arXiv subjects

Cyril Feau

Publications and source records attributed to Cyril Feau.

7 recordsLinked to original sources

arXiv2026

Multi-fidelity Monte Carlo estimation of floor response spectra under combined seismic and structural parameter uncertainties

Floor response spectra (FRS) are essential tools for the design of non-structural elements (such as equipment or components). Given the various physical phenomena influencing FRS, high-fidelity (HF) mechanical models of the primary structure may be required to estimate them. Since numerical simulations based on such models are generally computationally expensive, this paper proposes using a multi-fidelity Monte Carlo (MFMC) approach for the efficient estimation of FRS. The method relies on using observations from a fast low-fidelity (LF) model as control variables. If the absolute value of the correlation between LF and HF samples is close to 1, this approach reduces both variance and estimation error compared to a standard Monte Carlo estimate based solely on HF data samples. Through a case study involving the reactor building of the Kashiwazaki-Kariwa nuclear power plant, we demonstrate the suitability of this method for FRS estimation. It effectively reduces variance and estimation error, even when using a LF model as simple as a single-degree-of-freedom system. We also show that the method accounts for modeling uncertainties while maintaining comparable performance. Its ease of use makes it a valuable tool for practitioners.

physics.data-an↗

arXiv2025

Multi-fidelity Gaussian process regression for noisy outputs and non-nested experimental designs: a comparison between the recursive and non-recursive formulations

This paper investigates a recursive formulation of auto-regressive multi-fidelity Gaussian process regression in the challenging setting of noisy and non-nested high- and low-fidelity data. We propose a decoupled optimization strategy based on the expectation-maximization algorithm, which exploits the structure of the recursive model. In particular, we derive closed-form update formulas when the scaling factor is modeled as a parametric linear predictor. This approach is compared with the fully coupled likelihood maximization of the classical non-recursive formulation introduced by Kennedy and O'Hagan. A series of benchmark experiments, covering applications of increasing complexity, highlights the performance of both approaches. The results demonstrate that the proposed recursive strategy significantly reduces training time, especially when large low-fidelity datasets are available, while maintaining competitive predictive accuracy and uncertainty estimation.

stat.AP↗

arXiv2025

Robust a posteriori estimation of probit-lognormal seismic fragility curves via sequential design of experiments and constrained reference prior

A seismic fragility curve expresses the probability of failure of a structure conditional to an intensity measure (IM) derived from seismic signals. When only limited data is available, the practitioner often refers to the probit-lognormal model coupled with maximum likelihood estimation (MLE) to obtain estimates of these curves. This means that only a binary indicator of the state (BIS) of the structure is known, namely a failure or non-failure state indicator, when it is subjected to a seismic signal with an intensity measure IM. In this context, the objective of this work is to propose a method for optimally estimating such curves by obtaining the most precise estimate possible with the minimum of data. The novelty of our work is twofold. First, we present and show how to mitigate the likelihood degeneracy problem which is ubiquitous with small data sets and hampers frequentist approaches such as MLE. Second, we propose a novel strategy for sequential design of experiments (DoE) that selects seismic signals from a large database of synthetic or real signals via their IM values, to be applied to structures to evaluate the corresponding BISs. This strategy relies on a criterion based on information theory in a Bayesian framework. It therefore aims to sequentially designate the IM value such that the pair (IM, BIS) has on average, with respect to the BIS of the structure, the greatest impact on the posterior distribution of the fragility curve. The methodology is applied to a case study from the nuclear industry. The results demonstrate its ability to efficiently and robustly estimate the fragility curve, and to avoid degeneracy even with a limited amount of data, i.e., less than 100. Furthermore, we demonstrate that the estimates quickly reach the model bias induced by the probit-lognormal modeling. Eventually, two criteria are suggested to help the user stop the DoE algorithm.

stat.AP↗

arXiv2024

Reference prior for Bayesian estimation of seismic fragility curves

One of the key elements of probabilistic seismic risk assessment studies is the fragility curve, which represents the conditional probability of failure of a mechanical structure for a given scalar measure derived from seismic ground motion. For many structures of interest, estimating these curves is a daunting task because of the limited amount of data available; data which is only binary in our framework, i.e., only describing the structure as being in a failure or non-failure state. A large number of methods described in the literature tackle this challenging framework through parametric log-normal models. Bayesian approaches, on the other hand, allow model parameters to be learned more efficiently. However, the impact of the choice of the prior distribution on the posterior distribution cannot be readily neglected and, consequently, neither can its impact on any resulting estimation. This paper proposes a comprehensive study of this parametric Bayesian estimation problem for limited and binary data. Using the reference prior theory as a cornerstone, this study develops an objective approach to choosing the prior. This approach leads to the Jeffreys prior, which is derived for this problem for the first time. The posterior distribution is proven to be proper with the Jeffreys prior but improper with some traditional priors found in the literature. With the Jeffreys prior, the posterior distribution is also shown to vanish at the boundaries of the parameters' domain, which means that sampling the posterior distribution of the parameters does not result in anomalously small or large values. Therefore, the use of the Jeffreys prior does not result in degenerate fragility curves such as unit-step functions, and leads to more robust credibility intervals. The numerical results obtained from different case studies-including an industrial example-illustrate the theoretical predictions.

stat.AP↗

arXiv2022

Uncertainty quantification and global sensitivity analysis of seismic fragility curves using kriging

Seismic fragility curves have been introduced as key components of Seismic Probabilistic Risk Assessment studies. They express the probability of failure of mechanical structures conditional to a seismic intensity measure and must take into account the inherent uncertainties in such studies, the so-called epistemic uncertainties (i.e. coming from the uncertainty on the mechanical parameters of the structure) and the aleatory uncertainties (i.e. coming from the randomness of the seismic ground motions). For simulation-based approaches we propose a methodology to build and calibrate a Gaussian process surrogate model to estimate a family of non-parametric seismic fragility curves for a mechanical structure by propagating both the surrogate model uncertainty and the epistemic ones. Gaussian processes have indeed the main advantage to propose both a predictor and an assessment of the uncertainty of its predictions. In addition, we extend this methodology to sensitivity analysis. Global sensitivity indices such as aggregated Sobol indices and kernel-based indices are proposed to know how the uncertainty on the seismic fragility curves is apportioned according to each uncertain mechanical parameter. This comprehensive Uncertainty Quantification framework is finally applied to an industrial test case consisting in a part of a piping system of a Pressurized Water Reactor.

stat.AP↗

arXiv2022

Importance sampling based active learning for parametric seismic fragility curve estimation

The key elements of seismic probabilistic risk assessment studies are the fragility curves which express the probabilities of failure of structures conditional to a seismic intensity measure. A multitude of procedures is currently available to estimate these curves. For modeling-based approaches which may involve complex and expensive numerical models, the main challenge is to optimize the calls to the numerical codes to reduce the estimation costs. Adaptive techniques can be used for this purpose, but in doing so, taking into account the uncertainties of the estimates (via confidence intervals or ellipsoids related to the size of the samples used) is an arduous task because the samples are no longer independent and possibly not identically distributed. The main contribution of this work is to deal with this question in a mathematical and rigorous way. To this end, we propose and implement an active learning methodology based on adaptive importance sampling for parametric estimations of fragility curves. We prove some theoretical properties (consistency and asymptotic normality) for the estimator of interest. Moreover, we give a convergence criterion in order to use asymptotic confidence ellipsoids. Finally, the performances of the methodology are evaluated on analytical and industrial test cases of increasing complexity.

stat.ML↗

arXiv2018

Efficient Seismic fragility curve estimation by Active Learning on Support Vector Machines

Fragility curves which express the failure probability of a structure, or critical components, as function of a loading intensity measure are nowadays widely used (i) in Seismic Probabilistic Risk Assessment studies, (ii) to evaluate impact of construction details on the structural performance of installations under seismic excitations or under other loading sources such as wind. To avoid the use of parametric models such as lognormal model to estimate fragility curves from a reduced number of numerical calculations, a methodology based on Support Vector Machines coupled with an active learning algorithm is proposed in this paper. In practice, input excitation is reduced to some relevant parameters and, given these parameters, SVMs are used for a binary classification of the structural responses relative to a limit threshold of exceedance. Since the output is not only binary, this is a score, a probabilistic interpretation of the output is exploited to estimate very efficiently fragility curves as score functions or as functions of classical seismic intensity measures.

cs.LG↗