Nicolas Fischer

Aerosol size distribution estimation and associated uncertainty for measurement with a Scanning Mobility Particle Sizer (SMPS)

Scanning Mobility Particle Sizer (SMPS) is a high resolution nanoparticle sizing system that has long been hailed as the researchers choice for airborne nanoparticle size characterization for nano applications including nanotechnology research and development. SMPS is widely used as the standard method to measure airborne particle size distributions below 1 m. It is composed of two devices: a Dierential Mobility Analyzer (DMA) selects particle sizes thanks to their electrical mobility and a Condensation Particle Counter (CPC) enlarges particles to make them detectable by common optical counters. System raw data represent the number of particles counted over several classes of mobility diameters. Then, common inversion procedures lead to the estimation of the aerosol size distribution. In this paper, we develop a methodology to compute the uncertainties associated with the estimation of the size distribution when several experiences have been carried out. The requirement to repeat the measure ensures a realistic variability on the simulated data to be generated. The work we present consists in considering both the uncertainties coming from the experimental dispersion and the uncertainties induced by the lack of knowledge on physical phenomena. Experimental dispersion is quantied with the experimental data while the lack of knowledge is modelled via the existing physical theories and the judgements of experts in the eld of aerosol science. Thus, running Monte-Carlo simulations give an estimation of the size distribution and its corresponding condence region.

A multi-thermogram-based Bayesian model for the determination of the thermal diffusivity of a material

The determination of thermal diffusivity is at the heart of modern materials characterisation. The evaluation of the associated uncertainty is difficult because the determination is performed in an indirect way, in the sense that the thermal diffusivity cannot be measured directly. The well-known GUM uncertainty framework does not provide a reliable evaluation of measurement uncertainty for such inverse problems, because in that framework the underlying measurement model is supposed to be a direct relationship between the measurand (the quantity intended to be measured) and the input quantities on which the measurand depends. This paper is concerned with the development of a Bayesian approach to evaluate the measurement uncertainty associated with thermal diffusivity. A Bayesian model is first developed for a single thermogram and is then extended to the case of several thermograms obtained under repeatability and reproducibility conditions. This multi-thermogram based model is able to take into consideration a large set of influencing quantities that occur during the measurements and yields a more reliable uncertainty evaluation than the one obtained from a single thermogram. Different aspects of the Bayesian model are discussed, including the sensitivity to the choice of the prior distribution, the Metropolis–Hastings algorithm used for the inference and the convergence of the Markov chains.

Modelling of the X,Y,Z positioning errors and uncertainty evaluation for the LNE's mAFM using the Monte Carlo method

In order to evaluate the uncertainty budget of the LNEs mAFM, a reference instrument dedicated to the calibration of nanoscale dimensional standards, a numerical model has been developed to evaluate the measurement uncertainty of the metrology loop involved in the XYZ positioning of the tip relative to the sample. The objective of this model is to overcome difficulties experienced when trying to evaluate some uncertainty components which cannot be experimentally determined and more specifically, the one linked to the geometry of the metrology loop. The model is based on object-oriented programming and developed under Matlab. It integrates one hundred parameters that allow the control of the geometry of the metrology loop without using analytical formulae. The created objects, mainly the reference and the mobile prism and their mirrors, the interferometers and their laser beams, can be moved and deformed freely to take into account several error sources. The Monte Carlo method is then used to determine the positioning uncertainty of the instrument by randomly drawing the parameters according to their associated tolerances and their probability density functions (PDFs). The whole process follows Supplement 2 to The Guide to the Expression of the Uncertainty in Measurement (GUM). Some advanced statistical tools like Morris design and Sobol indices are also used to provide a sensitivity analysis by identifying the most influential parameters and quantifying their contribution to the XYZ positioning uncertainty. The approach validated in the paper shows that the actual positioning uncertainty is about 6 nm. As the final objective is to reach 1 nm, we engage in a discussion to estimate the most effective way to reduce the uncertainty.

Aerosol size distribution measurement using a SMPS: Scanning mode and uncertainty analysis

A model to simulate SMPS (Scanning Mobility Particle Sizer) measurement and the associated uncertainty analysis when axial DMA (Differential Mobility Analyser) classifier operates under scanning mode conditions is described. Starting from simulated SMPS raw data, a fast estimation of aerosol size distribution measurement using regularization technique is performed. Then, global sensitivity analysis is used to discriminate significant parameters of the system and, as a preliminary result, a 95% confidence region is obtained by Monte Carlo simulations on an atmospheric aerosol size distribution.