Intelligent Diagnosis and Smart Detection of Crack in a Structure from its Vibration Signatures

In recent years, there has been a growing interest in the development of structural health monitoring for vibrating structures, especially crack detection methodologies and on-line diagnostic techniques. In the current research, methodologies have been developed for damage detection of a cracked cantilever beam using analytical, fuzzy logic, neural network and fuzzy neuro techniques. The presence of a crack in a structural member introduces a local flexibility that affects its dynamic response. For finding out the deviation in the vibrating signatures of the cracked cantilever beam the local stiffness matrices are taken into account. Theoretical analyses have been carried out to calculate the natural frequencies and mode shapes of the cracked cantilever beam using local stiffness matrices. Strain energy release rate has been used for calculating the local stiffness of the beam. The fuzzy inference system has been designed using the first three relative natural frequencies and mode shapes as input parameters. The output from the fuzzy controller is relative crack location and relative crack depth. Several fuzzy rules have been developed using the vibration signatures of the cantilever beam. A Neural Network technique using multi layered back propagation algorithm has been developed for damage assessment using the first three relative natural frequencies and mode shapes as input parameters and relative crack location and relative crack depth as output parameters. Several training patterns are derived for designing the Neural Network. A hybrid fuzzy-neuro intelligent system has been formulated for fault identification. The fuzzy controller is designed with six input parameters and two output parameters. The input parameters to the fuzzy system are relative deviation of first three natural frequencies and first three mode shapes. The output parameters of the fuzzy system are initial relative crack depth and initial relative crack location. The input parameters to the neural controller are relative deviation of first three natural frequencies and first three mode shapes along with the interim outputs of fuzzy controller. The output parameters of the fuzzy-neuro system are final relative crack depth and final relative crack location. A series of fuzzy rules and training patterns are derived for the fuzzy and neural system respectively to predict the final crack location and final crack depth.To diagnose the crack in the vibrating structure multiple adaptive neuro-fuzzy inference system (MANFIS) methodology has been applied. The final outputs of the MANFIS are relative crack depth and relative crack location. Several hundred fuzzy rules and neural network training patterns are derived using natural frequencies, mode shapes, crack depths and crack locations. The proposed research work aims to broaden the development in the area of fault detection of dynamically vibrating structures. This research also addresses the accuracy for detection of crack location and depth with considerably low computational time. The objective of the research is related to design of an intelligent controller for prediction of damage location and severity in a uniform cracked cantilever beam using AI techniques (i.e. Fuzzy, neural, adaptive neuro-fuzzy and Manfis)

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

Fuzzy practical exponential tracking of an electrohydraulic servosystem

Cilj ovog rada je da doprinese teorijskoj i praktičnoj primeni fazi logičkog upravljanja korišćenjem koncepta praktičnog praćenja. Predlaže se novi fazi upravljački algoritam za ostvarivanje željenog kvaliteta praćenja jednog elektrohidrauličkog pozicionog servosistema, koji se može naći u mnogim industrijskim uređajima. Fazi logički kontroler je jedan od najjednostavnijih. On koristi samo jednu ulaznu veličinu, sa linearnom metodom zaključivanja. Fazi prateći algoritam upravljanja je zasnovan na principu samoprilagodljivosti. Strukturna karakteristika takvog sistema upravljanja je postojanje dve povratne sprege: globalne, negativne po izlaznoj veličini i lokalne, pozitivne po upravljačkoj veličini. Takva struktura obezbeđuje sintezu upravljanja bez poznavanja unutrašnje dinamike objekta i bez merenja poremećajnih veličina. Predloženi fazi prateći algoritam upravljanja obezbeđuje promenu greške izlazne veličine po unapred definisanom eksponencijalnom zakonu. Prezentuju se rezultati simulacije nelinearnog matematičkog modela hidrauličkog servosistema.The aim of this paper is to contribute to the theoretical and practical applications of fuzzy logic control using practical tracking concept. A new fuzzy control algorithm is proposed to achieve the desired tracking performance of a nonlinear electrohydraulic position servo system, which can be found in many manufacturing devices. The fuzzy logic controller is one of the simplest. It employs only one input, with linear fuzzy inference method. The practical tracking control algorithm is based on the selfadjustment principle. The structural characteristic of such a control system is the existence of two feedback sources: the global negative of the output value and the local positive of the control value. Such a structure ensures the synthesis of the control without the internal dynamics knowledge and without measurements of disturbance values. The proposed fuzzy practical control algorithm ensures the change of the output error value according to a prespecified exponential law. The simulation results of the nonlinear mathematical model of the hydraulic servo system are presented

Fuzzy practical exponential tracking of an electrohydraulic servosystem

Cilj ovog rada je da doprinese teorijskoj i praktičnoj primeni fazi logičkog upravljanja korišćenjem koncepta praktičnog praćenja. Predlaže se novi fazi upravljački algoritam za ostvarivanje željenog kvaliteta praćenja jednog elektrohidrauličkog pozicionog servosistema, koji se može naći u mnogim industrijskim uređajima. Fazi logički kontroler je jedan od najjednostavnijih. On koristi samo jednu ulaznu veličinu, sa linearnom metodom zaključivanja. Fazi prateći algoritam upravljanja je zasnovan na principu samoprilagodljivosti. Strukturna karakteristika takvog sistema upravljanja je postojanje dve povratne sprege: globalne, negativne po izlaznoj veličini i lokalne, pozitivne po upravljačkoj veličini. Takva struktura obezbeđuje sintezu upravljanja bez poznavanja unutrašnje dinamike objekta i bez merenja poremećajnih veličina. Predloženi fazi prateći algoritam upravljanja obezbeđuje promenu greške izlazne veličine po unapred definisanom eksponencijalnom zakonu. Prezentuju se rezultati simulacije nelinearnog matematičkog modela hidrauličkog servosistema.The aim of this paper is to contribute to the theoretical and practical applications of fuzzy logic control using practical tracking concept. A new fuzzy control algorithm is proposed to achieve the desired tracking performance of a nonlinear electrohydraulic position servo system, which can be found in many manufacturing devices. The fuzzy logic controller is one of the simplest. It employs only one input, with linear fuzzy inference method. The practical tracking control algorithm is based on the selfadjustment principle. The structural characteristic of such a control system is the existence of two feedback sources: the global negative of the output value and the local positive of the control value. Such a structure ensures the synthesis of the control without the internal dynamics knowledge and without measurements of disturbance values. The proposed fuzzy practical control algorithm ensures the change of the output error value according to a prespecified exponential law. The simulation results of the nonlinear mathematical model of the hydraulic servo system are presented

North American Fuzzy Logic Processing Society (NAFIPS 1992), volume 2

This document contains papers presented at the NAFIPS '92 North American Fuzzy Information Processing Society Conference. More than 75 papers were presented at this Conference, which was sponsored by NAFIPS in cooperation with NASA, the Instituto Tecnologico de Morelia, the Indian Society for Fuzzy Mathematics and Information Processing (ISFUMIP), the Instituto Tecnologico de Estudios Superiores de Monterrey (ITESM), the International Fuzzy Systems Association (IFSA), the Japan Society for Fuzzy Theory and Systems, and the Microelectronics and Computer Technology Corporation (MCC). The fuzzy set theory has led to a large number of diverse applications. Recently, interesting applications have been developed which involve the integration of fuzzy systems with adaptive processes such a neural networks and genetic algorithms. NAFIPS '92 was directed toward the advancement, commercialization, and engineering development of these technologies

Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity

Modelling and design of the eco-system of causality for real-time systems

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London.The purpose of this research work is to propose an improved method for real-time sensitivity analysis (SA) applicable to large-scale complex systems. Borrowed from the EventTracker principle of the interrelation of causal events, it deploys the Rank Order Clustering (ROC) method to automatically group every relevant system input to parameters that represent the system state (i.e. output). The fundamental principle of event modelling is that the state of a given system is a function of every acquirable piece of knowledge or data (input) of events that occur within the system and its wider operational environment unless proven otherwise. It therefore strives to build the theoretical and practical foundation for the engineering of input data. The event modelling platform proposed attempts to filter unwanted data, and more importantly, include information that was thought to be irrelevant at the outset of the design process. The underpinning logic of the proposed Event Clustering technique (EventiC) is to build causal relationship between the events that trigger the inputs and outputs of the system. EventiC groups inputs with relevant corresponding outputs and measures the impact of each input variable on the output variables in short spans of time (relative real-time). It is believed that this grouping of relevant input-output event data by order of its importance in real-time is the key contribution to knowledge in this subject area. Our motivation is that components of current complex and organised systems are capable of generating and sharing information within their network of interrelated devices and systems. In addition to being an intelligent recorder of events, EventiC could also be a platform for preliminary data and knowledge construction. This improvement in the quality, and at times the quantity of input data, may lead to improved higher level mathematical formalism. It is hoped that better models will translate into superior controls and decision making. It is therefore believed that the projected outcome of this research work can be used to predict, stabilize (control), and optimize (operational research) the work of complex systems in the shortest possible time. For proof of concept, EventiC was designed using the MATLAB package and implemented using real-time data from the monitoring and control system of a typical cement manufacturing plant. The purpose for this deployment was to test and validate the concept, and to demonstrate whether the clusters of input data and their levels of importance against system performance indicators could be approved by industry experts. EventiC was used as an input variable selection tool for improving the existing fuzzy controller of the plant. Finally, EventiC was compared with its predecessor EventTracker using the same case study. The results revealed improvements in both computational efficiency and the quality of input variable selection

Analysis and Applications of the Km Algorithm in Type-2 Fuzzy Logic Control and Decision Making

Ph.DDOCTOR OF PHILOSOPH

Design of stable adaptive fuzzy control.

by John Tak Kuen Koo.Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.Includes bibliographical references (leaves 217-[220]).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Introduction --- p.1Chapter 1.2 --- "Robust, Adaptive and Fuzzy Control" --- p.2Chapter 1.3 --- Adaptive Fuzzy Control --- p.4Chapter 1.4 --- Object of Study --- p.10Chapter 1.5 --- Scope of the Thesis --- p.13Chapter 2 --- Background on Adaptive Control and Fuzzy Logic Control --- p.17Chapter 2.1 --- Adaptive control --- p.17Chapter 2.1.1 --- Model reference adaptive systems --- p.20Chapter 2.1.2 --- MIT Rule --- p.23Chapter 2.1.3 --- Model Reference Adaptive Control (MRAC) --- p.24Chapter 2.2 --- Fuzzy Logic Control --- p.33Chapter 2.2.1 --- Fuzzy sets and logic --- p.33Chapter 2.2.2 --- Fuzzy Relation --- p.40Chapter 2.2.3 --- Inference Mechanisms --- p.43Chapter 2.2.4 --- Defuzzification --- p.49Chapter 3 --- Explicit Form of a Class of Fuzzy Logic Controllers --- p.51Chapter 3.1 --- Introduction --- p.51Chapter 3.2 --- Construction of a class of fuzzy controller --- p.53Chapter 3.3 --- Explicit form of the fuzzy controller --- p.57Chapter 3.4 --- Design criteria on the fuzzy controller --- p.65Chapter 3.5 --- B-Spline fuzzy controller --- p.68Chapter 4 --- Model Reference Adaptive Fuzzy Control (MRAFC) --- p.73Chapter 4.1 --- Introduction --- p.73Chapter 4.2 --- "Fuzzy Controller, Plant and Reference Model" --- p.75Chapter 4.3 --- Derivation of the MRAFC adaptive laws --- p.79Chapter 4.4 --- "Extension to the Multi-Input, Multi-Output Case" --- p.84Chapter 4.5 --- Simulation --- p.90Chapter 5 --- MRAFC on a Class of Nonlinear Systems: Type I --- p.97Chapter 5.1 --- Introduction --- p.98Chapter 5.2 --- Choice of Controller --- p.99Chapter 5.3 --- Derivation of the MRAFC adaptive laws --- p.102Chapter 5.4 --- Example: Stabilization of a pendulum --- p.109Chapter 6 --- MRAFC on a Class of Nonlinear Systems: Type II --- p.112Chapter 6.1 --- Introduction --- p.113Chapter 6.2 --- Fuzzy System as Function Approximator --- p.114Chapter 6.3 --- Construction of MRAFC for the nonlinear systems --- p.118Chapter 6.4 --- Input-Output Linearization --- p.130Chapter 6.5 --- MRAFC with Input-Output Linearization --- p.132Chapter 6.6 --- Example --- p.136Chapter 7 --- Analysis of MRAFC System --- p.140Chapter 7.1 --- Averaging technique --- p.140Chapter 7.2 --- Parameter convergence --- p.143Chapter 7.3 --- Robustness --- p.152Chapter 7.4 --- Simulation --- p.157Chapter 8 --- Application of MRAFC scheme on Manipulator Control --- p.166Chapter 8.1 --- Introduction --- p.166Chapter 8.2 --- Robot Manipulator Control --- p.170Chapter 8.3 --- MRAFC on Robot Manipulator Control --- p.173Chapter 8.3.1 --- Part A: Nonlinear-function feedback fuzzy controller --- p.174Chapter 8.3.2 --- Part B: State-feedback fuzzy controller --- p.182Chapter 8.4 --- Simulation --- p.186Chapter 9 --- Conclusion --- p.199Chapter A --- Implementation of MRAFC Scheme with Practical Issues --- p.203Chapter A.1 --- Rule Generation by MRAFC scheme --- p.203Chapter A.2 --- Implementation Considerations --- p.211Chapter A.3 --- MRAFC System Design Procedure --- p.215Bibliography --- p.21

Geometric Fuzzy Logic Systems

There has recently been a significant increase in academic interest in the field oftype-2 fuzzy sets and systems. Type-2 fuzzy systems offer the ability to model and reason with uncertain concepts. When faced with uncertainties type-2 fuzzy systems should, theoretically, give an increase in performance over type-l fuzzy systems. However, the computational complexity of generalised type-2 fuzzy systems is significantly higher than type-l systems. A direct consequence of this is that, prior to this thesis, generalised type-2 fuzzy logic has not yet been applied in a time critical domain, such as control. Control applications are the main application area of type-l fuzzy systems with the literature reporting many successes in this area. Clearly the computational complexity oftype-2 fuzzy logic is holding the field back. This restriction on the development oftype-2 fuzzy systems is tackled in this research. This thesis presents the novel approach ofdefining fuzzy sets as geometric objects - geometric fuzzy sets. The logical operations for geometric fuzzy sets are defined as geometric manipulations of these sets. This novel geometric approach is applied to type-I, type-2 interval and generalised type-2 fuzzy sets and systems. The major contribution of this research is the reduction in the computational complexity oftype-2 fuzzy logic that results from the application of the geometric approach. This reduction in computational complexity is so substantial that generalised type-2 fuzzy logic has, for the first time, been successfully applied to a control problem - mobile robot navigation. A detailed comparison between the performance of the generalised type-2 fuzzy controller and the performance of the type-l and type-2 interval controllers is given. The results indicate that the generalised type-2 fuzzy logic controller outperforms the other robot controllers. This outcome suggests that generalised type-2 fuzzy systems can offer an improved performance over type-l and type-2 interval systems