Optimal Nonlinear Control and Estimation for a Reusable Launch Vehicle During Reentry Phase

In this paper a nonlinear optimal controller has been designed for aerodynamic control during the reentry phase of the Reusable Launch Vehicle (RLV). The controller has been designed based on a recently developed technique Optimal Dynamic Inversion (ODI). For full state feedback the controller has required full information about the system states. In this work an Extended Kalman filter (EKF) is developed to estimate the states. The vehicle (RLV) has been has been consider as a nonlinear Six-Degree-Of-Freedom (6-DOF) model. The simulation results shows that EKF gives a very good estimation of the states and it is working well with ODI. The resultant trajectories are very similar to those obtained by perfect state feedback using ODI only.

Nonlinear structural dynamical system identification using adaptive particle filters

The problem of identifying parameters of nonlinear vibrating systems using spatially incomplete, noisy, time-domain measurements is considered. The problem is formulated within the framework of dynamic state estimation formalisms that employ particle filters. The parameters of the system, which are to be identified, are treated as a set of random variables with finite number of discrete states. The study develops a procedure that combines a bank of self-learning particle filters with a global iteration strategy to estimate the probability distribution of the system parameters to be identified. Individual particle filters are based on the sequential importance sampling filter algorithm that is readily available in the existing literature. The paper develops the requisite recursive formulary for evaluating the evolution of weights associated with system parameter states. The correctness of the formulations developed is demonstrated first by applying the proposed procedure to a few linear vibrating systems for which an alternative solution using adaptive Kalman filter method is possible. Subsequently, illustrative examples on three nonlinear vibrating systems, using synthetic vibration data, are presented to reveal the correct functioning of the method. (c) 2007 Elsevier Ltd. All rights reserved.

Multi-Tone Testing of Linear and Nonlinear Analog Circuits using Polynomial Coefficients

A method of testing for parametric faults of analog circuits based on a polynomial representation of fault-free function of the circuit is presented. The response of the circuit under test (CUT) is estimated as a polynomial in the applied input voltage at relevant frequencies in addition to DC. Classification or Cur is based on a comparison of the estimated polynomial coefficients with those of the fault free circuit. This testing method requires no design for test hardware as might be added to the circuit fly some other methods. The proposed method is illustrated for a benchmark elliptic filter. It is shown to uncover several parametric faults causing deviations as small as 5% from the nominal values.

Towards the Use of Radar Winds in Numerical Weather Prediction

Numerical weather prediction (NWP) models provide the basis for weather forecasting by simulating the evolution of the atmospheric state. A good forecast requires that the initial state of the atmosphere is known accurately, and that the NWP model is a realistic representation of the atmosphere. Data assimilation methods are used to produce initial conditions for NWP models. The NWP model background field, typically a short-range forecast, is updated with observations in a statistically optimal way. The objective in this thesis has been to develope methods in order to allow data assimilation of Doppler radar radial wind observations. The work has been carried out in the High Resolution Limited Area Model (HIRLAM) 3-dimensional variational data assimilation framework. Observation modelling is a key element in exploiting indirect observations of the model variables. In the radar radial wind observation modelling, the vertical model wind profile is interpolated to the observation location, and the projection of the model wind vector on the radar pulse path is calculated. The vertical broadening of the radar pulse volume, and the bending of the radar pulse path due to atmospheric conditions are taken into account. Radar radial wind observations are modelled within observation errors which consist of instrumental, modelling, and representativeness errors. Systematic and random modelling errors can be minimized by accurate observation modelling. The impact of the random part of the instrumental and representativeness errors can be decreased by calculating spatial averages from the raw observations. Model experiments indicate that the spatial averaging clearly improves the fit of the radial wind observations to the model in terms of observation minus model background (OmB) standard deviation. Monitoring the quality of the observations is an important aspect, especially when a new observation type is introduced into a data assimilation system. Calculating the bias for radial wind observations in a conventional way can result in zero even in case there are systematic differences in the wind speed and/or direction. A bias estimation method designed for this observation type is introduced in the thesis. Doppler radar radial wind observation modelling, together with the bias estimation method, enables the exploitation of the radial wind observations also for NWP model validation. The one-month model experiments performed with the HIRLAM model versions differing only in a surface stress parameterization detail indicate that the use of radar wind observations in NWP model validation is very beneficial.

Exploiting ground-based measurements of the Global Positioning System for numerical weather prediction

Data assimilation provides an initial atmospheric state, called the analysis, for Numerical Weather Prediction (NWP). This analysis consists of pressure, temperature, wind, and humidity on a three-dimensional NWP model grid. Data assimilation blends meteorological observations with the NWP model in a statistically optimal way. The objective of this thesis is to describe methodological development carried out in order to allow data assimilation of ground-based measurements of the Global Positioning System (GPS) into the High Resolution Limited Area Model (HIRLAM) NWP system. Geodetic processing produces observations of tropospheric delay. These observations can be processed either for vertical columns at each GPS receiver station, or for the individual propagation paths of the microwave signals. These alternative processing methods result in Zenith Total Delay (ZTD) and Slant Delay (SD) observations, respectively. ZTD and SD observations are of use in the analysis of atmospheric humidity. A method is introduced for estimation of the horizontal error covariance of ZTD observations. The method makes use of observation minus model background (OmB) sequences of ZTD and conventional observations. It is demonstrated that the ZTD observation error covariance is relatively large in station separations shorter than 200 km, but non-zero covariances also appear at considerably larger station separations. The relatively low density of radiosonde observing stations limits the ability of the proposed estimation method to resolve the shortest length-scales of error covariance. SD observations are shown to contain a statistically significant signal on the asymmetry of the atmospheric humidity field. However, the asymmetric component of SD is found to be nearly always smaller than the standard deviation of the SD observation error. SD observation modelling is described in detail, and other issues relating to SD data assimilation are also discussed. These include the determination of error statistics, the tuning of observation quality control and allowing the taking into account of local observation error correlation. The experiments made show that the data assimilation system is able to retrieve the asymmetric information content of hypothetical SD observations at a single receiver station. Moreover, the impact of real SD observations on humidity analysis is comparable to that of other observing systems.

On the behaviour of some physical parameterization methods in high-resolution numerical weather prediction models

Modern-day weather forecasting is highly dependent on Numerical Weather Prediction (NWP) models as the main data source. The evolving state of the atmosphere with time can be numerically predicted by solving a set of hydrodynamic equations, if the initial state is known. However, such a modelling approach always contains approximations that by and large depend on the purpose of use and resolution of the models. Present-day NWP systems operate with horizontal model resolutions in the range from about 40 km to 10 km. Recently, the aim has been to reach operationally to scales of 1 4 km. This requires less approximations in the model equations, more complex treatment of physical processes and, furthermore, more computing power. This thesis concentrates on the physical parameterization methods used in high-resolution NWP models. The main emphasis is on the validation of the grid-size-dependent convection parameterization in the High Resolution Limited Area Model (HIRLAM) and on a comprehensive intercomparison of radiative-flux parameterizations. In addition, the problems related to wind prediction near the coastline are addressed with high-resolution meso-scale models. The grid-size-dependent convection parameterization is clearly beneficial for NWP models operating with a dense grid. Results show that the current convection scheme in HIRLAM is still applicable down to a 5.6 km grid size. However, with further improved model resolution, the tendency of the model to overestimate strong precipitation intensities increases in all the experiment runs. For the clear-sky longwave radiation parameterization, schemes used in NWP-models provide much better results in comparison with simple empirical schemes. On the other hand, for the shortwave part of the spectrum, the empirical schemes are more competitive for producing fairly accurate surface fluxes. Overall, even the complex radiation parameterization schemes used in NWP-models seem to be slightly too transparent for both long- and shortwave radiation in clear-sky conditions. For cloudy conditions, simple cloud correction functions are tested. In case of longwave radiation, the empirical cloud correction methods provide rather accurate results, whereas for shortwave radiation the benefit is only marginal. Idealised high-resolution two-dimensional meso-scale model experiments suggest that the reason for the observed formation of the afternoon low level jet (LLJ) over the Gulf of Finland is an inertial oscillation mechanism, when the large-scale flow is from the south-east or west directions. The LLJ is further enhanced by the sea-breeze circulation. A three-dimensional HIRLAM experiment, with a 7.7 km grid size, is able to generate a similar LLJ flow structure as suggested by the 2D-experiments and observations. It is also pointed out that improved model resolution does not necessary lead to better wind forecasts in the statistical sense. In nested systems, the quality of the large-scale host model is really important, especially if the inner meso-scale model domain is small.

Prediction of flame liftoff height of diffusion/partially premixed jet flames and modeling of mild combustion burners

In this article, a new flame extinction model based on the k/epsilon turbulence time scale concept is proposed to predict the flame liftoff heights over a wide range of coflow temperature and O-2 mass fraction of the coflow. The flame is assumed to be quenched, when the fluid time scale is less than the chemical time scale ( Da < 1). The chemical time scale is derived as a function of temperature, oxidizer mass fraction, fuel dilution, velocity of the jet and fuel type. The present extinction model has been tested for a variety of conditions: ( a) ambient coflow conditions ( 1 atm and 300 K) for propane, methane and hydrogen jet flames, ( b) highly preheated coflow, and ( c) high temperature and low oxidizer concentration coflow. Predicted flame liftoff heights of jet diffusion and partially premixed flames are in excellent agreement with the experimental data for all the simulated conditions and fuels. It is observed that flame stabilization occurs at a point near the stoichiometric mixture fraction surface, where the local flow velocity is equal to the local flame propagation speed. The present method is used to determine the chemical time scale for the conditions existing in the mild/ flameless combustion burners investigated by the authors earlier. This model has successfully predicted the initial premixing of the fuel with combustion products before the combustion reaction initiates. It has been inferred from these numerical simulations that fuel injection is followed by intense premixing with hot combustion products in the primary zone and combustion reaction follows further downstream. Reaction rate contours suggest that reaction takes place over a large volume and the magnitude of the combustion reaction is lower compared to the conventional combustion mode. The appearance of attached flames in the mild combustion burners at low thermal inputs is also predicted, which is due to lower average jet velocity and larger residence times in the near injection zone.

Prediction of fatigue strength in plain and reinforced concrete beams

A fatigue crack propagation model for concrete is proposed based on the concepts of fracture mechanics. This model takes into account the loading history, frequency of applied load, and size, effect parameters. Using this model, a method is described based on linear elastic fracture mechanics to assess the residual strength of cracked plain and reinforced concrete (RC) beams. This could be used to predict the residual strength (load carrying capacity) of cracked or damaged plain and reinforced concrete beams at a given level of damage. It has been seen that the fatigue crack propagation rate increases as. the size of plain concrete, beam increases indicating an increase in brittleness. In reinforced concrete (RC) beams, the fracture process becomes stable only when the beam is sufficiently reinforced.

Studies on orographic effects in a numerical weather prediction model

Numerical models, used for atmospheric research, weather prediction and climate simulation, describe the state of the atmosphere over the heterogeneous surface of the Earth. Several fundamental properties of atmospheric models depend on orography, i.e. on the average elevation of land over a model area. The higher is the models' resolution, the more the details of orography directly influence the simulated atmospheric processes. This sets new requirements for the accuracy of the model formulations with respect to the spatially varying orography. Orography is always averaged, representing the surface elevation within the horizontal resolution of the model. In order to remove the smallest scales and steepest slopes, the continuous spectrum of orography is normally filtered (truncated) even more, typically beyond a few gridlengths of the model. This means, that in the numerical weather prediction (NWP) models, there will always be subgridscale orography effects, which cannot be explicitly resolved by numerical integration of the basic equations, but require parametrization. In the subgrid-scale, different physical processes contribute in different scales. The parametrized processes interact with the resolved-scale processes and with each other. This study contributes to building of a consistent, scale-dependent system of orography-related parametrizations for the High Resolution Limited Area Model (HIRLAM). The system comprises schemes for handling the effects of mesoscale (MSO) and small-scale (SSO) orographic effects on the simulated flow and a scheme of orographic effects on the surface-level radiation fluxes. Representation of orography, scale-dependencies of the simulated processes and interactions between the parametrized and resolved processes are discussed. From the high-resolution digital elevation data, orographic parameters are derived for both momentum and radiation flux parametrizations. Tools for diagnostics and validation are developed and presented. The parametrization schemes applied, developed and validated in this study, are currently being implemented into the reference version of HIRLAM.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Diagnostic Tests Based on Quantile Residuals for Nonlinear Time Series Models

This thesis studies quantile residuals and uses different methodologies to develop test statistics that are applicable in evaluating linear and nonlinear time series models based on continuous distributions. Models based on mixtures of distributions are of special interest because it turns out that for those models traditional residuals, often referred to as Pearson's residuals, are not appropriate. As such models have become more and more popular in practice, especially with financial time series data there is a need for reliable diagnostic tools that can be used to evaluate them. The aim of the thesis is to show how such diagnostic tools can be obtained and used in model evaluation. The quantile residuals considered here are defined in such a way that, when the model is correctly specified and its parameters are consistently estimated, they are approximately independent with standard normal distribution. All the tests derived in the thesis are pure significance type tests and are theoretically sound in that they properly take the uncertainty caused by parameter estimation into account. -- In Chapter 2 a general framework based on the likelihood function and smooth functions of univariate quantile residuals is derived that can be used to obtain misspecification tests for various purposes. Three easy-to-use tests aimed at detecting non-normality, autocorrelation, and conditional heteroscedasticity in quantile residuals are formulated. It also turns out that these tests can be interpreted as Lagrange Multiplier or score tests so that they are asymptotically optimal against local alternatives. Chapter 3 extends the concept of quantile residuals to multivariate models. The framework of Chapter 2 is generalized and tests aimed at detecting non-normality, serial correlation, and conditional heteroscedasticity in multivariate quantile residuals are derived based on it. Score test interpretations are obtained for the serial correlation and conditional heteroscedasticity tests and in a rather restricted special case for the normality test. In Chapter 4 the tests are constructed using the empirical distribution function of quantile residuals. So-called Khmaladze s martingale transformation is applied in order to eliminate the uncertainty caused by parameter estimation. Various test statistics are considered so that critical bounds for histogram type plots as well as Quantile-Quantile and Probability-Probability type plots of quantile residuals are obtained. Chapters 2, 3, and 4 contain simulations and empirical examples which illustrate the finite sample size and power properties of the derived tests and also how the tests and related graphical tools based on residuals are applied in practice.

Prediction of estrus cyclicity in Asian elephants (Elephas maximus) through estimation of fecal progesterone metabolite: development of an enzyme-linked immuno-sorbent assay

Asian elephants (Dephas maximus), prominent ``flagship species'', arelisted under the category of endangered species (EN - A2c, ver. 3.1, IUCN Red List 2009) and there is a need for their conservation This requires understanding demographic and reproductive dynamics of the species. Monitoring reproductive status of any species is traditionally being carried out through invasive blood sampling and this is restrictive for large animals such as wild or semi-captive elephants due to legal. ethical, and practical reasons Hence. there is a need for a non-invasive technique to assess reproductive cyclicity profiles of elephants. which will help in the species' conservation strategies In this study. we developed an indirect competitive enzyme linked immuno-sorbent assay (ELISA) to estimate the concentration of one of the progesterone-metabolites i.e, allopregnanolone (5 alpha-P-3OH) in fecal samples of As elephants We validated the assay which had a sensitivity of 0.25 mu M at 90% binding with an EC50 value of 1 37 mu M Using female elephants. kept under semi-captive conditions in the forest camps of Mudumalar Wildlife Sanctuary, Tamil Nadu and Bandipur National Park, Karnataka, India. we measured fecal progesterone-metabolite (5 alpha-P-3OH) concentrations in six an and showed their clear correlation with those of scrum progesterone measured by a standard radio-immuno assay. Statistical analyses using a Linear Mixed Effect model showed a positive correlation (P < 0 1) between the profiles of fecal 5 alpha-P-3OH (range 0 5-10 mu g/g) and serum progesterone (range: 0 1-1 8 ng/mL) Therefore, our studies show, for the first time, that the fecal progesterone-metabolite assay could be exploited to predict estrus cyclicity and to potentially assess the reproductive status of captive and free-ranging female Asian elephants, thereby helping to plan their breeding strategy (C) 2010 Elsevier Inc.All rights reserved.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.