The size characterization of particles present in the form of agglomerates in images measured by scanning electron microscopy (SEM) requires a powerful image segmentation tool in order to properly define the boundaries of each particle. In this work, we propose to use an algorithm from the deep statistical learning community, the Mask-RCNN, coupled with transfer learning to overcome the problem of generalization of the commonly used image processing methods such as watershed or active contour. Indeed, the adjustment of the parameters of these algorithms is almost systematically necessary and slows down the automation of the processing chain. The Mask-RCNN is adapted here to the case study and we present results obtained on titanium dioxide samples (non-spherical particles) with a level of performance evaluated by different metrics such as the DICE coefficient, which reaches an average value of 0.95 on the test images.

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.

The European Metrology Research Programme (EMRP) is currently funding project EMRP-NEW04 on novel mathematical and statistical approaches to uncertainty evaluation. One focus of the project is uncertainty evaluation in the context of regression and parametric inverse problems. The development of methods for such problems will be carried out in close connection with four application examples. Here we outline these application examples, and present some first results.

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.