The Alpha-Method Direct Transcription In Path Constrained Dynamic Optimization

Numerically discretized dynamic optimization problems having active inequality and equality path constraints that along with the dynamics induce locally high index differential algebraic equations often cause the optimizer to fail in convergence or to produce degraded control solutions. In many applications, regularization of the numerically discretized problem in direct transcription schemes by perturbing the high index path constraints helps the optimizer to converge to usefulm control solutions. For complex engineering problems with many constraints it is often difficult to find effective nondegenerat perturbations that produce useful solutions in some neighborhood of the correct solution. In this paper we describe a numerical discretization that regularizes the numerically consistent discretized dynamics and does not perturb the path constraints. For all values of the regularization parameter the discretization remains numerically consistent with the dynamics and the path constraints specified in the, original problem. The regularization is quanti. able in terms of time step size in the mesh and the regularization parameter. For full regularized systems the scheme converges linearly in time step size.The method is illustrated with examples.

Regularized numerical integration of multibody dynamics with the generalized alpha method*

This paper discusses the consistent regularization property of the generalized α method when applied as an integrator to an initial value high index and singular differential-algebraic equation model of a multibody system. The regularization comes from within the discretization itself and the discretization remains consistent over the range of values the regularization parameter may take. The regularization involves increase of the smallest singular values of the ill-conditioned Jacobian of the discretization and is different from Baumgarte and similar techniques which tend to be inconsistent for poor choice of regularization parameter. This regularization also helps where pre-conditioning the Jacobian by scaling is of limited effect, for example, when the scleronomic constraints contain multiple closed loops or singular configuration or when high index path constraints are present. The feed-forward control in Kane's equation models is additionally considered in the numerical examples to illustrate the effect of regularization. The discretization presented in this work is adopted to the first order DAE system (unlike the original method which is intended for second order systems) for its A-stability and same order of accuracy for positions and velocities.

The alpha method for solving differential algebraic inequality (DAI) systems

This paper describes an algorithm for ``direct numerical integration'' of the initial value Differential-Algebraic Inequalities (DAI) in a time stepping fashion using a sequential quadratic programming (SQP) method solver for detecting and satisfying active path constraints at each time step. The activation of a path constraint generally increases the condition number of the active discretized differential algebraic equation's (DAE) Jacobian and this difficulty is addressed by a regularization property of the alpha method. The algorithm is locally stable when index 1 and index 2 active path constraints and bounds are active. Subject to available regularization it is seen to be stable for active index 3 active path constraints in the numerical examples. For the high index active path constraints, the algorithm uses a user-selectable parameter to perturb the smaller singular values of the Jacobian with a view to reducing the condition number so that the simulation can proceed. The algorithm can be used as a relatively cheaper estimation tool for trajectory and control planning and in the context of model predictive control solutions. It can also be used to generate initial guess values of optimization variables used as input to inequality path constrained dynamic optimization problems. The method is illustrated with examples from space vehicle trajectory and robot path planning.

Influence of substrate temperature on the properties of oxygen‐ion‐assisted deposited CeO2 films

Substrate temperature and ion bombardment during deposition have been observed to modify significantly the optical and structural properties of dielectric thin films. Single‐layer films of CeO2 have been deposited by electron beam evaporation with simultaneous oxygen‐ion bombardment using a Kaufman broad beam ion source and maintaining the substrates at elevated temperature. A systematic study has been made on the influence of (a) substrate temperature in the range ambient to 300 °C, (b) ion energy in the range 300–700 eV, and (c) ion current density 100–220 μA/cm2 on optical properties such as refractive index, extinction coefficient, inhomogeneity, packing density, and structural properties. The refractive index increased with in increase in substrate temperature: ion energy up to 600 eV and ion current density. Homogeneous, absorption free and high index (2.48) films have been obtained at 600 eV, 220 μA/cm2 and at substrate temperature of 300 °C. The packing density of the films was observed to be unity for the same deposition conditions. Substrate temperature with simultaneous ion bombardment modified the structure of the films from highly ordered to fine grain structure.

Nonlinear Refraction and Two-Photon Absorption in Dense 2Bi(2)O(3)-B2O3 Glasses

High density transparent glasses (7.86 g/cc) were fabricated in the 2Bi(2)O(3)-B2O3 (BBO) system. Optical band gap of the obtained glasses was found to be 2.6eV. The refractive index measured for these glasses was 2.25 +/- 0.05 at lambda=543 nm. Nonlinear refraction and absorption studies were carried out on the BBO glasses using z-scan technique a lambda=532 nm of 10 ns pulse width. The nonlinear refractive index obtained was n(2)=12.1x10(-14) cm(2)/W and nonlinear absorption coefficient was beta=15.2 cm/GW. The n(2) and beta values of the BBO glasses were large compared to the other reported high index bismuth based oxide glass systems in the literature. These were attributed to the high density, high linear refractive index, low band gap and two photon absorption associated with these glasses. The electronic origin of large nonlinearities was discussed based on bond-orbital theory.

Nanocrystallization of TiO2 Anatase Phase in Hydrophobic BaO-TiO2-B2O3 Glass System

Transparent colorless glasses in the ternary BaOTiO2B2O3 system were fabricated via conventional melt-quenching technique. The glasses with certain molar concentrations of BaO and TiO2 on heat treatment at appropriate temperatures yielded nanocrystalline phase of TiO2 associated with the crystallite size in the 515 nm range. Nanocrystallized glasses exhibited high refractive index (n = 2.15) measured at lambda = 543 nm. These glasses were found to be hydrophobic in nature associated with the contact angle of 90 degrees. These high-index glass nanocrystal composites would be of potential interest for optical device applications.

Tuning the chiro-plasmonic response using high refractive index-dielectric templates

Chiral metamaterials have recently gained attention due to their applicability in developing polarization devices and in the detection of chiral molecules. A common approach towards fabricating plasmonic chiral nanostructures has been decorating metallic nanoparticles on dielectric chiral scaffolds, such as a helix. This resulted in the generation of a large chiro-optical response over a wide range of the electromagnetic spectrum. It has been shown previously that the optical tunability of these chiral metamaterials depends on the geometrical aspects of the overall structure, as well as the nature of the plasmonic constituents. In this study, we have investigated the role of the underlying dielectric scaffold with numerical simulations, and experimentally demonstrated that it is possible to enhance and engineer their chiro-plasmonic response significantly by choosing dielectric scaffolds of appropriate materials.

EEG seizure in bilateral ECT is different between low and high stimulus doses

Melancholic depressive patients referred for ECT were randomized to receive either low dose (n = 20) or high dose (n = 20) stimulus applied bifrontotemporally. The two stimulus groups were comparable on the clinical variables. The EEG seizure was recorded on two channels (right and left frontal), digitized, coded and analyzed offline without knowledge of ECT parameters. EEG seizure was of comparable duration in the two stimulus (high dose and low dose) groups. A new composite measure, Strength-Symmetry-Index (SSI), based on strength and symmetry of seizure EEG was computed using fractal geometry. The SSI of the early-seizure was higher in the high dose than in the low dose ECT group. In a stepwise, logistic regression model, this variable contributed to 65% with correct classification of high dose and low dose ECT seizures.

Development of Very High Frequency Damped Sine Wave Generator

In order to protect the critical electronic equipment/system against damped sine transient currents induced into its cables due to transient electromagnetic fields, switching phenomena, platform resonances, etc. it is necessary to provide proper hardening. The hardness assurance provided can be evaluated as per the test CS 116 of MIL STD 461E/F in laboratory by generating & inducing the necessary damped sine currents into the cables of the Equipment Under Test (EUT). The need and the stringent requirements for building a damped sine wave current generator for generation of damped sine current transients of very high frequencies (30 MHz & 100 MHz) have been presented. A method using LC discharge for the generation has been considered in the development. This involves building of extremely low & nearly loss less inductors (about 5 nH & 14 nH) as well as a capacitor & a switch with much lower inductances. A technique for achieving this has been described. Two units (I No for 30 MHz. & 100 MHz each) have been built. Experiments to verify the output are being conducted.

Ultracapacitor Based Ride Through System for Control Power Supplies in High Power Converters

High power converters are used in variable speed induction motor drive applications. Riding through a short term power supply glitch is becoming an important requirement in these power converters. The power converter uses a large number of control circuit boards for its operation. The control power supply need to ensure that any glitch in the grid side does not affect any of these control circuit boards. A power supply failure of these control cards results in shut down of the entire system. The paper discusses the ride through system developed to overcome voltage sags and short duration outages at the power supply terminals of the control cards in these converters. A 240VA non-isolated, bi-directional buck-boost converter has been designed to be used along with a stack of ultracapacitors to achieve the same. A micro-controller based digital control platform made use of to achieve the control objective. The design of the ultracapacitor stack and the bidirectional converter is described the performance of the experimental set-up is evaluated.

Remote detection and distinction of ants using nest-site specific LISS-derived Normalised Difference Vegetation Index

This study in Western Ghats, India, investigates the relation between nesting sites of ants and a single remotely sensed variable: the Normalised Difference Vegetation Index (NDVI). We carried out sampling in 60 plots each measuring 30 x 30 m and recorded nest sites of 13 ant species. We found that NDVI values at the nesting sites varied considerably between individual species and also between the six functional groups the ants belong to. The functional groups Cryptic Species, Tropical Climate Specialists and Specialist Predators were present in regions with high NDVI whereas Hot Climate Specialists and Opportunists were found in sites with low NDVI. As expected we found that low NDVI values were associated with scrub jungles and high NDVI values with evergreen forests. Interestingly, we found that Pachycondyla rufipes, an ant species found only in deciduous and evergreen forests, established nests only in sites with low NDVI (range = 0.015 - 0.1779). Our results show that these low NDVI values in deciduous and evergreen forests correspond to canopy gaps in otherwise closed deciduous and evergreen forests. Subsequent fieldwork confirmed the observed high prevalence of P. rufipes in these NDVI-constrained areas. We discuss the value of using NDVI for the remote detection and distinction of ant nest sites.

High-rate analysis of channel-optimized vector quantization

High-rate analysis of channel-optimized vector quantizationThis paper considers the high-rate performance of channel optimized source coding for noisy discrete symmetric channels with random index assignment. Specifically, with mean squared error (MSE) as the performance metric, an upper bound on the asymptotic (i.e., high-rate) distortion is derived by assuming a general structure on the codebook. This structure enables extension of the analysis of the channel optimized source quantizer to one with a singular point density: for channels with small errors, the point density that minimizes the upper bound is continuous, while as the error rate increases, the point density becomes singular. The extent of the singularity is also characterized. The accuracy of the expressions obtained are verified through Monte Carlo simulations.

High-Rate Vector Quantization for Noisy Channels With Applications to Wideband Speech Spectrum Compression

This paper considers the high-rate performance of source coding for noisy discrete symmetric channels with random index assignment (IA). Accurate analytical models are developed to characterize the expected distortion performance of vector quantization (VQ) for a large class of distortion measures. It is shown that when the point density is continuous, the distortion can be approximated as the sum of the source quantization distortion and the channel-error induced distortion. Expressions are also derived for the continuous point density that minimizes the expected distortion. Next, for the case of mean squared error distortion, a more accurate analytical model for the distortion is derived by allowing the point density to have a singular component. The extent of the singularity is also characterized. These results provide analytical models for the expected distortion performance of both conventional VQ as well as for channel-optimized VQ. As a practical example, compression of the linear predictive coding parameters in the wideband speech spectrum is considered, with the log spectral distortion as performance metric. The theory is able to correctly predict the channel error rate that is permissible for operation at a particular level of distortion.