A Nearly Exact Reformulation of the Girsanov Linearization for Stochastically Driven Nonlinear Oscillators

The Girsanov linearization method (GLM), proposed earlier in Saha, N., and Roy, D., 2007, ``The Girsanov Linearisation Method for Stochastically Driven Nonlinear Oscillators,'' J. Appl. Mech., 74, pp. 885-897, is reformulated to arrive at a nearly exact, semianalytical, weak and explicit scheme for nonlinear mechanical oscillators under additive stochastic excitations. At the heart of the reformulated linearization is a temporally localized rejection sampling strategy that, combined with a resampling scheme, enables selecting from and appropriately modifying an ensemble of locally linearized trajectories while weakly applying the Girsanov correction (the Radon-Nikodym derivative) for the linearization errors. The semianalyticity is due to an explicit linearization of the nonlinear drift terms and it plays a crucial role in keeping the Radon-Nikodym derivative ``nearly bounded'' above by the inverse of the linearization time step (which means that only a subset of linearized trajectories with low, yet finite, probability exceeds this bound). Drift linearization is conveniently accomplished via the first few (lower order) terms in the associated stochastic (Ito) Taylor expansion to exclude (multiple) stochastic integrals from the numerical treatment. Similarly, the Radon-Nikodym derivative, which is a strictly positive, exponential (super-) martingale, is converted to a canonical form and evaluated over each time step without directly computing the stochastic integrals appearing in its argument. Through their numeric implementations for a few low-dimensional nonlinear oscillators, the proposed variants of the scheme, presently referred to as the Girsanov corrected linearization method (GCLM), are shown to exhibit remarkably higher numerical accuracy over a much larger range of the time step size than is possible with the local drift-linearization schemes on their own.

NESP: Nonlinear enhancement and selection of plane for optimal segmentation and recognition of scene word images

In this paper, we report a breakthrough result on the difficult task of segmentation and recognition of coloured text from the word image dataset of ICDAR robust reading competition challenge 2: reading text in scene images. We split the word image into individual colour, gray and lightness planes and enhance the contrast of each of these planes independently by a power-law transform. The discrimination factor of each plane is computed as the maximum between-class variance used in Otsu thresholding. The plane that has maximum discrimination factor is selected for segmentation. The trial version of Omnipage OCR is then used on the binarized words for recognition. Our recognition results on ICDAR 2011 and ICDAR 2003 word datasets are compared with those reported in the literature. As baseline, the images binarized by simple global and local thresholding techniques were also recognized. The word recognition rate obtained by our non-linear enhancement and selection of plance method is 72.8% and 66.2% for ICDAR 2011 and 2003 word datasets, respectively. We have created ground-truth for each image at the pixel level to benchmark these datasets using a toolkit developed by us. The recognition rate of benchmarked images is 86.7% and 83.9% for ICDAR 2011 and 2003 datasets, respectively.

Capturability of augmented proportional navigation (APN) guidance with nonlinear engagement dynamics

Proportional Navigation (PN) and its variants are widely used guidance philosophies. However, in the presence of target maneuver, PN guidance law is effective only for a restrictive set of initial geometries. To account for target maneuvers, the concept of Augmented Proportional Navigation (APN) guidance law was introduced and analyzed in a linearized interceptor-target engagement framework presented in literature. However, there is no work in the literature, that addresses the capturability performance of the APN guidance law in a nonlinear engagement framework. This paper presents such an analysis and obtains the conditions for capturability. It also shows that a shorter time of interception is obtained when APN is formulated in the nonlinear framework as proposed in this paper. Simulation results are given to support the theoretical findings.

Simultaneous attitude control and trajectory tracking of a micro quadrotor: a SNAC aided nonlinear dynamic inversion approach

This paper presents an advanced single network adaptive critic (SNAC) aided nonlinear dynamic inversion (NDI) approach for simultaneous attitude control and trajectory tracking of a micro-quadrotor. Control of micro-quadrotors is a challenging problem due to its small size, strong coupling in pitch-yaw-roll and aerodynamic effects that often need to be ignored in the control design process to avoid mathematical complexities. In the proposed SNAC aided NDI approach, the gains of the dynamic inversion design are selected in such a way that the resulting controller behaves closely to a pre-synthesized SNAC controller for the output regulation problem. However, since SNAC is based on optimal control theory, it makes the dynamic inversion controller to operate near optimal and enhances its robustness property as well. More important, it retains two major benefits of dynamic inversion: (i) closed form expression of the controller and (ii) easy scalability to command tracking application even without any apriori knowledge of the reference command. Effectiveness of the proposed controller is demonstrated from six degree-of-freedom simulation studies of a micro-quadrotor. It has also been observed that the proposed SNAC aided NDI approach is more robust to modeling inaccuracies, as compared to the NDI controller designed independently from time domain specifications.

Formation flying of small satellites using suboptimal MPSP guidance

Using the recently developed model predictive static programming (MPSP), a suboptimal guidance logic is presented in this paper for formation flying of small satellites. Due to the inherent nature of the problem formulation, MPSP does not require the system dynamics to be linearized. The proposed guidance scheme is valid both for high eccentricity chief satellite orbits as well as large separation distance between chief and deputy satellites. Moreover, since MPSP poses the desired conditions as a set of `hard constraints', the final accuracy level achieved is very high. The proposed guidance scheme has been tested successfully for a variety of initial conditions and for a variety of formation commands as well. Comparison with standard Linear Quadratic Regulator (LQR) solution (which serves as a guess solution for MPSP) and another nonlinear controller, State Dependent Riccati Equation (SDRE) reveals that MPSP guidance achieves the objective with higher accuracy and with lesser amount of control usage as well.

Linear and nonlinear optical studies on 3,6-bis (2 pyridyl) pyridazine

3,6-Bis (2 pyridyl) pyridazine has been synthesized and characterized by NMR, XRD and elemental analyses. The vibrational studies were carried out by using FTIR and Raman spectroscopy and the modes of vibrations were analysed and compared with the theoretically calculated values. The nonlinear optical property of the title compound was examined by Kurtz-Perry method and Hyper Raleigh scattering with the fundamental wavelength of 1064nm. This compound possesses less SHG efficiency but large first hyperpolarizability. (C) 2013 Elsevier GmbH. All rights reserved.

A scaled unscented transformation based directed Gaussian sum filter for nonlinear dynamic system identification

Impoverishment of particles, i.e. the discretely simulated sample paths of the process dynamics, poses a major obstacle in employing the particle filters for large dimensional nonlinear system identification. A known route of alleviating this impoverishment, i.e. of using an exponentially increasing ensemble size vis-a-vis the system dimension, remains computationally infeasible in most cases of practical importance. In this work, we explore the possibility of unscented transformation on Gaussian random variables, as incorporated within a scaled Gaussian sum stochastic filter, as a means of applying the nonlinear stochastic filtering theory to higher dimensional structural system identification problems. As an additional strategy to reconcile the evolving process dynamics with the observation history, the proposed filtering scheme also modifies the process model via the incorporation of gain-weighted innovation terms. The reported numerical work on the identification of structural dynamic models of dimension up to 100 is indicative of the potential of the proposed filter in realizing the stated aim of successfully treating relatively larger dimensional filtering problems. (C) 2013 Elsevier Ltd. All rights reserved.

Electric field activated nonlinear anisotropic charge transport in doped polypyrrole

Electric field activated nonlinear transport is investigated in polypyrrole thin film in both in-plane and out-of-plane geometries down to 5 K and strong anisotropy is observed. A morphological model is suggested to explain the anisotropy through inter-chain and intra-chain transport. The deviation from the variable range hopping at low temperature is accounted by fluctuation assisted transport. From Zabrodaskii plots, it is found that electric field can tune the transport from insulating to metallic regime. Glazman-Matveev model is used to describe the nonlinear conduction. Field scaling analysis shows that conductance data at different temperature falls on to a single curve. Nonlinearity exponent, m(T) and characteristic length, L-E are estimated to characterize the transport in both the geometries. (C) 2013 AIP Publishing LLC.

Chemical vapor detection using nonlinear electrical properties of carbon nanotube bundles

We demonstrate the electrical transport behavior of carbon nanotubes (CNTs) upon exposure to organic analytes (namely ethanol, benzene, acetone and toluene). The resulting nonlinear current-voltage characteristics revealed a power law dependence of the differential conductivity on the applied bias voltage. Moreover, suppression of differential conductivity at zero bias is found to be dependent on different selective analytes. The power law exponent values have been monitored before, during and after exposure to the chemicals, which revealed a reversible change in the number of electron conducting channels. Therefore, the reduction in the number of conductive paths can be attributed to the interaction of the chemical analyte on the CNT surfaces, which causes a decrease in the differential conductivity of the CNT sample. These results demonstrate chemical selectivity of CNTs due to varying electronic interaction with different chemical analytes.

Biased PN based impact angle constrained guidance using a nonlinear engagement model

Impact angle constrained guidance laws are important in many applications such as guidance of torpedoes, anti-ballistic missiles and reentry vehicles. In this paper, we design a guidance law which is capable of achieving a wide range of impact angles. Biased proportional navigation guidance uses a bias term in addition to the basic PN command to satisfy additional constraints. Angle constrained BPNG (ACBPNG) uses small angle approximations to derive the bias term for impact angle requirement. We design a modified ACBPNG (MACBPNG) where the required bias term is derived in a closed form considering non-linear equations of motion. Simulations are carried out for a wide range of impact angle requirements. We also analyze capturability from different initial positions and also the launch angles possible at each initial position. The performance of the proposed law is compared with an existing law.

Nonlinear and linear autopilot performance comparison of tactical flight vehicle

n this paper, three-axis autopilot of a tactical flight vehicle has been designed for surface to air application. Both nonlinear and linear design synthesis and analysis have been carried out pertaining to present flight vehicle. Lateral autopilot performance has been compared by tracking lateral acceleration components along yaw and pitch plane at higher angles of attack in presence of side force and aerodynamic nonlinearity. The nonlinear lateral autopilot design is based on dynamic inversion and time scale separation principle. The linear lateral autopilot design is based on three-loop topology. Roll autopilot robustness performance has been enhanced against unmodeled roll disturbances by backstepping technique. Complete performance comparison results of both nonlinear and linear controller based on six degrees of freedom simulation along with stability and robustness studies with respect to plant parameter variation have been discussed in the paper.

Closed-form nonlinear sectional analysis of pretwisted anisotropic beam with multiple delaminations

Fiber reinforced laminated composite open-section beams are widely used as bearingless rotor flex beams because of their high specific strength and stiffness as well as fatigue life. These laminated composite structures exhibit a number of different failure modes, including fiber-matrix debonding within individual layers, delamination or separation of the layers, transverse cracks through one or more layers and fiber fracture. Delamination is a predominant failure mode in continuous fiber reinforced laminated composites and often initiate near the free edges of the structure. The appearance of delaminations in the composite rotorcraft flexbeams can lead to deterioration of the mechanical properties and, in turn, the helicopter performance as well as safety. Understanding and predicting the influence of free-edge delamination on the overall behavior of the laminates will provide quantitative measures of the extent of the damage and help ensure their damage tolerance.

A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification

A Monte Carlo filter, based on the idea of averaging over characteristics and fashioned after a particle-based time-discretized approximation to the Kushner-Stratonovich (KS) nonlinear filtering equation, is proposed. A key aspect of the new filter is the gain-like additive update, designed to approximate the innovation integral in the KS equation and implemented through an annealing-type iterative procedure, which is aimed at rendering the innovation (observation prediction mismatch) for a given time-step to a zero-mean Brownian increment corresponding to the measurement noise. This may be contrasted with the weight-based multiplicative updates in most particle filters that are known to precipitate the numerical problem of weight collapse within a finite-ensemble setting. A study to estimate the a-priori error bounds in the proposed scheme is undertaken. The numerical evidence, presently gathered from the assessed performance of the proposed and a few other competing filters on a class of nonlinear dynamic system identification and target tracking problems, is suggestive of the remarkably improved convergence and accuracy of the new filter. (C) 2013 Elsevier B.V. All rights reserved.

Nonlinear optical second harmonic generation in ZnS quantum dots and observation on optical properties of ZnS/PMMA nanocomposites

ZnS quantum dots (QDs) of different sizes are synthesized by a simple chemical co-precipitation method at room temperature, by varying pH value of the reaction mixture. Samples are characterized by an X-ray diffractometer, transmission electron microscope, energy-dispersive X-ray analysis, etc. Linear optical properties, including UV-visible absorption and photoluminescence emission characteristics, of as-prepared QDs are measured. Size dependent nonlinear optical property, such as second harmonic generation (SHG) of 1064 nm Nd:YAG laser fundamental radiation in the synthesized ZnS QDs, is reported for the first time, to the best of our knowledge, by using the standard Kurtz-Perry powder method. In not to study the possibility of the synthesized ZnS QDs in different device applications ZnS/PMMA (polymethylmethacrylate) nanocomposites are also synthesized. The presence of weak chemical interaction between the polymer matrix and ZnS QDs is confirmed by Fourier transform infrared spectroscopy. Thermal properties of the nanocomposites are studied by differential scanning calorimetry and thermo-gravimetric analysis techniques, which show that the composites are stable up to similar to 300 degrees C temperature. (C) 2013 Elsevier B.V. All rights reserved.