Development and Evaluation of Blind Identification Techniques for Nonlinear Systems

Identification and Control of Non‐linear dynamical systems are challenging problems to the control engineers.The topic is equally relevant in communication,weather prediction ,bio medical systems and even in social systems,where nonlinearity is an integral part of the system behavior.Most of the real world systems are nonlinear in nature and wide applications are there for nonlinear system identification/modeling.The basic approach in analyzing the nonlinear systems is to build a model from known behavior manifest in the form of system output.The problem of modeling boils down to computing a suitably parameterized model,representing the process.The parameters of the model are adjusted to optimize a performanace function,based on error between the given process output and identified process/model output.While the linear system identification is well established with many classical approaches,most of those methods cannot be directly applied for nonlinear system identification.The problem becomes more complex if the system is completely unknown but only the output time series is available.Blind recognition problem is the direct consequence of such a situation.The thesis concentrates on such problems.Capability of Artificial Neural Networks to approximate many nonlinear input-output maps makes it predominantly suitable for building a function for the identification of nonlinear systems,where only the time series is available.The literature is rich with a variety of algorithms to train the Neural Network model.A comprehensive study of the computation of the model parameters,using the different algorithms and the comparison among them to choose the best technique is still a demanding requirement from practical system designers,which is not available in a concise form in the literature.The thesis is thus an attempt to develop and evaluate some of the well known algorithms and propose some new techniques,in the context of Blind recognition of nonlinear systems.It also attempts to establish the relative merits and demerits of the different approaches.comprehensiveness is achieved in utilizing the benefits of well known evaluation techniques from statistics. The study concludes by providing the results of implementation of the currently available and modified versions and newly introduced techniques for nonlinear blind system modeling followed by a comparison of their performance.It is expected that,such comprehensive study and the comparison process can be of great relevance in many fields including chemical,electrical,biological,financial and weather data analysis.Further the results reported would be of immense help for practical system designers and analysts in selecting the most appropriate method based on the goodness of the model for the particular context.

Nonlinear Optical Properties of Organic and Polymer Systems

Present thesis has discussed the design and synthesis of polymers suitable for nonlinear optics. Most of the molecules that were studied have shown good nonlinear optical activity. The second order nonlinear optical activity of the polymers was measured experimentally by Kurtz and Perry powder technique. The thesis comprises of eight chapters.The theory of NLO phenomenon and a review about the various nonlinear optical polymers has been discussed in chapter 1. The review has provided a survey of NLO active polymeric materials with a general introduction, which included the principles and the origin of nonlinear optics, and has given emphasis to polymeric materials for nonlinear optics, including guest-host systems, side chain polymers, main chain polymers, crosslinked polymers, chiral polymers etc.Chapter 2 has discussed the stability of the metal incorporated tetrapyrrole molecules, porphyrin, chlorin and bacteriochlorin.Chapter 3 has provided the NLO properties of certain organic molecules by computational tools. The chapter is divided into four parts. The first part has described the nonlinear optical properties of chromophore (D-n-A) and bichromophore (D-n-A-A-n-D) systems, which were separated by methylene spacer, by making use of DPT and semiempirical calculations.Chapter 4: A series of polyurethanes was prepared from cardanol, a renewable resource and a waste of the cashew industry by previously designed bifunctional and multifunctional polymers using quantum theoretical approach.Chapter 5: A series of chiral polyurethanes with main chain bis azo diol groups in the polymer backbone was designed and NLO activity was predicted by ZlNDO/ CV methods.In Chapter 7, polyurethanes were first designed by computational methods and the NLO properties were predicted by correction vector method. The designed bifunctional and multifunctional polyurethanes were synthesized by varying the chiral-achiral diol compositions

Studies on underwater propagation development of programmable arrays

The thesis presented here includes the designing of underwater transducer arrays, taking into account the ‘interaction effects’ [30] among the closely packed radiators. Methods of minimizing the ‘interaction effects‘ by modifying the radiating aperture, are investigated. The need for this study arises as it is one of the important peculiar limitations that stands in the way of achieving maximum range of transmission of acoustic signals. Application of the modified array format for the generation of narrow beam low frequency sound waves, through nonlinear interactions, is discussed. Other techniques that can be advantageously exploited in array synthesis are also investigated

Beam shaping of sectoral electromagnetic horn antennas using corner reflector technique

In the present thesis, possibility of beam shaping of sectoral horns and corner reflector systems'has been studied in detail. The experimental results obtained in the above two cases are compared. As far as the flanged sectoral horns are concerned, the special advantage is that the gain is increased without impairing impedance conditions. An intense study on corner reflector antennas shows that the been broadening or focussing will be possible by adjusting parameters involved. Beam tilting by imposing asymmetries is another interesting property of the systems. A comprehensive study of these fields has been presented in Chapter II. Chapter III is exclusively for describing the experimental techniques used in the present investigation. In Chapter IV, experimental results on flanged sectoral horns and corner reflector eyetses are presented. A comparative analysis of the experimental results obtained with flanged sectoral horns and corner reflector systems is presented in the Chapter V. The similarity and close resemblance in each aspects are shown by presenting typical results from these two eysteee. Theoretical aspects of both types of antennas are considered in Chapter VI. Attempts are made for co-ordinating the theoretical aspects and drawing a final conclusion. In Chapter VII. the final conclusion that the flanged sectoral horn may be considered as a corner reflector system has been drawn. The importance of the conclusions and usefulness are pointed out. The scope for further work in these lines has been indicated.

Studies on nonlinear dynamics of certain reaction systems

The nonlinear dynamics of certain important reaction systems are discussed and analysed in this thesis. The interest in the theoretical and the experimental studies of chemical reactions showing oscillatory dynamics and associated properties is increasing very rapidly. An attempt is made to study some nonlinear phenomena exhibited by the well known chemical oscillator, the BelousovZhabotinskii reaction whose mathematical properties are much in common with the properties of biological oscillators. While extremely complex, this reaction is still much simpler than biological systems at least from the modelling point of view. A suitable model [19] for the system is analysed and the researcher has studied the limit cycle behaviour of the system, for different values of the stoichiometric parameter f, by keeping the value of the reaction rate (k6) fixed at k6 = l. The more complicated three-variable model is stiff in nature.

Corrugated flange technique for beam shaping of sectoral electromagnetic horn antennas

The need for improved feed systems for large reflector antennas employed in Radio Astronomy and Satellite tracking spurred the interest in horn antenna research in the 1960's. The major requirements were to reduce spill over, cross-polarisation losses,and to enhance the aperture efficiency to the order of about 75-8O%L The search for such a feed culminated in the corrugated horn. The corrugat1e 1 horn triggered widespread interest and enthusiasm, and a large amount of work(32’34’49’5O’52’53’58’65’75’79)has already been done on this type of antennas. The properties of corrugated surfaces has been investigated in detail. It was strongly felt that the flange technique and the use of corrugated surfaces could be merged together to obtain the advantages of both. This is the idea behind the present work. Corrugations are made on the surface of flange elements. The effect of various corrugation parameters are studied. By varying the flange parameters, a good amount of data is collected and analysed to ascertain the effects of corrugated flanges. The measurements are repeated at various frequencies, in the X— and S-bands. The following parameters of the system were studied: (a) beam shaping (b) gain (c) variation of V.S.U.R. (d) possibility of obtaining circularly polarised radiation from the flanged horn. A theoretical explanation to the effects of corrugated flanges is attempted on the basis of the line-source theory. Even though this theory utilises a simplified model for the calculation of radiation patterns, fairly good agreement between the computed pattern and experimental results are observed.

Studies on some nonlinear schrodinger type equations describing pulse propagation through optical fibers

The discovery of the soliton is considered to be one of the most significant events of the twentieth century. The term soliton refers to special kinds of waves that can propagate undistorted over long distances and remain unaffected even after collision with each other. Solitons have been studied extensively in many fields of physics. In the context of optical fibers, solitons are not only of fundamental interest but also have potential applications in the field of optical fiber communications. This thesis is devoted to the theoretical study of soliton pulse propagation through single mode optical fibers.

Studies on some nonlinear optical phenomena-optical phase conjugation and continuous wave second harmonic generation

Nonlinear optics has emerged as a new area of physics , following the development of various types of lasers. A number of advancements , both theoretical and experimental . have been made in the past two decades . by scientists al1 over the world. However , onl y few scientists have attempted to study the experimental aspects of nonlinear optical phenomena i n I ndian laboratories. This thesis is the report of an attempt made in this direction. The thesis contains the details of the several investigations which the author has carried out in the past few years, on optical phase conjugation (OPC) and continuous wave CCVD second harmonic generation CSHG). OPC is a new branch of nonlinear optics, developed only in the past decade. The author has done a few experiments on low power OPC in dye molecules held in solid matrices, by making use of a degenerate four wave mixing CDFWND scheme. These samples have been characterised by studies on their absorption-spectra. fluorescence spectra. triplet lifetimes and saturation intensities. Phase conjugation efficiencies with r espect to the various parameters have been i nvesti gated . DFWM scheme was also employed i n achievi ng phase conjugation of a br oadband laser C Nd: G1ass 3 using a dye solution as the nonlinear medium.

Studies on some aspects of wave propagation through nonlinear media

Nonlinearity is a charming element of nature and Nonlinear Science has now become one of the most important tools for the fundamental understanding of the nature. Solitons— solutions of a class of nonlinear partial differential equations — which propagate without spreading and having particle— like properties represent one of the most striking aspects of nonlinear phenomena. The study of wave propagation through nonlinear media has wide applications in different branches of physics.Different mathematical techniques have been introduced to study nonlinear systems. The thesis deals with the study of some of the aspects of electromagnetic wave propagation through nonlinear media, viz, plasma and ferromagnets, using reductive perturbation method. The thesis contains 6 chapters

Studies on integrability of some perturbed nonlinear evolution equations

Usually typical dynamical systems are non integrable. But few systems of practical interest are integrable. The soliton concept is a sophisticated mathematical construct based on the integrability of a class ol' nonlinear differential equations. An important feature in the clevelopment. of the theory of solitons and of complete integrability has been the interplay between mathematics and physics. Every integrable system has a lo11g list of special properties that hold for integrable equations and only for them. Actually there is no specific definition for integrability that is suitable for all cases. .There exist several integrable partial clillerential equations( pdes) which can be derived using physically meaningful asymptotic teclmiques from a very large class of pdes. It has been established that many 110nlinear wa.ve equations have solutions of the soliton type and the theory of solitons has found applications in many areas of science. Among these, well-known equations are Korteweg de-Vries(KdV), modified KclV, Nonlinear Schr6dinger(NLS), sine Gordon(SG) etc..These are completely integrable systems. Since a small change in the governing nonlinear prle may cause the destruction of the integrability of the system, it is interesting to study the effect of small perturbations in these equations. This is the motivation of the present work.

Formation of elliptically polarized beam from h-plane sectoral horns using corrugated flanges

The flange technique, suggested by Reynolds72 is simple technique to improve antenna characteristics. Using flange technique we can trim the antenna characteristic by suitably adjusting the flange parameters75. Later corrugated flanges87 are used for beam shaping. The important parameters of the corrugated flanges are (a) flange angle, (b) flange width, (c) flange position, (d) conductivity of the flange, (e) amplitude excitation of the flange elements, (f) period of corrugation etc. Compared to a compound horn the flange technique offers great convenience in trimming antenna characteristics. Horns are commonly used as a feed in radar and satellite communications. A large number of work had been done to improve the characteristics of horn antennas. It is an established fact that grooved walls on the inner surface of a horn can improve the antenna characteristics44. Corrugated comb surface can be used for the circular polarization98, tilt of polarization99 etc. This suggests the possibility to combine these two phenomena and to obtain a resultant beam. This thesis presents the result of an investigation to study the possibility of controlling different antenna characteristics like polarization, beam shaping, matching etc, using corrugated flange techniques.

Investigations on some amino acid based single crystals for nonlinear optical applications and amino acid capped nanocrystals

Organic crystals possess extremely large optical nonlinearity compared to inorganic crystals. Also organic compounds have the amenability for synthesis and scope for introducing desirable characteristics by inclusions. A wide variety of organic materials having electron donor and acceptor groups, generate high order of nonlinearity. In the present work, a new nonlinear optical crystal, L-citrulline oxalate (LCO) based on the aminoacid L-citrulline was grown using slow evaporation technique. Structural characterization was carried out by single crystal XRD. It crystallizes in the noncentrosymmetric, orthorhombic structure with space group P21 P21 P21. Functional groups present in the sample were identified by Fourier transform infra red (FTIR) and FT-Raman spectral analysis. On studying the FTIR and Raman spectra of the precursors L-citrulline and oxalic acid, used for growing L-citrulline oxalate crystal, it is found that the significant peaks of the precursors are present in the spectra of the L-citrulline oxalate crystal . This observation along with the presence of NH3 + group in the spectra of L-citrulline oxalate, confirms the formation of the charge transfer complex

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‘.

Effects of new nonlinear couplings in relativistic effective field theory

We extend the relativistic mean field theory model of Sugahara and Toki by adding new couplings suggested by modern effective field theories. An improved set of parameters is developed with the goal to test the ability of the models based on effective field theory to describe the properties of finite nuclei and, at the same time, to be consistent with the trends of Dirac-Brueckner-Hartree-Fock calculations at densities away from the saturation region. We compare our calculations with other relativistic nuclear force parameters for various nuclear phenomena.

" Nonlinear Signal Processing of Electroencephalogram .' Application in the Study of Neurodynamics. "

Interfacings of various subjects generate new field ofstudy and research that help in advancing human knowledge. One of the latest of such fields is Neurotechnology, which is an effective amalgamation of neuroscience, physics, biomedical engineering and computational methods. Neurotechnology provides a platform to interact physicist; neurologist and engineers to break methodology and terminology related barriers. Advancements in Computational capability, wider scope of applications in nonlinear dynamics and chaos in complex systems enhanced study of neurodynamics. However there is a need for an effective dialogue among physicists, neurologists and engineers. Application of computer based technology in the field of medicine through signal and image processing, creation of clinical databases for helping clinicians etc are widely acknowledged. Such synergic effects between widely separated disciplines may help in enhancing the effectiveness of existing diagnostic methods. One of the recent methods in this direction is analysis of electroencephalogram with the help of methods in nonlinear dynamics. This thesis is an effort to understand the functional aspects of human brain by studying electroencephalogram. The algorithms and other related methods developed in the present work can be interfaced with a digital EEG machine to unfold the information hidden in the signal. Ultimately this can be used as a diagnostic tool.