Trained Radial Basis Function Neural Network Research Articles

Development of a novel RBFNN‐trained nonlinear channel equalizer based on GDEBOA technique

AbstractThe equalization of digital channels is generally known to be a nonlinear classification problem. Applications such as these can benefit from networks that approximate nonlinear mappings. It gets good performance by adjusting only one coefficient and one center closest to the input vector of the radial basis function network (RBFN), which is a simplified version of stochastic gradient techniques. Artificial Neural Networks (ANNs) are suitable for channel equalization because they have the capability to map between variables. Having only one hidden layer in Radial Basis Function Neural Network (RBFNN) makes it the most preferred equalizer to mitigate distortions in the channels. The ability to equalize nonlinear channels is strength of radial RBFNN, which is a simplified version of stochastic gradient techniques. The conventional “hit and trial” approach poses the greatest difficulty when designing RBFNN Equalizers. As a solution to these limitations, this work suggests a training strategy based on Gaussian distribution estimation strategy (GDE) in hybrid butterfly optimization algorithm (GDEBOA) for RBFNN channel equalizer. The proposed RBFNN equalizer is being trained using a population‐based optimization algorithm. An algorithm, called GDEBOA, based on a GDE approach is developed in this paper. The proposed training scheme significantly outperforms existing metaheuristic algorithms in terms of mean square error (MSE) and bit error rate (BER). Furthermore, based on burst error scenarios and bit error probability (BEP), the proposed method has demonstrated greater robustness than other methods when faced with such scenarios. The effectiveness of the suggested scheme over a wide range of signal‐to‐noise ratios has been validated by several simulation studies. Additionally, statistical importance of the suggested technique is analyzed. It is visualized that GDEBOA performs better than existing algorithms for training RBFNN equalizer.

Calibration of DEM models for fertilizer particles based on numerical simulations and granular experiments

The discrete element method (DEM) can accurately predict and describe the motion behavior of granular materials; it has been widely used in related research in all walks of life. However, the material microscopic parameters involved in a simulation are difficult to measure using experimental methods, and the accuracy of the microscopic parameters has a direct impact on the predicted material motion behavior. In this study, a new calibration method was used to calibrate contact parameters commonly used in DEM simulations for fertilizer particles. The angle of repose (AoR) and the bulk height were selected as macroscopic response indicators, and the coefficient of restitution, coefficient of static friction, and coefficient of rolling friction of fertilizer particles were used as the parameters to be calibrated in the study. The input parameters required for the training of the radial basis function neural network (RBFNN) were obtained by combining Latin hypercube sampling with funnel stacking simulations. Finally, a multi-island genetic algorithm (MIGA) was used to optimally solve the approximate model, and comparative experiments and discharge experiments were conducted to validate the model. The results show that the sphericity of the fertilizer particles in the study is 90%, and spherical particles can be used instead in the simulation. Additionally, the approximate model obtained from the RBFNN training has a high model fit to the input and output parameters and a good prediction capability for the macroscopic behavior generated by the input parameters of the fertilizer particles. The result generated from the calibration was a set of data solutions, and the errors were less than 5% after validation of the data. Further experimental validation was done using the discharge experiment, which was consistent with the simulation results, indicating that the calibration results can accurately reflect the macroscopic motion behavior of the fertilizer particles, further illustrating the reliability of the method.

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.

Fuzzy whale optimisation algorithm: a new hybrid approach for automatic sonar target recognition

ABSTRACT In this paper, a radial basis function neural network (RBF-NN) automatic sonar target recognition system is proposed. For the RBF-NN training phase, a whale optimisation algorithm (WOA) developed with a fuzzy system has been used (which is called FWOA). The reason for using the fuzzy system is the lack of correct identification of the boundary between the two stages of exploration and exploitation. Thus, the tuning of the effective parameters of the WOA is left to the fuzzy system of the Mamdani type. RBF-NN was trained by chimp optimisation algorithm (ChOA), genetic algorithm (GA), Evolution Strategy (ES), league championship algorithm (LCA), grey wolf algorithms (GWO), gravitational search algorithm (GSA), and WOA to compare the proposed algorithm. The measured criteria are convergence speed, ability to avoid local optimisation, and classification rate. The simulation results showed that FWOA with 97.49% classification accuracy rate in sonar data performed better than the other seven benchmark algorithms.

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.

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.

Beamforming against main lobe interference based on radial basis function neural network

Aiming at the problem that the performance of traditional beamforming algorithm deteriorates sharply in the presence of main lobe interference, a beamforming algorithm based on radial basis function (RBF) neural network is proposed. Firstly, the minimum variance distortionless response (MVDR) is used to solve the optimal beam pattern in the presence of side lobe interference. Then, the training set of RBF neural network is constructed according to the optimal beam pattern and the direction information of main lobe interference to train the network, so that the trained RBF neural network can suppress the main lobe interference while maintaining the ability of optimal beamforming. The simulation results show that the method can overcome the limitations of traditional beamforming algorithm, suppress the main lobe interference and side lobe interference, and form the correct beam direction. At the same time, the algorithm also has good real-time performance.

The Application of RBF Neural Network Optimized by K-means and Genetic-backpropagation in Fault Diagnosis of Power Transformer

Through the dissolved gas analysis (DGA) in transformer oil, the fault of the power transformer can be diagnosed. However, the DGA method has the disadvantage of low accuracy because it couldn’t exactly reflect the nonlinear relationship between the characteristic gases and fault types. Radial basis function neural network (RBFNN) has the advantage of dealing with complex nonlinear problems, so it can be applied to transformer fault diagnosis based on DGA. The centers, widths and weights has important effects on the performance of the RBFNN. However, it is difficult to find the global optimal solution of these parameters when RBFNN training. This paper creatively designs a method to improve these parameters of RBFNN, firstly using the K-means algorithm to optimize the centers and widths of RBFNN, then using the genetic algorithm-backpropagation (GA-BP) algorithm optimize the weights. Finally, establish the K-means RBF-genetic backpropagation (KRBF-GBP) algorithm model through a large amount of training data. The test results show that the fault diagnosis accuracy of the KRBF-GBP algorithm is 96.4%, higher than the unoptimized RBFNN with 71.43%.

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.

Automated diabetic retinopathy detection using radial basis function

Diabetic mellitus is a major reason of visual impairment an around the world. Early automatic diagnosis of diabetic retinopathy (DR) may avoid vision loss and blindness. The goal of this paper is to automatically detect retinal image as Non DR or DR based on radial basis function (RBF) neural network classifier. This experiment address to explore ophthalmic features such as blood vessels, exudates & microaneurysms and it’s segmented from retinal background using A-IFS histon based segmentation method. This obtained feature set delivers to train RBF neural network. The Receiver operation characteristics (ROC) curve is plotted based on evaluated result. The projected experiment has been done on 130 DIARETDB0 & 89 DIARETDB1 retinal images database by using RBF neural network. The experiment perceive the accuracy of 71.2%, Sensitivity 0.83 & Specificity 0.043 for DIARETDB0 and the accuracy of 89.4% Sensitivity 0.94 & Specificity 0.16 for DIARETDB1.

Fast Multi-Objective Antenna Optimization Based on RBF Neural Network Surrogate Model Optimized by Improved PSO Algorithm

In this paper, a radial basis function neural network (RBFNN) surrogate model optimized by an improved particle swarm optimization (PSO) algorithm is developed to reduce the computation cost of traditional antenna design methods which rely on high-fidelity electromagnetic (EM) simulations. Considering parameters adjustment and update mechanism simultaneously, two modifications are proposed in this improved PSO. First, time-varying learning factors are designed to balance exploration and exploitation ability of particles in the search space. Second, the local best information is added to the updating process of particles except for personal and global best information for better population diversity. The improved PSO is applied to train RBFNN for determining optimal network parameters. As a result, the constructed improved PSO-RBFNN model can be used as a surrogate model for antenna performance prediction with better network generalization capability. By integrating the improved PSO-RBFNN surrogate model with multi-objective evolutionary algorithms (MOEAs), a fast multi-objective antenna optimization framework for multi-parameter antenna structures is then established. Finally, a Pareto-optimal planar miniaturized multiband antenna design is presented, demonstrating that the proposed model provides better prediction performance and considerable computational savings compared to those previously published approaches.

Identification of generator criticality and transient instability by supervising real-time rotor angle trajectories employing RBFNN

Identification of transient stability state in real-time and maintaining stability through preventive control technology are challenging tasks for a large power system while integrating deregulation constraints. Widely employment of the phasor measurement units (PMUs) in a power system and development of wide area management systems (WAMS) give relaxation to monitoring, measurement and control hurdles. This paper focuses on two research objectives; the first is transient stability assessment (TSA) and second is selection of the appropriate member for the control operation in unstable operating scenario. A model based on the artificial machine learning and PMU data is constructed for achieving both the objectives. This model works through prompt TSA status with radial basis function neural network (RBFNN) and validates it with PMU data to determine the criticality level of the generators. To reduce the complexity of the model a transient stability index (TSI) is proposed in this paper. A RBFNN is used to determine the transient stability aspects like stability status of system, coherent group and criticality rank of generator and preventive control action, following a large perturbation. PMUs measure post-fault rotor angle values and these are used as input for training RBFNN. The proposed approach is demonstrated on the IEEE 10-generator 39-bus, 16-generator 68-bus and 50-generator 145-bus test power systems successfully and the effectiveness of the approaches is discussed.

The Application of Radial Basis Function (RBF) Neural Network for Mechanical Fault Diagnosis of Gearbox

In this paper, the radial basis function (RBF) neural network is used for the mechanical fault diagnosis of a gearbox. We introduce the basic principles of the RBF neural network which is used for pattern classification and features a fast learning pace and strong nonlinear mapping capability; thus, it can be employed for fault diagnosis. The gearbox is a widely-used piece of equipment in engineering, and diagnosing mechanical faults is of great significance for engineers. A numerical example is presented to demonstrate the capability of the proposed method. The results indicate that the mechanical faults of a gearbox can be correctly diagnosed with a trained RBF neural network.

Combining SOM and evolutionary computation algorithms for RBF neural network training

This paper intends to enhance the learning performance of radial basis function neural network (RBFnn) using self-organizing map (SOM) neural network (SOMnn). In addition, the particle swarm optimization (PSO) and genetic algorithm (GA) based (PG) algorithm is employed to train RBFnn for function approximation. The proposed mix of SOMnn with PG (MSPG) algorithm combines the automatically clustering ability of SOMnn and the PG algorithm. The simulation results revealed that SOMnn, PSO and GA approaches can be combined ingeniously and redeveloped into a hybrid algorithm which aims for obtaining a more accurate learning performance among relevant algorithms. On the other hand, method evaluation results for four continuous test function experiments and the demand estimation case showed that the MSPG algorithm outperforms other algorithms and the Box–Jenkins models in accuracy. Additionally, the proposed MSPG algorithm is allowed to be embedded into business’ enterprise resource planning system in different industries to provide suppliers, resellers or retailers in the supply chain more accurate demand information for evaluation and so to lower the inventory cost. Next, it can be further applied to the intelligent manufacturing system to cope with real situation in the industry to meet the need of customization.

An Application of DWT and RBFNN for Fault Location for Single Line to Ground Fault on Hvac Transmission Line

This article demonstrates a technique for diagnosis of fault location on overhead transmission lines for single line to ground fault. The proposed method is based on discrete wavelet transform (DWT) and radial basis function neural network (RBFNN). A number of features have been extracted from faulty signal using DWT and are used for training of RBFNN for fault detection. It has been found that fault locator based on discrete wavelet transform and RBFNN neural network can accurately locate the fault with an average accuracy 2.31%. From the result it can be concluded that the proposed method for fault location estimation for a single line to ground fault (LG fault) is capable of giving results with acceptable accuracy.

Online identification using radial basis function neural network coupled with KPCA

In this paper, we are going to propose an online radial basis function (RBF) neural network algorithm without any preprocessing step. Then a kernel principal component analysis (KPCA) is coupled with the proposed online RBF neural network algorithm. Indeed, the KPCA method is used as a preprocessing step to reduce the feature dimension which fed to the RBF neural network. Reducing memory requirements of the models makes RBF neural network training efficient and fast. These two proposed algorithms are applied, with success, for identification of a mobile robot position. The simulation results present that the used sigmoid function as a kernel, compared to other kernel functions, which gives an excellent model and a minimum mean square error.

RBF neural network-based online intelligent management of a battery energy storage system for stand-alone microgrids

An offline optimization approach based on energy storage management response in a microgrid was not fast and not reliable enough to control and adjust the system efficiently after the loss of the utility grid. Thus, it causes system inefficiency and collapse in the presence of violent changes of loads or outage of distributed generations. To solve such a problem, more real-time management is needed. Any changes in loads/generations should be compensated successfully by a battery energy storage system (BESS) in a short period of time. This paper presents a new method for the intelligent online management of both active and reactive power of a BESS based on a radial basis function neural network (RBFNN) incorporating particle swarm optimization (PSO) to prevent the stand-alone microgrid from instability and system collapse. BESS is centrally controlled by a controller developed by the proposed RBFNN. PSO is used to determine the optimized active and reactive power at every load/generation changing situation to monitor the effect of system frequency, voltage, and reference power regulation. These optimized power data are then employed as target data for the RBFNN generalization and training process. To enable the online updating of the operating parameters, the proposed RBFNN is implemented in the management process. With an appropriate RBFNN training, the optimum active and reactive power can directly be obtained without the necessity of performing the PSO optimization process at any change of load/generation. The results show that the predictive results of the proposed RBFNN model only slightly differed from the target results based on PSO and have a minimum statistical error compared to the predictive results based on the multilayer perceptron neural network (MLPNN) model. The proposed RBFNN is suitable for the online estimation of the active and reactive power of BESS and can be used for real-time energy storage management as an online controller.

光伏电站输出功率的主因隐藏型RBFNN预测方法

提出了一种光伏电站功率的主因隐藏型径向基神经网络(RBFNN)预测方法。先合理隐去影响光伏电站功率的主要气象因素“太阳辐射强度”，建立RBFNN预测模型。再按与预测时点气象因素记录的马氏距离从历史记录中筛选出相似样本集，对RBFNN模型进行学习训练。运用训练好的RBFNN实现短期光伏电站功率的预测。这种方法不仅合理隐去了预测中难以获取的地面太阳辐射强度、使光伏功率预测易于实现，而且运用马氏距离筛选样本、改进了预测精度。仿真结果验证了本文方法的有效性。 A radial basis function neural network (RBFNN) based photovoltaic power prediction method with hiding of main influencing factor is proposed in this paper. Firstly, the main influencing factor of solar radiation intensity on photovoltaic power is hidden rationally, and RBFNN based photovoltaic power prediction model is built. Then the similar samples are screened out from historical records of meteorological factors according to their Mahalanobis distances from the record of meteorological factors of the prediction time point, which are used to train the RBFNN model. At last, the trained RBFNN is used to predict the output power of the photovoltaic power station. The proposed method hides rationally the ground solar radiation intensity that is difficult to obtain and has important influence on photovoltaic power in the prediction, which makes photovoltaic power prediction easy to implement. In addition, the screening of similar samples by Mahalanobis distance improves the accuracy of photovoltaic power prediction. Simulation results show the effectiveness of the proposed method.

Training Radial Basis Function Neural Networks for Classification via Class-Specific Clustering.

In training radial basis function neural networks (RBFNNs), the locations of Gaussian neurons are commonly determined by clustering. Training inputs can be clustered on a fully unsupervised manner (input clustering), or some supervision can be introduced, for example, by concatenating the input vectors with weighted output vectors (input-output clustering). In this paper, we propose to apply clustering separately for each class (class-specific clustering). The idea has been used in some previous works, but without evaluating the benefits of the approach. We compare the class-specific, input, and input-output clustering approaches in terms of classification performance and computational efficiency when training RBFNNs. To accomplish this objective, we apply three different clustering algorithms and conduct experiments on 25 benchmark data sets. We show that the class-specific approach significantly reduces the overall complexity of the clustering, and our experimental results demonstrate that it can also lead to a significant gain in the classification performance, especially for the networks with a relatively few Gaussian neurons. Among other applied clustering algorithms, we combine, for the first time, a dynamic evolutionary optimization method, multidimensional particle swarm optimization, and the class-specific clustering to optimize the number of cluster centroids and their locations.

Immunological Algorithm-based Neural Network Learning for Sales Forecasting

This study proposes a variation immunological system (VIS) algorithm with radial basis function neural network (RBFN) learning for function approximation and the exercise of industrial computer (IC) sales forecasting. The proposed VIS algorithm was applied to the RBFN to execute the learning process for adjusting the network parameters involved. To compare the performance of relevant algorithms, three benchmark problems were used to justify the results of the experiment. With better accuracy in forecasting, the trained RBFN can be practically utilized in the IC sales forecasting exercise to make predictions and could enhance business profit.