Generalized Methods for Global Sensitivity Analysis

Abstract

The complexity of chemical systems that are of practical interest has naturally increased in recentyears. These systems are often characterized as being high-dimensional, with many tunable input controls as well as parameters all accompanied by inherent uncertainty. Such systems also typically have a broad range of observable output responses. Further, the relationship between the inputs and outputs are typically nonlinear. In many scenarios, the system is often viewed as a "black box" where only the initial input and output responses are recorded, leaving little information about the system's internal workings. Regardless of the scenario, revealing how the input variables influence the outputs is the domain of sensitivity analysis, which provides statistical assessments that can guide the understanding of complex systems. The primary focus of this thesis is to develop new data driven tools to analyze the input-outputinformation content of complex systems. The first advancement in this thesis is a new kernel-based global sensitivity analysis (GSA) methodology. The mathematical formulation of kernel GSA is developed and several key advantages are demonstrated over that of traditional GSA routines: (1) the kernel techniques can be applied on arbitrary types of data, (2) the algorithmic complexity scales independent of output dimensionality, and (3) the kernel choice may be tuned to the desired goals of the analysis. Beyond the mathematical principles set out, this thesis presents numerical algorithms that can applied to practical experimental data as well as to the treatment of complicated input-output models. This will include the treatment of systems where there are inherent stochastic sources of input variability that yield a distribution of system output responses for a fixed set of inputs. Additionally, two fundamental concepts within GSA are explored within the thesis and newinsights are provided. The first concept investigates issues that arise in selecting input sampling procedures, specifically when there are multiple alternative distribution choices over the inputs. The second concept addresses what is called trend analysis, or how to visualize marginal input influences on the output. In trend analysis, there are many different techniques present in the literature, and in certain circumstances, the different techniques disagree in explaining how the output is influenced by the inputs. The thesis research explores the underlying cause of this behavior and makes recommendations on how to utilize trend analysis under such scenarios. The collective new procedures in this thesis are applied to a wide range of practical illustrative input-output systems including continuous flow chemical reactors, the manufacturing of lithium-ion batteries, climate economy models, and COVID-19 pandemic models.