Constraint satisfaction techniques under uncertain conditions for fault diagnosis in nonlinear dynamic systems

The speed of fault isolation is crucial for the design and reconfiguration of fault tolerant control (FTC). In this paper the fault isolation problem is stated as a constraint satisfaction problem (CSP) and solved using constraint propagation techniques. The proposed method is based on constraint satisfaction techniques and uncertainty space refining of interval parameters. In comparison with other approaches based on adaptive observers, the major advantage of the presented method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements and model errors and without the monotonicity assumption. In order to illustrate the proposed approach, a case study of a nonlinear dynamic system is presented

The counter-propagating Rossby-wave perspective on baroclinic instability. Part IV: Nonlinear life cycles

Pairs of counter-propagating Rossby waves (CRWs) can be used to describe baroclinic instability in linearized primitive-equation dynamics, employing simple propagation and interaction mechanisms at only two locations in the meridional plane—the CRW ‘home-bases’. Here, it is shown how some CRW properties are remarkably robust as a growing baroclinic wave develops nonlinearly. For example, the phase difference between upper-level and lower-level waves in potential-vorticity contours, defined initially at the home-bases of the CRWs, remains almost constant throughout baroclinic wave life cycles, despite the occurrence of frontogenesis and Rossby-wave breaking. As the lower wave saturates nonlinearly the whole baroclinic wave changes phase speed from that of the normal mode to that of the self-induced phase speed of the upper CRW. On zonal jets without surface meridional shear, this must always act to slow the baroclinic wave. The direction of wave breaking when a basic state has surface meridional shear can be anticipated because the displacement structures of CRWs tend to be coherent along surfaces of constant basic-state angular velocity, U. This results in up-gradient horizontal momentum fluxes for baroclinically growing disturbances. The momentum flux acts to shift the jet meridionally in the direction of the increasing surface U, so that the upper CRW breaks in the same direction as occurred at low levels

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Nonlinear refractive index of RECOB (RE = Gd and La) crystals

The Z-scan technique is employed to obtain the nonlinear refractive index (n (2)) of the Ca(4)REO(BO(3))(3) (RECOB, where RE = Gd and La) single crystals using 30 fs laser pulses centered at 780 nm for the two orthogonal orientations determined by the optical axes (X and Z) relative to the direction of propagation of the laser beam (k//Y// crystallographic b-axis). The large values of n (2) indicate that both GdCOB and LaCOB are potential hosts for Yb:RECOB lasers operating in the Kerr-lens mode locking (KLM) regime.

Time-resolved study electronic and thermal contributions to the nonlinear refractive index of Nd3+: SBN laser crystals

The propagation of an optical beam through dielectric media induces changes in the refractive index, An, which causes self-focusing or self-defocusing. In the particular case of ion-doped solids, there are thermal and non-thermal lens effects, where the latter is due to the polarizability difference, Delta alpha, between the excited and ground states, the so-called population lens (PL) effect. PL is a pure electronic contribution to the nonlinearity, while the thermal lens (TL) effect is caused by the conversion of part of the absorbed energy into heat. In time-resolved measurements such as Z-scan and TL transient experiments, it is not easy to separate these two contributions to nonlinear refractive index because they usually have similar response times. In this work, we performed time-resolved measurements using both Z-scan and mode mismatched TL in order to discriminate thermal and electronic contributions to the laser-induced refractive index change of the Nd3+-doped Strontium Barium Niobate (SrxBa1-xNb2O6) laser crystal. Combining numerical simulations with experimental results we could successfully distinguish between the two contributions to An. (C) 2007 Elsevier B.V. All rights reserved.

Computational aspects of harmonic wavelet Galerkin methods and an application to a precipitation front propagation model

This article is dedicated to harmonic wavelet Galerkin methods for the solution of partial differential equations. Several variants of the method are proposed and analyzed, using the Burgers equation as a test model. The computational complexity can be reduced when the localization properties of the wavelets and restricted interactions between different scales are exploited. The resulting variants of the method have computational complexities ranging from O(N(3)) to O(N) (N being the space dimension) per time step. A pseudo-spectral wavelet scheme is also described and compared to the methods based on connection coefficients. The harmonic wavelet Galerkin scheme is applied to a nonlinear model for the propagation of precipitation fronts, with the front locations being exposed in the sizes of the localized wavelet coefficients. (C) 2011 Elsevier Ltd. All rights reserved.

A mathematical model for wave propagation in elastic tubes with inhomogeneities: Application to blood waves propagation

We study the propagation of waves in an elastic tube filled with an inviscid fluid. We consider the case of inhomogeneity whose mechanical and geometrical properties vary in space. We deduce a system of equations of the Boussinesq type as describing the wave propagation in the tube. Numerical simulations of these equations show that inhomogeneities prevent separation of right-going from left-going waves. Then reflected and transmitted coefficients are obtained in the case of localized constriction and localized rigidity. Next we focus on wavetrains incident on various types of anomalous regions. We show that the existence of anomalous regions modifies the wavetrain patterns. (c) 2007 Elsevier B.V. All rights reserved.

Periodic waves and solitons in a nonlinear fibre with resonant impurities

We shall consider a coupled nonlinear Schrodinger equation- Bloch system of equations describing the propagation of a single pulse through a nonlinear dispersive waveguide in the presence of resonances; this could be, for example, a doped optical fibre. By making use of the integrability of the dynamic equations, we shall apply the finite-gap integration method to obtain periodic solutions for this system. Next, we consider the problem of the formation of solitons at a sharp front pulse and, by means of the Whitham modulational theory, we derive the amplitude and velocity of the largest soliton.

Nonlinear Gravitational Waves: Their Form and Effects

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Soliton dynamics at an interface between a uniform medium and a nonlinear optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Soliton propagation in a medium with Kerr nonlinearity and resonant impurities: A variational approach

The soliton propagation in a medium with Kerr nonlinearity and resonant impurities was studied by a variational approach. The existence of a solitary wave was shown within the framework of a combined nonintegrable system composed of one nonlinear Schrödinger and a pair of Bloch equations. The analytical solution which was obtained, was tested through numerical simulations confirming its solitary wave nature.

Harmonic propagation analysis in electric energy distribution systems

An important alteration of the equivalent loads profile has been observed in the electrical energy distribution systems, for the last years. Such fact is due to the significant increment of the electronic processors of electric energy that, in general, behave as nonlinear loads, generating harmonic distortions in the currents and voltages along the electric network. The effects of these nonlinear loads, even if they are concentrated in specific sections of the network, are present along the branch circuits, affecting the behavior of the entire electric network. For the evaluation of this phenomenon it is necessary the analysis of the harmonic currents flow and the understanding of the causes and effects of the consequent voltage harmonic distortions. The usual tools for calculation the harmonic flow consider one-line equivalent networks, balanced and symmetrical systems. Therefore, they are not tools appropriate for analysis of the operation and the influence/interaction of mitigation elements. In this context, this work proposes the development of a computational tool for the analysis of the three-phase harmonic propagation using Norton modified models and considering the real nature of unbalanced electric systems operation. © 2011 IEEE.

Causal structure and birefringence in nonlinear electrodynamics

We investigate the causal structure of general nonlinear electrodynamics and determine which Lagrangians generate an effective metric conformal to Minkowski. We also prove that there is only one analytic nonlinear electrodynamics not presenting birefringence.

Wide localized solutions of the parity-time-symmetric nonautonomous nonlinear Schrodinger equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonlinear / electromagnetic co-simulation and co-design of microwave links in highly polluted and / or strongly inhomogeneous environments

The objective of the Ph.D. thesis is to put the basis of an all-embracing link analysis procedure that may form a general reference scheme for the future state-of-the-art of RF/microwave link design: it is basically meant as a circuit-level simulation of an entire radio link, with – generally multiple – transmitting and receiving antennas examined by EM analysis. In this way the influence of mutual couplings on the frequency-dependent near-field and far-field performance of each element is fully accounted for. The set of transmitters is treated as a unique nonlinear system loaded by the multiport antenna, and is analyzed by nonlinear circuit techniques. In order to establish the connection between transmitters and receivers, the far-fields incident onto the receivers are evaluated by EM analysis and are combined by extending an available Ray Tracing technique to the link study. EM theory is used to describe the receiving array as a linear active multiport network. Link performances in terms of bit error rate (BER) are eventually verified a posteriori by a fast system-level algorithm. In order to validate the proposed approach, four heterogeneous application contexts are provided. A complete MIMO link design in a realistic propagation scenario is meant to constitute the reference case study. The second one regards the design, optimization and testing of various typologies of rectennas for power generation by common RF sources. Finally, the project and implementation of two typologies of radio identification tags, at X-band and V-band respectively. In all the cases the importance of an exhaustive nonlinear/electromagnetic co-simulation and co-design is demonstrated to be essential for any accurate system performance prediction.