2021/05/15 by Azzedine Abdedou, Abdedou, Azzedine, Azzeddine Soulaïmani +1
Decision Sciences · Engineering · Physics and Astronomy · #Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #Finance #Fluid Dynamics and Vibration Analysis #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2105.09300
openalex publication_date 2021/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A proper orthogonal decomposition-based B-splines Bézier elements method (POD-BSBEM) is proposed as a non-intrusive reduced-order model for uncertainty propagation analysis for stochastic time-dependent problems. The method uses a two-step proper orthogonal decomposition (POD) technique to extract the reduced basis from a collection of high-fidelity solutions called snapshots. A third POD level is then applied on the data of the projection coefficients associated with the reduced basis to separate the time-dependent modes from the stochastic parametrized coefficients. These are approximated in the stochastic parameter space using B-splines basis functions defined in the corresponding Bézier element. The accuracy and the efficiency of the proposed method are assessed using benchmark steady-state and time-dependent problems and compared to the reduced order model-based artificial neural network (POD-ANN) and to the full-order model-based polynomial chaos expansion (Full-PCE). The POD-BSBEM is then applied to analyze the uncertainty propagation through a flood wave flow stemming from a hypothetical dam-break in a river with a complex bathymetry. The results confirm the ability of the POD-BSBEM to accurately predict the statistical moments of the output quantities of interest with a substantial speed-up for both offline and online stages compared to other techniques.