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Various improvements which have been made to the vehicle (reduced engine noise, reducedaerodynamic related NVH), have resulted in tire road noise as the dominant source of thevehicle interior noise. Generally, vehicle interior noise has two main sources, 1) travellinglow frequency excitation below 800 Hz from road surface through a structure- borne pathand 2) the high frequency (above 800 Hz) air-borne noise that is caused by air- pumpingnoise caused by tread pattern.The structure-borne waves of the circumference of the tire are generated by excitation atthe contact patch due to the road surface texture and characteristics. These vibrations arethen transferred from the sidewalls of the tire to the rim and then are transmitted throughthe spindle-wheel interface, resulting in high frequency vibration of vehicle body panels andwindows.The focus of this study is to develop several statistical-based models for analyzing the roadsurface and using them to predict the tire-road noise structure-borne component. In order todo this, a new methodology for sensing the road characteristics, such as asperities and roadsurface condition, were developed using virtual sensing and intelligent tire technology. In ad-dition, the spindle forces were used as an indicator to the structure-borne noise of the vehicle.Several data mining and multivariate analysis-based methods were developed to extractfeatures and to develop an empirical model to predict the power of structure-borne noiseunder different operational and road conditions. Finally, multiple data driven models-basedmodels were developed to classify the road types, and conditions and use them for the noisefrequency spectrum prediction.

The problem of estimating underlying signals is well studied that has ubiquitous applications, such as signal processing. In network and image analysis, the tasks of signal estimation usually involve denoising a matrix based on structural information. In the situations where the information structure could be modeled by a network, graph trend filtering is a useful estimator with penalizing the $\ell_1$ norm of discrete derivatives based on some graph structures. A special case of graph trend filtering, based on penalizing an incidence matrix of a graph, is called graph fused lasso. In this dissertation, we proposed power graph fused lasso, an approach to denoising a response matrix with a graph, where both rows and columns of the matrix correspond to the vertices in the graph. There are two categories of graph fused lasso algorithms, solving the problem with a fixed hyperparameter and path algorithms solving for every hyperparameter. An overview of projected Newton-type method for graph fused lasso and ADMM-based graph trend filtering algorithms was provided. Ensemble graph fused lasso algorithms were proposed with some numerical results presented. We further discussed graph trend filtering with Kullback-Leibler divergence loss and how to solve the problem with a Bregman ADMM-based algorithm. We demonstrated the desired property that the GTF reconstructed signal is piecewise polynomial with an application to Covid-19 test positive data. Two other applications were also presented.

Electron Spin Resonance (ESR) Spectroscopy is a powerful method to study structure and dynamics of biomolecules. It detects magnetic resonance signals from the spin labels (or paramagnetic tags) attached at specific locations of a biological sample such as proteins, DNA, RNA, and lipids, among others. Despite many improvements in ESR instrument sensitivity, experimental signals lack sufficient strength that is needed to study complex biomolecules. We introduce signal processing methods as an alternate approach to remove noise present in the experimental ESR signals. We developed new methods based on wavelet transforms that are effectively able to retrieve signals, including weak signals. The methods are developed for one-dimensional continuous wave electron spin resonance (cw-ESR) signals and pulsed dipolar signals. The denoising methods achieve more than two orders-of-magnitude improvement in Signal-to-Noise Ratio (SNR) as well as can be used to reduce signal acquisition time by similar orders. In cw-ESR, the experimental signals obtained from the spectrometer are directly analyzed. Hence, there is no need for further data processing. In pulsed dipolar spectroscopy, the acquired signal needs to be processed to obtain desired information, i.e. distance distribution between a pair of spin labels. In addition to wavelet denoising, we developed a singular value decomposition (SVD) method to obtain well-resolved accurate distance distributions from the dipolar signals. The SVD method overcomes the limitations of standard Tikhonov regularization method that yields are compromise between a good resolution and a stable solution, as well as the limitation of model fitting methods that require a priori information. Further, we conducted the uncertainty analysis of the SVD solution. This research is first step towards utilizing the power of data processing methods to improve signal analysis in ESR spectroscopy.