Applying Uncertainty Quantification to Structural Systems: Parameter Reduction for Evaluating Model Complexity

Abstract

Different mathematical models can be developed to represent the dynamic behavior of structural systems and assess properties, such as risk of failure and reliability. Selecting an adequate model requires choosing a model of sufficient complexity to accurately capture the output responses under various operational conditions. However, as model complexity increases, the functional relationship between input parameters varies and the number of parameters required to represent the physical system increases, reducing computational efficiency and increasing modeling difficulty. The process of model selection is further exacerbated by uncertainty introduced from input parameters, noise in experimental measurements, numerical solutions, and model form. The purpose of this research is to evaluate the acceptable level of uncertainty that can be present within numerical models, while reliably capturing the fundamental physics of a subject system. However, before uncertainty quantification can be performed, a sensitivity analysis study is required to prevent numerical ill-conditioning from parameters that contribute insignificant variability to the output response features of interest. The main focus of this paper, therefore, is to employ sensitivity analysis tools on models to remove low sensitivity parameters from the calibration space. The subject system in this study is a modular spring-damper system integrated into a space truss structure. Six different cases of increasing complexity are derived from a mathematical model designed from a two-degree of freedom (2DOF) mass spring-damper that neglects single truss properties, such as geometry and truss member material properties. Model sensitivity analysis is performed using the Analysis of Variation (ANOVA) and the Coefficient of Determination R ². The global sensitivity results for the parameters in each 2DOF case are determined from the R ² calculation and compared in performance to evaluate levels of parameter contribution. Parameters with a weighted R ² value less than .02 account for less than 2% of the variation in the output responses and are removed from the calibration space. This paper concludes with an outlook on implementing Bayesian inference methodologies, delayed-acceptance single-component adaptive Metropolis (DA-SCAM) algorithm and Gaussian Process Models for Simulation Analysis (GPM/SA), to select the most representative mathematical model and set of input parameters that best characterize the system’s dynamic behavior.