An investigation into alternative methods for the defuzzification of an interval type-2 fuzzy set.

The number of applications of interval type-2 fuzzy logic to real world problems is growing. To date such systems have used type-reduction or an approximation of typereduction to arrive at final crisp output from the system. This paper describes the novel direct defuzzifier for interval type-2 fuzzy sets. A number of fuzzy systems are compared with direct defuzzifier. We compare each defuzzifiers output surface in a simple rule-based system. The direct defuzzifier compares favourably with the type-reduction method under the minimum t-norm. Also, we found that the non-stationary approach provided interesting results

Enhancement of Set-Based Design Practices Via Introduction of Uncertainty Through Use of Interval Type-2 Modeling and General Type-2 Fuzzy Logic Agent Based Methods.

The goal of this research was to discern the effects of introducing uncertainty representation into a set-based design process with applications in ship design. The hypothesis was that introduction of design uncertainty would enhance the facilitation of set-based design practices. A presentation of three fuzzy logic agent based methods for facilitation of set-based ship design practices is offered. The first method utilized a type-1 fuzzy logic system to facilitate set-based design practices and possessed no uncertainty modeling. The next two methods included representation of design uncertainty in the set-based design space. Of these two methods, one utilized a novel approach that harnessed techniques of randomization to model an interval type-2 fuzzy logic system, the other method made use of general type-2 fuzzy logic methods that were well-known, but still relatively under-utilized in academics and industry when compared to type-1 fuzzy logic systems. Comparisons of the newly developed fuzzy logic systems with each other, and the type-1 agent based fuzzy logic system provided the basis for conclusions as to the effects of introducing uncertainty modeling into a set-based design process. The results of this experimental research have shown that the inclusion of uncertainty modeling in the set-based design process for the negotiation of design variables enhances the overall set-based design progression, especially when working with highly constrained designs. In the case of a highly constrained design, the type-1 fuzzy logic system was unable to promote set-convergence within the allotted experimental time without repeated design failures, while the use of uncertainty modeling allowed the interval type-2 modeling and general type-2 fuzzy logic systems to achieve feasible set-based design convergence. When performing a simplistic, loosely constrained design, all three fuzzy logic systems were capable of facilitating the principle practices of set-based design within the feasible solution space; specifically, the set-based practices of delaying design decisions and gradual reduction of the feasible solution space. This research has led to the enhancement of the set-based design process by providing capabilities to now represent uncertainty in the set-based design space though the use of either the newly developed interval type-2 or general type-2 fuzzy logic systems.Ph.D.Naval Architecture & Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86265/1/grayale_1.pd

Development of Self-Learning Type-2 Fuzzy Systems for System Identification and Control of Autonomous Systems

Modelling and control of dynamic systems are faced by multiple technical challenges, mainly due to the nature of uncertain complex, nonlinear, and time-varying systems. Traditional modelling techniques require a complete understanding of system dynamics and obtaining comprehensive mathematical models is not always achievable due to limited knowledge of the systems as well as the presence of multiple uncertainties in the environment. As universal approximators, fuzzy logic systems (FLSs), neural networks (NNs) and neuro-fuzzy systems have proved to be successful computational tools for representing the behaviour of complex dynamical systems. Moreover, FLSs, NNs and learning-based techniques have been gaining popularity for controlling complex, ill-defined, nonlinear, and time-varying systems in the face of uncertainties. However, fuzzy rules derived by experts can be too ad-hoc, and the performance is less than optimum. In other words, generating fuzzy rules and membership functions in fuzzy systems is a potential challenge especially for systems with many variables. Moreover, under the umbrella of FLSs, although type-1 fuzzy logic control systems (T1-FLCs) have been applied to control various complex nonlinear systems, they have limited capability to handle uncertainties. Aiming to accommodate uncertainties, type-2 fuzzy logic control systems (T2-FLCs) were established. This thesis aims to address the shortcomings of existing fuzzy techniques by utilisation of type-2 FLCs with novel adaptive capabilities. The first contribution of this thesis is a novel online system identification technique by means of a recursive interval type-2 Takagi-Sugeno fuzzy C-means clustering technique (IT2-TS-FC) to accommodate the footprint-of-uncertainties (FoUs). This development is meant to specifically address the shortcomings of type-1 fuzzy systems in capturing the footprint-of-uncertainties such as mechanical wear, rotor damage, battery drain and sensor and actuator faults. Unlike previous type-2 TS fuzzy models, the proposed method constructs two fuzzifiers (upper and lower) and two regression coefficients in the consequent part to handle uncertainties. The weighted least square method is employed to compute the regression coefficients. The proposed method is validated using two benchmarks, namely, real flight test data of a quadcopter drone and Mackey-Glass time series data. The algorithm has the capability to model uncertainties (e.g., noisy dataset). The second contribution of this thesis is the development of a novel self-adaptive interval type-2 fuzzy controller named the SAF2C for controlling multi-input multi-output (MIMO) nonlinear systems. The adaptation law is derived using sliding mode control (SMC) theory to reduce the computation time so that the learning process can be expedited by 80% compared to separate single-input single-output (SISO) controllers. The system employs the `Enhanced Iterative Algorithm with Stop Condition' (EIASC) type-reduction method, which is more computationally efficient than the `Karnik-Mendel' type-reduction algorithm. The stability of the SAF2C is proven using the Lyapunov technique. To ensure the applicability of the proposed control scheme, SAF2C is implemented to control several dynamical systems, including a simulated MIMO hexacopter unmanned aerial vehicle (UAV) in the face of external disturbance and parameter variations. The ability of SAF2C to filter the measurement noise is demonstrated, where significant improvement is obtained using the proposed controller in the face of measurement noise. Also, the proposed closed-loop control system is applied to control other benchmark dynamic systems (e.g., a simulated autonomous underwater vehicle and inverted pendulum on a cart system) demonstrating high accuracy and robustness to variations in system parameters and external disturbance. Another contribution of this thesis is a novel stand-alone enhanced self-adaptive interval type-2 fuzzy controller named the ESAF2C algorithm, whose type-2 fuzzy parameters are tuned online using the SMC theory. This way, we expect to design a computationally efficient adaptive Type-2 fuzzy system, suitable for real-time applications by introducing the EIASC type-reducer. The proposed technique is applied on a quadcopter UAV (QUAV), where extensive simulations and real-time flight tests for a hovering QUAV under wind disturbances are also conducted to validate the efficacy of the ESAF2C. Specifically, the control performance is investigated in the face of external wind gust disturbances, generated using an industrial fan. Stability analysis of the ESAF2C control system is investigated using the Lyapunov theory. Yet another contribution of this thesis is the development of a type-2 evolving fuzzy control system (T2-EFCS) to facilitate self-learning (either from scratch or from a certain predefined rule). T2-EFCS has two phases, namely, the structure learning and the parameters learning. The structure of T2-EFCS does not require previous information about the fuzzy structure, and it can start the construction of its rules from scratch with only one rule. The rules are then added and pruned in an online fashion to achieve the desired set-point. The proposed technique is applied to control an unmanned ground vehicle (UGV) in the presence of multiple external disturbances demonstrating the robustness of the proposed control systems. The proposed approach turns out to be computationally efficient as the system employs fewer fuzzy parameters while maintaining superior control performance

A Multilayer Interval Type-2 Fuzzy Extreme Learning Machine for the Recognition of Walking Activities and Gait Events using Wearable Sensors

In this paper, a novel Multilayer Interval Type-2 Fuzzy Extreme Learning Machine (ML-IT2-FELM) for the recognition of walking activities and Gait events is presented. The ML-IT2-FELM uses a hierarchical learning scheme that consists of multiple layers of IT2 Fuzzy Autoencoders (FAEs), followed by a final classification layer based on an IT2-FELM architecture. The core building block in the ML-IT2-FELM is an IT2-FELM, which is a generalised model of the Interval Type-2 Radial Basis Function Neural Network (IT2-RBFNN) and that is functionally equivalent to a class of simplified IT2 Fuzzy Logic Systems (FLSs). Each FAE in the ML-IT2-FELM employs an output layer with a direct-defuzzification process based on the Nie-Tan algorithm, while the IT2-FELM classifier includes a Karnik-Mendel type-reduction method (KM). Real data was collected using three inertial measurements units attached to the thigh, shank and foot of twelve healthy participants. The validation of the ML-IT2-FELM method is performed with two different experiments. The first experiment involves the recognition of three different walking activities: Level-Ground Walking (LGW), Ramp Ascent (RA) and Ramp Descent (RD). The second experiment consists of the recognition of stance and swing phases during the gait cycle. In addition, to compare the efficiency of the ML-IT2-FELM with other ML fuzzy methodologies, a kernel-based ML-IT2-FELM that is inspired by kernel learning and called KML-IT2-FELM is also implemented. The results from the recognition of walking activities and gait events achieved an average accuracy of 99.98% and 99.84% with a decision time of 290.4ms and 105ms, respectively, by the ML-IT2-FELM, while the KML-IT2-FELM achieved an average accuracy of 99.98% and 99.93% with a decision time of 191.9ms and 94ms. The experiments demonstrate that the ML-IT2-FELM is not only an effective Fuzzy Logic-based approach in the presence of sensor noise, but also a fast extreme learning machine for the recognition of different walking activities

Adaptive non-singular fast terminal sliding mode control and synchronization of a chaotic system via interval type-2 fuzzy inference system with proportionate controller

This paper introduces a novel adaptive nonsingular fast terminal sliding mode approach that benefits from an interval type-2 fuzzy logic estimator and a gain for control and synchronization of chaotic systems in the presence of uncertainty. The nonsingular fast terminal sliding mode controller is developed to increase the convergence rate and remove the singularity problem of the system. Using the proposed method, the finite-time convergence has been ensured. To eliminate the chattering phenomenon in the conventional sliding mode controller, the discontinuous sign function is estimated using an interval type-2 fuzzy inference system (FIS) based on the center of sets type reduction followed by defuzzification. By adding the proportionate gain to the interval type-2 FIS, the robustness and speed of the controller system is enhanced. An appropriate Lyapunov function is utilized to ensure the closed-loop stability of the control system. The performance of the controller is evaluated for a nonlinear time-varying second-order magnetic space-craft chaotic system with different initial conditions in the presence of uncertainty. The simulation results show the efficacy of the proposed approach for the tracking control problems. The time and frequency domain analysis of the control signal demonstrates that the chattering phenomenon is successfully diminished

A Multilayer Interval Type-2 Fuzzy Extreme Learning Machine for the recognition of walking activities and gait events using wearable sensors

In this paper, a novel Multilayer Interval Type-2 Fuzzy Extreme Learning Machine (ML-IT2-FELM) for the recognition of walking activities and Gait events is presented. The ML-IT2-FELM uses a hierarchical learning scheme that consists of multiple layers of IT2 Fuzzy Autoencoders (FAEs), followed by a final classification layer based on an IT2-FELM architecture. The core building block in the ML-IT2-FELM is the IT2-FELM, which is a generalised model of the Interval Type-2 Radial Basis Function Neural Network (IT2-RBFNN) and that is functionally equivalent to a class of simplified IT2 Fuzzy Logic Systems (FLSs). Each FAE in the ML-IT2-FELM employs an output layer with a direct-defuzzification process based on the Nie-Tan algorithm, while the IT2-FELM classifier includes a Karnik-Mendel type-reduction method (KM). Real data was collected using three inertial measurements units attached to the thigh, shank and foot of twelve healthy participants. The validation of the ML-IT2-FELM method is performed with two different experiments. The first experiment involves the recognition of three different walking activities: Level-Ground Walking (LGW), Ramp Ascent (RA) and Ramp Descent (RD). The second experiment consists of the recognition of stance and swing phases during the gait cycle. In addition, to compare the efficiency of the ML-IT2-FELM with other ML fuzzy methodologies, a kernel-based ML-IT2-FELM that is inspired by kernel learning and called KML-IT2-FELM is also implemented. The results from the recognition of walking activities and gait events achieved an average accuracy of 99.98% and 99.84% with a decision time of 290.4ms and 105ms, respectively, by the ML-IT2-FELM, while the KML-IT2-FELM achieved an average accuracy of 99.98% and 99.93% with a decision time of 191.9ms and 94ms. The experiments demonstrate that the ML-IT2-FELM is not only an effective Fuzzy Logic-based approach in the presence of sensor noise, but also a fast extreme learning machine for the recognition of different walking activities

A novel technique for load frequency control of multi-area power systems

In this paper, an adaptive type-2 fuzzy controller is proposed to control the load frequency of a two-area power system based on descending gradient training and error back-propagation. The dynamics of the system are completely uncertain. The multilayer perceptron (MLP) artificial neural network structure is used to extract Jacobian and estimate the system model, and then, the estimated model is applied to the controller, online. A proportional–derivative (PD) controller is added to the type-2 fuzzy controller, which increases the stability and robustness of the system against disturbances. The adaptation, being real-time and independency of the system parameters are new features of the proposed controller. Carrying out simulations on New England 39-bus power system, the performance of the proposed controller is compared with the conventional PI, PID and internal model control based on PID (IMC-PID) controllers. Simulation results indicate that our proposed controller method outperforms the conventional controllers in terms of transient response and stability