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Changes in precipitation patterns, temperature, and other climatic variables have been shown to modify thehydrological cycle and hydrological systems, potentially resulting in a shift in river runoff behavior and an increasedrisk of floods. There have been several instances of devastating floods throughout Europe’s history, which haveresulted in devastation and enormous economic losses. As a result of the effects of climate change, floods areoccurring more frequently in Sweden as well as across Europe. Research on the subject of flood prediction has beengoing on for decades, where particularly data-driven models have advanced in recent years. This study examinedtwo different machine learning (data-driven) models for forecasting river discharge in the Nissan River: Linearregression and Random Forrest regression (RFR), with the use of ECMWF Reanalysis v5 ( ERA5 ) data and historicaldischarge data. The Linear regression model yielded a r2 score of 0.45 and could not be considered an acceptablemodel. The RFR model had a r2 score of 0.71. This implies, given ERA5 reanalysis data, that one might generatea moderately performing machine learning model for Nissan river. An additional investigation was carried out,to see if the trained model could be used with EC-EARTH CMIP6 future projection. The findings resulting fromapplying the EC-EARTH CMIP6 future data on the trained RFR indicated too many uncertainties, necessitatingmore investigation before any conclusions can be drawn.

Current eastern wild turkey (<I>Meleagris gallopavo silvestris</I>) harvest models assume density-independent population dynamics despite indications that populations are subject to a form of density dependence. I suggest that both density-dependent and independent factors operate simultaneously on wild turkey populations, where the relative strength of each is governed by population density. I attempt to estimate the form of the density dependence relationship in wild turkey population growth using the theta-Ricker model. Density-independent relationships are explored between production and rainfall and temperature correlates for possible inclusion in the harvest model. Density-dependent and independent effects are then combined in the model to compare multiple harvest strategies. To estimate a functional relationship between population growth and density, I fit the theta-Ricker model to harvest index time-series from 11 state wildlife agencies. To model density-independent effects on population growth, I explored the ability of rainfall, temperature, and mast during the nesting and brooding season to predict observed production indices for 7 states. I then built a harvest model incorporating estimates to determine their influence on the mean and variability of the fall and spring harvest. Estimated density-dependent growth rates produced a left-skewed yield curve maximized at ~40% of carrying capacity, with large residuals. Density-independent models of production varied widely and were characterized by high model uncertainty. Results indicate a non-linear density dependence effect strongest at low population densities. High residuals from the model fit indicate that extrinsic factors will overshadow density-dependent factors at most population densities. However, environmental models were weak, requiring more data with higher precision. This indicates that density-independence can be correctly and more easily modeled as random error. The constructed model uses both density dependence and density-independent stochastic error as a tool to explore harvest strategies for biologists. The inclusion of weak density dependence changes expected harvest rates little from density-independent models. However, it does lower the probability of overharvest at low densities. Alternatives to proportional harvesting are explored to reduce the uncertainty in annual harvests. / Ph. D.

Functional data analysis (FDA) studies data in the form of measurements over a domain as whole entities. Our first focus is on the post-hoc analysis with pairwise and contrast comparisons of the popular functional ANOVA model comparing groups of functional data. Existing contrast tests assume independent functional observations within group. In reality, this assumption may not be satisfactory since functional data are often collected continually overtime on a subject. In this work, we introduce a new linear contrast test that accounts for time dependency among functional group members. For a significant contrast test, it can be beneficial to identify the region of significant difference. In the second part, we propose a non-parametric regression procedure to obtain a locally sparse estimate of functional contrast. Our work is motivated by a biomedical study using Raman spectroscopy to monitor hemodialysis treatment near real-time. With contrast test and sparse estimation, practitioners can monitor the progress of the hemodialysis within session and identify important chemicals for dialysis adequacy monitoring. In the third part, we propose a functional data model for degradation analysis of functional data. Motivated by degradation analysis application of rechargeable Li-ion batteries, we combine state-of-the-art functional linear models to produce fully functional prediction for curves on heterogenous domains. Simulation studies and data analysis demonstrate the advantage of the proposed method in predicting degradation measure than existing method using aggregation method. / Doctor of Philosophy / Functional data analysis (FDA) studies complex data structure in the form of curves and shapes. Our work is motivated by two applications concerning data from Raman spectroscopy and battery degradation study. Raman spectra of a liquid sample are curves with measurements over a domain of wavelengths that can identify chemical composition and whose values signify the constituent concentrations in the sample. We first propose a statistical procedure to test the significance of a functional contrast formed by spectra collected at beginning and at later time points during a dialysis session. Then a follow-up procedure is developed to produce a sparse representation of the contrast functional contrast with clearly identified zero and nonzero regions. The use of this method on contrast formed by Raman spectra of used dialysate collected at different time points during hemodialysis sessions can be adapted for evaluating the treatment efficacy in real time. In a third project, we apply state-of-the-art methodologies from FDA to a degradation study of rechargeable Li-ion batteries. Our proposed methods produce fully functional prediction of voltage discharge curves allowing flexibility in monitoring battery health.

The ability to predict accurately the critical quality characteristics of aircraft engines is essential for modeling the degradation of engine performance over time. The acceptable margins for error grow smaller with each new generation of engines. This paper focuses on turbine gas temperature (TGT). The goal is to improve the first principles predictions through the incorporation of the pure thermodynamics, as well as available information from the engine health monitoring (EHM) data and appropriate maintenance records. The first step in the approach is to develop the proper thermodynamics model to explain and to predict the observed TGTs. The resulting residuals provide the fundamental information on degradation. The current engineering models are ad hoc adaptations of the underlying thermodynamics not properly tuned by actual data. Interestingly, pure thermodynamics model uses only two variables: atmospheric temperature and a critical pressure ratio. The resulting predictions of TGT are at least similar, and sometimes superior to these ad hoc models. The next steps recognize that there are multiple sources of variability, some nested within others. Examples include version to version of the engine, engine to engine within version, route to route across versions and engines, maintenance to maintenance cycles within engine, and flight segment to flight segment within maintenance cycle. The EHM data provide an opportunity to explain the various sources of variability through appropriate regression models. Different EHM variables explain different contributions to the variability in the residuals, which provides fundamental insights as to the causes of the degradation over time. The resulting combination of the pure thermodynamics model with proper modeling based on the EHM data yield significantly better predictions of the observed TGT, allowing analysts to see the impact of the causes of the degradation much more clearly. / Doctor of Philosophy / AEM is major civilian aircraft gas turbine engine manufacturer, serving different airliners and airlines. However, one of its newest models has had performance issues; the engines degraded faster than their in-house model had anticipated, leading to more frequent maintenance and causing significant financial losses to the company. The key objectives of our research project are to produce a model that has higher predictive capabilities than AEM's in-house predictive model (DTGT), and develop a model selection algorithm that allows for direct comparisons among models of vastly different architecture. There are three major components to our research: 1) interdisciplinary studies merging the theory of thermodynamics and regression, 2) the sequential modeling, and 3) the modified Mallows's Cp. We propose a layered sequential approach to the regression modeling, where one regression model is followed by another regression on the residuals of the previous model. We also propose the modified Mallows's Cp, a modification of the Mallows's Cp, as a viable model selection criterion. Our results demonstrated that the sequential approach both outperformed the AEM's in-house model and was found to be more useful than the traditional multiple linear regression. Our results also demonstrated that the modified Mallows's Cp prefer smaller number of parameters than other standard model selection criterion without sacrificing predictive capabilities of its models.

Machine learning methods are now extensively applied in various scientific research areas to make models. Unlike regular models, machine learning based models use a data-driven approach. Machine learning algorithms can learn knowledge that are hard to be recognized, from available data. The data-driven approaches enhance the role of algorithms and computers and then accelerate the computation using alternative views. In this thesis, we explore the possibility of applying machine learning models in the prediction of chromatographic retention behaviors. Chromatographic separation is a key technique for the discovery and analysis of fullerenes. In previous studies, differential equation models have achieved great success in predictions of chromatographic retentions. However, most of the differential equation models require experimental measurements or theoretical computations for many parameters, which are not easy to obtain. Fullerenes/metallofullerenes are rigid and spherical molecules with only carbon atoms, which makes the predictions of chromatographic retention behaviors as well as other properties much simpler than other flexible molecules that have more variations on conformations. In this thesis, I propose the polarizability of a fullerene molecule is able to be estimated directly from the structures. Structural motifs are used to simplify the model and the models with motifs provide satisfying predictions. The data set contains 31947 isomers and their polarizability data and is split into a training set with 90% data points and a complementary testing set. In addition, a second testing set of large fullerene isomers is also prepared and it is used to testing whether a model can be trained by small fullerenes and then gives ideal predictions on large fullerenes. / Machine learning models are capable to be applied in a wide range of areas, such as scientific research. In this thesis, machine learning models are applied to predict chromatography behaviors of fullerenes based on the molecular structures. Chromatography is a common technique for mixture separations, and the separation is because of the difference of interactions between molecules and a stationary phase. In real experiments, a mixture usually contains a large family of different compounds and it requires lots of work and resources to figure out the target compound. Therefore, models are extremely import for studies of chromatography. Traditional models are built based on physics rules, and involves several parameters. The physics parameters are measured by experiments or theoretically computed. However, both of them are time consuming and not easy to be conducted. For fullerenes, in my previous studies, it has been shown that the chromatography model can be simplified and only one parameter, polarizability, is required. A machine learning approach is introduced to enhance the model by predicting the molecular polarizabilities of fullerenes based on structures. The structure of a fullerene is represented by several local structures. Several types of machine learning models are built and tested on our data set and the result shows neural network gives the best predictions.

In obtaining a regression fit to a set of data, ordinary least squares regression depends directly on the parametric model formulated by the researcher. If this model is incorrect, a least squares analysis may be misleading. Alternatively, nonparametric regression (kernel or local polynomial regression, for example) has no dependence on an underlying parametric model, but instead depends entirely on the distances between regressor coordinates and the prediction point of interest. This procedure avoids the necessity of a reliable model, but in using no information from the researcher, may fit to irregular patterns in the data. The proper combination of these two regression procedures can overcome their respective problems. Considered is the situation where the researcher has an idea of which model should explain the behavior of the data, but this model is not adequate throughout the entire range of the data. An extension of partial linear regression and two methods of model robust regression are developed and compared in this context. These methods involve parametric fits to the data and nonparametric fits to either the data or residuals. The two fits are then combined in the most efficient proportions via a mixing parameter. Performance is based on bias and variance considerations. / Ph. D. / incomplete_metadata