Gradient angle estimation by uniform directional simulation on a cone

Ove Dalager Ditlevsen

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    Abstract

    A sample of uniformly distributed unit vectors on an n-dimensional spherical cone is generated. The distances to a given limit state surface in the directions of the unit vectors of the sample are calculated and each of these distances are projected on the cone axis. The theoretical distribution of these projections is derived assuming the limit-state surface to be a hyperplane. This distribution depends on the angle between the cone axis and the normal vector to the hyperplane. Assuming sufficient flatness of the actual limit-state surface within a neighbourhood of the cut point with the cone axis, the cone top angle can be chosen small enough that this distribution can be taken as the basis for the formulation of the likelihood function of the angle given the sample of projections. The angle of maximum likelihood is then the indicator of whether the cut point can be taken as a sufficiently accurate approximation to a locally most central limit state point. Moreover, the estimated angle can be used to correct the geometric reliability index.\bfseries Keywords: Directional simulation, effectivity factor, gradient angle estimation, maximum likelihood, model-correction-factor method, Monte Carlo simulation, most central Limit-state point, beta-point check, reliability index correction.
    Original languageEnglish
    Title of host publicationReliability and Optimization of Structural Systems
    Place of PublicationKidlington, Oxford
    PublisherPergamon
    Publication date1997
    Pages127-132
    Publication statusPublished - 1997
    EventIFIP 7th WG 7.5 Working Conference on Reliability and Optimization of Structural Systems - Boulder, Colorado
    Duration: 1 Jan 1997 → …

    Conference

    ConferenceIFIP 7th WG 7.5 Working Conference on Reliability and Optimization of Structural Systems
    CityBoulder, Colorado
    Period01/01/1997 → …

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