Tiantian Xie

Advantages of Radial Basis Function Networks for Dynamic System Design

Radial basis function (RBF) networks have advantages of easy design, good generalization, strong tolerance to input noise, and online learning ability. The properties of RBF networks make it very suitable to design flexible control systems. This paper presents a review on different approaches of designing and training RBF networks. The recently developed algorithm is introduced for designing compact RBF networks and performing efficient training process. At last, several problems are applied to test the main properties of RBF networks, including their generalization ability, tolerance to input noise, and online learning ability. RBF networks are also compared with traditional neural networks and fuzzy inference systems.

Fast and Efficient Second-Order Method for Training Radial Basis Function Networks

This paper proposes an improved second order (ISO) algorithm for training radial basis function (RBF) networks. Besides the traditional parameters, including centers, widths and output weights, the input weights on the connections between input layer and hidden layer are also adjusted during the training process. More accurate results can be obtained by increasing variable dimensions. Initial centers are chosen from training patterns and other parameters are generated randomly in limited range. Taking the advantages of fast convergence and powerful search ability of second order algorithms, the proposed ISO algorithm can normally reach smaller training/testing error with much less number of RBF units. During the computation process, quasi Hessian matrix and gradient vector are accumulated as the sum of related sub matrices and vectors, respectively. Only one Jacobian row is stored and used for multiplication, instead of the entire Jacobian matrix storage and multiplication. Memory reduction benefits the computation speed and allows the training of problems with basically unlimited number of patterns. Several practical discrete and continuous classification problems are applied to test the properties of the proposed ISO training algorithm.

Comparison between traditional neural networks and radial basis function networks

The paper presents the properties of two types of neural networks: traditional neural networks and radial basis function (RBF) networks, both of which are considered as universal approximators. In this paper, the advantages and disadvantages of the two types of neural network architectures are analyzed and compared based on four different examples. The comparison results indicate approaches to be taken relative to the network model selection for practical applications.

An Incremental Design of Radial Basis Function Networks

This paper proposes an offline algorithm for incrementally constructing and training radial basis function (RBF) networks. In each iteration of the error correction (ErrCor) algorithm, one RBF unit is added to fit and then eliminate the highest peak (or lowest valley) in the error surface. This process is repeated until a desired error level is reached. Experimental results on real world data sets show that the ErrCor algorithm designs very compact RBF networks compared with the other investigated algorithms. Several benchmark tests such as the duplicate patterns test and the two spiral problem were applied to show the robustness of the ErrCor algorithm. The proposed ErrCor algorithm generates very compact networks. This compactness leads to greatly reduced computation times of trained networks.

Replacing fuzzy systems with neural networks

In this paper, a neural architecture which gives identical TSK fuzzy system is proposed based on the area selection concept in neural network design. Instead of using traditional membership functions for selection the range of operation, the monotonic pair-wire or sigmoidal activation function is used. In the comparison to popular neuro-fuzzy systems [18], the proposed approach does not require signal normalization or division. This neural system does not need training process. All parameters of constructed neural networks are directly derived from specifications of fuzzy systems.

Comparison of Fuzzy and Neural Systems for Implementation of Nonlinear Control Surfaces

In this paper, a comparison between different fuzzy and neural systems is presented. Instead of using traditional membership functions, such as triangular, trapezoidal and Gaussian, in fuzzy systems, the monotonic pair-wire or sigmoidal activation function is used for each neuron. Based on the concept of area selection, the neural systems can be designed to implement the identical properties like fuzzy systems have. All parameters of the proposed neural architecture are directly obtained from the specified design and no training process is required. Comparing with traditional neuro-fuzzy systems, the proposed neural architecture is more flexible and simplifies the design process by removing division/normalization units.

Recent advances in industrial control

The paper presents the state-of-the-art study on the recently published literatures subjected to industrial control in various industrial applications. Controllers are classified into several types according to different control technologies, including PID algorithm, Kalman filter, least squares regression, network-based automation, fuzzy inference systems, neural networks, radial basis function networks, sliding-mode based control and so on. For each paper, a brief summary is given to introduce the related control technologies and applications.

Comparison of different neural network architectures for digit image recognition

The paper presents the design of three types of neural networks with different features, including traditional backpropagation networks, radial basis function networks and counterpropagation networks. Traditional backpropagation networks require very complex training process before being applied for classification or approximation. Radial basis function networks simplify the training process by the specially organized 3-layer architecture. Counterpropagation networks do not need training process at all and can be designed directly by extracting all the parameters from input data. Both design complexity and generalization ability of the three types of neural network architectures are compared, based on a digit image recognition problem.

Current trends in power aware design

This paper outlines the state-of-the-art of recently published papers on the subject of power aware design in various industrial applications. First, the basic concept of power aware design is given and then current trends are summarized. A summary is given of a wide variety of techniques and applications of power awareness.

Current trends in industrial control

This paper demonstrates the outline of the recently published literatures on the field of industrial control and gives an overview about the current trends of control issues in various industrial applications. Controllers can be divided into different categories according to different control algorithms and technologies, which includes PID algorithm, Kalman filter, least squares regression, network-based automation, fuzzy inference systems, neural networks, radial basis function networks and sliding-mode control and so on. A brief introduction will be given for every paper related to these control technologies and applications.