Sung-Kwun Oh

The design of self-organizing polynomial neural networks

Abstract In this study, we introduce and investigate a class of neural architectures of Polynomial Neural Networks (PNNs), discuss a comprehensive design methodology and carry out a series of numeric experiments. PNN is a flexible neural architecture whose structure (topology) is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but becomes generated on the fly. In this sense, PNN is a self-organizing network. The essence of the design procedure dwells on the Group Method of Data Handling (GMDH). Each node of the PNN exhibits a high level of flexibility and realizes a polynomial type of mapping (linear, quadratic, and cubic) between input and output variables. The experimental part of the study involves two representative time series such as Box–Jenkins gas furnace data and a pH neutralization process.

Identification of fuzzy systems by means of an auto-tuning algorithm and its application to nonlinear systems

Abstract The study concerns a design procedure of rule-based systems. The proposed rule-based fuzzy modeling implements system structure and parameter identification in the efficient form of “IF …, THEN … ” statements, and exploits the theory of system optimization and fuzzy implication rules. Two types of methods for rule-based fuzzy modeling are studied. This classification concerns the form of the conclusion part of the rules that can be either constant or formed by some linear functions. Both triangular and Gaussian-like membership function are studied. The optimization hinges on an auto-tuning algorithm that covers a modified constrained optimization method known as a complex method. The study introduces a weighted performance index (objective function) that helps achieve a sound balance between the quality of results produced for the training and testing set. This methodology sheds light on the role and impact of different parameters of the model on its performance (in-particular, the mapping and predicting capabilities of the rule-based computing). The study is illustrated with the aid of several representative numerical examples.

Polynomial neural networks architecture: analysis and design

Abstract In this study, we introduce and investigate a class of neural architectures of Polynomial Neural Networks (PNNs), discuss a comprehensive design methodology and carry out a series of numeric experiments. Two kinds of PNN architectures, namely a basic PNN and a modified PNN architecture are discussed. Each of them comes with two types such as the generic and the advanced type. The essence of the design procedure dwells on the Group Method of Data Handling. PNN is a flexible neural architecture whose structure is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but becomes dynamically meaning that the network grows over the training period. In this sense, PNN is a self-organizing network. A comparative analysis shows that the proposed PNN are models with higher accuracy than other fuzzy models.

Hybrid identification in fuzzy-neural networks

This paper introduces an identification method for nonlinear models in the form of Fuzzy-Neural Networks (FNN). In this model, we use two forms of the fuzzy inference methods--a simplified and linear fuzzy inference, and exploit a standard Error Back Propagation learning algorithm. The FNN modeling and identification environment realizes parameter identification through a synergistic usage of clustering techniques, genetic optimization and a complex search method. We use a Hard C-Means (HCM) clustering algorithm to determine initial apexes of the membership functions of the information granules used in this fuzzy model. The parameters such as apexes of membership functions, learning rates, and momentum coefficients are then adjusted using hybrid algorithm. The proposed hybrid identification algorithm is carried out by combining both genetic optimization (genetic algorithm, GA) and the improved complex method. An aggregate objective function (performance index) with a weighting factor is introduced to achieve a sound balance between approximation and generalization of the model. According to the selection and adjustment of the weighting factor of this objective function, we reveal how to design a model with sound approximation and generalization abilities. The proposed model is experimented with using several time series data (gas furnace, sewage treatment process and NOx emission process data of gas turbine power plant).

Fuzzy polynomial neural networks: hybrid architectures of fuzzy modeling

We introduce a concept of fuzzy polynomial neural networks (FPNNs), a hybrid modeling architecture combining polynomial neural networks (PNNs) and fuzzy neural networks (FNNs). The development of the FPNNs dwells on the technologies of computational intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms. The structure of the FPNN results from a synergistic usage of FNN and PNN. FNNs contribute to the formation of the premise part of the rule-based structure of the FPNN. The consequence part of the FPNN is designed using PNNs. The structure of the PNN is not fixed in advance as it usually takes place in the case of conventional neural networks, but becomes organized dynamically to meet the required approximation error. We exploit a group method of data handling (GMDH) to produce this dynamic topology of the network. The performance of the FPNN is quantified through experimentation that exploits standard data already used in fuzzy modeling. The obtained experimental results reveal that the proposed networks exhibit high accuracy and generalization capabilities in comparison to other similar fuzzy models.

A comparative experimental study of type-1/type-2 fuzzy cascade controller based on genetic algorithms and particle swarm optimization

In this study, we introduce the design methodology of an optimized fuzzy controller with the aid of particle swarm optimization (PSO) for ball and beam system. The ball and beam system is a well-known control engineering experimental setup which consists of servo motor, beam and ball. This system exhibits a number of interesting and challenging properties when being considered from the control perspective. The ball and beam system determines the position of ball through the control of a servo motor. The displacement change of the position of ball leads to the change of the angle of the beam which determines the position angle of a servo motor. The fixed membership function design of type-1 based fuzzy logic controller (FLC) leads to the difficulty of rule-based control design when representing linguistic nature of knowledge. In type-2 FLC as the expanded type of type-1 FL, we can effectively improve the control characteristic by using the footprint of uncertainty (FOU) of the membership functions. Type-2 FLC exhibits some robustness when compared with type-1 FLC. Through computer simulation as well as real-world experiment, we apply optimized type-2 fuzzy cascade controllers based on PSO to ball and beam system. To evaluate performance of each controller, we consider controller characteristic parameters such as maximum overshoot, delay time, rise time, settling time, and a steady-state error. In the sequel, the optimized fuzzy cascade controller is realized and also experimented with through running two detailed comparative studies including type-1/type-2 fuzzy controller and genetic algorithms/particle swarm optimization.

Parameter estimation of fuzzy controller and its application to inverted pendulum

Abstract In this paper, a new approach to estimate scaling factors of the fuzzy PID controller is presented. The performance of the fuzzy PID controller is sensitive to the variety of scaling factors. The design procedure dwells on the use of evolutionary computing (more specifically, a genetic algorithm) and estimation algorithm. The tuning of the scaling factors of the fuzzy PID controller is essential to the entire optimization process. And then we estimate scaling factors of the fuzzy PID controller by means of three types of estimation algorithms such as HCM (Hard C-Means) clustering-based regression polynomial, neuro-fuzzy networks, and regression polynomials. Numerical studies are presented in detail along with a detailed comparative analysis.

Fuzzy Polynomial Neuron-Based Self-Organizing Neural Networks

We propose a new category of neurofuzzy networks—self-organizing neural networks (SONN) with fuzzy polynomial neurons (FPNs) and discuss a comprehensive design methodology supporting their development. Two kinds of SONN architectures, namely a basic SONN and a modified SONN architecture are discussed. Each of them comes with two topologies such as a generic and advanced type. Especially in the advanced type, the number of nodes in each layer of the SONN architecture can be modified with new nodes added, if necessary. SONN dwells on the ideas of fuzzy rule-based computing and neural networks. The architecture of the SONN is not fixed in advance as it usually takes place in the case of conventional neural networks, but becomes organized dynamically through a growth process. Simulation involves a series of synthetic as well as real-world data used across various neurofuzzy systems. A comparative analysis shows that the proposed SONN are models exhibiting higher accuracy than some other fuzzy models.

Self-organizing neural networks with fuzzy polynomial neurons

Abstract We propose a new category of neurofuzzy networks—self-organizing neural networks (SONNs) with fuzzy polynomial neurons (FPNs). For these networks we discuss a comprehensive design methodology. SONN dwells on the ideas of fuzzy rule-based computing and neural networks thus emerging as a sound construct of computational intelligence. SONN is a flexible neural architecture whose structure is not fixed in advance but becomes developed through a growth (generation of layer) process. In particular, the number of layers of the SONN is not fixed in advance unlike in the case of conventional neural networks, but is generated in a dynamic way. Simulation studies involve a series of synthetic as well as experimental data used across various neurofuzzy systems. A comparative analysis is included as well.

Self-organizing neurofuzzy networks in modeling software data

Experimental software data sets describing software projects in terms of their complexity and development time have been a subject of intensive modeling. A number of various modeling methodologies and modeling designs have been proposed including neural networks, fuzzy, and neurofuzzy models. In this study, we introduce a concept of Self-organizing neurofuzzy networks (SONFN), a hybrid modeling architecture combining neurofuzzy networks (NFN) and polynomial neural networks (PNN). The development of the SONFN dwells on the technologies of Computational Intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms. The architecture of the SONFN results from a synergistic usage of neurofuzzy networks (NFNs) and polynomial neural networks (PNNs). NFNs contribute to the formation of the premise part of the rule-based structure of the SONFN. The consequence part of the SONFN is designed using PNNs. We discuss two classes of SONFN architectures and propose comprehensive learning algorithms. The experimental results include well-known software data such as the NASA data set concerning software cost estimation and the one describing software modules of the Medical Imaging System (MIS).