Probability density evolution method for dynamic response analysis of structures with uncertain parameters

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Strategy for selecting representative points via tangent spheres in the probability density evolution method (2008, neutral): “DOI: 10.1002/nme.2246 Strategy for selecting representative points via tangent spheres in the probability density evolution method Jian-Bing Chen‡ and Jie Li∗,†,§ School of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, People’s Republic of China”
Probability density evolution analysis of engineering structures via cubature points (2012, methodology): “To overcome the difficulty, the thought of physical stochastic systems was put forward and the probability density evolution method (PDEM) was developed [18,22,23].”
The probability density evolution method for dynamic response analysis of non‐linear stochastic structures (2006, methodology): “In the past few years, a new family of PDEM, through which the instantaneous PDF of the response and its evolution is available, was developed for response analysis of linear stochastic structures [ 20 ] , and was further successfully applied in dynamic reliability evaluation [ 21 ] .”
Advances of the probability density evolution method for nonlinear stochastic systems (2012, methodology): “The GDEE was firstly obtained as the uncoupled version of the parametric Liouville equation for linear systems [27,28].”