Estimating statistical moments of random systems based on appropriate reference variables

2017 ◽  
Vol 34 (6) ◽  
pp. 2001-2030 ◽  
Author(s):  
Wenliang Fan ◽  
Pengchao Yang ◽  
Yule Wang ◽  
Alfredo H.-S. Ang ◽  
Zhengliang Li
Keyword(s):  
Linear Transformation ◽  
High Efficiency ◽  
Random Systems ◽  
Random Variables ◽  
Statistical Moments ◽  
Point Estimate ◽  
Content Type ◽  
Point Estimate Method ◽  
Estimate Method ◽  
Theoretical And Numerical Analysis

Purpose The purpose of this paper is to find an accurate, efficient and easy-to-implement point estimate method (PEM) for the statistical moments of random systems. Design/methodology/approach First, by the theoretical and numerical analysis, the approximate reference variables for the frequently used nine types of random variables are obtained; then by combining with the dimension-reduction method (DRM), a new method which consists of four sub-methods is proposed; and finally, several examples are investigated to verify the characteristics of the proposed method. Findings Two types of reference variables for the frequently used nine types of variables are proposed, and four sub-methods for estimating the moments of responses are presented by combining with the univariate and bivariate DRM. Research limitations/implications In this paper, the number of nodes of one-dimensional integrals is determined subjectively and empirically; therefore, determining the number of nodes rationally is still a challenge. Originality/value Through the linear transformation, the optimal reference variables of random variables are presented, and a PEM based on the linear transformation is proposed which is efficient and easy to implement. By the numerical method, the quasi-optimal reference variables are given, which is the basis of the proposed PEM based on the quasi-optimal reference variables, together with high efficiency and ease of implementation.

scholarly journals A New Method for Reliability-Based Sensitivity Analysis of Dynamic Random Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Qianqian Wang ◽  
Changchun Wang ◽  
Hui Wang
Keyword(s):  
Sensitivity Analysis ◽  
Random Process ◽  
Random Systems ◽  
Expansion Method ◽  
Point Estimate ◽  
Random Structure ◽  
Fourth Moment ◽  
Dynamic Reliability ◽  
Point Estimate Method ◽  
Estimate Method

A novel numerical method for investigating time-dependent reliability and sensitivity issues of dynamic systems is proposed, which involves random structure parameters and is subjected to stochastic process excitation simultaneously. The Karhunen–Loève (K-L) random process expansion method is used to express the excitation process in the form of a series of deterministic functions of time multiplied by independent zero-mean standard random quantities, and the discrete points are made to be the same as Legendre integration points. Then, the precise Gauss–Legendre integration is used to solve the oscillation differential functions. Considering the independent relationship of the structural random parameters and the parameters of random process, the time-varying moments of the response are evaluated by the point estimate method. Combining with the fourth-moment method theory of reliability analysis, the dynamic reliability response can be evaluated. The dynamic reliability curve is useful for getting the weakness time so as to avoid breakage. Reliability-based sensitivity analysis gives the importance sort of the distribution parameters, which is useful for increasing system reliability. The result obtained by the proposed method is accurate enough compared with that obtained by the Monte Carlo simulation (MCS) method.

Comparing unscented transformation and point estimate method for probabilistic power flow computation

2018 ◽  
Vol 37 (3) ◽  
pp. 1290-1303 ◽  
Author(s):  
Qing Xiao ◽  
Shaowu Zhou
Keyword(s):  
Power Flow ◽  
Quadrature Rule ◽  
Point Estimate ◽  
Unscented Transformation ◽  
Content Type ◽  
Point Estimate Method ◽  
Estimate Method ◽  
Gauss Type ◽  
Probability Spaces ◽  
Probabilistic Power Flow

Purpose Unscented transformation (UT) and point estimate method (PEM) are two efficient algorithms for probabilistic power flow (PPF) computation. This paper aims to show the relevance between UT and PEM and to derive a rule to determine the accuracy controlling parameters for UT method. Design/methodology/approach The authors derive the underlying sampling strategies of UT and PEM and check them in different probability spaces, where quadrature nodes are selected. Findings Gauss-type quadrature rule can be used to determine the accuracy controlling parameters of UT. If UT method and PEM select quadrature nodes in two probability spaces related by a linear transform, these two algorithms are equivalent. Originality/value It shows that UT method can be conveniently extended to (km + 1) scheme (k = 4; 6; : : : ) by Gauss-type quadrature rule.

scholarly journals Hermite polynomial normal transformation for structural reliability analysis

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jinsheng Wang ◽  
Muhannad Aldosary ◽  
Song Cen ◽  
Chenfeng Li
Keyword(s):  
Reliability Analysis ◽  
Hermite Polynomial ◽  
Structural Reliability ◽  
Hermite Polynomials ◽  
Random Variables ◽  
Transformation Method ◽  
Statistical Moments ◽  
Content Type ◽  
Structural Reliability Analysis ◽  
Normal Transformation

Purpose Normal transformation is often required in structural reliability analysis to convert the non-normal random variables into independent standard normal variables. The existing normal transformation techniques, for example, Rosenblatt transformation and Nataf transformation, usually require the joint probability density function (PDF) and/or marginal PDFs of non-normal random variables. In practical problems, however, the joint PDF and marginal PDFs are often unknown due to the lack of data while the statistical information is much easier to be expressed in terms of statistical moments and correlation coefficients. This study aims to address this issue, by presenting an alternative normal transformation method that does not require PDFs of the input random variables. Design/methodology/approach The new approach, namely, the Hermite polynomial normal transformation, expresses the normal transformation function in terms of Hermite polynomials and it works with both uncorrelated and correlated random variables. Its application in structural reliability analysis using different methods is thoroughly investigated via a number of carefully designed comparison studies. Findings Comprehensive comparisons are conducted to examine the performance of the proposed Hermite polynomial normal transformation scheme. The results show that the presented approach has comparable accuracy to previous methods and can be obtained in closed-form. Moreover, the new scheme only requires the first four statistical moments and/or the correlation coefficients between random variables, which greatly widen the applicability of normal transformations in practical problems. Originality/value This study interprets the classical polynomial normal transformation method in terms of Hermite polynomials, namely, Hermite polynomial normal transformation, to convert uncorrelated/correlated random variables into standard normal random variables. The new scheme only requires the first four statistical moments to operate, making it particularly suitable for problems that are constraint by limited data. Besides, the extension to correlated cases can easily be achieved with the introducing of the Hermite polynomials. Compared to existing methods, the new scheme is cheap to compute and delivers comparable accuracy.

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