Uncertainty propagation analysis using sparse grid technique and saddlepoint approximation based on parameterized p-box representation

Uncertainty propagation analysis, which assesses the impact of the uncertainty of input variables on responses, is an important component in risk assessment or reliability analysis of structures. This paper proposes an uncertainty propagation analysis method for structures with parameterized probabi...

Full description

Saved in:
Bibliographic Details
Published in:Structural and multidisciplinary optimization 2019, Vol.59 (1), p.61-74
Main Authors: Liu, H. B., Jiang, C., Liu, J., Mao, J. Z.
Format: Article
Language:English
Subjects:
Approximation
Component reliability
Computational Mathematics and Numerical Analysis
Economic models
Engineering
Engineering Design
Numerical integration
Optimization
Parameterization
Propagation
Reliability analysis
Reliability engineering
Representations
Research Paper
Response functions
Risk analysis
Risk assessment
Statistical analysis
Structural reliability
Theoretical and Applied Mechanics
Uncertainty
Uncertainty analysis
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Uncertainty propagation analysis, which assesses the impact of the uncertainty of input variables on responses, is an important component in risk assessment or reliability analysis of structures. This paper proposes an uncertainty propagation analysis method for structures with parameterized probability-box (p-box) representation, which could efficiently compute both the bounds on statistical moments and also the complete probability bounds of the response function. Firstly, based on the sparse grid numerical integration (SGNI) method, an optimized SGNI (OSGNI) is presented to calculate the bounds on the statistical moments of the response function and the cumulants of the cumulant generating function (CGF), respectively. Then, using the bounds on the first four cumulants, an optimization procedure based on the saddlepoint approximation is proposed to obtain the whole range of probability bounds of the response function. Through using the saddlepoint approximation, the present approach can achieve a good accuracy in estimating the tail probability bounds of a response function. Finally, two numerical examples and an engineering application are investigated to demonstrate the effectiveness of the proposed method.
ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-018-2049-5