Dr Marco De Angelis, Institute for Risk and Uncertainty, University of Liverpool, UK

Digital simulation with uncertain numbers: feeding models with intervals and p-boxes
When Oct 22, 2018
from 02:00 PM to 03:00 PM
Where LR1, Thom Building
Contact Name
Contact Phone 01865-273030
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Digital simulation is used by engineers as never before to describe the physical world and envision potential catastrophic events during design. Nonetheless, we are far from being able to trust our digital high-fidelity models, because of their complexity, their modelling limitations, and their error-prone setup process. Verification and validation - V&V - lie at the basis of a sound engineering analysis. Very often probability distributions are used to achieve V&V via Monte Carlo simulation for the verification and via Bayesian analysis for the validation. In the research we challenge these approaches providing an alternative route to V&V based on intervals and pboxes.

 

Intervals provide a more rigorous way than Monte Carlo simulation to verify digital models, even though there isn't a universal formula for its application to every models. In this first part of the talk I will present the technological challenges related to the projection of intervals through digital models, and also what is currently possible to bypass the existing limitations. In spite of their rigour, intervals can not be propagated through the so called black-box models and therefore alternative strategies commonly based on sampling will be presented. Nonetheless, engineering models, however complex, are seldom black-boxes, but rather a long and intricate list of interconnected logical instructions ready to be sent to the processor. This opens up to the possibility of performing the uncertainty propagation by means of an additional layer of compilers that are capable of replacing the ordinary arithmetic operations with the equivalent “uncertain” version.

 

The step onto validation requires the inclusion of experimental data. Data is often noisy and imprecise. Statistical probability is therefore essential tool to be able to identify trends in the available data. Imprecise statistics come to the rescue when data is also imprecise as well as noisy. Data imprecision can be modelled without making the assumption on the statistical model or probability distribution. In this part of the talk I will present how we can perform forward propagation with imprecise probability distributions, a.k.a. p-boxes, and subsequently how can this lead to the validation. Model validation comes as a byproduct of the forward propagation and I will show how this can be achieved with a simple area metric method. Calibration and updating of the model come next to close the V&V loop, but they will not be included in this particular talk.

 

The research is being funded by the EPSRC programme grant on “digital twins for improved dynamic design” led by Sheffield University (digitwin.ac.uk).