Fire detection, location and heat release rate through inverse problem solution. Part I: Theory

Abstract

A proposed method of detecting, locating and sizing accidental fires, based on the solution of an inverse heat transfer problem, is described. The inverse heat transfer problem to be solved is that of the convective heating of a compartment ceiling by the hot plume of combustion gases rising from an accidental fire. The inverse problem solution algorithm employs transient temperature data gathered at the ceiling of the compartment to determine the location and heat release rate of the fire. An evaluation of the proposed fire detection system, demonstrating the limits on the accuracy of the inverse problem solution algorithm, is presented. The evaluation involves operating the inverse problem solution algorithm on transient temperature data from computer simulated compartment fires. The simulated fire data are generated assuming fires with quadratic growth rates, burning in a 20 m wide by 20 m deep by 3 m high enclosure with a smooth, adiabatic ceiling. The accuracy of the inverse problem solution algorithm in determining the location of a fire is shown to be insensitive to the errors in the fire model used in the forward problem solution, but sensitive to errors in the measured temperature data. The accuracy of the heat release rate of the fire is sensitive to both errors in the fire model and errors in the temperature data. The validity of the use of computer simulated data in the evaluation is verified with a second evaluation using fire data interpolated from published measurements taken in large-scale compartment fire burns.