Radial Basis Neural Network Model Research Articles

Modeling of Asphalt Pavement Surface Temperature for Prevention of Icing on the Surface

Hydronic heating systems are emerging as one of the best methods, which are environmentally friendly, clean, and sustainable modern ice prevention methods, an alternative to traditional ice precautions in the pavements. In this present study, temperatures were measured on asphalt samples prepared using the hydronic heating system when the air temperature in situ fell below 0 °C. T(minute), the temperature of influent (°C), air temperature (°C), temperature of effluent (°C) and pavement mean temperature (°C) were measured for four different asphalt samples. The results of the measurements were then modeled separately for four samples (345×4=1380 data) by using multiple linear regression (MLR), multi-layer perceptron (MLP), and radial basis neural network (RBNN). The results were discussed as tables and graphs. The performances of the models were evaluated using the root mean square error (RMSE), mean absolute error (MAE), and determination coefficient (R2). According to the results, the RBNN models of four inputs had the best performance for each sample. The RBNN (4,0.6,9) model, which refers to 4-inputs, spread coefficient of 0.6 and hidden nodes of 9, of sample-3 with RMSE=0.76 °C and MAE=0.63 °C and R2=0.91 had the best performance among all models. In addition, it is thought that the models having low errors in this concept can be evaluated for early warning systems for the ice condition of the roads.

Electric Vehicle NiMH Battery State of Charge Estimation Using Artificial Neural Networks of Backpropagation and Radial Basis

The state of charge of a battery depends on many magnitudes, but only voltage and intensity are included in mathematical equations because other variables are complex to integrate into. The contribution of this work was to obtain a model to determine the state of charge with these complex variables. This method was developed considering four models, the multilayer feed-forward backpropagation models of two and three input variables used supervised training, with the variable-learning-rate backpropagation training function, five and seven neurons in the hidden layer, respectively, achieving an optimal training. Meanwhile, the radial basis neural network models of two and three input variables were trained with the hybrid method, the propagation constant with a value of 1 and 80 neurons in the hidden layer. As a result, the radial basis neural network with the variable-learning-rate training function, considering the discharge temperature, was the one with the best performance, with a correlation coefficient of 0.99182 and a confidence interval of 95% (0.98849; 0.99516). It is then concluded that artificial neural networks have high performance when modeling nonlinear systems, whose parameters are difficult to measure with time variation, so estimating them in formulas where they are omitted is no longer necessary, which means an accurate SOC.

A study on the aesthetic characteristics of ethnic music based on radial basis neural network model

Abstract To explore the aesthetic features of folk music, this paper takes the radial basis neural network model as the basis and takes the zither piece “Flowing Water” and “Spring River Flower and Moonlight Night” as the examples, and unearths and analyzes the examples to understand the harmonious beauty, unique beauty and contextual beauty under the aesthetic characteristics. The results show that among the harmonious beauty, the average percentage of the characteristic vocabulary tranquility of the zither piece “Flowing Water” is 80.34% after learning by the radial-based neural network model, and the remaining percentages are 69.56%, 85.35%, 80.27% and 86.30% respectively, which shows that the radial-based neural network-based model can well resolve the characteristic vocabulary in the music through training and learning This shows that the radial basis neural network-based model can, through training and learning, well parse out the characteristic words in the music, and then explore the aesthetic features of the music. From the viewpoint of unique beauty, the musicalization of poetry and the poetization of music have been the main themes from ancient times to the present, with changes of 838% increase and 74.91% decrease, respectively, which also shows that the current degree of our attention to national music is not as much as that of the Tang, Song and Yuan dynasties, and we should strengthen the excavation of national music and create a unique humanistic environment. From the perspective of the beauty of the context, 67.81% of those who listened to “Spring River Moon Night Song” thought that the rhythm and context were full, and 79.48% thought that the theme melody and performance method were eye-catching, but there were still voices of dissatisfaction. Therefore, with the radial basis neural network model, we can intuitively see the aesthetic characteristics of folk music, and we can improve folk music according to its shortcomings so that folk music can be further renewed through a new interpretation.

Developing empirical formulae for scour depth in front of Inclined bridge piers

Because of the complex flow mechanism around inclined bridge piers, previous studies have proposed different empirical correlations to predict the scouring depth in front of piers, which include regression analysis developed from laboratory measurements. However, because these correlations were developed for particular datasets, a general equation is still required to accurately predict the scour depth in front of inclined bridge piers. The aim of this study is to develop a general equation to predict the local scour depth in front of inclined bridge pier systems using multilayer perceptron (MLP) and radial-basis neural-network (RBNN) techniques. The experimental datasets used in this study were obtained from previous research. The equation for the scour depth of the front pier was developed using five variables. The results of the artificial neural-network (ANN) analyses revealed that the RBNN and MLP models provided more accurate predictions than the previous empirical correlations for the output variables. Accordingly, analytical equations derived from the RBNN and MLP models were proposed to accurately predict the scouring depth in front of inclined bridge piers. Moreover, from the sensitivity analyses results, we determined that the scour depths in front of the front and back piers were primarily influenced by the inclination angle and flow intensity, respectively.

Multiaxial Strength Criterion Model of Concrete Based on Random Forest

The concrete strength criterion is the basis of strength analysis and evaluation under a complex stress state. In this paper, a large number of multiaxial strength tests were carried out, and many mathematical expressions of strength criteria were proposed based on the geometric characteristics and the assumption of a convex function. However, the rationality of the assumption of a convex function limits the use of these strength criteria. In particular, misjudgment will occur near the failure curve surface. Therefore, this paper does not assume the shape function of the criterion in advance. By collecting experimental data and using a machine learning method, it proposes a method of hidden function of failure curve surface. Based on 777 groups of experimental data, the random forest (RF), the back propagation neural network (BP) and the radial basis neural network (RBF) models were used to analyze and verify the feasibility and effectiveness of the method. Subsequently, the results were compared with the Ottosen strength criterion, the Guo Wang strength criterion and the Drucker–Prager (DP) strength criterion. The results show that the consistency between the strength criterion model established by the machine learning algorithm (especially random forest) and the experimental data is higher than the convex function multiaxis strength criterion of the preset failure surface shape. Moreover, the physical significance is clearer, the deficiency of the convex function failure surface hypothesis is avoided and the established multiaxial strength criterion of concrete is more universal.

Multi-Variate Optimization of Polymer Electrolyte Membrane Fuel Cells in Consideration of Effects of GDL Compression and Intrusion

This study applies, tests, and compares comprehensive surrogate-based optimization techniques to optimize the performance of polymer electrolyte membrane fuel cells (PEMFCs). Moreover, parametric cases considering four important design variables, i.e., gas diffusion layer thickness (), channel depth (), channel width (), and land width (), are defined using the latin hypercube sampling technique under reasonable constraint conditions. Multidimensional, two-phase PEMFC model simulations are performed to generate the training and test data under these design conditions. Three famous surrogate models, i.e., response surface approximation (RSA), radial basis neural network (RBNN), and kriging (KRG), are employed to construct objective functions for the PEMFC cell voltages operating in the galvanostatic mode, and their accuracies are tested and compared using root mean square error and adjusted R-square. The surrogates are then linked to stochastic optimization algorithms, i.e., genetic algorithm and particle swarm optimization, to determine the optimal design points. A comparative study of these surrogates reveals that the KRG model outperforms the RBNN and RSA models in terms of prediction capability. Furthermore, the PEMFC model simulations at the optimal design points clearly demonstrate that performance improvements of around 56–69 mV at 2.0 A cm−2 are achieved with the optimum design values compared to typical PEMFC design conditions.

Heat dissipation optimization and prediction for three-dimensional fan-out package

Excessive heat would reduce the service life and threaten the reliability of electronic devices. To optimize the heat conduction in Fan-out (FO) package, we proposed a hybrid method using Taguchi design of experiments, radial basis neural network (RBNN) and genetic algorithm (GA). The heat transfer models of the FO package were constructed. The hybrid method was used to examine the influence of eight geometric parameters on heat dissipation. It was revealed by using the Taguchi design method that the parameters the chip size (A), the ratio of package side length to chip side length (D), and the critical dimension of RDL (G) have the most significant impact on the thermal resistance of FO package, and others are less important. The RBNN model was established to predict the thermal resistance, which was optimized by using the GA. We obtained the optimal design of the FO package with the structure parameter vector [100, 250, 50, 2, 2, 2, 10, 100]. The thermal resistance of the RBNN-GA optimized model is 280.58 K/W. The difference between the maximum junction temperature and the ambient temperature was reduced by around 33.22%. It proved that the hybrid method is effective for optimizing the heat dissipation of FO package, which can be used for structure design and thermal management of the electronic devices.

Design and development of a machine vision system using artificial neural network-based algorithm for automated coal characterization

Coal is heterogeneous in nature, and thus the characterization of coal is essential before its use for a specific purpose. Thus, the current study aims to develop a machine vision system for automated coal characterizations. The model was calibrated using 80 image samples that are captured for different coal samples in different angles. All the images were captured in RGB color space and converted into five other color spaces (HSI, CMYK, Lab, xyz, Gray) for feature extraction. The intensity component image of HSI color space was further transformed into four frequency components (discrete cosine transform, discrete wavelet transform, discrete Fourier transform, and Gabor filter) for the texture features extraction. A total of 280 image features was extracted and optimized using a step-wise linear regression-based algorithm for model development. The datasets of the optimized features were used as an input for the model, and their respective coal characteristics (analyzed in the laboratory) were used as outputs of the model. The R-squared values were found to be 0.89, 0.92, 0.92, and 0.84, respectively, for fixed carbon, ash content, volatile matter, and moisture content. The performance of the proposed artificial neural network model was also compared with the performances of performances of Gaussian process regression, support vector regression, and radial basis neural network models. The study demonstrates the potential of the machine vision system in automated coal characterization.

Stability enhancement of a centrifugal compressor using inclined discrete cavities

Inclined discrete cavities are proposed to improve the operating stability of a centrifugal compressor while minimizing the flow loss, and optimized to simultaneously maximize the adiabatic efficiency and stall margin. Aerodynamic analysis was performed using three-dimensional Reynolds-averaged Navier–Stokes equations. The numerical results obtained for the total pressure ratio and adiabatic efficiency were validated with experimental data for the centrifugal compressor with a smooth casing. The angle of the cavity port, axial distance between cavities, and inclined angle of the cavity were selected as design variables based on sensitivity analysis. The stall margin and adiabatic efficiency at the design point were used as the objective functions for the design. Latin hypercube sampling was used to select 24 design points in the design space. Two neural network models, that is, the radial basis and deep neural networks, were tested with respect to surrogate models and their performances were compared using statistical analysis. A hybrid PSO–GA algorithm was used to identify the optimal solutions for the surrogate models. The deep neural network model has a better overall performance than the radial basis neural network model. The optimization results show that the stall margin increases, with increments of up to 6.41% and 11.32% compared with the reference design and compressor with a smooth casing, respectively.

Optimization Design of a Two-Vane Pump for Wastewater Treatment Using Machine-Learning-Based Surrogate Modeling

This paper deals with three-objective optimization, using machine-learning-based surrogate modeling to improve the hydraulic performances of a two-vane pump for wastewater treatment. For analyzing the internal flow field in the pump, steady Reynolds-averaged Navier-Stokes equations were solved with the shear stress transport turbulence model as a turbulence closure model. The radial basis neural network model, which is an artificial neural network, was used as the surrogate model and trained to improve prediction accuracy. Three design variables related to the geometry of blade and volute were selected to optimize concurrently the objective functions with the total head and efficiency of the pump and size of the waste solids. The optimization results obtained by using the model showed highly accurate prediction values, and compared with the reference design, the optimum design provided improved hydraulic performances.

A prediction model of milling force for aviation 7050 aluminum alloy based on improved RBF neural network

Semi-finishing is an important step to reduce the cutting vibration and deformation caused by the thin-walled stiffening rib parts of aeronautical inertial control products during the finishing process. In the semi-finishing process, the variation of cutting force is a key factor of machining deformation. A large number of samples considering the effect of cutting parameters, such as spindle speed, feed per tooth, and milling width were simulated by the finite element simulation software AdvantEdge to obtain the milling forces based on 7050 aluminum alloy (Al7050) for aviation. Moreover, the standardized Euclidean distance was introduced to the radial basis neural network model (RBF-NN) to develop an improved RBF neural network model (IRBF-NN), and a high-precision model to predict the effect of cutting parameters on the thin-walled semi-finishing milling forces was established based on the proposed IRBF-NN. Results show that the maximum relative errors of milling force obtained by the genetic algorithm–optimized BP neural network model (GA-BP-NN), RBF-NN, and IRBF-NN are 13.9%, 12.5%, and 4.1%, respectively. Accordingly, the proposed IRBF-NN has high accuracy and effectiveness to predict milling force for the semi-finishing of aerospace Al7050 thin-walled stiffening rib parts.

Multi-objective Structural Optimization of VL Seal Ring Based on Isight

To obtain the best geometric size of VL sealing ring and improve its sealing performance, this paper carried out multi-objective optimization research on VL sealing ring by Isight software. Firstly, according to the working principle and geometric size of the VL seal ring, determined the constraint conditions, established the optimization objective equation, and given the value range of the structural parameters was. Then, verified the validity of the approximate model by fitting the radial basis neural network model provided. Finally, analyzed the sensitivity of influencing factors of oil film thickness at lip, and established the optimization module by NSGA-II multi-objective optimization algorithm. As a result, the best geometric size is obtained from multi-objective optimization, and the structure of VL seal ring has achieved the goal of more suitable high speed dynamic seal and longer service life.

Radial-Basis Function Neural Network Synthesis on the Basis of Decision Tree

The problem of neural network synthesis on the precedents is addressed. The aim of the study is to create methods for radial-basis neural network model constructing having high levels of generalization and accuracy, which do not require user participation in the process of model building. The method of decision tree transforming into a neural network model is proposed. For a given sample, a decision tree is built, on the basis of which leaf nodes the cluster centers' are allocated, after which the structure of the radial-basis network is synthesized by associating of selected clusters with neurons of the first layer, the cluster centers coordinates are placed into the weights of neurons of the first layer, and then the weights are adjusted. The method for transforming a regression tree into a radial-basis network is proposed. It allocates clusters for solved problem as a regression tree, but to improve accuracy for each cluster, it builds a particular linear regression model of the output feature dependence from the neuron???s output determining belonging to the corresponding cluster. The method of converting a random forest into a neural network model is proposed. Trees of the forest, built on a given sample, are transformed into separate neural network models, which are combined into joint network. The experiments on practical problems solving were carried out. Their results were confirmed the efficiency of the proposed methods.

The viability of co-active fuzzy inference system model for monthly reference evapotranspiration estimation: case study of Uttarakhand State

Abstract Reference evapotranspiration (ETo) is a major component of the hydrological cycle linking the irrigation water requirement and planning and management of water resources. In this research, the potential of co-active neuro-fuzzy inference system (CANFIS) was investigated against the multilayer perceptron neural network (MLPNN), radial basis neural network (RBNN), self-organizing map neural network (SOMNN) and multiple linear regression (MLR) to estimate the monthly ETo at Pantnagar and Ranichauri stations, located in the foothills of Indian central Himalayas of Uttarakhand State, India. The significant combination of input variables for implemented techniques was decided by the Gamma test (GT). The results obtained by CANFIS models were compared with MLPNN, RBNN, SOMNN and MLR models based on performance evaluation indicators and visual inspection using line, scatter and Taylor plots for both the stations. The results of comparison revealed that CANFIS-5/CANFIS-9 models (RMSE = 0.0978/0.1394, SI = 0.0261/0.0475, COE = 0.9963/0.9846, PCC = 0.9982/0.9942 and WI = 0.9991/0.9959) with three and five input variables provide superior results for estimating monthly ETo at Pantnagar and Ranichauri stations, respectively. Also, the adopted modelling strategy can build a truthful expert intelligent system for estimating the monthly ETo at the study stations.

Dynamic heartbeat detection algorithm based on RBFNN

The operational environment faced by modern radars is becoming increasingly complex. The timely detection of the failure of a node and the adoption of countermeasures to ensure the stable operation of the system have become the focus of radar network management. In this study, based on traditional heartbeat detection algorithm, we use a radial-basis neural network model to predict the timeout value. Therefore, a neural network heartbeat detection algorithm is proposed, which is used to detect the failure of the combat platform. The experimental results show that the proposed algorithm can be used to reduce the failure detection delay and misjudge rate as compared with the existing algorithms, and can be applied to a complex radar network environment.

Evaluating the performance of four different heuristic approaches with Gamma test for daily suspended sediment concentration modeling.

Accurate prediction of suspended sediment concentration (SSC) carried by a river or watershed basin is essential for understanding the hydrology of basin in terms of water quality, river bed sustainability and aquatic habitats. In this study, four heuristic methods, namely, radial basis neural network (RBNN), self-organizing map neural network (SOMNN), least square support vector regression (LSSVR), and multivariate adaptive regression spline (MARS) were employed for daily SSC modeling at Ashti, Bamini, and Tekra stations located in Godavari River basin, Andhra Pradesh, India. The Gamma test (GT) was utilized for identifying the most significant input variables for the applied heuristic approaches. The results obtained by RBNN, SOMNN, LSSVR, and MARS models were compared with those of the traditional sediment rating curve (SRC). The performance of the models was evaluated based on the root mean square error (RMSE), coefficient of efficiency (COE), Pearson correlation coefficient (PCC), Willmott index (WI), and pooled average relative error (PARE) indices, as well as the visual inspection using line diagram, scatter diagram, and Taylor diagram (TD). The results of comparison revealed that the four heuristic methods gave higher accuracy than the SRC model. Among the heuristic models, the RBNN-3 (RMSE = 0.045, 0.062, 0.131g/l; COE = 0.884, 0.883, 0.914; PCC = 0.955, 0.961, 0.958; and WI = 0.970, 0.963, 0.976) outperformed the other models in simulating daily SSC records in the studied stations.

Application of soft computing models in streamflow forecasting

The accuracy of five soft computing techniques was assessed for the prediction of monthly streamflow of the Gilgit river basin by a cross-validation method. The five techniques assessed were the feed-forward neural network (FFNN), the radial basis neural network (RBNN), the generalised regression neural network (GRNN), the adaptive neuro fuzzy inference system with grid partition (Anfis-GP) and the adaptive neuro fuzzy inference system with subtractive clustering (Anfis-SC). The interaction between temperature and streamflow was considered in the study. Two statistical indexes, mean square error (MSE) and coefficient of determination (R2), were used to evaluate the performances of the models. In all applications, RBNN and Anfis-SC were found to give more accurate results than the FFNN, GRNN and Anfis-GP models. The effect of periodicity was also examined by adding a periodicity component into the applied models and the results were compared with a statistical model (seasonal autoregressive integrated moving average (Sarima)) to check the prediction accuracy. The results of this comparison showed that periodicity inputs improved the prediction accuracy of the applied models and, in all cases, the soft computing models performed much better than the Sarima model. The periodic RBNN and Anfis-SC models increased the MSE accuracy of Sarima by 25·5–24·7%.

On-line chemical oxygen demand estimation models for the photoelectrocatalytic oxidation advanced treatment of papermaking wastewater.

Chemical oxygen demand (COD), an important indicative measure of the amount of oxidizable pollutants in wastewater, is often analyzed off-line due to the expensive sensor required for on-line analysis. However, its off-line analysis is time-consuming. An on-line COD estimation method was developed with photoelectrocatalytic (PEC) technology. Based on the on-line data of the oxidation-reduction potential (ORP), dissolved oxygen (DO) and pH of wastewater, four different artificial neural network methods were applied to develop working models for COD estimation. Six different batches of sequence batch reactor (SBR) effluent from a paper mill were treated with PEC oxidation for 90 minutes, and 546 data points were collected from the on-line measurements of ORP, DO and pH, and the off-line COD analysis. After having training and validation with 75% and 25% of data, and evaluation with four statistical criteria (R2, RMSE, MAE and MAPE), the estimation results indicated that the developed radial basis neural network (RBNN) model demonstrated the highest precision. Subsequently, the application of the RBNN model to a new batch of SBR effluent from the paper mill revealed that the RBNN model was acceptable for COD estimation during the PEC advanced treatment process of papermaking wastewater, which implied its possible application in the future.

Soft-sensing modeling of chemical oxygen demand in photo-electro-catalytic oxidation treatment of papermaking wastewater

Photo-electro-catalytic (PEC) oxidation has been widely recognized as an effective technology for advanced treatment of papermaking wastewater. To optimize the oxidation process, it is important of monitor continuously the chemical oxygen demand (COD) of inflow and outflow wastewater. However, online COD sensors are expensive difficult to maintain, and therefore COD is usually analyzed off-line in laboratories in most cases. The objective of this study is to develop an inexpensive method for on-line COD measurement. The oxidation-reduction potential (ORP), pH, and dissolved oxygen (DO) of wastewater were selected as the key parameters, which consists of four different types of artificial neural network (ANNs) methods:multi-layer perceptron neural network (MLP), back propagation neural network (BPNN), radial basis neural network (RBNN) and generalized regression neural network (GRNN). These parameters were applied in the development of COD soft-sensing models. Six batches of papermaking wastewater with different pollution loads were treated with PEC technology over a period of 90 minutes, and a total of 546 data points was collected, including the on-line measurements of ORP, pH and DO, as well as off-line COD data. The 546 data points were divided into training set (410 data, 75% of total) and validation set (136 data, 25% of total). Four statistical criteria, namely, root mean square error (RMSE), mean absolute error (MAE), mean absolute relative error (MARE), and determination coefficient (R²) were used to assess the performance of the models developed with the training set of data. The comparison of results for the four ANN models for COD soft-sensing indicated that the RBNN model behaved most favorably, which possessed precise and predictable results with R²=0.913 for the validation set. Lastly, the proposed RBNN model was applied to a new batch of PEC oxidation of papermaking wastewater, and the results indicated that the model could be applied successfully for COD soft-sensing for the wastewater.

Sediment yield prediction using neural networks at a watershed in south east India

In this article, feed-forward backpropagation neural network (BPNN) and the radial basis neural network (RBNN) are used to predict daily sediment yield during monsoon. The performance of BPNN and RBNN models for sediment yield during July, August, and September over 16 year’s data, has been evaluated. It is found that in the small watershed of Lahunipada, India, BPNN performs best for estimating sediment yield. With BPNN, the coefficient of determination (R2) values for July, August, and September are found to be 0.9553, 0.9437, and 0.9864, respectively. Similarly, with RBNN the R2 values for July, August, and September are 0.9521, 0.9361, and 0.959, respectively. Over all, results show that with the same scenario, performance for July, August, and September agreed to RBNN with less coefficient of determination as compared to BPNN. Furthermore, BPNN model using sigmoid transfer function predicts the sediment yield within a range of 0.0219–1.54 t/ha during July, 0.013–1.778 t/ha during August and 0.001–1.389 t/ha during September and sheer deviations in RBNN with Gaussian transfer function. This study confirms that BPNN and RBNN are useful techniques for predicting sediment yield in small watersheds of south east India.