Adaptive Non-singleton Type-2 Fuzzy Logic Systems: A Way Forward for Handling Numerical Uncertainties in Real World Applications

Real world environments are characterized by high levels of linguistic and numerical uncertainties. A Fuzzy Logic System (FLS) is recognized as an adequate methodology to handle the uncertainties and imprecision available in real world environments and applications. Since the invention of fuzzy logic, it has been applied with great success to numerous real world applications such as washing machines, food processors, battery chargers, electrical vehicles, and several other domestic and industrial appliances. The first generation of FLSs were type-1 FLSs in which type-1 fuzzy sets were employed. Later, it was found that using type-2 FLSs can enable the handling of higher levels of uncertainties. Recent works have shown that interval type-2 FLSs can outperform type-1 FLSs in the applications which encompass high uncertainty levels. However, the majority of interval type-2 FLSs handle the linguistic and input numerical uncertainties using singleton interval type-2 FLSs that mix the numerical and linguistic uncertainties to be handled only by the linguistic labels type-2 fuzzy sets. This ignores the fact that if input numerical uncertainties were present, they should affect the incoming inputs to the FLS. Even in the papers that employed non-singleton type-2 FLSs, the input signals were assumed to have a predefined shape (mostly Gaussian or triangular) which might not reflect the real uncertainty distribution which can vary with the associated measurement. In this paper, we will present a new approach which is based on an adaptive non-singleton interval type-2 FLS where the numerical uncertainties will be modeled and handled by non-singleton type-2 fuzzy inputs and the linguistic uncertainties will be handled by interval type-2 fuzzy sets to represent the antecedents’ linguistic labels. The non-singleton type-2 fuzzy inputs are dynamic and they are automatically generated from data and they do not assume a specific shape about the distribution associated with the given sensor. We will present several real world experiments using a real world robot which will show how the proposed type-2 non-singleton type-2 FLS will produce a superior performance to its singleton type-1 and type-2 counterparts when encountering high levels of uncertainties.</jats:p

Implementation Of Various Types Of Fuzzy Controls On A Mobile Robot Using Sonar Sensors [QA9.64. N438 2008 f rb].

Dalam penyelidikan ini, sebuah robot bergerak telah digunakan untuk mengimplementasikan kawalan fuzzy jenis ‘Non-Singleton Type-2’ untuk kawalan pergerakan pengemudian dan tepian dinding dengan bantuan penderia sonar. In this work, non-singleton type-2 fuzzy control has been implemented on a mobile robot for steering and sidewall movement control with the aid of ultrasonic sensors to compare its performances with the singleton type-2 and type-1 fuzzy control

Learning of Type-2 Fuzzy Logic Systems using Simulated Annealing.

This thesis reports the work of using simulated annealing to design more efficient fuzzy logic systems to model problems with associated uncertainties. Simulated annealing is used within this work as a method for learning the best configurations of type-1 and type-2 fuzzy logic systems to maximise their modelling ability. Therefore, it presents the combination of simulated annealing with three models, type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and general type-2 fuzzy logic systems to model four bench-mark problems including real-world problems. These problems are: noise-free Mackey-Glass time series forecasting, noisy Mackey-Glass time series forecasting and two real world problems which are: the estimation of the low voltage electrical line length in rural towns and the estimation of the medium voltage electrical line maintenance cost. The type-1 and type-2 fuzzy logic systems models are compared in their abilities to model uncertainties associated with these problems. Also, issues related to this combination between simulated annealing and fuzzy logic systems including type-2 fuzzy logic systems are discussed. The thesis contributes to knowledge by presenting novel contributions. The first is a novel approach to design interval type-2 fuzzy logic systems using the simulated annealing algorithm. Another novelty is related to the first automatic design of general type-2 fuzzy logic system using the vertical slice representation and a novel method to overcome some parametrisation difficulties when learning general type-2 fuzzy logic systems. The work shows that interval type-2 fuzzy logic systems added more abilities to modelling information and handling uncertainties than type-1 fuzzy logic systems but with a cost of more computations and time. For general type-2 fuzzy logic systems, the clear conclusion that learning the third dimension can add more abilities to modelling is an important advance in type-2 fuzzy logic systems research and should open the doors for more promising research and practical works on using general type-2 fuzzy logic systems to modelling applications despite the more computations associated with it

Improved uncertainty capture for nonsingleton fuzzy systems

In non-singleton fuzzy logic systems (NSFLSs), input uncertainties are modelled with input fuzzy sets in order to capture input uncertainty (e.g., sensor noise). The performance of NSFLSs in handling such uncertainties depends on both: the appropriate modelling in the input fuzzy sets of the uncertainties present in the system’s inputs, and on how the input fuzzy sets (and their inherent model of uncertainty) interact with the antecedent and thus affect the inference within the remainder of the NSFLS. This paper proposes a novel development on the latter. Specifically, an alteration to the standard composition method of type-1 fuzzy relations is proposed, and applied to build a new type of NSFLS. The proposed approach is based on employing the centroid of the intersection of input and antecedent sets as origin of the firing degree, rather than the traditional maximum of their intersection, thus making the NSFLS more sensitive to changes in the input’s uncertainty characteristics. The traditional and novel approach to NSFLSs are experimentally compared for two well-known problems of Mackey-Glass and Lorenz chaotic time series predictions, where the NSFLSs’ inputs have been perturbed with different levels of Gaussian noise. Experiments are repeated for system training under noisy and noise-free conditions. Analyses of the results show that the new method outperforms the traditional approach. Moreover, it is shown that while formally more complex, in practice, the new method has no significant computational overhead compared to the standard approach

Modelo fuzzy genético para a estimação de forças em correntes a partir da medição das frequências naturais

Orientador: Milton Dias JuniorDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: As instalações em alto mar possuem linhas de ancoragem, chamadas de amarras, para proporcionar estabilidade, suporte e sustentação às estruturas. Essas linhas de ancoragem são geralmente compostas por cabos, correntes e cordas de fibra sintética. Quando a solicitação de carga é alta, as linhas de ancoragem devem ser constituídas por corrente. O monitoramento da força atuando nestas correntes é vital para a confiabilidade e segurança da produção de energia. Os métodos atuais para supervisionar as cargas nas amarras são caros e têm muitas incertezas envolvidas. Nesse contexto, propõe-se uma nova metodologia para a estimativa de força em correntes através da medição de suas frequências naturais. Um sistema de inferência difuso e otimizado por um algoritmo genético foi desenvolvido para estimar da carga nas correntes. As entradas dos modelos difusos são as frequências naturais das correntes e a saída é a força estimada. As metodologias Mamdani e Sugeno foram implementadas e comparadas. Funções de pertinência triangular e gaussiana foram usadas para modelar as entradas e a saída. As regras foram definidas de acordo com as relações entre as frequências naturais e a força na corrente. Para otimizar o sistema, o algoritmo genético pode usar como dados de treinamento os resultados fornecidos por um modelo matemático ou por um conjunto de medições. O modelo matemático desenvolvido apresenta boa concordância com os dados experimentais. O modelo genético difuso foi simulado e testado, fornecendo boa precisão na estimativa da força. Finalmente, demonstrou-se que a fuzzificação não singleton pode ser uma ferramenta útil quando as entradas são ruidosasAbstract: Offshore facilities have mooring lines to provide stability, support and holding to the structures. These mooring lines are commonly made up of synthetic fiber ropes, cables and chains. When the load solicitation is high, the mooring lines must be made up of chain. The monitoring of the strength of these chains is vital for the reliability and security of the production of energy. The current methods for supervising the loads on the chains are expensive and have many uncertainties involved. In this context, it is proposed a new methodology for the force estimation in chains through the measurements of their natural frequencies. The present dissertation arises as an improvement of this approach. A fuzzy inference system optimized by a genetic algorithm is introduced to enhance the estimation of the load on the chains. The inputs of the fuzzy models are the natural frequencies of the chains and the output is the estimated force. The Mamdani and Sugeno methodologies were implemented and compared. Triangular and Gaussian membership functions were used to model the inputs and the output. The rules were set according to the relations between the natural frequencies and the force on the chain. To optimize the system, the genetic algorithm can use the results provided by a mathematical model or by a set of measurements as training data. The mathematical model has good agreement with the experimental data. The fuzzy genetic model was simulated and tested providing good accuracy in estimating the force. In addition, the non-singleton fuzzification demonstrated that can be a helpful tool when the entries are noisyMestradoMecanica de Solidos e Projeto MecanicoMestre em Engenharia Mecânica33003017CAPE

Comparing the Performance Potentials of Singleton and Non-singleton Type-1 and Interval Type-2 Fuzzy Systems in Terms of Sculpting the State Space

This paper provides a novel and better understanding of the performance potential of a nonsingleton (NS) fuzzy system over a singleton (S) fuzzy system. It is done by extending sculpting the state space works from S to NS fuzzification and demonstrating uncertainties about measurements, modeled by NS fuzzification: first, fire more rules more often, manifested by a reduction (increase) in the sizes of first-order rule partitions for those partitions associated with the firing of a smaller (larger) number of rules—the coarse sculpting of the state space; second, this may lead to an increase or decrease in the number of type-1 (T1) and interval type-2 (IT2) first-order rule partitions, which now contain rule pairs that can never occur for S fuzzification—a new rule crossover phenomenon —discovered using partition theory; and third, it may lead to a decrease, the same number, or an increase in the number of second-order rule partitions, all of which are system dependent—the fine sculpting of the state space. The authors' conjecture is that it is the additional control of the coarse sculpting of the state space, accomplished by prefiltering and the max–min (or max-product) composition, which provides an NS T1 or IT2 fuzzy system with the potential to outperform an S T1 or IT2 system when measurements are uncertain

Development of FPGA based Standalone Tunable Fuzzy Logic Controllers

Soft computing techniques differ from conventional (hard) computing, in that unlike hard computing, it is tolerant of imprecision, uncertainty, partial truth, and approximation. In effect, the role model for soft computing is the human mind and its ability to address day-to-day problems. The principal constituents of Soft Computing (SC) are Fuzzy Logic (FL), Evolutionary Computation (EC), Machine Learning (ML) and Artificial Neural Networks (ANNs). This thesis presents a generic hardware architecture for type-I and type-II standalone tunable Fuzzy Logic Controllers (FLCs) in Field Programmable Gate Array (FPGA). The designed FLC system can be remotely configured or tuned according to expert operated knowledge and deployed in different applications to replace traditional Proportional Integral Derivative (PID) controllers. This re-configurability is added as a feature to existing FLCs in literature. The FLC parameters which are needed for tuning purpose are mainly input range, output range, number of inputs, number of outputs, the parameters of the membership functions like slope and center points, and an If-Else rule base for the fuzzy inference process. Online tuning enables users to change these FLC parameters in real-time and eliminate repeated hardware programming whenever there is a need to change. Realization of these systems in real-time is difficult as the computational complexity increases exponentially with an increase in the number of inputs. Hence, the challenge lies in reducing the rule base significantly such that the inference time and the throughput time is perceivable for real-time applications. To achieve these objectives, Modified Rule Active 2 Overlap Membership Function (MRA2-OMF), Modified Rule Active 3 Overlap Membership Function (MRA3-OMF), Modified Rule Active 4 Overlap Membership Function (MRA4-OMF), and Genetic Algorithm (GA) base rule optimization methods are proposed and implemented. These methods reduce the effective rules without compromising system accuracy and improve the cycle time in terms of Fuzzy Logic Inferences Per Second (FLIPS). In the proposed system architecture, the FLC is segmented into three independent modules, fuzzifier, inference engine with rule base, and defuzzifier. Fuzzy systems employ fuzzifier to convert the real world crisp input into the fuzzy output. In type 2 fuzzy systems there are two fuzzifications happen simultaneously from upper and lower membership functions (UMF and LMF) with subtractions and divisions. Non-restoring, very high radix, and newton raphson approximation are most widely used division algorithms in hardware implementations. However, these prevalent methods have a cost of more latency. In order to overcome this problem, a successive approximation division algorithm based type 2 fuzzifier is introduced. It has been observed that successive approximation based fuzzifier computation is faster than the other type 2 fuzzifier. A hardware-software co-design is established on Virtex 5 LX110T FPGA board. The MATLAB Graphical User Interface (GUI) acquires the fuzzy (type 1 or type 2) parameters from users and a Universal Asynchronous Receiver/Transmitter (UART) is dedicated to data communication between the hardware and the fuzzy toolbox. This GUI is provided to initiate control, input, rule transfer, and then to observe the crisp output on the computer. A proposed method which can support canonical fuzzy IF-THEN rules, which includes special cases of the fuzzy rule base is included in Digital Fuzzy Logic Controller (DFLC) architecture. For this purpose, a mealy state machine is incorporated into the design. The proposed FLCs are implemented on Xilinx Virtex-5 LX110T. DFLC peripheral integration with Micro-Blaze (MB) processor through Processor Logic Bus (PLB) is established for Intellectual Property (IP) core validation. The performance of the proposed systems are compared to Fuzzy Toolbox of MATLAB. Analysis of these designs is carried out by using Hardware-In-Loop (HIL) test to control various plant models in MATLAB/Simulink environments

Switching control systems and their design automation via genetic algorithms

The objective of this work is to provide a simple and effective nonlinear controller. Our strategy involves switching the underlying strategies in order to maintain a robust control. If a disturbance moves the system outside the region of stability or the domain of attraction, it will be guided back onto the desired course by the application of a different control strategy. In the context of switching control, the common types of controller present in the literature are based either on fuzzy logic or sliding mode. Both of them are easy to implement and provide efficient control for non-linear systems, their actions being based on the observed input/output behaviour of the system. In the field of fuzzy logic control (FLC) using error feedback variables there are two main problems. The first is the poor transient response (jerking) encountered by the conventional 2-dimensional rule-base fuzzy PI controller. Secondly, conventional 3-D rule-base fuzzy PID control design is both computationally intensive and suffers from prolonged design times caused by a large dimensional rule-base. The size of the rule base will increase exponentially with the increase of the number of fuzzy sets used for each input decision variable. Hence, a reduced rule-base is needed for the 3-term fuzzy controller. In this thesis a direct implementation method is developed that allows the size of the rule-base to be reduced exponentially without losing the features of the PID structure. This direct implementation method, when applied to the reduced rule-base fuzzy PI controller, gives a good transient response with no jerking

Embedded Interval Type-2 Neuro-Fuzzy Speed Controller for Marine Diesel Engines

Marine diesel engines operate in highly dynamic and uncertain environments, hence they require robust and accurate speed controllers that can handle the uncertainties encountered in these environments. The current speed controllers for marine diesel engines are based on PID and type-1 Fuzzy Logic Controllers (FLCs) which cannot fully handle the uncertainties encountered in such environments. Type-2 FLCs can handle such uncertainties to produce a better control performance. However, manually designing a type-2 FLC is a difficult task. In this paper, we will introduce an embedded type-2 Neuro-Fuzzy Controller (T2NFC) which learns the parameters of interval type-2 FLC to control marine diesel engines. We have performed numerous experiments on a real diesel engine testing platform in which the T2NFC operated on an industrial embedded controller and handled the uncertainties to produce an accurate and robust speed controller that outperformed the currently used commercial engine controller, even though we have trained the T2NFC with data collected from the commercial controlle