A Multi-observable Approach to Address the Ill-Posed Nature of Inverse Fire Modeling Problems

This study considers the development and evaluation of a prototype inverse fire model (IFM) aimed at predicting the heat release rate of a compartment fire using smoke layer information gained from building environmental sensors. The proposed methodology consists in: performing a search for the unknown heat release rate (HRR) by performing hundreds of different zone model simulations; comparing model predictions to observation data and thereby formulating an error function; using an optimization technique to minimize the error function and thereby producing a best estimate of HRR. The prototype IFM algorithm uses a zone fire model called BRI2002 (developed by the Building Research Institute in Japan) in conjunction with a genetic algorithm for optimization. The IFM algorithm is here applied to a reduced-scale laboratory experiment consisting of steady, over-ventilated, fire conditions in a simple multi-compartment (three rooms) configuration. The IFM algorithm is applied using a multiple-variable formulation in which both the fire size and the fire compartment venting conditions are assumed unknown, and using a one-observable or a two-observable scheme providing information on either the smoke layer temperature or on both the smoke layer temperature and depth. This framework is of particular interest because in the case of a one-observable scheme, the inverse fire problem is ill-posed, i.e. the optimization problem features multiple solutions and may converge to incorrect predictions of the fire size. This study shows that the two-observable scheme provides a way to regularize the inverse fire modeling problem, i.e. a way to provide a unique fire size solution. Our tests indicate that IFM-based estimates of HRR have an accuracy of better than 40%.