideration. The analytical model is newly formulated by using the Boltzmann transport equation, and the artificial neural network (ANN) models are employed for the computational integration of the thermoelectric coefficients. In order to incorporate the realistic band structures in Bi2 Te 3 materials, the integrand of the thermoelectric coefficients is simulated by using both the integration of ANN and the radial basis function ANN (RBF-ANN). It is found that the RBF-ANN model has a good performance for predicting the thermoelectric transport.

A comparative research of different ensemble surrogate models based on set pair analysis for the DNAPL-contaminated aquifer remediation strategy optimization

Surrogate-based simulation-optimization technique is an effective approach for optimizing the surfactant enhanced aquifer remediation (SEAR) strategy for clearing DNAPLs. The performance of the surrogate model, which is used to replace the simulation model for the aim of reducing computation burden, is the key of corresponding researches. However, previous researches are generally based on a stand-alone surrogate model, and rarely make efforts to improve the approximation accuracy of the surrogate model to the simulation model sufficiently by combining various methods. In this regard, we present set pair analysis (SPA) as a new method to build ensemble surrogate (ES) model, and conducted a comparative research to select a better ES modeling pattern for the SEAR strategy optimization problems. Surrogate models were developed using radial basis function artificial neural network (RBFANN), support vector regression (SVR), and Kriging. One ES model is assembling RBFANN model, SVR model, and Kriging model using set pair weights according their performance, and the other is assembling several Kriging (the best surrogate modeling method of three) models built with different training sample datasets. Finally, an optimization model, in which the ES model was embedded, was established to obtain the optimal remediation strategy. The results showed the residuals of the outputs between the best ES model and simulation model for 100 testing samples were lower than 1.5%. Using an ES model instead of the simulation model was critical for considerably reducing the computation time of simulation-optimization process and maintaining high computation accuracy simultaneously.

Measurement-based frequency dynamic response estimation using geometric template matching and recurrent artificial neural network

Understanding power system dynamics after an event occurs is essential for the purpose of online stability assessment and control applications. Wide area measurement systems (WAMS) based on synchrophasors make power system dynamics visible to system operators, delivering an accurate picture of overall operating conditions. However, in actual field implementations, some measurements can be inaccessible for various reasons, e.g., most notably communication failure. To reconstruct these inaccessible measurements, in this paper, the radial basis function artificial neural network (RBF-ANN) is used to estimate the system dynamics. In order to find the best input features of the RBF-ANN model, geometric template matching (GeTeM) and quality-threshold (QT) clustering are employed from the time series analysis to compute the similarity of frequency dynamic responses in different locations of the power system. The proposed method is tested and verified on the Eastern Interconnection (EI) transmission system in the United States. The results obtained indicate that the proposed approach provides a compact and efficient RBF-ANN model that accurately estimates the inaccessible frequency dynamic responses under different operating conditions and with fewer inputs.

QSPR study on normal boiling point of acyclic oxygen containing organic compounds by radial basis function artificial neural network

Radial basis function artificial neural network (RBF-ANN) model was developed to predict the normal boiling point (NBP) of 240 acyclic oxygen containing organic compounds, including alcohols, ethers, aldehydes, ketones, carboxylic acids and esters. The total database was randomly divided into a training set (192), a validation set (24) and a test set (24). 8 significant molecular descriptors, which were used to build the RBF-ANN model, were selected from a pool of descriptors by multi-stepwise regression method. The RBF-ANN model was trained by the Orthogonal Least Squares (OLS) learning algorithm. The biharmonic response surface analysis was used for the optimization of two main tuning parameters in the neural network. The final optimum RBF-ANN model represented by [8-22(32)-1] was tested and evaluated by graphic and statistical methods. Y-randomization test and a random split cross validation confirmed the robustness of the RBF-ANN model. The comparison results with the best multiple linear regression function and literature QSPR models showed the superiority of the RBF-ANN model.

QSPR study on the flash point of organic binary mixtures by using electrotopological state index

The quantitative structure property relationship (QSPR) for the flash point of 288 organic binary mixtures was investigated. The electrotopological state (E-state) index of the components in each mixture was calculated and weight summed to generate the quantitative descriptor of the investigated mixtures. Multivariable linear regression (MLR), stepwise regression and radial basis function artificial neural network (RBF-ANN) was respectively used to build the calibration model. The weight summed E-state index was used as the independent variable of the established models. The prediction performance of the developed models were assessed with external test validation, k-fold cross validation and Monte Carlo cross validation (MCCV). The results of the three validations demonstrate that the RBF-ANN model which includes five input variables is the best one among the developed models. The prediction root mean square relative error (RMSRE) of the external test validation, k-fold cross validation and MCCV is 1.86, 1.11 and 1.07 respectively for this model. It is demonstrated that there is a quantitative relationship between the E-state index and flash point of the investigated mixtures. MLR, stepwise regression and RBF-ANN are all practicable for modeling this relationship. The developed RBF-ANN model involving five input variables is the most promising method for predicting the flash point of organic binary mixtures.

A comparison of three prediction models for predicting monthly precipitation in Liaoyuan city, China

Accurate prediction of precipitation is of great importance for irrigation management and disaster prevention. In this study, back propagation artificial neural network (BPANN), radial basis function artificial neural network (RBFANN) and Kriging methods were applied and compared to predict the monthly precipitation of Liaoyuan city, China. An autocorrelation analysis method was used to determine model input variables first, and then BPANN, RBFANN and Kriging methods were applied to recognize the relationship between previous precipitation and later precipitation with the monthly precipitation data of 1971–2009 in Liaoyuan city. Finally, the three models' performances were compared based on models accuracy, models stability and models computational cost. Comparison results showed that for model accuracy, RBFANN performed best, followed by Kriging, and BPANN performed worst; for stability and computational cost, RBFANN and Kriging models performed better than the BPANN model. In conclusion, RBFANN is the best method for precipitation prediction in Liaoyuan city. Therefore, the developed RBFANN model was applied to predict the monthly precipitation for 2010–2019 in the study area.

Springback and tensile strength of 2A97 aluminum alloy during age forming

The analysis of variance (ANOVA), multiple quadratic regression and radial basis function artificial neural network (RBFANN) methods were used to study the springback and tensile strength in age forming of 2A97 aluminum alloy based on orthogonal array. The ANOVA analysis indicates that the springback reaches the minimum value when age forming is performed at 210 °C for 20 h using a single-curvature die with a radius of 400 mm, and the tensile strength reaches the maximum value when age forming is performed at 180 °C for 15 h using a single-curvature die with a radius of 1000 mm. The orders of the importance for the three factors of pre-deformation radius, aging temperature and aging time on the springback and tensile strength were determined. By analyzing the predicted results of the multiple quadratic regression and RBFANN methods, the prediction accuracy of the RBFANN model is higher than that of the regression model.

Comparison of surrogate models with different methods in groundwater remediation process

Surrogate modelling is an effective tool for reducing computational burden of simulation optimization. In this article, polynomial regression (PR), radial basis function artificial neural network (RBFANN), and kriging methods were compared for building surrogate models of a multiphase flow simulation model in a simplified nitrobenzene contaminated aquifer remediation problem. In the model accuracy analysis process, a 10-fold cross validation method was adopted to evaluate the approximation accuracy of the three surrogate models. The results demonstrated that: RBFANN surrogate model and kriging surrogate model had acceptable approximation accuracy, and further that kriging model’s approximation accuracy was slightly higher than RBFANN model. However, the PR model demonstrated unacceptably poor approximation accuracy. Therefore, the RBFANN and kriging surrogates were selected and used in the optimization process to identify the most cost-effective remediation strategy at a nitrobenzene-contaminated site. The optimal remediation costs obtained with the two surrogate-based optimization models were similar, and had similar computational burden. These two surrogate-based optimization models are efficient tools for optimal groundwater remediation strategy identification.

QSPR study on the relative retention time of polybrominated diphenyl ethers (PBDEs) by using molecular distance-edge vector index

The quantitative structure property relationship (QSPR) for the relative retention time (RRT) of polybrominated diphenyl ethers (PBDEs) was investigated. Molecular distance-edge vector (MDEV) index was used as the structural descriptor of PBDEs. The quantitative relationship between the MDEV index and RRT of PBDEs was modeled by using multivariate linear regression (MLR), partial least square (PLS) and radial basis function artificial neural network (RBF-ANN) respectively. Three QSPR models, MLR model, PLS model and RBF-ANN model, were established. External validation was carried out to assess the predictive ability of the developed models. The investigated 126 PBDEs were randomly divided into two groups: a calibration set, which comprises 88 PBDEs, and a test set, which comprises 38 PBDEs. For the MLR model, the prediction RMSRE of test set is 12.58. For the PLS model, the prediction RMSRE of test set is 12.58. For the RBF-ANN model, the prediction RMSRE of test set is 8.21. It is demonstrated that the MDEV index of PBDEs is quantitatively related to the RRT of PBDEs. The developed three models are all practicable for predicting the RRT of PBDEs. Compared with the MLR and PLS models, the RBF-ANN model shows higher prediction accuracy.

Sobol′ sensitivity analysis of NAPL-contaminated aquifer remediation process based on multiple surrogates

Sobol′ sensitivity analyses based on different surrogates were performed on a trichloroethylene (TCE)-contaminated aquifer to assess the sensitivity of the design variables of remediation duration, surfactant concentration and injection rates at four wells to remediation efficiency First, the surrogate models of a multi-phase flow simulation model were constructed by applying radial basis function artificial neural network (RBFANN) and Kriging methods, and the two models were then compared. Based on the developed surrogate models, the Sobol′ method was used to calculate the sensitivity indices of the design variables which affect the remediation efficiency. The coefficient of determination (R2) and the mean square error (MSE) of these two surrogate models demonstrated that both models had acceptable approximation accuracy, furthermore, the approximation accuracy of the Kriging model was slightly better than that of the RBFANN model. Sobol′ sensitivity analysis results demonstrated that the remediation duration was the most important variable influencing remediation efficiency, followed by rates of injection at wells 1 and 3, while rates of injection at wells 2 and 4 and the surfactant concentration had negligible influence on remediation efficiency. In addition, high-order sensitivity indices were all smaller than 0.01, which indicates that interaction effects of these six factors were practically insignificant. The proposed Sobol′ sensitivity analysis based on surrogate is an effective tool for calculating sensitivity indices, because it shows the relative contribution of the design variables (individuals and interactions) to the output performance variability with a limited number of runs of a computationally expensive simulation model. The sensitivity analysis results lay a foundation for the optimal groundwater remediation process optimization.

A mixed-integer non-linear programming with surrogate model for optimal remediation design of NAPLs contaminated aquifer

A mixed-integer non-linear programming (MINLP) with surrogate model was introduced to derive the optimal surfactant enhanced aquifer remediation (SEAR) process (remediation cost minimisation and removal rate maximisation) at a nitrobenzene-contaminated site. First, a 3D multi-phase flow simulation model was developed to simulate the SEAR process; using a radial basis function artificial neural network (RBFANN), the surrogate model was built which was an approximation of the simulation model; a MINLP was built to identify the optimal remediation strategies and genetic algorithm (GA) and penalty function were combined to solve the model; at last, the optimal remediation strategies were obtained. The approximation result of RBFANN was compared with that of back-propagation artificial neural network (BPANN), mean absolute error, mean relative error and coefficient of determination of the developed RBFANN model were 0.01, 2.27% and 0.85 respectively, which indicated much higher approximation accuracy than BPANN. The MINLP with surrogate model is a powerful tool for non-aqueous phase liquids (NAPLs) contaminated site remediation optimisation problem and it can greatly improve computational efficiency.

Prediction of critical cooling rate for glass forming alloys by artificial neural network

A radial basis function artificial neural network (RBFANN) model was established for the simulation and prediction of critical cooling rate Rc of glass forming alloys. The RBFANN model was trained, learned and examined using the data from the published literature as well as own experimental data. The performance of RBFANN model is examined by the linearly dependent coefficient between the predicted Rc and the corresponding experimental/calculated one; the influence of the type of alloys and elements and the large and minor change of element content on the Rc. In addition, a group of Zr–Al–Ni–Cu metallic glasses were designed and their Rcs were predicted by the RBFANN model. The results show that the established RBFANN model is reliable and adequate and can be used to design the composition and predict the Rc of glass forming alloys since the predicted Rc is inherent with the experimental/calculated one.

SIMULTANEOUS SPECTROPHOTOMETRIC DETERMINATION OF NORFLOXACIN, OFLOXACIN AND LOMEFLOXACIN IN RABBIT BLOOD SERUM BY USE OF CHEMOMETRICS

A spectrophotometric method for the simultaneous determination of norfloxacin, ofloxacin and lomefloxacin, is described. The spectrophotometric analysis is made possible with the aid of chemometric methods, such as classical least square (CLS), principal component regression (PCR), partial least square (PLS), and radial basis function-artificial neural network (RBF-ANN). Spectra were collected in the 190-400 nm range from a set of samples of three compounds in a Britton-Robinson buffer solution (pH=1.81). This approach overcomes the significant practical difficulties of severe spectral overlap. It was found that peak intensities are proportional to the concentration for each analyte. The obtained linear calibration concentration ranges are 0.6-13.8, 0.5-15.0, and 0.5-15.0 mg L-1 for norfloxacin, ofloxacin and lomefloxacin, respectively, and the LODs for the three analytes were found to be approximately 6-24× 10 -2 mg L-1. The proposed method was applied to a prediction set of synthetic mixtures of three analytes. The results were shown that the RBF-ANN model gave the best results (RPE T = 3.0%). This method was also applied for the determination of norfloxacin, ofloxacin and lomefloxacin in rabbit blood serum, and these compared well with those from the alternative analysis by HPLC.

A nonlinear data‐driven model for synthetic generation of annual streamflows

AbstractA hybrid model that blends two non‐linear data‐driven models, i.e. an artificial neural network (ANN) and a moving block bootstrap (MBB), is proposed for modelling annual streamflows of rivers that exhibit complex dependence. In the proposed model, the annual streamflows are modelled initially using a radial basis function ANN model. The residuals extracted from the neural network model are resampled using the non‐parametric resampling technique MBB to obtain innovations, which are then added back to the ANN‐modelled flows to generate synthetic replicates. The model has been applied to three annual streamflow records with variable record length, selected from different geographic regions, namely Africa, USA and former USSR. The performance of the proposed ANN‐based non‐linear hybrid model has been compared with that of the linear parametric hybrid model. The results from the case studies indicate that the proposed ANN‐based hybrid model (ANNHM) is able to reproduce the skewness present in the streamflows better compared to the linear parametric‐based hybrid model (LPHM), owing to the effective capturing of the non‐linearities. Moreover, the ANNHM, being a completely data‐driven model, reproduces the features of the marginal distribution more closely than the LPHM, but offers less smoothing and no extrapolation value. It is observed that even though the preservation of the linear dependence structure by the ANNHM is inferior to the LPHM, the effective blending of the two non‐linear models helps the ANNHM to predict the drought and the storage characteristics efficiently. Copyright © 2007 John Wiley &amp; Sons, Ltd.