arXiv subjects

Sylvain Dubreuil

Publications and source records attributed to Sylvain Dubreuil.

5 recordsLinked to original sources

arXiv2026

Stochastic Modeling of Composite Interfaces: Sensitivity to Spatial Correlation and Bayesian Identification from Standard Fracture Tests

To enable a numerical handling of uncertainties in composite structures, this work presents a stochastic finite-element framework aimed at improving the reliability assessment of aerospace composites, with particular attention to stiffener debonding. By representing interface variability between laminate parts with spatially correlated random fields, the method aims at considering scattering effect at a higher scale of simulation and testing. A parametric study carried out on standardized Mode I and Mode II fracture tests reveals that the correlation length is the primary driver of observed variability, while the regularity of the covariance kernel has only a marginal impact. To guarantee industrial relevance, we demonstrate that this key parameter can be extracted from experimental fracture data using an Approximate Bayesian Computation approach. The proposed methodology therefore offers a robust route to high-fidelity virtual testing and to the predictive management of uncertainties in the design of damage-tolerant composite airframes.

stat.AP↗

arXiv2026

Efficient Estimation of A-basis and B-Basis Value under Epistemic Uncertainty using Importance Sampling and Control Variates

In aerospace certification and other safety-critical domains, conservative quantile estimation such as A- and B-basis values is essential to guarantee reliability. While these metrics are traditionally derived from experimental campaigns, this work focuses on their estimation using a validated deterministic numerical model. The problem is formulated under mixed aleatory-epistemic uncertainty, accounting for limited material data, finite sampling effects, and surrogate modeling errors. We propose a methodology for estimating conservative design quantiles with statistical guarantees under mixed uncertainties. The proposed method leverages importance sampling and control variates to achieve accurate and efficient estimates within a fixed computational budget. One key point is the surrogate model's role solely as a variance reduction device, which guarantees unbiased and consistent quantile estimation. By explicitly integrating all sources of uncertainty, the proposed framework provides a numerical alternative to estimate A-basis and B-Basis. Furthermore, Sobol-based sensitivity indices are obtained at no additional cost, offering insight into the dominant epistemic sources. Numerical experiments on structural models demonstrate the method's reliability and computational efficiency. In particular, the application to large-scale industrial simulations confirms its suitability for aerospace certification workflows and highlights its relevance for real world engineering environments.

stat.AP↗

arXiv2026

PFEM-GP-dPHS : a finite element framework for combining Gaussian processes and infinite-dimensional port-Hamiltonian systems

In order to learn distributed port-Hamiltonian systems (dPHS) using Gaussian processes (GPs), the partitioned finite element method (PFEM) is combined with the Gp-dPHS method. By following a late lumping approach, the discretization of the functional hyperparameters of the GP prior over the Hamiltonian functional is chosen independently from the discretization of the dPHS, thus reducing the numerical complexity of our method. We next model the mean of the GP prior of the Hamiltonian as a quadratic form, enabling the GP kernel to focus on the nonlinear part of a given dPHS. We illustrate our method on a nonlinear one dimensional wave equation with unknown physical parameters (tension and linear mass).

math.AP↗

arXiv2025

High-Dimensional Bayesian Optimization Using Both Random and Supervised Embeddings

Bayesian optimization (BO) is one of the most powerful strategies to solve computationally expensive-to-evaluate blackbox optimization problems. However, BO methods are conventionally used for optimization problems of small dimension because of the curse of dimensionality. In this paper, a high-dimensionnal optimization method incorporating linear embedding subspaces of small dimension is proposed to efficiently perform the optimization. An adaptive learning strategy for these linear embeddings is carried out in conjunction with the optimization. The resulting BO method, named efficient global optimization coupled with random and supervised embedding (EGORSE), combines in an adaptive way both random and supervised linear embeddings. EGORSE has been compared to state-of-the-art algorithms and tested on academic examples with a number of design variables ranging from 10 to 600. The obtained results show the high potential of EGORSE to solve high-dimensional blackbox optimization problems, in terms of both CPU time and the limited number of calls to the expensive blackbox simulation.

math.OC↗

arXiv2020

Variance based sensitivity analysis for Monte Carlo and importance sampling reliability assessment with Gaussian processes

Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive, requiring advanced simulation methods to reduce the overall numerical cost. Gaussian process based active learning methods for reliability analysis have emerged as a promising way for reducing this computational cost. The learning phase of these methods consists in building a Gaussian process surrogate model of the performance function and using the uncertainty structure of the Gaussian process to enrich iteratively this surrogate model. For that purpose a learning criterion has to be defined. Then, the estimation of the probability of failure is typically obtained by a classification of a population evaluated on the final surrogate model. Hence, the estimator of the probability of failure holds two different uncertainty sources related to the surrogate model approximation and to the sampling based integration technique. In this paper, we propose a methodology to quantify the sensitivity of the probability of failure estimator to both uncertainty sources. This analysis also enables to control the whole error associated to the failure probability estimate and thus provides an accuracy criterion on the estimation. Thus, an active learning approach integrating this analysis to reduce the main source of error and stopping when the global variability is sufficiently low is introduced. The approach is proposed for both a Monte Carlo based method as well as an importance sampling based method, seeking to improve the estimation of rare event probabilities. Performance of the proposed strategy is then assessed on several examples.

stat.ML↗