火灾安全设计中参数不确定性分析及耦合风险的设计方法研究
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摘要
在火灾安全设计中,通常利用火灾动力学模型、探测模型和人员疏散模型来计算得到合理的火灾安全设计方案。由于火灾动力学和疏散过程的高度复杂性,这些模型的输入参数往往具有一定的不确定性。对火灾安全设计中的参数不确定性进行科学有效地量化对于保证火灾安全设计结果的科学性、可信性具有重要意义。在目前的火灾安全设计中,经常忽视这些参数的不确定性,将这些参数视为定值或者通过设定安全系数来表示这些不确定性。这样的处理方法很难对参数不确定性进行有效处理,因而所得到设计结果的准确性和可信性缺乏有效验证。针对这一问题,本论文提出了定量分析参数不确定性影响的方法以及考虑参数不确定性的火灾安全设计方法,主要研究工作与成果如下：
基于拉丁超立方抽样(LHS)的Monte Carlo模拟建立了分析热释放速率不确定性对可用安全疏散时间(ASET)影响的方法。根据t2火假设,分析了火灾增长系数和最大热释放速率的不确定性,并采用概率方法来表征其不确定性。在分析了确定性火灾增长系数和最大热释放速率对ASET的影响基础上,利用基于拉丁超立方抽样(Latin Hypercube Sampling, LHS)的Monte Carlo模拟分析了当分别考虑火灾增长系数和最大热释放速率的不确定性时对ASET的影响,最后讨论了二者均为不确定性参数时对ASET的影响。此外,本部分还给出了如何利用概率信息如累积概率函数和补充累积概率函数来帮助火灾安全设计人员设定合理的火灾规模。
提出了RSET相关计算模型的全局参数敏感性分析方法。为减少参数不确定性分析的计算量并保证计算的精度,需要利用参数敏感性分析方法确定各输入参数对结果的影响程度。由于RSET计算所涉及模型的复杂性,模型的输入参数与输出结果之间往往是非线性的且输入参数之间的交互作用也会对模型输出产生影响。因此,传统的局部参数敏感性分析方法不适合RSET相关计算模型的参数敏感性分析。为此,本研究提出了适用于RSET计算模型的全局参数敏感性分析方法,包括输入参数不确定性的表征、基于散点图的初步敏感性分析以及傅里叶谱敏感性测试(Fourier amplitude sensitivity test,FAST)和Sobol指数法的全局参数敏感性分析方法。在给定参数取值范围和分布的情况下,对感温探测模型和人员疏散模型进行了全局参数敏感性分析。首先利用散点图来检验输入参数与输出结果之间是否存在线性关系。基于散点图的分析结果,利用FAST和Sobol一阶指数对感温探测模型和疏散模型进行了全局参数敏感性分析；以Sobol二阶指数为指标定量分析了输入参数的交互作用对探测时间和疏散时间的影响；通过将某一不确定性参数取做定值时的累积概率曲线与考虑所有参数不确定性时的累积概率曲线比较,验证了本研究中参数敏感性分析方法的有效性。
在分析了热释放速率不确定性对ASET影响的基础上,提出了一种火灾安全设计中火灾规模的定量计算方法。该方法将可接受风险水平的概念引入到了目标失效概率的设定中,在考虑热释放速率不确定性的前提下,提出利用可靠性理论和全局优化算法来计算不同火灾场景下所需要设定的火灾规模。工程算例分析结果表明该方法可以用于火灾安全设计中火灾规模的定量计算。
提出了将安全系数与目标失效概率联系起来的计算方法。由于目前安全系数取值依赖设计人员的主观判断且设计人员无法确定所选定的安全系数对应多大的失效概率,在考虑ASET和RSET计算过程中参数不确定性的前提下,将传统的安全系数概念进行了拓展,提出了随机安全系数的概念。基于随机安全系数的概率分布,建立了安全系数与失效概率之间的关系。针对ASET和RSET的概率分布较为复杂,无法得到随机安全系数的概率分布表达式的不足,利用基于LHS的Monte Carlo模拟确定随机安全系数的概率分布。工程算例分析结果表明,本文所提出的方法可以有效地将安全系数与失效概率联系起来,从而使得火灾安全设计人员在选取安全系数时能够充分考虑可接受的火灾风险水平,为安全系数的选取提供科学依据。此外,该方法也能够为设计人员提供现有设计方案的改进建议,使最终的设计结果更为科学可信。
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.
基于拉丁超立方抽样(LHS)的Monte Carlo模拟建立了分析热释放速率不确定性对可用安全疏散时间(ASET)影响的方法。根据t2火假设,分析了火灾增长系数和最大热释放速率的不确定性,并采用概率方法来表征其不确定性。在分析了确定性火灾增长系数和最大热释放速率对ASET的影响基础上,利用基于拉丁超立方抽样(Latin Hypercube Sampling, LHS)的Monte Carlo模拟分析了当分别考虑火灾增长系数和最大热释放速率的不确定性时对ASET的影响,最后讨论了二者均为不确定性参数时对ASET的影响。此外,本部分还给出了如何利用概率信息如累积概率函数和补充累积概率函数来帮助火灾安全设计人员设定合理的火灾规模。
提出了RSET相关计算模型的全局参数敏感性分析方法。为减少参数不确定性分析的计算量并保证计算的精度,需要利用参数敏感性分析方法确定各输入参数对结果的影响程度。由于RSET计算所涉及模型的复杂性,模型的输入参数与输出结果之间往往是非线性的且输入参数之间的交互作用也会对模型输出产生影响。因此,传统的局部参数敏感性分析方法不适合RSET相关计算模型的参数敏感性分析。为此,本研究提出了适用于RSET计算模型的全局参数敏感性分析方法,包括输入参数不确定性的表征、基于散点图的初步敏感性分析以及傅里叶谱敏感性测试(Fourier amplitude sensitivity test,FAST)和Sobol指数法的全局参数敏感性分析方法。在给定参数取值范围和分布的情况下,对感温探测模型和人员疏散模型进行了全局参数敏感性分析。首先利用散点图来检验输入参数与输出结果之间是否存在线性关系。基于散点图的分析结果,利用FAST和Sobol一阶指数对感温探测模型和疏散模型进行了全局参数敏感性分析；以Sobol二阶指数为指标定量分析了输入参数的交互作用对探测时间和疏散时间的影响；通过将某一不确定性参数取做定值时的累积概率曲线与考虑所有参数不确定性时的累积概率曲线比较,验证了本研究中参数敏感性分析方法的有效性。
在分析了热释放速率不确定性对ASET影响的基础上,提出了一种火灾安全设计中火灾规模的定量计算方法。该方法将可接受风险水平的概念引入到了目标失效概率的设定中,在考虑热释放速率不确定性的前提下,提出利用可靠性理论和全局优化算法来计算不同火灾场景下所需要设定的火灾规模。工程算例分析结果表明该方法可以用于火灾安全设计中火灾规模的定量计算。
提出了将安全系数与目标失效概率联系起来的计算方法。由于目前安全系数取值依赖设计人员的主观判断且设计人员无法确定所选定的安全系数对应多大的失效概率,在考虑ASET和RSET计算过程中参数不确定性的前提下,将传统的安全系数概念进行了拓展,提出了随机安全系数的概念。基于随机安全系数的概率分布,建立了安全系数与失效概率之间的关系。针对ASET和RSET的概率分布较为复杂,无法得到随机安全系数的概率分布表达式的不足,利用基于LHS的Monte Carlo模拟确定随机安全系数的概率分布。工程算例分析结果表明,本文所提出的方法可以有效地将安全系数与失效概率联系起来,从而使得火灾安全设计人员在选取安全系数时能够充分考虑可接受的火灾风险水平,为安全系数的选取提供科学依据。此外,该方法也能够为设计人员提供现有设计方案的改进建议,使最终的设计结果更为科学可信。
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.
引文
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