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Uncertainty Quantification of Existing Bridge using Polynomial Chaos Expansion

Michael Krizek, Lukas Novak
Transactions of the VSB - Technical University of Ostrava, Civil Engineering Series
2023, Volume 23, Issue 2, Pages 13-19
Doi: 10.35181/tces-2023-0009
This paper is focused on uncertainty quantification (UQ) of an existing bridge structure represented by non-linear finite element model (NLFEM). The 3D model was created according to the original drawings and recent inspections of the bridge. In order to reflect the realistic mechanical behavior, the mathematical model is based on non-linear fracture mechanics and the calculation consists of the three construction stages. The single calculation of the NLFEM is very costly and thus even the elementary task of stochastic analysis - the propagation of uncertainties through a mathematical model - is not feasible by Monte Carlo-type approach. Thus, UQ is performed via efficient surrogate modeling technique - Polynomial Chaos Expansion (PCE). PCE is a well-known technique for approximation of the costly mathematical models with random inputs, reflecting their distributions and offering fast and accurate post-processing including statistical and sensitivity analysis. Once the PCE was constructed, it was possible to analyze all quantities of interest (QoIs) and analytically estimate Sobol indices as well as the first four statistical moments. Sobol indices directly measure the influence of the input variability to a variability of QoIs. Statistical moments were used for reconstruction of the probability distributions of QoIs, which will be further used for semi-probabilistic assessment. Moreover, once the PCE is available it could be possible to use it for further standard probabilistic or reliability analysis as a computationally efficient approximation of the original mathematical model.
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