Robust fuzzy Gustafson-Kessel clustering for nonlinear system identification

This paper deals with Takagi-Sugeno (TS) fuzzy model identification of nonlinear systems using fuzzy clustering. In particular, an extended fuzzy Gustafson-Kessel (EGK) clustering algorithm, using robust competitive agglomeration (RCA), is developed for automatically constructing a TS fuzzy model from system input-output data. The EGK algorithm can automatically determine the 'optimal' number of clusters from the training data set. It is shown that the EGK approach is relatively insensitive to initialization and is less susceptible to local minima, a benefit derived from its agglomerate property. This issue is often overlooked in the current literature on nonlinear identification using conventional fuzzy clustering. Furthermore, the robust statistical concepts underlying the EGK algorithm help to alleviate the difficulty of cluster identification in the construction of a TS fuzzy model from noisy training data. A new hybrid identification strategy is then formulated, which combines the EGK algorithm with a locally weighted, least-squares method for the estimation of local sub-model parameters. The efficacy of this new approach is demonstrated through function approximation examples and also by application to the identification of an automatic voltage regulation (AVR) loop for a simulated 3 kVA laboratory micro-machine system.

A New Gradient Descent Approach for Local Learning of Fuzzy Neural Models

The majority of reported learning methods for Takagi-Sugeno-Kang fuzzy neural models to date mainly focus on the improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behaviour when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, to identify the corresponding consequent models which can be directly explained in terms of system behaviour presents a critical step in fuzzy neural modelling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practised in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. A new Jacobian matrix is thus proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues about the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.

Fuzzy Coding of Genetic Algorithms

A well-cited paper suggesting fuzzy coding as an alternative to the conventional binary, grey and floating-point representations used in genetic algorithms.

A recursive rule base adjustment algorithm for a fuzzy logic controller

This paper introduces a recursive rule base adjustment to enhance the performance of fuzzy logic controllers. Here the fuzzy controller is constructed on the basis of a decision table (DT), relying on membership functions and fuzzy rules that incorporate heuristic knowledge and operator experience. If the controller performance is not satisfactory, it has previously been suggested that the rule base be altered by combined tuning of membership functions and controller scaling factors. The alternative approach proposed here entails alteration of the fuzzy rule base. The recursive rule base adjustment algorithm proposed in this paper has the benefit that it is computationally more efficient for the generation of a DT, and advantage for online realization. Simulation results are presented to support this thesis. (c) 2005 Elsevier B.V. All rights reserved.

An Investigation of Fuzzy Multiple Heuristic Orderings in the Construction of University Examination Timetables

In this paper, we present an investigation into using fuzzy methodologies to guide the construction of high quality feasible examination timetabling solutions. The provision of automated solutions to the examination timetabling problem is achieved through a combination of construction and improvement. The enhancement of solutions through the use of techniques such as metaheuristics is, in some cases, dependent on the quality of the solution obtained during the construction process. With a few notable exceptions, recent research has concentrated on the improvement of solutions as opposed to focusing on investigating the ‘best’ approaches to the construction phase. Addressing this issue, our approach is based on combining multiple criteria in deciding on how the construction phase should proceed. Fuzzy methods were used to combine three single construction heuristics into three different pair wise combinations of heuristics in order to guide the order in which exams were selected to be inserted into the timetable solution. In order to investigate the approach, we compared the performance of the various heuristic approaches with respect to a number of important criteria (overall cost penalty, number of skipped exams, number of iterations of a rescheduling procedure required and computational time) on twelve well-known benchmark problems. We demonstrate that the fuzzy combination of heuristics allows high quality solutions to be constructed. On one of the twelve problems we obtained lower penalty than any previously published constructive method and for all twelve we obtained lower penalty than when any of the single heuristics were used alone. Furthermore, we demonstrate that the fuzzy approach used less backtracking when constructing solutions than any of the single heuristics. We conclude that this novel fuzzy approach is a highly effective method for heuristically constructing solutions and, as such, has particular relevance to real-world situations in which the construction of feasible solutions is often a difficult task in its own right.