Structural and Multidisciplinary Optimization

, Volume 59, Issue 2, pp 323–333 | Cite as

Uncertainty characterization under measurement errors using maximum likelihood estimation: cantilever beam end-to-end UQ test problem

  • Taejin Kim
  • Guesuk Lee
  • Byeng D. YounEmail author
Research Paper


One goal of uncertainty characterization is to develop a probability distribution that is able to properly characterize uncertainties in observed data. Observed data may vary due to various sources of uncertainty, which include uncertainties in geometry and material properties, and measurement errors. Among them, measurement errors, which are categorized as systematic and random measurement errors, are often disregarded in the uncertainty characterization process, even though they may be responsible for much of the variability in the observed data. This paper proposes an uncertainty characterization method that considers measurement errors. The proposed method separately distinguishes each source of uncertainty by using a specific type of probability distribution for each source. Next, statistical parameters of each assumed probability distribution are estimated by adopting the maximum likelihood estimation. To demonstrate the proposed method, as a case study, the method was implemented to characterize the uncertainties in the observed deflection data from the tip of a cantilever beam. In this case study, the proposed method showed greater accuracy as the amount of available observed data increased. This study provides a general guideline for uncertainty characterization of observed data in the presence of measurement errors.


Uncertainty characterization Uncertainty modeling Measurement error Systematic measurement error Random measurement error Maximum likelihood estimation 


Funding information

This work was partially supported by the Technology Innovation Program (10048305, Launching Plug-in Digital Analysis Framework for Modular System Design) of the Ministry of Trade, Industry & Energy (MI, Korea). This work was also supported by a grant from the Institute of Advanced Machinery and Design at Seoul National University (SNU-IAMD).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringSeoul National UniversitySeoulSouth Korea
  2. 2.Institute of Advanced Machines and DesignSeoul National UniversitySeoulSouth Korea

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