My dissertation consists of six essays which contribute new theoretical results

to two econometrics frontiers: nonparametrics and finite sample econometrics. Chapters 2 to 3 discuss the estimation and inference of the nonparametric and semiparametric models. In chapter 2 an efficient two-step estimator is developed in single nonparametric regression model with a general parametric error covariance. By fully utilizing the information incorporated in the error covariance into estimation, the newly developed method is more efficient compared to the conventional local linear estimator (LLLS) and some other two-step estimator. The corresponding asymptotic theorems are derived. Monte Carlo study shows the relative efficiency gain of the newly proposed estimator. Chapter 3 systematically develops a new set of results for seemingly unrelated regression (SUR) analysis within nonparametric and semiparametric framework. We study the properties of LLLS and local linear weighted least squares (LLWLS) estimators, provide an efficient two-step estimation for the system and establish the asymptotic theorems under both unconditional and conditional error variance-covariance cases. The procedures of estimation for various nonparametric and semiparametric SUR models are proposed. In addition, two nonparametric goodness-of-fit measures for the system are given. Chapter 4 applies the estimation method developed in chapter 2 and 3 to an empirical analysis on return to public capital in U.S.

Chapters 5 to 6 study the finite sample properties of the mean reversion parameter estimator in continuous time models. In chapter 5 we approximate the bias of the estimator for the Levy-based Ornstein-Uhlenbeck (OU) process, and propose bias corrected estimators. In chapter 6 the exact distribution of the MLE is investigated under different scenarios: known or unknown drift term, fixed or random start-up value, and zero or positive . The numerical calculations demonstrate the remarkably reliable performance of the proposed exact approach.

In chapter 7 we study the efficiency of the coefficient of determination based on

final prediction error and compare it with conventional goodness-of-fit measures

in linear regression models with both normal and non-normal disturbances. The

efficiency results show that R2 based on

final prediction error has practical use in empirical analysis, for examples,

panel data analysis and time series analysis.

Carbon dioxide (CO2) emissions from fossil fuels are a major concern, which is widely regarded as a major cause of climate change. Electrochemical energy systems, such as hydrogen PEM fuel cells and batteries, can potentially address carbon dioxide emissions. PEM fuel cells operate at low temperatures with high power density, making them a promising candidate as the next-generation engine for vehicles, while Lithium-ion (Li-ion) batteries are widely used due to their high energy density, low and falling cost, and long lifetimes. However, major challenges exist in the future development of these electrochemical technologies, such as water management in PEM fuel cells and thermal management of Li-ion batteries.

In PEM fuel cells, improper water management will cause electrode “flooding” and consequently performance loss. To resolve such problems with rapid processing and on-line monitoring, a machine learning approach was developed to analyze neutron radiography images using the convolutional neural network (CNN). The CNN model for water detection in PEM fuel cells was trained on labeled radiography images constructed from a contour legend containing information on the water areal mass density. Image enhancement was carried out to generate additional data for CNN training. The properly trained CNN model is then applied to radiography images to obtain the corresponding average water areal mass density and water spatial variation under various current densities, relative humidity (RH), and flow fields. Compared with conventional pixelation methods, the proposed CNN method performs better in speed for high-resolution images.

In Li-ion batteries, thermal management can significantly impact battery performance, safety, and lifespan in applications. Once the operating temperature exceeds the safety range, Li-ion batteries may subject to fast degradation and safety concerns such as burning and explosion. To improve battery thermal management, the second approach proposed a CNN integrated with a Long Short-Term Memory (LSTM) network to investigate the State of Charge (SOC) and the average temperature of a battery. A physics-based thermally coupled battery (TCB) model was applied to study the physical processes during battery operation and generate the large dataset for the network training. Effects of the heat transfer coefficient, operating temperature, and material thermal conductivities were analyzed for 18650 cylindrical batteries. The TCB model and the machine learning network were validated against both experimental and literature data. The results show that the proposed network achieves better performance compared with CNN and LSTM model.

In addition to water management and thermal management of PEM fuel cells and Li-ion batteries, the developed tools can be used for integration with control algorithms to improve system operation and for image analysis for other energy systems.

This study reports experimental measurements of the thermal resistances of a thermal diode structure, consisting of microscale-thickness layers of distinct physical properties. The concept was developed based on the cathode structure of PEM fuel cell, which promotes water and heat removal in one direction by heat pipe effects in porous media. The diode layers have an overall thickness of 100-1,000 micrometers, similar to the overall thickness of the cathode in a PEM fuel cell. The unique thermal property is enabled by the heat pipe effects, directed by the arrangement of the sublayers through the capillary action. Experimental measurement is carried out on the simplest structure that consists of two sublayers with one being hydrophilic and the other hydrophobic. Various materials of distinct wettability properties are used and tested, including printing paper, carbon paper, cellulose paper, and polypropylene paper. The testing was also conducted under various conditions such as temperature, water contents, and sublayer properties, which may greatly influence the unique thermal property of this type of thermal diodes. Two water contents, 40% and 60% (volume percent) and temperature range of 30 ˚C-90 ˚C were examined. Results show that under 90 ˚C and 60% water contents. we achieve resistance 0.280 K/W in the conductive direction, over three times smaller than that in the opposite direction (0.874 K/W) for cellulose paper and polypropylene paper materials. For the sample of printing paper with carbon paper, and the sample of cellulose paper with carbon paper, the thermal resistances also have about two times difference. The thermal diodicity increases with temperature and water content in the most cases. Future work is to fabricate the diodicity materials for larger than 10 thermal diodicity.

Lithium oxygen battery has the potential to outdo the best battery system on the market due to its high theoretical specific energy of 11,400 Wh/kg (Li) which is comparable to that of gasolines. However, their practical implementation is still facing challenges, including low cyclic performance, high charging voltage, insoluble discharge product formation, and electrolyte degradation. Air cathodes, where oxygen reacts with Li ions and electrons to produce insoluble discharge oxides, are often considered as the most challenging component in nonaqueous Li-air batteries. To understand the voltage loss mechanisms in air cathodes due to insoluble discharge oxides, a mathematical model is developed, which incorporates the major thermodynamic, transport, and kinetic processes, and comprehensive analysis is conducted. Experiment is also designed and conducted for the model formulation and validation. Li battery components were fabricated, then assembled in an argon filled glove box. Electrochemical testing was conducted on the experimental Li air battery by using the PARSTAT MC Multichannel Potentiostat. An X-ray Diffraction, scanning electron microscope, and high-precision mass scale were employed to determine the composition, morphology, and spatial variation of Li oxide products. Through the model analysis, it is found that the electric passivation and oxygen transport blockage caused by the Li oxides precipitates reduce the battery voltage and energy capacity. The first stage of voltage drop is dominated by the electrode passivation and surface loss, while the latter stage of voltage drop is dominated by the oxygen blockage. In addition, several morphologies of oxides are identified in the cathode structure under various current densities, thus the proposed surface coverage model is superior to the traditional film-resistor approach. Further, it is found there exists spatial variations in discharge Li oxides in terms of mass and morphology, and experimental data show a good agreement with the theoretical analysis in term of the spatial variation of the Li oxides mass. The Da number is identified as a major parameter governing the spatial variation.

Laser powder bed fusion (LPBF), as a popular additive manufacturing (AM) technique, has gained a great deal of research attention and industrial application. Its capability of producing complicated shapes and structures enables this technique to be favored for manufacturing critical prototypes and complex parts. Meanwhile, LPBF techniques also have a significant advantage over many other AM processes that is they do not require support structure which allows more interest in producing parts with higher complexity since overhangs and unconnected islands are supported by surrounding unfused powder bed instead. However, in fabrication, the constant melting and cooling of metal powders by layers leads to a large gradient and rapid evolution of temperature, causing considerable residual stress and deformation. Fuel cells are widely regarded as a promising candidate as the next-generation energy device, which electrochemically converts the chemical energy in the injected fuel, such as hydrogen gas, directly to electricity. Fuel cell components are required to be free of distortion to avoid leakage of reactant gases and contaminants and interfacial resistance. In this study, a three-dimensional thermal analysis model is employed to numerically study the residual stress and deformation in the LPBF fabricated inlet/outlet of a fuel cell that connects to its bipolar plate. Inconel 718 and stainless steel SS316L are used as the powder materials, respectively. The results of distortion are validated against both experimental and other modeling data. Additionally, the validated tool is employed to investigate several major parameters in LPBF fabrication and their impacts on distortion, including the laser power, laser speed, and layer thickness. It is found that the laser power and speed have a significant impact on the distortion of the pipe wall, while the scan pattern shows little influence. Additionally, SS316L shows a much less distortion (about 40 µm) than that of In718 which is about 90 µm for the maximum distortion and a nearly 30% smaller average distortion at all measuring locations.

In response to the growing challenge of energy and power management caused by increasing

implementation of volatile sustainable energy sources, a case study of forecasting building

electric loads using statistical and machine learning methods is conducted for a multi-purpose

LEED-certified institutional building on the UC Irvine campus. Four data-driven methods,

which require no detailed building information and strong building energy knowledge, are

employed and compared, including the polynomial regression, Autoregressive Integrated

Moving Average (ARIMA), TBATS (Trigonometric seasonal formulation, Box-Cox

transformation, ARMA errors, Trend, and Seasonal components), and backpropagation Artificial

Neural Networks (ANN). These models are investigated to satisfy the ASHRAE standards and

optimize the prediction performance. A full year of hourly electric load and meteorological data

of the building in 2019 was obtained using the existing meters for this data-driven study. Root

Mean Square Error (RMSE), Coefficient of Variance (CV), Mean Absolute Percentage of Error

(MAPE) and R2 are calculated as evaluation criteria to compare the performances of these datadriven

methods in terms of prediction accuracy. Akaike’s Information Criteria (AIC) is

introduced as a guideline to determine the optimal model for several prediction models. The polynomial regression is performed using MATLAB and is shown capable of only data fitting

instead of forecasting when the total hour is used as the independent variable. When using the

daily and weekly data, the polynomial regression method fails for forecasting. For the wholemonth

data, ARIMA, TBATS, and ANN methods are used to predict hourly power load in the

next month with Python. The ARIMA model shows relatively low accuracy, indicating that it is

unable to handle multiple seasonlities in the data. TBATS shows a substantially improved

accuracy and satisfactory prediction. The backpropagation ANN is also conducted with its

configuration, including inputs, number of hidden layers and neurons, optimizer, and activation

functions, optimized after extensive testing. Different sets of training data are examined for both

TBATS and ANN. The ANN’s forecasting accuracy is found to be about 5~20% better than

TBATS’ when only using one month’s data for training. The residuals of these forecasting

methods show there could be information uncaptured in forecasting. It is speculated that

operation and activity schedules can serve as additional inputs for the ANN to achieve better

forecasting accuracy.

Two-phase flow in a microscale channel with a characteristic pressure drop, flow pattern, and liquid saturation occurs in a variety of applications. Understanding the behavior of two-phase flows and predicting the two-phase pressure drop can aid in the development and assessment of engineering designs; PEM fuel cells serve as a test case for this work. The experimental investigation of this work consists of measuring the two-phase pressure drop in a high aspect-ratio microchannel of dimensions 3.23mm wide by 0.304mm high combined with visualization of the two-phase flow. The tested superficial velocities represent common fuel cell operating conditions. In the first case, the microchannel consists of hydrophilic surfaces and the flow forms a stratified pattern. The two-phase pressure measurements led to the determination of a new relative permeability exponent (Wang, 2009) for stratified flow equal to 1.159, which predicts the two-phase pressure with a mean absolute percent error of 3.25%. The X-model and the correlations proposed by Lee & Lee (2001) and Kim & Mudawar (2012) well predict the experimental data with mean absolute percent errors of 3.32%, 4.1%, and 4.2%, respectively. Measurements of the water film thickness extracted from images of the flow follow the analytical result of Steinbrenner (2011). The new relative permeability exponent reasonably predicts the liquid saturation (dimensionless water film thickness).

In the second case, the base of the channel becomes hydrophobic while the other walls remain hydrophilic. This configuration forms a mixed-wettability microchannel, similar to the gas-supply channels found in PEM fuel cells. The change of the base wettability results in primarily rivulet flow along the hydrophobic surface and an increase in the two-phase pressure drop compared to the hydrophilic case. Researchers have presented inconsistent trends of the two-phase pressure drop with changing contact angle. This work proposes a critical liquid Capillary number in the range of 1.38×10 −4 to 9.63×10 −4 to clarify the trend for adiabatic flow in a single mixed-wettability microchannel. Furthermore, the work demonstrates the variability of the flow in the mixed-wettability channel. This suggests an instability of the rivulet flow, which prevents existing two-phase pressure models from collapsing the data. Optimizing the relative permeability exponent in the two-fluid model for rivulet flow led to a value of 1.747, which predicts the two-phase pressure measurements with a mean absolute percent error of 14.9%. The existing correlations of English & Kandlikar (2006) and Sun & Mishima (2009) predict the entire experimental data set with mean absolute percent errors of 22.7% and 23.7%, respectively.

Proton exchange membrane fuel cells' (PEMFCs') degradation is a main problem that must be solved for their commercialization. In this thesis, we employ data-driven prognostic models to forecast PEMFC voltage degradation utilizing artificial neural networks (ANN), deep neural networks (DNN), and long short-term memory (LSTM) techniques. The suggested models are developed and tested using experimental information obtained through PEMFC stack testing, and their performance is assessed using a variety of metrics, such as root mean square error (RMSE). The findings show that the DNN technique performs better than the other methods, indicating that the model can reliably and precisely forecast the PEMFC stack voltage decline. In addition, we examined the models' performance in terms of the neural network designs' number of neurons and layers. The results demonstrate a trade-off between prediction accuracy and computational complexity, with an increase in neurons and layers able to enhance prediction accuracy. In conclusion, the suggested data-driven prognostic models may offer precise and trustworthy forecasts of PEMFC stack voltage degradation, which can aid in optimizing system design and operation. In order to improve the precision and effectiveness of the prediction process, future research can concentrate on investigating the applicability of these models to specific degradation modes, such as catalyst and membrane degradation, and developing more sophisticated data-driven prognostic models. Moreover, combining data-driven and physics-based models can offer a thorough strategy for PEMFC degradation prognostics.Keywords: Proton exchange membrane fuel cell, Degradation, Prognostics, Artificial neural network, Deep neural network, Long short-term memory, Data-driven model.

GDL is an important component of Proton Exchange Membrane Fuel Cell, which provides multi-functions: reactant transport, heat/water removal, mechanical support to the membrane electrode assembly (MEA), and protection of the catalyst layer from corrosion or erosion. GDLs are located between MPLs and bipolar plates, and gases reactants are distributed in the flow field channels and diffuses to the catalyst layer via GDLs. This study is to investigate the deformation or intrusion of GDL upon compression, which alters the channel cross-section and hence the flow conductance for PEM fuel cells. A 3-dimensional finite element model by ANSYS was developed to simulate the GDL deformation under various compression. Deformation or intrusion of GDL will reduce the space of gas flow channel and thus affect the performance of PEM fuel cell. As the compression pressure increases, the GDL intrusion area into the channel increases. The intrusion also increases with the increasing of width of the channel under the same pressure if the GDL-MPL interface is fixed. In addition, if the height of GDL increases, the intrusion of GDL into the channel also increases. When the GDL is 0.2 mm, channel width is 2mm, the pressure is 1 MPa, the intrusion of GDL is 0.05749 mm. When the GDL is 0.3 mm, channel width is 2mm, the pressure is 1 MPa, the intrusion of GDL is 0.08314 mm. To investigate the GDL-MPL interfacial force, the MPL is added to be in touch with the GDL. The simulation shows that the force will change with the increasing pressure. That means they may separate when the pressure increases to a point. In this study, the effect of porous media to the deformation of GDL and the delamination between GDL and MPL are studied. It was investigated in comparison with the traditional hollow channel configuration. Porous media flow field was first proposed by Wang in 2008, which uses porous materials such as metal foams and carbon felts in the channel space and utilizes the multi-functions of porous materials for heat, electron, and flow conductance. It is found that this new porous media flow field reduces the intrusion of GDLs under land compression with reduction dependent on the channel depth and Young’s modulus of the porous material. For a channel depth of 0.3 mm and Young’s modulus of 6.3 MPa, the intrusion was reduced by 21.1%. In addition, the tensile force between GDL and MPL is also depressed by introducing the porous media flow field. For the cases of channel full of porous media, only compressive stress was predicted, which avoids any separation or delamination between the GDL and MPL. The impact on the interfacial force is found to be a function of the channel width, Young’s modulus of the porous material, and land compression. The findings are important to design porous media flow field for PEM fuel cell applications.