Nonlinear system identification with modified differential evolution and RBF networks

Radial Basis Function (RBF) Network is popularly used for solving pattern recognition problems. The training of RBF Network is faster compared to multi layer perceptron using error backpropagation. However, the RBF Network uses the pseudo inverse matrix to calculate weights from the hidden layer to the output layer. Thus calculation cost increases when the number of data and the number of hidden units increase. In addition, in RBF Network the decision of optimum number of hidden units is difficult. It is also more prone to overtraining, needing repeated train and test cycles to ascertain a proper number of the Network hidden units, so that generalization performance is good. In this work, we propose a technique to set up RBF network parameters which is fast, as well as the number of hidden units are automatically determined. We start with training a Self-Organizing Maps (SOM), which is a unsupervised training, though our samples are labeled. SOM can find the distribution of data in multidimensional space, and map it on a two dimensional display. The results of SOM network is used to calculate the RBF parameters. It is shown by experiments that using the proposed method, RBF network parameters can be determined much faster compared to existing technique. Moreover, the recognition rate for the test data was higher, showing better generalization performance.

In this paper, a novel radial basis function (RBF) neural network is proposed and applied successively for online stable identification and control of nonlinear discrete-time systems. The proposed RBF network has one hidden layer neural network (NN) with its all parameters being adaptable. The RBF network parameters are optimized by gradient descent method with stable learning rate whose stable convergence behavior is proved by Lyapunov stability approach. The aim of construction of the proposed RBF network is to combine power of the networks which have different mapping abilities. These networks are auto-regressive exogenous input model, nonlinear static NN model and nonlinear dynamic NN model. In simulations, the proposed network is applied for the direct inverse control of one benchmark nonlinear functioned system and Van de Vusse reaction in a CSTR discrete system even there exist large disturbances. From simulations, it is seen that the RBF network with stable learning rate identifies and controls nonlinear systems accurately.

Continuous-Time Identification of Nonlinear Systems Using Radial Basis Function Network Model and Genetic Algorithm

The characteristics of hydraulic automatic gage control System(AGC) of cold rolling mill is analyzed. the principle of identification using Radial Basis Function(RBF) network is introduced. The RBF network structure, train algorithm are given in detail. Finally, the nonlinear model of HAGC is established with RBF network. To improving the accuracy of identification. the input and output data is filtered with wavelet denoising technique. The experimental results indicate that the combination of wavelet denoising and RBF network can provide an efficient method for system identification.

Three learning phases for radial-basis-function networks

The paper demonstrates that radial basis function network (RBFN) with adaptive centers and width can be used effectively for identification of nonlinear dynamic system. The proposed RBFN is trained by hybrid learning algorithm, which uses conjugate gradient optimization algorithm to obtain the center and width of each radial basis function and the least squares method to obtain the weights. To avoid capturing a local optimum, regularization error energy function is used and the centers of basis functions are initialized using a fuzzy C-means clustering method. Simulation results reveal that the identification schemes based on RBFN gives considerably better performance and show faster learning in comparison to previous methods

In order to forecast missile storage reliability better, the paper researched a forecasting method based on neural network which is with the ability of actualizing multi-nonlinear mapping from input to output, and discussed steps of forecasting based on back propagation (BP) network and radial basis function (RBF) network respectively. At last, the storage reliability of one type ship-to-ship missile is forecasted based on BP network and RBF network respectively. The results show that both of the BP and RBF are suitable for Missile storage reliability forecasting, and the precision of the train goal is better by using RBF network. RBF network is more suitable for dealing with this problem.

This paper presents a method for analog circuit fault diagnosis by using neural networks. This method exploits a DC approach for constructing a dictionary in fault diagnosis using the neural network's classification capability. Also, Radial Basis Function (RBF) and backward error propagation (BEP) networks are considered and compared for analog fault diagnosis. The primary focus of the paper is to provide robust diagnosis using a mechanism to deal with the problem of component tolerance and reduce testing time. Simulation results show that the radial basis function network with reasonable dimension has double precision in fault classification but its classification is local, while the backward error propagation network with reasonable dimension has single precision in fault classification but its classification is global.

This paper describes four neural networks multilayer perceptron (MLP) network, Elman network, NARXSP network and radial basis function (RBF) network. Neural networks are applied for identification and control of DC servo motor and benchmark nonlinear system. Number of epochs required and time taken to train the controller are shown in the form of bar plots for four neural networks. Levenberg-Marquardt algorithm is used for training the controller using neural network toolbox in MATLAB. Each neural network controller is run ten times. Their performances are compared for each run in terms of number of epochs required and time taken to train each controller for tracking a reference trajectory.

The radial basis function (RBF) neural network is a powerful method for remote sensing image classification. It has a simple architecture and the learning algorithm corresponds to the solution of a linear regression problem, resulting in a fast training process. The main drawback of this strategy is the requirement of an efficient algorithm to determine the number, position, and dispersion of the RBF. Traditional methods to determine the centers are: randomly choose input vectors from the training data set; vectors obtained from unsupervised clustering algorithms, such as k-means, applied to the input data. These conduce that traditional RBF neural network is sensitive to the center initialization. In this paper, the artificial immune network (aiNet) model, a new computational intelligence based on artificial immune networks (AIN), is applied to obtain appropriate centers for remote sensing image classification. In the aiNet-RBF algorihtm, each input pattern corresonds to an antigenic stimulus, while each RBF candidate center is considered to be an element, or cell, of the immune network model. The steps are as follows: A set of candidate centers is initialized at random, where the initial number of candidates and their positions is not crucial to the performance. Then, the clonal selection principle will control which candidates will be selected and how they will be upadated. Note that the clonal selection principle will be responsible for how the centers will represent the training data set. Finally, the immune network will identify and eliminate or suppress self-recognizing individuals to control the number of candidate centers. After the above learning phase, the aiNet network centers represent internal images of the inuput patterns presented to it. The algorithm output is taken to be the matrix of memory cells' coordinates that represent the final centers to be adopted by the RBF network. The stopping criterion of the proposed algorithm is given by a pre-defined number of iterations. The classification results are evaluated by comparing with that of the k-means center selection procedures and other results from the literature using remote sensing imagery. It is shown that aiNet-RBF NN algorithm outperform other algorithms and provides an effective option for remote sensing image classification.

Radial basis function (RBF) network can be viewed as a fuzzy rule base with specified membership functions and fuzzy inference operations. However, there is a trade-off between the approximation performance of RBF network and the number of hidden neurons. To tackle this problem, this paper proposes a dynamic RBF (DRBF) network with a constructive learning. This DRBF network not only can create the new hidden neurons, but also can prune the insignificant hidden neurons. Then, an adaptive dynamic RBF fuzzy neural control (ADRFNC) system, including a neural controller and a saturation compensator, is developed. The neural controller uses a DRBF network to on-line mimic an ideal controller and the saturation compensator is designed to dispel the approximation error introduced by the neural controller. Finally, the proposed ADRFNC system is applied to a chaotic circuit and a DC motor control system. Simulation and experimental results show the proposed ADRFNC system can achieve a favorable tracking performance when the controller’s parameters have been learned and the network structure has been constructed by the proposed learning algorithm.

Generalized [formula omitted]-sparse algorithms for constructing fault tolerant RBF networks

A new learning method of radial basis function (RBF) network based on fuzzy C-means (FCM) clustering and ant colony optimization (ACO) is presented in the paper. Generally, the crucial problem of learning RBF network is the selection of the unit number, the centers and widths of the Gaussian radial basis function in hidden layer, and the weights between hidden layer and output layer. In this work, the centers are determined by FCM clustering, and the weights are determined by least mean squares (LMS) method. In addition, ACO is introduced to optimize two important parameters of FCM including the weighting exponent which impacts its performance, and the clustering number that is equal to the hidden unit number which impacts the generalization of RBF network, by minimizing an objective function integrated the generalization error with the hidden unit number of RBF network. Simulation results of identifying a nonlinear system illustrate the effectiveness of designing the RBF network with smaller structure but stronger generalization ability, comparing with K-means and orthogonal least squares (OLS) based learning methods.

We propose a differential radial basis function (RBF) network termed RBF-DiffNet—whose hidden layer blocks are partial differential equations (PDEs) linear in terms of the RBF—to make the baseline RBF network robust to noise in sequential data. Assuming that the sequential data derives from the discretisation of the solution to an underlying PDE, the differential RBF network learns constant linear coefficients of the PDE, consequently regularising the RBF network by following modified backward-Euler updates. We experimentally validate the differential RBF network on the logistic map chaotic timeseries as well as on 30 real-world timeseries provided by Walmart in the M5 forecasting competition. The proposed model is compared with the normalised and unnormalised RBF networks, ARIMA, and ensembles of multilayer perceptrons (MLPs) and recurrent networks with long short-term memory (LSTM) blocks. From the experimental results, RBF-DiffNet consistently shows a marked reduction in the prediction error over the baseline RBF network (e.g., 41% reduction in the root mean squared scaled error on the M5 dataset, and 53% reduction in the mean absolute error on the logistic map); RBF-DiffNet also shows a comparable performance to the LSTM ensemble but requires 99% less computational time. Our proposed network consequently enables more accurate predictions—in the presence of observational noise—in sequence modelling tasks such as timeseries forecasting that leverage the model interpretability, fast training, and function approximation properties of the RBF network.

The increasing use of computer numerical control (CNC) machines requires better prediction of the reliability of their servo control systems. A novel reliability prediction model based on radial basis function (RBF) neural network optimized by improved particle swarm optimization (IPSO) was proposed. It can overcome the disadvantages of conventional methods, which are time consuming and resource intensive. The major influences on the reliability of servo system include torque, temperature, current, and complexity. An improved algorithm for predicting the mean time between failure (MTBF) of servo systems based on a particle swarm optimization (PSO) and an RBF neural network algorithm is proposed. Two common problem of the PSO: local minimization and slow convergence were solved by the IPSO. “Zero failure” data preprocessing, data normalization, and small-sample data enhancement were performed on the original data. A homogenized sampling method is proposed to extract training and testing samples. Experimental results show that the improved PSO-based RBF neural network is superior to back propagation (BP) and RBF networks in terms of accuracy in servo system reliability prediction.