Recurrence Quantification Analysis of System Signals for Detecting Tool and Chatter in Turning

In this thesis, the applications of the recurrence quantification analysis in metal cutting operation in a lathe, with specific objective to detect tool wear and chatter, are presented.This study is based on the discovery that process dynamics in a lathe is low dimensional chaotic. It implies that the machine dynamics is controllable using principles of chaos theory. This understanding is to revolutionize the feature extraction methodologies used in condition monitoring systems as conventional linear methods or models are incapable of capturing the critical and strange behaviors associated with the metal cutting process.As sensor based approaches provide an automated and cost effective way to monitor and control, an efficient feature extraction methodology based on nonlinear time series analysis is much more demanding. The task here is more complex when the information has to be deduced solely from sensor signals since traditional methods do not address the issue of how to treat noise present in real-world processes and its non-stationarity. In an effort to get over these two issues to the maximum possible, this thesis adopts the recurrence quantification analysis methodology in the study since this feature extraction technique is found to be robust against noise and stationarity in the signals.The work consists of two different sets of experiments in a lathe; set-I and set-2. The experiment, set-I, study the influence of tool wear on the RQA variables whereas the set-2 is carried out to identify the sensitive RQA variables to machine tool chatter followed by its validation in actual cutting. To obtain the bounds of the spectrum of the significant RQA variable values, in set-i, a fresh tool and a worn tool are used for cutting. The first part of the set-2 experiments uses a stepped shaft in order to create chatter at a known location. And the second part uses a conical section having a uniform taper along the axis for creating chatter to onset at some distance from the smaller end by gradually increasing the depth of cut while keeping the spindle speed and feed rate constant.The study concludes by revealing the dependence of certain RQA variables; percent determinism, percent recurrence and entropy, to tool wear and chatter unambiguously. The performances of the results establish this methodology to be viable for detection of tool wear and chatter in metal cutting operation in a lathe. The key reason is that the dynamics of the system under study have been nonlinear and the recurrence quantification analysis can characterize them adequately.This work establishes that principles and practice of machining can be considerably benefited and advanced from using nonlinear dynamics and chaos theory.

Studies on Chaos and Synchronization in ac-driven Josephson junctions

The main goal of this thesis is to study the dynamics of Josephson junction system in the presence of an external rf-biasing.A system of two chaotically synchronized Josephson junction is studied.The change in the dynamics of the system in the presence of at phase difference between the applied fields is considered. Control of chaos is very important from an application point of view. The role Of phase difference in controlling chaos is discussed.An array of three Josephson junctions iS studied for the effect of phase difference on chaos and synchronization and the argument is extended for a system of N Josephson junctions. In the presence of a phase difference between the external fields, the system exhibits periodic behavior with a definite phase relationship between all the three junctions.Itdeals with an array of three Josephson junctions with a time delay in the coupling term. It is observed that only the outer systems synchronize while the middle system remain uncorrelated with t-he other two. The effect of phase difference between the applied fields and time-delay on system dynamics and synchronization is also studied. We study the influence of an applied ac biasing on a serniannular Josephson junction. It is found the magnetic field along with the biasing induces creation and annihilation of fluxons in the junction. The I-V characteristics of the junction is studied by considering the surface loss term also in the model equation. The system is found to exhibit chaotic behavior in the presence of ac biasing.

Dynamics of coupled Josephson junctions under the influence of applied fields

We investigate the effect of the phase difference of appliedfields on the dynamics of mutually coupledJosephsonjunctions. A phase difference between the appliedfields desynchronizes the system. It is found that though the amplitudes of the output voltage values are uncorrelated, a phase correlation is found to exist for small values of applied phase difference. The dynamics of the system is found to change from chaotic to periodic for certain values of phase difference. We report that by keeping the value of phase difference as π, the system continues to be in periodic motion for a wide range of values of system parameters. This result may find applications in devices like voltage standards, detectors, SQUIDS, etc., where chaos is least desired.

Phase synchronization in an array of driven Josephson junctions

We consider an array of N Josephson junctions connected in parallel and explore the condition for chaotic synchronization. It is found that the outer junctions can be synchronized while they remain uncorrelated to the inner ones when an external biasing is applied. The stability of the solution is found out for the outer junctions in the synchronization manifold. Symmetry considerations lead to a situation wherein the inner junctions can synchronize for certain values of the parameter. In the presence of a phase difference between the applied fields, all the junctions exhibit phase synchronization. It is also found that chaotic motion changes to periodic in the presence of phase differences.

Studies on the effect of randoniness on the synchronization of coupled systems and on the dynamics of intermittently driven systems

It has been shown recently that systems driven with random pulses show the signature of chaos ,even without non linear dynamics.This shows that the relation between randomness and chaos is much closer than it was understood earlier .The effect of random perturbations on synchronization can be also different. In some cases identical random perturbations acting on two different chaotic systems induce synchronizations. However most commonly ,the effect of random fluctuations on the synchronizations of chaotic system is to destroy synchronization. This thesis deals with the effect of random fluctuations with its associated characteristic timescales on chaos and synchronization. The author tries to unearth yet another manifestation of randomness on chaos and sychroniztion. This thesis is organized into six chapters.

Speech sample estimation from composite zerocrossings and encoding via adaptive switching of transforms

This thesis investigates the potential use of zerocrossing information for speech sample estimation. It provides 21 new method tn) estimate speech samples using composite zerocrossings. A simple linear interpolation technique is developed for this purpose. By using this method the A/D converter can be avoided in a speech coder. The newly proposed zerocrossing sampling theory is supported with results of computer simulations using real speech data. The thesis also presents two methods for voiced/ unvoiced classification. One of these methods is based on a distance measure which is a function of short time zerocrossing rate and short time energy of the signal. The other one is based on the attractor dimension and entropy of the signal. Among these two methods the first one is simple and reguires only very few computations compared to the other. This method is used imtea later chapter to design an enhanced Adaptive Transform Coder. The later part of the thesis addresses a few problems in Adaptive Transform Coding and presents an improved ATC. Transform coefficient with maximum amplitude is considered as ‘side information’. This. enables more accurate tfiiz assignment enui step—size computation. A new bit reassignment scheme is also introduced in this work. Finally, sum ATC which applies switching between luiscrete Cosine Transform and Discrete Walsh-Hadamard Transform for voiced and unvoiced speech segments respectively is presented. Simulation results are provided to show the improved performance of the coder

Onset And Characterisation Of Chaos In A Two Dimensional Nonlinear Deterministic Model

Nature is full of phenomena which we call "chaotic", the weather being a prime example. What we mean by this is that we cannot predict it to any significant accuracy, either because the system is inherently complex, or because some of the governing factors are not deterministic. However, during recent years it has become clear that random behaviour can occur even in very simple systems with very few number of degrees of freedom, without any need for complexity or indeterminacy. The discovery that chaos can be generated even with the help of systems having completely deterministic rules - often models of natural phenomena - has stimulated a lo; of research interest recently. Not that this chaos has no underlying order, but it is of a subtle kind, that has taken a great deal of ingenuity to unravel. In the present thesis, the author introduce a new nonlinear model, a ‘modulated’ logistic map, and analyse it from the view point of ‘deterministic chaos‘.

Study of Synchronisalion and Control of Chaos in Directly Modulated Semiconductor Lasers

Chaos is a subject oftopical interest and, studied in great detail in relation to its relevance in almost all branches of science, which include physical, chemical, and biological fields. Chaos in the literal sense signifies utter confusion, but the scientific community has differentiated chaos as deterministic chaos and white noise. Deterministic chaos implies the complex behaviour of systems, which are governed by deterministic laws. Behaviour of such systems often become unpredictable in the long run. This unpredictability arises from the sensitivity of the system to its initial conditions. The essential requirement for ‘sensitivity to initial condition’ is nonlinearity of the system. The only method for determining the future of such systems is numerically simulating its final state from a set ofinitial conditions. Synchronisation