Singular Perturbations and Time-Scale Methods in Control Theory: Survey 1976-1982

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / N00014-79-C-0424U.S. Air Force / AFOSR 78-363

Control Strategies for Complex Systems for Use in Aerospace Avionics

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryAir Force Office of Scientific Research (AFSC) / AF-AFOSR 78-363

Health Monitoring of Nonlinear Systems with Application to Gas Turbine Engines

Health monitoring and prognosis of nonlinear systems is mainly concerned with system health tracking and its evolution prediction to future time horizons. Estimation and prediction schemes constitute as principal components of any health monitoring framework. In this thesis, the main focus is on development of novel health monitoring techniques for nonlinear dynamical systems by utilizing model-based and hybrid prognosis and health monitoring approaches. First, given the fact that particle filters (PF) are known as a powerful tool for performing state and parameter estimation of nonlinear dynamical systems, a novel dual estimation methodology is developed for both time-varying parameters and states of a nonlinear stochastic system based on the prediction error (PE) concept and the particle filtering scheme. Estimation of system parameters along with the states generate an updated model that can be used for a long-term prediction problem. Next, an improved particle filtering-based methodology is developed to address the prediction step within the developed health monitoring framework. In this method, an observation forecasting scheme is developed to extend the system observation profiles (as time-series) to future time horizons. Particles are then propagated to future time instants according to a resampling algorithm in the prediction step. The uncertainty in the long-term prediction of the system states and parameters are managed by utilizing dynamic linear models (DLM) for development of an observation forecasting scheme. A novel hybrid architecture is then proposed to develop prognosis and health monitoring methodologies for nonlinear systems by integration of model-based and computationally intelligent-based techniques. Our proposed hybrid health monitoring methodology is constructed based on a framework that is not dependent on the structure of the neural network model utilized in the implementation of the observation forecasting scheme. Moreover, changing the neural network model structure in this framework does not significantly affect the prediction accuracy of the entire health prediction algorithm. Finally, a method for formulation of health monitoring problems of dynamical systems through a two-time scale decomposition is introduced. For this methodology the system dynamical equations as well as the affected damage model, are investigated in the two-time scale system health estimation and prediction steps. A two-time scale filtering approach is developed based on the ensemble Kalman filtering (EnKF) methodology by taking advantage of the model reduction concept. The performance of the proposed two-time scale ensemble Kalman filters is shown to be more accurate and less computationally intensive as compared to the well-known particle filtering approach for this class of nonlinear systems. All of our developed methods have been applied for health monitoring and prognosis of a gas turbine engine when it is affected by various degradation damages. Extensive comparative studies are also conducted to validate and demonstrate the advantages and capabilities of our proposed frameworks and methodologies

Advancements in mesoscale ensemble prediction strategies: Application to Mediterranean high-impact weather

[cat] La predictibilitat d'esdeveniments d'alt impacte a la regi o Mediterr ania ha millorat substancialment al llarg de les darreres d ecades. No obstant aix o, una representaci o precisa d'aspectes dels sistemes convectius rellevants per la societat, tals com el moment en qu e es produeixen, i la seva localitzaci o i intensitat encara suposen un repte. Aquestes febleses de la predicci o a escala convectiva provenen d'imprecisions a l'estimaci o de l'estat atmosf eric inicial, la formulaci o de processos f sics rellevants i la natura ca otica dels sistema associada a la seva no linealitat. En el marc probabil stic imposat per les incerteses intr nseques implicades en la predicci o num erica del temps, l'entitat matem atica que quanti ca la incertesa en l'estat atmosf eric es la funci o densitat de probabilitat. Malgrat aix o, el c alcul de la seva evoluci o temporal es inviable per situacions realistes amb els recursos computacionals disponibles actualment. La modesta aproximaci o habitual per estimar aquesta evoluci o es l' us d'un discret i petit nombre de mostres de l'estat del sistema, que es coneix com a predicci o per conjunts (ensemble forecasting). L'objectiu general d'aquesta Tesi es entendre millor els l mits de la predictibilitat i contribuir a una millora de la predicci o de temps sever a la regi o Mediterr ania. En primer lloc, s'avalua l'evoluci o temporal de les funcions densitat de probabilitat per sistemes de baixa complexitat amb un cert grau de realisme adoptant el formalisme de Liouville. En segon lloc, es dissenya una estrat egia de mostreig per crear pertorbacions a les condicions inicials per abastos de predicci o curts (24-36 h). La t ecnica es basa en el m etode de breeding, que utilitza la din amica completa no lineal per identi car modes de creixement r apid. La modi caci o proposada est a dirigida a ajustar l'escala de les pertorbacions per tal de cobrir l'ample rang d'escales rellevants per la predicci o de curt abast. En tercer lloc, s'investiga el potencial de varis m etodes per tenir en compte la incertesa en el model per a un episodi recent de precipitacions intenses i inundacions que va oc orrer al llarg de la costa Mediterr ania espanyola (12-13 setembre de 2019). S'avaluen m ultiples estrat egies estoc astiques en front l'aproximaci o ordin aria de multif sica en termes de diversitat i habilitat de l'ensemble. Les t ecniques considerades inclouen pertorbacions estoc astiques a les tend encies f siques i pertorbacions a par ametres in uents de l'esquema de microf sica. Finalment, aquestes estrat egies de generaci o d'ensembles s'utilitzen com a for cament meteorol ogic per a un model hidrol ogic per tal d'investigar la predictibilitat 21 22 CONTENTS hidrometeorol ogica de l'episodi del 12-13 setembre de 2019. Les t ecniques desenvolupades, juntament amb l'assimilaci o de dades mitjan cant Ensemble Kalman Filter es comparen amb altres estrat egies populars, tals com el downscaling d'un model global i l'aproximaci o de multif sica. Els resultats d'aquesta Tesi s on rellevants des d'una perspectiva te orica, ja que la soluci o de l'equaci o de Liouville revela estructures complexes per la funci o densitat de probabilitat que podrien comprometre les hip otesis de compacitat i suavitat assumides per la majoria d'eines d'interpretaci o i post proc es d'ensembles. Per altra banda, les estrat egies de generaci o d'ensembles desenvolupades mostren potencial per millorar la predicci o d'esdeveniments d'alt impacte, que es demostra per una major diversitat i habilitat dels ensembles comparades amb les estrat egies de refer encia. Aquests resultats prometedors posen les bases per un sistema avan cat d'alertes a la regi o Mediterr ania per encarar els esdeveniments de temps sever.[spa] La predictibilidad de eventos de alto impacto en la regi on Mediterr anea ha mejorado sustancialmente a lo largo de las ultimas d ecadas. No obstante, una representaci on precisa de aspectos relevantes de los sistemas convectivos relevantes para la sociedad, como el momento en el que se producen, su localizaci on e intensidad a un suponen un reto. Estas debilidades de la predicci on a escala convectiva provienen de imprecisiones en la estimaci on del estado atmosf erico inicial, la formulaci on de los procesos f sicos relevantes y la naturaleza ca otica del sistema asociada a su no linealidad. En el marco probabilista impuesto por las incertidumbres intr nsecas implicadas en la predicci on num erica del tiempo, la entidad matem atica que cuanti ca la incertidumbre en el estado atmosf erico inicial es la funci on densidad de probabilidad. Sin embargo, el c alculo de su evoluci on temporal es inviable para situaciones realistas con los recursos computacionales disponibles actualmente. La modesta aproximaci on habitual para estimar esta evoluci on en el uso de un discreto y peque~no n umero de muestras del estado del sistema, lo que se conoce como predicci on por conjuntos (ensemble forecasting). El objetivo general de esta Tesis es entender mejor los l mites de la predictibilidad y contribuir a una mejora de la predicci on del tiempo severo en la regi on Mediterr anea. En primer lugar, se eval ua la evoluci on temporal de las funciones densidad de probabilidad para sistemas de baja complejidad con un cierto grado de realismo adoptando el formalismo te orico de Liouville. En segundo lugar, se dise~na una estrategia de muestreo para crear perturbaciones en les condiciones iniciales para alcances de predicci on cortos (24-36 h). La t ecnica se basa en el m etodo de breeding, que utiliza la din amica completa no lineal para identi car modos de crecimiento r apido. La modi caci on propuesta est a dirigida a ajustar la escala de las perturbaciones para cubrir el amplio rango de escalas relevantes para la predicci on de corto alcance. En tercer lugar, se investiga el potencial de varios m etodos para tener en cuenta la incertidumbre en el modelo para un episodio reciente de precipitaciones intensas e inundaciones que ocurri o a lo largo de la costa Mediterr anea espa~nola (12-13 de septiembre de 2019). Se eval uan m ultiples estrategias estoc asticas frente a la aproximaci on ordinaria de multif sica en t erminos de diversidad y habilidad del ensemble. Las t ecnicas consideradas incluyen perturbaciones estoc asticas en las tendencias f sicas y perturbaciones en par ametros in uyentes del esquema de microf sica. Finalmente, estas estrategias de generaci on de ensembles se usan como forzamiento meteorol ogico para un modelo hidrol ogico con el n de investigar la predictibilidad hidrometeorol ogica del episodio del 12-13 de septiembre de 2019. Las t ecnicas desarrolladas, junto a la asimilaci on de datos mediante Ensemble Kalman Filter se comparan con otras estrategias populares, como el dowscaling de un modelo global y la aproximaci on de multif sica. Los resultados de esta Tesis son relevantes desde una perspectiva te orica, ya que la soluci on de la ecuaci on de Liouville revela estructuras complejas para la funci on densidad de probabilidad que podr an comprometer las hip otesis de compacidad y suavidad asumidas por la mayor a de herramientas de interpretaci on y pos proceso de ensembles. Por otro lado, las estrategias de generaci on de ensembles desarrolladas muestran potencial para mejorar la predicci on de eventos de alto impacto, que se demuestra por una mayor diversidad y habilidad de los ensembles comparadas con las estrategias de referencia. Estos resultados prometedores sientan las bases para un sistema avanzado de alertas en la regi on Mediterr anea para afrontar los eventos de tiempo severo.[eng] The predictability of meteorological high-impact events in the Mediterranean region has substantially improved over the last decades. Nevertheless, a precise representation of socially relevant aspects of convective systems, such as their timing, location, and intensity is still challenging. These weaknesses of convective-scale forecasting stem from inaccuracies in the estimation of the atmospheric initial state, formulation of relevant physical processes, and the chaotic nature of the system associated with its nonlinearity. In the probabilistic framework imposed by the intrinsic uncertainties involved in numerical weather prediction, the mathematical entity that quanti es the uncertainty in the atmospheric state is the probability density function. However, the computation of its time evolution is unfeasible for realistic situations with the current available computational resources. The usual modest approach to estimate this evolution is the use of a discrete and small number of samples of the state of the system, which is known as ensemble forecasting. The general aim of this Thesis is to better understand the predictability limits and contribute towards the improvement of severe weather forecasting in the Mediterranean region. Firstly, the time evolution of probability density functions for low complexity systems with a certain degree of realism is evaluated by adopting the Liouville formalism. Secondly, a sampling strategy to create initial condition perturbations for the short-range (24-36 h) is designed. The technique is based on the breeding method, which uses the full nonlinear dynamics to identify fast-growing modes. The proposed modi cation is aimed at tailoring the scale of the perturbations in order to cover the wide range of scales relevant for short-range forecasting. Thirdly, the potential of several methods to account for model uncertainty is investigated for a recent heavy precipitation and ash ood episode occurred along the Spanish Mediterranean coast (12-13 September 2019). Multiple stochastic strategies are evaluated against the ordinary multiphysics approach in terms of ensemble diversity and skill. The considered techniques include stochastically perturbed physics tendencies and perturbations to in uential parameters within the microphysics scheme. Finally, these ensemble generation strategies are used as the meteorological forcing for a hydrological model in order to investigate the hydrometeorological predictability of the 12-13 September 2019 episode. The developed techniques, along with data assimilation by means of Ensemble Kalman Filter are compared to other popular strategies, such as the downscaling from a global model and the multiphysics approach. The results of this Thesis are relevant from a theoretical perspective, as the solution of the Liouville equation reveals complex structures for the probability density function that could compromise the hypothesis of compactness and smoothness assumed by most current ensemble interpretation and postprocessing tools. Conversely, the ensemble generation strategies developed show potential to improve the forecasting of high-impact events, proven by higher ensemble diversity and skill compared to the benchmark strategies. These encouraging results lay the foundations for an advanced warning system in the Mediterranean region to deal with severe weather events

Survey on Flight Control Technology for Large-Scale Helicopter

A literature review of flight control technology is presented for large-scale helicopter. Challenges of large-scale helicopter flight control system (FCS) design are illustrated. Following this, various flight control methodologies are described with respect to their engineering implementation and theoretical developments, whose advantages and disadvantages are also analyzed. Then, the challenging research issues on flight control technology are identified, and future directions are highlighted

Nonlinear Dimensionality Reduction Methods in Climate Data Analysis

Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be appropriate for the analysis of data arising from nonlinear processes occurring in the climate system. Numerous techniques for nonlinear dimensionality reduction have been developed recently that may provide a potentially useful tool for the identification of low-dimensional manifolds in climate data sets arising from nonlinear dynamics. In this thesis I apply three such techniques to the study of El Nino/Southern Oscillation variability in tropical Pacific sea surface temperatures and thermocline depth, comparing observational data with simulations from coupled atmosphere-ocean general circulation models from the CMIP3 multi-model ensemble. The three methods used here are a nonlinear principal component analysis (NLPCA) approach based on neural networks, the Isomap isometric mapping algorithm, and Hessian locally linear embedding. I use these three methods to examine El Nino variability in the different data sets and assess the suitability of these nonlinear dimensionality reduction approaches for climate data analysis. I conclude that although, for the application presented here, analysis using NLPCA, Isomap and Hessian locally linear embedding does not provide additional information beyond that already provided by principal component analysis, these methods are effective tools for exploratory data analysis.Comment: 273 pages, 76 figures; University of Bristol Ph.D. thesis; version with high-resolution figures available from http://www.skybluetrades.net/thesis/ian-ross-thesis.pdf (52Mb download

CONFORMATIONAL DYNAMICS OF DNA AND PROTEIN-DNA COMPLEXES AT SINGLE-STRANDED-DOUBLE-STRANDED DNA JUNCTIONS

Most biological systems, particularly protein-DNA complexes, leverage a dynamic evolution of their structure to perform a myriad of functions within the context of the cell. Decades of detailed biophysical research have established that the intricacies of such systems stem heavily from their dynamic evolution, abandoning the previous notion of a purely static ‘structure-function’ relationship. This dissertation introduces a new polarization-sensitive methodology for studying the dynamic evolution of local conformation in single-molecules of dsDNA containing an i(Cy3)2 dimer. The methodology developed during this dissertation is applied to DNA under a variety of experimental conditions as well as protein-DNA complexes. A massively parallel computational pipeline was developed in the course of this work to aid the optimization of kinetic network models, which forms the basis for all current analyses of single-molecule data in the Marcus and von Hippel lab. The primary discovery of this work is the persistence of four relevant conformational macrostates in DNA only systems and five relevant conformational macrostates in the protein-DNA systems examined. The thermodynamic and mechanical stability of these systems is analyzed in detail and structural mechanisms are proposed to merge the observed dynamics with hypothesized local conformations during the dynamic evolution of these ubiquitous biological systems

Technology for large space systems: A bibliography with indexes (supplement 16)

This bibliography lists 673 reports, articles and other documents introduced into the NASA scientific and technical information system between July 1, 1986 and December 31, 1986. Its purpose is to provide helpful information to the researcher, manager, and designer in technology development and mission design according to system interactive analysis and design, structural and thermal analysis and design, structural concepts and control systems, electronics, advanced materials, assembly concepts, propulsion, and solar power satellite systems

Mathematical Modelling of Stem Cell Dynamics during Post-embryonic Organ Growth

The current work is devoted to the mathematical modelling of the development of fish respiratory organs, called gills or branchiae. The model organism chosen for the task is the Japanese rice fish (Oryzias latipes), more colloquially known as medaka. Their gills are analysed in the attempt to answer three main developmental questions via mathematical modelling, with possible applications beyond the scope of this thesis. Firstly, how many stem cells are needed to build the organ? What kind of heterogeneities exist among these stem cells? And, finally, what properties and relations with each-other do these stem cells have, that give the organ its shape? Relying on experimental data from our collaborators in the group of Prof. Lazaro Centanin, Centre for Organismal Studies, Heidelberg University, we use a variety of methods to study the aforementioned aspects. These methods were selected, adapted and developed based on the goal of each project and on the available data. Thus, a combination of stochastic and deterministic techniques are employed throughout the thesis, including Gillespie-type simulations, Markov chains theory and compartmental models. The study of stem cell numbers and heterogeneities is approached via stochastic simulations extended from the algorithm of Gillespie, and further improved by Markov chains methods. Results suggest that not only very few stem cells are sufficient to build and maintain the organ but, more importantly, these stem cells are heterogeneous in their division behaviour. In particular, they rely on alternating activation and quiescence phases, such that once a stem cell has divided, it becomes activated and divides multiple times before allowing another one to take the lead. For the study of growth and shape of gills, multiple deterministic models based on different assumptions and investigating various hypotheses have been developed. All these models have a compartmental structure, with increasing number of compartments governed by indicator functions which, in turn, depend on explicit or implicit algebraic equations. For each model, the existence, uniqueness and non-negativity of solutions are proved, the analytical solutions are found and their regularity is discussed. The models are compared based on their ability to reproduce part of the data, and the best one is selected. The chosen model is then applied to further data and speculations on hypotheses supporting the model are made. Results suggest that the main stem cell types, responsible for growing the organ, slow down their proliferation in time, either due to ageing or to the lack of sufficient nutrients. The main results and strengths of this thesis consist of the high variety of models developed and methods employed, their capability to answer important biological questions and, even more, to uncover new insights on mechanisms previously unknown