Probability theory and seismic design

  • Haym Benaroya
Part of the Springer Praxis Books book series (PRAXIS)


Uncertainties always exist in engineering analysis and design. Even when they can be ignored, designers need to account for them by using safety factors. Uncertainty is the difference between what is known and what is reality. Of course, reality is only approximated by designers via tests and experiments. Uncertainty can be aleatory (random) and epistemic (subjective). Aleatory uncertainty refers to the inherent variability of a physical system, which can be modeled as a random variable or a random process, as described below. When data are scarce, probability distributions cannot be obtained, and epistemic uncertainty approaches are used. Epistemic uncertainty is defined as the lack of knowledge or information about some aspect of the system or model. Epistemic uncertainty can be reduced with the collection of more information. Sometimes, physical processes are so complex that, even with additional data, they are modeled as though they are inherently probabilistic. Examples of this include aerodynamic forces and seismic forces. In such cases, probability is used as an organizing principle. A review of reliability under epistemic uncertainty was provided by Kang et al. [1].


  1. 1.
    R. Kang, Q. Zhang, Z. Zeng, E. Zio, and X. Li: Measuring reliability under epistemic uncertainty: Review on non-probabilistic reliability metrics, Chinese Journal of Aeronautics, (2016) 29(3): pp.571–579.Google Scholar
  2. 2.
    Probabilistic Models for Dynamical Systems, Second Edition, H. Benaroya, S.M. Han, and M. Nagurka, CRC Press, Boca Raton 2013.Google Scholar
  3. 3.
    Y. Nakamura: New identification of deep moonquakes in the Apollo lunar seismic data, Physics of the Earth and Planetary Interiors, Vol.139, 2003, pp.197–205.Google Scholar
  4. 4.
    A.M. Jablonski, and K.A. Ogden: Technical Requirements for Lunar Structures, Journal of Aerospace Engineering, Vol.21, No.2, April 2008, pp.72–90.Google Scholar
  5. 5.
    S. Mottaghi: Design of a Lunar Surface Structure, thesis submitted in partial fulfillment of the M.S. Degree, Rutgers University, October 2013.Google Scholar
  6. 6.
    S. Mottaghi and H. Benaroya: Design of a Lunar Structure. II: Seismic Structural Analysis, Journal of Aerospace Engineering, Vol.28, Issue 1, January 2015.Google Scholar
  7. 7.
    H. Benaroya, S. Indyk, and S. Mottaghi (2012): Advance system concept for autonomous construction and self-repair of lunar surface ISRU structures. Moon: Prospective, Energy, and Material Resources, V. Badescu, Editor, Springer, Berlin Heidelberg, pp.641–660.Google Scholar
  8. 8.
    J.A. Happel (1993): Indigenous materials for lunar construction. Applied Mechanics Reviews, 46(6), pp.313–325.Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Haym Benaroya
    • 1
  1. 1.Professor of Mechanical & Aerospace EngineeringRutgers UniversityNew BrunswickUSA

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