Radial basis function network training using a nonsymmetric partition of the input space and particle swarm optimization

Data-Knowledge-Driven Self-Organizing Fuzzy Neural Network

Fuzzy neural networks (FNNs) hold the advantages of knowledge leveraging and adaptive learning, which have been widely used in nonlinear system modeling. However, it is difficult for FNNs to obtain the appropriate structure in the situation of insufficient data, which limits its generalization performance. To solve this problem, a data-knowledge-driven self-organizing FNN (DK-SOFNN) with a structure compensation strategy and a parameter reinforcement mechanism is proposed in this article. First, a structure compensation strategy is proposed to mine structural information from empirical knowledge to learn the structure of DK-SOFNN. Then, a complete model structure can be acquired by sufficient structural information. Second, a parameter reinforcement mechanism is developed to determine the parameter evolution direction of DK-SOFNN that is most suitable for the current model structure. Then, a robust model can be obtained by the interaction between parameters and dynamic structure. Finally, the proposed DK-SOFNN is theoretically analyzed on the fixed structure case and dynamic structure case. Then, the convergence conditions can be obtained to guide practical applications. The merits of DK-SOFNN are demonstrated by some benchmark problems and industrial applications.

A Machine Learning Model Ensemble for Mixed Power Load Forecasting across Multiple Time Horizons

The increasing penetration of renewable energy sources tends to redirect the power systems community's interest from the traditional power grid model towards the smart grid framework. During this transition, load forecasting for various time horizons constitutes an essential electric utility task in network planning, operation, and management. This paper presents a novel mixed power-load forecasting scheme for multiple prediction horizons ranging from 15 min to 24 h ahead. The proposed approach makes use of a pool of models trained by several machine-learning methods with different characteristics, namely neural networks, linear regression, support vector regression, random forests, and sparse regression. The final prediction values are calculated using an online decision mechanism based on weighting the individual models according to their past performance. The proposed scheme is evaluated on real electrical load data sensed from a high voltage/medium voltage substation and is shown to be highly effective, as it results in R² coefficient values ranging from 0.99 to 0.79 for prediction horizons ranging from 15 min to 24 h ahead, respectively. The method is compared to several state-of-the-art machine-learning approaches, as well as a different ensemble method, producing highly competitive results in terms of prediction accuracy.

A high accuracy modeling scheme for dynamic systems: spacecraft reaction wheel model

Reaction wheels are crucial actuators in spacecraft attitude control subsystem (ACS). The precise modeling of reaction wheels is of fundamental need in spacecraft ACS for design, analysis, simulation, and fault diagnosis applications. The complex nature of the reaction wheel leads to modeling difficulties utilizing the conventional modeling schemes. Additionally, the absence of reaction wheel providers’ parameters is crucial for triggering a new modeling scheme. The Radial Basis Function Neural Network (RBFNN) has an efficient architecture, alluring generalization properties, invulnerability against noise, and amazing training capabilities. This research proposes a promising modeling scheme for the spacecraft reaction wheel utilizing RBFNN and an improved variant of the Quantum Behaved Particle Swarm Optimization (QPSO). The problem of enhancing the network parameters of the RBFNN at the training phase is formed as a nonlinear constrained optimization problem. Thus, it is proposed to efficiently resolve utilizing an enhanced version of QPSO with mutation strategy (EQPSO-2M). The proposed technique is compared with the conventional QPSO algorithm and different variants of PSO algorithms. Evaluation criteria rely upon convergence speed, mean best fitness value, stability, and the number of successful runs that has been utilized to assess the proposed approach. A non-parametric test is utilized to decide the critical contrast between the results of the proposed algorithm compared with different algorithms. The simulation results demonstrated that the training of the proposed RBFNN-based reaction wheel model with enhanced parameters by EQPSO-2M algorithm furnishes a superior prediction accuracy went with effective network architecture.

Exploring Development Trends of Terrestrial Ecosystem Health—A Case Study from China

Terrestrial ecosystem health (TEH) is the basis of regional sustainability development. The state of TEH is an important research direction in the land science field. The purpose of this paper was to explore the development trends and influencing factors of the. By using the radial basis function (RBF), neural network model, geographic information system (GIS), and the comprehensive index method, this paper predicted the land ecological changes of Henan Province from 2007 to 2025 based on a comprehensive evaluation of the system. The results show that the TEH of Henan Province exhibited a general trend of improvement from 2007 to 2025. The predictions exhibited a tendency to fluctuate and increase, from “severe warning” to “moderate warning” and even to “no warning” state. The early warning index of the subsystem showed a fluctuating upward trend except for the press subsystem, which fluctuated between “extraordinary warning” and “heavy warning” states. The overall TEH level is improving but is largely dependent on effective corresponding measures. The health status of the land ecosystem in Henan Province is guaranteed to be stable due to improvements in rural residential incomes, mechanization levels of cultivated land, domestic sewage treatment rates, and the numbers of scientific and technological personnel per unit of land. The TEH is mainly restricted by the population densities, urbanization levels, inputs of fertilizers and pesticides, and average wastewater load factors of the land. To improve the health level of the land ecosystem, it is necessary to reduce the use of fertilizers and pesticides and to control the urbanization rate. At the same time, improving the level of forest coverage and the effective irrigation rate play a positive role in improving ecosystem health. The results provide a reference for land-use planning and management decisions.

Adaptive Neuro-Fuzzy Inference System Predictor with an Incremental Tree Structure Based on a Context-Based Fuzzy Clustering Approach

We propose an adaptive neuro-fuzzy inference system (ANFIS) with an incremental tree structure based on a context-based fuzzy C-means (CFCM) clustering process. ANFIS is a combination of a neural network with the ability to learn, adapt and compute, and a fuzzy machine with the ability to think and to reason. It has the advantages of both models. General ANFIS rule generation methods include a method employing a grid division using a membership function and a clustering method. In this study, a rule is created using CFCM clustering that considers the pattern of the output space. In addition, multiple ANFISs were designed in an incremental tree structure without using a single ANFIS. To evaluate the performance of ANFIS in an incremental tree structure based on the CFCM clustering method, a computer performance prediction experiment was conducted using a building heating-and-cooling dataset. The prediction experiment verified that the proposed CFCM-clustering-based ANFIS shows better prediction efficiency than the current grid-based and clustering-based ANFISs in the form of an incremental tree.

Coverage and k-Coverage Optimization in Wireless Sensor Networks Using Computational Intelligence Methods: A Comparative Study

The domain of wireless sensor networks is considered to be among the most significant scientific regions thanks to the numerous benefits that their usage provides. The optimization of the performance of wireless sensor networks in terms of area coverage is a critical issue for the successful operation of every wireless sensor network. This article pursues the maximization of area coverage and area k-coverage by using computational intelligence algorithms, i.e., a genetic algorithm and a particle swarm optimization algorithm. Their performance was evaluated via comparative simulation tests, made not only against each other but also against two other well-known algorithms. This appraisal was made using statistical testing. The test results, that proved the efficacy of the algorithms proposed, were analyzed and concluding remarks were drawn.

A Machine Learning Ensemble Approach Based on Random Forest and Radial Basis Function Neural Network for Risk Evaluation of Regional Flood Disaster: A Case Study of the Yangtze River Delta, China

The Yangtze River Delta (YRD) is one of the most developed regions in China. This is also a flood-prone area where flood disasters are frequently experienced; the situations between the people-land nexus and the people-water nexus are very complicated. Therefore, the accurate assessment of flood risk is of great significance to regional development. The paper took the YRD urban agglomeration as the research case. The driving force, pressure, state, impact and response (DPSIR) conceptual framework was established to analyze the indexes of flood disasters. The random forest (RF) algorithm was used to screen important indexes of floods risk, and a risk assessment model based on the radial basis function (RBF) neural network was constructed to evaluate the flood risk level in this region from 2009 to 2018. The risk map showed the I-V level of flood risk in the YRD urban agglomeration from 2016 to 2018 by using the geographic information system (GIS). Further analysis indicated that the indexes such as flood season rainfall, urban impervious area ratio, gross domestic product (GDP) per square kilometer of land, water area ratio, population density and emergency rescue capacity of public administration departments have important influence on flood risk. The flood risk has been increasing in the YRD urban agglomeration during the past ten years under the urbanization background, and economic development status showed a significant positive correlation with flood risks. In addition, there were serious differences in the rising rate of flood risks and the status quo among provinces. There are still a few cities that have stabilized at a better flood-risk level through urban flood control measures from 2016 to 2018. These results were basically in line with the actual situation, which validated the effectiveness of the model. Finally, countermeasures and suggestions for reducing the urban flood risk in the YRD region were proposed, in order to provide decision support for flood control, disaster reduction and emergency management in the YRD region.

Robot Motion Control via an EEG-Based Brain–Computer Interface by Using Neural Networks and Alpha Brainwaves

Modern achievements accomplished in both cognitive neuroscience and human–machine interaction technologies have enhanced the ability to control devices with the human brain by using Brain–Computer Interface systems. Particularly, the development of brain-controlled mobile robots is very important because systems of this kind can assist people, suffering from devastating neuromuscular disorders, move and thus improve their quality of life. The research work presented in this paper, concerns the development of a system which performs motion control in a mobile robot in accordance to the eyes’ blinking of a human operator via a synchronous and endogenous Electroencephalography-based Brain–Computer Interface, which uses alpha brain waveforms. The received signals are filtered in order to extract suitable features. These features are fed as inputs to a neural network, which is properly trained in order to properly guide the robotic vehicle. Experimental tests executed on 12 healthy subjects of various gender and age, proved that the system developed is able to perform movements of the robotic vehicle, under control, in forward, left, backward, and right direction according to the alpha brainwaves of its operator, with an overall accuracy equal to 92.1%.

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.

Radial Basis Functions With Adaptive Input and Composite Trend Representation for Portfolio Selection

We propose a set of novel radial basis functions with adaptive input and composite trend representation (AICTR) for portfolio selection (PS). Trend representation of asset price is one of the main information to be exploited in PS. However, most state-of-the-art trend representation-based systems exploit only one kind of trend information and lack effective mechanisms to construct a composite trend representation. The proposed system exploits a set of RBFs with multiple trend representations, which improves the effectiveness and robustness in price prediction. Moreover, the input of the RBFs automatically switches to the best trend representation according to the recent investing performance of different price predictions. We also propose a novel objective to combine these RBFs and select the portfolio. Extensive experiments on six benchmark data sets (including a new challenging data set that we propose) from different real-world stock markets indicate that the proposed RBFs effectively combine different trend representations and AICTR achieves state-of-the-art investing performance and risk control. Besides, AICTR withstands the reasonable transaction costs and runs fast; hence, it is applicable to real-world financial environments.

An Inverse Neural Controller Based on the Applicability Domain of RBF Network Models

This paper presents a novel methodology of generic nature for controlling nonlinear systems, using inverse radial basis function neural network models, which may combine diverse data originating from various sources. The algorithm starts by applying the particle swarm optimization-based non-symmetric variant of the fuzzy means (PSO-NSFM) algorithm so that an approximation of the inverse system dynamics is obtained. PSO-NSFM offers models of high accuracy combined with small network structures. Next, the applicability domain concept is suitably tailored and embedded into the proposed control structure in order to ensure that extrapolation is avoided in the controller predictions. Finally, an error correction term, estimating the error produced by the unmodeled dynamics and/or unmeasured external disturbances, is included to the control scheme to increase robustness. The resulting controller guarantees bounded input-bounded state (BIBS) stability for the closed loop system when the open loop system is BIBS stable. The proposed methodology is evaluated on two different control problems, namely, the control of an experimental armature-controlled direct current (DC) motor and the stabilization of a highly nonlinear simulated inverted pendulum. For each one of these problems, appropriate case studies are tested, in which a conventional neural controller employing inverse models and a PID controller are also applied. The results reveal the ability of the proposed control scheme to handle and manipulate diverse data through a data fusion approach and illustrate the superiority of the method in terms of faster and less oscillatory responses.

Model predictive control for systems with fast dynamics using inverse neural models

In this work, a novel model predictive control (MPC) scheme is introduced, by integrating direct and indirect neural control methodologies. The proposed approach makes use of a robust inverse radial basis function (RBF) model taking into account the applicability domain criterion, in order to provide a suitable initial starting point for the optimizer, thus helping to solve the optimization problem faster. The performance of the proposed controller is evaluated on the control of a highly nonlinear system with fast dynamics and compared with different control schemes. Results show that the proposed approach outperforms the rivaling schemes in terms of response; moreover, it solves the optimization problem in less than one sampling period, thus effectively rendering MPC-based controllers capable of handling systems with fast dynamics.

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.

A Fast and Efficient Method for Training Categorical Radial Basis Function Networks

This brief presents a novel learning scheme for categorical data based on radial basis function (RBF) networks. The proposed approach replaces the numerical vectors known as RBF centers with categorical tuple centers, and employs specially designed measures for calculating the distance between the center and the input tuples. Furthermore, a fast noniterative categorical clustering algorithm is proposed to accomplish the first stage of RBF training involving categorical center selection, whereas the weights are calculated through linear regression. The method is applied on 22 categorical data sets and compared with several different learning schemes, including neural networks, support vector machines, naïve Bayes classifier, and decision trees. Results show that the proposed method is very competitive, outperforming its rivals in terms of predictive capabilities in the majority of the tested cases.

Sensing Attribute Weights: A Novel Basic Belief Assignment Method

Dempster-Shafer evidence theory is widely used in many soft sensors data fusion systems on account of its good performance for handling the uncertainty information of soft sensors. However, how to determine basic belief assignment (BBA) is still an open issue. The existing methods to determine BBA do not consider the reliability of each attribute; at the same time, they cannot effectively determine BBA in the open world. In this paper, based on attribute weights, a novel method to determine BBA is proposed not only in the closed world, but also in the open world. The Gaussian model of each attribute is built using the training samples firstly. Second, the similarity between the test sample and the attribute model is measured based on the Gaussian membership functions. Then, the attribute weights are generated using the overlap degree among the classes. Finally, BBA is determined according to the sensed attribute weights. Several examples with small datasets show the validity of the proposed method.

Solubility prediction of gases in polymers based on an artificial neural network: a review

Solubility prediction model based on a hybrid artificial neural network.

Global nonlinear kernel prediction for large data set with a particle swarm-optimized interval support vector regression

A new global nonlinear predictor with a particle swarm-optimized interval support vector regression (PSO-ISVR) is proposed to address three issues (viz., kernel selection, model optimization, kernel method speed) encountered when applying SVR in the presence of large data sets. The novel prediction model can reduce the SVR computing overhead by dividing input space and adaptively selecting the optimized kernel functions to obtain optimal SVR parameter by PSO. To quantify the quality of the predictor, its generalization performance and execution speed are investigated based on statistical learning theory. In addition, experiments using synthetic data as well as the stock volume weighted average price are reported to demonstrate the effectiveness of the developed models. The experimental results show that the proposed PSO-ISVR predictor can improve the computational efficiency and the overall prediction accuracy compared with the results produced by the SVR and other regression methods. The proposed PSO-ISVR provides an important tool for nonlinear regression analysis of big data.

An Empirical Analysis of Evolved Radial Basis Function Networks and Support Vector Machines with Mixture of Kernels

Classification is one of the most fundamental and formidable tasks in many domains including biomedical. In biomedical domain, the distributions of data in most of the datasets into predefined number of classes is significantly different (i.e., the classes are distributed unevenly). Many mathematical, statistical, and machine learning approaches have been developed for classification of biomedical datasets with a varying degree of success. This paper attempts to analyze the empirical performance of two forefront machine learning algorithms particularly designed for classification problem by adding some novelty to address the problem of imbalanced dataset. The evolved radial basis function network with novel kernel and support vector machine with mixture of kernels are suitably designed for the purpose of classification of imbalanced dataset. The experimental outcome shows that both algorithms are promising compared to simple radial basis function neural networks and support vector machine, respectively. However, on an average, support vector machine with mixture kernels is better than evolved radial basis function neural networks.

Predictive calculation of carbon dioxide solubility in polymers

Novel calculation model of CO₂ solubility in polymers using a hybrid intelligence algorithm.

Solubility prediction of supercritical carbon dioxide in 10 polymers using radial basis function artificial neural network based on chaotic self-adaptive particle swarm optimization and K-harmonic means

Excellent prediction modeling of CO₂ solubility in polymers using hybrid computation algorithm.

Pinning distributed synchronization of stochastic dynamical networks: a mixed optimization approach

This paper is concerned with the problem of pinning synchronization of nonlinear dynamical networks with multiple stochastic disturbances. Two kinds of pinning schemes are considered: 1) pinned nodes are fixed along the time evolution and 2) pinned nodes are switched from time to time according to a set of Bernoulli stochastic variables. Using Lyapunov function methods and stochastic analysis techniques, several easily verifiable criteria are derived for the problem of pinning distributed synchronization. For the case of fixed pinned nodes, a novel mixed optimization method is developed to select the pinned nodes and find feasible solutions, which is composed of a traditional convex optimization method and a constraint optimization evolutionary algorithm. For the case of switching pinning scheme, upper bounds of the convergence rate and the mean control gain are obtained theoretically. Simulation examples are provided to show the advantages of our proposed optimization method over previous ones and verify the effectiveness of the obtained results.

ESTIMATING PARAMETERS OF MUSKINGUM MODEL USING AN ADAPTIVE HYBRID PSO ALGORITHM

In order to accelerate the convergence and improve the calculation accuracy for parameter optimization of the Muskingum model, we propose a novel, adaptive hybrid particle swarm optimization (AHPSO) algorithm. With the decreasing of inertial weight factor proposed, this method can gradually converge to a global optimal with elite individuals obtained by hybrid PSO. In the paper, we analyzed the feasibility and the advantages of the AHPSO algorithm. Then, we verified its efficiency and superiority by application of the Muskingum model. We intensively evaluated the error fitting degree based on the comparison with four known formulas: the test method (TM), the least residual square method (LRSM), the nonlinear programming method (NPM), and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. The results show that the AHPSO has a higher precision. In addition, we compared the AHPSO algorithm with the binary-encoded genetic algorithm (BGA), the Gray genetic algorithm (GGA), the Gray-encoded accelerating genetic algorithm (GAGA) and the particle swarm optimization (PSO), and results show that AHPSO has faster convergent speed. Moreover, AHPSO has a competitive advantage compared with the above eight methods in terms of robustness. With the efficiency of this approach it can be extended to estimate parameters of other dynamic models.

Evolving RBF neural networks for adaptive soft-sensor design

This work presents an adaptive framework for building soft-sensors based on radial basis function (RBF) neural network models. The adaptive fuzzy means algorithm is utilized in order to evolve an RBF network, which approximates the unknown system based on input-output data from it. The methodology gradually builds the RBF network model, based on two separate levels of adaptation: On the first level, the structure of the hidden layer is modified by adding or deleting RBF centers, while on the second level, the synaptic weights are adjusted with the recursive least squares with exponential forgetting algorithm. The proposed approach is tested on two different systems, namely a simulated nonlinear DC Motor and a real industrial reactor. The results show that the produced soft-sensors can be successfully applied to model the two nonlinear systems. A comparison with two different adaptive modeling techniques, namely a dynamic evolving neural-fuzzy inference system (DENFIS) and neural networks trained with online backpropagation, highlights the advantages of the proposed methodology.

RBF-based technique for statistical demodulation of pathological tremor

This paper presents an innovative technique based on the joint approximation capabilities of radial basis function (RBF) networks and the estimation capability of the multivariate iterated Hilbert transform (IHT) for the statistical demodulation of pathological tremor from electromyography (EMG) signals in patients with Parkinson's disease. We define a stochastic model of the multichannel high-density surface EMG by means of the RBF networks applied to the reconstruction of the stochastic process (characterizing the disease) modeled by the multivariate relationships generated by the Karhunen-Loéve transform in Hilbert spaces. Next, we perform a demodulation of the entire random field by means of the estimation capability of the multivariate IHT in a statistical setting. The proposed method is applied to both simulated signals and data recorded from three Parkinsonian patients and the results show that the amplitude modulation components of the tremor oscillation can be estimated with signal-to-noise ratio close to 30 dB with root-mean-square error for the estimates of the tremor instantaneous frequency. Additionally, the comparisons with a large number of techniques based on all the combinations of the RBF, extreme learning machine, backpropagation, support vector machine used in the first step of the algorithm; and IHT, empirical mode decomposition, multiband energy separation algorithm, periodic algebraic separation and energy demodulation used in the second step of the algorithm, clearly show the effectiveness of our technique. These results show that the proposed approach is a potential useful tool for advanced neurorehabilitation technologies that aim at tremor characterization and suppression.

Efficient VLSI architecture for training radial basis function networks

This paper presents a novel VLSI architecture for the training of radial basis function (RBF) networks. The architecture contains the circuits for fuzzy C-means (FCM) and the recursive Least Mean Square (LMS) operations. The FCM circuit is designed for the training of centers in the hidden layer of the RBF network. The recursive LMS circuit is adopted for the training of connecting weights in the output layer. The architecture is implemented by the field programmable gate array (FPGA). It is used as a hardware accelerator in a system on programmable chip (SOPC) for real-time training and classification. Experimental results reveal that the proposed RBF architecture is an effective alternative for applications where fast and efficient RBF training is desired.