Design and analysis of dynamic compressive sensing in distribution grids

Doctor of PhilosophyDepartment of Electrical and Computer EngineeringBalasubramaniam NatarajanThe transition to a smart distribution grid is powered by enhanced sensing and advanced metering infrastructure that can provide situational awareness. However, aggregating data from spatially dispersed sensors/smart meters can present a significant challenge. Additionally, the lack of reliability in communication network used for aggregating this data, prevents its use for real time operations such as state estimation and control. With these challenges associated with measurement availability and accessibility, current distribution systems are typically unobservable. To cope with the unobservability issue, compressive sensing (CS) theory allows us to recover system state information from a small number of measurements provided the states of the distribution system exhibit sparsity. The spatio-temporal correlation of loads and/or rooftop photovoltaic (PV) generation results in sparsity of distribution system states. In this dissertation, we first validate this system sparsity property and exploit it to develop two (direct/indirect) voltage state estimation strategies for a three-phase unbalanced distribution network. Secondly, we focus on addressing the challenge of sparse signal recovery from limited measurements while incorporating their temporal dependence. Specifically, we implement two recursive dynamic CS approaches namely, streaming modified weighted-L1 CS and Kalman filtered CS that reconstruct a sparse signal using the current underdetermined measurements and the prior information about the sparse signal and its support set. Using practical distribution system power measurements as a case study, we quantify, for the first time, the performance improvement achievable with such recursive techniques relative to batch algorithms. CS based signal recovery efforts typically assume that a limited number of measurements are available. However, in practice, due to communication network impairments, there is no guarantee that even this limited set of information might be available at the time of processing at the fusion/control center. Therefore, for the first time, we investigate the impact of intermittent measurement availability and random delays on recursive dynamic CS. Specifically, we quantify the error dynamics in both sparse signal estimation and support set estimation for a modified Kalman filter-CS based strategy in the presence of measurement losses. Using input-to-state stability analysis, we provide an upper bound for the expected covariance of the estimation error for a given rate of information loss. Next, we develop a modified CS algorithm that leverages apriori knowledge of signal correlation to project delayed measurements to the current signal recovery instant. We derive a new result quantifying the impact of errors in the apriori correlation model on signal recovery error. Lastly, we study the robustness of CS based state estimation to uncertainty in distribution network topology knowledge. Topology identification is a challenging problem in distribution systems in general and especially, when there are limited number of available measurements. We tackle this problem by jointly estimating the states and network topology via an integrated mixed integer nonlinear program formulation. By developing convex relaxations of the original formulation as well Markovian models for dynamic topology transitions, we illustrate the superior performance achieved in both state estimation and in topology identification. In summary, this dissertation offers the first comprehensive treatment of dynamic CS in smart distribution grids and can serve as the foundation of numerous follow-on efforts related to networked state estimation and control

Vision-Aided Navigation for GPS-Denied Environments Using Landmark Feature Identification

In recent years, unmanned autonomous vehicles have been used in diverse applications because of their multifaceted capabilities. In most cases, the navigation systems for these vehicles are dependent on Global Positioning System (GPS) technology. Many applications of interest, however, entail operations in environments in which GPS is intermittent or completely denied. These applications include operations in complex urban or indoor environments as well as missions in adversarial environments where GPS might be denied using jamming technology. This thesis investigate the development of vision-aided navigation algorithms that utilize processed images from a monocular camera as an alternative to GPS. The vision-aided navigation approach explored in this thesis entails defining a set of inertial landmarks, the locations of which are known within the environment, and employing image processing algorithms to detect these landmarks in image frames collected from an onboard monocular camera. These vision-based landmark measurements effectively serve as surrogate GPS measurements that can be incorporated into a navigation filter. Several image processing algorithms were considered for landmark detection and this thesis focuses in particular on two approaches: the continuous adaptive mean shift (CAMSHIFT) algorithm and the adaptable compressive (ADCOM) tracking algorithm. These algorithms are discussed in detail and applied for the detection and tracking of landmarks in monocular camera images. Navigation filters are then designed that employ sensor fusion of accelerometer and rate gyro data from an inertial measurement unit (IMU) with vision-based measurements of the centroids of one or more landmarks in the scene. These filters are tested in simulated navigation scenarios subject to varying levels of sensor and measurement noise and varying number of landmarks. Finally, conclusions and recommendations are provided regarding the implementation of this vision-aided navigation approach for autonomous vehicle navigation systems

Wireless Positioning and Tracking for Internet of Things in GPS-denied Environments

Wireless positioning and tracking have long been a critical technology for various applications such as indoor/outdoor navigation, surveillance, tracking of assets and employees, and guided tours, among others. Proliferation of Internet of Things (IoT) devices, the evolution of smart cities, and vulnerabilities of traditional localization technologies to cyber-attacks such as jamming and spoofing of GPS necessitate development of novel radio frequency (RF) localization and tracking technologies that are accurate, energy-efficient, robust, scalable, non-invasive and secure. The main challenges that are considered in this research work are obtaining fundamental limits of localization accuracy using received signal strength (RSS) information with directional antennas, and use of burst and intermittent measurements for localization. In this dissertation, we consider various RSS-based techniques that rely on existing wireless infrastructures to obtain location information of corresponding IoT devices. In the first approach, we present a detailed study on localization accuracy of UHF RF IDentification (RFID) systems considering realistic radiation pattern of directional antennas. Radiation patterns of antennas and antenna arrays may significantly affect RSS in wireless networks. The sensitivity of tag antennas and receiver antennas play a crucial role. In this research, we obtain the fundamental limits of localization accuracy considering radiation patterns and sensitivity of the antennas by deriving Cramer-Rao Lower Bounds (CRLBs) using estimation theory techniques. In the second approach, we consider a millimeter Wave (mmWave) system with linear antenna array using beamforming radiation patterns to localize user equipment in an indoor environment. In the third approach, we introduce a tracking and occupancy monitoring system that uses ambient, bursty, and intermittent WiFi probe requests radiated from mobile devices. Burst and intermittent signals are prominent characteristics of IoT devices; using these features, we propose a tracking technique that uses interacting multiple models (IMM) with Kalman filtering. Finally, we tackle the problem of indoor UAV navigation to a wireless source using its Rayleigh fading RSS measurements. We propose a UAV navigation technique based on Q-learning that is a model-free reinforcement learning technique to tackle the variation in the RSS caused by Rayleigh fading

Reconstrução de sinais por Compressive Sensing dinâmico e filtragem de Kalman com estudo de caso em eletrocardiografia

Trabalho de Conclusão de Curso (graduação)—Universidade de Brasília, Faculdade UnB Gama, 2019.A aquisição de sinais digitais com uma quantidade reduzida de medidas é possibilitada por Compressive Sensing (CS). O Filtro de Kalman Adaptativo Baseado em CS é um exemplo de algoritmo que foi elaborado no contexto de streaming. Seu processo de reconstrução considera que os sinais são recebidos de forma contínua e realiza estimativas de suporte para melhorar seus resultados. Entretanto, seu funcionamento foi observado apenas para sinais simulados e esparsos no domínio de Fourier. A aplicação desse algoritmo considerando sinais reais foi investigada no presente trabalho. Para tanto, modificações foram feitas com o objetivo de se obter melhores resultados no cenário específico Para estudo de caso, decidiu-se por adotar sinais de eletrocardiografia. Inicialmente, foram estudadas transformadas esparsificantes para essa nova classe de sinais. Além do domínio de Fourier, foram avaliadas reconstruções utilizando a transformada de Daubechies 4 e uma criada com Análise de Componentes Principais. A observação de resultados parciais permitiram que se propusesse: (i) a atualização iterativa da matriz de covariância do modelo e (ii) modificações na etapa de estimação de suporte. Nas reconstruções, observouse um nível médio de relação sinal ruído de 15, 6 \u1d451\u1d435, porém atingiu-se, nos melhores casos, valores próximos a 40 \u1d451\u1d435.Compressive Sensing (CS) allows a digital signal acquisition with a small amount of measurements. Adaptive Kalman Filter Based on CS is an algorithm created for streaming signals. Its reconstruction approach assumes that the signals are continuously received and support estimations are made to enhance the results. However, its behavior was analyzed only for simulated signals sparse on Fourier domain. The use of this algorithm with real signals was investigated at the present work. Thus, some modifications were made in order to get better results in the new specific scenario. As a case study, electrocardiography signals was chosen. Firstly, sparsifying transforms for the new class of signals were studied. Daubechies 4 transform and one defined by Principal Component Analysis was evaluated, besides the Fourier domain. Partial results enabled us to propose: (i) iterative update of model covariance matrix and (ii) a new method to estimate the support. The reconstructions showed 15, 6 \u1d451\u1d435 as average signal to noise ratio, however the best situations achieved values close to 40 \u1d451\u1d435

Transmission Rate Compression Based on Kalman Filter Using Spatio-temporal Correlation for Wireless Sensor Networks

Wireless sensor networks (WSNs) composed of spatially distributed autonomous sensor nodes have been applied to a wide variety of applications. Due to the limited energy budget of the sensor nodes and long-term operation requirement of the network, energy efficiency is a primary concern in almost any application. Radio communication, known as one of the most expensive processes, can be suppressed thanks to the temporal and spatial correlations. However, it is a challenge to compress the communication as much as possible, while reconstructing the system state with the highest quality. This work proposes the PKF method to compress the transmission rate for cluster based WSNs, which combines a k-step ahead Kalman predictor with a Kalman filter (KF). It provides the optimal reconstruction solution based on the compressed information of a single node for a linear system. Instead of approximating the noisy raw data, PKF aims to reconstruct the internal state of the system. It achieves data filtering, state estimation, data compression and reconstruction within one KF framework and allows the reconstructed signal based on the compressed transmission to be even more precise than transmitting all of the raw measurements without processing. The second contribution is the detailed analysis of PKF. It not only characterizes the effect of the system parameters on the performance of PKF but also supplies a common framework to analyze the underlying process of prediction-based schemes. The transmission rate and reconstruction quality are functions of the system parameters, which are calculated with the aid of (truncated) multivariate normal (MVN) distribution. The transmission of the node using PKF not only determines the current optimal estimate of the system state, but also indicates the range and the transmission probability of the k-step ahead prediction of the cluster head. Besides, one of the prominent results is an explicit expression for the covariance of the doubly truncated MVN distribution. This is the first work that calculates it using the Hessian matrix of the probability density function of a MVN distribution, which improves the traditional methods using moment-generating function and has generality. This contribution is important for WSNs, but also for other domains, e.g., statistics and economics. The PKF method is extended to use spatial correlation in multi-nodes systems without any intra-communication or a coordinator based on the above analysis. Each leaf node executes a PKF independently. The reconstruction quality is further improved by the cluster head using the received information, which is equivalent to further reduce the transmission rate of the node under the guaranteed reconstruction quality. The optimal reconstruction solution, called Rand-ST, is obtained, when the cluster head uses the incomplete information by taking the transmission of each node as random. Rand-ST actually solves the KF fusion problem with colored and randomly transmitted observations, which is the first work addressing this problem to the best of our knowledge. It proves the KF with state augment method is more accurate than the measurement differencing approach in this scenario. The suboptimality of Rand-ST by neglecting the useful information is analyzed, when the transmission of each node is controlled by PKF. The heuristic EPKF methods are thereupon proposed to utilize the complete information, while solving the nonlinear problem through linear approximations. Compared with the available techniques, EPKF methods not only ensure an error bound of the reconstruction for each node, but also allow them to report the emergency event in time, which avoids the loss of penitential important information

Force and response estimation on bottom-founded structures prone to ice-induced vibrations

Various types of bottom-founded structures, including lighthouses, quay structures, mono-pod platforms, multi-legged platforms, caisson-retained islands and bridges, are located in ice-infested waters. Level ice can interact with bottom-founded structures in various manners, and over fifty years of extensive measurement campaigns has brought attention to ice-induced vibrations. This phenomenon is caused by repeated ice crushing failures across the ice-structure interface and may entail violent vibrations of the structure, thereby potentially harming the structural integrity, secondary installations and operational safety. Such ice-induced vibrations are commonly divided into three regimes: 1) Intermittent crushing 2) Frequency lock-in 3) Continuous brittle crushing in which the ice velocity increase from regime 1 to regime 3. The ice conditions leading to each of the three regimes are not yet fully understood. Therefore, measurement campaigns both in the field and in the laboratory must address these regimes, wherein two of the major ingredients are the ice force and the structural response. A laboratory-scale ice-induced vibration measurement campaign was conducted at the Hamburg Ship Model Basin during August-September 2011, from which data were obtained for this thesis. Data measured at the Nordströmsgrund lighthouse in Sweden during the winter of 2003 and structural information on the Hanko-1 channel marker in Finland constitute the full-scale basis in this thesis. The ice forces present during ice-induced vibrations are traditionally measured by load panels or inverse techniques. Load panels are expensive; thus, inverse techniques are favorable. This thesis assessed a deterministic-stochastic framework to identify both the ice forces and responses at both the model scale and full scale. All of the considered data were limited to scenarios of ice-induced vibrations, and the considered ice conditions were primarily level ice. The framework as it is applied in this thesis consists of a joint input-state estimation algorithm, a model of the structure and a set of response measurements. Both full-order finite element models and modally reduced order models were used in this thesis. Using the laboratory measurements, the force and response identification was performed by employing two different full-order finite element models. One model was entirely based on the blueprints of the structure. The other model was tuned to more accurately reproduce the measured first natural frequency. The results were presented for two different regimes of ice-induced vibrations: the intermittent crushing regime and the continuous brittle crushing regime. The accuracy of the identified forces using the joint input-state estimation algorithm was assessed by comparing the forces with those obtained by a frequency-domain deconvolution method based on experimentally obtained frequency response functions. The results demonstrated the successful identification of the level-ice forces for both the intermittent and continuous brittle crushing regimes even when significant modeling errors were present. The responses (displacements) identified in conjunction with the forces were also compared to those measured during the experiment. Here, the estimated response was found to be sensitive to the modeling errors in the blueprint model. Simple tuning of the model, however, enabled high-accuracy response estimation. The joint input-state estimation algorithm was further used as a means to analyze the laboratory data, from which the global structural response was simultaneously identified with the forces. Novel insights into ice-induced vibration phenomena were obtained by comparing, on different time scales, measured and estimated response quantities and forces/pressures. First, the identified forces, ice velocities and time-frequency maps of the measured responses were presented for a series of ice-induced vibration tests. It was shown that the ice forces excited more than one mode of the structure and that the transition ice velocity at which the vibrations shifted from the first mode to the second mode increased with decreased foundation stiffness and superstructure mass. Second, a detailed analysis of the interaction between the structure and the ice edge was performed on a smaller time scale by comparing the locally measured pressures at the ice-structure interface to the identified structural responses and forces. It was shown that structural vibrations at a frequency that is higher than the dominant vibration frequency caused cyclic loading of the ice edge during intermittent crushing. These vibrations led to an increasing loading rate prior to ice failure. During an event that showed the tendencies of frequency lock-in vibrations, the structural response was dominated by a single vibration frequency. At full scale, a comparison between the measured and identified dynamic ice forces acting on the Nordströmsgrund lighthouse is presented. The dynamic ice forces were identified from the measured responses using the joint input-state estimation algorithm in conjunction with a reduced-order finite element model. A convincing agreement between the measured and identified forces was found. The algorithm was further used to estimate the response of the structure at unmeasured locations, including the iceaction point. The structural velocity amplitudes when the structure was subject to frequency lock-in vibrations were occasionally higher than the ice velocity and within the range of observations for other structures. A measurement campaign at the Hanko-1 channel marker in the Gulf of Finland is planned to monitor the forces leading to ice-induced vibrations via force identification. The ice forces are to be identified using the joint input-state estimation algorithm in conjunction with a modally reduced order model. Recently developed guidelines were used to determine the optimal response measurement types and locations that ensure the identifiability of the dynamic ice forces from only a limited number of sensors and a selection of vibration modes

Understanding the Role of Dynamics in Brain Networks: Methods, Theory and Application

The brain is inherently a dynamical system whose networks interact at multiple spatial and temporal scales. Understanding the functional role of these dynamic interactions is a fundamental question in neuroscience. In this research, we approach this question through the development of new methods for characterizing brain dynamics from real data and new theories for linking dynamics to function. We perform our study at two scales: macro (at the level of brain regions) and micro (at the level of individual neurons). In the first part of this dissertation, we develop methods to identify the underlying dynamics at macro-scale that govern brain networks during states of health and disease in humans. First, we establish an optimization framework to actively probe connections in brain networks when the underlying network dynamics are changing over time. Then, we extend this framework to develop a data-driven approach for analyzing neurophysiological recordings without active stimulation, to describe the spatiotemporal structure of neural activity at different timescales. The overall goal is to detect how the dynamics of brain networks may change within and between particular cognitive states. We present the efficacy of this approach in characterizing spatiotemporal motifs of correlated neural activity during the transition from wakefulness to general anesthesia in functional magnetic resonance imaging (fMRI) data. Moreover, we demonstrate how such an approach can be utilized to construct an automatic classifier for detecting different levels of coma in electroencephalogram (EEG) data. In the second part, we study how ongoing function can constraint dynamics at micro-scale in recurrent neural networks, with particular application to sensory systems. Specifically, we develop theoretical conditions in a linear recurrent network in the presence of both disturbance and noise for exact and stable recovery of dynamic sparse stimuli applied to the network. We show how network dynamics can affect the decoding performance in such systems. Moreover, we formulate the problem of efficient encoding of an afferent input and its history in a nonlinear recurrent network. We show that a linear neural network architecture with a thresholding activation function is emergent if we assume that neurons optimize their activity based on a particular cost function. Such an architecture can enable the production of lightweight, history-sensitive encoding schemes

Large Scale Inverse Problems

This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation &amp Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. This collection of survey articles focusses on the large inverse problems commonly arising in simulation and forecasting in the earth sciences

Intelligent Sensor Networks

In the last decade, wireless or wired sensor networks have attracted much attention. However, most designs target general sensor network issues including protocol stack (routing, MAC, etc.) and security issues. This book focuses on the close integration of sensing, networking, and smart signal processing via machine learning. Based on their world-class research, the authors present the fundamentals of intelligent sensor networks. They cover sensing and sampling, distributed signal processing, and intelligent signal learning. In addition, they present cutting-edge research results from leading experts