Training Radial Basis Function Networks Research Articles

Design of Software Reliability Prediction using Radial Basis Function Networks with Nonlinear Analysis and Topological Considerations

This study presents a thorough methodology for predicting software reliability by employing Radial Basis Function Networks (RBFNs). By using machine learning methodologies such as Radial Basis Function Networks (RBFNs), software development teams are enabled to make well-informed decisions, optimize resource allocation, and proactively mitigate potential dependability concerns. Consequently, this results in improved software quality and heightened customer happiness. This methodology involves multiple stages, starting with data collection and preprocessing. We assemble a comprehensive dataset comprising historical software performance metrics, defect reports, and relevant development process information. After data cleansing and feature engineering, we split the dataset into training, validation, and testing subsets. The core of this approach lies in the construction and training of RBFNs. These neural networks consist of an input layer, a hidden layer with radial basis functions, and an output layer. The architecture parameters, particularly the number of hidden neurons and the spread parameter of the radial basis functions, are optimized through a systematic hyperparameter tuning process using the validation dataset. Upon achieving an optimal model configuration, we rigorously evaluate the RBFN predictive capabilities using the testing dataset.

Robust packet loss compensation in the cloud‐based TT&C receiver using a predictive tracking loop with RBF network identification

AbstractIn recent years, ground‐based aerospace tracking, telemetry and control (TT&C) systems have been shifting towards an IP‐based cloud TT&C network architecture to improve signal transmission efficiency and system flexibility. However, this new architecture presents new challenges for the performance of tracking loops in the cloud‐based TT&C receiver. The authors present a predictive compensation tracking loop that addresses the problem of packet loss. The loop utilises radial basis function (RBF) online network identification for robust carrier and code frequency offset tracking. To account for packet loss, the phenomenon is modelled as a Bernoulli random process, and the predictive compensation loop uses the trained RBF network to maintain the system's tracking state. When normal data are received again, the loop can track the received information well and align the frequency offset locking state. The authors compare the performance of the proposed predictive compensation tracking loop with traditional loop tracking performance using data hold strategies under different packet loss rates. The results demonstrate the effectiveness of the proposed approach in maintaining stable tracking and solving in the discontinuous reception of the loop under packet loss environments. The proposed predictive compensation tracking loop offers a practical solution for addressing packet loss, which is a common issue in real‐world applications.

A Brand-New Simple, Fast, and Effective Residual-Based Method for Radial Basis Function Neural Networks Training

The radial basis function (RBF) neural network is a type of universal approximator, and has been widely used in various fields. Improving the training speed and compactness of RBF networks are critical for promoting their applications. In the present study, we propose a simple, fast, and effective RBF networks training method, which is based on the residual extreme points and their neighborhoods (thus called the REN method for short in this paper). The REN method calculates RBF centers and widths through a two-level iterative process, and realizes two main functionalities, namely 1) adding multiple centers within one pass through the whole data set, and 2) calculating RBF widths specifically for each center. The use of this algorithm does not need any parameter adjustments, and the models for approximation or classification can be obtained by only one run. The performance of the proposed REN algorithm is compared with the classic and powerful orthogonal least squares (OLS) algorithm. By reaching the same accuracies, the REN algorithm trains RBF networks 50 and 320 times faster, in the chirp (0˜50 Hz, 2 s, 1 kHz, 2001 samples) and two-dimensional peaks (2401 samples) signal approximation tasks respectively, than the OLS algorithm does, and the number of centers obtained by the REN algorithm is reduced by half. When incorporating the same number of centers, the REN algorithm achieves accuracies up to 3 orders of magnitude higher than the best results obtained by the OLS algorithm. In the classification task of a real discrete breast cancer data, both methods result in accuracies comparable to many existent methods, but the REN algorithm has the advantages of fast training speeds and no requirements for parameter adjustments. The REN algorithm proposed in this study may potentially be used for tasks with large scale of data or applications that require high model performances.

Mercury prediction in groundwater of Naameh Landfill using an Artificial Neural Network (ANN) model

Mercury is a highly poisonous metal which is mostly found in environment. It is considered at the top of the parameters of water quality that requires investigations for planning and management. To understand the status of mercury in the groundwater of Naameh Landfill, Artificial Neural Network (ANN) models were used as indicators of water quality and for the prediction of Mercury. Two types of feed forward networks have been used including multilayer perceptron (MLP) and radial basis function (RBF). A number of different MLP neural networks algorithms and RBF networks trained and developed with reference to pH, EC, TDS, TON, calcium and magnesium to predict Mercury concentration in groundwater. Six scenarios were used to train MLP and RBF networks for choosing the best-fit model for predicting water quality parameters in groundwater of Naameh Landfill. The performances of MLP and RBF models were evaluated by utilizing the coefficient of determination (R2). The results showed that the computed values of R2 for MLP and RBF were 0.791 and 0.881respectively. In addition, the prediction results showed that both types of networks are very good for predicting Mercury concentration in the ground water of our study area. Moreover, the results showed that there are mercury residues for 2 years ahead even if there is no discharge in this place. As a matter of fact, there are no studies that encompass status of heavy metals in municipal solid waste landfills in Lebanon or neighboring countries using ANN models. Thus, this study can be described as unique as it demonstrated a 9 year groundwater data (2011-2019), presented data and projected data for two upcoming years. This is crucial especially in the continual waste crisis that Lebanon is facing and the absence of sustainable disposal practices. This data is a rigid base and a solid reference for developing adequate solutions to prevent future contamination of groundwater with its associated negative impacts on the health and wellbeing of individuals.

Development of Fault Diagnosing System for Ice-Storage Air-Conditioning Systems

This paper proposes a fault diagnosing system for the Ice-Storage Air-Conditioning System (ISACS) to supervise the operation conditions of the brine chillers. Combining the Radial Basis Function Network (RBFN) and Robust Quality Design (RQD), an Enhanced RBFN (ERBFN) is proposed to pursue fast and accurate fault diagnosis. The RQD method is used to adjust the parameters in the RBFN training stage to improve the searching ability, and good performance with a close spike tracking capability can be seen. The efficiency of the brine chiller in the ISACS was considered as the quality characteristics, the values measured by all instruments were considered as control factors, and noise factors were abnormal variable control factors in the system. ERBFN can improve the efficiency of the ISACS and prevent the equipment from being damaged without warning. ERBFN is used for fault diagnosis to ensure the ISACS performance is normal. Experimental results are provided to show the effectiveness of the proposed method. The new artificial neural network algorithm proposed in this paper was successfully applied to the fault diagnosis of ISACS. It not only provides a reference for enterprises but can also be applied to studies on other topics in the future.

Adaptive Learning for Robust Radial Basis Function Networks.

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.

Gradient-based training and pruning of radial basis function networks with an application in materials physics

Many applications, especially in physics and other sciences, call for easily interpretable and robust machine learning techniques. We propose a fully gradient-based technique for training radial basis function networks with an efficient and scalable open-source implementation. We derive novel closed-form optimization criteria for pruning the models for continuous as well as binary data which arise in a challenging real-world material physics problem. The pruned models are optimized to provide compact and interpretable versions of larger models based on informed assumptions about the data distribution. Visualizations of the pruned models provide insight into the atomic configurations that determine atom-level migration processes in solid matter; these results may inform future research on designing more suitable descriptors for use with machine learning algorithms.

Hybrid Learning Algorithm of Radial Basis Function Networks for Reliability Analysis

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.

Evaluation of Financial Performance of Port Enterprises Based on Radial Basis Function Neural Network

Li, J., 2020. Evaluation of financial performance of port enterprises based on radial basis function neural network. In: Gong, D.; Zhang, M., and Liu, R. (eds.), Advances in Coastal Research: Engineering, Industry, Economy, and Sustainable Development. Journal of Coastal Research, Special Issue No. 106, pp. 255–258. Coconut Creek (Florida), ISSN 0749-0208.An objective, fair, and accurate evaluation of the financial performance of the port enterprises is an important measure to mobilize and improve the enthusiasm of the port enterprises employees and the progress of scientific and technological innovation. This paper proposes a refined evaluation model of the financial performance of port enterprise companies based on the radial basis function (RBF) neural network. The normalized financial performance index data of port enterprise companies are multiplied by the corresponding weight coefficient as the network input, using excellent, good, middle, and F5 grade evaluations as output. The particle swarm optimization algorithm was used to cross-validate the RBF network structure parameters. Through analyzing the RBF network structure and enter and export characteristics, it was found that the trained RBF network weights are highly correlated with the five-level evaluation results and can more accurately distinguish scientific research performance differences than the five-level evaluation results. This weight can be directly used to conduct a detailed evaluation of the financial performance of the port enterprises. This paper promotes the application of RBF networks in the evaluation of financial performance of port enterprise companies and provides new ideas for similar evaluations.

Filtering out Antenna Effects From GPR Data by an RBF Neural Network

When sounding pavement layers using ground penetrating radar (GPR), antenna effects including dispersion and multiple reflections usually degrade the vertical resolution. In far-field conditions, these effects can be analytically filtered out by a linear method. However, for near-field operation, the antenna model tends to be nonlinear, and thus, these unwanted effects cannot be analytically removed anymore. In this letter, a method based on the radial basis function (RBF) neural network is proposed to filter out antenna effects under near-field conditions. A well-developed GPR model is used to simulate the input training data, and the corresponding zero-offset Green’s function is calculated as the desired output for each training data. The trained RBF network is applied to the simulated and measured data. The results show that the proposed method is effective in filtering out the antenna effects and increasing the vertical resolution of GPR.

Estimation of evapotranspiration and its parameters for pine, switchgrass, and intercropping with remotely-sensed images based geospatial modeling

Intercropping switchgrass (Panicum virgatum) with pine can increase bioenergy feedstock production without land opportunity costs but can potentially alter water budgets. Measuring evapotranspiration (ET) and its parameters (stomatal conductance (gs), leaf area index (LAI), canopy temperature (Tc), and soil moisture (SM)) across cropping systems is costly and time-consuming. However, interpretation of remotely-sensed data can facilitate the effective assessment of relative ET demands among competing forest landuses. This study develops and tests geospatial models informed by a normalized difference vegetation index (NDVI), soil adjusted vegetation index (SAVI), vegetation vigor index (VVI), and other spectral information to estimate ET and its parameters, which are measured on experimental watersheds with young pines and natural understory (YP), switchgrass only (SG), and young pine intercropped with switchgrass (IC). The treatment watersheds were replicated on three sites located across the Southeastern U.S. in Carteret, NC; Calhoun, MS; and Greene, AL. Despite the growth inconsistency for the SG only treatment, remote modeling estimation of ET parameters yielded an acceptable R2 > 0.70, and the ET model yielded R2 of 0.50 and a standard error of prediction of 0.94. However, ET and ET parameter model estimation for the IC performed somewhat less satisfactorily, with an R2 of 0.47, 0.59, 0.56, 0.81, and 0.57 for ET, LAI, gs, Tc, and SM, respectively, potentially due to inconsistencies in Landsat image pixel size and landuse homogeneity. Moreover, ET parameter models for the YP site performed rather poorly, with R2 = 0.28, 0.63, and 0.76 for LAI, gs, and Tc, respectively. Additionally, image analysis automation was created with Python scripting and geospatial models. The findings from this study suggest that inclusion of more spatial variability, sound data mining, ultra-high resolution imagery and advanced image processing approaches to account for potential modeling uncertainties can enhance the predictive capability of models to remotely estimate environmental parameters including ET. Radial Basis Function Network (RBFN) based models provided promising results for estimating ET and ET parameters using remotely-sensed digital information when they are prepared with advanced data mining, but it is likely that laypersons may find these models difficult to use. However, forest managers with access to neural network software can use our devised RBFN training models for estimating those forest hydrologic parameters with better accuracy.

Comparative evaluation of MFP and RBF neural networks’ ability for instant estimation of r/c buildings’ seismic damage level

The problem of the seismic damage prediction of reinforced concrete (r/c) buildings utilizing two types of Artificial Neural Networks (ANN) is investigated in the present paper. More specifically, the problem is formulated and solved in terms of the Function Approximation problem as well as of the Pattern Recognition problem using Multilayer Feedforward Perceptron Networks (MFP) and Radial-Basis Function (RBF) networks. The required training data-sets are created by means of Nonlinear Time History Analyses of 90 r/c buildings which are subjected to 65 earthquakes. The selected buildings differ in total height, in structural system, in structural eccentricity as well as the existence or not of masonry infills. The seismic damage index which is used to describe the seismic damage state is the Maximum Interstorey Drift Ratio. The influence of the parameters which are used for the configuration and the training of MFP and RBF networks on the reliability of their predictions is also investigated. The generalization ability of the best configured ANNs is examined by means of two categories of seismic scenarios. The most significant conclusion that turned out is that the trained ANNs can reliably and rapidly classify the r/c buildings into pre-defined damage classes provided they are appropriately configured.

Quantum speedup of training radial basis function networks

Radial basis function (RBF) network is a simple but useful neural network model that contains wide applications in machine learning. The training of an RBF network reduces to solve a linear system, which is time consuming classically. Based on HHL algorithm, we propose two quantum algorithms to train RBF networks. To apply the HHL algorithm, we choose using the Hamiltonian simulation algorithm proposed in [P. Rebentrost, A. Steffens, I. Marvian and S. Lloyd, Phys. Rev. A 97, 012327, 2018]. However, to use this result, an oracle to query the entries of the matrix of the network should be constructed. We apply the amplitude estimation technique to build this oracle. The final results indicate that if the centers of the RBF network are the training samples, then the quantum computer achieves exponential speedup at the number and the dimension of training samples over the classical computer; if the centers are determined by the K-means algorithm, then the quantum computer achieves quadratic speedup at the number of samples and exponential speedup at the dimension of samples.

Quantum speedup of training radial basis function networks

Radial basis function (RBF) network is a simple but useful neural network model that contains wide applications in machine learning. The training of an RBF network reduces to solve a linear system,...

Back to the Future: Radial Basis Function Network Revisited.

Radial Basis Function (RBF) networks are a classical family of algorithms for supervised learning. The most popular approach for training RBF networks has relied on kernel methods using regularization based on a norm in a Reproducing Kernel Hilbert Space (RKHS), which is a principled and empirically successful framework. In this paper we aim to revisit some of the older approaches to training the RBF networks from a more modern perspective. Specifically, we analyze two common regularization procedures, one based on the square norm of the coefficients in the network and another one using centers obtained by k-means clustering. We show that both of these RBF methods can be recast as certain data-dependent kernels. We provide a theoretical analysis of these methods as well as a number of experimental results, pointing out very competitive experimental performance as well as certain advantages over the standard kernel methods in terms of both flexibility (incorporating of unlabeled data) and computational complexity. Finally, our results shed light on some impressive recent successes of using soft k-means features for image recognition and other tasks.

Distance Weighted K-Means Algorithm for Center Selection in Training Radial Basis Function Networks

The accuracies rates of the neural networks mainly depend on the selection of the correct data centers. The K-means algorithm is a widely used clustering algorithm in various disciplines for centers selection. However, the method is known for its sensitivity to initial centers selection. It suffers not only from a high dependency on the algorithm's initial centers selection but, also from data points. The performance of K-means has been enhanced from different perspectives, including centroid initialization problem over the years. Unfortunately, the solution does not provide a good trade-off between quality and efficiency of the centers produces by the algorithm. To solve this problem, a new method to find the initial centers and improve the sensitivity to the initial centers of K-means algorithm is proposed. This paper presented a training algorithm for the radial basis function network (RBFN) using improved K-means (KM) algorithm, which is the modified version of KM algorithm based on distance-weighted adjustment for each centers, known as distance-weighted K-means (DWKM) algorithm. The proposed training algorithm, which uses DWKM algorithm select centers for training RBFN obtained better accuracy in predictions and reduced network architecture compared to the standard RBFN. The proposed training algorithm was implemented in MATLAB environment; hence, the new network was undergoing a hybrid learning process. The network called DWKM-RBFN was tested against the standard RBFN in predictions. The experimental models were tested on four literatures nonlinear function and four real-world application problems, particularly in Air pollutant problem, Biochemical Oxygen Demand (BOD) problem, Phytoplankton problem, and forex pair EURUSD. The results are compared to proposed method for root mean square error (RMSE) in radial basis function network (RBFN). The proposed method yielded a promising result with an average improvement percentage more than 50 percent in RMSE.

An Improved Radial Basis Function Networks in Networks Weights Adjustment for Training Real-World Nonlinear Datasets

In neural networks, the accuracies of its networks are mainly relying on two important factors which are the centers and the networks weight. The gradient descent algorithm is a widely used weight adjustment algorithm in most of neural networks training algorithm. However, the method is known for its weakness for easily trap in local minima. It suffers from a random weight generated for the networks during initial stage of training at input layer to hidden layer networks. The performance of radial basis function networks (RBFN) has been improved from different perspectives, including centroid initialization problem to weight correction stage over the years. Unfortunately, the solution does not provide a good trade-off between quality and efficiency of the weight produces by the algorithm. To solve this problem, an improved gradient descent algorithm for finding initial weight and improve the overall networks weight is proposed. This improved version algorithm is incorporated into RBFN training algorithm for updating weight. Hence, this paper presented an improved RBFN in term of algorithm for improving the weight adjustment in RBFN during training process. The proposed training algorithm, which uses improved gradient descent algorithm for weight adjustment for training RBFN, obtained significant improvement in predictions compared to the standard RBFN. The proposed training algorithm was implemented in MATLAB environment. The proposed improved network called IRBFN was tested against the standard RBFN in predictions. The experimental models were tested on four literatures nonlinear function and four real-world application problems, particularly in Air pollutant problem, Biochemical Oxygen Demand (BOD) problem, Phytoplankton problem, and forex pair EURUSD. The results are compared to IRBFN for root mean square error (RMSE) values with standard RBFN. The IRBFN yielded a promising result with an average improvement percentage more than 40 percent in RMSE.

Recursive Particle Filter-Based RBF Network on Time Series Prediction of Measurement Data

Most physical phenomena in nature are chaotic or close to chaos. An irregular time series can be generated or measured with a purely deterministic equation of motion in nonlinear and chaotic systems. This paper presents an adaptive state-space particle filtering (PF)-based trained radial basis function (RBF) network for chaotic and nonstationary observation–prediction. The recursive Bayesian filtering algorithm, which uses the particle representation of density function, is adopted to accomplish nonlinear and non-Gaussian state estimation and achieve improved convergence rate and quality of solution. Four sampling importance resampling approaches, namely, multinomial, systematic, stratified, and residual resampling methods, are considered to resolve weight degeneracy. The effectiveness of our proposed methods is investigated using two chaotic time series and three measurement datasets, including the Mackey–Glass time series, Rossler time series, monthly Lake Erie levels, monthly water usage series, and SML2010 data set. The performances are evaluated through an extensive simulation by computing the average mean square error, mean absolute percentage error, and average relative variance metrics. Simulation results show that the proposed PF-based RBF structure can provide more effective and accurate prediction performances compared with the conventional gradient descent, extended Kalman filter (EKF), and decoupled EKF algorithms (DEKF).

Training radial basis function networks for wind speed prediction using PSO enhanced differential search optimizer.

This paper presents an integrated hybrid optimization algorithm for training the radial basis function neural network (RBF NN). Training of neural networks is still a challenging exercise in machine learning domain. Traditional training algorithms in general suffer and trap in local optima and lead to premature convergence, which makes them ineffective when applied for datasets with diverse features. Training algorithms based on evolutionary computations are becoming popular due to their robust nature in overcoming the drawbacks of the traditional algorithms. Accordingly, this paper proposes a hybrid training procedure with differential search (DS) algorithm functionally integrated with the particle swarm optimization (PSO). To surmount the local trapping of the search procedure, a new population initialization scheme is proposed using Logistic chaotic sequence, which enhances the population diversity and aid the search capability. To demonstrate the effectiveness of the proposed RBF hybrid training algorithm, experimental analysis on publicly available 7 benchmark datasets are performed. Subsequently, experiments were conducted on a practical application case for wind speed prediction to expound the superiority of the proposed RBF training algorithm in terms of prediction accuracy.

RBFN-based temperature compensation method for impedance monitoring in prestressed tendon anchorage

In this study, a temperature compensation method based on radial basis function network (RBFN) is developed to monitor damage-induced impedance signatures in prestressed tendon anchorages under temperature variation. First, an impedance monitoring technique via a piezoelectric interface device is outlined for prestress-loss detection in the tendon anchorage system. Second, an RBFN-based algorithm is designed to filter out the temperature-induced variation in impedance signatures for damage monitoring. Finally, the feasibility of the proposed algorithm is verified for the prestress-loss monitoring in the test structure under the temperature-varying condition. A series of impedance measurements are conducted for the temperature-varying and prestress force-varying conditions. The RBFN-based algorithm is used to train a set of baseline impedance signatures for varying temperatures, and also to quantify damage-induced impedance signatures of the test structure. The effect of the size of RBFN training patterns on the accuracy of the proposed temperature compensation algorithm is also evaluated.