Uncertainty Quantification of Existing Bridge using Polynomial Chaos Expansion

Abstract

This paper is focused on uncertainty quan- tification (UQ) of an existing bridge structure repre- sented 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 mathe- matical model is based on non-linear fracture mechan- ics 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 Ex- pansion (PCE). PCE is a well-known technique for approximation of the costly mathematical models with random inputs, reflecting their distributions and offer- ing fast and accurate post-processing including statis- tical and sensitivity analysis. Once the PCE was con- structed, it was possible to analyze all quantities of in- terest (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 assess- ment. Moreover, once the PCE is available it could be possible to use it for further standard probabilistic or reliability analysis as a computationally efficient ap- proximation of the original mathematical model.