Type-2 Fuzzy Logic Systems

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Learning of interval and general type 2 fuzzy logic systems using simulated annealing: theory and practice

Learning of interval and general type 2 fuzzy logic systems using simulated annealing: theory and practice

of type-1 fuzzy logic inappropriate in many cases especially with problems related to inefficiency of performance in fuzzy logic control [21]. Problems related to model- ing uncertainty using membership functions of type-1 fuzzy sets have been recognized early and [50] introduced higher types of fuzzy sets called type-n fuzzy sets including type-2 fuzzy sets [37]. Type-2 fuzzy logic systems have many advantages compared with type-1 fuzzy logic systems, including the ability to handle different types of uncer- tainties and the ability to model problems with fewer rules [21]. Two factors should be considered regarding the the widespread perception that a general type-2 fuzzy logic system should outperform the interval form which also should outperform a type-1 fuzzy logic system [46]. These two factors are the dependence of performance on the choice of the model parameters as well as on the variability of uncertainty within the application [46]. Therefore, a good choice of the model’s parameters using automated methods is desirable to get clearer conclusions regarding this comparison. Despite these promising indicators of the general type-2 fuzzy logic systems, almost all devel- opments of type-2 fuzzy logic systems have been based on interval type-2 fuzzy logic systems. However, new representations allow us to consider general type-2 fuzzy logic systems. These representations include geometric T2FLS [15], alpha-planes [41], al- pha cuts [22] and Z-slices [45, 10][47]. There have been a number of developments in reducing the computations for general type-2 fuzzy logic systems. For type-reduction, the geometric defuzzifier [15], the sampling defuzzifier [19] followed by importance sampling defuzzifier [31] and a centroid defuzzifier based on the alpha representation [32] have been proposed. One attempt to design general type-2 sets based on zSlices representation was proposed in [10] where survey data and device characteristics were used to build zSlices automatically
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Elliptic membership functions and the modeling uncertainty in type 2 fuzzy logic systems as applied to time series prediction

Elliptic membership functions and the modeling uncertainty in type 2 fuzzy logic systems as applied to time series prediction

Abstract—In this paper, our aim is to compare and contrast various ways of modeling uncertainty by using different type-2 fuzzy membership functions available in literature. In particular we focus on a novel type-2 fuzzy membership function, – ”Elliptic membership function”. After briefly explaining the motivation behind the suggestion of the elliptic membership function, we analyse the uncertainty distribution along its support, and we compare its uncertainty modeling capability with the existing membership functions. We also show how the elliptic membership functions perform in fuzzy arithmetic. In addition to its extra advantages over the existing type-2 fuzzy membership functions such as having decoupled parameters for its support and width, this novel membership function has some similar features to the Gaussian and triangular membership functions in addition and multiplication operations. Finally, we have tested the prediction capability of elliptic membership functions using interval type-2 fuzzy logic systems on US Dollar/Euro exchange rate prediction problem. Throughout the simulation studies, an extreme learning machine is used to train the interval type-2 fuzzy logic system. The prediction results show that, in addition to their various advantages mentioned above, elliptic membership functions have comparable prediction results when compared to Gaussian and triangular membership functions.
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Variable Impedance Control for Rehabilitation Robot using Interval Type-2 Fuzzy Logic

Variable Impedance Control for Rehabilitation Robot using Interval Type-2 Fuzzy Logic

Impedance control is an effective method in controlling the rehabilitation robots. The therapeutic exercises are performed well with satisfactory performances. The previous impedance control approaches were developed based on the torque control strategy whereas the proposed impedance control is based on the voltage control strategy. The proposed approach is free of manipulator dynamics, thus is simpler, less computational, and more effective compared with the torque based control approaches. Additionally, since it is difficult to be sure about the ideal value of the impedance parameters, interval type-2 fuzzy logic systems are used to regulate impedance parameters. The proposed technique for applying the adaptive impedance parameters is shown to be more efficient than using the constant impedance parameters. The control approach has been verified by stability analysis. The simulation results show the superiority of the proposed control approach over a constant impedance control scheme.
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Contrasting singleton type 1 and interval type 2 non singleton type 1 fuzzy logic systems

Contrasting singleton type 1 and interval type 2 non singleton type 1 fuzzy logic systems

Abstract—Most applications of both type-1 and type-2 fuzzy logic systems are employing singleton fuzzification due to its simplicity and reduction in its computational speed. However, using singleton fuzzification assumes that the input data (i.e., measurements) are precise with no uncertainty associated with them. This paper explores the potential of combining the uncer- tainty modelling capacity of interval type-2 fuzzy sets with the simplicity of type-1 fuzzy logic systems (FLSs) by using interval type-2 fuzzy sets solely as part of the non-singleton input fuzzifier. This paper builds on previous work and uses the methodological design of the footprint of uncertainty (FOU) of interval type-2 fuzzy sets for given levels of uncertainty. We provide a detailed investigation into the ability of both types of fuzzy sets (type- 1 and interval type-2) to capture and model different levels of uncertainty/noise through varying the size of the FOU of the underlying input fuzzy sets from type-1 fuzzy sets to very “wide” interval type-2 fuzzy sets as part of type-1 non-singleton FLSs using interval type-2 input fuzzy sets. By applying the study in the context of chaotic time-series prediction, we show how, as uncertainty/noise increases, interval type-2 input fuzzy sets with FOUs of increasing size become more and more viable.
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An Optimized Interval Type 2 Fuzzy Logic Control Scheme based on Optimal Defuzzification

An Optimized Interval Type 2 Fuzzy Logic Control Scheme based on Optimal Defuzzification

Liang and Mendel [5] introduced the theory and design procedures of Interval Type-2 Fuzzy Logic Systems (IT2 FLS). The IT2 FLS has always been considered to be a special case of a general T2 FLS; consequently, things that were developed for the latter were then specialized to the former. Research works about developing IT2 FLS were presented since Mendel et al. [6] have proposed a simple way to implement an IT2 FLS from T1 FLS mathematics. The use of IT2 FLS began to increase since then. Some papers [7] – [9] investigated the importance of IT2 FLS theoretically and practically, especially in intelligent control systems.
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Conceptual Framework Based On Type-2 Fuzzy Logic Theory for Predicting Childhood Obesity Risk

Conceptual Framework Based On Type-2 Fuzzy Logic Theory for Predicting Childhood Obesity Risk

This paper presents a review of the AI and data-driven approaches for preventing and predicting childhood obesity. In addition, it proposes conceptual frameworks that aim to use a type-2 fuzzy logic methodology, which can predict the risk of obesity for children on their family’s dirty habits patterns, characteristics, and other parameters. This prediction will be used as an intervention factor to remediate obesity, which will enhance public health and reduce the costs of later treatments for several obesity- related diseases. We will conduct the assessment of the proposed system on at least one thousand families in Saudi Arabia. The proposed type-2 fuzzy logic systems will be capable of handling the encountered uncertainties to achieve better modeling and more accurate results on the risk for obesity in children. it can also encode the extract- ed rules in comprehensive ways to provide insights into the best obesity prevention behaviors for lowering childhood obesity risk.
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Perpetual Learning Framework based on Type-2 Fuzzy Logic System for a Complex Manufacturing Process

Perpetual Learning Framework based on Type-2 Fuzzy Logic System for a Complex Manufacturing Process

two-step strategy: expanding the structure of the existing model by generating new rules to accommodate the new data without significantly disrupting the existing model and in the second step further fine-tune and/or prune the model. In this paper, the research study is focused on the idea of offline incremental learning in which additional knowledge is added to the model based on the second strategy. In the proposed learning strategy, the modelling structure is designed to learn from an initial database (via an appropriate learning/optimisation algorithm) but at the same time incrementally adapt to new data when these are available without deteriorating the core model knowledge acquired from the initial database. Additional system’s features include the system’s ability to interact with the environment in a perpetual mode and having an open structure in which the system has the ability to add and remove rules (knowledge maintenance). Several methods have been developed so far to demonstrate some of the aspects of incremental learning (Kasabov, 2015; Kasabov and Song, 2002; Panoutsos and Mahfouf, 2008). However, all of them use type-1 fuzzy logic systems. In the field of type-2 fuzzy logic systems, several models have been proposed to incrementally optimise the parameters of the model (Juang and Chen, 2014; Juang and Tsao, 2008; Lin et al., 2014). However, all these models are used for online structure learning for time varying data. To our knowledge, no pervious incremental type-2 neural fuzzy systems for offline learning have been reported. In this study, we present a new perpetual (incremental) learning framework that is based on granular computing interval type-2 neural fuzzy systems (GrC-IT2-FLSs). By using such a modelling framework, it is possible to achieve good modelling performance and at the same time good system transparency (interpretability). An iterative rule pruning mechanism is used as the main feature that removes the redundant fuzzy rules after each incremental step, which allows the model to be used in a lifelong learning mode. The proposed methodology is tested against a real- industrial problem. The prediction of spindle peak torque of Friction Stir Welding of steel is investigated. Such manufacturing process involves highly complex databases, containing data with high uncertainty (measurement noise, operator errors, etc.) and non-linear dynamics (complex thermo-mechanical behaviour) as well as sparse data (due to constraints on the process conditions).
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Type-2 Fuzzy Logic based Systems for Adaptive Learning and Teaching within Intelligent E-Learning Environments

Type-2 Fuzzy Logic based Systems for Adaptive Learning and Teaching within Intelligent E-Learning Environments

readable and linguistically interpretable manner by the fuzzy rules. Their transparency makes them perfect for quick assessment to explain the reason and method of certain combinations of inputs actuating specific rules, where a certain set of output conclusions has been yielded. The proposed environment employs a self-learning mechanism that generates a FL-based model from the data. We incorporated and gauged the student engagement levels, and we mapped them to suitable delivery needs, which match the knowledge and preferred learning styles of the students. The resulting practical and theoretical environments incorporate a novel system for gauging the student engagement levels based on utilising visual information to automatically calculate the engagement degree of the students. This differs from traditional methods that usually employ expensive and invasive sensors. Our approach only uses a low-cost Red Green Blue-Depth (RGB-D) video camera (Microsoft Kinect) operating in a non-intrusive mode, whereby the users are allowed to act and move without restrictions. This fuzzy model is generated from data representing various student capabilities and their desired learning needs. The learnt FL-based model is then used to improve the knowledge delivery to the various students based on their individual characteristics. The proposed environment is adaptive, where it is continuously adapting in a lifelong learning mode to ensure that the generated models adapt to the individual student preferences. This employed approach was not computationally demanding and generated easily read and analysed white box models, which can be checked by the lay user, which is mainly suitable for adapting the dynamic nature of the e-learning process.
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Interval type 2 intuitionistic fuzzy logic systems   a comparative evaluation

Interval type 2 intuitionistic fuzzy logic systems a comparative evaluation

Atanassov [3] introduced the concept of intuitionistic FS (IFS) with MF and NMF separately defined such that none is complementary to the other. In the literature, IFSs have been found to be one of the useful tools for dealing with imprecise information [4]. The reader is referred to [5] for more details on IFS. Similar to classical type-1 FSs, the MFs and NMFs of IFSs may not handle the plethora of uncertainty that fraught many applications. The T2FS introduced by Zadeh is a three dimensional structure which provides the extra degrees of freedom needed to handle higher forms of uncertainty. For the generalised T2FS, the third dimension is weighted differently which makes it complex and difficult to use [6, 7]. The simpler and manageable version - interval type-2 FS (IT2FS) - have values in the third dimension equal to 1 and this makes it easier for IT2FS to be represented on a two dimensional plane. The IFSs and IT2FSs have been widely and extensively adopted by researchers in uncertainty modeling in many applications. For example, in Nguyen et al. [8], IT2 fuzzy C-mean (FCM) cluster- ing using IFS is proposed. The authors show that the use of IFS with IT2FCM led to improved clustering quality particularly in the presence of noise. In Naim and Hagras [9, 10] and Naim et al. [11], IFS and IT2FS are combined to develop a multi-criteria group decision making (MCGDM) system for the assessment of post-graduate study, selection of appropriate lighting level in intelligent environ- ment and evaluation of different techniques for the choice of illumination in a shared environments respectively. The authors pointed out that the use of IFS and IT2FS in a MCGDM system provided decisions that are closer to the group decisions compared to some existing methods. However, in [9, 10, 11], only the IT2FS MFs are utilised and the intuitionistic fuzzy (IF) indices are evaluated on the primary MFs of the IT2FSs and no learning whatsoever is carried out on these sets.
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Interval Type-2 Fuzzy Logic Controller for DC-DC Converter

Interval Type-2 Fuzzy Logic Controller for DC-DC Converter

The controller mainly consists of five sections which are fuzzifier, rule base, inference engine, type-reducer and defuzzifier. In the IT2FL controller, as in the T1FL controller, the crisp inputs are first fuzzified into input fuzzy sets which then activate the inference engine and the rule base to produce output type-2 fuzzy sets. The type-2 fuzzy outputs of the inference engine are then processed by the type-reducer which combines the output sets and then performs a centroid calculation, which leads to type-1 fuzzy sets called type-reduced sets [11]. Then, the defuzzifier defuzzifies the type-reduced type-1 fuzzy outputs to produce crisp outputs that are used to generate PWM waveform. In interval type-2 fuzzy sets, the secondary membership function is either zero or one. As in the T1FL controller, the labels of type-2 fuzzy sets are assigned with Negative Big (NB), Negative Small (NS), Zero (Z), Positive Small (PS) and Positive Big (PB), respectively. In this paper a nonsingleton fuzzifier Output membership sets used. The IT2FL system has been designed by using GFS toolbox. Generalized Fuzzy Systems (GFS) is Graphical User Interface tool developed for visualizing fuzzification using almost all type of fuzzy sets. The IT2FS membership function can be formed from the type-1 fuzzy set. The membership function obtained from type-1 fuzzy sets can be used here. The type-1 fuzzy set is treated here as Principal Membership Function (PMF) and depending upon the uncertainty due to noise FOU may be specified to get Lower Membership Function (LMF) and Upper Membership Function (UMF). In the IT2FL controller, the rules remain the same as in Type-1 FL controller. The method of defuzzification for this controller is centroid [12].
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Application of Type-1 and Type-2 Fuzzy Logic Controller for The Real  Swarm Robot

Application of Type-1 and Type-2 Fuzzy Logic Controller for The Real Swarm Robot

One of important research in system swarm robot is how to coordinate multi robot in that systems. An intelligence of each individual robot in the swarm in interacting among them really depends on their environment. Each of them should be able to adapt their behavior to the situation and condition that they met. Therefore, the main function of their intelligence is used for adapting their position to the environment. Some of the tasks concerning to the environment that they should handle are: navigating [1][2], foraging [3], formation controlling and formation forming [4], aggregating [5], sorting [6], and collective construction [7].
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An Interval Type-2 Fuzzy Logic Approach for Instrument Fault Detection and Diagnosis

An Interval Type-2 Fuzzy Logic Approach for Instrument Fault Detection and Diagnosis

I N the last three decades process control and automation area had a tremendous improvement due to advances on computational tools. Many of regulatory control actions that were performed by human operators are now performed automatically with aid of computers. Nonetheless, in a pro- cess with hundreds of variables, instruments and actuators it is impossible that a person or a group can manage every and any alarm triggered by an abnormal event. Therefore the Fault Detection and Diagnosis (FDD) field had received extensive attention. According to [1], the current challenge for control engineers is the automation of Abnormal Event Management (AEM) using intelligent control systems. Inside this field, Instrument Fault Detection and Diagnosis is a potential tool to prevent process performance degradation, false alarms, missing actions, process shutdown and even safety problems. A well-known strategy related to this pro- blem is preventive maintenance. In that, periodical tests and calibration are made in instruments. This is a cumbersome task where instruments are dismantled, cleaned, reassembled and calibrated. Even so, this is not a guarantee that faults will not occur [2]. This paper presents an Interval Type- 2 Fuzzy Logic (IT2FL) classifier to detect and diagnose temperature sensor faults in an alternative compressor, named Sales Gas Compressor (SGC), operating in a Gas Processing Unit (GPU).
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Structural Damage Control with Interval Type-2 Fuzzy Logic Controller

Structural Damage Control with Interval Type-2 Fuzzy Logic Controller

In recent years, type-2 fuzzy systems have been used effectively in many engineering issues [19-23]. However, despite the ability of this method to deal with issues of high uncertainty, research on the use of these systems in the field of control of structures has been very limited. Shariatmadar et al. studied the seismic control of structures using active tuned mass dampers with an interval type-2 fuzzy controller. In their research, they showed that, despite the fact that an active tuned mass damper with a type-1 fuzzy controller functions is more effective than a passive damper, however, it is not able to manage uncertainty in the fuzzy rule base which does not lead to the desired reduction in responses under different types of earthquake excitations. Also, an interval type-2 fuzzy controller significantly reduces the structural response compared with type-1 fuzzy controller [24].
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Hybrid learning for interval type 2 intuitionistic fuzzy logic systems as applied to identification and prediction problems

Hybrid learning for interval type 2 intuitionistic fuzzy logic systems as applied to identification and prediction problems

In the work of Nguyen et al. [16], IT2 fuzzy C-mean (IT2FCM) and IFS are applied for image clustering with improved performance in the clustering quality compared to FCM and IT2FCM. Nghiem et al. [17] applied intuitionis- tic T2 FS to image thresholding using Sugeno intuitionistic fuzzy generator. Results show improved thresholding quality compared to standard algorithms such as type-1 FS and IFS. In Naim and Hagras [18], a hybrid approach using IT2 and IFS for multi-criteria group decision making (MCGDM) is proposed. In their study, IT2 FS is used to handle the linguistic uncertainty with intuitionistic evaluation used in the design of the NMF degrees. The proposed hybrid approach was evaluated on 10 candidates in a postgraduate study. Results of evaluation show better agreement with the human experts decision than IFS, FS and IT2 fuzzy systems. In the same vein, Naim et al. [19] presented a fuzzy logic-MCGDM (FL- MCGDM) for choosing appropriate and convenient lighting level to meet particular individual reading needs. The hybrid system adopted the concepts of IT2 FS and the hesitation indices of IFS with intuitionistic values used to represent the MFs of the IT2 FS for the left and right end-points. Results show that with T2 FS and IFS, the capability of FL-MDGDM is enhanced with improved capacity for decision making. In Naim and Hagras [20], FL-MCGDM is proposed for intelligent shared environment. Analysis of results indicate consistency
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Interval type 2 intuitionistic fuzzy logic system for non linear system prediction

Interval type 2 intuitionistic fuzzy logic system for non linear system prediction

Abstract—This paper presents an approach to prediction based on a new interval type-2 intuitionistic fuzzy logic system (IT2IFLS) of Takagi-Sugeno-Kang (TSK) fuzzy inference. The gradient descent algorithm (GDA) is used to adapt the parame- ters of the IT2IFLS. The empirical comparison is made on the designed system using two synthetic datasets. Analysis of our results reveal that the presence of additional degrees of freedom in terms of non-membership functions and hesitation indexes in IT2IFLS tend to reduce the root mean square error (RMSE) of the system compared to a type-1 fuzzy logic approach and some interval type-2 fuzzy systems.
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Improving security requirements adequacy: an interval type 2 fuzzy logic security assessment system

Improving security requirements adequacy: an interval type 2 fuzzy logic security assessment system

The rate of security attacks on different organizations has been increasing over recent years. According to the Global State of Information Security survey, security incidents increased in 2015 by 38% above reports from 2014, which led to a 56% increase in intellectual property theft [22]. The survey also reports that 53% of organizations are conducting employee training and awareness programs, and 54% designate a Chief Security Officer (CSO) to lead teams of security specialists [22]. The focus on establishing professional personnel to address this problem illustrates the reliance on human experts to comprehensively assess the security of systems. However, despite the abundance of security requirements, checklists, guidelines and best practices, such as the U.S. NIST Special Publication 800 Series, human analysts still face substantial challenges in the selection of the appropriate security requirements to mitigate threats. For example, depending on the chosen attack scenario, analysts must still evaluate a range of possible security authentication requirements, such as password complexity, single and multifactor authentication.
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Extended Kalman filter based learning of interval type 2 intuitionistic fuzzy logic system

Extended Kalman filter based learning of interval type 2 intuitionistic fuzzy logic system

Abstract—Fuzzy logic systems have been extensively applied for solving many real world application problems because they are found to be universal approximators and many methods, particularly, gradient descent (GD) methods have been widely adopted for the optimization of fuzzy membership functions. Despite its popularity, GD still suffers some drawbacks in terms of its slow learning and convergence. In this study, the use of decoupled extended Kalman filter (DEKF) to optimize the parameters of an interval type-2 intuitionistic fuzzy logic system of Tagagi-Sugeno-Kang (IT2IFLS-TSK) fuzzy inference is proposed and results compared with IT2IFLS gradient descent learning. The resulting systems are evaluated on a real world dataset from Australia’s electricity market. The IT2IFLS-DEKF is also compared with its type-1 variant and interval type-2 fuzzy logic system (IT2FLS). Analysis of results reveal performance superiority of IT2IFLS trained with DEKF (IT2IFLS-DEKF) over IT2IFLS trained with gradient descent (IT2IFLS-GD). The proposed IT2IFLS-DEKF also outperforms its type-1 variant and IT2FLS on the same learning platform.
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Type 2 Fuzzy Logic Controllers Based Genetic Algorithm for the Position Control of DC Motor

Type 2 Fuzzy Logic Controllers Based Genetic Algorithm for the Position Control of DC Motor

The simulated results show that, using a type-2 FLC in real world applications can be a good option since this type of system is a more suitable system to manage high levels of uncertainty, as we can see in the results shown in Tables 2-5. Simulation results indicate that the per- formance of the GA FLCT2 will better. That is mean the system will sense for change the value of IAE and ITAE. The results demonstrate that a type-2 FLC can outper- form type-1 FLCs that have more robustness design pa- rameters. The main advantage of the type-2 FLC appears to be its ability to eliminate persistent oscillations, espe- cially when unmodelled dynamics were introduced. This ability to handle modeling error is particularly useful when FLCs are tuned offline using GA and a model as the impact of unmodelled dynamics is reduced. The sig- nificance of the work is focused to manage the uncer- tainty of the system. The nonlinear of the systems are big problem therefore the one of successful methods to eli- minate or reduce nonlinearity system by using fuzzy type two. It is a good option for real time applications that limited time is needed such as robot system.
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IS-MRAS With On-Line Adaptation Parameters Based on Type-2 Fuzzy LOGIC for Sensorless Control of IM

IS-MRAS With On-Line Adaptation Parameters Based on Type-2 Fuzzy LOGIC for Sensorless Control of IM

L. Chrifi-Alaoui received the Ph.D. in Automatic Control from the Ecole Centrale de Lyon. Since 1999 he has a teaching position in automatic control in the Aisne University Institute of Technology, UPJV, Cuffies-Soissons, France. From 2004 to 2010 and 2014 to 2018 he was the Head of the Department of Electrical Engineering and industrial informatics. His research interests are mainly related to linear and non-linear control including sliding mode control, adaptive control, and robust control, with applications to electric drive and mechatronic systems.
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Genetically Tuned Interval Type-2 Fuzzy Logic for Fault Diagnosis of Induction Motor

Genetically Tuned Interval Type-2 Fuzzy Logic for Fault Diagnosis of Induction Motor

Sahraoui (2009) presented work on Fuzzy Logic Approach for the Diagnosis of Rotor Faults in Squirrel Cage Induction Motors. Motor Current Signature Analysis (MCSA) was used. The strategy rests on the follow-up (in amplitude and frequency) of the harmonics representing the defects of the broken bars, preparing and thus generating the adequate inputs for the treatment where the decision is made by fuzzy logic. Z. Ye, A. Sadeghian, B. Wu (2006) presented Mechanical fault diagnostics for induction motor with variable speed drives using adaptative neuro-fuzzy inference system. Takagi & Sugeno (1985) studied on the fuzzy identification of systems and its application to modeling and control of engineering systems. Jamshidi (1997) contributed on his work for fuzzy control of complex systems in soft computing methods. Mamdani E.H. (1974, 76) contributed his work on application of fuzzy algorithm for simple dynamic plant and advances in linguistic synthesis of fuzzy controllers. Tong R.M. (1978) reported on synthesis of fuzzy models for industrial process. R. Alcal´a, J. Alcal´a-Fdez, and F. Herrera (2007) introduced a proposal for the genetic lateral tuning of linguistic fuzzy systems and its interaction with rule selection. An innovative study on fault diagnosis of Induction Motor using hybrid FFT and soft computing techniques is proposed in this research work. In the proposed methodology a genetically tuned type-2 FFT fuzzy system and also ANFIS is to be developed. Before using the raw data available from the industrial and commercial sources, it will be normalized for mapping in 0,1 range. This section presented the literature review on different fuzzy techniques, various fault diagnosis of induction motor, fast Fourier transform implementation and fuzzy logic. Review covered variety of topic, methods, techniques and approaches
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