Tool wear assessment based on type-2 fuzzy uncertainty estimation on acoustic emission

In modern manufacturing industry, developing automated tool condition monitoring system become more and more import in order to transform manufacturing systems from manually operated production machines to highly automated machining centres. This paper presents a nouvelle cutting tool wear assessment in high precision turning process using type-2 fuzzy uncertainty estimation on acoustic Emission. Without understanding the exact physics of the machining process, type-2 fuzzy logic system identifies acoustic emission signal during the process and its interval set of output assesses the uncertainty information in the signal. The experimental study shows that the development trend of uncertainty in acoustic emission signal corresponds to that of cutting tool wear. The estimation of uncertainties can be used for proving the conformance with specifications for products or auto-controlling of machine system, which has great meaning for continuously improvement in product quality, reliability and manufacturing efficiency in machining industry.     

Parallel Interval Type-2 Subsethood Neural Fuzzy Inference System

Neuro-fuzzy models are being increasingly employed in the domains like weather forecasting, stock market prediction, computational finance, control, planning, physics, economics and management, to name a few. These models enable one to predict system behavior in a more human-like manner than their crisp counterparts. In the present work, an interval type-2 neuro-fuzzy evolutionary subsethood based model has been proposed for its use in finding solutions to some well-known problems reported in the literature such as regression analysis, data mining and research problems relevant to expert and intelligent systems. A novel subsethood based interval type-2 fuzzy inference system, named as Interval Type-2 Subsethood Neural Fuzzy Inference System (IT2SuNFIS) is proposed in the present work. Mathematical modeling and empirical studies clearly bring out the efficacy of this model in a wide variety of practical problems such as Truck backer-upper control, Mackey–Glass time-series prediction, Narazaki–Ralescu and bell function approximation. The simulation results demonstrate intelligent decision making capability of the proposed system based on the available data. The major contribution of this work lies in identifying subsethood as an efficient measure for finding correlation in interval type-2 fuzzy sets and applying this concept to a wide variety of problems pertaining to expert and intelligent systems. Subsethood between two type-2 fuzzy sets is different from the commonly used sup-star methods. In the proposed model, this measure assists in providing better contrast between dissimilar objects. This method, coupled with the uncertainty handling capacity of type-2 fuzzy logic system, results in better trainability and improved performance of the system. The integration of subsethood with type-2 fuzzy logic system is a novel idea with several advantages, which is reported for the first time in this paper.     

Interval type-2 fuzzy inverse controller design in nonlinear IMC structure

In the recent years it has been demonstrated that type-2 fuzzy logic systems are more effective in modeling and control of complex nonlinear systems compared to type-1 fuzzy logic systems. An inverse controller based on type-2 fuzzy model can be proposed since inverse model controllers provide an efficient way to control nonlinear processes. Even though various fuzzy inversion methods have been devised for type-1 fuzzy logic systems up to now, there does not exist any method for type-2 fuzzy logic systems. In this study, a systematic method has been proposed to form the inverse of the interval type-2 Takagi-Sugeno fuzzy model based on a pure analytical method. The calculation of inverse model is done based on simple manipulations of the antecedent and consequence parts of the fuzzy model. Moreover, the type-2 fuzzy model and its inverse as the primary controller are embedded into a nonlinear internal model control structure to provide an effective and robust control performance. Finally, the proposed control scheme has been implemented on an experimental pH neutralization process where the beneficial sides are shown clearly.     

Systematic design of a stable type-2 fuzzy logic controller

Stability is one of the more important aspects in the traditional knowledge of automatic control. Type-2 fuzzy logic is an emerging and promising area for achieving intelligent control (in this case, fuzzy control). In this work we use the fuzzy Lyapunov synthesis as proposed by Margaliot and Langholz [M. Margaliot, G. Langholz, New Approaches to Fuzzy Modeling and Control: Design and Analysis, World Scientific, Singapore, 2000] to build a Lyapunov stable type-1 fuzzy logic control system, and then we make an extension from a type-1 to a type-2 fuzzy logic control system, ensuring the stability on the control system and proving the robustness of the corresponding fuzzy controller.     

A type-2 fuzzy logic controller design for buck and boost DC–DC converters

Conventional (type-1) fuzzy logic controllers have been commonly used in various power converter applications. Generally, in these controllers, the experience and knowledge of human experts are needed to decide parameters associated with the rule base and membership functions. The rule base and the membership function parameters may often mean different things to different experts. This may cause rule uncertainty problems. Consequently, the performance of the controlled system, which is controlled with type-1 fuzzy logic controller, is undesirably affected. In this study, a type-2 fuzzy logic controller is proposed for the control of buck and boost DC–DC converters. To examine and analysis the effects of the proposed controller on the system performance, both converters are also controlled using the PI controller and conventional fuzzy logic controller. The settling time, the overshoot, the steady state error and the transient response of the converters under the load and input voltage changes are used as the performance criteria for the evaluation of the controller performance. Simulation results show that buck and boost converters controlled by type-2 fuzzy logic controller have better performance than the buck and boost converters controlled by type-1 fuzzy logic controller and PI controller.     

Applications of type-2 fuzzy logic system: handling the uncertainty associated with candidate-well selection for hydraulic fracturing

The problem of selecting a target formation(s) in a reservoir among a vast number of zones/sub-layers within huge number of hydrocarbon producing wells for hydraulic fracturing (HF) by using interval type-2 fuzzy logic system (IT2-FLS) to maximize their net present value is studied in this paper. Classical fuzzy system which is called type-1 fuzzy logic system is not capable of accurately capturing the linguistic and numerical uncertainties in the terms used and the inconsistency of the expert’s decision-making. IT2-FLS is very useful in circumstances where it is difficult to determine an exact membership function for a fuzzy set; hence it is very effective for dealing with uncertainties. In highlighting this need, the question has been answered why IT2-FLS should be used in this study. The procedure of applying this study in the area of HF candidate-well selection is illustrated through a case study in an oil reservoir.     

Finishing mill strip gage setup and control by interval type-1 non-singleton type-2 fuzzy logic systems

The setup and control of the finishing mill roll gap positions required to achieve the desired strip head thickness as measured by the finish mill exit X-ray gauge sensor is made by an intelligent controller based on an interval type-2 fuzzy logic system. The controller calculates the finishing mill stand screw positions required to achieve the strip finishing mill exit target thickness. The interval type-2 fuzzy head gage controller uses as inputs the transfer bar thickness, the width and the temperature at finishing mill entry, the strip target thickness, the width and the temperature at finishing mill exit, the stand work roll diameter, the stand work roll speed, the stand entry thickness, the stand exit thickness, the stand rolling force, and the %C of the strip. Taking into account that the measurements and inputs to the proposed system are modeled as type-1 non-singleton fuzzy numbers, we present the so called interval type-1 non-singleton type-2 fuzzy logic roll gap controller. As reported in the literature, interval type-2 fuzzy logic systems have greater non-linear approximation capacity than that of its type-1 counterpart and it has the advantage to develop more robust and reliable solutions than the latter. The experiments of these applications were carried out for three different types of coils, from a real hot strip mill. The results proved the feasibility of the developed system for roll gap control. Comparison against the mathematical based model shows that the proposed interval type-2 fuzzy logic system equalizes the performance in finishing mill stand screw positions setup and enhances the achieved strip thickness under the tested conditions characterized by high uncertainty levels.     

Optimization of interval type-2 fuzzy logic controllers using evolutionary algorithms

A method for designing optimal interval type-2 fuzzy logic controllers using evolutionary algorithms is presented in this paper. Interval type-2 fuzzy controllers can outperform conventional type-1 fuzzy controllers when the problem has a high degree of uncertainty. However, designing interval type-2 fuzzy controllers is more difficult because there are more parameters involved. In this paper, interval type-2 fuzzy systems are approximated with the average of two type-1 fuzzy systems, which has been shown to give good results in control if the type-1 fuzzy systems can be obtained appropriately. An evolutionary algorithm is applied to find the optimal interval type-2 fuzzy system as mentioned above. The human evolutionary model is applied for optimizing the interval type-2 fuzzy controller for a particular non-linear plant and results are compared against an optimal type-1 fuzzy controller. A comparative study of simulation results of the type-2 and type-1 fuzzy controllers, under different noise levels, is also presented. Simulation results show that interval type-2 fuzzy controllers obtained with the evolutionary algorithm outperform type-1 fuzzy controllers.     

Interval type-2 fuzzy expert system for prediction of carbon monoxide concentration in mega-cities

This paper presents an indirect approach to interval type-2 fuzzy logic system modeling to forecaste the level of air pollutants. The type-2 fuzzy logic system permits us to model the uncertainties among rules and the parameters related to data analysis. In this paper, we propose an indirect method to create an interval type-2 fuzzy logic system from a historical data, where Footprint of Uncertainties of fuzzy sets are extracted by implementation of an interval type-2 FCM algorithm and based on an upper and lower value for the level of fuzziness m in FCM. Finally, the proposed model is applied for prediction of carbon monoxide concentration in Tehran air pollution. It is shown that the proposed type-2 fuzzy logic system is superior in comparison to type-1 fuzzy logic systems in terms of two performance indices.     

A review on type-2 fuzzy logic applications in clustering,classification and pattern recognition

In this paper a review of type-2 fuzzy logic applications in pattern recognition, classification and clustering problems is presented. Recently, type-2 fuzzy logic has gained popularity in a wide range of applications due to its ability to handle higher degrees of uncertainty. In particular, there have been recent applications of type-2 fuzzy logic in the fields of pattern recognition, classification and clustering, where it has helped improving results over type-1 fuzzy logic. In this paper a concise and representative review of the most successful applications of type-2 fuzzy logic in these fields is presented. At the moment, most of the applications in this review use interval type-2 fuzzy logic, which is easier to handle and less computational expensive than generalized type-2 fuzzy logic.     

A simple design method for interval type-2 fuzzy pid controllers

In this study, a design method for single Input interval type-2 fuzzy PID controller has been developed. The most important feature of the proposed type-2 fuzzy controller is its simple structure consisting of a single input variable. The presented simple structure gives an opportunity to the designer to form the type-2 fuzzy controller output in closed form formulation for the first time in literature. This formulation cannot be achieved with present type-2 fuzzy PID controller structures which have employed the Karnik-Mendel type reduction. The closed form solution is derived in terms of the tuning parameters which are chosen as the heights of lower membership functions of the antecedent interval type-2 fuzzy sets. Elaborations are done on the derived closed form output and a simple strategy is presented for a single input type-2 fuzzy PID controller design. The presented interval type-2 fuzzy controller structure still keeps the most preferred features of the PID controller such as simplicity and easy design. We will illustrate how the extra degrees of freedom provided by the antecedent interval type-2 fuzzy sets can be used to enhance the control performance on linear and nonlinear benchmark systems by simulations. Moreover, the type-2 fuzzy controller structure has been implemented on experimental pH neutralization. The simulation and experimental results will illustrate that the proposed type-2 fuzzy controller produces superior control performance and can handle nonlinear dynamics, parameter uncertainties, noise and disturbances better in comparison with the standard PID controllers. Hence, the results and analyses of this study will give the control engineers an opportunity to draw a bridge and connect the type-2 fuzzy logic and control theory.     

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.     

A review on the applications of type-2 fuzzy logic in classification and pattern recognition

In this paper a review of type-2 fuzzy logic applications in pattern recognition, classification and clustering problems is presented. Recently, type-2 fuzzy logic has gained popularity in a wide range of applications due to its ability to handle higher degrees of uncertainty. In particular, there have been recent applications of type-2 fuzzy logic in the fields of pattern recognition, classification and clustering, where it has helped improving results over type-1 fuzzy logic. In this paper a concise and representative review of the most successful applications of type-2 fuzzy logic in these fields is presented.     

Experimental study of intelligent controllers under uncertainty using type-1 and type-2 fuzzy logic

Uncertainty is an inherent part in control systems used in real world applications. The use of new methods for handling incomplete information is of fundamental importance. Type-1 fuzzy sets used in conventional fuzzy systems cannot fully handle the uncertainties present in control systems. Type-2 fuzzy sets that are used in type-2 fuzzy systems can handle such uncertainties in a better way because they provide us with more parameters and more design degrees of freedom. This paper deals with the design of control systems using type-2 fuzzy logic for minimizing the effects of uncertainty produced by the instrumentation elements, environmental noise, etc. The experimental results are divided in two classes, in the first class, simulations of a feedback control system for a non-linear plant using type-1 and type-2 fuzzy logic controllers are presented; a comparative analysis of the systems’ response in both cases was performed, with and without the presence of uncertainty. For the second class, a non-linear identification problem for time-series prediction is presented. Based on the experimental results the conclusion is that the best results are obtained using type-2 fuzzy systems.     

Granular type-2 membership functions: A new approach to formation of footprint of uncertainty in type-2 fuzzy sets

In this study, a new approach for the formation of type-2 membership functions is introduced. The footprint of uncertainty is formed by using rectangular type-2 fuzzy granules and the resulting membership function is named as granular type-2 membership function. This new approach provides more degrees of freedom and design flexibility in type-2 fuzzy logic systems. Uncertainties on the grades of membership functions can be represented independently for any region in the universe of discourse and free of any functional form. So, the designer could produce nonlinear, discontinuous or hybrid membership functions in granular formation and therefore could model any desired discontinuity and nonlinearity. The effectiveness of the proposed granular type-2 membership functions is firstly demonstrated by simulations done on noise corrupted Mackey–Glass time series prediction. Secondly, flexible design feature of granular type-2 membership functions is illustrated by modeling a nonlinear system having dead zone with uncertain system parameters. The simulation results show that type-2 fuzzy logic systems formed by granular type-2 membership functions have more modeling capabilities than the systems using conventional type-2 membership functions and they are more robust to system parameter changes and noisy inputs.     

Direct adaptive interval type-2 fuzzy control of multivariable nonlinear systems

A fuzzy logic controller equipped with a training algorithm is developed such that the H^∞ tracking performance should be satisfied for a model-free nonlinear multiple-input multiple-output (MIMO) system, with external disturbances. Due to universal approximation theorem, fuzzy control provides nonlinear controller, i.e., fuzzy logic controllers, to perform the unknown nonlinear control actions and the tracking error, because of the matching error and external disturbance is attenuated to arbitrary desired level by using H^∞ tracking design technique. In this paper, a new direct adaptive interval type-2 fuzzy controller is developed to handle the training data corrupted by noise or rule uncertainties for nonlinear MIMO systems involving external disturbances. Therefore, linguistic fuzzy control rules can be directly incorporated into the controller and combine the H^∞ attenuation technique. Simulation results show that the interval type-2 fuzzy logic system can handle unpredicted internal disturbance, data uncertainties, very well, but the adaptive type-1 fuzzy controller must spend more control effort in order to deal with noisy training data. Furthermore, the adaptive interval type-2 fuzzy controller can perform successful control and guarantee the global stability of the resulting closed-loop system and the tracking performance can be achieved.     

广义二型模糊逻辑系统降型及其采样离散Nie-Tan算法

广义二型模糊逻辑系统在近年来成为学术研究的热点问题,而降型是该系统中的核心模块。最近的研究证明了连续Nie-Tan(CNT)算法是计算区间二型模糊集质心的准确方法。发现了离散Nie-Tan(NT)算法中的求和运算和CNT算法中的求积分运算的内在联系,用2类算法完成基于广义二型模糊集α-平面表达理论的广义二型模糊逻辑系统质心降型。3个计算机仿真实验表明,当适当增加主变量采样点个数时,所提出的基于主变量采样的离散NT算法计算出的广义二型模糊逻辑系统质心降型集和解模糊化值结果可以精确地逼近基准的CNT算法,且采样离散NT算法的计算效率远远高于CNT算法的效率。     

Design of interval type-2 fuzzy sliding-mode controller

In this paper, an interval type-2 fuzzy sliding-mode controller (IT2FSMC) is proposed for linear and nonlinear systems. The proposed IT2FSMC is a combination of the interval type-2 fuzzy logic control (IT2FLC) and the sliding-mode control (SMC) which inherits the benefits of these two methods. The objective of the controller is to allow the system to move to the sliding surface and remain in on it so as to ensure the asymptotic stability of the closed-loop system. The Lyapunov stability method is adopted to verify the stability of the interval type-2 fuzzy sliding-mode controller system. The design procedure of the IT2FSMC is explored in detail. A typical second order linear interval system with 50% parameter variations, an inverted pendulum with variation of pole characteristics, and a Duffing forced oscillation with uncertainty and disturbance are adopted to illustrate the validity of the proposed method. The simulation results show that the IT2FSMC achieves the best tracking performance in comparison with the type-1 Fuzzy logic controller (T1FLC), the IT2FLC, and the type-1 fuzzy sliding-mode controller (T1FSMC).     

基于FPSO的电力巡检机器人的广义二型模糊逻辑控制

针对电力巡检机器人(Power-line inspection robot, PLIR)的平衡调节问题, 设计了广义二型模糊逻辑控制器(General type-2 fuzzy logic controller, GT2FLC); 针对GT2FLC中隶属函数参数难以确定的问题, 通过模糊粒子群(Fuzzy particle swarm optimization, FPSO)算法来优化隶属函数参数. 将GT2FLC的控制性能与区间二型模糊逻辑控制器(Interval type-2 fuzzy logic controller, IT2FLC)和一型模糊逻辑控制器(Type-1 fuzzy logic controller, T1FLC) 的控制性能进行对比. 除此之外, 还考虑了外部干扰对三种控制器控制效果的影响. 仿真结果表明, GT2FLC具有更好的性能和处理不确定性的能力.     

Polynomial regression interval-valued fuzzy systems

In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system (FLS). In order to make the type-2 FLS reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and probability type reduce reasoning method for the interval-valued FLS are developed. We have implemented the proposed non-linear (polynomial regression) statistical interval-valued type-2 FLS to perform smart washing machine control. The results show that our quadratic statistical method is more robust to design a reliable type-2 FLS and also can be extend to polynomial model.