Theoretical studies have indicated that structure function (SF) analysis is likely a viable tool for studying interstellar magnetohydrodynamic (MHD) turbulence. Turbulence plays a critical role in important galactic processes including the structure and evolution of giant molecular clouds (GMCs) as well as the formation of sub-structures known to spawn stellar progenitors. This study investigates the limitations of SF analysis as a tool for gauging MHD turbulence in GMCs. There exist many different methods of extracting GMCs from survey data, yet there is no known studies investigating their effects on SF accuracy. Despite the consensus in recent literature this study finds that SF analysis may have potential accuracy issues when its necessary to extract components from larger survey data.

High fidelity finite element (FE) models are widely used to simulate the dynamic responses of geometrically nonlinear structures. The high computational cost of running long time duration analyses, however, has made nonlinear reduced order models (ROMs) attractive alternatives. While there are a variety of reduced order modeling techniques, in general, their shared goal is to project the nonlinear response of the system onto a smaller number of degrees of freedom. Implicit Condensation (IC), a popular and non-intrusive technique, identifies the ROM parameters by fitting a polynomial model to static force-displacement data from FE model simulations. A notable drawback of these models, however, is that the number of polynomial coefficients increases cubically with the number of modes included within the basis set of the ROM. As a result, model correlation, updating and validation become increasingly more expensive as the size of the ROM increases. This work presents simultaneous regression and selection as a method for filtering the polynomial coefficients of a ROM based on their contributions to the nonlinear response. In particular, this work utilizes the method of least absolute shrinkage and selection (LASSO) to identify a sparse set of ROM coefficients during the IC regression step. Cross-validation is used to demonstrate accuracy of the sparse models over a range of loading conditions.