A points estimation and series approximation method for uncertainty analysis

Zhang, X F; Zhao, Yuee; Zhang, Y M; Huang, Xianzhen; Li, H

doi:10.1243/09544062jmes1229

Cited by 9 publications

(8 citation statements)

References 20 publications

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“…The integration of one-dimensional function in equation (17) can be efficiently estimated using the weighted Gaussian integration scheme. 37 It should also be pointed that the derivation of equation 17is based on the assumption of the independence of the input variables, thus it is only suitable for the problem without correlation of the inputs. More details for establishing the Gaussian integration grid to calculate FMs are provided in Appendix 4.…”

Section: Fm-based Maxent Methods For Estimating Marginal Pdfsmentioning

confidence: 99%

A vine copula–based method for analyzing the moment-independent importance measure of the multivariate output

Zhou

Yan

Cheng

2018

Proceedings of the Institution of Mechanical Engineers, Part O:

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The moment-independent importance measure technique for exploring how uncertainty allocates from output to inputs has been widely used to help engineers estimate the degree of confidence of decision results and assess risks. Solving the Borgonovo moment-independent importance measure in the presence of the multivariate output is still a challenging problem due to “curse of dimensionality,” and it is investigated in this contribution. For easily estimating the moment-independent importance measure, a novel method based on the vine copula is proposed. In the proposed method for estimating moment-independent importance measure, three steps are included. First, the moment-independent importance measure is expressed as a product of bivariate copula density functions through the vine copula trees. Second, the marginal probability density functions are obtained by the maximum entropy under the constraint of the fractional moments. Finally, the post-processed is executed to directly estimate the moment-independent importance measure by estimated copula density functions. The proposed method can handle multivariate output easily. The results of several examples indicate the validity and benefits of the proposed method.

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Section: Fm-based Maxent Methods For Estimating Marginal Pdfsmentioning

confidence: 99%

A vine copula–based method for analyzing the moment-independent importance measure of the multivariate output

Zhou

Yan

Cheng

2018

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…Noting that t k � t k− 1 + Δt, the relationship between v(t k− 1 ) and v(t k ) obtained from equations (12) and 13is…”

Section: Precise Gauss-legendre Integration Pointsmentioning

confidence: 99%

“…In these conditions, the analytical reliability methods are seldom applicable. erefore, more suitable methods are developed for implicit limit-state functions, e.g., the response surface method [6][7][8][9], the artificial neutral network method [10], and the point estimate method [11,12]. Within all these methods, the point estimate method is convenient for implicit multivariate state functions [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

A New Method for Reliability‐Based Sensitivity Analysis of Dynamic Random Systems

Wang

2019

Mathematical Problems in Engineering

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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.

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“…In addition, more and more researchers pay attention to the polynomial chaotic expansion theory and numerous achievements have been reported. 36–42…”

Section: Introductionmentioning

confidence: 99%

Modeling of the rotor-bearing system and dynamic reliability analysis of rotor’s positioning precision

Zhang

Liu

2020

Proceedings of the Institution of Mechanical Engineers, Part O:

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On the basis of the classical two degree of freedom (2-DOF) rotor-bearing system, the stochastic dynamic equations are solved and the dynamic reliability of the rotor’s positioning precision is examined in this paper. Firstly, the stochastic dynamic equations are converted to several deterministic dynamic equations by orthogonal polynomial approximation method. The contact uncertainty coefficient is described by Bernoulli distribution and the instantaneous contact probability of the ball-inner race contact of the rolling bearing is obtained. Then the state function of the system is defined and the statistical fourth moment method is adopted to determine the first four moments of the system response and state function. Edgeworth series technique is used to approach the cumulative distribution function (CDF) of the maximum displacement of the response and the system state function. Different parameters effects on the characteristics of the responses and the reliability of the system are investigated. The comparisons of the results obtained from the Monte Carlo simulation (MCS), the previous study and the present study illustrate the effectiveness of the study.

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A points estimation and series approximation method for uncertainty analysis

Cited by 9 publications

References 20 publications

A vine copula–based method for analyzing the moment-independent importance measure of the multivariate output

A vine copula–based method for analyzing the moment-independent importance measure of the multivariate output

A New Method for Reliability‐Based Sensitivity Analysis of Dynamic Random Systems

Modeling of the rotor-bearing system and dynamic reliability analysis of rotor’s positioning precision

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