Evaluating Risks of Dam-Reservoir Systems Using Efficient Importance Sampling

The occurrence frequency of failure events serve as critical indexes representing the safety status of dam-reservoir systems. Although overtopping is the most common failure mode with significant consequences, this type of event, in most cases, has a small probability. Estimation of such rare event risks for dam-reservoir systems with crude Monte Carlo (CMC) simulation techniques requires a prohibitively large number of trials, where significant computational resources are required to reach the satisfied estimation results. Otherwise, estimation of the disturbances would not be accurate enough. In order to reduce the computation expenses and improve the risk estimation efficiency, an importance sampling (IS) based simulation approach is proposed in this dissertation to address the overtopping risks of dam-reservoir systems. Deliverables of this study mainly include the following five aspects: 1) the reservoir inflow hydrograph model; 2) the dam-reservoir system operation model; 3) the CMC simulation framework; 4) the IS-based Monte Carlo (ISMC) simulation framework; and 5) the overtopping risk estimation comparison of both CMC and ISMC simulation. In a broader sense, this study meets the following three expectations: 1) to address the natural stochastic characteristics of the dam-reservoir system, such as the reservoir inflow rate; 2) to build up the fundamental CMC and ISMC simulation frameworks of the dam-reservoir system in order to estimate the overtopping risks; and 3) to compare the simulation results and the computational performance in order to demonstrate the ISMC simulation advantages. The estimation results of overtopping probability could be used to guide the future dam safety investigations and studies, and to supplement the conventional analyses in decision making on the dam-reservoir system improvements. At the same time, the proposed methodology of ISMC simulation is reasonably robust and proved to improve the overtopping risk estimation. The more accurate estimation, the smaller variance, and the reduced CPU time, expand the application of Monte Carlo (MC) technique on evaluating rare event risks for infrastructures.

DEVELOPMENT OF LI+ AND NA+ CONDUCTING CERAMICS AND CERAMIC STRUCTURES FOR USE IN SOLID STATE BATTERIES

A solid state lithium metal battery based on a lithium garnet material was developed, constructed and tested. Specifically, a porous-dense-porous trilayer structure was fabricated by tape casting, a roll-to-roll technique conducive to high volume manufacturing. The high density and thin center layer (< 20 μm) effectively blocks dendrites even over hundreds of cycles. The microstructured porous layers, serving as electrode supports, are demonstrated to increase the interfacial surface area available to the electrodes and increase cathode loading. Reproducibility of flat, well sintered ceramics was achieved with consistent powderbed lattice parameter and ball milling of powderbed. Together, the resistance of the LLCZN trilayer was measured at an average of 7.6 ohm-cm2 in a symmetric lithium cell, significantly lower than any other reported literature results. Building on these results, a full cell with a lithium metal anode, LLCZN trilayer electrolyte, and LiCoO2 cathode was cycled 100 cycles without decay and an average ASR of 117 ohm-cm2. After cycling, the cell was held at open circuit for 24 hours without any voltage fade, demonstrating the absence of a dendrite or short-circuit of any type. Cost calculations guided the optimization of a trilayer structure predicted that resulting cells will be highly competitive in the marketplace as intrinsically safe lithium batteries with energy densities greater than 300 Wh/kg and 1000 Wh/L for under $100/kWh. Also in the pursuit of solid state batteries, an improved Na+ superionic conductor (NASICON) composition, Na3Zr2Si2PO12, was developed with a conductivity of 1.9x10-3 S/cm. New super-lithiated lithium garnet compositions, Li7.06La3Zr1.94Y0.06O12 and Li7.16La3Zr1.84Y0.16O12, were developed and studied revealing insights about the mechanisms of conductivity in lithium garnets.

Nested Sampling and its Applications in Stable Compressive Covariance Estimation and Phase Retrieval with Near-Minimal Measurements

Compressed covariance sensing using quadratic samplers is gaining increasing interest in recent literature. Covariance matrix often plays the role of a sufficient statistic in many signal and information processing tasks. However, owing to the large dimension of the data, it may become necessary to obtain a compressed sketch of the high dimensional covariance matrix to reduce the associated storage and communication costs. Nested sampling has been proposed in the past as an efficient sub-Nyquist sampling strategy that enables perfect reconstruction of the autocorrelation sequence of Wide-Sense Stationary (WSS) signals, as though it was sampled at the Nyquist rate. The key idea behind nested sampling is to exploit properties of the difference set that naturally arises in quadratic measurement model associated with covariance compression. In this thesis, we will focus on developing novel versions of nested sampling for low rank Toeplitz covariance estimation, and phase retrieval, where the latter problem finds many applications in high resolution optical imaging, X-ray crystallography and molecular imaging. The problem of low rank compressive Toeplitz covariance estimation is first shown to be fundamentally related to that of line spectrum recovery. In absence if noise, this connection can be exploited to develop a particular kind of sampler called the Generalized Nested Sampler (GNS), that can achieve optimal compression rates. In presence of bounded noise, we develop a regularization-free algorithm that provably leads to stable recovery of the high dimensional Toeplitz matrix from its order-wise minimal sketch acquired using a GNS. Contrary to existing TV-norm and nuclear norm based reconstruction algorithms, our technique does not use any tuning parameters, which can be of great practical value. The idea of nested sampling idea also finds a surprising use in the problem of phase retrieval, which has been of great interest in recent times for its convex formulation via PhaseLift, By using another modified version of nested sampling, namely the Partial Nested Fourier Sampler (PNFS), we show that with probability one, it is possible to achieve a certain conjectured lower bound on the necessary measurement size. Moreover, for sparse data, an l1 minimization based algorithm is proposed that can lead to stable phase retrieval using order-wise minimal number of measurements.