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Sensitivity and Reliability Analysis of Engineering Structures: Sampling Based Methods

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Computational Engineering

Abstract

This chapter intends to present an overview of Monte Carlo-type methods currently in use in the probabilistic analysis of large engineering structures. It starts with an introduction to the generation of multi-dimensional random quantities. Next, spatially distributed random properties, e.g., material or geometrical properties in continuum mechanics, are modeled as random fields. Approximations to random fields by means of Karhunen–Loève expansion and polynomial chaos expansion are introduced. These tools are employed to study the response of continuous structures with loads, material or geometrical properties given by random fields. The main focus is on sensitivity analysis of large engineering structures, where small Monte Carlo sample sizes are mandatory. The transition to reliability is undertaken by means of the concept of tolerance intervals. Further, current sampling methods for accurate reliability estimates are discussed, and practical applications are presented.

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Notes

  1. 1.

    ICONA-project 2006–2008, supported by TransIT Innsbruck, ACOSTA-project 2008–2010, supported by The Austrian Research Promotion Agency, MDP-NE 2011–2013, supported by Astrium GmbH; main partners: Intales GmbH Engineering Solutions, Institute of Basic Sciences in Engineering Science and Institute of Mathematics, University of Innsbruck, Czech Technical University in Prague.

  2. 2.

    We follow the common statistical practice that random variables are denoted by capital letters, while their realizations are denoted by small letters.

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Acknowledgements

The development, adaptation, and implementation in the mentioned research projects is chiefly due to the essential contributions of Christoph Aichinger, Vincent De Groof, Julian King, Katharina Riedinger, Helene Roth, and Martin Schwarz [1, 10, 11, 24, 41, 44, 49]. Many ideas have been developed in discussions with Barbara Goller and Herbert Haller of Intales GmbH, whose continuous support I gratefully acknowledge.

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Authors and Affiliations

  1. Unit of Engineering Mathematics, University of Innsbruck, Technikerstr. 13, A6020, Innsbruck, Austria

    M. Oberguggenberger

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  1. M. Oberguggenberger
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Correspondence to M. Oberguggenberger .

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  1. Institute of Basic Sciences in Engineering Science, University of Innsbruck, Innsbruck, Austria

    Günter Hofstetter

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Oberguggenberger, M. (2014). Sensitivity and Reliability Analysis of Engineering Structures: Sampling Based Methods. In: Hofstetter, G. (eds) Computational Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-05933-4_4

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  • DOI: https://doi.org/10.1007/978-3-319-05933-4_4

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