RESUMEN
Current mechanistic chromatography process modeling methods lack the ability to account for the impact of experimental errors beyond detector noise (e.g. pump delays and variable feed composition) on the uncertainty in calibrated model parameters and the resulting model-predicted chromatograms. This paper presents an uncertainty quantification method that addresses this limitation by determining the probability distribution of parameters in calibrated models, taking into consideration multiple realistic sources of experimental error. The method, which is based on Bayes' theorem and utilizes Markov chain Monte Carlo with an ensemble sampler, is demonstrated to be robust and extensible using synthetic and industrial data. The corresponding software is freely available as open-source code at https://github.com/modsim/CADET-Match.
Asunto(s)
Industrias , Incertidumbre , Teorema de Bayes , Cromatografía Liquida , ProbabilidadRESUMEN
The emergence of additive manufacture (AM) for metallic material enables components of near arbitrary complexity to be produced. This has potential to disrupt traditional engineering approaches. However, metallic AM components exhibit greater levels of variation in their geometric and mechanical properties compared to standard components, which is not yet well understood. This uncertainty poses a fundamental barrier to potential users of the material, since extensive post-manufacture testing is currently required to ensure safety standards are met. Taking an interdisciplinary approach that combines probabilistic mechanics and uncertainty quantification, we demonstrate that intrinsic variation in AM steel can be well described by a generative statistical model that enables the quality of a design to be predicted before manufacture. Specifically, the geometric variation in the material can be described by an anisotropic spatial random field with oscillatory covariance structure, and the mechanical behaviour by a stochastic anisotropic elasto-plastic material model. The fitted generative model is validated on a held-out experimental dataset and our results underscore the need to combine both statistical and physics-based modelling in the characterization of new AM steel products.
RESUMEN
River water quality monitoring at limited temporal resolution can lead to imprecise and inaccurate classification of physicochemical status due to sampling error. Bayesian inference allows for the quantification of this uncertainty, which can assist decision-making. However, implicit assumptions of Bayesian methods can cause further uncertainty in the uncertainty quantification, so-called second-order uncertainty. In this study, and for the first time, we rigorously assessed this second-order uncertainty for inference of common water quality statistics (mean and 95th percentile) based on sub-sampling high-frequency (hourly) total reactive phosphorus (TRP) concentration data from three watersheds. The statistics were inferred with the low-resolution sub-samples using the Bayesian lognormal distribution and bootstrap, frequentist t test, and face-value approach and were compared with those of the high-frequency data as benchmarks. The t test exhibited a high risk of bias in estimating the water quality statistics of interest and corresponding physicochemical status (up to 99% of sub-samples). The Bayesian lognormal model provided a good fit to the high-frequency TRP concentration data and the least biased classification of physicochemical status (< 5% of sub-samples). Our results suggest wide applicability of Bayesian inference for water quality status classification, a new approach for regulatory practice that provides uncertainty information about water quality monitoring and regulatory classification with reduced bias compared to frequentist approaches. Furthermore, the study elucidates sizeable second-order uncertainty due to the choice of statistical model, which could be quantified based on the high-frequency data.