Estimation of parameters in a truncated trivariate normal distribution

The backbone modeling in ground-motion characterization (GMC) is a useful methodology to describe the epistemic uncertainty in median ground-motion predictions. The approach uses a backbone ground-motion model (GMM) and populates the GMC logic tree with the scaled and/or adjusted versions of the backbone GMM to capture the epistemic uncertainty in median ground motions. The scaling and/or adjustment should represent the specific features and uncertainties involved in source, path, and site effects at the target site. The identification of the backbone model requires different considerations specific to the nature of the ground-motion hazard problem. In this article, we present a scaled backbone modeling approach that considers the magnitude- and distance-scaling predictors as well as their correlation to address the epistemic uncertainty in median ground-motion predictions. This approach results in a trivariate normal distribution to fully define a range of epistemic uncertainty in a model sample space. The simultaneous consideration of magnitude and distance scaling while defining the epistemic uncertainty and the methodology followed for the simplified representation of trivariate normal distribution in ground-motion logic tree are the two important features in our procedure. We first present the proposed approach that is followed by a case study for Central and Eastern North America (CENA) stable continental region. The case study discusses the underlying assumptions and limitations of the proposed approach.

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An improved bootstrap method introducing error ellipse for numerical analysis of fatigue life parameters

Engineering Computations ◽

10.1108/ec-02-2020-0111 ◽

2020 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Haiyan Ge ◽

Xintian Liu ◽

Yu Fang ◽

Haijie Wang ◽

Xu Wang ◽

...

Keyword(s):

Normal Distribution ◽

Bootstrap Method ◽

Small Samples ◽

Estimation Of Parameters ◽

Error Ellipse ◽

Content Type ◽

Ellipse Model ◽

Ellipse Method ◽

Virtual Samples ◽

The Bootstrap Method

Purpose The purpose of this paper is to introduce error ellipse into the bootstrap method to improve the reliability of small samples and the credibility of the S-N curve. Design/methodology/approach Based on the bootstrap method and the reliability of the original samples, two error ellipse models are proposed. The error ellipse model reasonably predicts that the discrete law of expanded virtual samples obeys two-dimensional normal distribution. Findings By comparing parameters obtained by the bootstrap method, improved bootstrap method (normal distribution) and error ellipse methods, it is found that the error ellipse method achieves the expansion of sampling range and shortens the confidence interval, which improves the accuracy of the estimation of parameters with small samples. Through case analysis, it is proved that the tangent error ellipse method is feasible, and the series of S-N curves is reasonable by the tangent error ellipse method. Originality/value The error ellipse methods can lay a technical foundation for life prediction of products and have a progressive significance for the quality evaluation of products.

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