Study On Parameter Uncertainty Analysis And Risk-based Design Method In Fire Safety Design

In fire safety design, various models including the fire dynamic models, detection models and evacuation models, are being employed to derive reasonable fire protection design solution. Due to the complexity of the fire dynamics and the evacuation process, many uncertainties are inevitably associated with the fire safety design. However, these uncertainties are simply ignored or represented by conservative values or by an assigned safety factor in the current fire safety design. Such methods are difficult to be believed effective way to treat uncertainties. Correspondingly, the results derived from these methods are hardly reasonable and credible. Thus, how to treat these uncertainties quantitatively in the fire protection design is essential for obtaining reasonable and credible results.In this dissertation, the quantitative methods of analyzing the effect of uncertainties and treating such uncertainties in fire safety design are proposed. The main studies are focused on these following aspects: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 with peak heat release rate and the fire growth rate are discussed:the former parameter is characterized by normal distribution while the latter one is characterized by log-normal distribution. The deterministic effect of both parameters is first 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. How to employ the probability information to help the fire safety engineers develop the proper design fires is also illustrated.Taking the calculation model of RSET as an example, the global sensitivity analysis method for the related models in fire safety design is developed. Since the models currently employed in fire safety design are high complex, such models are usually nonlinear and the interaction between input parameters may exist. The local sensitivity analysis methods, which are main sensitivity analysis methods in the current fire safety design, cannot effectively deal with the nonlinear models and quantify the effect of parameter interaction. Thus, a systematic global sensitivity analysis method is proposed 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 of analyzing the sensitivity of input parameters on the model of RSET is demonstrated. A scatter plots were first employed to obtain a visual identification of the important parameters and identify if there is a linear relationship between input and output. Based on the preliminary sensitivity analysis results from scatter plots, the global sensitivity analyses of heat fire detection model and evacuation model were made by the first order indices of FAST and Sobol. The second order of Sobol indices were also calculated to quantify the effect of the interaction of input parameters on the detection time and evacuation time. The comparison of the CDF curves of fixing one uncertain parameter at its base value with the CDF curve of all uncertain parameter was employed to validate the sensitivity analysis results. The conclusions drawn from the comparison of CDF curves are consistent with that from the sensitivity analysis, which indicates the sensitivity analysis procedure in this study is suitable and the sensitivity analysis results are reasonable.Based on the analysis of the effect of uncertain heat release rate on ASET and considering the high importance of the prescribing a proper heat release rate, a method of quantitatively deriving the value of proper heat release rate is proposed. In the proposed method, the acceptable fire risk level is integrated into the determination of the target probability of failure for each fire scenario. With consideration of uncertainties with heat release rate, the reliability theory and the optimization procedure are employed to determine the values of the heat release rate for each fire scenario. A case study is provided to illustrate that the proposed method can be applied into the practical fire safety design.Aiming at the defect that there is little effort on linking the safety factor and the probability of failure, a method of bridging these two concepts are developed. The concept of random safety factor is proposed considering uncertainties with the calculation of ASET and RSET. Based on the distribution of the random safety factor, the relationship between safety factor and the probability of failure can be established. Due to the complexity of the distribution of ASET and RSET, the Monte Carlo simulation using LHS is employed to determine the distribution of random safety factor. The case study demonstrates that the proposed method could link the safety factor and the probability of failure effectively and provide the fire safety designers with a reasonable guide in selecting an appropriate safety factor to meet the required safety level. Such method can also provide suggestions for the improvement of the current design solution and make the final design results more reasonable and credible.