Structural Health Monitoring (SHM) refers to the process of nondestructive autonomous in situ monitoring of the integrity of critical engineering structures such as airplanes, bridges and buildings. Ultrasonic wave propagation is an ideal interrogation method for SHM because ultrasound is the elastic vibration of the material itself and is thus directly affected by any structural damage occurring in the paths of the propagating waves. The objective of this thesis is to provide a comprehensive damage detection strategy for SHM using diffuse ultrasonic waves. This strategy includes a systematic temperature compensation method, differential feature extraction methods optimized for discriminating benign surface condition changes from damage, and data fusion methods to determine the structural status. The temperature compensation method is based upon a set of pre-recorded baselines. Using the methods of baseline selection and baseline correction, a baseline that best matches a monitored signal in temperature is provided. For the differential feature extraction, three types of features are proposed. The first type includes basic differential features such as mean squared error. The second type is derived from a matching pursuit based signal decomposition. An ultrasonic signal is decomposed into a sum of characteristic wavelets, and differential features are extracted based upon changes in the decomposition between a baseline signal and a monitored signal. The third type is a phase space feature extraction method, where an ultrasonic signal is embedded into phase space and features are extracted based on changes of the phase portrait. The structural status is determined based on a data fusion strategy consisting of a threshold selection method, fusion at the feature level, and fusion at the sensor level. The proposed damage detection strategy is applied to experiments on aluminum specimens with artificial defects subjected to a variety of environmental variations. Results as measured by the probability of detection, the false alarm rate, and the size of damage detected demonstrate the viability of the proposed techniques.

Chaotic dynamics are at the center of multiple studies to perfect encrypted communication systems. Indeed, the particular time evolution nature of chaotic signals constitutes the fundamentals of their application to secure telecommunications. The pseudo random signal constitutes the carrier wave for the communication. The information coded on the carrier wave can be extracted with knowledge of the system dynamic evolution law. This evolution law consists of a second-order delay differential equation in which intervene the various parameters of the physical system setup. The set of precise parameter values forms the key, in a cryptographic sense, of the encrypted transmission. This thesis work presents the implementation of an experimental encryption system using chaos. The optical intensity of the emitter fluctuates chaotically and serves as carrier wave. A message of small amplitude, hidden inside the fluctuations of the carrier wave, is extracted from the transmitted signal by a properly tuned receiver. The influence of the message modulation format on the communication quality both in the back to back case and after propagation is investigated numerically.

We study some topological properties of dynamical systems. In particular the rela- tionship between spatio-temporal chaotic and Li-Yorke sensitive dynamical systems establishing that for minimal dynamical systems those properties are equivalent. In the same direction we show that being a Li-Yorke sensitive dynamical system implies that the system is also Li-Yorke chaotic. On the other hand we survey the possibility of lifting some topological properties from a given dynamical system (Y, S) to an- other (X, T). After studying some basic facts about topological dynamical systems, we move to the particular case of interval maps. We know that through the knowl- edge of interval maps, f : I → I, precious information about the chaotic behavior of general nonlinear dynamical systems can be obtained. It is also well known that the analysis of the spectrum of time series encloses important material related to the signal itself. In this work we look for possible connections between chaotic dynamical systems and the behavior of its Fourier coefficients. We have found that a natural bridge between these two concepts is given by the total variation of a function and its connection with the topological entropy associated to the n-th iteration, fn(x), of the map. Working in a natural way using the Sobolev spaces Wp,q(I) we show how the Fourier coefficients are related to the chaoticity of interval maps.

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M. Tech. Electrical Engineering. / This dissertation presents encryption and decryption of digital message signal and image data based on Qi hyper chaos system. The field of telecommunication has grown rapidly especially with the introduction of mobile phone and internet networks. Associated with this growth, there is a vital need to have a secure communication of information.

M. Tech. Electrical engineering. / Discusses a desirable chaos-based encryption scheme for image storage and transmission is one that can resist different types of attacks in less time and with successful decryption. To resist different kinds of attacks, a higher security level is required. As a result, there is a need to enhance the security level of existing chaos-based image encryption schemes using hyper-chaos. To increase the level of security using hyper-chaos, the research will present a scheme that combines two different techniques that are used to improve the degree of security of chaos-based cryptography; a classical chaos-based cryptographic technique and a hyper-chaos masking technique. The first technique focuses on the efficient combination and transformation of image characteristics based on hyper-chaos pseudorandom numbers. The second technique focuses on driving the hyper-chaos system by using the results of the first technique to change the transmitted chaos dynamic as well as using synchronisation and a high-order differentiator for decryption. To achieve the objective of our research the following sub-problems are addressed.

published_or_final_version / abstract / Electrical and Electronic Engineering / Master / Master of Philosophy

Judėjimas yra pagrindinis žmogaus veiklos komponentas. Buvo atlikta daug mėginimų atskleisti jo principus pasitelkiant fiziką bei dinamiką. Kartu kompiuterinė grafika ir robotų technika plėtoja šias pastangas, tačiau daug problemų lieka neišspręstų, netgi ir aprašant paprasčiausią atvejį: linijinį, tiesiaeigį, ritmišką ėjimą. Taigi netiesinių sistemų tyrimo tikslas yra surasti tvarką chaose; surasti įrodymų, kad nereguliari elgsena yra valdoma nedidelės deterministinių lygčių sistemos, pritaikant ją eksperimentiniams signalams laike. Tokio tyrimo sėkmės galima tikėtis, nustačius, kad šios sistemos būsenos kintamieji yra tvirtai suporuoti tarpusavyje. Chaotiškų sistemų tyrimų tikslas yra nustatyti dvi pagrindines jų savybes: dimensiją ir entropijos spektrą. Paprastai kalbant, dimensija yra dydis, parodantis diferencialinių lygčių skaičių, reikalingą aprašyti sistemai, o entropija yra dydis, parodantis informacijos apie sistemos būseną praradimą laiko bėgyje. Teigiama baigtinė entropija yra chaoso egzistavimo įrodymas. Šio darbo tikslas yra sukurti chaotiško signalo analizės sistemą, kuri leistų ištirti elementarius monotoniškus žmogaus rankos judesius dvimatėje plokštumoje. / Since we encounter many phenomena with irregular motion, e.g. the weather, turbulence, carbon resistor noise, chemical reactions and biological signals (human motion), we are tempted to investigate whether we could model the dynamics with nonlinear differential equations. Our aim is to find order within the chaos; to find evidence that the irregular behavior is governed by a small set of deterministic equations, using experimental time series. We might be successful in particular when the state variables of the system are strongly coupled. In this report, we will restrict ourselves to the determination of several properties that describe a chaotic system, including the dimension and entropy spectra. Loosely speaking, the dimension is a measure for the number of differential equations needed to describe the system, while the entropy is a measure for the loss of information about the state of the system in the course of time. Positive but finite entropy is a hall-mark of chaos. In this paper, we will describe few experiments that were performed on a portion of human motion data, and compare the results to theoretical model of system for signal analysis.

This thesis describes the comparison of time-lapse field observations of suncups on alpine snow with numerical simulations. The simulations consist of solutions to a nonlinear partial differential equation which exhibits spontaneous pattern formation from a low amplitude, random initial surface. Both the field observations and the numerical solutions are found to saturate at a characteristic height and fluctuate chaotically with time. The timescale of these fluctuations is found to be instrumental in determining the full set of parameters for the numerical model such that it mimics the nonlinear dynamics of suncups. These parameters in turn are related to the change in albedo of the snow surface caused by the presence of suncups. This suggests the more general importance of dynamical behaviour in gaining an understanding of pattern formation phenomena.

Chaos theory is well known as one of three revolutions in physical sciences in 20th-century, as one physicist called it: Relativity eliminated the Newtonian illusion of absolute space and time; quantum theory eliminated the Newtonian dream of a controllable measurable process; and chaos eliminates the Laplacian fantasy of deterministic predictability". Specially, when chaos synchronization was found in 1991, chaos theory becomes more and more attractive. Chaos has been widely applied to many scientific disciplines: mathematics, programming, microbiology, biology, computer science, economics, engineering, finance, philosophy, physics, politics, population dynamics, psychology, and robotics. One of most important engineering applications is secure communication because of the properties of random behaviours and sensitivity to initial conditions of chaos systems. Noise-like dynamical behaviours can be used to mask the original information in symmetric cryptography. Sensitivity to initial conditions and unpredictability make chaotic systems very suitable to construct one-way function in public-key cryptography. In chaos-based secure communication schemes, information signals are masked or modulated (encrypted) by chaotic signals at the transmitter and the resulting encrypted signals are sent to the corresponding receiver across a public channel (unsafe channel). Perfect chaos synchronization is usually expected to recover the original information signals. In other words, the recovery of the information signals requires the receiver's own copy of the chaotic signals which are synchronized with the transmitter ones. Thus, chaos synchronization is the key technique throughout this whole process. Due to the difficulties of generating and synchronizing chaotic systems and the limit of digital computer precision, there exist many challenges in chaos-based secure communication. In this thesis, we try to solve chaos generation and chaos synchronization problems. Starting from designing chaotic and hyperchaotic system by first-order delay differential equation, we present a family of novel cell attractors with multiple positive Lyapunov exponents. Compared with previously reported hyperchaos systems with complex mathematic structure (more than 3 dimensions), our system is relatively simple while its dynamical behaviours are very complicated. We present a systemic parameter control method to adjust the number of positive Lyapunov exponents, which is an index of chaos degree. Furthermore, we develop a delay feedback controller and apply it to Chen system to generate multi-scroll attractors. It can be generalized to Chua system, Lorenz system, Jerk equation, etc. Since chaos synchronization is the critical technique in chaos-based secure communication, we present corresponding impulsive synchronization criteria to guarantee that the receiver can generate the same chaotic signals at the receiver when time delay and uncertainty emerge in the transmission process. Aiming at the weakness of general impulsive synchronization scheme, i.e., there always exists an upper boundary to limit impulsive intervals during the synchronization process, we design a novel synchronization scheme, intermittent impulsive synchronization scheme (IISS). IISS can not only be flexibly applied to the scenario where the control window is restricted but also improve the security of chaos-based secure communication via reducing the control window width and decreasing the redundancy of synchronization signals. Finally, we propose chaos-based public-key cryptography algorithms which can be used to encrypt synchronization signals and guarantee their security across the public channel.