Abstract: Credit rating is an important part of bank credit risk management. Since the traditional radial basis function network model is more susceptible to outliers and cannot effectively process the classification data, it is very sensitive in terms of the initial center and class width of the selected model. This paper mainly studies the application of the radial basis function neural network model combined with the optimal segmentation algorithm in the personal loan credit rating model of banks or other financial institutions. The optimal segmentation algorithm is improved and applied to the training of RBF neural network parameters in this paper to increase the center and width of the class, and the center and width of the RBF network model are further improved. Finally, the adaptive selection of the number of hidden nodes is realized by using the differential objective function of the class to adjust dynamically the structure of the radial basis function network model, which is used to establish the credit rating model. The experimental results show that the improved model has higher precision when dealing with non-numeric data, and the robustness of the improved model has been improved.

Abstract: With the wide application of industrial robots in the field of precision machining, reliability analysis of positioning accuracy becomes increasingly important for industrial robots. Since the industrial robot is a complex nonlinear system, the traditional approximate reliability methods often produce unreliable results in analyzing its positioning accuracy. In order to study the positioning accuracy reliability of industrial robot more efficiently and accurately, a radial basis function network is used to construct the mapping relationship between the uncertain parameters and the position coordinates of the end-effector. Combining with the Monte Carlo simulation method, the positioning accuracy reliability is then evaluated. A novel hybrid learning algorithm for training radial basis function network, which integrates the clustering learning algorithm and the orthogonal least squares learning algorithm, is proposed in this article. Examples are presented to illustrate the high proficiency and reliability of the proposed method.

Abstract: Spatial interpolation has been frequently encountered in earth sciences and engineering. A reasonable appraisal of subsurface heterogeneity plays a significant role in planning, risk assessment and decision making for geotechnical practice. Geostatistics is commonly used to interpolate spatially varying properties at un-sampled locations from scatter measurements. However, successful application of classic geostatistical models requires prior characterization of spatial auto-correlation structures, which poses a great challenge for unexperienced engineers, particularly when only limited measurements are available. Data-driven machine learning methods, such as radial basis function network (RBFN), require minimal human intervention and provide effective alternatives for spatial interpolation of non-stationary and non-Gaussian data, particularly when measurements are sparse. Conventional RBFN, however, is direction independent (i.e. isotropic) and cannot quantify prediction uncertainty in spatial interpolation. In this study, an ensemble RBFN method is proposed that not only allows geotechnical anisotropy to be properly incorporated, but also quantifies uncertainty in spatial interpolation. The proposed method is illustrated using numerical examples of cone penetration test (CPT) data, which involve interpolation of a 2D CPT cross-section from limited continuous 1D CPT soundings in the vertical direction. In addition, a comparative study is performed to benchmark the proposed ensemble RBFN with two other non-parametric data-driven approaches, namely, Multiple Point Statistics (MPS) and Bayesian Compressive Sensing (BCS). The results reveal that the proposed ensemble RBFN provides a better estimation of spatial patterns and associated prediction uncertainty at un-sampled locations when a reasonable amount of data is available as input. Moreover, the prediction accuracy of all the three methods improves as the number of measurements increases, and vice versa. It is also found that BCS prediction is less sensitive to the number of measurement data and outperforms RBFN and MPS when only limited point observations are available.

Abstract: This article addresses the robust estimation of the output layer linear parameters in a radial basis function network (RBFN). A prominent method used to estimate the output layer parameters in an RBFN with the predetermined hidden layer parameters is the least-squares estimation, which is the maximum-likelihood (ML) solution in the specific case of the Gaussian noise. We highlight the connection between the ML estimation and minimizing the Kullback–Leibler (KL) divergence between the actual noise distribution and the assumed Gaussian noise. Based on this connection, a method is proposed using a variant of a generalized KL divergence, which is known to be more robust to outliers in the pattern recognition and machine-learning problems. The proposed approach produces a surrogate-likelihood function, which is robust in the sense that it is adaptive to a broader class of noise distributions. Several signal processing experiments are conducted using artificially generated and real-world data. It is shown that in all cases, the proposed adaptive learning algorithm outperforms the standard approaches in terms of mean-squared error (MSE). Using the relative increase in the MSE for different noise conditions, we compare the robustness of our proposed algorithm with the existing methods for robust RBFN training and show that our method results in overall improvement in terms of absolute MSE values and consistency.

Abstract: Separable nonlinear least squares (SNLLS) problems have attracted interest in a wide range of research fields such as machine learning, computer vision, and signal processing. During the past few decades, several algorithms, including the joint optimization algorithm, alternated least squares (ALS) algorithm, embedded point iterations (EPI) algorithm, and variable projection (VP) algorithms, have been employed for solving SNLLS problems in the literature. The VP approach has been proven to be quite valuable for SNLLS problems and the EPI method has been successful in solving many computer vision tasks. However, no clear explanations about the intrinsic relationships of these algorithms have been provided in the literature. In this paper, we give some insights into these algorithms for SNLLS problems. We derive the relationships among different forms of the VP algorithms, EPI algorithm and ALS algorithm. In addition, the convergence and robustness of some algorithms are investigated. Moreover, the analysis of the VP algorithm generates a negative answer to Kaufman’s conjecture. Numerical experiments on the image restoration task, fitting the time series data using the radial basis function network based autoregressive (RBF-AR) model, and bundle adjustment are given to compare the performance of different algorithms.

Abstract: In this article, the synchronization control problem of bilateral teleoperation systems with time-varying delays and input dead zones is addressed. A novel radial basis function network (RBFN)-based adaptive finite-time synchronization control scheme is proposed, where system uncertainties, asymmetric time-varying delays, and dead-zone phenomena are considered simultaneously. Specifically, an RBFN is designed to approximate system uncertainties and unknown nonlinearities. The approximation error as well as the time-associated uncertainty and the nonlinear margin of the dead zone is compensated by an adaptive compensator. Using a Lyapunov–Krasovskii function and the finite-time stability criteria, the system is proved to be semiglobally practically finite-time stable. The theoretical analysis is given to prove the stability of the closed-loop system. The tracking performance of the designed controller is demonstrated by comparative simulation studies and experiment results.

Abstract: In this paper, a novel dynamic recurrent functional link neural network (DRFLNN) is proposed for the identification of unknown dynamics of the nonlinear systems. The proposed structure contains a self-feedback loop(s) as well as the adjustable weighted feed-through of the input signals to the output neuron(s). A learning algorithm is developed using the combination of Lyapunov stability and dynamic back-propagation method and is applied to derive the stable parameter adjustment equations. The performance evaluation of the proposed DRFLNN model is done by comparing it with the multi-layer perceptron (consisting of a single hidden layer), radial basis function network, Elman recurrent neural network (ERNN), nonlinear auto-regressive moving average, and the conventional functional link neural network. Three benchmark systems have been used on which all these models are applied. From the results, it is found that ERNN provided better prediction accuracy as compared to the remaining models and the second-best accuracy is obtained from the proposed model. Further, the ERNN model is more complex and offers more parameters to be tuned as compared to the DRFLNN model. Thus, the training of the ERNN model is quite difficult as compared to the DRFLNN.

Abstract: Climate change has had worst and extreme impacts all over the world. Due to rise in global temperature some region faces drought and then a sudden bout of excessive rainfall. Rainfall in excess causes one of the most destructive and dangerous natural hazard called flooding that causes serious damage to life and property on earth every year. There are several complexities in nature and pattern of floods which makes flooding an important and challenging task for the researcher. To solve this problem, there are three Artificial Neural Networks (ANNs) techniques namely Support Vector Machine (SVM), Back Propagation Neural Network (BPNN) and Radial Basis Function Network (RBFN). These techniques are capable of modelling nonlinear and complex systems. The capability of these techniques is presented in this paper. In this research, to measure the performance of models, three performance criteria, including a coefficient of determination (R2), mean square error and root mean square error are utilized. The result shows that the SVM model performs best among the three models and can be accepted as a suitable and appropriate method to predict flood.

Abstract: Aiming at the time-consuming problem of the full-wave (FW) simulation of the scattering characteristics of the traditional graphene reconfigurable reflectarray antenna, a fast prediction method of electromagnetic (EM) response based on deep learning is proposed. The convolutional neural network (CNN) method in deep learning is effectively used in the research of this paper. This method first discretizes the input vector (patch geometry, chemical potential, frequency, incident angle, etc.) of the graphene reflectarray antenna, and then preprocesses the data into a two-dimensional image suitable for CNN training, and finally uses CNN to train the model instead of extensive FW simulation calculations, the EM response of the reflectarray antenna is calculated. The training results of three algorithms of support vector regression (SVR), radial basis function network (RBFN) and CNN are comprehensively compared. The experimental results show that CNN method has good performance and accuracy in the EM response prediction of the graphene reconfigurable reflectarray antenna, with an accuracy of over 99%, and can also save at least 99% of time.

Abstract: Clustering is a classical unsupervised learning task that aims to reveal data similarity patterns. Numerous algorithms have been proposed to address this task from different aspects. In the field of swarm intelligence and evolutionary algorithms, most existing algorithms strive to identify a set of cluster centers. However, it is difficult for centroid-based algorithms to process data with clusters of arbitrary shapes. Thus, a clustering algorithm named Swarm Clustering Algorithm (SCA) was proposed to cluster data from a novel aspect, which regards each point in the dataset as a particle, and particles fly towards denser areas to form clusters automatically. In this article, a novel efficient swarm clustering algorithm named SCA2 is proposed, which extends SCA in terms of three aspects: (1) the radial basis function network is adopted as the surrogate model to reduce the time complexity; (2) there are $k$ leaders for each particle, and the particle may follow one of them to decrease misleading; and (3) a simplified strategy is used to update the position of each particle. The performance of SCA2 on different types of synthetic and real-world datasets was compared with the performance of four classical algorithms, SCA as well as a PSO-based clustering algorithm. The experimental results demonstrate that SCA2 is more competitive.

Abstract: Data mining is the progress of instinctively find out valuable information from huge depot. In educational data mining predicting the academic performance of the student is a well-known research. The intention of the research work is to examine the classification algorithms as a hybrid classification. We used Radial Basis Function network, Multilayer Perceptron, C4.5 and Random Forest Algorithms for classification. Initially classification accuracy was computed individually by the classification algorithms. The Radial Basis Function network, Multilayer Perceptron, C4.5 and Random Forest Algorithm’s individual classification gave the accuracy of 72.9167%, 75.4167%, 75% and 73.125% vice versa. To increase more accuracy of classification algorithm the Radial Basis Function network is combined with multilayer perceptron. This hybrid algorithm provides 75.625% of classification accuracy. Then we combined C4.5 algorithm with random forest algorithm which gives 76.4583% classification accuracy. In this study we found hybrid classification algorithm gives more accuracy than individual classification algorithm.

Abstract: In the current scenario, worldwide renewable energy systems receive renewed interest because of the global reduction of greenhouse gas emissions. This paper proposes a long-term wind speed prediction model based on various artificial neural network approaches such as Improved Back-Propagation Network (IBPN), Multilayer Perceptron Network (MLPN), Recursive Radial Basis Function Network (RRBFN), and Elman Network with five inputs such as wind direction, temperature, relative humidity, precipitation of water content and wind speed. The proposed ANN-based wind speed forecasting models help plan, integrate, and control power systems and wind farms. The simulation result confirms that the proposed Recursive Radial Basis Function Network (RRBFN) model improves the wind speed prediction accuracy and minimizes the error to a minimum compared to other proposed IBPN, MLPN, and Elman Network-based wind speed prediction models.

Abstract: The radial basis function network-based state-dependent autoregressive (RBF-AR) model has been widely used in modeling and prediction of nonlinear time series. The parameter identification of RBF-AR model can be reformulated as a separable nonlinear least squares problem. The variable projection (VP) algorithm has been proven to be valuable in solving such problems. However, for ill-posed problems, the classical VP algorithm usually yields unstable models. In this paper, we consider a novel regularized separable algorithm that takes advantage of the VP method and the expectation–maximization (EM) method. The proposed algorithm utilizes the VP algorithm to optimize the nonlinear parameters and automatically picks out the regularization parameters during the search process. Numerical results on real-world data and synthetic time series confirm the effectiveness of the proposed algorithm.

Abstract: Our goal is to understand and optimize human concept learning by predicting the ease of learning of a particular exemplar or category. We propose a method for estimating ease values, quantitative measures of ease of learning, as an alternative to conducting costly empirical training studies. Our method combines a psychological embedding of domain exemplars with a pragmatic categorization model. The two components are integrated using a radial basis function network (RBFN) that predicts ease values. The free parameters of the RBFN are fit using human similarity judgments, circumventing the need to collect human training data to fit more complex models of human categorization. We conduct two category-training experiments to validate predictions of the RBFN. We demonstrate that an instance-based RBFN outperforms both a prototype-based RBFN and an empirical approach using the raw data. Although the human data were collected across diverse experimental conditions, the predicted ease values strongly correlate with human learning performance. Training can be sequenced by (predicted) ease, achieving what is known as fading in the psychology literature and curriculum learning in the machine-learning literature, both of which have been shown to facilitate learning.

Abstract: In this paper, a new radial basis function network-based model predictive control (RBFN-MPC) is presented to control the steam temperature of a power plant boiler. For the first time in this paper the Laguerre polynomials are used to obtain local boiler models based on different load modes. Recursive least square (RLS) method is used as observer of the Laguerre polynomials coefficient. Then a new locally recurrent radial basis function neural network with self-organizing mechanism is used to model these local transfer function and it used to estimate the boiler future behavior. The recurrent RBFN tracks system is dynamic online and updates the model. In this recurrent RBFN, the output of hidden layer nodes at the past moment is used in modelling, So the boiler model behaves exactly like a real boiler. Various uncertainties have been added to the boiler and these uncertainties are immediately recognized by the recurrent RBFN. In the simulation, the proposed method has been compared with traditional MPC (based on boiler mathematical model). Simulation results showed that the recurrent RBFN-based MPC perform better than mathematical model-based MPC. This is due to the neural network's online tracking of boiler dynamics, while in the traditional way the model is always constant. As the amount of uncertainty increases, the difference between our proposed method and existing methods can clearly be observed.

Abstract: The increasing complexity of industrial systems is at the heart of the development of many fault diagnosis methods. The artificial neural networks (ANNs), which are part of these methods, are widely used in fault diagnosis due to their flexibility and diversification which makes them one of the most appropriate fault diagnosis methods. The purpose of this paper is to detect and locate in real time any parameter deviations that can affect the operation of the blowout preventer (BOP) system using ANNs.,The starting data are extracted from the tables of the HAZOP (HAZard and OPerability) method where the deviations of the parameters of normal BOP operating (pressure, flow, level and temperature) are associated with an initial rule base for establishing cause and effect of relationships between the causes of deviations and their consequences; these data are used as a database for the neural network. Three ANNs were used, the multi-layer perceptron network (MLPN), radial basis functions network (RBFN) and generalized regression neural networks (GRNN). These models were trained and tested, then, their comparative performances were presented. The respective performances of these models are highlighted following their application to the BOP system.,The performances of the models are evaluated using determination coefficient (R2), root mean square error (RMSE) and mean absolute error (MAE) statistics and time execution. The results of this study show that the RMSE, MAE and R2 values of the GRNN model are better than those corresponding to the RBFN and MLPN models. The GRNN model can be applied with better performance, to establish a diagnostic model that can detect and to identify the different causes of deviations in the parameters of the BOP system.,The performance of the trained network is found to be satisfactory for the real-time fault diagnosis. Therefore, future studies on modeling the BOP system with soft computing techniques can be concentrated on the ANNs. Consequently, with the use of these techniques, the performance of the BOP system can be ensured performing only a limited number of monitoring operations, thus saving engineering effort, time and funds.

Abstract: The deployment and allocation of network resources are important in the application of edge computing. As an important resource allocation technology in edge computing, network virtualization faces the challenge of the virtual network mapping problem. Most existing studies are limited to static resource allocation, ignoring the time-varying properties of user resource demands, which results in wasted resources. Since user resource demands vary over time, resource allocation with predictive mechanism is a promising solution. However, there are few studies on the application of predictive algorithm as radial basis function network (RBF) algorithms in virtual network dynamic resource allocation. In addition, due to the excessive use of hidden RBF units, this method suffers from expensive inner product calculations and long training times. In this paper, we propose a dynamic network resource demand predicting algorithm based on the group search optimizer (GSO) and incremental design of the RBF (GSO-INC-RBFDM). In the network mapping, the GSO is first used to optimize the node solution. Then, the incremental design is utilized to eliminate the maximum error value and reduce the inner product calculation and training time by adding the RBF unit one by one. Finally, we apply the improved RBF to predict the user demand and reallocate resources based on the predicted results. Simulation results shows that the GSO-INC-RBFDM demonstrates good performance in terms of the acceptance rate, network cost, link pressure and average revenue compared with traditional algorithms.

Abstract: Dynamic frequency scaling (DFS) is one of the most important approaches to saving power in modern day processors. With ever-increasing complexity at system, circuit and device levels, the problem of achieving an efficient DFS boils down to multi-parametric nonlinear optimization. Therefore, it is imperative to explore ingenuous approaches to DFS which could identify an optimal underclocking frequency on-the-fly using an adaptive mechanism. This paper proposes an offline neural network approach to DFS of a ubiquitous single-core processor where several performance parameters of the processor were monitored under application of a number of clocking frequencies. The dataset thus generated was used to train two classifiers, viz. the radial basis function network and the probabilistic neural network. Under changing parametric conditions of the proposed network, the model was fit to performance-monitoring data while running 64-point and 1024-point FFT applications, and one benchmark application named basicmath. To demonstrate the generalization of the classifiers, the models were trained offline by the dataset obtained by clubbing the aforementioned applications. The performance of both the classifiers was found to be promising, and good generalization was obtained with all the datasets. The results indicate toward suitability of trained radial basis family of networks for on-chip deployment for implementing on-the-fly DFS.

Abstract: The continuous increase in energy consumption has brought worldwide attention to its significant environmental effect, which is triggered by the increase in greenhouse gas emissions, global warming, and rapid climate change. As such, more energy efficient buildings are required to minimize the energy consumption of heating and cooling. The present study introduces a set of machine learning-based models to predict the heating and cooling loads in buildings. This includes back-propagation artificial neural network, generalized regression neural network, radial basis neural network, radial kernel support vector machines and ANOVA kernel support vector machines. The comparisons were conducted as per mean absolute percentage error (MAPE), mean absolute error (MAE), relative absolute error (RAE), root relative squared error (RRSE) and root-mean squared error (RMSE). The significances of the capacities of the machine learning models are evaluated using two-tailed student’s t-tests. Eventually, a holistic evaluation of the machine learning models is conducted using average ranking algorithm. Results demonstrate that the radial basis function network outperformed the afore-mentioned machine learning models significantly.

Abstract: In this article, a novelty control structure of grid-connected doubly-fed induction generator (DFIG) based on a function link (FL)-based Wilcoxon radial basis function network (FLWRBFN) controller is proposed. The back-propagation (BP) method is used online to train the node connecting weights of the FLWRBFN. To improve the online learning capability of FLWBFN, differential evolution with particle swarm optimization (DEPSO) is used to tune the learning rates of FLWRBFN. For high randomness of wave energy generation, the transmission power between generators and electrical grids is easy to unstable and AC bus voltage and DC voltage will also lose constant under the conditions of variable generator speed and variable load. Therefore, the proposed intelligent controller can maintain the above power balance and voltage constant and reduce fluctuation. Finally, PSCAD/EMTDC software is used to simulate and study various cases to confirm the robustness and usefulness of the proposed intelligent control technology applied to an ocean wave energy conversion system.

Abstract: In recent decades, hybridization of superior attributes of few algorithms was proposed to aid in covering more areas of complex application as well as improves performance. Condition monitoring is a major component in predictive maintenance which monitors the condition and identifies significant changes in the machinery parameter to perform early detection and prevent equipment defects that could cause unplanned downtime or incur unnecessary expenditures. An effective condition monitoring model is helpful to reduce the frequency of unexpected breakdown incidents and thus, facilitates in maintenance. ANN has shown effective in various condition monitoring and fault detection applications. ANN is popular due to its capability of identifying the complex nonlinear relationships among features in a large dataset and hence, it can perform with an accurate prediction. However, a drawback is that the performance of ANN is sensitive to the parameters (i.e., number of hidden neurons and the initial values of connection weights) in its architecture where the settings of these parameters are subject to tuning on a trial-and-error basis. Hence, a wide range of studies have been focused on determining the optimal weight values of ANN models and the number of hidden neurons. In this research work, the motivation is to develop an autonomous learning model based on the hybridization of an adaptive ANN and a metaheuristic algorithm for optimizing ANN parameters so that the network could perform learning and adaptation in a more flexible way and handle condition classification tasks more accurately in industries, such as in power systems. This paper presents an intelligent system integrating a Radial Basis Function Network with Dynamic Decay Adjustment (RBFN-DDA) with a Harmony Search (HS) to perform condition monitoring in industrial processes. RBFN-DDA performs incremental learning wherein its structure expands by adding new hidden units to include new information. As such, its training can reach stability in a shorter time compared to the gradient-descent based methods. To achieve optimal RBFN-DDA performance, HS is proposed to optimize the center and the width of each hidden unit in a trained RBFN. By integrating with the HS algorithm, the proposed metaheuristic neural network (RBFN-DDA-HS) can optimize the RBFN-DDA parameters and improve classification performances from the original RBFN-DDA by 2.2% up to 22.5% in two benchmarks datasets, which are numerical records from a bearing and steel plate system and a condition-monitoring system in a power plant (i.e., the circulating water (CW) system). The results also show that the proposed RBFN-DDA-HS is compatible, if not better than, the classification performances of other state-of-the-art machine learning methods.