Efficient sensitivity analysis of chaotic systems and applications to control and data assimilation

Sensitivity analysis is indispensable for aeronautical engineering applications that require optimisation, such as flow control and aircraft design. The adjoint method is the standard approach for sensitivity analysis, but it cannot be used for chaotic systems. This is due to the high sensitivity of the system trajectory to input perturbations; a characteristic of many turbulent systems. Although the instantaneous outputs are sensitive to input perturbations, the sensitivities of time-averaged outputs are well-defined for uniformly hyperbolic systems, but existing methods to compute them cannot be used. Recently, a set of alternative approaches based on the shadowing property of dynamical systems was proposed to compute sensitivities. These approaches are computationally expensive, however. In this thesis, the Multiple Shooting Shadowing (MSS) [1] approach is used, and the main aim is to develop computational tools to allow for the implementation of MSS to large systems. The major contributor to the cost of MSS is the solution of a linear matrix system. The matrix has a large condition number, and this leads to very slow convergence rates for existing iterative solvers. A preconditioner was derived to suppress the condition number, thereby accelerating the convergence rate. It was demonstrated that for the chaotic 1D Kuramoto Sivashinsky equation (KSE), the rate of convergence was almost independent of the #DOF and the trajectory length. Most importantly, the developed solution method relies only on matrix-vector products. The adjoint version of the preconditioned MSS algorithm was then coupled with a gradient descent method to compute a feedback control matrix for the KSE. The adopted formulation allowed all matrix elements to be computed simultaneously. Within a single iteration, a stabilising matrix was computed. Comparisons with standard linear quadratic theory (LQR) showed remarkable similarities (but also some differences) in the computed feedback control kernels. A preconditioned data assimilation algorithm was then derived for state estimation purposes. The preconditioner was again shown to accelerate the rate of convergence significantly. Accurate state estimations were computed for the Lorenz system.Open Acces

Online Geometric Human Interaction Segmentation and Recognition

The goal of this work is the temporal localization and recognition of binary people interactions in video. Human-human interaction detection is one of the core problems in video analysis. It has many applications such as in video surveillance, video search and retrieval, human-computer interaction, and behavior analysis for safety and security. Despite the sizeable literature in the area of activity and action modeling and recognition, the vast majority of the approaches make the assumption that the beginning and the end of the video portion containing the action or the activity of interest is known. In other words, while a significant effort has been placed on the recognition, the spatial and temporal localization of activities, i.e. the detection problem, has received considerably less attention. Even more so, if the detection has to be made in an online fashion, as opposed to offline. The latter condition is imposed by almost the totality of the state-of-the-art, which makes it intrinsically unsuited for real-time processing. In this thesis, the problem of event localization and recognition is addressed in an online fashion. The main assumption is that an interaction, or an activity is modeled by a temporal sequence. One of the main challenges is the development of a modeling framework able to capture the complex variability of activities, described by high dimensional features. This is addressed by the combination of linear models with kernel methods. In particular, the parity space theory for detection, based on Euclidean geometry, is augmented to be able to work with kernels, through the use of geometric operators in Hilbert space. While this approach is general, here it is applied to the detection of human interactions. It is tested on a publicly available dataset and on a large and challenging, newly collected dataset. An extensive testing of the approach indicates that it sets a new state-of-the-art under several performance measures, and that it holds the promise to become an effective building block for the analysis in real-time of human behavior from video

Self-organizing nonlinear output (SONO): A neural network suitable for cloud patch-based rainfall estimation at small scales

Accurate measurement of rainfall distribution at various spatial and temporal scales is crucial for hydrological modeling and water resources management. In the literature of satellite rainfall estimation, many efforts have been made to calibrate a statistical relationship (including threshold, linear, or nonlinear) between cloud infrared (IR) brightness temperatures and surface rain rates (RR). In this study, an automated neural network for cloud patch-based rainfall estimation, entitled self-organizing nonlinear output (SONO) model, is developed to account for the high variability of cloud-rainfall processes at geostationary scales (i.e., 4 km and every 30 min). Instead of calibrating only one IR-RR function for all clouds the SONO classifies varied cloud patches into different clusters and then searches a nonlinear IR-RR mapping function for each cluster. This designed feature enables SONO to generate various rain rates at a given brightness temperature and variable rain/no-rain IR thresholds for different cloud types, which overcomes the one-to-one mapping limitation of a single statistical IR-RR function for the full spectrum of cloud-rainfall conditions. In addition, the computational and modeling strengths of neural network enable SONO to cope with the nonlinearity of cloud-rainfall relationships by fusing multisource data sets. Evaluated at various temporal and spatial scales, SONO shows improvements of estimation accuracy, both in rain intensity and in detection of rain/no-rain pixels. Further examination of the SONO adaptability demonstrates its potentiality as an operational satellite rainfall estimation system that uses the passive microwave rainfall observations from low-orbiting satellites to adjust the IR-based rainfall estimates at the resolution of geostationary satellites. Copyright 2005 by the American Geophysical Union