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The restructuring of the electric energy market and the proliferation of intermittent renewable-energy based power generation have introduced serious challenges to power system operation emanating from the uncertainties introduced to the system variables (electricity prices, congestion levels etc.). In order to economically operate the system and efficiently run the energy market, a statistical analysis of the system variables under uncertainty is needed. Such statistical analysis can be performed through an estimation of the statistical moments of these variables. In this thesis, the Point Estimate Methods (PEMs) are applied to the optimal power flow (OPF) problem to estimate the statistical moments of the locational marginal prices (LMPs) and total generation cost under system uncertainty. An extensive mathematical examination and risk analysis of existing PEMs are performed and a new PEM scheme is introduced. The applied PEMs consist of two schemes introduced by H.P. Hong, namely, the 2n and 2n+1 schemes, and a proposed combination between Hong's and M. E Harr's schemes. The accuracy of the applied PEMs in estimating the statistical moments of system LMPs is illustrated and the performance of the suggested combination of Harr's and Hong's PEMs is shown. Moreover, the risks of the application of Hong's 2n scheme to the OPF problem are discussed by showing that it can potentially yield inaccurate LMP estimates or run into unfeasibility of the OPF problem. In addition, a new PEM configuration is also introduced. This configuration is derived from a PEM introduced by E. Rosenblueth. It can accommodate asymmetry and correlation of input random variables in a more computationally efficient manner than its Rosenblueth's counterpart. / Master of Science

In part to search for a possible critical point (CP) in the phase diagram of hot nuclear matter, a beam energy scan was performed at the Relativistic Heavy-Ion Collider at Brookhaven National Laboratory. The Solenoidal Tracker at RHIC (STAR) collected Au+Au data sets at beam energies, √sNN , of 7.7, 11.5, 19.6, 27, 39, 62.4, and 200 GeV. Such a scan produces hot nuclear matter at different locations in the phase diagram. Lattice and phenomenological calculations suggest that the presence of a CP might result in divergences of the thermodynamic susceptibilities and correlation lengths. The statistical moments of the identified-particle multiplicity distributions directly depend on both the thermodynamic susceptibilities and correlation lengths, possibly making the shapes of these multiplicity distributions sensitive tools for the search for the critical point. The statistical moments of the multiplicity distributions of a number of different groups of identified particle species were analyzed. Care was taken to remove a number of experimental artifacts that can modify the shapes of the multiplicity distributions. The observables studied include the lowest four statistical moments (mean, variance, skewness, kurtosis) and some products of these moments. These observables were compared to the predictions from several approaches lacking critical behavior, such as the Hadron Resonance Gas model, mixed events, (negative) binomial, and Poisson statistics. In addition, the data were analyzed after gating on the event-by-event antiproton-to-proton ratio, which is expected to more tightly constrain the event trajectories on the phase diagram.

This research study presents a new vibration-based non-destructive global structural damage identification and condition monitoring technique that can be used for detection, localization and quantification of damage. A two-stage damage identification process that combines non-model based and model-based damage identification approaches is proposed to overcome the main difficulties associated with the solution of structural damage identification problems. In the first stage, performance assessment of various response parameters obtained from the time-domain, frequency-domain and spectral-domain analysis is conducted using a non model-based damage detection and localization approach. In addition, vibration response parameters that are sensitive to local and global damage and that possess strong physical relationships with key structural dynamic properties are identified. Moreover, in order to overcome the difficulties associated with damage identification in the presence of structural nonlinearity and response nonstationarity, a wavelet transform based damage-sensitive parameter is presented for detection and localization of damage in the space domain. The level of sensitivity and effectiveness of these parameters for detection and localization of damage are demonstrated using various numerical experimental data determined from one-dimensional and two-dimensional plate-like structures.