Unbestimmtheit und veränderliche Bedingungen

Uncertainty Quantification and Risk Reduction in Vague and Changing Environments

© Rohan Makhecha (CC0)

We pursue extensive research on dealing with rare and imprecise information in various types of engineering analyses. In practice, information comes in diverse forms, which include variability, imprecision, incompleteness, vagueness, ambiguity, indeterminacy, dubiety, subjective experience and expert knowledge, etc. Our methods and techniques help to quantify such critical input information properly and to process this information through engineering analyses in order to arrive at realistic results and reasonable decisions from engineering analyses. By means of comprehensive modelling of uncertainty and imprecision we can reveal new insight into engineering problems, for example, helping to identify robust optimal solutions and decisions.

Our methods and tailored solutions to address these problematic cases are not only based on probabilistic including Bayesian approaches but include set-theoretical approaches and combinations of probabilistic and set theoretical components in a hybrid manner. With the aid of intervals, fuzzy sets and imprecise probabilities we process uncertainty and imprecision in its natural form and avoid artificial model assumptions, which are often too narrow - a phenomenon known as expert overconfidence. Using set-valued descriptors we only limit the models to some domain. The results are then obtained in form of bounded quantities covering all plausible options in the light of the deficient information on input quantities and boundary conditions. This helps to avoid wrong decisions due to artificial restrictions in the modelling. We complement this approach by analysing accidents to identify critical issues, in particular with focus on human factors in design and operations.

Application areas include but are not limited to reliability assessment, analysis of model output sensitivities, model validation and verification, model updating, and risk reduction.

We provide tailored solutions for a variety of problems from this spectrum and beyond.


  • Valdebenito, M.A.; Beer, M.; Jensen, H.A.; Chen, J.B.; Wei, P.F. (2020): Fuzzy Failure Probability Estimation Applying Intervening VariablesStructural Safety, Structural Safety, 83, Article 101909
    DOI: 10.1016/j.strusafe.2019.101909
  • Bi, S.F.; Broggi, M.; Wei, P.F.; Beer, M. (2019): The Bhattacharyya distance: enriching the P-box in stochastic sensitivity analysisMechanical Systems and Signal Processing, 129, pp. 265-281
    DOI: 10.1016/j.ymssp.2019.04.035
  • Faes, M.; Broggi, M.; Patelli, E.; Govers, Y.; Mottershead, J.; Beer, M.; Moens, D. (2019): A multivariate interval approach for inverse uncertainty quantification with limited experimental dataMechanical Systems and Signal Processing, 118, 534–548
    DOI: 10.1016/j.ymssp.2018.08.050
  • Faes, M.; Sadeghi, J.; Broggi, M.; De Angelis, M.; Patelli, E.; Beer, M.; Moens, D. (2019): On the robust estimation of small failure probabilities for strong non-linear modelsASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 5, Article 041007
    DOI: 10.1115/1.4044044
  • Wei, P.; Song, J.; Bi, S.; Broggi, M.; Beer, M.; Lu, Z.; Yue, Z. (2019): Non-intrusive stochastic analysis with parameterized imprecise probability models: II. Reliability and rare events analysisMechanical Systems and Signal Processing, 126:227-247
    DOI: 10.1016/j.ymssp.2019.02.015
  • Wei, P.F.; Song, J.W.; Bi, S.F.; Broggi, M.; Beer, M.; Lu, Z.Z.; Yue, Z.F. (2019): Non-intrusive stochastic analysis with parameterized imprecise probability models: I. Performance estimationMechanical Systems and Signal Processing, 124, 349-368
    DOI: 10.1016/j.ymssp.2019.01.058
  • Bi, S.F.; Broggi, M.; Beer, M. (2018): The role of the Bhattacharyya distance in stochastic model updatingMechanical Systems and Signal Processing, 117: 437-452
    DOI: 10.1016/j.ymssp.2018.08.017
  • Wang, C.; Zhang, H.; Beer, M. (2018): Computing tight bounds of structural reliability under imprecise probabilistic informationComputers and Structures, 208, 92–104
    DOI: 10.1016/j.compstruc.2018.07.003
  • Zhang, Y.; Kim, C.-W.; Beer, M.; Dai, H.L.; Soares, C.G. (2018): Modeling multivariate ocean data using asymmetric copulasCoastal Engineering, 135: 91-111
    DOI: 10.1016/j.coastaleng.2018.01.008
  • Comerford, L.; Jensen, H.A.; Mayorgab, F.; Beer, M.; Kougioumtzoglou, I.A. (2017): Compressive sensing with an adaptive wavelet basis for structural system response and reliability analysis under missing dataComputers and Structures; 182: 26-40
    DOI: 10.1016/j.compstruc.2016.11.012
  • Moura, R.; Beer, M.; Patelli, E.; Lewis, J.; Knoll, F. (2016): Learning from major accidents to improve system designSafety Science; 84: 37—45
    DOI: 10.1016/j.ssci.2015.11.022
  • Patelli, E.; Alvarez, D. A.; Broggi, M.; de Angelis, M. (2015): Uncertainty Management in Multidisciplinary Design of Critical Safety SystemsJournal of Aerospace Information Systems; 12(1): 140-169
  • Beer, M.; Ferson, S.; Kreinovich, V. (2013): Imprecise probabilities in engineering analysesMechanical Systems and Signal Processing; 37(1-2): 4—29.
  • Beer, M.; Zhang, Y.; Quek, S. T.; Phoon, K. K. (2013): Reliability analysis with scarce information: Comparing alternative approaches in a geotechnical engineering contextStructural Safety; 41: 1—10.
    DOI: 10.1016/j.strusafe.2012.10.003
Prof. Dr.-Ing. Michael Beer
Callinstraße 34
30167 Hannover
Prof. Dr.-Ing. Michael Beer
Callinstraße 34
30167 Hannover
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