Distribution of Quadratic Forms in Normal Space—Application to Structural Reliability

Tvedt, Lars

doi:10.1061/(asce)0733-9399(1990)116:6(1183)

Cited by 263 publications

(72 citation statements)

References 10 publications

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“…An exact result in form of a one dimensional integral has been derived in [7] for the incomplete representation and an asymptotic result, sufficiently accurate for large β value, has been developed [8].…”

Section: Approximate Reliability Methods (Form and Sorm)mentioning

confidence: 99%

A Novel Technique for Evaluating Failure Probability of Random Structure

Kadry¹,

Hami²

2015

WJM

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The purpose of this article is to develop a new methodology to evaluate the statistical characteristic of the response of structures subjecting to random excitation, by combining the Finite Element Method (FEM) with the Transforming Density Function (TDF). Uncertainty modeling of structure with random variables encourages the coupling of advanced TDF for reliability analysis to analyze problems of stochastic mechanical systems. The TDF is enthusiastically applicable in the situation where the relationship between input and output of structures is available in explicit analytical form. However, the situation is much more involved when it is necessary to perform the evaluation of implicit expression between input and output of structures through numerical models. For this aim, we propose a new technique that combines the FEM software, and the TDF method to evaluate the most important statistical parameter the Probability Density Function (PDF) of the response where the expression between input and output of structures is implicit. Once the PDF is evaluated, all other statistical parameters are derived easily. This technique is based on the numerical simulations of the FEM and the TDF by making a middleware between Finite Element software and Matlab. Some problems, range from simple to complex, of structures are analyzed using our proposed technique. Its accuracy is validated through Monte-Carlo simulation.

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Section: Approximate Reliability Methods (Form and Sorm)mentioning

confidence: 99%

A Novel Technique for Evaluating Failure Probability of Random Structure

Kadry¹,

Hami²

2015

WJM

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“…Traditional first-order reliability method (FORM) ( [2], [3], [4]) and the second-order reliability method (SORM) ( [5]; [6]; [7]; [8]) belong to this class. The simulation techniques have their origin in Monte Carlo simulation (MCS) method, which generates a large sample set of limit state evaluations and approximates the true value of the probability of failure by = , where is the number of samples lying in the failure region and S the total number of samples.…”

Section: Introductionmentioning

confidence: 99%

Review and application of Artificial Neural Networks models in reliability analysis of steel structures

et al. 2015

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“…(Tvedt 1990) develops alternative SORM formulations. Tvedt's method uses a parabolic and a general second-order approximation to the limit state, and it does not use asymptotic approximations.…”

Section: Reliability Theorymentioning

confidence: 99%