Journal Article10.1007/S00466-004-0583-8
Probability density evolution method for dynamic response analysis of structures with uncertain parameters
Jie Li,Jianbing Chen +1 more
292
TL;DR: In this paper, a probability density evolution equation (PDEE) is derived according to the principle of preservation of probability, and the PDEE is further reduced to a one-dimensional partial differential equation.
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Abstract: Probability density evolution method is proposed for dynamic response analysis of structures with random parameters. In the present paper, a probability density evolution equation (PDEE) is derived according to the principle of preservation of probability. With the state equation expression, the PDEE is further reduced to a one-dimensional partial differential equation. The numerical algorithm is studied through combining the precise time integration method and the finite difference method with TVD schemes. The proposed method can provide the probability density function (PDF) and its evolution, rather than the second-order statistical quantities, of the stochastic responses. Numerical examples, including a SDOF system and an 8-story frame, are investigated. The results demonstrate that the proposed method is of high accuracy and efficiency. Some characteristics of the PDF and its evolution of the stochastic responses are observed. The PDFs evidence heavy variance against time. Usually, they are much irregular and far from well-known regular distribution types. Additionally, the coefficients of variation of the random parameters have significant influence on PDF and second-order statistical quantities of responses of the stochastic structure.
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Citations
The equivalent extreme-value event and evaluation of the structural system reliability
TL;DR: In this paper, the idea of equivalent extreme-value event and a new approach to evaluate the structural system reliability are elaborated, and the proposed approach is discussed in detail on how to construct the equivalent extreme value event and then implement the procedure numerically.
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The principle of preservation of probability and the generalized density evolution equation
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TL;DR: A uniform and rigorous theoretical basis for the family of newly developed probability density evolution method is provided and the principle of preservation of probability is revisited from the two descriptions: the state space description and the random event description.
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The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters
Jianbing Chen,Jie Li +1 more
TL;DR: In this article, a new approach for evaluation of the extreme value distribution and dynamic reliability assessment of nonlinear structures with uncertain parameters is proposed based on the thoughts of the newly developed probability density evolution method, which is capable of capturing the instantaneous probability density function (PDF) and its evolution of the responses of the nonlinear stochastic structures.
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Advances of the probability density evolution method for nonlinear stochastic systems
TL;DR: In this paper, the generalized density evolution equation (GDEE) is derived for nonlinear stochastic systems, which is a unified basis for the probability density evolution equations holding for different types of systems.
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The Number Theoretical Method in Response Analysis of Nonlinear Stochastic Structures
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TL;DR: In this paper, a strategy of determining representative point sets through the number theoretical method (NTM) in analysis of nonlinear stochastic structures is proposed, which is applicable to general nonlinear structures involving random parameters, is capable of capturing instantaneous probability density function.
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