Details
| Translated title of the contribution | Functional perspective of uncertainty quantification for stochastic parametric systems and global sensitivity analysis |
|---|---|
| Original language | Chinese |
| Pages (from-to) | 837-854 |
| Number of pages | 18 |
| Journal | Lixue Xuebao/Chinese Journal of Theoretical and Applied Mechanics |
| Volume | 53 |
| Issue number | 3 |
| Early online date | 28 Dec 2020 |
| Publication status | Published - Mar 2021 |
Abstract
Uncertainty exists broadly in real engineering design and analysis. For instance, some mechanical parameters of structures in civil engineering may be of randomness and usually cannot be ignored. Therefore, the process of uncertainty quantification, e.g., the sensitivity analysis on parameters of stochastic systems is, of paramount significance to reasonable engineering design and decision-making. In the present paper, the perspective of functional space analysis on uncertainty quantification and propagation in stochastic systems is firstly stated. On this basis, the global sensitivity index (GSI) is introduced based on the functional Fréchet derivative, of which some basically mathematical and physical properties are studied. Besides, the correspondingly defined importance measure and direction sensitivity of the GSI are also discussed, in terms of their geometric and physical meanings. Moreover, based on the definition of ε-equivalent distribution, the parametric form of the proposed GSI is elaborated in detail. By incorporating the probability density evolution method (PDEM) and the change of probability measure (COM), the numerical algorithm of the GSI and the procedure of sensitivity analysis are illustrated. Four numerical examples, including the analytical function of the linear combination of normal random variables, stability analysis of the rock bolting system of tunnel, the analysis of steadystate confined seepage below the dam, and the stochastic structural analysis of the reinforced concrete frame, are analyzed to demonstrate the effectiveness and significance of the GSI.
Keywords
- Change of probability measure, Fréchet derivative, Probability density evolution method, Sensitivity analysis, Uncertainty quantification
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Mathematics(all)
- Applied Mathematics
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In: Lixue Xuebao/Chinese Journal of Theoretical and Applied Mechanics, Vol. 53, No. 3, 03.2021, p. 837-854.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - 随机参数系统不确定性量化的泛函观点与整体灵敏度分析
AU - Wan, Zhiqiang
AU - Chen, Jianbing
AU - Beer, Michael
PY - 2021/3
Y1 - 2021/3
N2 - Uncertainty exists broadly in real engineering design and analysis. For instance, some mechanical parameters of structures in civil engineering may be of randomness and usually cannot be ignored. Therefore, the process of uncertainty quantification, e.g., the sensitivity analysis on parameters of stochastic systems is, of paramount significance to reasonable engineering design and decision-making. In the present paper, the perspective of functional space analysis on uncertainty quantification and propagation in stochastic systems is firstly stated. On this basis, the global sensitivity index (GSI) is introduced based on the functional Fréchet derivative, of which some basically mathematical and physical properties are studied. Besides, the correspondingly defined importance measure and direction sensitivity of the GSI are also discussed, in terms of their geometric and physical meanings. Moreover, based on the definition of ε-equivalent distribution, the parametric form of the proposed GSI is elaborated in detail. By incorporating the probability density evolution method (PDEM) and the change of probability measure (COM), the numerical algorithm of the GSI and the procedure of sensitivity analysis are illustrated. Four numerical examples, including the analytical function of the linear combination of normal random variables, stability analysis of the rock bolting system of tunnel, the analysis of steadystate confined seepage below the dam, and the stochastic structural analysis of the reinforced concrete frame, are analyzed to demonstrate the effectiveness and significance of the GSI.
AB - Uncertainty exists broadly in real engineering design and analysis. For instance, some mechanical parameters of structures in civil engineering may be of randomness and usually cannot be ignored. Therefore, the process of uncertainty quantification, e.g., the sensitivity analysis on parameters of stochastic systems is, of paramount significance to reasonable engineering design and decision-making. In the present paper, the perspective of functional space analysis on uncertainty quantification and propagation in stochastic systems is firstly stated. On this basis, the global sensitivity index (GSI) is introduced based on the functional Fréchet derivative, of which some basically mathematical and physical properties are studied. Besides, the correspondingly defined importance measure and direction sensitivity of the GSI are also discussed, in terms of their geometric and physical meanings. Moreover, based on the definition of ε-equivalent distribution, the parametric form of the proposed GSI is elaborated in detail. By incorporating the probability density evolution method (PDEM) and the change of probability measure (COM), the numerical algorithm of the GSI and the procedure of sensitivity analysis are illustrated. Four numerical examples, including the analytical function of the linear combination of normal random variables, stability analysis of the rock bolting system of tunnel, the analysis of steadystate confined seepage below the dam, and the stochastic structural analysis of the reinforced concrete frame, are analyzed to demonstrate the effectiveness and significance of the GSI.
KW - Change of probability measure
KW - Fréchet derivative
KW - Probability density evolution method
KW - Sensitivity analysis
KW - Uncertainty quantification
UR - http://www.scopus.com/inward/record.url?scp=85105247286&partnerID=8YFLogxK
U2 - 10.6052/0459-1879-20-336
DO - 10.6052/0459-1879-20-336
M3 - Article
AN - SCOPUS:85105247286
VL - 53
SP - 837
EP - 854
JO - Lixue Xuebao/Chinese Journal of Theoretical and Applied Mechanics
JF - Lixue Xuebao/Chinese Journal of Theoretical and Applied Mechanics
SN - 0459-1879
IS - 3
ER -