Treatment of uncertainties in fire safety design

Abstract

In fire safety design, various models including fire dynamic models, detection models and evacuation models, are being employed to derive reasonable fire protection design solutions. Due to the complexity of fire dynamics and the evacuation process, many uncertainties are inevitably associated with fire safety design. However, these uncertainties are simply ignored, or represented by conservative values or by an assigned safety factor in current fire safety design, and it is difficult to believe that such methods are truly effective in their treatment of uncertainties. Thus, the results derived from these methods are hardly credible and a quantitative method of processing uncertainties in fire safety design is essential. In this dissertation, quantitative methods of analyzing the effect of uncertainties and treating such uncertainties in fire safety design are proposed. The principal focus areas of this study are as follows: A Monte Carlo analysis method of quantifying the influence of heat release rate uncertainties on available safe egress time (ASET) is established. The heat release rate is characterized by a time-squared fire. The uncertainties relating to peak heat release rate and fire growth rate are discussed: the former parameter is characterized by normal distribution while the latter is characterized by log-normal distribution. The deterministic effect of both parameters is studied. Then, the effect of uncertainties in peak heat release rate and fire growth rate is investigated separately. Finally, the effect of uncertainties in both parameters is analyzed. The use of probability data to help fire safety engineers develop appropriate design fires is also illustrated. Taking the calculation model of RSET as an example, the global sensitivity analysis method for the relevant models in the fire safety design is developed. The models currently employed in fire safety design are highly complex, such models are usually nonlinear, and interaction between input parameters may exist. Thus, a systematic global sensitivity analysis method is developed to quantify these effects in our study, which includes the characterization of uncertainties with input parameters, a preliminary sensitivity analysis by scatter plots, and global sensitivity analysis by Fourier amplitude sensitivity test (FAST) method and Sobol indices method. A case study analyzing the sensitivity of input parameters on an RSET model is demonstrated. Scatter plots are first employed to obtain a visual identification of the important parameters and determine whether a linear relationship between input and output exists. From the scatter plot analysis, global sensitivity analyses of the heat fire detection model and evacuation model are conducted using FAST and Sobol first indices. The second order of Sobol indices are also calculated, to quantify the effect of the interaction of input parameters on detection and evacuation times. A comparison of CDF curve with one uncertain parameter fixed at its base value with the CDF curve with all uncertain parameters is conducted and the comparison results for the CDF curves validate the sensitivity analysis results, confirming that the sensitivity analysis procedure in this study is appropriate. Based on the analysis of the effect of uncertain heat release rate on ASET, and given the high importance of correctly prescribing the heat release rate, a method of quantitatively deriving the heat release rate is developed. In this method, the acceptable fire risk level is integrated into the determination of the target probability of failure for each fire scenario. With consideration given to uncertainties relevant to the heat release rate, reliability theory and optimization procedure are employed to determine the values of the heat release rate for each fire scenario. A case study is provided to illustrate the application of the proposed method to practical fire safety design. In response to the lack of research attempting to link safety factors with the probability of failure, a method of bridging these two concepts is developed. The concept of a random safety factor is proposed for use when considering uncertainties in ASET and RSET calculation. From the distribution of the random safety factor, the relationship between safety factors and the probability of failure is established. Due to the complexity of ASET and RSET distributions, Monte Carlo simulation is employed to determine the distribution of random safety factors. A case study demonstrates that the proposed method is capable of effectively linking safety factors with the probability of failure and providing fire safety designers with a reasonable guide in selecting appropriate safety factors to meet the required safety level. This method can also provide suggestions for improvements to current design solutions and render the final design results more accurate and credible.

Date of Award	2 Oct 2013
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Siu Ming LO (Supervisor)