Data Science Methods for Analyzing Nanomaterial Images and Videos

A large amount of nanomaterial characterization data has been routinely collected by using electron microscopes and stored in image or video formats. A bottleneck in making effective use of the image/video data is the lack of the development of sophisticated data science methods capable of unlocking valuable material pertinent information buried in the raw data. To address this problem, the research of this dissertation begins with understanding the physical mechanisms behind the concerned process to determine why the generic methods fall short. Afterwards, it designs and improves image processing and statistical modeling tools to address the practical challenges. Specifically, this dissertation consists of two main tasks: extracting useful information from images or videos of nanomaterials captured by electron microscopes, and designing analytical methods for modeling/monitoring the dynamic growth of nanoparticles. In the first task, a two-pipeline framework is proposed to fuse two kinds of image information for nanoscale object detection that can accurately identify and measure nanoparticles in transmission electron microscope (TEM) images of high noise and low contrast. To handle the second task of analyzing nanoparticle growth, this dissertation develops dynamic nonparametric models for time-varying probability density functions (PDFs) estimation. Unlike simple statistics, a PDF contains fuller information about the nanoscale objects of interests. Characterizing the dynamic changes of the PDF as the nanoparticles grow into different sizes and morph into different shapes, the proposed nonparametric methods are capable of analyzing an in situ TEM video to delineate growth stages in a retrospective analysis, or tracking the nanoparticle growth process in a prospective analysis. The resulting analytic methods have applications in areas beyond the nanoparticle growth process such as the image-based process control tasks in additive manufacturing

Introduction to Dynamic Linear Models for Time Series Analysis

Dynamic linear models (DLM) offer a very generic framework to analyse time series data. Many classical time series models can be formulated as DLMs, including ARMA models and standard multiple linear regression models. The models can be seen as general regression models where the coefficients can vary in time. In addition, they allow for a state space representation and a formulation as hierarchical statistical models, which in turn is the key for efficient estimation by Kalman formulas and by Markov chain Monte Carlo (MCMC) methods. A dynamic linear model can handle non-stationary processes, missing values and non-uniform sampling as well as observations with varying accuracies. This chapter gives an introduction to DLM and shows how to build various useful models for analysing trends and other sources of variability in geodetic time series.Comment: A chapter submitted to a book with a proposed title: Geodetic Time Series Analysis and Applications, editors. J.-P. Montillet and M. Bo

Retrospective Cost Adaptive Control with Concurrent Closed-Loop Identification

Retrospective cost adaptive control (RCAC) is a discrete-time direct adaptive control algorithm for stabilization, command following, and disturbance rejection. RCAC is known to work on systems given minimal modeling information which is the leading numerator coefficient and any nonminimum-phase (NMP) zeros of the plant transfer function. This information is normally needed a priori and is key in the development of the filter, also known as the target model, within the retrospective performance variable. A novel approach to alleviate the need for prior modeling of both the leading coefficient of the plant transfer function as well as any NMP zeros is developed. The extension to the RCAC algorithm is the use of concurrent optimization of both the target model and the controller coefficients. Concurrent optimization of the target model and controller coefficients is a quadratic optimization problem in the target model and controller coefficients separately. However, this optimization problem is not convex as a joint function of both variables, and therefore nonconvex optimization methods are needed. Finally, insights within RCAC that include intercalated injection between the controller numerator and the denominator, unveil the workings of RCAC fitting a specific closed-loop transfer function to the target model. We exploit this interpretation by investigating several closed-loop identification architectures in order to extract this information for use in the target model.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138440/1/fsobolic_1.pd

Ecological non-linear state space model selection via adaptive particle Markov chain Monte Carlo (AdPMCMC)

We develop a novel advanced Particle Markov chain Monte Carlo algorithm that is capable of sampling from the posterior distribution of non-linear state space models for both the unobserved latent states and the unknown model parameters. We apply this novel methodology to five population growth models, including models with strong and weak Allee effects, and test if it can efficiently sample from the complex likelihood surface that is often associated with these models. Utilising real and also synthetically generated data sets we examine the extent to which observation noise and process error may frustrate efforts to choose between these models. Our novel algorithm involves an Adaptive Metropolis proposal combined with an SIR Particle MCMC algorithm (AdPMCMC). We show that the AdPMCMC algorithm samples complex, high-dimensional spaces efficiently, and is therefore superior to standard Gibbs or Metropolis Hastings algorithms that are known to converge very slowly when applied to the non-linear state space ecological models considered in this paper. Additionally, we show how the AdPMCMC algorithm can be used to recursively estimate the Bayesian Cram\'er-Rao Lower Bound of Tichavsk\'y (1998). We derive expressions for these Cram\'er-Rao Bounds and estimate them for the models considered. Our results demonstrate a number of important features of common population growth models, most notably their multi-modal posterior surfaces and dependence between the static and dynamic parameters. We conclude by sampling from the posterior distribution of each of the models, and use Bayes factors to highlight how observation noise significantly diminishes our ability to select among some of the models, particularly those that are designed to reproduce an Allee effect

A New Formulation of the Filter-Error Method for Aerodynamic Parameter Estimation in Turbulence

A new formulation of the filter-error method for estimating aerodynamic parameters in nonlinear aircraft dynamic models during turbulence was developed and demonstrated. The approach uses an estimate of the measurement noise covariance to identify the model parameters, their uncertainties, and the process noise covariance, in a relaxation method analogous to the output-error method. Prior information on the model parameters and uncertainties can be supplied, and a post-estimation correction to the uncertainty was included to account for colored residuals not considered in the theory. No tuning parameters, needing adjustment by the analyst, are used in the estimation. The method was demonstrated in simulation using the NASA Generic Transport Model, then applied to the subscale T-2 jet-engine transport aircraft flight. Modeling results in different levels of turbulence were compared with results from time-domain output error and frequency- domain equation error methods to demonstrate the effectiveness of the approach

Input and State Estimation for Discrete-Time Linear Systems with Application to Target Tracking and Fault Detection

This dissertation first presents a deterministic treatment of discrete-time input reconstruction and state estimation without assuming the existence of a full-rank Markov parameter. Algorithms based on the generalized inverse of a block-Toeplitz matrix are given for 1) input reconstruction in the case where the initial state is known; 2) state estimation in the case where the initial state is unknown, the system has no invariant zeros, and the input is unknown; and 3) input reconstruction and state estimation in the case where the initial state is unknown and the system has no invariant zeros. In all cases, the unknown input is an arbitrary deterministic or stochastic signal. In addition, the reconstruction/estimation algorithm is deadbeat, which means that, in the absence of sensor noise, exact input reconstruction and state estimation are achieved in a finite number of steps. Next, asymptotic input and state estimation for systems with invariant zeros is considered. Although this problem has been widely studied, existing techniques are confined to the case where the system is minimum phase. This dissertation presents retrospective cost input estimation (RCIE), which is based on retrospective cost optimization. It is shown that RCIE automatically develops an internal model of the unknown input. This internal model provides an asymptotic estimate of the unknown input regardless of the location of the zeros of the plant, including the case of nonminimum-phase dynamics. The input and state estimation method developed in this dissertation provides a novel approach to a longstanding problem in target tracking, namely, estimation of the inertial acceleration of a body using only position measurements. It turns out that, for this problem, the discretized kinematics have invariant zeros on the unit circle, and thus the dynamics is nonminimum-phase. Using optical position data for a UAV, RCIE estimates the inertial acceleration, which is modeled as an unknown input. The acceleration estimates are compared to IMU data from onboard sensors. Finally, based on exact kinematic models for input and state estimation, this dissertation presents a method for detecting sensor faults. A numerical investigation using the NASA Generic Transport Model shows that the method can detect stuck, bias, drift, and deadzone sensor faults. Furthermore, a laboratory experiment shows that RCIE can estimate the inertial acceleration (3-axis accelerometer measurements) and angular velocity (3-axis rate-gyro measurements) of a quadrotor using vision data; comparing these estimates to the actual accelerometer and rate-gyro measurements provide the means for assessing the health of the accelerometer and rate gyro.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145813/1/ansahmad_1.pd

New ultrasonic signal processing techniques for NDE applications

New ultrasonic signal processing techniques have been developed for nondestructive evaluation (NDE) applications. This dissertation has two parts. The first part is about the application of the wavelet transform to ultrasonic flaw detection. Wavelet transform is a newly developed signal analysis tool that handles time-localized signals such as an ultrasonic flaw signal quite well. A wavelet transform based signal processing technique has been developed which uses only partial knowledge of the flaw signal waveform that may be obtained from a reference experiment. The detection performance of the proposed technique is found to be comparable to that of the matched filter which requires exact knowledge of the flaw signal waveform and the noise autocorrelation function to obtain good detection performance. The proposed technique based on the wavelet transform can therefore be quite useful in situations where the flaw signal waveform is unknown or partially known. The detection performance of the proposed technique which was evaluated for hard-alpha detection in titanium samples using experimentally obtained grain noise data and simulated flaw data was very close to that of the matched filter;The second part of this dissertation describes a Kalman filter based deconvolution algorithm for ultrasonic signals and its application to material characterization and hard-alpha detection. The Kalman filter based deconvolution algorithm is based on state-space modeling of the ultrasonic measurement system. Since the Kalman filter can handle time-varying systems and non-stationary statistics quite naturally, it is better suited for such situations than the Wiener filter approach. A signal processing technique using Kalman filter based deconvolution algorithm has been developed and applied to characterize materials with different grain sizes and to detect inclusions from host material. The proposed method was tested using experimentally obtained ultrasonic data from pure titanium samples with different grain sizes. The results showed good detection performance for detecting inclusions larger that 4 mm

Extremum-Seeking Guidance and Conic-Sector-Based Control of Aerospace Systems

This dissertation studies guidance and control of aerospace systems. Guidance algorithms are used to determine desired trajectories of systems, and in particular, this dissertation examines constrained extremum-seeking guidance. This type of guidance is part of a class of algorithms that drives a system to the maximum or minimum of a performance function, where the exact relation between the function's input and output is unknown. This dissertation abstracts the problem of extremum-seeking to constrained matrix manifolds. Working with a constrained matrix manifold necessitates mathematics other than the familiar tools of linear systems. The performance function is optimized on the manifold by estimating a gradient using a Kalman filter, which can be modified to accommodate a wide variety of constraints and can filter measurement noise. A gradient-based optimization technique is then used to determine the extremum of the performance function. The developed algorithms are applied to aircraft and spacecraft. Control algorithms determine which system inputs are required to drive the systems outputs to follow the trajectory given by guidance. Aerospace systems are typically nonlinear, which makes control more challenging. One approach to control nonlinear systems is linear parameter varying (LPV) control, where well-established linear control techniques are extended to nonlinear systems. Although LPV control techniques work quite well, they require an LPV model of a system. This model is often an approximation of the real nonlinear system to be controlled, and any stability and performance guarantees that are derived using the system approximation are usually void on the real system. A solution to this problem can be found using the Passivity Theorem and the Conic Sector Theorem, two input-output stability theories, to synthesize LPV controllers. These controllers guarantee closed-loop stability even in the presence of system approximation. Several control techniques are derived and implemented in simulation and experimentation, where it is shown that these new controllers are robust to plant uncertainty.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143993/1/aexwalsh_1.pd