Dejan Dovžan

Recursive clustering based on a Gustafson–Kessel algorithm

In this paper an on-line fuzzy identification of Takagi Sugeno fuzzy model is presented. The presented method combines a recursive Gustafson–Kessel clustering algorithm and the fuzzy recursive least squares method. The on-line Gustafson–Kessel clustering method is derived. The recursive equations for fuzzy covariance matrix, its inverse and cluster centers are given. The use of the method is presented on two examples. First example demonstrates the use of the method for monitoring of the waste water treatment process and in the second example the method is used to develop an adaptive fuzzy predictive functional controller for a pH process. The results for the Mackey–Glass time series prediction are also given.

Recursive fuzzy c-means clustering for recursive fuzzy identification of time-varying processes.

In this paper we propose a new approach to on-line Takagi-Sugeno fuzzy model identification. It combines a recursive fuzzy c-means algorithm and recursive least squares. First the method is derived and than it is tested and compared on a benchmark problem of the Mackey-Glass time series with other established on-line identification methods. We showed that the developed algorithm gives a comparable degree of accuracy to other algorithms. The proposed algorithm can be used in a number of fields, including adaptive nonlinear control, model predictive control, fault detection, diagnostics and robotics. An example of identification based on a real data of the waste-water treatment process is also presented.

Self-tuning of 2 DOF control based on evolving fuzzy model

Abstract In this paper we present a self-tuning of two degrees-of-freedom control algorithm that is designed for use on a non-linear single-input single-output system. The control algorithm is developed based on the Takagi-Sugeno fuzzy model, and it consists of two loops: a feedforward loop and feedback loop. The feedforward part of the controller should drive the system output to the vicinity of the reference signal. It is developed from the inversion of the T-S fuzzy model. To achieve accurate error-free reference tracking a feedback part of the controller is added. A time-varying error-model predictive controller is used in the feedback loop. The error-model is obtained from the T-S fuzzy model. The T-S fuzzy model of the system, required in the controller, is obtained with evolving fuzzy modelling, which is based on recursive Gustafson-Kessel clustering algorithm and recursive fuzzy least squares. It employs evolving mechanisms for adding, removing, merging and splitting the clusters. The presented control approach was experimentally validated on a non-linear second-order SISO system helio-crane in simulation and real environment. Several criteria functions were defined to evaluate the reference-tracking and disturbance rejection performance of the control algorithm. The presented control approach was compared to another fuzzy control algorithm. The experimental results confirm the applicability of the approach.

Evolving Gustafson-kessel Possibilistic c-Means Clustering☆

Abstract This paper presents an idea of evolving Gustafson-Kessel possibilistic c-means clustering (eGKPCM). This approach is extension of well known possiblilistic c-means clustering (PCM) which was proposed to address the drawbacks associated with the constrained membership functions used in fuzzy c-means algorithms (FCM). The idea of possiblistic clustering is ap- pealing when the data samples are highly noisy. The extension to Gustafson-Kessel possibilistic clustering enables us to deal with the clusters of different shapes and the evolving structure enables us to cope with the data structures which vary during the time. The evolving nature of the algorithm makes it also appropriate for dealing with big-data problems. The proposed approach is shown on a simple classification problem of unlabelled data.

Fuzzy Control of a Helio-Crane

In this paper we present a comparison of two fuzzy-control approaches that were developed for use on a non-linear single-input single-output (SISO) system. The first method is Fuzzy Model Reference Learning Control (FMRLC) with a modified adaptation mechanism that tunes the fuzzy inverse model. The basic idea of this method is based on shifting the output membership functions in the fuzzy controller and in the fuzzy inverse model. The second approach is a 2 degrees-of-freedom (2 DOF) control that is based on the Takagi-Sugeno fuzzy model. The T-S fuzzy model is obtained by identification of evolving fuzzy model and then used in the feed-forward and feedback parts of the controller. An error-model predictive-control approach is used for the design of the feedback loop. The controllers were compared on a non-linear second-order SISO system named the helio-crane. We compared the performance of the reference tracking in a simulation environment and on a real system. Both methods provided acceptable tracking performance during the simulation, but on the real system the 2 DOF FMPC gave better results than the FMRLC.

Large-scale cyber attacks monitoring using Evolving Cauchy Possibilistic Clustering

Abstract We are living in an information age where all our personal data and systems are connected to the Internet and accessible from more or less anywhere in the world. Such systems can be prone to cyber-attacks; therefore the monitoring and identification of cyber-attacks play a significant role in preventing the abuse of our data and systems. The majority of such systems proposed in the literature are based on a model/classifiers built with the help of classical/off-line learning methods on a learning data set. Since cyber-attacks evolve over time such models or classifiers sooner or later become outdated. To keep a proper system functioning the models need to be updated over a period of time. When dealing with models/classifiers learned by classical off-line methods, this is an expensive and time-consuming task. One way to keep the models updated is to use evolving methodologies to learn and adapt the models in an on-line manner. Such methods have been developed, extensively studied and implemented for regression problems. The presented paper introduces a novel evolving possibilistic Cauchy clustering (eCauchy) method for classification problems. The given method is used as a basis for large-scale monitoring of cyber-attacks. By using the presented method a more flexible system for detection of attacks is obtained. The approach was tested on a database from 1999 KDD intrusion detection competition. The obtained results are promising. The presented method gives a comparable degree of accuracy on raw data to other methods found in the literature; however, it has the advantage of being able to adapt the classifier in an on-line manner. The presented method also uses less labeled data to learn the classifier than classical methods presented in the literature decreasing the costs of data labeling. The study is opening a new possible application area for evolving methodologies. In future research, the focus will be on implementing additional data filtering and new algorithms to optimize the classifier for detection of cyber-attacks.