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    <title>Response Surface Modelling of Monte-Carlo Fire Data</title>
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    <keywords>surface modelling; fire behaviour; fire models</keywords>
    <abstract>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.</abstract>
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    <pages>291</pages>
    <institution>Victoria University</institution>
    <department>Centre for Environmental Safety And Risk Engineering</department>
    <thesis_type>phd</thesis_type>
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