Modern manufacturing needs to optimize the entire product lifecycle to satisfy the customer needs. The advancement of sensing technologies has brought a data rich environment for manufacturing and provide a great opportunity for real-time, proactive quality assurance. However, due to the lack of methods for analyzing heterogeneous types of data, the transformation of data to information and knowledge for effective decision making in manufacturing is still a challenging problem. In particular, functional variables can represent the in situ process conditions and rich product performance information, and are widely encountered in various manufacturing processes. In this dissertation, I will focus on modeling of manufacturing processes with in situ process (functional) variables, and integrating these functional variables and other measured variables for the manufacturing modeling. The modeling is explored by extracting informative features through the integration of multiple functional variables, functional variables and offline setting variables, and quantitative and qualitative quality variables. After an introduction in Chapter 1, three research tasks are investigated. First, a functional variable selection problem is studied in Chapter 2 to identify the significant functional variables as well as their features in a logistic regression model. A hierarchical non-negative garrote constrained estimation method is proposed. Second, the quality-process relationships for scalar offline setting variables, functional in situ process variables, and manufacturing quality responses are studied in Chapter 3. A functional graphical model that can integrate functional variables in a graphical model is proposed and investigated. Third, the quantitative and qualitative quality responses are jointly modeled with scalar offline setting variables and functional in situ process variables in Chapter 4. A functional quantitative and qualitative model is proposed and investigated. Finally, I summarize the research contribution and discuss future research directions in Chapter 5. The proposed methodologies have broad applications in manufacturing processes with functional variables, and are demonstrated in a crystal growth process with multiple functional variables (Chapter 2), a plasma spray process with multiple scalar and functional variables (Chapter 3), and an additive manufacturing process called fused deposition modeling with quantitative and qualitative quality responses (Chapter 4). / Ph. D. / Advanced manufacturing has attracted much attention in recent years. One unique requirement in advanced manufacturing is that the entire product lifecycle needs to be optimized to satisfy the customer needs. Thanks to the advancement of sensing and information technology, various types of manufacturing data are collect, which provide a great opportunity for real-time, proactive quality assurance. At the current status, there is a lack of data analytics methods to analyze these manufacturing data, based on which effective decisions and actions can be made to improve the advanced manufacturing quality and efficiency. Among these sensor data, the continuously measured functional variables during the manufacturing processes, which can represent the <i>in situ</i> process conditions and rich product performance information, are widely encountered. In this dissertation, I will focus on the modeling of manufacturing processes with <i>in situ</i> process (functional) variables, and integrating these functional variables and other measured variables for the manufacturing modeling. In particular, multiple functional variables, functional variables and scalar offline setting variables, and quantitative and qualitative quality variables are modeled in advanced manufacturing. After an introduction in Chapter 1, three research tasks are investigated. First, a functional variable selection problem is studied in Chapter 2 to identify the significant functional variables as well as their features in a logistic regression model for product quality condition classification. Second, the quality-process relationships for scalar offline setting variables, functional <i>in situ</i> process variables, and manufacturing quality responses are studied in Chapter 3. A functional graphical model that can integrate functional variables in a graphical model is proposed and investigated. Third, the quantitative and qualitative quality responses are jointly modeled with scalar offline setting variables and functional <i>in situ</i> process variables in Chapter 4. A functional quantitative and qualitative model is proposed and investigated. Finally, I summarize the research contribution and discuss future research directions in Chapter 5. The proposed methodologies have broad applications in manufacturing processes with functional variables, and are demonstrated in a crystal growth process with multiple functional variables (Chapter 2), a plasma spray process with multiple scalar and functional variables (Chapter 3), and an additive manufacturing process with quantitative and qualitative quality responses (Chapter 4).

Extracellular neuroelectronic interfacing has important applications in the fields of neural prosthetics, biological computation and whole-cell biosensing for drug screening and toxin detection. While the field of neuroelectronic interfacing holds great promise, the recording of high-fidelity signals from extracellular devices has long suffered from the problem of low signal-to-noise ratios and changes in signal shapes due to the presence of highly dispersive dielectric medium in the neuron-microelectrode cleft. This has made it difficult to correlate the extracellularly recorded signals with the intracellular signals recorded using conventional patch-clamp electrophysiology. For bringing about an improvement in the signalto-noise ratio of the signals recorded on the extracellular microelectrodes and to explore strategies for engineering the neuron-electrode interface there exists a need to model, simulate and characterize the cell-sensor interface to better understand the mechanism of signal transduction across the interface. Efforts to date for modeling the neuron-electrode interface have primarily focused on the use of point or area contact linear equivalent circuit models for a description of the interface with an assumption of passive linearity for the dynamics of the interfacial medium in the cell-electrode cleft. In this dissertation, results are presented from a nonlinear dynamic characterization of the neuroelectronic junction based on Volterra-Wiener modeling which showed that the process of signal transduction at the interface may have nonlinear contributions from the interfacial medium. An optimization based study of linear equivalent circuit models for representing signals recorded at the neuron-electrode interface subsequently iv proved conclusively that the process of signal transduction across the interface is indeed nonlinear. Following this a theoretical framework for the extraction of the complex nonlinear material parameters of the interfacial medium like the dielectric permittivity, conductivity and diffusivity tensors based on dynamic nonlinear Volterra-Wiener modeling was developed. Within this framework, the use of Gaussian bandlimited white noise for nonlinear impedance spectroscopy was shown to offer considerable advantages over the use of sinusoidal inputs for nonlinear harmonic analysis currently employed in impedance characterization of nonlinear electrochemical systems. Signal transduction at the neuron-microelectrode interface is mediated by the interfacial medium confined to a thin cleft with thickness on the scale of 20-110 nm giving rise to Knudsen numbers (ratio of mean free path to characteristic system length) in the range of 0.015 and 0.003 for ionic electrodiffusion. At these Knudsen numbers, the continuum assumptions made in the use of Poisson-Nernst-Planck system of equations for modeling ionic electrodiffusion are not valid. Therefore, a lattice Boltzmann method (LBM) based multiphysics solver suitable for modeling ionic electrodiffusion at the mesoscale neuron-microelectrode interface was developed. Additionally, a molecular speed dependent relaxation time was proposed for use in the lattice Boltzmann equation. Such a relaxation time holds promise for enhancing the numerical stability of lattice Boltzmann algorithms as it helped recover a physically correct description of microscopic phenomena related to particle collisions governed by their local density on the lattice. Next, using this multiphysics solver simulations were carried out for the charge relaxation dynamics of an electrolytic nanocapacitor with the intention of ultimately employing it for a simulation of the capacitive coupling between the neuron and the v planar microelectrode on a microelectrode array (MEA). Simulations of the charge relaxation dynamics for a step potential applied at t = 0 to the capacitor electrodes were carried out for varying conditions of electric double layer (EDL) overlap, solvent viscosity, electrode spacing and ratio of cation to anion diffusivity. For a large EDL overlap, an anomalous plasma-like collective behavior of oscillating ions at a frequency much lower than the plasma frequency of the electrolyte was observed and as such it appears to be purely an effect of nanoscale confinement. Results from these simulations are then discussed in the context of the dynamics of the interfacial medium in the neuron-microelectrode cleft. In conclusion, a synergistic approach to engineering the neuron-microelectrode interface is outlined through a use of the nonlinear dynamic modeling, simulation and characterization tools developed as part of this dissertation research.