Structural reliability and stochastic finite element methods

Abstract

Purpose This paper aims to provide a comprehensive review of uncertainty quantification methods supported by evidence-based comparison studies. Uncertainties are widely encountered in engineering practice, arising from such diverse sources as heterogeneity of materials, variability in measurement, lack of data and ambiguity in knowledge. Academia and industries have long been researching for uncertainty quantification (UQ) methods to quantitatively account for the effects of various input uncertainties on the system response. Despite the rich literature of relevant research, UQ is not an easy subject for novice researchers/practitioners, where many different methods and techniques coexist with inconsistent input/output requirements and analysis schemes. Design/methodology/approach This confusing status significantly hampers the research progress and practical application of UQ methods in engineering. In the context of engineering analysis, the research efforts of UQ are most focused in two largely separate research fields: structural reliability analysis (SRA) and stochastic finite element method (SFEM). This paper provides a state-of-the-art review of SRA and SFEM, covering both technology and application aspects. Moreover, unlike standard survey papers that focus primarily on description and explanation, a thorough and rigorous comparative study is performed to test all UQ methods reviewed in the paper on a common set of reprehensive examples. Findings Over 20 uncertainty quantification methods in the fields of structural reliability analysis and stochastic finite element methods are reviewed and rigorously tested on carefully designed numerical examples. They include FORM/SORM, importance sampling, subset simulation, response surface method, surrogate methods, polynomial chaos expansion, perturbation method, stochastic collocation method, etc. The review and comparison tests comment and conclude not only on accuracy and efficiency of each method but also their applicability in different types of uncertainty propagation problems. Originality/value The research fields of structural reliability analysis and stochastic finite element methods have largely been developed separately, although both tackle uncertainty quantification in engineering problems. For the first time, all major uncertainty quantification methods in both fields are reviewed and rigorously tested on a common set of examples. Critical opinions and concluding remarks are drawn from the rigorous comparative study, providing objective evidence-based information for further research and practical applications.

A Systematic Review of Structural Reliability Methods for Deformation and Fatigue Analysis of Offshore Jacket Structures

“…This section collates and discusses key aspects from the studies that stand out as particularly important. Tables 1-4 summarize the most popular SR methods and their capabilities and limitations [1,5,6,16,17,19,22,[28][29][30]55,64,80].…”

“…The conventional SR methods, such as FORM/SORM and MCS, still remain the de facto methods and serve as the basis for enhanced methods that overcome their inherent limitations. Recent research [80] shows that the FORM is the most efficient SRA method ahead of the SORM. The concepts underlining the intricate FORM/SORM algorithms, including the application of numerical optimization methods that form the basis of advancements already discussed in Section 2, are examined in depth and elucidated below [17].…”

“…Global methods, such as the Active Learning Reliability Method combining Kriging and MCS (AK-MCS) and the EGRA [56], have been found to be very efficient, as they give accurate results for implicit, time-consuming, unaffordable PFs, as demonstrated in [14]. For the treatment of problems, such as complex geotechnical designs and those involving high-frequency vibrations and of elastic stability, SFEM has been found to be ideal as it accounts for spatially varying stochastic structural heterogeneity [80,83]. Numerous studies were carried out on reliability analysis in other related areas such as in geotechnical engineering, fluid mechanics, rock engineering, etc.…”

“…The major techniques include Perturbation Techniques, Neumann expansion solution, RS approach, and branch and bound techniques [8,9]. A state-of-the-art review on SFEM is presented in [80].…”

Theoretical Guarantees for the Statistical Finite Element Method

“…There has been extensive research on deriving numerical methods for solving various classes of SPDEs. For detailed reviews of such methods the reader is referred to [20,23,32,29,34,2]. Some of these methods, for example the Stochastic Galerkin Finite Element method (SG-FEM) and its many variants, also finds their roots in the classical finite element method, but differ fundamentally from StatFEM.…”