The extended Davenport peak factor as an extreme-value estimation method for linear combinations of correlated non-Gaussian random variables

2016 ◽  
Vol 157 ◽  
pp. 125-139 ◽  
Author(s):  
Pedro Folgueras ◽  
Sebastián Solari ◽  
Mónica Mier-Torrecilla ◽  
Manuel Doblaré ◽  
Miguel Ángel Losada
Keyword(s):  
Estimation Method ◽  
Random Variables ◽  
Extreme Value ◽  
Linear Combinations ◽  
Gaussian Random Variables ◽  
Peak Factor ◽  
Value Estimation ◽  
Non Gaussian

Hermite Extreme Value Estimation of Non-Gaussian Wind Load Process on a Long-Span Roof Structure

2014 ◽  
Vol 140 (9) ◽  
pp. 04014061 ◽  
Author(s):  
M. F. Huang ◽  
Wenjuan Lou ◽  
Xiaotao Pan ◽  
C. M. Chan ◽  
Q. S. Li
Keyword(s):  
Wind Load ◽  
Extreme Value ◽  
Long Span ◽  
Roof Structure ◽  
Value Estimation ◽  
Non Gaussian

Reliability Analysis Using Second-Order Saddlepoint Approximation and Mixture Distributions

2018 ◽  
Author(s):  
Dimitrios I. Papadimitriou ◽  
Zissimos P. Mourelatos ◽  
Zhen Hu
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Random Variables ◽  
Saddlepoint Approximation ◽  
Gaussian Mixture ◽  
Second Order ◽  
State Function ◽  
Gaussian Random Variables ◽  
Non Gaussian ◽  
Nataf Transformation

This paper proposes a new second-order Saddlepoint Approximation (SOSA) method for reliability analysis of nonlinear systems with correlated non-Gaussian and multimodal random variables. The proposed method overcomes the limitation of current available SOSA methods which are applicable to problems with only Gaussian random variables, by employing a Gaussian Mixture Model (GMM). The latter is first constructed using the Expectation Maximization (EM) method to approximate the joint probability density function of the input variables. Expressions of the statistical moments of the response variables are then derived using a second-order Taylor expansion of the limit-state function and the GMM. The standard SOSA method is finally integrated with the GMM to effectively analyze the reliability of systems with correlated non-Gaussian random variables. The accuracy of the proposed method is compared with existing methods including a SOSA based on Nataf transformation. Numerical examples demonstrate the effectiveness of the proposed approach.

Fisher Information and Uncertainty Principle for Skew-Gaussian Random Variables

2021 ◽  
pp. 2150039
Author(s):  
Javier E. Contreras-Reyes
Keyword(s):  
Fisher Information ◽  
Shannon Entropy ◽  
Uncertainty Principle ◽  
Gaussian Distribution ◽  
Heavy Tails ◽  
Random Variables ◽  
Gaussian Random Variables ◽  
Evolving Systems ◽  
Non Gaussian ◽  
Estimate System

Fisher information is a measure to quantify information and estimate system-defining parameters. The scaling and uncertainty properties of this measure, linked with Shannon entropy, are useful to characterize signals through the Fisher–Shannon plane. In addition, several non-gaussian distributions have been exemplified, given that assuming gaussianity in evolving systems is unrealistic, and the derivation of distributions that addressed asymmetry and heavy–tails is more suitable. The latter has motivated studying Fisher information and the uncertainty principle for skew-gaussian random variables for this paper. We describe the skew-gaussian distribution effect on uncertainty principle, from which the Fisher information, the Shannon entropy power, and the Fisher divergence are derived. Results indicate that flexibility of skew-gaussian distribution with a shape parameter allows deriving explicit expressions of these measures and define a new Fisher–Shannon information plane. Performance of the proposed methodology is illustrated by numerical results and applications to condition factor time series.

Reliability Analysis Using Second-Order Saddlepoint Approximation and Mixture Distributions

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Dimitrios I. Papadimitriou ◽  
Zissimos P. Mourelatos ◽  
Zhen Hu
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Random Variables ◽  
Saddlepoint Approximation ◽  
Gaussian Mixture ◽  
Second Order ◽  
State Function ◽  
Gaussian Random Variables ◽  
Non Gaussian ◽  
Nataf Transformation

This paper proposes a new second-order saddlepoint approximation (SOSA) method for reliability analysis of nonlinear systems with correlated non-Gaussian and multimodal random variables. The proposed method overcomes the limitation of current available SOSA methods, which are applicable to problems with only Gaussian random variables, by employing a Gaussian mixture model (GMM). The latter is first constructed using the expectation maximization (EM) method to approximate the joint probability density function (PDF) of the input variables. Expressions of the statistical moments of the response variables are then derived using a second-order Taylor expansion of the limit-state function and the GMM. The standard SOSA method is finally integrated with the GMM to effectively analyze the reliability of systems with correlated non-Gaussian random variables. The accuracy of the proposed method is compared with existing methods including a SOSA based on Nataf transformation. Numerical examples demonstrate the effectiveness of the proposed approach.

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