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- All Subjects: Electrical Engineering
- Creators: Papandreou-Suppappola, Antonia
- Creators: Yu, Hongbin
- Resource Type: Text
- Status: Published
Description
The propagation of waves in solids, especially when characterized by dispersion, remains a topic of profound interest in the field of signal processing. Dispersion represents a phenomenon where wave speed becomes a function of frequency and results in multiple oscillatory modes. Such signals find application in structural healthmonitoring for identifying potential damage sensitive features in complex materials.
Consequently, it becomes important to find matched time-frequency representations
for characterizing the properties of the multiple frequency-dependent modes of propagation in dispersive material. Various time-frequency representations have been
used for dispersive signal analysis. However, some of them suffered from poor timefrequency localization or were designed to match only specific dispersion modes with
known characteristics, or could not reconstruct individual dispersive modes. This
thesis proposes a new time-frequency representation, the nonlinear synchrosqueezing
transform (NSST) that is designed to offer high localization to signals with nonlinear time-frequency group delay signatures. The NSST follows the technique used
by reassignment and synchrosqueezing methods to reassign time-frequency points of
the short-time Fourier transform and wavelet transform to specific localized regions
in the time-frequency plane. As the NSST is designed to match signals with third
order polynomial phase functions in the frequency domain, we derive matched group
delay estimators for the time-frequency point reassignment. This leads to a highly localized representation for nonlinear time-frequency characteristics that also allow for
the reconstruction of individual dispersive modes from multicomponent signals. For
the reconstruction process, we propose a novel unsupervised learning approach that
does not require prior information on the variation or number of modes in the signal.
We also propose a Bayesian group delay mode merging approach for reconstructing
modes that overlap in time and frequency. In addition to using simulated signals, we demonstrate the performance of the new NSST, together with mode extraction, using
real experimental data of ultrasonic guided waves propagating through a composite
plate.
ContributorsIkram, Javaid (Author) / Papandreou-Suppappola, Antonia (Thesis advisor) / Chattopadhyay, Aditi (Thesis advisor) / Bertoni, Mariana (Committee member) / Sinha, Kanu (Committee member) / Arizona State University (Publisher)
Created2023
Description
The integration of Distributed Energy Resources (DER), including wind energy and photovoltaic (PV) panels, into power systems, increases the potential for events that could lead to outages and cascading failures. This risk is heightened by the limited dynamic information in energy grid datasets, primarily due to sparse Phasor Measurement Units (PMUs) placement. This data quality issue underscores the need for effective methodologies to manage these challenges. One significant challenge is the data gaps in low-resolution (LR) data from RTU and smart meters, hindering robust machine learning (ML) applications. To address this, a systematic approach involves preparing data effectively and designing efficient event detection methods, utilizing both intrinsic physics and extrinsic correlations from power systems. The process begins by interpolating LR data using high-resolution (HR) data, aiming to create virtual PMUs for improved grid management. Current interpolation methods often overlook extrinsic spatial-temporal correlations and intrinsic governing equations like Ordinary Differential Equations (ODEs) or Differential Algebraic Equations (DAEs). Physics-Informed Neural Networks (PINNs) are used for this purpose, though they face challenges with limited LR samples. The solution involves exploring the embedding space governed by ODEs/DAEs, generating extrinsic correlations for initial LR data imputation, and enforcing intrinsic physical constraints for refinement. After data preparation, event data dimensions such as spatial, temporal, and measurement categories are recovered in a tensor. To prevent overfitting, common in traditional ML methods, tensor decomposition is used. This technique merges intrinsic and physical information across dimensions, yielding informative and compact feature vectors for efficient feature extraction and learning in event detection. Lastly, in grids with insufficient data, knowledge transfer from grids with similar event patterns is a viable solution. This involves optimizing projected and transferred vectors from tensor decomposition to maximize common knowledge utilization across grids. This strategy identifies common features, enhancing the robustness and efficiency of ML event detection models, even in scenarios with limited event data.
ContributorsMa, Zhihao (Author) / Weng, Yang (Thesis advisor) / Wu, Meng (Committee member) / Yu, Hongbin (Committee member) / Matavalam, Amarsagar Reddy Ramapuram (Committee member) / Arizona State University (Publisher)
Created2023
Description
This dissertation centers on the development of Bayesian methods for learning differ- ent types of variation in switching nonlinear gene regulatory networks (GRNs). A new nonlinear and dynamic multivariate GRN model is introduced to account for different sources of variability in GRNs. The new model is aimed at more precisely capturing the complexity of GRN interactions through the introduction of time-varying kinetic order parameters, while allowing for variability in multiple model parameters. This model is used as the drift function in the development of several stochastic GRN mod- els based on Langevin dynamics. Six models are introduced which capture intrinsic and extrinsic noise in GRNs, thereby providing a full characterization of a stochastic regulatory system. A Bayesian hierarchical approach is developed for learning the Langevin model which best describes the noise dynamics at each time step. The trajectory of the state, which are the gene expression values, as well as the indicator corresponding to the correct noise model are estimated via sequential Monte Carlo (SMC) with a high degree of accuracy. To address the problem of time-varying regulatory interactions, a Bayesian hierarchical model is introduced for learning variation in switching GRN architectures with unknown measurement noise covariance. The trajectory of the state and the indicator corresponding to the network configuration at each time point are estimated using SMC. This work is extended to a fully Bayesian hierarchical model to account for uncertainty in the process noise covariance associated with each network architecture. An SMC algorithm with local Gibbs sampling is developed to estimate the trajectory of the state and the indicator correspond- ing to the network configuration at each time point with a high degree of accuracy. The results demonstrate the efficacy of Bayesian methods for learning information in switching nonlinear GRNs.
ContributorsVélez-Cruz, Nayely (Author) / Papandreou-Suppappola, Antonia (Thesis advisor) / Moraffah, Bahman (Committee member) / Tepedelenlioğlu, Cihan (Committee member) / Berisha, Visar (Committee member) / Arizona State University (Publisher)
Created2023