A general framework for probabilistic sensitivity analysis with respect to distribution parameters

TY - JOUR

T1 - A general framework for probabilistic sensitivity analysis with respect to distribution parameters

AU - Yang, Jiannan

N1 - Funding Information: This work has been funded by the Engineering and Physical Sciences Research Council, United Kingdom through the award of a Programme Grant “Digital Twins for Improved Dynamic Design”, Grant No. EP/R006768. For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising. The author is grateful to Professor Robin Langley, University of Cambridge, for the support to publish this work. Funding Information: This work has been funded by the Engineering and Physical Sciences Research Council, United Kingdom through the award of a Programme Grant “Digital Twins for Improved Dynamic Design”, Grant No. EP/R006768 . For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising. The author is grateful to Professor Robin Langley, University of Cambridge, for the support to publish this work. Publisher Copyright: © 2023 The Author(s)

PY - 2023/4/1

Y1 - 2023/4/1

N2 - Probabilistic sensitivity analysis identifies the influential uncertain input to guide decision-making. We propose a general sensitivity framework with respect to the input distribution parameters that unifies a wide range of sensitivity measures, including information theoretical metrics such as the Fisher information. The framework is derived analytically via a constrained maximisation and the sensitivity analysis is reformulated into an eigenvalue problem. There are only two main steps to implement the sensitivity framework utilising the likelihood ratio/score function method, a Monte Carlo type sampling followed by solving an eigenvalue equation. The resulting eigenvectors then provide the directions for simultaneous variations of the input parameters and guide the focus to perturb uncertainty the most. Not only is it conceptually simple, but numerical examples demonstrate that the proposed framework also provides new sensitivity insights, such as the combined sensitivity of multiple correlated uncertainty metrics, robust sensitivity analysis with an entropic constraint, and approximation of deterministic sensitivities. Three different examples, ranging from a simple cantilever beam to an offshore marine riser, are used to demonstrate the potential applications of the proposed sensitivity framework to applied mechanics problems.

AB - Probabilistic sensitivity analysis identifies the influential uncertain input to guide decision-making. We propose a general sensitivity framework with respect to the input distribution parameters that unifies a wide range of sensitivity measures, including information theoretical metrics such as the Fisher information. The framework is derived analytically via a constrained maximisation and the sensitivity analysis is reformulated into an eigenvalue problem. There are only two main steps to implement the sensitivity framework utilising the likelihood ratio/score function method, a Monte Carlo type sampling followed by solving an eigenvalue equation. The resulting eigenvectors then provide the directions for simultaneous variations of the input parameters and guide the focus to perturb uncertainty the most. Not only is it conceptually simple, but numerical examples demonstrate that the proposed framework also provides new sensitivity insights, such as the combined sensitivity of multiple correlated uncertainty metrics, robust sensitivity analysis with an entropic constraint, and approximation of deterministic sensitivities. Three different examples, ranging from a simple cantilever beam to an offshore marine riser, are used to demonstrate the potential applications of the proposed sensitivity framework to applied mechanics problems.

KW - Combined sensitivity

KW - Decision under uncertainty

KW - Information theoretical sensitivity

KW - Parametric sensitivity

KW - Sensitivity matrix

UR - http://www.scopus.com/inward/record.url?scp=85147731891&partnerID=8YFLogxK

U2 - 10.1016/j.probengmech.2023.103433

DO - 10.1016/j.probengmech.2023.103433

M3 - Article

AN - SCOPUS:85147731891

SN - 0266-8920

VL - 72

JO - Probabilistic Engineering Mechanics

JF - Probabilistic Engineering Mechanics

M1 - 103433

ER -