Identification of time-varying systems using multiresolution wavelet models

Identification of linear and nonlinear time-varying systems is investigated and a new wavelet model identification algorithm is introduced. By expanding each time-varying coefficient using a multiresolution wavelet expansion, the time-varying problem is reduced to a time invariant problem and the identification reduces to regressor selection and parameter estimation. Several examples are included to illustrate the application of the new algorithm

Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario

A variety of methods is available to quantify uncertainties arising with\-in the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons. Usually, raw data from such storage sites can hardly be described by theoretical statistical distributions since only very limited data is available. Hence, exact information on distribution shapes for all uncertain parameters is very rare in realistic applications. We discuss and compare four different methods tested for data-driven uncertainty quantification based on a benchmark scenario of carbon dioxide storage. In the benchmark, for which we provide data and code, carbon dioxide is injected into a saline aquifer modeled by the nonlinear capillarity-free fractional flow formulation for two incompressible fluid phases, namely carbon dioxide and brine. To cover different aspects of uncertainty quantification, we incorporate various sources of uncertainty such as uncertainty of boundary conditions, of conceptual model definitions and of material properties. We consider recent versions of the following non-intrusive and intrusive uncertainty quantification methods: arbitary polynomial chaos, spatially adaptive sparse grids, kernel-based greedy interpolation and hybrid stochastic Galerkin. The performance of each approach is demonstrated assessing expectation value and standard deviation of the carbon dioxide saturation against a reference statistic based on Monte Carlo sampling. We compare the convergence of all methods reporting on accuracy with respect to the number of model runs and resolution. Finally we offer suggestions about the methods' advantages and disadvantages that can guide the modeler for uncertainty quantification in carbon dioxide storage and beyond

Finite dimensional nonlinear estimation in continuous and discrete time

Bibliography: p. 19-20.Caption title. "October 2, 1978."Supported in part by the DoD Joint Services Electronics Program through the Air Force Office of Scientific Research (AFSC) Contract F49620-77-C-0101 Air Force Office of Scientific Research Contract AFOSR 77-3281 National Science Foundation Grant ENG 76-11106Steven I. Marcus, Sanjoy K. Mitter, Daniel Ocone

Machine Learning and System Identification for Estimation in Physical Systems

In this thesis, we draw inspiration from both classical system identification and modern machine learning in order to solve estimation problems for real-world, physical systems. The main approach to estimation and learning adopted is optimization based. Concepts such as regularization will be utilized for encoding of prior knowledge and basis-function expansions will be used to add nonlinear modeling power while keeping data requirements practical.The thesis covers a wide range of applications, many inspired by applications within robotics, but also extending outside this already wide field.Usage of the proposed methods and algorithms are in many cases illustrated in the real-world applications that motivated the research.Topics covered include dynamics modeling and estimation, model-based reinforcement learning, spectral estimation, friction modeling and state estimation and calibration in robotic machining.In the work on modeling and identification of dynamics, we develop regularization strategies that allow us to incorporate prior domain knowledge into flexible, overparameterized models. We make use of classical control theory to gain insight into training and regularization while using tools from modern deep learning. A particular focus of the work is to allow use of modern methods in scenarios where gathering data is associated with a high cost.In the robotics-inspired parts of the thesis, we develop methods that are practically motivated and make sure that they are implementable also outside the research setting. We demonstrate this by performing experiments in realistic settings and providing open-source implementations of all proposed methods and algorithms

Novel methods to quantify aleatory and epistemic uncertainty in high speed networks

2017 Summer.Includes bibliographical references.With the sustained miniaturization of integrated circuits to sub-45 nm regime and the increasing packaging density, random process variations have been found to result in unpredictability in circuit performance. In existing literature, this unpredictability has been modeled by creating polynomial expansions of random variables. But the existing methods prove inefficient because as the number of random variables within a system increase, the time and computational cost increases in a near-polynomial fashion. In order to mitigate this poor scalability of conventional approaches, several techniques are presented, in this dissertation, to sparsify the polynomial expansion. The sparser polynomial expansion is created, by identifying the contribution of each random variable on the total response of the system. This sparsification is performed primarily using two different methods. It translates to immense savings, in the time required, and the memory cost of computing the expansion. One of the two methods presented is applied to aleatory variability problems while the second method is applied to problems involving epistemic uncertainty. The accuracy of the proposed approaches is validated through multiple numerical examples

Assessment of spontaneous cardiovascular oscillations in Parkinson's disease

Parkinson's disease (PD) has been reported to involve postganglionic sympathetic failure and a wide spectrum of autonomic dysfunctions including cardiovascular, sexual, bladder, gastrointestinal and sudo-motor abnormalities. While these symptoms may have a significant impact on daily activities, as well as quality of life, the evaluation of autonomic nervous system (ANS) dysfunctions relies on a large and expensive battery of autonomic tests only accessible in highly specialized laboratories. In this paper we aim to devise a comprehensive computational assessment of disease-related heartbeat dynamics based on instantaneous, time-varying estimates of spontaneous (resting state) cardiovascular oscillations in PD. To this end, we combine standard ANS-related heart rate variability (HRV) metrics with measures of instantaneous complexity (dominant Lyapunov exponent and entropy) and higher-order statistics (bispectra). Such measures are computed over 600-s recordings acquired at rest in 29 healthy subjects and 30 PD patients. The only significant group-wise differences were found in the variability of the dominant Lyapunov exponent. Also, the best PD vs. healthy controls classification performance (balanced accuracy: 73.47%) was achieved only when retaining the time-varying, non-stationary structure of the dynamical features, whereas classification performance dropped significantly (balanced accuracy: 61.91%) when excluding variability-related features. Additionally, both linear and nonlinear model features correlated with both clinical and neuropsychological assessments of the considered patient population. Our results demonstrate the added value and potential of instantaneous measures of heartbeat dynamics and its variability in characterizing PD-related disabilities in motor and cognitive domains