تجزیه و تحلیل حساسیت از مدل های آتش نشانی با استفاده از طراحی فاکتوریل جزئی

This work presents a sensitivity analysis, conducted in the framework of the PRISME OECD programme, using fractional factorial design. Several field and zone computer codes have been used to study the influence of some factors characterizing either the fuel, or the compartment or the ventilation network on relevant responses for fire safety studies. More specifically, the effects of these factors on gas and wall temperatures, the concentration of oxygen in the room, total and radiative heat flux to the walls and the total pressure in the compartment were examined. The results have mainly allowed to organize in a hierarchy the importance of various factors on these responses. Along with this sensitivity study, three methods for generating samples were compared: the Monte-Carlo method, the full and fractional experimental designs. The results have shown that a fractional factorial design, composed of eight runs, gave the same information than a full factorial design, composed of 64 runs or than a Monte-Carlo method, composed of 200 runs.

Sensitivity analysis is an essential part of any fire simulation project. The sensitivity of the simulation results, with respect to the physical input parameters, is needed to evaluate the justification of the conclusions in the light of the input uncertainty. The overall quality of the simulations, in turn, can be evaluated by a systematic validation and by studying the sensitivity to the numerical parameters, such as the numerical discretization or the turbulence model. In case of several varying parameters, performing a thorough sensitivity analysis can be quite laborious. For the ease of interpretation, it may be temptating to change only one input parameter at the time but this may prevent one from perceiving the possible synergistic effects between the parameters. The classical methods of experimental design, such as full and fractional factorial design, should therefore be used to find the efficient yet comprehensive set of inputs giving good picture about the variability of possible simulation results. This variability is often investigated in the context of the probabilistic risk assessment, where the range of input values is treated as a random space. Numerical integration over a random space can be performed using a Monte-Carlo method, where a relatively large number of input values is chosen from the parameter space and deterministic simulations are carried out for all of them. The sensitivity of the simulation results to the input values can then be determined in terms of correlation coefficients, considering the internal parts of the input space. The purpose of this work is to illustrate the use of fractional factorial design as a means of performing the sensitivity analysis for numerical fire simulations. Several field and zone computer codes have been used to study the influence of factors characterizing either the fuel, the compartment or the ventilation network on relevant responses for fire safety studies. The work has been carried out within the OECD PRISME programme of fire experiments. Concurrently to the experimental programme, the results of one test were used to perform a numerical fire simulation benchmark with the aim to validate the different fire models used by the current project participants. The exercise involved 12 organizations and six fire models detailed in Table 1. A description of the fire models and some references are available in [1] where the use of metric operators to quantify the differences between numerical results and experimental measurements was investigated in order to avoid qualitative comparisons. Table 1. List of participants and fire models. Organization Participant Fire model version BelV N. Notterman, F. Bonte CFAST 6 CSN J. Peco FDS 4.06 DGA C. Lallemand OEIL 1.5.1 EdF L. Gay MAGIC 4.1.3 GRS W. Klein-Hessling, M. Pelzer COCOSYS 2.4 beta 5 iBMB V. Hohm FDS 5 IRSN S. Suard SYLVIA 1.4 JNES T. Ito FDS 4 CFAST 6.1 Vattenfall & Lund University T. Magnusson, P. Van-Hees FDS 5.4.0 NRG A. Siccama, P. Sathiah FDS 4 CFAST 6 Tractebel E. Gorza MAGIC 4.1.3 VTT S. Hostikka FDS 5.4.3 Table options The outline of the document is as follows. The first section presents a brief introduction to the sensitivity analysis (SA) and to the process of choosing a design of experiments (DoE). The objectives of the study are recalled in this part. The second section describes in detail the responses and the different input factors which have been selected for the construction of the sensibility analysis and DoE. A justification for using fractional design instead of full factorial design or Monte-Carlo methods is provided in the second part of this section. The last section presents the SA performed with a fractional factorial design. Because some user effects were highlighted in the early phase of the study, the final work presented here was only conducted for each fire model instead of each user.

A sensitivity analysis was performed on several fire models using a fractional experimental design. The used codes were CFAST, COCOSYS, FDS, MAGIC, OEIL and SYLVIA. The influence of six inputs factors was tested on five responses including gas and wall temperature, oxygen concentration and the total (net) wall heat flux. These responses were selected for their general importance in fire safety studies. The considered input factors were the fuel mass loss rate, the radiative fraction of combustion, thermo-physical properties of the compartment boundaries (conductivity, heat capacity and emissivity) and the ventilation mass flow rate through the ventilation network. The comparison of three alternative sampling methods (Monte-Carlo method, full factorial design and fractional factorial designed) indicated that all the three methods gave almost identical results for the sensitivity measures. The calculations were performed with the SYLVIA, FDS and COCOSYS fire models and the sensitivity analysis with the SUNSET software. This result is important both for experimental studies but also for numerical simulations performed with fire field models because it shows that the fractional design (FD) can provide the same sensitivity information as the other two methods that require much more computations. In this particular case, the fractional FD with eight runs provided the same information as a Monte-Carlo method with 200 runs or a full FD with 64 runs. The construction of a fractional FD has been performed in this work for six parameters but can be extended to a higher number of parameters. In this case, a new fractional FD could be proposed following the same strategy as in Section 2.2 keeping in mind that since the number of runs is reduced compared to a full FD, there is an aliasing effect. Therefore the construction of a fractional FD cannot be decoupled from a physical analysis in order to exhibit the parameter interactions the analyst intends to focus on. Since it drastically reduces the number of runs to perform, fractional FD makes a systematic sensitivity analysis feasible for industrial applications. However, care should be taken when choosing the input range to ensure that the physical nature of the fire does not drastically change, and that the fire model in question is valid over the whole range of inputs. The sensitivity analysis with six different numerical fire models showed that both the mutual rankings and actual sensitivity measures were very similar among the fire models. This major result increases the overall confidence on the quantification of input importance for the different responses. The results show that the main factor for each response is the fuel mass loss rate. This is, obviously, in line with expectations because fire heat release rate is known to be the single most important parameter of the fire simulations. According to the results, the oxygen concentration seems to be affected by the ventilation mass flow rate whereas the mean gas temperature variations can be due to a changes in the wall emissivity. These results should orient the interests inside the fire community and contribute to the requirement that the fire model input parameters should be reliably and accurately determined for each individual case, instead of using the handbook values that cannot be challenged.