A Response Surface Methodology for Probabilistic Life Safety Analysis using Advanced Fire Engineering Tools

In the paper, we evaluate the reliability of a successful evacuation using a CFD fire simulation tool and an evacuation model. Obviously, it is not possible to perform Monte Carlo analysis in a reasonable amount of time because of the high computational costs. Hence, we utilize an adaptive response surface method based on moving least squares in order to compute the reliability. To further decrease the necessary number of numerical evaluations, a preceding sensitivity analysis yields information about the variance of the results and the relevance of the input parameters and hence helps to identify a surrogate model of optimal prognosis. The preliminary scan of the random space for the sensitivity analysis can also be used to obtain information about the approximate location of the design point so that further support points can be concentrated in this relevant area. Using this information for the subsequent reliability analysis leads to a faster convergence. The methodology described will be utilized to evaluate the reliability of a typical example in fire protection engineering.

[1]  Sanjay R. Arwade,et al.  Computational Analysis of Randomness in Structural Mechanics , 2011 .

[2]  W. Mendenhall,et al.  A Second Course in Statistics: Regression Analysis , 1996 .

[3]  Douglas W. Hubbard,et al.  The Failure of Risk Management: Why It's Broken and How to Fix It , 2009 .

[4]  Abraham M. Hasofer,et al.  Response surface modelling of monte carlo fire data , 2002 .

[5]  Glenn P. Forney,et al.  Fire Dynamics Simulator (Version 2) -- Technical Reference Guide | NIST , 2001 .

[6]  Glenn P. Forney,et al.  Fire dynamics simulator- technical reference guide , 2000 .

[7]  N. Draper,et al.  Applied Regression Analysis: Draper/Applied Regression Analysis , 1998 .

[8]  Håkan Frantzich,et al.  Fire Safety Design Based on Calculations. Uncertainty Analysis and Safety Verification , 1996 .

[9]  Johannes Will,et al.  Meta-model of Optimal Prognosis-An automatic approach for variable reduction and optimal meta-model selection , 2009 .

[10]  C. Bucher,et al.  A fast and efficient response surface approach for structural reliability problems , 1990 .

[11]  Carsten Proppe,et al.  Estimation of failure probabilities by local approximation of the limit state function , 2008 .

[12]  David Yung.  Principles of Fire Risk Assessment in Buildings , 2009 .

[13]  C. Bucher.  Adaptive sampling — an iterative fast Monte Carlo procedure , 1988 .

[14]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[15]  P. F. Nolan,et al.  An analysis of fire sizes, fire growth rates and times between events using data from fire investigations , 2004 .

[17]  Andy J. Keane,et al.  Engineering Design via Surrogate Modelling - A Practical Guide , 2008 .

[18]  Craig Beyler.  Toxicity Assessment Of Products Of Combustion Of Flexible Polyurethane Foam , 2005 .

[19]  A. M. Hasofer,et al.  Risk Analysis in Building Fire Safety Engineering , 2006 .

[20]  Thomas Most,et al.  New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares , 2008 .

[21]  Matthias Kunle.  Entwicklung und Untersuchung von Moving Least Square Verfahren zur numerischen Simulation hydrodynamischer Gleichungen , 2001 .

[22]  William Mendenhall,et al.  A Second Course in Statistics , 2011 .

[23]  Robert W. Fitzgerald.  Building Fire Performance Analysis , 2004 .

[24]  P. Lancaster,et al.  Surfaces generated by moving least squares methods , 1981 .

[25]  I N Bronstein,et al.  Taschenbuch der Mathematik , 1966 .

[26]  Takeyoshi Tanaka.  Risk-Based Selection of Design Fires to Ensure an Acceptable Level of Evacuation Safety , 2008 .