Training Radial Basis Function Research Articles

Hybrid hyperplane gradient learning algorithm for RBF neural network

Gradient-based algorithms are still popularly used for training radial basis function neural network (RBFNN). However, these algorithms may lead to the vanishing gradient (saddle point or local minimum) problem, which is one of the common problems that limit learning performance. To cope with this, a hybrid hyperplane gradient learning algorithm (HHGLA) is proposed to improve the learning performance of the RBFNN in this paper. First, a hyperplane gradient (HPG), based on a hyperspace constructed by a solution population (SP), is introduced. Thus, the search process can cross the surface of the cost function to avoid the appearance of vanishing gradient. Second, an adaptive learning rate is designed to restrict the search process into this hyperspace. Then, during the learning process, the hyperspace is constantly contracted to approximate the global optimal solution. Third, the convergence property of HHGLA-based RBFNN is thoroughly analyzed to ensure its application success. Finally, empirical comparisons of the proposed HHGLA-RBFNN are given to illustrate its superiority. The simulation results show the feasibility of HHGLA-RBFNN of accuracy.

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.

Training RBF neural networks for the solution of elliptic boundary value problems

We propose a radial basis function (RBF) neural network method for solving two- and three–dimensional second and fourth order elliptic boundary value problems (BVPs). The neural network in question is trained by minimizing a nonlinear least squares functional, thus determining the optimal values of the various RBF parameters involved. The functional minimization is carried out using standard MATLAB® software efficiently. Several numerical experiments are presented to demonstrate the efficacy of the proposed method.

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.

RBFNN Design Based on Modified Nearest Neighbor Clustering Algorithm for Path Tracking Control.

Radial basis function neural networks are a widely used type of artificial neural network. The number and centers of basis functions directly affect the accuracy and speed of radial basis function neural networks. Many studies use supervised learning algorithms to obtain these parameters, but this leads to more parameters that need to be determined, thereby making the system more complex. This study proposes a modified nearest neighbor-based clustering algorithm for training radial basis function neural networks. The calculation of this clustering algorithm is not large, and it can adapt to varying densities. Furthermore, it does not require researchers to set parameters based on experience. Simulation proves that the clustering algorithm can effectively cluster samples and optimize the abnormal samples. The radial basis function neural network based on modified nearest neighbor-based clustering has higher accuracy in curve fitting than the conventional radial basis function neural network. Finally, the path tracking control based on a radial basis function neural network of a magnetic microrobot is investigated, and its effectiveness is verified through simulation. The test accuracy and training accuracy of the radial basis function neural network was improved by 23.5% and 7.5%, respectively.

Modeling biogas production from anaerobic wastewater treatment plants using radial basis function networks and differential evolution

This study presents a new method for modeling biogas production obtained from anaerobic digestion treatment plants with increased accuracy. The method is based on artificial neural networks (ANNs) and more specifically on the efficient architecture of radial basis function (RBF) networks. A novel RBF training scheme is proposed, based on the non-symmetric fuzzy means (NSFM) algorithm, which has been shown to offer increased accuracy compared to other ANN methods, but cannot handle efficiently a large number of input variables. As this is the case in biogas production modeling, the algorithm is enhanced with an optimizer based on differential evolution (DE), which helps to properly tune the algorithm, ultimately boosting the accuracy of the produced models. The proposed approach is applied for modeling the biogas production on a real world, full-scale operational wastewater treatment plant. A comparison study shows the superiority of the proposed model, compared to different machine learning approaches.

Self-organizing radial basis function neural network using accelerated second-order learning algorithm

Gradient-based algorithms are commonly used for training radial basis function neural network (RBFNN). However, it is still difficult to avoid vanishing gradient to improve the learning performance in the training process. For this reason, in this paper, an accelerated second-order learning (ASOL) algorithm is developed to train RBFNN. First, an adaptive expansion and pruning mechanism (AEPM) of gradient space, based on the integrity and orthogonality of hidden neurons, is designed. Then, the effective gradient information is constantly added to gradient space and the redundant gradient information is eliminated from gradient space. Second, with AEPM, the neurons are generated or pruned accordingly. In this way, a self-organizing RBFNN (SORBFNN) which reduces the structure complexity and improves the generalization ability is obtained. Then, the structure and parameters in the learning process can be optimized by the proposed ASOL-based SORBFNN(ASOL-SORBFNN). Third, some theoretical analyses including the efficiency of the proposed AEPM on avoiding the vanishing gradient and the stability of SORBFNN in the process of structural adjustment are given, then the successful application of the proposed ASOL-SORBFNN is guaranteed.Finally, to illustrate the advantages of the proposed ASOL-SORBFNN, several experimental studies are examined. By comparing with other existing approaches, the results show that ASOL-SORBFNN performs well in terms of both learning speed and prediction accuracy.

Surface Roughness Prediction and Optimization in the Orthogonal Cutting of Graphite/Polymer Composites Based on Artificial Neural Network

Graphite/polymer composites are brittle materials that are prone to producing cracks and concavities on machined surfaces, and their surface quality shows greater randomness. This work aims to overcome the large fluctuations in the machined surface quality of graphite/polymer composites, realize the prediction of machined surface roughness under different machining conditions and optimize the process parameters. A graphite/polymer composite material was cut orthogonally using different machining parameters, and the machined surface roughness of the cut samples was measured by a noncontact surface profiler to obtain training samples for Artificial Neural Network (ANN). In this study, a trained radial basis function neural network was used to predict the machined surface roughness, and the prediction accuracy was more than 93%. A Genetic Algorithm (GA) was used to optimize the established ANN, and then grey relational analysis was used to compare the accuracy of the GA optimization results. The ANN prediction after GA optimization showed that the lowest machined surface roughness of the graphite/polymer composites was 1.81 μm, and the corresponding optimal cutting speed, cutting depth, tool rake angle, and rounded edge radius were 11.2 m/min, 0.1 mm, 6.85°, and 11.16 μm, respectively. A verification experiment showed that the lowest machined surface roughness was obtained when the above process parameters were selected, which was only 1.95 μm, and the prediction error of the ANN was approximately 7%. The combination of a GA and an ANN can accurately predict the surface roughness of graphite/polymer composite materials and optimize the process parameters.

Energy optimization of internet of things in wireless sensor network models using type‐2 fuzzy neural systems

SummaryIn this paper, type‐2 fuzzy logic design is employed to find the weight values of the radial basis function (RBF) neural network model, and thereby, the trained RBF neural network (RBFNN) model is intended to perform network energy optimization of the cloud‐assisted internet of things in wireless sensor networks (WSNs). RBF neural model comes under the class of feed forward neural network architecture and is a network with better generalization capability. RBFNN employs Gaussian activation function to determine the output of the network and the special feature of this activation function is that it follows a normal probability density function; hence it is a continuous activation function and provides better solutions than the other discrete activation functions. Due to which, in this work RBFNN is employed to determine network energy and to increase the life time of the network by selecting best cluster heads and also the network route. In RBFNN modelling, basically, the weights are initialized in a random manner, and this random initialization of weights at time results in the occurrences of global and local minima. The weights are tuned for their optimal values using type‐2 fuzzy model due to their capability of handling uncertainties, and since this problem of identifying optimal weight values of RBF neural model possesses highest level of uncertainties, type‐2 fuzzy system is applied here. Simulation process is done, and the results prove the effectiveness of the proposed approach in comparison with that of the existing approaches from previous literatures for the energy optimization problem.

Hybridization of harmonic search algorithm in training radial basis function with dynamic decay adjustment for condition monitoring

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.

Accelerated gradient algorithm for RBF neural network

Gradient-based algorithms are commonly used for training radial basis function neural network (RBFNN). However, one of the challenges in the training process is determining how to avoid vanishing gradient. To solve this problem, an accelerated gradient algorithm (AGA) is designed to improve the learning performance of RBFNN in this paper. First, an indirect detection mechanism, based on the instantaneous gradient decay rate (IGDR) and instantaneous convergence rate (ICR), is developed to identify the vanishing gradient in learning process. Second, an amplification gradient strategy (AGS), which can increase the gradient value of learning parameters, is designed to accelerate the learning speed of RBFNN. Third, the analysis of AGA-based RBFNN (AGA-RBFNN) is given to guarantee the successful application. Finally, some benchmark and real problems are used to illustrate the effectiveness of AGA-RBFNN. The results demonstrate the effectiveness of AGA-RBFNN.

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.

Data classification based on fractional order gradient descent with momentum for RBF neural network

ABSTRACT The weight-updating methods have played an important role in improving the performance of neural networks. To ameliorate the oscillating phenomenon in training radial basis function (RBF) neural network, a fractional order gradient descent with momentum method for updating the weights of RBF neural network (FOGDM-RBF) is proposed for data classification. Its convergence is proved. In order to speed up the convergence process, an adaptive learning rate is used to adjust the training process. The Iris data set and MNIST data set are used to test the proposed algorithm. The results verify the theoretical results of the proposed algorithm such as its monotonicity and convergence. Some non-parametric statistical tests such as Friedman test and Quade test are taken for the comparison of the proposed algorithm with other algorithms. The influence of fractional order, learning rate and batch size is analysed and compared. Error analysis shows that the algorithm can effectively accelerate the convergence speed of gradient descent method and improve its performance with high accuracy and validity.

Ship Traffic Flow Prediction Based on Fractional Order Gradient Descent with Momentum for RBF Neural Network

To prevent the maritime traffic accidents and make scientific decision, scientific and accurate prediction of the traffic flow is useful, which has often been made by neural network. The weight updating methods have played an important role in improving the performance of neural networks. To ameliorate the oscillating phenomenon in training radial basis function (RBF) neural network, a fractional order gradient descent (GD) with momentum method for updating the weights of RBF neural network (FOGDM-RBF) is proposed. Its convergence is proved. The new algorithm is used to predict vessel traffic flow at Xiamen Port. It performs stable and converges to zero as the iteration increases. The results verify the theoretical results of the proposed algorithm such as its monotonicity and convergence. The descending curve of error values by fractional order GDM is smoother than the GD and GDM method. Error analysis shows that the algorithm can effectively accelerate the convergence speed of the GD method and improve its performance with high accuracy and validity. The influence of fractional order, number of hidden layer neurons, tide peak hours, and ship size is analyzed and compared. 1. Introduction As the world shipping becomes more and more busy, the large ship traffic flow leads to frequent maritime traffic accidents, resulting in huge economic losses. Ship traffic flow is a basic system in marine traffic engineering and an important index to measure the construction of marine traffic infrastructure. Its prediction results can provide basis for formulating scientific Port management planning and ship navigation management. Therefore, to ensure the accuracy and rationality of ship traffic flow forecasting is of great significance for improving port infrastructure construction and formulating scientific port management strategies. Many advanced artificial intelligence optimization algorithms have been used for ship traffic flow forecasting, such as artificial neural network (Zhai 2013; Zhang 2015). Neural network can deal with complex nonlinear problems and has achieved some results. However, the neural network itself has some shortcomings, such as slow learning speed, easy to fall into the local extremum, learning and memory instability, etc.

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.

Radial basis function Kalman filter for attitude estimation in GPS‐denied environment

This study presents a radial basis function (RBF) aided extended Kalman filter (EKF) (namely, novel RBFEKF: NRBFEKF) to improve attitude estimation solutions in GPS-Denied environments. The NRBFEKF has been developed and applied for attitude estimation using only the outputs of strap-down IMU (gyroscopes and accelerometers) and strap-down magnetometer. In general, neural networks have the capability to map input-output relationships of a system without a-priori knowledge about them. A properly designed RBF neural network is able to learn and extract complex relationships given enough training. Furthermore, if there is a platform with inputs, outputs and many sensors, the RBF is able to adapt all the changes of sensors output. The RBFEKF, which is based on EKF aided by RBF network is validated in Matlab environment using simulated trip data and real data acquired during an UAV's trip. The RBFEKF has increased the accuracy of attitude estimation compared to typical EKF. In addition, the RBF is trained to map the vehicle manoeuvre for tuning measurement noise covariance matrix. Simulation results show that estimated measurement noise covariance matrix is closed to the nominal values in cruise flight (stationary phase), while in non-stationary phase the trained RBF neglects measurements from accelerometers, where accelerometer measurement model is not valid during this phase.

IOT and cloud computing based parallel implementation of optimized RBF neural network for loader automatic shift control

One of the key issues in automatic shift control of V-type cyclical loaders is determining how to find the best gear for the current conditions according to a certain mapping relation, but this complex and nonlinear mapping is difficult to express by a mathematical relation. However, to solve such nonlinear problems, a radial basis function (RBF) neural network is the best choice. In this paper, a certain type of wheel loader is taken as the research object, and an RBF neural network algorithm based on an improved genetic algorithm (GA) optimization is proposed. The global search ability of the GA is improved by adaptively adjusting the crossover probability and mutation probability. The RBF neural network expansion coefficient is optimized by an improved GA. Using industrial IOT technology, an optimized RBF neural network based on Map-Reduce on a cloud computing cluster is designed. The diesel engine computer and transmission computer on the loader are integrated to achieve dual-processor distributed parallel data processing and calculation. Then the loader automatic variable speed control algorithm model of improved GA optimized RBF neural network based on IOT cloud computing is established. The network model is trained and simulated using real vehicle automatic shift test data. The simulation results show that the improved GA-RBF neural network algorithm can achieve a correct recognition rate of 97.92%. The error matrix norm reaches the minimum value when the algorithm is iterated to the 17th generation. The improved algorithm has the advantages of a high gear recognition rate, fast convergence speed and strong real-time shift performance and is an effective new shift control method. The test results show that the shift boost time is less than 0.15 s and has a certain gradient. Compared with the manual shift process performed in the past, some improvements are achieved in the optimal shift time, shift response speed and shift quality. Compared with the traditional single computer based on serial training RBF neural network learning algorithm, whether it is Great progress has been made in convergence speed, training time, recognition rate, and data processing capabilities. Through the simulation and test, the validity of the intelligent shift control method of the improved GA optimized RBF neural network based on IOT cloud computing is verified. It has better engineering application value.

Scene classification using a new radial basis function classifier and integrated SIFT–LBP features

Scene classification is one of the most significant and challenging tasks in computer vision. This paper presents a new method for scene classification using bag of visual words and a particle swarm optimization (PSO)-based artificial neural network classifier. Contributions of this paper are introducing a novel feature integration method using scale invariant feature transform (SIFT) and local binary pattern (LBP) and a new framework for training radial basis function neural network, combining optimum steepest decent method with a specially designed PSO-based optimizer for center adjustment of radial basis function neural network. Our study shows that using LBP increases the performance of classification task compared to using SIFT only. In addition, our experiments on Proben1 dataset demonstrate improvements in classification performance (averagely about 6.04%) and convergence speed of the proposed radial basis function neural network. The proposed radial basis function neural network is then employed in scene classification task. Results are reported for classification of the Oliva and Torralba, Fei–Fei and Perona and Lazebnik et al. datasets. We compare the performance of the proposed classifier with a multi-way SVM classifier. Experimental results show the superiority of the proposed classifier over the state-of-the-art on the three datasets.

Constrained PSO Based Center Selection for RBF Networks Under Concurrent Fault Situation

In the training of radial basis function (RBF) networks, one important issue is to select RBF centers before constructing the networks. Most existing center selection methods are designed for the fault-free situation only. However, as the implementation of the networks may be perturbed by faults, these algorithms may lead to networks with degraded performance. This paper considers the center selection problem for RBF networks under the concurrent fault situation where multiplicative weight noise and open weight fault exist simultaneously. In particular, we introduce a binary label vector indicating the centers selected from training samples. Using the label vector, the fault-tolerant RBF model under the concurrent fault situation is reformulated as a constrained optimization problem, so that fault-tolerance can be considered in the procedure of center selection. To solve this constrained optimization problem, a constrained particle swarm optimization based algorithm is developed to select centers and train the network simultaneously. Simulation results show that the proposed algorithm is superior than state-of-the-art center selection algorithms.

Two-step optimization of electric discharge machining using neural network based approach and TOPSIS

The process performance of Electric Discharge Machining (EDM) process directly depends on the combination of input parameters. In this work, a two-step optimization has been performed to find the optimal combination of process parameters. In the first step, a neural network based multi-objective optimization technique is proposed and employed. The proposed approach generates the total possible combinations of input parameters taking the number and levels of each parameter into account. The performance measures for each combination is obtained by a trained neural network model of EDM process. Then, the optimal solution(s) are found following the concept of dominance. By employing the proposed approach, 24 non-dominated combinations of input parameters are obtained in this work. In the second step of optimization, Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) has been employed to award rank to each non-dominated solutions. Prior to that, experiments have been designed by Taguchi’s L36 orthogonal array and the experimental data has been used to train Radial Basis Function Neural Network (RBFNN) model.