Tato práce se zabývá úlohou odhadování prostorové funkce z hlediska regrese pomocí Gaussovských procesů (GPR) za současné nejistoty tréninkových pozic (pozic senzorů). Nejdříve je zde popsána teorie v pozadí GPR metody pracující se známými tréninkovými pozicemi. Tato teorie je poté aplikována při odvození výrazů prediktivní distribuce GPR v testovací pozici při uvážení nejistoty tréninkových pozic. Kvůli absenci analytického řešení těchto výrazů byly výrazy aproximovány pomocí metody Monte Carlo. U odvozené metody bylo demonstrováno zlepšení kvality odhadu prostorové funkce oproti standardnímu použití GPR metody a také oproti zjednodušenému řešení uvedenému v literatuře. Dále se práce zabývá možností použití metody GPR s nejistými tréninkovými pozicemi v~kombinaci s výrazy s dostupným analytickým řešením. Ukazuje se, že k dosažení těchto výrazů je třeba zavést značné předpoklady, což má od počátku za následek nepřesnost prediktivní distribuce. Také se ukazuje, že výsledná metoda používá standardní výrazy GPR v~kombinaci s upravenou kovarianční funkcí. Simulace dokazují, že tato metoda produkuje velmi podobné odhady jako základní GPR metoda uvažující známé tréninkové pozice. Na druhou stranu prediktivní variance (nejistota odhadu) je u této metody zvýšena, což je žádaný efekt uvážení nejistoty tréninkových pozic.

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Unmanned autonomous vehicles, airborne or terrestrial, can be used to solve many varying tasks in vastly different environments. This thesis describes a proposed collaboration between two types of such vehicles, namely unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs). The vehicles' objective is to traverse unknown terrain in order to access a target area. The exploration of the unknown terrain is in this thesis divided into three parts. These parts are terrain mapping, informative path planning (IPP) for the UAVs and path planning for the UGV. A Gaussian Process (GP) is used to model the terrain. The use of a GP map makes it possible to model spatial dependence and to interpolate data between measurements. Furthermore, sequential update of the map is achieved with a Kalman filter when new measurements are collected. In the second part, IPP is used to decide the best locations for the terrain height measurements. The IPP algorithm will prioritize measurements in locations with uncertain terrain height estimates in order to lower the overall map uncertainty. Finally, when the map is complete, the UGV plans an optimal path through the mapped terrain using A* graph search, while minimizing the total altitude difference for the path and respecting the map uncertainty. Collaborative behavior of autonomous vehicles requires highly accurate position estimates. In this thesis RTK is investigated and its accuracy and precision evaluated for the positioning of autonomous UAVs and UGVs through a series of experiments. The experiments range from stationary and dynamic accuracy to investigation of the consistency of the positioning estimates. The results are promising, RTK outperforms standard GNSS and can be used for centimeter-level accuracy when positioning a UAV in-flight. The proposed exploration algorithms are evaluated in simulations. The results show that the algorithms successfully solves the task of mapping and traversing unknown terrain. IPP makes the mapping of the unknown terrain efficient, which enables the possibility to use the resulting map to plan safe paths for the UGV. Traversing unknown terrain is hard for a single UGV but with the help from one or more UAVs the process is much more efficient. The use of multiple cooperating autonomous vehicles makes it possible to solve tasks complicated for the individual vehicle in an efficient manner.

The purpose of this thesis is to investigate how data from a residential property owner can be utilized to enable better energy management for their building stock. Specifically, this is done through the development of two machine learning models with the objective of detecting anomalies in the existing data of electricity consumption. The dataset consists of two years of residential electricity consumption for 193 substations belonging to the residential property owner Uppsalahem. The first of the developed models uses the K-means method to cluster substations with similar consumption patterns to create electricity profiles, while the second model uses Gaussian process regression to predict electricity consumption of a 24 hour timeframe. The performance of these models is evaluated and the optimal models resulting from this process are implemented to detect anomalies in the electricity consumption data. Two different algorithms for anomaly detection are presented, based on the differing properties of the two earlier models. During the evaluation of the models, it is established that the consumption patterns of the substations display a high variability, making it difficult to accurately model the full dataset. Both models are shown to be able to detect anomalies in the electricity consumption data, but the K-means based anomaly detection model is preferred due to it being faster and more reliable. It is concluded that substation electricity consumption is not ideal for anomaly detection, and that if a model should be implemented, it should likely exclude some of the substations with less regular consumption profiles.

<div>This dissertation develops an exclusive workflow driven by data analytics algorithms, to support the optimization of the economic performance of an Integrated Energy System (IES). The objective of this research is to determine the optimum mix of capacities from a set of different energy producers (e.g., nuclear, coal, gas, wind, and solar). The main contribution of this dissertation addresses several major challenges in current optimization methods of the energy portfolios in IES. First, the feasibility of generating the synthetic time series of the periodic peak data. </div><div>Second, the computational burden of conventional stochastic optimization of the energy portfolio, associated with the need for repeated executions of system models.</div><div>Third, the inadequacies of previous studies about the comparisons of the impact of the economic parameters.</div><div><br></div><div>Several algorithmic developments are proposed to tackle these challenges. A stochastic-based optimizer, which employs Gaussian Process modeling, is developed. The optimizer requires a large number of samples for its training, with each sample consisting of a time series describing the electricity demand or other operational and economic profiles for multiple types of energy producers. These samples are synthetically generated using a reduced order modeling algorithm that reads limited set of historical data, such as demand and weather data from past years. To construct the Reduced Order Models (ROMs), several data analysis methods are used, such as the Auto Regressive Moving Average (ARMA), the Fourier series decomposition, the peak detection algorithm, etc. The purpose of using these algorithms is to detrend the data and extract features that can be used to produce synthetic time histories that maintain the statistical characteristics of the original limited historical data. The optimization cost function is based on an economic model that assesses the effective cost of energy based on two figures of merit (FOM), the specific cash flow stream for each energy producer and the total Net Present Value (NPV). The Screening Curve Method (SCM) is employed to get the initial estimate of the optimal capacity. Results obtained from a model-based optimization of the Gaussian Process are evaluated using an exhaustive Monte Carlo search. </div><div><br></div><div>The workflow has been implemented inside the Idaho National Laboratory’s Risk Analysis and Virtual Environment (RAVEN) framework. The proposed workflow can provide a comprehensive, efficient, and scientifically dependable strategy to support the decision-making in the electricity market and to help energy distributors develop a better understanding of the performance of IES.</div><div><br></div>

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The dynamic structural equation modeling (DSEM) framework incorporates hierarchical latent modeling (HLM), structural equation modeling (SEM), time series analysis (TSA), and time-varying effects modeling (TVEM) to model the dynamic relationship between latent and observed variables. To model the functional relationships between variables, a Gaussian process (GP), by definition of its covariance function(s), allows researchers to define Gaussian distributions over functions of input variables. Therefore, by incorporating GPs to model the presence of significant trend in either latent or observed variables, this dissertation explores the adequacy and performance of GPs in manipulated conditions of sample size using the flexible Bayesian analysis approach. The overall results of these Monte Carlo simulation studies showcase the ability of the multi-output GPs to properly explore the presence of trends. Also, in modeling intensive longitudinal data, GPs can be specified to properly account for trends, without generating significantly biased and imprecise estimates.

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