A deep learning approach for the solution of probability density evolution of stochastic systems

Pourtakdoust, Seid H.; Khodabakhsh, Amir H.

doi:10.1016/j.strusafe.2022.102256

Cited by 8 publications

(2 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Various numerical schemes for solving hyperbolic PDEs, that is, Equation (), can be employed in this step, such as the finite difference method, 38,52 the direct probability integral method, 56,57 the finite element method, 46 the reproducing kernel particle method, 58,59 or deep learning methods, 60,61 to obtain the sub‐PDFs

p_{{Z}_{{\mathrm{IM}}}}^{(q)}( {{z}_1,t} )

and

p_{{Z}_{{\mathrm{EDP}}}}^{(q)}( {{z}_2,t} )

. Step 4.…”

Section: Numerical Implementation Proceduresmentioning

confidence: 99%

“…Various numerical schemes for solving hyperbolic PDEs, that is, Equation (15), can be employed in this step, such as the finite difference method, 38,52 the direct probability integral method, 56,57 the finite element method, 46 the reproducing kernel particle method, 58,59 or deep learning methods, 60,61 to obtain the sub-PDFs 𝑝 Step 4. Calculating the joint PDF of IM-EDP and the fragility function.…”

Section: Numerical Implementation Proceduresmentioning

confidence: 99%

See 1 more Smart Citation

A full‐probabilistic cloud analysis for structural seismic fragility via decoupled M‐PDEM

Lyu,

Feng,

Cao

et al. 2024

Earthq Engng Struct Dyn

View full text Add to dashboard Cite

Performance‐based earthquake engineering (PBEE) is essential for ensuring engineering safety. Conducting seismic fragility analysis within this framework is imperative. Existing methods for seismic fragility analysis often rely heavily on double loop reanalysis and empirical data fitting, leading to challenges in obtaining high‐precision results with a limited number of representative structural analysis instances. In this context, a new methodology for seismic fragility based on a full‐probabilistic cloud analysis is proposed via the decoupled multi‐probability density evolution method (M‐PDEM). In the proposed method, the assumption of a log‐normal distribution is not required. According to the random event description of the principle of preservation of probability, the transient probability density functions (PDFs) of intensity measure (IM) and engineering demand parameter (EDP), as key response quantities of the seismic‐structural system, are governed by one‐dimensional Li‐Chen equations, where the physics‐driven forces are determined by representative analysis data of the stochastic dynamic system. By generating ground motions based on representative points of basic random variables and performing structural dynamic analysis, the decoupled M‐PDEM is employed to solve the one‐dimensional Li‐Chen equations. This yields the joint PDF of IM and EDP, as well as the conditional PDF of EDP given IM, resulting in seismic fragility analysis outcomes. The numerical implementation procedure is elaborated in detail, and validation is performed using a six‐story nonlinear reinforced concrete (RC) frame subjected to non‐stationary stochastic ground motions. Comparative analysis against Monte Carlo simulation (MCS) and traditional cloud analysis based on least squares regression (LSR) reveals that the proposed method achieves higher computational precision at comparable structural analysis costs. By directly solving the physics‐driven Li‐Chen equations, the method provides the full‐probabilistic joint information of IM and EDP required for cloud analysis, surpassing the accuracy achieved by traditional methods based on statistical moment fitting and empirical distribution assumptions.

show abstract