A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Velocity divergence—Generalized adaptive probability density evolution method
This study proposes a novel velocity divergence‐generalized adaptive probability density evolution method (VD‐GAPDEM) for calculating the probability density function of the stochastic response process of stochastic structures under stochastic dynamic loads. First, based on the principle of probability conservation, the velocity divergence‐generalized adaptive probability density evolution equation (VD‐GAPDEE) is derived for a stochastic system that can effectively consider the shape and location changes of the joint transitional probability density of representative points (RPs) in the stochastic response process. Second, a novel VD‐GAPDEM is proposed to solve the VD‐GAPDEE directly using the point selection technique based on the generalized F discrepancy and the second‐order Runge–Kutta method with a smoothing kernel method (Runge–Kutta‐SKFAM). Furthermore, the differences and connections between VD‐GAPDEM and the existing probability density evolution method are analyzed. Additionally, the high computational efficiency and accuracy of the proposed VD‐GAPDEM are demonstrated through three typical examples of stochastic response analysis, involving stochastic systems subjected to stochastic dynamic loads.
Velocity divergence—Generalized adaptive probability density evolution method
This study proposes a novel velocity divergence‐generalized adaptive probability density evolution method (VD‐GAPDEM) for calculating the probability density function of the stochastic response process of stochastic structures under stochastic dynamic loads. First, based on the principle of probability conservation, the velocity divergence‐generalized adaptive probability density evolution equation (VD‐GAPDEE) is derived for a stochastic system that can effectively consider the shape and location changes of the joint transitional probability density of representative points (RPs) in the stochastic response process. Second, a novel VD‐GAPDEM is proposed to solve the VD‐GAPDEE directly using the point selection technique based on the generalized F discrepancy and the second‐order Runge–Kutta method with a smoothing kernel method (Runge–Kutta‐SKFAM). Furthermore, the differences and connections between VD‐GAPDEM and the existing probability density evolution method are analyzed. Additionally, the high computational efficiency and accuracy of the proposed VD‐GAPDEM are demonstrated through three typical examples of stochastic response analysis, involving stochastic systems subjected to stochastic dynamic loads.
Velocity divergence—Generalized adaptive probability density evolution method
Xu, Qiang (author) / Chen, Jianyun (author) / Wang, Jingkai (author) / Li, Jing (author) / Wang, Yin (author)
Earthquake Engineering & Structural Dynamics ; 53 ; 3678-3700
2024-09-01
23 pages
Article (Journal)
Electronic Resource
English
The principle of preservation of probability and the generalized density evolution equation
| Online Contents | 2008
The principle of preservation of probability and the generalized density evolution equation
| British Library Online Contents | 2008