Self-organizing Radial Basis Function Research Articles

Self-organizing RBF neural network based on IPSO and neural strength1

In this paper, a self-organizing RBF (SORBF) neural network with an adaptive threshold is proposed based on improved particle swarm optimization (IPSO) and neural strength (NS). The parameters and structure of SORBF can be optimized simultaneously and dynamically. Moreover, the tiresome problem of threshold setting is solved. Firstly, the network size and parameters of SORBF are mapped into the particle information of PSO. Secondly, an IPSO algorithm, based on diversity inertia weight and elite knowledge guiding, is proposed to reduce the probability of the population falling into the local optimum. Then, IPSO is used for optimizing the parameters of SORBF. Based on neuron growth intensity and competition intensity, SORBF can realize the hidden neuron addition and deletion adaptively. Moreover, the thresholds during the structure adjustment can be provided adaptively based on the network scale and neuron strength, which avoids the subjectivity setting and can improve the adaptive ability. Finally, the convergence analysis of IPSO is provided to ensure the performance of SORBF. Experiment results show that the proposed SORBF has good self-organizing ability and compact network structure compared with other methods.

A Multitask Learning Model for the Prediction of NOx Emissions in Municipal Solid Waste Incineration Processes

Selective non-catalytic reduction (SNCR) is a commercially available technology that can effectively reduce the nitrogen oxides ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm {NO}}_{x}$ </tex-math></inline-formula> ) emissions in municipal solid waste incineration (MSWI) processes. Real-time measurement of NOx emissions is important to improve the denitration efficiency of SNCR. However, there are commonly time delays to obtain the measurement results from the traditional continuous emission monitoring system (CEMS). In this study, a prediction model based on multitask learning (MTL) is proposed for real-time measurement of NOx emissions. First, time delays are analyzed by using the maximum average cross-correlation function (MACCF) method, and sequences are adjusted according to the time delays, thereby recovering the original data pattern. Second, input variables are selected using a maximal information coefficient (MIC) method to reduce redundant information. Then, an MTL model is constructed for the prediction of NOx emissions. By using the MTL mechanism to share information of related prediction tasks, the potential correlations of industrial time-series data are mined, therefore improving the generalization performance of the model. Also, a self-organizing radial basis function neural network is designed as the module of the MTL model to further improve the prediction accuracy of the model. A strategy for incrementally constructing the MTL model is developed to guarantee the computational efficiency of the model. Finally, the established model is tested using a benchmark dataset and the real industrial data from an MSWI plant. The experimental results show that the proposed MTL model outperforms other state-of-the-art models on computational efficiency and prediction accuracy, demonstrating the potentiality of the MTL model in real-time measurement of NOx emissions in MSWI processes.

Enhanced artificial ecosystem-based optimization self-organizing RBF neural network

Enhanced artificial ecosystem-based optimization self-organizing RBF neural network

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.

Non-Singular Fast Terminal Sliding Mode Control of High-Speed Train Network System Based on Improved Particle Swarm Optimization Algorithm

This paper proposes a non-singular fast terminal sliding mode control strategy based on the self-organizing radial basis function neural network (RBFNN) approximation for the train key network system to realize the safe and reliable operation of the train. In order to improve the RBFNN approximation performance and speed, an improved multi-strategy particle swarm optimization (IMPSO) algorithm, which utilizes multi-strategy evolution ways with a nonlinear deceasing inertia weight to improve the global optimizing performance of particle swarm, is proposed to optimize the structure and parameters for better mapping the highly nonlinear characteristics of train traction braking. In addition, the IMPSO is also introduced into a non-singular fast terminal sliding mode (NFTSM) controller to obtain the most appropriate tuning parameters of the controller and suppresses the chattering phenomenon from sliding mode controller. The stability characteristic of the system under the proposed NFTSM controller is studied based on the Lyapunov theory. Further combined with effective delay prediction and delay compensation methods, the NFTSM high-precision control of the train key nonlinear network system is implemented. The simulation results show that the proposed method has more efficient and robust tracking performance and real-time performance compared with other control methods, which can provide effective means for realizing the symmetrical bus control by automatic train operation (ATO) at both ends of the train, with the safe operation of the train under every complex motion condition.

A Hybrid Model based on Radial basis Function Neural Network for Intrusion Detection

An Intrusion Detection System (IDS) is a system that monitors the network for identifying malicious activities. Upon identifying the unusual activities, IDS sends a notification to the network administrators to warn about the hackers’ hostile activities. To detect intrusion, signature-based systems are consid-ered to be one of the most effective methods. However, they cannot detect new attacks. Additionally, it is costly and challenging to keep the attack signatures database up to date with known signatures, which constructed a significant drawback. Neural networks are capable of learning through input patterns and have the potential to generalize data. In this paper, we propose a hybrid model based on Directed Batch Growing Self-Organizing Map (DBGSOM) combined with a Radial Basis Function Neural Network (RBFNN) detecting abnormalities in the network. Based on our experiment, the proposed model performed well and has resulted in satisfactory performance measures compared to Self-Organizing Maps and Radial Basis Function Neural Network (SOM&RBFNN) model.

A self-organizing RBF neural network based on distance concentration immune algorithm

Radial basis function neural network &#x0028 RBFNN &#x0029 is an effective algorithm in nonlinear system identification. How to properly adjust the structure and parameters of RBFNN is quite challenging. To solve this problem, a distance concentration immune algorithm &#x0028 DCIA &#x0029 is proposed to self-organize the structure and parameters of the RBFNN in this paper. First, the distance concentration algorithm, which increases the diversity of antibodies, is used to find the global optimal solution. Secondly, the information processing strength &#x0028 IPS &#x0029 algorithm is used to avoid the instability that is caused by the hidden layer with neurons split or deleted randomly. However, to improve the forecasting accuracy and reduce the computation time, a sample with the most frequent occurrence of maximum error is proposed to regulate the parameters of the new neuron. In addition, the convergence proof of a self-organizing RBF neural network based on distance concentration immune algorithm &#x0028 DCIA-SORBFNN &#x0029 is applied to guarantee the feasibility of algorithm. Finally, several nonlinear functions are used to validate the effectiveness of the algorithm. Experimental results show that the proposed DCIA-SORBFNN has achieved better nonlinear approximation ability than that of the art relevant competitors.

Long term electric load forecasting based on TS-type recurrent fuzzy neural network model

It is of great demand in the power industry to use hourly information to establish the appropriate predictive model and improve the forecasting accuracy in the short/long term load forecasting processes. In this paper, we propose a new load forecasting approach to provide a more accurate and defensible forecast on the long term load forecasting process. The proposed method consists of two stages: weather station selection stage and Takagi–Sugeno (TS) fuzzy model based prediction stage. In the first stage, a new weather station selection method is developed, in which the most relevant 3 weather stations are combined to generate 5 temperature series for each zone and the temperature series with the least mean absolute percentage error (MAPE) is chosen as the weather station information used to forecast. At the second stage, an improved self-organizing radial basis function recurrent neural network with TS fuzzy model (ISO-TS-RBF-RFNN) is exploited in view of the conditions such as the appearing uncertainties of holiday feature component in different years, the violation of Gaussian distribution on feature component and the temperature measurement divergence. In the proposed ISO-TS-RBF-RFNN model, a computing method on current firing strength of the fuzzy modes is developed by using a novel type of activation mechanism and robust-type fuzzy rules to improve the robustness of the predictive model. Finally, we use the same partition in the dataset from GEFCom2012 to train and demonstrate the application of the proposed model. Compared with the other five models i.e., MLR, SVR, FIR, GA-LSTM and traditional SO-TS-RBF-RFNN, the proposed model has higher forecasting accuracy than others under four evaluation criteria.

A proposed self-organizing radial basis function network for aero-engine thrust estimation

This paper proposes a new algorithm to construct self-organizing radial basis function neural networks (RBFNNs) for aero-engine thrust estimation. The algorithm can not only optimize centers and network size of the RBFNN but also automatically determine the connection weights. To reduce the dimensionality of particle and speed up the optimization process, spreads of an RBFNN are randomly initialized. Its weights are dynamically derived and adjusted by the product between the Moore–Penrose inverse of the hidden layer's outputs and the desired outputs. To optimize the centers and network size of the RBFNN, a strategy named multi-Gbest is adopted. Based on all these strategies, the proposed algorithm can effectively generate self-organizing RBFNNs with high accuracy. The successful application to aero-engine thrust estimation shows the practicability and effectiveness of the proposed algorithm.

Infrared flame detection based on a self-organizing TS-type fuzzy neural network

The radial basis function neural network (RBF-NN) integrating Takagi-Sugeno (TS) fuzzy model has been widely used in pattern recognition and intelligence system for its relatively simple structure, good local approximating capability, interpretably and function equivalence. In this paper, we propose a new scheme to generate the variable structure of the model by adding, merging or deleting corresponding nodes (fuzzy rules). Then an adaptive learning algorithm is developed to overcome the local minimum by adjusting parameters just with the gradient descent. To improve the robustness of the model, a bias of firing strength is proposed to suppress the outputs of the outliers as well as the recognition of the faults in infrared flame detection. Finally, experimental data obtained from a developed triple-channel infrared flame detector are used to demonstrate the performance of the improved self-organizing radial basis function fuzzy neural network (ISO-TS-RBF) compared with SO-TS-RBF in [1], TS-RBF in [2] and TS-type fuzzy neural network with particle swarm optimization (PSO-TS-RBF) in [3]. The comparison results show that the model we proposed has the best accuracy, generalization ability and robustness that it can well recognize the outliers caused by the real faults occurred in the infrared flame detection procedure.

Nonlinearities compensator based on SORBFNN in ultra-long-haul high-capacity CO-OFDM systems

Radial basis function neural network is recognized as being the most useful type of neural network for a nonlinear equalizer in the CO-OFDM system. In the history of nonlinear equalizers, the focus has always been on mitigation of nonlinearity. Despite this interest, no one to the best of our knowledge has studied ultra-long-haul transmission length. Previous work has been limited to normal transmission length, i.e., up to 1400 km. In ultra-long-haul optical fiber communication systems, the optical signal becomes very much complex at longer distance, i.e., around over 8000 km. It has not yet been established whether radial basis function neural network can do the same improvement in performance at ultra-long-haul transmission length. A basic issue of a customary radial basis function neural system is its low performance at such a long distance. This paper presents a new approach to compensating nonlinearities in ultra-long-haul optical fiber communication CO-OFDM systems. In this new approach, a radial basis function with nonlinear equalizer (first hidden layer with automatically adjusted structure, i.e., number of neuron nodes in the hidden layer and the different parameters of the structure through learning, and second hidden layer with fixed structure) based on two hidden layers has been recommended. The aim of this study is to examine the performance of a self-organizing radial basis function neural network-based nonlinear equalizer (SORBFNN-NLE) for the mitigation of nonlinearities in ultra-long-haul CO-OFDM systems. Better performance of the SORBFNN is attributed due to self-organizing structure and training of network. From this study, it has been observed that the proposed SORBFNN-NLE performs well regarding Q-factor and OSNR at an ultra-long distance.

Evaluation for Sortie Generation Capacity of the Carrier Aircraft Based on the Variable Structure RBF Neural Network with the Fast Learning Rate

The neural network has the advantages of self‐learning, self‐adaptation, and fault tolerance. It can establish a qualitative and quantitative evaluation model which is closer to human thought patterns. However, the structure and the convergence rate of the radial basis function (RBF) neural network need to be improved. This paper proposes a new variable structure radial basis function (VS‐RBF) with a fast learning rate, in order to solve the problem of structural optimization design and parameter learning algorithm for the radial basis function neural network. The number of neurons in the hidden layer is adjusted by calculating the output information of neurons in the hidden layer and the multi‐information between neurons in the hidden layer and output layer. This method effectively solves the problem that the RBF neural network structure is too large or too small. The convergence rate of the RBF neural network is improved by using the robust regression algorithm and the fast learning rate algorithm. At the same time, the convergence analysis of the VS‐RBF neural network is given to ensure the stability of the RBF neural network. Compared with other self‐organizing RBF neural networks (self‐organizing RBF (SORBF) and rough RBF neural networks (RS‐RBF)), VS‐RBF has a more compact structure, faster dynamic response speed, and better generalization ability. The simulations of approximating a typical nonlinear function, identifying UCI datasets, and evaluating sortie generation capacity of an carrier aircraft show the effectiveness of VS‐RBF.

Self-Organizing Brain Emotional Learning Controller Network for Intelligent Control System of Mobile Robots

The trajectory tracking ability of mobile robots suffers from uncertain disturbances. This paper proposes an adaptive control system consisting of a new type of self-organizing neural network controller for mobile robot control. The newly designed neural network contains the key mechanisms of a typical brain emotional learning controller network and a self-organizing radial basis function network. In this system, the input values are delivered to a sensory channel and an emotional channel, and the two channels interact with each other to generate the final outputs of the proposed network. The proposed network possesses the ability of online generation and elimination of fuzzy rules to achieve an optimal neural structure. The parameters of the proposed network are online tunable by the brain emotional learning rules and gradient descent method; in addition, the stability analysis theory is used to guarantee the convergence of the proposed controller. In the experimentation, a simulated mobile robot was applied to verify the feasibility and effectiveness of the proposed control system. The comparative study using the cutting-edge neural network-based control systems confirms that the proposed network is capable of producing better control performances with high computational efficiency.

Self-Organizing RBF Neural Network Using an Adaptive Gradient Multiobjective Particle Swarm Optimization.

One of the major obstacles in using radial basis function (RBF) neural networks is the convergence toward local minima instead of the global minima. For this reason, an adaptive gradient multiobjective particle swarm optimization (AGMOPSO) algorithm is designed to optimize both the structure and parameters of RBF neural networks in this paper. First, the AGMOPSO algorithm, based on a multiobjective gradient method and a self-adaptive flight parameters mechanism, is developed to improve the computation performance. Second, the AGMOPSO-based self-organizing RBF neural network (AGMOPSO-SORBF) can optimize the parameters (centers, widths, and weights), as well as determine the network size. The goal of AGMOPSO-SORBF is to find a tradeoff between the accuracy and the complexity of RBF neural networks. Third, the convergence analysis of AGMOPSO-SORBF is detailed to ensure the prerequisite of any successful applications. Finally, the merits of our proposed approach are verified on multiple numerical examples. The results indicate that the proposed AGMOPSO-SORBF achieves much better generalization capability and compact network structure than some other existing methods.

Modelling and Evaluation of Sequential Batch Reactor Using Artificial Neural Network

The main objective of wastewater treatment plant is to release safe effluent not only to human health but also to the natural environment. An aerobic granular sludge technology is used for nutrient removal of wastewater treatment process using sequential batch reactor system. The nature of the process is highly complex and nonlinear makes the prediction of biological treatment is difficult to achieve. To study the nonlinear dynamic of aerobic granular sludge, high temperature real data at 40˚C were used to model sequential batch reactor using artificial neural network. In this work, the radial basis function neural network for modelling of nutrient removal process was studied. The network was optimized with self-organizing radial basis function neural network which adjusted the network structure size during learning phase. Performance of both network were evaluated and compared and the simulation results showed that the best prediction of the model was given by self-organizing radial basis function neural network.

An Adaptive-PSO-Based Self-Organizing RBF Neural Network.

In this paper, a self-organizing radial basis function (SORBF) neural network is designed to improve both accuracy and parsimony with the aid of adaptive particle swarm optimization (APSO). In the proposed APSO algorithm, to avoid being trapped into local optimal values, a nonlinear regressive function is developed to adjust the inertia weight. Furthermore, the APSO algorithm can optimize both the network size and the parameters of an RBF neural network simultaneously. As a result, the proposed APSO-SORBF neural network can effectively generate a network model with a compact structure and high accuracy. Moreover, the analysis of convergence is given to guarantee the successful application of the APSO-SORBF neural network. Finally, multiple numerical examples are presented to illustrate the effectiveness of the proposed APSO-SORBF neural network. The results demonstrate that the proposed method is more competitive in solving nonlinear problems than some other existing SORBF neural networks.

Modeling corporate customers’ credit risk considering the ensemble approaches in multiclass classification: evidence from Iranian corporate credits

The credit scoring system is one of the most significant credit risk control tools in the banking industry. Usually, the existing credit scoring models classify customers into "good credit" and "bad credit" groups. In this study, a novel model is proposed to classify corporate client accounts into four groups - good credit, past due, overdue and doubtful - according to the definitions of the Central Bank of the Islamic Republic of Iran. This model enables lenders to develop specific policies for credit granting by predicting the solvency and insolvency rates of their corporate clients. For validation, the proposed model, trained by the hybrid approach of a self-organizing map and radial basis function (RBF) neural network, is compared with a single-step, four-class classification model and a model trained by support vector machines. The results show that the proposed model trained by the hybrid approach of a self-organizing map and RBF neural network outperforms the existing methods in terms of its final accuracy with regard to the four classes at the test stage.

An Efficient Hybrid Neural Network Model for Wind Speed Prediction

This paper deals with renewable energy system needs a hybrid neural network model on predicting the accurate wind speed. The wind speed and wind direction is fluctuating in nature. Therefore short term and long term wind speed forecast is more significant for establishing the availability of wind power generation. The objective is to compute the wind speed using hybrid neural network models which includes Self-Organizing Map and Radial Basis Function neural network. The proposed SOM-RBF model uses three input data such as wind speed (m/s), wind direction (degree) and temperature (degree Celsius) collected from Coimbatore wind farm. In this work, the SOM-RBF hybrid model used to predict a day ahead wind speed using past data. The experimental results show that root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) is much lesser and correlation coefficient is reaches to one. This validates the suitability of SOM-RBF model for wind speed prediction task than single models.

Modeling and optimum operating conditions for FCCU using artificial neural network

A self-organizing radial basis function (RBF) neural network (SODM-RBFNN) was presented for predicting the production yields and operating optimization. Gradient descent algorithm was used to optimize the widths of RBF neural network with the initial parameters obtained by k-means learning method. During the iteration procedure of the algorithm, the centers of the neural network were optimized by using the gradient method with these optimized width values. The computational efficiency was maintained by using the multi-threading technique. SODM-RBFNN consists of two RBF neural network models: one is a running model used to predict the product yields of fluid catalytic cracking unit (FCCU) and optimize its operating parameters; the other is a learning model applied to construct or correct a RBF neural network. The running model can be updated by the learning model according to an accuracy criterion. The simulation results of a five-lump kinetic model exhibit its accuracy and generalization capabilities, and practical application in FCCU illustrates its effectiveness.

A direct self-constructing neural controller design for a class of nonlinear systems.

This paper is concerned with the problem of adaptive neural control for a class of uncertain or ill-defined nonaffine nonlinear systems. Using a self-organizing radial basis function neural network (RBFNN), a direct self-constructing neural controller (DSNC) is designed so that unknown nonlinearities can be approximated and the closed-loop system is stable. The key features of the proposed DSNC design scheme can be summarized as follows. First, different from the existing results in literature, a self-organizing RBFNN with adaptive threshold is constructed online for DSNC to improve the control performance. Second, the control law and adaptive law for the weights of RBFNN are established so that the closed-loop system is stable in the term of Lyapunov stability theory. Third, the tracking error is guaranteed to uniformly asymptotically converge to zero with the aid of an additional robustifying control term. An example is finally given to demonstrate the design procedure and the performance of the proposed method. Simulation results reveal the effectiveness of the proposed method.