Bayesian calibration and sensitivity analysis of heat transfer models for fire insulation panels

TL;DR

This paper introduces a Bayesian framework for calibrating heat transfer models of fire insulation panels, improving efficiency and accuracy through surrogate modeling and enabling sensitivity analysis with Sobol' indices.

Contribution

It reformulates heat transfer model calibration in a probabilistic Bayesian setting and accelerates it with polynomial chaos surrogates, also facilitating sensitivity analysis.

Findings

Bayesian calibration provides confidence bounds on material properties.

Surrogate models significantly speed up the calibration process.

Sensitivity analysis identifies key parameters affecting heat transfer.

Abstract

A common approach to assess the performance of fire insulation panels is the component additive method (CAM). The parameters of the CAM are based on the temperature-dependent thermal material properties of the panels. These material properties can be derived by calibrating finite element heat transfer models using experimentally measured temperature records. In the past, the calibration of the material properties was done manually by trial and error approaches, which was inefficient and prone to error. In this contribution, the calibration problem is reformulated in a probabilistic setting and solved using the Bayesian model calibration framework. This not only gives a set of best-fit parameters but also confidence bounds on the latter. To make this framework feasible, the procedure is accelerated through the use of advanced surrogate modelling techniques: polynomial chaos expansions combined with principal component analysis. This surrogate modelling technique additionally allows one to conduct a variance-based sensitivity analysis at no additional cost by giving access to the Sobol' indices. The calibration is finally validated by using the calibrated material properties to predict the temperature development in different experimental setups.