Response Surface Modelling of Monte-Carlo Fire Data

Deterministic computer fire models have progressed over recent years to the point of providing good predictions for some parameters of fire behaviour. However, input data are not always available, and many factors that affect the course of a fire are probabilistic in nature and cannot be determined from physics. One way of surmounting the problem of unavailability of the values of the input parameters is to take them as random variables. By specifying an unsafe region in the output space and calculating its probability, we can obtain a figure for the reliability of the design being tested, in terms of the probability of the unsafe region. In practice, evaluation of the probability distribution of the output space cannot in general be carried out analytically because of the complexity of the computer fire models. An alternative method is to use Monte-Carlo simulation. But it usually requires a large amount of calculation to reach sufficient accuracy, particularly if the probability of the unsafe region is small, as it should be if the design is to be reasonably reliable. Also, if the probability distribution of the input is changed, the whole Monte-Carlo simulation must be redone ab initio. An approach that has been recently advocated in the structural reliability context is that of the response surface method. It consists in representing each output parameter by a nonlinear function of the input parameters. Usually, a quadratic function of the input parameters turns out to be sufficient. Fitting of the response surface is carried out by regression. However, if the range of the input parameters is comparatively large, it is unlikely that one quadratic function will fit the whole range. It then becomes necessary to break up the full range of input parameters into smaller subranges and fit a quadratic function separately to each subrange