Modelling of Nonlinear Oscillator System via Double Loop Radial Basis Function Neural Networks With Adaptive Radius and Lattices

Flexible manipulators have been widely used in industrial production. However, due to the poor rigidity of the flexible manipulator, it is easy to generate vibration. This will reduce the working accuracy and service life of the flexible manipulator. It is necessary to suppress vibration during the operation of the flexible manipulator. Based on the energy method and the Hamilton principle, the partial differential equations of the manipulator were established. Secondly, an improved radial basis function (RBF) neural network was combined with the fuzzy backstepping method to identify and suppress random vibration during the operation of the flexible manipulator, and the Lyapunov function and control law were designed. Finally, Simulink was used to build a simulation platform, three different external disturbances were set up, and the effect of vibration suppression was observed through the change curves of the final velocity error and displacement error. Compared with the RBF neural network boundary control method and the RBF neural network inversion method, the simulation results show that the effect of the RBF neural network fuzzy inversion method is better than the previous two control methods, the system convergence is faster, and the equilibrium position error is smaller.

Presents a systematic approach for constructing reformulated radial basis function (RBF) neural networks, which was developed to facilitate their training by supervised learning algorithms based on gradient descent. This approach reduces the construction of radial basis function models to the selection of admissible generator functions. The selection of generator functions relies on the concept of the blind spot, which is introduced in the paper. The paper also introduces a new family of reformulated radial basis function neural networks, which are referred to as cosine radial basis functions. Cosine radial basis functions are constructed by linear generator functions of a special form and their use as similarity measures in radial basis function models is justified by their geometric interpretation. A set of experiments on a variety of datasets indicate that cosine radial basis functions outperform considerably conventional radial basis function neural networks with Gaussian radial basis functions. Cosine radial basis functions are also strong competitors to existing reformulated radial basis function models trained by gradient descent and feedforward neural networks with sigmoid hidden units.

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.

In this paper, we present a novel method for controlling an unmanned ground vehicle (UGV) by using a new machine learning technique, Deterministic Learning (DL). With DL the robot is able to learn and recognize four specifically designed body gestures, which represent four corresponding moving directions (i.e., left, right, forward, and backward) of the controlled UGV. A Kinect camera is employed to collect human body skeleton data of a user. Eight specifically-designed features are extracted and utilized to train radial basis function neural networks (RBFNNs). The dynamics of the human arm waving motion is guaranteed to be accurately identified, represented, and stored as an RBFNN model with converged constant NN weights, which facilitates rapid recognition in the online identification phase. However, learning time of and storage space of RBFNNs grow exponentially with the number of features. In order drastically reduce required computations and storage space, we propose to split the features in subgroups, and use each subgroup to learn a smaller independent. In the online identification phase, the trained RBFNNs are used to analyze and identify any new incoming gestures. The identification results of all RBFNNs are then fused together following a probabilistic approach, and the gestures of the user are interpreted as commands for the UGV.

Forecasting for a time series signal carrying single pattern characteristics can be done properly using function mapping-based principle by a well-designed artificial neural network model. But the performances degraded very much when time series carried the mixture of different patterns characteristics. The level of difficulty increases further when there is a need to predict far time samples. Among several possible mixtures of patterns, the trend-cycle time series is having its importance because of its occurrence in many real-life applications like in electric power generation, fuel consumption and automobile sales. Over the mixed characteristics of patterns, a neural model, suffered heavily in getting generalized learning, in result poor performances appeared over test data. To overcome this issue in this work, a decomposition-based approach has been applied to separate the component patterns of trend and cyclic patterns, and a dedicated model has been developed for predicting the individual data patterns. The linear characteristic of the trend data pattern has been modeled through a linear regression model while the nonlinearity behavior of cyclic pattern has been model by an adaptive radial basis function neural network. The final predicted outcome has been considered as the linear combination of individual model outcomes. The Gaussian function has been considered as the kernel function in the radial basis function neural network because of its wider and efficient applicability in function mapping. The performance of the neural model has been improved very much by providing the adaptive value of spreads and centers of basis function along with weights values. In this paper, two different applications of forecasting in the area of electric power demand by the individual house and month-wise annual power generation have been considered. Based on house characteristics parameters, the power demanded by a house have been considered which carried a moderate complexity of function mapping problem while in another case, total power generation needed to be predicted on the monthly basis for a year from just the previous year observation, which carried the mixed behavior of trend and cyclic pattern. For house power demand forecasting the adaptive kernel-based radial basis function has shown very satisfactory performances and much better against static kernel radial basis function and multilayer perceptron neural network. The integrated approach of neural model and linear regression has shown very efficient outcomes for the mixture pattern while individual neural models were failed to do so. The coefficient of determination (R2) has been applied to estimate the quality of predicted outcomes and comparison.

Due to increasing awareness of global warming, solar photovoltaics have received much attention. However, solar photovoltaic power generation is associated with intermittence and uncertainty as a result of the meteorological conditions. Accordingly, accurate predictions of the power output from photovoltaic arrays is important for the efficient operation of power systems. This paper presents a supervised learning-based Radial Basis Function Neural Network (RBFNN) neural network for 1-hour ahead solar irradiance/power forecasting. The proposed RBFNN employed double-Gaussian functions as its basis functions, which are type-II fuzzy activation functions. It was found that the type-II fuzzy activation is able to deal with the uncertainty of data. The genetic algorithm was used to optimize the weighting/bias parameters as well as two means/standard deviations of each double Gaussian function. In order to explore the performance of the proposed RBFNN, three structures of RBFNNs are examined: parallel, cascaded and separated RBFNNs. From the simulation results, it was found that the proposed parallel RBFNN outperforms the cascaded and separated RBFNNs. Moreover, the proposed RBFNN with double-Gaussian activation functions attains better accuracy than traditional multi-layer feedforward neural network and RBFNN with single-Gaussian activation functions.

Creep is a fundamental time-dependent property of rock. As one of the main surrounding rocks of underground engineering, layered siltstone is governed by creep to a great extent because of special structure. Based on the structural characteristics of layered siltstone, a viscoelastic–viscoplastic model was proposed to simulate and present its creep property. To verify the accuracy of the model, governing equation of the viscoelastic–viscoplastic model was introduced into finite element difference program to simulate a series of creep tests of layered siltstone. Meanwhile, creep tests on layered siltstone were conducted. Numerical simulation results of the viscoelastic–viscoplastic model were compared with creep test data. Mean relative error of creep test data and numerical simulation result was 0.41%. Combined with Lyapunov function, the radial basis function (RBF) neural network trained with creep test data was adopted. Mean relative error of creep test data and RBF neural network data was 0.57%. The results further showed high accuracy and stability of RBF neural network and the viscoelastic–viscoplastic model.

As RBF (Radial Basis Function) neural networks can approximate any nonlinear function in a compact set with arbitrary precision, this paper presents an approach of the state observer design for a class of nonlinear systems by using the RBF neural network. In order to enhance the learning ability of the RBF neural network, a hybrid black stork foraging process algorithm based on PSO (Particle Swarm Optimization) is proposed. Furthermore, a Lyapunov function is used for analyzing the stability of the RBF state observer. The simulation results demonstrate that the proposed RBF neural network state observer can estimate the state quickly and accurately.

In order to solve the problem of trajectory tracking control of unmanned surface vehicles (USV) with unknown speed information, an adaptive control algorithm based on Radial Basis Function (RBF) neural network and back-stepping method is proposed. This algorithm uses the back-stepping method to design an easy-to-implement control input based on the model parameters, uses the high-gain observer to estimate the speed information, and uses the RBF neural network to estimate the model parametric uncertainties and the environmental disturbances such as wind and wave. Then the control law and the weight update law of RBF neural network are designed. Finally, the systemic stability is proved by Lyapunov function. Simulational experiments and physical experiments verify the feasibility and effectiveness of this algorithm.

Representing the concept of numerical data by linguistic rules is often desirable. In this paper, we present a novel rule-extraction algorithm from the radial basis function (RBF) neural network classifier for representing the hidden concept of numerical data. Gaussian function is used as the basis function of the RBF network. When training the RBF neural network, we allow for large overlaps between clusters corresponding to the same class, thereby reducing the number of hidden units while improving classification accuracy. The weights connecting the hidden units with the output units are then simplified. The interval for each input in the condition part of each rule is adjusted in order to obtain high accuracy in the extracted rules. Simulations using some bench-marking data sets demonstrate that our approach leads to more accurate and compact rules compared to other methods for extracting rules from RBF neural networks.

Aiming at the uncertainty of high-speed train model and time-varying nonlinear systems with external disturbances, this paper proposes a single-parameter direct robust adaptive algorithm based on radial basis function (RBF) neural network for train Tracking control. Based on the characteristics of RBF neural network, a single parameter direct robust adaptive controller is designed for train tracking. First, a single particle train model with external disturbances is proposed; Then based on the single particle train model, based on the RBF neural network's adaptive control closed-loop system, a single parameter direct robust adaptive controller based on the RBF neural network is designed. It can track the position and speed of the train better in the presence of external disturbances. The stability of the closed-loop system was analyzed based on Lyapunov method, and the rationality of the controller design was proved. Finally, in combination with simulink, the CRH2 train is used as a simulation object to simulate the train position and speed, and the errors are analyzed.

The priority of buyer order is a key issue in production scheduling in MTO (make to order) enterprises. In view of the deficiencies in current studies related to the assessment of the priority, a new emerging method for determining the priority in supply chain based on radial basis function (RBF) neural network is put forward which considers the constraint in supply chain and the complicated relation between the evaluation-index system and the priority. The evaluation-index system covers the constraints or determining factors not only in the enterprise and buyers but also in supply chain, and hence is a more complete and effective. A 3-layer RBF neural network model which takes form of the Gauss Function is built for determining the priority of buyer order. And finally by the testing and contradistinctive analysis of the three different methods, this study showed that the evaluation method ground on RBF neural network exceeds that on traditional AHP and BP neural network under supply chain environment, the assessment result is more accurate while the model training time is shorter using the RBF neural network in supply chain.

Since the trajectory-tracking control performance of multi-joint robot manipulator may be degraded due to modeling errors and external disturbances, this paper designs a new adaptive robot manipulator trajectory tracking control method through improved genetic algorithm and radial basis function neural network sliding mode control (IGA-RBFNNSMC). Firstly, the genetic algorithm (GA) is improved by establishing superior populations centered on individuals with high fitness values and selecting individuals in the superior populations for crossover and variation. Secondly, the improved genetic algorithm (IGA) is used for the optimization of the center vector and width vector of the Gaussian basis function in radial basis function (RBF) neural network. Then, based on the dynamics model of the robot manipulator, the modeling errors are approximated by RBF neural network and eliminated by sliding mode control (SMC), and the Lyapunov theorem is used to prove the stability and convergence of the control system. Finally, a two-joint robot manipulator is taken as the research objective and the simulation results show that IGA can significantly reduce the solution time on the basis of guaranteed accuracy and IGA-RBFNNSMC can make the trajectory tracking control accurate and more efficient, which proves the effectiveness of the proposed control method.

Radial basis function(RBF) neural network was applied to determine soil types of hilly and mountainous terrains in Fengdu County of the Three Gorges region in China, the elevation in which ranges between 118.5m and 2000m, combining landsat enhanced thematic mapper plus (ETM+) data and topographic information from a digital elevation model (DEM). We designed a RBF network using newrb P,T,GOAL,SPREAD) function in MATLAB software, in newrb function orthogonal least squares learning algorithm be used to choose Gaussian kernel function centers and the weights of the network. Two sets of training samples were selected for training. One was a set of 3606 training samples; the other was a set of 57905 training samples, also for maximum likelihood classification. Considering training time, we divided these 57905 samples into 3063 small sample areas, so a set of averages of which was selected to input the network for training at last. The classification results with RBF neural network showed that the second training samples set generated 60.3% producer's accuracy, higher than that of the first samples set. But the producer's accuracies of RBF neural network trained by both sets were lower than that of using maximum likelihood classifier with the same training samples, which was 66.6%. On the other hand, the Kappa coefficient of RBF neural network trained by the second training samples set was 0.5587, higher than that of maximum likelihood classifier with the same training samples, which was 0.4919. So, it is indicated that RBF neural network for soil classification is not the best method under limited training samples for more samples more training time consumption to the unacceptable extent.

Hysteresis widely exists in civil structures, and dissipates the mechanical energy of systems. Research on the random vibration of hysteretic systems, however, is still insufficient, particularly when the excitation is non-Gaussian. In this paper, the radial basis function (RBF) neural network (RBF-NN) method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations. The solution to the reduced generalized Fokker-Planck-Kolmogorov (GFPK) equation is expressed in terms of the RBF-NNs with the Gaussian activation functions, whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition. A steel fiber reinforced ceramsite concrete (SFRCC) column loaded by the Poisson white noise is studied as an example to illustrate the solution process. The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated, and the obtained results are compared with those obtained by the Monte Carlo simulations (MCSs). The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.