Orthogonal polynomial expansion of Pearson's probability densities for non-Markov processes

1994 ◽  
Vol 37 (12) ◽  
pp. 1012-1016 ◽  
Author(s):  
V. A. Kazakov ◽  
A. M. Lavrov
Keyword(s):  
Orthogonal Polynomial ◽  
Markov Processes ◽  
Polynomial Expansion ◽  
Orthogonal Polynomial Expansion ◽  
Probability Densities

scholarly journals An Efficient Polynomial Chaos Method for Stiffness Analysis of Air Spring Considering Uncertainties

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Feng Kong ◽  
Penghao Si ◽  
Shengwen Yin
Keyword(s):  
Orthogonal Polynomial ◽  
Polynomial Chaos ◽  
Random Variables ◽  
Expansion Method ◽  
Polynomial Expansion ◽  
Response Analysis ◽  
Air Spring ◽  
Stiffness Analysis ◽  
Orthogonal Polynomial Expansion ◽  
Sparse Quadrature

Traditional methods for stiffness analysis of the air spring are based on deterministic assumption that the parameters are fixed. However, uncertainties have widely existed, and the mechanic property of the air spring is very sensitive to these uncertainties. To model the uncertainties in the air spring, the interval/random variables models are introduced. For response analysis of the interval/random variables models of the air spring system, a new unified orthogonal polynomial expansion method, named as sparse quadrature-based interval and random moment arbitrary polynomial chaos method (SQ-IRMAPC), is proposed. In SQ-IRMAPC, the response of the acoustic system related to both interval and random variables is approximated by the moment-based arbitrary orthogonal polynomial expansion. To efficiently calculate the coefficient of the interval and random orthogonal polynomial expansion, the sparse quadrature is introduced. The proposed SQ-IRMAPC was employed to analyze the mechanic performance of an air spring with interval and/or random variables, and its effectiveness has been demonstrated by fully comparing it with the most recently proposed orthogonal polynomial-based interval and random analysis method.

Seismic Response Analysis of Reinforced Concrete Frame Structures Considering the Variation of Parameters

2013 ◽  
Vol 639-640 ◽  
pp. 859-865
Author(s):  
Qiao Yun Wu ◽  
Hong Ping Zhu
Keyword(s):  
Dynamic Response ◽  
Orthogonal Polynomial ◽  
Expansion Method ◽  
Polynomial Expansion ◽  
Reinforced Concrete Frame ◽  
Structural Dynamic ◽  
Concrete Frame ◽  
Orthogonal Polynomial Expansion ◽  
Polynomial Expansion Method ◽  
The Impact

The orthogonal polynomial expansion method expression of stochastic structure was deduced. Then, based on orthogonal polynomial expansion method, taking a 20-storey reinforced concrete frame structure as an example, the impact of the randomness of structural parameters on time history response was researched. Meanwhile, in order to verify the correctness of analysis program, the calculation results of orthogonal polynomial expansion method were compared with the Monte-Carlo method which based on Newmark integral. The results show that it can get relatively accurate results when the number of terms of the orthogonal polynomial is 5. Structural mass and stiffness have a greater impact on the structural dynamic response. And the greater number of random parameters, the greater the impact on structural dynamic response.

scholarly journals Local orthogonal polynomial expansion for density estimation

2017 ◽  
Vol 29 (4) ◽  
pp. 806-830
Author(s):  
D.P. Amali Dassanayake ◽  
Igor Volobouev ◽  
A. Alexandre Trindade
Keyword(s):  
Orthogonal Polynomial ◽  
Density Estimation ◽  
Polynomial Expansion ◽  
Orthogonal Polynomial Expansion
Sign in / Sign up

Export Citation Format

Share Document