Global response sensitivity and reliability analyses of structural dynamical systems with parameter and excitation uncertainties

Abstract

This thesis develops computational methods for global response sensitivity analysis (GRSA) and time-variant reliability analysis in structural dynamical systems with parameter and excitation uncertainties. The primary motivation for this work is the need to develop computationally efficient methods for quantifying the influence of uncertainties arising from system parameters and/or external excitations on the performance of engineering systems. The efficacies of the proposed methods are demonstrated on selected structural engineering problems. Chapter 1 presents an overview of GRSA and reliability analyses, which establishes the necessary background for the subsequent developments in the thesis. Chapter 2 provides a detailed review of the literature on global response sensitivity analysis and time-variant reliability analysis, particularly focusing on Girsanov’s transformation-based approaches. It categorizes existing GRSA methods into variance-based approaches, model-distance-based approaches, and factor mapping methods while outlining their applicability and limitations in structural engineering contexts. It also reviews sampling variance reduction techniques, particularly in the estimation of rare-event probabilities under stochastic excitations. The motivation for this chapter is to identify open problems that guide the research objectives of this thesis. Chapter 3 introduces a simulation-based GRSA framework using the factor mapping method, extending its capability to handle grouped random variables. The chapter explores the use of alternative probability distance measures, including the Bhattacharyya distance, within this framework to assess the influence of groups of dependent and non-Gaussian random variables on system responses. Within the framework of the proposed GRSA, we examine different approaches for joint probability density estimation, such as Nataf’s model, copula models, and independent component analysis (ICA). The proposed approach is assessed against traditional GRSA methods, demonstrating its advantages in computational speed, ease of implementation, and accuracy, particularly when handling grouped input variables. Chapters 4 through 6 present the application of the proposed GRSA framework to three representative structural engineering problems: (i) the seismic global damage assessment of a moment-resisting steel frame, (ii) the global response sensitivity analysis of performance measures in a semi-actively controlled building frame, and (iii) the posterior sensitivity evaluation of an instrumented structure using available probability distributions of model parameters. Up to this point in the thesis, only parameter uncertainty has been considered, with excitations treated as deterministic. However, an important class of problems in structural engineering involves reliability analysis of systems subjected to both parameter and excitation uncertainties. Chapter 7 presents a Girsanov’s transformation-based method for time-variant reliability estimation in dynamical systems under combined uncertainties. The method integrates importance sampling for system parameters with Girsanov’s control for excitation processes, achieving variance reduction in the estimation of small failure probabilities. Numerical examples, including single and multi-degree-of-freedom, linear and nonlinear systems under stochastic excitations, are used to demonstrate the successful performance of the proposed approach. Chapter 8 summarises the research work carried out in this thesis and provides the scope of future research based on this thesis. This thesis is supplemented by six annexures that provide supporting technical details. Annexures A-F provide supplementary details that augment information presented in the main body of the thesis with an aim to make the document self-contained.