Zuverlässigkeit und Robustheit von Bauwerken

Reliability and Robustness of Structures and Systems

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The assessment of reliability and robustness of structures and systems as well as the design for reliability and robustness is in the centre of our expertise. Structures and systems are exposed to uncertain environments, which can be characterized by stochastic loads and boundary conditions. This includes randomly fluctuating static loads as well as dynamic loads, such as wind or earthquake excitations, traffic loads and sea states, and conditions that describe the interaction of the structure or system with its environment, for example, foundation soil characteristics. In addition, uncertainties are inevitably present in structures and systems themselves, specifically in form of fluctuating material properties, geometrical imperfections, tolerances in production and construction, deviations of the mechanical behaviour of joints from the model assumptions, etc. These uncertainties can depend not only on time but also on spatial coordinates, e.g. be fluctuating over the structure or system, and possess dependencies on one another. Use and operation of our structures and systems add on another layer of uncertainties.

Our developments target at a comprehensive and realistic modelling and processing of this wide range of uncertainties including dependencies as a basis to ensure a safe use and operation of our structures and systems. We develop advanced stochastic models and high performance algorithms for stochastic simulation in order to enable a realistic uncertainty quantification for industry size structures and systems. These algorithms and associated techniques can be combined with high fidelity deterministic models for structural and systems analysis, including nonlinear models, to arrive at most realistic results. Highly efficient numerical algorithms formulated for high performance computing enable large-scale stochastic analyses. On this basis we analyse not only the reliability and robustness of structures and systems but also their life time, life cycle performance, and time dependent inspection and maintenance needs.

We develop algorithms and techniques for design under uncertainty, which ensure a safe and robust performance of our structures and systems under real world conditions with all uncertainties and even under harsh, extreme or safety critical conditions. Our approaches help to design structures and systems superior to those designed with traditional deterministic approaches in terms of reliability, performance, maintenance and cost. Performance objectives are met with greater efficiency and confidence. Performance criteria are met in an optimal manner while avoiding over-engineered solutions.

Application areas include but are not limited to robust and reliable product life-cycle management, efficient and realistic analysis and optimization of structures, systems and processes, quality assurance of systems and components, reduction of development time & costs using computer experiments and efficient simulation strategies, realistic uncertainty modelling and risk reduction.

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


  • Eckert, C., Beer, M.; Spanos, P.D. (2020) (2020): A Polynomial Chaos Method for Arbitrary Random Inputs using B-SplinesProbabilistic Engineering Mechanics, 60, Article 103051
    DOI: 10.1016/j.probengmech.2020.103051
  • Jiang, Y.B.; Zhao, L.J.; Beer, M.; Wang, L.; Zhang, J.R. (2020): Dominant failure mode analysis using representative samples obtained by multiple response surfaces methodProbabilistic Engineering Mechanics, 59, Article 103005
    DOI: 10.1016/j.probengmech.2019.103005
  • Song, J.W.; Valdebenito, M.; Wei, P.F.; Beer, M.; Lu, Z.Z. (2020): Non-intrusive imprecise stochastic simulation by line samplingStructural Safety, 84, Article 101936
    DOI: 10.1016/j.ymssp.2019.01.058
  • Wei, P.F.; Zhang, X.; Beer, M. (2020): Adaptive Experiment Design for Probabilistic IntegrationComputer Methods in Applied Mechanics and Engineering, 365, Article 113035
    DOI: 10.1016/j.cma.2020.113035
  • Yan, W.J.; Zhao, M.Y.; Beer, M.; Ren, W.X.; Chronopoulos, D. (2020) (2020): A Unified Scheme to Solving Arbitrary Complex-valued Ratio Distribution with Application to Statistical Inference for Frequency Response Functions and Transmissibility FunctionsMechanical Systems and Signal Processing, 145, Article 106886
  • Feng, J.W.; Liu, L.; Wu, D.; Li, G.Y.; Beer, M.; Gao, W. (2019): Dynamic reliability analysis using the extended support vector regression (X-SVR)Mechanical Systems and Signal Processing, 126, 368-391
    DOI: 10.1016/j.ymssp.2019.02.027
  • Fragkoulis, V.C.; Kougioumtzoglou, I.A.; Pantelous, A.A.; Beer, M. (2019): Non-stationary response statistics of nonlinear oscillators with fractional derivative elements under evolutionary stochastic excitationNonlinear Dynamics, 7, 1–13, doi 10.1007/s11071-019-05124-0
  • Mitseas, I.P.; Beer, M. (2019): Modal decomposition method for response spectrum based analysis of nonlinear and non-classically damped systemsMechanical Systems and Signal Processing, 131:469-485
    DOI: 10.1016/j.ymssp.2019.05.056
  • Song, Y.P.; Chen, J.B.; Beer, M.; Comerford, L. (2019): Wind Speed Field Simulation via Stochastic Harmonic Function Representation based on Wavenumber-Frequency SpectrumASCE Journal of Engineering Mechanics, 145(11), 04019086
  • Wang, C.; Zhang, H.; Beer, M. (2019): Structural Time-dependent Reliability Assessment with A New Power Spectral Density FunctionASCE's Journal of Structural Engineering, 145(12): 04019163, 10 pages
    DOI: 10.1061/(ASCE)ST.1943-541X.0002476
  • Zhang, Y.; Gomes, A.T.; Beer, M.; Neumann, I.; Nackenhorst, U.; Kim, C.-W. (2019): Reliability analysis with consideration of asymmetrically dependent variables: discussion and application to geotechnical examplesReliability Engineering and System Safety, 185, 261-277
    DOI: 10.1016/j.ress.2018.12.025
  • de Angelis, M.; Patelli, E.; Beer, M. (2017): Forced Monte Carlo Simulation Strategy for the Design of Maintenance Plans with Multiple InspectionsASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 3(2), D4016001, 1–9
    DOI: 10.1061/AJRUA6.0000868
  • Jiang, Y.B.; Luo, J.; Beer, M.; Patelli, E.; Broggi, M.; He, Y.H.; Zhang, J.R. (2017): Multiple response surfaces method with advanced classification of samples for structural failure function fittingStructural Safety; 64: 87-97
    DOI: 10.1016/j.strusafe.2016.10.002
  • Mitseas, I. P.; Kougioumtzoglou, I. A.; Beer, M. (2016): An approximate stochastic dynamics approach for nonlinear structural system performance-based multi-objective optimum designStructural Safety; 60: 67—76
    DOI: 10.1016/j.strusafe.2016.01.003
  • Beer, M.; Liebscher, M. (2008): Designing robust structures - A nonlinear simulation based approachComputers and Structures; 86(10): 1102—1122.
  • Spanos, P. D.; Beer, M.; Red-Horse, J. (2007): Karhunen–Loéve Expansion of Stochastic Processes with a Modified Exponential Covariance KernelJournal of Engineering Mechanics; 133(7): 773—779.
Prof. Dr.-Ing. Michael Beer
Callinstraße 34
30167 Hannover
Prof. Dr.-Ing. Michael Beer
Callinstraße 34
30167 Hannover
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