The main objective of this work is to give contribution in both additive manufacturing (AM) and tribometry derived from the application and study of materials available with the use of biomimetic designs. Additional contributions are determining what effects treatments for flooring surfaces may have on the dynamic coefficient of friction and the effects of these products on common surfaces. The validity of the proposed methodology for a proof of concept was demonstrated by comparing measured dynamic coefficient of friction for designs using standardized equipment and comparing these values to plantar skin tested using an accepted and standardized testing method that has been extensively researched and validated. Initial biomimetic designs and characteristics unique to each design were researched and compared. Eleven designs were selected to be fabricated, tested, and compared to select the most desirable applications for further investigation. Research into potential treatments commercially available for use was done to determine the efficacy of these products. Prototype sensor designs were selected and fabricated using direct light processing (DLP) technology. Examination of the measured values was done through an analysis of the variances in the response variable and comparisons using Fisher and Tukey pairwise comparison method. Future work recommendations are provided for further development and improvement of the topics presented in this thesis.

The advances in data-collecting technologies provides great opportunities to access large sample-size data sets with high dimensionality. Variable selection is an important procedure to extract useful knowledge from such complex data. While in many real-data applications, appropriate selection of variables should facilitate the model interpretation and computation efficiency. It is thus important to incorporate domain knowledge of underlying data generation mechanism to select key variables for improving the model performance. However, general variable selection techniques, such as the best subset selection and the Lasso, often do not take the underlying data generation mechanism into considerations. This thesis proposal aims to develop statistical modeling methodologies with a focus on the structured variable selection towards better model interpretation and computation efficiency. Specifically, this thesis proposal consists of three parts: an additive heredity model with coefficients incorporating the multi-level data, a regularized dynamic generalized linear model with piecewise constant functional coefficients, and a structured variable selection method within the best subset selection framework. In Chapter 2, an additive heredity model is proposed for analyzing mixture-of-mixtures (MoM) experiments. The MoM experiment is different from the classical mixture experiment in that the mixture component in MoM experiments, known as the major component, is made up of sub-components, known as the minor components. The proposed model considers an additive structure to inherently connect the major components with the minor components. To enable a meaningful interpretation for the estimated model, we apply the hierarchical and heredity principles by using the nonnegative garrote technique for model selection. The performance of the additive heredity model was compared to several conventional methods in both unconstrained and constrained MoM experiments. The additive heredity model was then successfully applied in a real problem of optimizing the Pringlestextsuperscript{textregistered} potato crisp studied previously in the literature. In Chapter 3, we consider the dynamic effects of variables in the generalized linear model such as logistic regression. This work is motivated from the engineering problem with varying effects of process variables to product quality caused by equipment degradation. To address such challenge, we propose a penalized dynamic regression model which is flexible to estimate the dynamic coefficient structure. The proposed method considers modeling the functional coefficient parameter as piecewise constant functions. Specifically, under the penalized regression framework, the fused lasso penalty is adopted for detecting the changes in the dynamic coefficients. The group lasso penalty is applied to enable a sparse selection of variables. Moreover, an efficient parameter estimation algorithm is also developed based on alternating direction method of multipliers. The performance of the dynamic coefficient model is evaluated in numerical studies and three real-data examples. In Chapter 4, we develop a structured variable selection method within the best subset selection framework. In the literature, many techniques within the LASSO framework have been developed to address structured variable selection issues. However, less attention has been spent on structured best subset selection problems. In this work, we propose a sparse Ridge regression method to address structured variable selection issues. The key idea of the proposed method is to re-construct the regression matrix in the angle of experimental designs. We employ the estimation-maximization algorithm to formulate the best subset selection problem as an iterative linear integer optimization (LIO) problem. the mixed integer optimization algorithm as the selection step. We demonstrate the power of the proposed method in various structured variable selection problems. Moverover, the proposed method can be extended to the ridge penalized best subset selection problems. The performance of the proposed method is evaluated in numerical studies. / Doctor of Philosophy / The advances in data-collecting technologies provides great opportunities to access large sample-size data sets with high dimensionality. Variable selection is an important procedure to extract useful knowledge from such complex data. While in many real-data applications, appropriate selection of variables should facilitate the model interpretation and computation efficiency. It is thus important to incorporate domain knowledge of underlying data generation mechanism to select key variables for improving the model performance. However, general variable selection techniques often do not take the underlying data generation mechanism into considerations. This thesis proposal aims to develop statistical modeling methodologies with a focus on the structured variable selection towards better model interpretation and computation efficiency. The proposed approaches have been applied to real-world problems to demonstrate their model performance.

Two-bay hall for warehouse and manufacturing purposes with supporting steel structure and thermally insulating sheating with width of 36 metres and lenght of 72 metres. The hall incorporates two overhead cranes with maximum load of 32 and 40 tonnes. The main supporting structure is a system of plate girders and beams. The beams are connected with hinges and are placed with intervals of 6 metres. The hall design is intended for 1st snowing area