An Empirically Based Stochastic Turbulence Simulator with Temporal Coherence for Wind Energy Applications

In this dissertation, we develop a novel methodology for characterizing and simulating nonstationary, full-field, stochastic turbulent wind fields.

In this new method, nonstationarity is characterized and modeled via temporal coherence, which is quantified in the discrete frequency domain by probability distributions of the differences in phase between adjacent Fourier components.

The empirical distributions of the phase differences can also be extracted from measured data, and the resulting temporal coherence parameters can quantify the occurrence of nonstationarity in empirical wind data.

This dissertation (1) implements temporal coherence in a desktop turbulence simulator, (2) calibrates empirical temporal coherence models for four wind datasets, and (3) quantifies the increase in lifetime wind turbine loads caused by temporal coherence.

The four wind datasets were intentionally chosen from locations around the world so that they had significantly different ambient atmospheric conditions.

The prevalence of temporal coherence and its relationship to other standard wind parameters was modeled through empirical joint distributions (EJDs), which involved fitting marginal distributions and calculating correlations.

EJDs have the added benefit of being able to generate samples of wind parameters that reflect the characteristics of a particular site.

Lastly, to characterize the effect of temporal coherence on design loads, we created four models in the open-source wind turbine simulator FAST based on the \windpact turbines, fit response surfaces to them, and used the response surfaces to calculate lifetime turbine responses to wind fields simulated with and without temporal coherence.

The training data for the response surfaces was generated from exhaustive FAST simulations that were run on the high-performance computing (HPC) facilities at the National Renewable Energy Laboratory.

This process was repeated for wind field parameters drawn from the empirical distributions and for wind samples drawn using the recommended procedure in the wind turbine design standard \iec.

The effect of temporal coherence was calculated as a percent increase in the lifetime load over the base value with no temporal coherence.

Role of Hydrological Process Representation on Erosion, Deposition, and Sediment Yield Estimate

Soil erosion by water is a major driven force causing land degradation. Laboratory experiments, on-site field study, and suspended sediments measurements were major fundamental approaches to study the mechanisms of soil water erosion and to quantify the erosive losses during rain events. The experimental research faces the challenge to extent the result to a wider spatial scale. Soil water erosion modeling provides possible solutions for scaling problems in erosion research, and is of principal importance to better understanding the governing processes of water erosion. However, soil water erosion models were considered to have limited value in practice. Uncertainties in hydrological simulations are among the reasons that hindering the development of water erosion model. Hydrological models gained substantial improvement recently and several water erosion models took advantages of the improvement of hydrological models. It is crucial to know the impact of changes in hydrological processes modeling on soil erosion simulation.

This dissertation work first created an erosion modeling tool (GEOtopSed) that takes advantage of the comprehensive hydrological model (GEOtop). The newly created tool was then tested and evaluated at an experimental watershed. The GEOtopSed model showed its ability to estimate multi-year soil erosion rate with varied hydrological conditions. To investigate the impact of different hydrological representations on soil erosion simulation, a 11-year simulation experiment was conducted for six models with varied configurations. The results were compared at varied temporal and spatial scales to highlight the roles of hydrological feedbacks on erosion. Models with simplified hydrological representations showed agreement with GEOtopSed model on long temporal scale (longer than annual). This result led to an investigation for erosion simulation at different rainfall regimes to check whether models with different hydrological representations have agreement on the soil water erosion responses to the changing climate. Multi-year ensemble simulations with different extreme precipitation scenarios were conducted at seven climate regions. The differences in erosion simulation results showed the influences of hydrological feedbacks which cannot be seen by purely rainfall erosivity method.

Assessment of the Spatial and Temporal Distribution of Functional Connectivity in Resting-State BOLD fMRI

Recent research into resting-state functional magnetic resonance imaging (fMRI) has shown that the brain is very active during rest. This thesis work utilizes blood oxygenation level dependent (BOLD) signals to investigate the spatial and temporal functional network information found within resting-state data, and aims to investigate the feasibility of extracting functional connectivity networks using different methods as well as the dynamic variability within some of the methods. Furthermore, this work looks into producing valid networks using a sparsely-sampled sub-set of the original data.

In this work we utilize four main methods: independent component analysis (ICA), principal component analysis (PCA), correlation, and a point-processing technique. Each method comes with unique assumptions, as well as strengths and limitations into exploring how the resting state components interact in space and time.

Correlation is perhaps the simplest technique. Using this technique, resting-state patterns can be identified based on how similar the time profile is to a seed region’s time profile. However, this method requires a seed region and can only identify one resting state network at a time. This simple correlation technique is able to reproduce the resting state network using subject data from one subject’s scan session as well as with 16 subjects.

Independent component analysis, the second technique, has established software programs that can be used to implement this technique. ICA can extract multiple components from a data set in a single analysis. The disadvantage is that the resting state networks it produces are all independent of each other, making the assumption that the spatial pattern of functional connectivity is the same across all the time points. ICA is successfully able to reproduce resting state connectivity patterns for both one subject and a 16 subject concatenated data set.

Using principal component analysis, the dimensionality of the data is compressed to find the directions in which the variance of the data is most significant. This method utilizes the same basic matrix math as ICA with a few important differences that will be outlined later in this text. Using this method, sometimes different functional connectivity patterns are identifiable but with a large amount of noise and variability.

To begin to investigate the dynamics of the functional connectivity, the correlation technique is used to compare the first and second halves of a scan session. Minor differences are discernable between the correlation results of the scan session halves. Further, a sliding window technique is implemented to study the correlation coefficients through different sizes of correlation windows throughout time. From this technique it is apparent that the correlation level with the seed region is not static throughout the scan length.

The last method introduced, a point processing method, is one of the more novel techniques because it does not require analysis of the continuous time points. Here, network information is extracted based on brief occurrences of high or low amplitude signals within a seed region. Because point processing utilizes less time points from the data, the statistical power of the results is lower. There are also larger variations in DMN patterns between subjects. In addition to boosted computational efficiency, the benefit of using a point-process method is that the patterns produced for different seed regions do not have to be independent of one another.

This work compares four unique methods of identifying functional connectivity patterns. ICA is a technique that is currently used by many scientists studying functional connectivity patterns. The PCA technique is not optimal for the level of noise and the distribution of the data sets. The correlation technique is simple and obtains good results, however a seed region is needed and the method assumes that the DMN regions is correlated throughout the entire scan. Looking at the more dynamic aspects of correlation changing patterns of correlation were evident. The last point-processing method produces a promising results of identifying functional connectivity networks using only low and high amplitude BOLD signals.

A Molecular-scale Programmable Stochastic Process Based On Resonance Energy Transfer Networks: Modeling And Applications

While molecular and cellular processes are often modeled as stochastic processes, such as Brownian motion, chemical reaction networks and gene regulatory networks, there are few attempts to program a molecular-scale process to physically implement stochastic processes. DNA has been used as a substrate for programming molecular interactions, but its applications are restricted to deterministic functions and unfavorable properties such as slow processing, thermal annealing, aqueous solvents and difficult readout limit them to proof-of-concept purposes. To date, whether there exists a molecular process that can be programmed to implement stochastic processes for practical applications remains unknown.

In this dissertation, a fully specified Resonance Energy Transfer (RET) network between chromophores is accurately fabricated via DNA self-assembly, and the exciton dynamics in the RET network physically implement a stochastic process, specifically a continuous-time Markov chain (CTMC), which has a direct mapping to the physical geometry of the chromophore network. Excited by a light source, a RET network generates random samples in the temporal domain in the form of fluorescence photons which can be detected by a photon detector. The intrinsic sampling distribution of a RET network is derived as a phase-type distribution configured by its CTMC model. The conclusion is that the exciton dynamics in a RET network implement a general and important class of stochastic processes that can be directly and accurately programmed and used for practical applications of photonics and optoelectronics. Different approaches to using RET networks exist with vast potential applications. As an entropy source that can directly generate samples from virtually arbitrary distributions, RET networks can benefit applications that rely on generating random samples such as 1) fluorescent taggants and 2) stochastic computing.

By using RET networks between chromophores to implement fluorescent taggants with temporally coded signatures, the taggant design is not constrained by resolvable dyes and has a significantly larger coding capacity than spectrally or lifetime coded fluorescent taggants. Meanwhile, the taggant detection process becomes highly efficient, and the Maximum Likelihood Estimation (MLE) based taggant identification guarantees high accuracy even with only a few hundred detected photons.

Meanwhile, RET-based sampling units (RSU) can be constructed to accelerate probabilistic algorithms for wide applications in machine learning and data analytics. Because probabilistic algorithms often rely on iteratively sampling from parameterized distributions, they can be inefficient in practice on the deterministic hardware traditional computers use, especially for high-dimensional and complex problems. As an efficient universal sampling unit, the proposed RSU can be integrated into a processor / GPU as specialized functional units or organized as a discrete accelerator to bring substantial speedups and power savings.