arXiv subjects

Geraldo de Freitas Maciel

Publications and source records attributed to Geraldo de Freitas Maciel.

3 recordsLinked to original sources

arXiv2026

Metamodel-based methodology for uncertainty propagation and global sensitivity analysis of tailings dam-breach flows

Tailings dam-breach analyses are essential for flood-hazard assessment, emergency planning and risk estimation, but their results are strongly affected by uncertainties in breach development, released volume and tailings rheology. This study proposes an efficient probabilistic methodology that integrates uncertainty quantification and global sensitivity analysis for tailings dam-breach studies. High-dimensional outputs (spatial maps) and the computational cost of deterministic simulations are addressed through dimensionality reduction and metamodeling. The methodology is demonstrated on a benchmark case with complex terrain using HEC-RAS v6.6 and considering uncertainties in breach parameters and rheological properties. The results quantify uncertainty in maximum flow depth and arrival time, characterize their statistical distributions and identify the spatial influence of the main input variables through sensitivity maps. Sensitivity indices reveal the dominance of breach parameters near the dam and yield stress farther downstream. The modular and non-intrusive framework can be coupled with other deterministic models and applied to different dam-breach scenarios, supporting more standardized and risk-informed assessments.

stat.AP↗

arXiv2025

Estimation and model errors in Gaussian-process-based Sensitivity Analysis of functional outputs

Global sensitivity analysis (GSA) of functional-output models is usually performed by combining statistical techniques, such as basis expansions, metamodeling and sampling based estimation of sensitivity indices. By neglecting truncation error from basis expansion, two main sources of errors propagate to the final sensitivity indices: the metamodeling related error and the sampling-based, or pick-freeze (PF), estimation error. This work provides an efficient algorithm to estimate these errors in the frame of Gaussian processes (GP), based on the approach of Le Gratiet et al. [16]. The proposed algorithm takes advantage of the fact that the number of basis coefficients of expanded model outputs is significantly smaller than output dimensions. Basis coefficients are fitted by GP models and multiple conditional GP trajectories are sampled. Then, vector-valued PF estimation is used to speed-up the estimation of Sobol indices and generalized sensitivity indices (GSI). We illustrate the methodology on an analytical test case and on an application in non-Newtonian hydraulics, modelling an idealized dam-break flow. Numerical tests show an improvement of 15 times in the computational time when compared to the application of Le Gratiet et al. [16] algorithm separately over each output dimension.

stat.ME↗

arXiv2024

Fast pick-freeze estimation of Sobol' sensitivity maps using basis expansions

Global sensitivity analysis (GSA) aims at quantifying the contribution of input variables over the variability of model outputs. In the frame of functional outputs, a common goal is to compute sensitivity maps (SM), i.e sensitivity indices at each output dimension (e.g. time step for time series, or pixels for spatial outputs). In specific settings, some works have shown that the computation of Sobol' SM can be speeded up by using basis expansions employed for dimension reduction. However, how to efficiently compute such SM in a general setting has not received too much attention in the GSA literature.In this work, we propose fast computations of Sobol' SM using a general basis expansion, with a focus on statistical estimation. First, we write a closed-form expression of SM in function of the matrix-valued Sobol' index of the vector of basis coefficients. Secondly, we consider pick-freeze (PF) estimators, which have nice statistical properties (in terms of asymptotical efficiency) for Sobol' indices of any order. We provide similar basis-derived formulas for the PF estimator of Sobol' SM in function of the matrix-valued PF estimator of the vector of basis coefficients. We give the computational cost, and show that, compared to a dimension-wise approach, the computational gain is substantial and allows to calculate both SM and their associated bootstrap confidence bounds in a reasonable time. Finally, we illustrate the whole methodology on an analytical test case and on an application in non-Newtonian hydraulics, modelling an idealized dam-break flow.

math.ST↗