Woei Wan Tan

Towards an efficient type-reduction method for interval type-2 fuzzy logic systems

This paper introduces an alternative type-reduction method for interval type-2 (IT2) fuzzy logic systems (FLSs), with either continuous or discrete secondary membership function. Unlike the Karnik-Mendel type reducer which is based on the wavy-slice representation of a type-2 fuzzy set, the proposed type reduction algorithm is developed using the vertical-slice representation. One advantage of the approach is the output of the type reducer can be expressed in closed form, thereby providing a tool for the theoretical analysis of IT2 FLSs. The computational complexity of the proposed method is also lower than the uncertainty bounds method and the enhanced Karnik-Mendel method. To assess the feasibility of the proposed type-reducer, it is used to calculate the output of an IT2 fuzzy logic controller (FLCs). Results from a simulated coupled tank experiment demonstrated that IT2 FLCs that employ the proposed type reduction algorithm share similar robustness properties as FLCs based on the Karnik-Mendel type reducer.

A type-2 fuzzy logic controller for the liquid-level process

This paper focuses on evolving type-2 fuzzy logic controllers (FLCs) genetically and examining whether they are better able to handle modelling uncertainties. The study is conducted by utilizing a type-2 FLC, evolved by a genetic algorithm (GA), to control a liquid-level process. A two stage strategy is employed to design the type-2 FLC. First, the parameters of a type-1 FLC are optimized using GA. Next, the footprint of uncertainty is evolved by blurring the fuzzy input set. Experimental results show that the type-2 FLC copes well with the complexity of the plant, and can handle the modelling uncertainty better than its type-1 counterpart.

Computationally Efficient Type-Reduction Strategies for a Type-2 Fuzzy Logic Controller

A type-2 fuzzy set is characterized by a concept called footprint of uncertainty (FOU). It provides the extra mathematical dimension that equips type-2 fuzzy logic systems (FLSs) with the potential to outperform their type-1 counterparts. While a type-2 FLS has the capability to model more complex relationships, the output of a type-2 fuzzy inference engine needs to be type-reduced. As type-reduction is very computationally intensive, type-2 FLSs may not be suitable for certain real-time applications. This paper aims at developing more computationally efficient type-reducers. The proposed type-reducer is based on the concept known as equivalent type-1 sets (ET1Ss), a collection of type-1 sets that replicates the input-output map of a type-2 FLS. Simulations are presented to demonstrate that the proposed type-reducing algorithms have lower computational cost and better performances than the Karnik-Mendel type-reducer

A generic neurofuzzy model-based approach for detecting faults in induction motors

Many fault detection and diagnosis schemes are based on the concept of comparing the plant output with a model in order to generate residues. A fault is deemed to have occurred if the residue exceeds a predetermined threshold. Unfortunately, the practical usefulness of model-based fault detection schemes is limited because of the difficulty in acquiring sufficiently rich experimental data to identify an accurate model of the system characteristics. This paper aims at developing a generic neurofuzzy model-based strategy for detecting broken rotor bars, which is one of the most common type of faults that may occur in a squirrel-cage induction motor. A neurofuzzy model that captures the generic characteristics of a class of asynchronous motor is the key component of the proposed approach. It is identified using data generated by a simulation model that is constructed using information on the name plate of the motor. Customization for individual motors is then carried out by selecting the threshold for fault detection via an empirical steady-state torque-speed curve. Since data obtained from a practical motor are used to select the threshold and not to build a complete model, the objective of reducing the amount of experimental input-output data required to design a model-based fault detector may be realized. Experimental results are presented to demonstrate the viability of the proposed fault detection scheme.

Type-2 FLS Modeling Capability Analysis

There has been an increasing amount of research on type-2 fuzzy logic systems (FLSs) recently. The interest is fueled by results demonstrating that type-2 fuzzy sets offer a framework for effectively solving problems where uncertainties are present A concept, known as the footprint of uncertainty (FOU), is mainly responsible for the improved modeling capability of type-2 FLSs. This paper aims at providing insight into how the extra mathematical dimension provided by the FOU differentiates type-2 FLSs from type-1 FLSs. Since the input-output relationships of both types of FLS are fixed once the parameters are selected, the analysis is performed by finding a set of equivalent type-1 sets (ET1Ss) that re-produces the input-output map of a type-2 FLS. Results are presented to demonstrate that a type-2 fuzzy system is able to model more complex input-output relationship because the ET1S changes as the input varies. The technique for converting a type-2 fuzzy set into a group of type-1 sets is also useful as it provides a framework for extending the entire wealth of type-1 fuzzy control/identification/design/analysis techniques to type-2 systems

The nonlinearity cancellation phenomenon in micromechanical resonators

In this paper, we present comprehensive analysis of the nonlinearities in a micromechanical clamped-clamped beam resonator. A nonlinear model which incorporates both mechanical and electrostatic nonlinear effects is established for the resonator and verified by experimental results. Both the nonlinear model and experimental results show that the first-order cancellation between the mechanical and electrostatic nonlinear spring constants occurs at about 45 V dc polarization voltage for a 193 kHz resonator in vacuum pressure of 37.5 µTorr. Our study also reveals that the nonlinearity cancellation is helpful in optimizing the overall resonator performance. On top of improving the frequency stability of the resonator by reducing its amplitude-frequency coefficient to almost zero, the nonlinearity cancellation also boosts the critical vibration amplitude of the resonator (0.57 µm for the beam resonator with 2 µm nominal gap spacing), leading to better power handling capabilities. The results from the clamped-clamped beam resonator studied in this work can be easily generalized and applied to other types of resonators.

Analytical Structure and Characteristics of Symmetric Karnik–Mendel Type-Reduced Interval Type-2 Fuzzy PI and PD Controllers

This paper presents the analytical structure of a class of interval type-2 (IT2) fuzzy proportional derivative (PD) and proportional integral (PI) controllers that have symmetrical rule base and symmetrical consequent sets. Two assumptions are made: 1) The Zadeh AND operator is employed as the t-norm operator; 2) type-reduction is performed by the Karnik-Mendel (KM) type-reduction method. The main contributions are the methodology that identifies the input conditions, where the KM algorithm uses a new switch point to compute the bounds of the type-reduced set, the closed-form expressions that relate the inputs and output of an IT2 fuzzy controller, and insights into the potential performance improvement because of the inclusion of the footprint of uncertainty (FOU). Compared with its T1 counterpart, two additional FOU parameters generate 31 extra local regions, each providing a unique relationship between the inputs and output signals. The generation of a relatively large number of local regions at the cost of two extra design parameters indicates that an IT2 fuzzy controller may be able to provide better performance. Furthermore, by comparing the analytical structure with the corresponding T1 counterpart, the potential advantages to use the IT2 over the T1 fuzzy controller are studied. Four interesting characteristics are identified, and they provide insights into why the IT2 fuzzy controller may better balance the conflicting aims of fast rise time and small overshoot.

Type-2 Fuzzy System for ECG Arrhythmic Classification

This paper aims at assessing the feasibility of using a type-2 fuzzy system for ECG arrhythmic beat classification. Three types of ECG signals, namely the normal sinus rhythm (NSR), ventricular fibrillation (VF) and ventricular tachycardia (VT), are considered. The inputs to the fuzzy classifier are the average period and the pulse width, two features that are commonly used for computer-assisted arrhythmia recognition and are readily extracted from pre-processed ECG waveforms. Using a combination of the fuzzy C-means clustering algorithm and the amount of dispersion in each cluster, a method for designing the antecedent type-2 MFs of the classifier from a training data set is formulated. Tests using data from the MIT-BIH Arrhythmia Database show that the proposed type-2 fuzzy classifier yields an accuracy of 90.91 % for VT events and 84 % for VF events and 100 % for NSR events.

A simplified architecture for type-2 FLSs and its application to nonlinear control

A type-2 fuzzy logic system (FLS) is one that has at least one type-2 membership function (MF) in its rule base. Consequently, the output of the inference engine is a type-2 fuzzy set and must be type-reduced before the defuzzifier is able to convert the output set into a crisp value, type-2 FLS may not be suitable for certain real-time applications because type-reduction is very computationally intensive, especially when there are many MFs and the rule base is large. In this paper a simplified architecture for type-2 FLSs is proposed, where only one fuzzy set for each input domain is type-2 and all others are type-1. This architecture relieves the computational burden of the type-2 fuzzy system, while preserving its advantages over traditional type-1 FLSs. Two FLSs that have the proposed architecture are used to control a nonlinear SISO plant. Experimental results show that they cope well with the complexity of the plant, and can handle the modelling uncertainties better than their type-1 counterpart.

Non-singleton genetic fuzzy logic system for arrhythmias classification

This paper aims at analyzing a non-singleton fuzzy logic classifier (NSFLC) and assessing its ability to cope with uncertainties in pattern classification problems. The analysis demonstrate that the NSFLC has fuzzy classification boundary and noise suppression capability. These characteristics means that the NSFLC is particulary suitable for problems where the boundaries between classes is non-distinct. To further demonstrate the benefits offered by a NSFLC, a non-singleton fuzzy logic classifier evolved using Genetic Algorithm (GA) is assessed using a benchmark cardiac arrhythmias classification problem. Results indicate that a NSFLC achieved good classification accuracy using features that are easier to extract, but contain more uncertainties.