This article deals with the sequential design of experiments for (deterministic or stochastic) multi-fidelity numerical simulators, that is, simulators that offer control over the accuracy of simulation of the physical phenomenon or system under study. Accurate simulations usually entail a high computational effort, while coarse simulations are obtained at a lower cost. The cost can be measured, for example, by the run time of the simulator or the financial cost of the computing resources. In this setting, simulation results obtained at several levels of fidelity can be combined in order to estimate quantities of interest (the optimal value of the output, the probability that the output exceeds a given threshold, etc.) in an efficient manner. We propose a new Bayesian sequential strategy called maximal rate of stepwise uncertainty reduction (MR-SUR), that selects additional simulations to be performed by maximizing the ratio between the expected reduction of uncertainty and the cost of simulation. This generic strategy unifies several existing methods, and provides a principled approach to develop new ones. We assess its performance on several examples, including a computationally intensive problem of fire safety analysis where the quantity of interest is the probability of exceeding a tenability threshold during a building fire.

In this paper we provide guidance on a Bayesian uncertainty evaluation for a large class of GUM measurement models covering linear and non-linear models. Bayesian analysis takes advantage of useful prior knowledge on the measurand, which is often available from a metrologist’s genuine expertise and opinion, or from previous experiments and which is neither taken into account by the GUM nor by its Supplement 1. For the considered class of measurement models, we establish the equivalence with the related statistical models and derive analytical expressions of the posterior distribution for an appropriate family of prior distributions, which allows one to gain insight into the result of the Bayesian uncertainty evaluation. We extend this work to the formulation of arbitrary prior distributions for the measurand and provide some guidance to set hyperparameter values within a class of priors based on elicitation techniques, so that the resulting priors reflect the prior knowledge. Posterior distributions are calculated by Markov Chain Monte Carlo methods. We apply the Bayesian uncertainty evaluation to the mass calibration example of Supplement 1 and compare our results with those obtained by the GUM and its Supplement 1. In order to study the impact of the choice of method for this example, we carry out a sensitivity analysis of the results with respect to the choice of prior. We show a virtually strong effect of the prior distribution which results in reduced uncertainty estimates for a small number of observations. When using noninformative priors, we obtain results comparable to those achieved by GUM-S1. Python code is made available that enables a Bayesian uncertainty evaluation also in other applications covered by the considered class of GUM measurement models.

Thermal management is a key issue for the downsizing of electronic components in order to optimise their performance. These devices incorporate more and more nanostructured materials, such as thin films or nanowires, requiring measurement techniques suitable to characterise thermal properties at the nanoscale, such as Scanning Thermal Microscopy (SThM). In active mode, a hot thermoresistive probe scans the sample surface, and its electrical resistance R changes as a function of heat transfers between the probe and sample. This paper presents the measurement and calibration protocols developed to perform quantitative and traceable measurements of thermal conductivity k using the SThM technique, provided that the heat transfer conditions between calibration and measurement are identical, i.e., diffusive thermal regime for this study. Calibration samples with a known k measured at the macroscale are used to establish the calibration curve linking the variation of R to k. A complete assessment of uncertainty (influencing factors and computational techniques) is detailed for both the calibration parameters and the estimated k value. Outcome analysis shows that quantitative measurements of thermal conductivity with SThM (with an uncertainty value of $10\%$) are limited to materials with low thermal conductivity ($k<10\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$).

International audienceNowadays, fire safety engineers are increasingly relying on sophisticated numerical simulators, typically based on Computational Fluid Dynamics (CFD) solvers, to conduct their analyses. However, the complexity of these numerical models often limits drastically the number of simulations that can be afforded, making traditional methods of safety analysis difficult or impossible to apply. This paper proposes a statistical method to evaluate a quantity of interest with an expensive simulator while saving computation time. The method is based on Bayesian statistics and multi-fidelity. We use Gaussian process regression to construct a Bayesian model of the complex simulator. This model is based on a multi-fidelity approach, which consists in simulating at different levels of accuracy, for instance by varying the spatial discretization in a CFD solver. We illustrate the method on an example of fire safety analysis, where the quantity of interest is the probability of exceeding a tenability threshold in a building on fire

To improve the confidence and quality of measurements produced by regional and international infrasound monitoring networks, this work investigates a methodology for propagating uncertainty associated with on-site measurement systems. We focus on the propagation of sensor calibration uncertainties. The proposed approach is applied to synthetic infrasound signals with known back azimuth and trace velocity, recorded at the array elements. Relevant input uncertainties are investigated for propagation targeting the incoming signals (noise), instrumentation (microbarometers, calibration system, wind noise reduction system), and the time-delay-of-arrival (TDOA) model (frequency band). Uncertainty propagation is performed using the Monte Carlo method to obtain the corresponding uncertainties of the relevant output quantities of interest, namely back azimuth and trace velocity. The results indicate that, at high frequencies, large sensor uncertainties are acceptable. However, at low frequencies (<0.1 Hz), even a 2${}^{\circ }$ sensor phase uncertainty can lead to errors in the back azimuth of up to 5${}^{\circ }$ and errors in the trace velocity of 20 m/s.