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 -