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AAMKS offers a variety of statistics to quantify and describe comprehensively the level of fire safety in the building. As Monte Carlo approach is used to evaluate those quantities the vast majority of parameters is expressed as probabilities functions or risks. However, this section provides the description of parameters and methods used to evaluate those summaries.

Results can be accessed in web-based GUI in "Simulations" section at the moment. User can also download all data on his/her computer. Keep in mind that the software is extensively developed at the moment and some fundamental changes may be introduced in the future.

AAMKS software uses CFAST zone model by NIST to calculate fire behaviour. You can find detailed documentation of CFAST here. However, issues of the most significant importance for AAMKS post-process will be revoked here.

CFAST returns two sets of results functions, uniform in each layer (accordingly named upper and lower or hot and cold). Default time resolution for result output coded in our scripts is 10 s. (Note that .smv animation is written every 100 s). We use the following data from each iteration to evaluate conditions in the building:

• gas temperature;
• smoke obscuration;
• concentrations of the following species:
  • carbon monoxide ($CO$),
  • carbon dioxide ($CO_2$),
  • hydrogen cyanide ($HCN$),
  • hydrogen chloride ($HCl$),
  • oxygen ($O_2$).

This detailed data is not directly available from user-level interface of AAMKS. More advanced users, however, can easily access it from worker-level directories, ie. /home/aamks_users/user1/project1/scenario1/workers/*/ (see chapter ???about catalogues structure???).

Available Safe Egress Time is reached when at least one agent reaches $FED=1$. However, utilization of ASET in probabilistic analysis is rather marginal and assisting than decisive.

We use our own A-Evac model to calculate the egress process. This is simple hydraulic agent model with collision-avoiding implemented via RVO2 library. Also the model is in active development stage at the moment and major improvements will be introduced in the future. Although, the aim of the model will remain the same: to calculate the position of each agent at certain timestep. Detailed description of the model can be found [here].

The evacuation process is assumed to be finished when all evacuees escaped from building. This time is RSET (Required Safe Egrees Time) in the whole post-processing.

However, there are particular and isolated cases when some agents are "stuck". In order to prevent endless evacuation due to the error that cannot be predicted we introduced also another criterion for RSET. If the first criterion (all out) is not met we assume RSET is the time when 98% of agents evacuated successfully plus 30 s.

On the other hand, if many evacuees do not egress this iteration is not taken into account when RSET distribution is calculated.

Source for this subsection: Purser, D. and McAllister J. Assesment of Hazards to Occupants from Smoke, Toxic Gases and Heat [in:] Hurley, M. et al. SFPE Handbook of Fire Protection Engineering, vol. 3, 5th ed., 2016.

To assess the impact of fire effluents to each evacuee we use Fractional Effective Dose (FED) concept. It states that incapacitating effects of those species ($FED_{CO}$, $FED_{HCN}$, $FED_{HCl}$, $FED_{O_2}$) are mainly additive. However, effect of asphyxants and toxins has to be multiplied by factor of hyperventilation $V_{CO_2}$ caused by rise in carbon dioxide concentration and breathing rate $V_E$. General term for total fractional effective dose $FED_{tot}$ absorbed by an agent form time $t_1$ to $t_2$ is presented below.

$$FED_{tot}= \int_{t_1}^{t_2}((FED_{CO} + FED_{HCN} + FED_{HCl}) \cdot V_{CO_2} \cdot V_E + FED_{O_2}) dt$$

where each component is described below.

$FED_{tot}$ is calculated for each individual separately for each time step of evacuation simulation. Concentrations of species are imported form CFAST result files for location of agent at given time. Unless neutral plane is of height 1.8 m lower layer data are used.

Additional references for this subsection: R.D. Stewart, “The Effects of Carbon Monoxide on Man,” Journal of Combustion Toxicology, 1, pp. 167–176 (1974) and R.D. Stewart et al., “Experimental Human Exposure to High Concentrations of Carbon Monoxide,” Archives of Environmental Health, 26, p. 1 (1973).

Stewart equation was used to model asphyxiating effect of $CO$. It relates $CO$ concentration at given location and time to the level of carboxyhemoglobin $\%COHb$ present in blood of victims. Reference level of carboxyhemoglobin that causes incapacitation $\%COHb_{inc}$ depends on the activity level: resting, walking or climbing stairs and is 40 %CHb, 30 %CHb and 20 %CHb respectively.

$$</code>FED_{CO}= \frac{3.317\times10^{-5} \cdot {C_{CO}}^{1.036}}{<code>\%COHb_{inc}</code>}<code>$$

where: $C_{CO}$ is the concentration of carbon monoxide [ppm].

An expotential relation derived from experiments on primates was used to assess hydrogen cyanide impact on human. $$FED_{HCN} = \frac{{C_{HCN}}^{2.36}}{2.43\times10^7}$$

where: $C_{HCN}$ is the concentration of hydrogen cyanide [ppm].

Following Purser and McAllister, 2016 we used incapacitating dose of 60,000 ppm$\cdot$min as a reference level for assessment of $HCl$ contribution to incapacitation of evacuee. This assumption is compliant with as well 5 min (12,000 ppm) as 30 min (2,000 ppm) concentrations that incapacitated 50% of exposed population. $$FED_{HCl} = \frac{C_{HCl}}{60000}$$

where: $C_{HCl}$ is the concentration of hydrogen chloride [ppm].

The asphyxiating effect of low oxygen concentrations was introduced alongside other species. Nevertheless, positive effect of hyperventilation to organism oxygenation was neglected.

$$FED_{O_2} = \frac{1}{e^{8.13 - 0.54(20.9 - C_{O_2})}}$$

where: $C_{O_2}$ is the concentration of oxygen [%mol].

Exposition to small carbon dioxide concentrations increases the breathing rate and, as a consequence, also doses of fire effluents inhaled.

$$V_{CO_2} = e^{0.1903 \cdot C_{CO_2} + 2.0004}$$

where: $C_{CO_2}$ is the concentration of carbon dioxide [%mol].

Hyperventilation factor is then multiplied by actual breathing rate depending on activity level (resting, walking or climbing stairs) and takes 8 l/min, 25 l/min and 50 l/min respectively.

To assess the risk linked to the iteration and, furthermore, to whole scenario we need to convert fractional effective dose obtained for each agent $FED_i$ to the probability of his/her incapacitation $P_{inc,i}$. Following the literature default log-normal distribution was used and $P_{inc}$ can be defined as its cumulative distribution function. $$X \sim LogN(\mu=0|\sigma=1)$$

hence: $$P_{inc} = \frac{1}{2}erfc\left(-\frac{log(FED)}{\sqrt{2}}\right)$$

It results in $P_{inc} = 0.5$ for $FED=1$ and $P_{inc} = 0.1143$ for $FED=0.3$ as stated in the Purser and McAllister, 2016. For further assessment we use $P_{inc}$ as the probability of serious injury or death alternatively. In the future we will introduce differentiation of effects (i.e. negligible, minor, major, lethal).

Text file containing data from Risk indices and Multisimulation output sections in GUI.

Database of each iteration input and output parameters. This is the most low-level set of data that our software provides. For more user have to modify the code on his/her own. Detailed description of parameters will be available in this section in the future.

Archive containing of all plots produced by the program (PNG format).

Archive of full results provides all previous files and also aamks.log file with detailed log record of the multisimulation. Keep in mind that aamks.log is server-owned, so it contains data of all multisimulation ever launched in the cluster.

Iteration output data are processed on each node right after finishing the fire and evacuation calculations. Next, processed results are collected and send to the server in order to be written to overall database. Server gathers preliminary processed iteration results consequently from each node. It is user's call when this data will be prepared to be visualised. One can run visualisation script at any moment and look up the results summary in "Simulations" section. Keep in mind that at early stage of multisimulation not all results may be available.

Pie chart delivers the simple message: what fraction of iterations results in success. The success is defined in this case as evacuation completed with keeping all agents $FED$ below unity. Every iteration where at least one agent absorbed at least $FED$=1 is denoted as failure.

The main assumption whenever fatality is mentioned in the software is that whoever absorbed $FED=1$ is incapacitated and unable to escape. Hence, distribution described in Probability of incapacitation subsection above is also valid for fatalities. Because result from the software are in terms of $FED$ for each agent, in order to find the probability of death of each agent the incapacitation CDF is used.

To obtain the number of fatalities in iteration, however, we use Monte Carlo (MC) simulation. Binary agent state (dead/alive) is subsequentially drawn from Bernoulli distribution for each agent. This process is repeated as long as the RMSE of fatalities number for the iteration drops below 0.001 threshold. That MC-derived for each iteration values are used to create Fatalities histogram that represents the share of iterations with given fatalities number. Please note that ordinates are expressed as density - number of occurrences within the bin divided by the bin width. Minimal bin width is 1, it has to be natural number and there will be no more than 25 bins in the plot. The line in the plot is kernel density function (from seaborn package).

Complementary and including whole spectra of consequences are presented with frequency - fatalities number curve. It is a complementary cumulative distribution function of the number of fatalities. Both axes in the plot are log-scaled, while abscissa is limited to the maximum number of agents across the scenario.

Colloquially speaking the plot answers the question: what are the chances that in case of fire the will be N fatalities or more. The more concave and flat is the curve the better.

Basic output statistics are PDFs (Probability Density Functions) and CDFs (Cumulative Distribution Functions) of each of the following values:

• RSET,
• ASET,
• RSET travel (moving) component,
• maximal smoke (upper layer) temperature,
• minimum layer interface level.

Risk assessment, as all the other results, are calculated for each iteration separately. Those preliminary postprocess calculations are performed on nodes (workers) right after single simulation is finished. Then, on results gathering stage, server averages those parameters for whole scenario. However, in the future risks statistics will be available in postprocess section also for each iteration separately.

Since one scenario should represent single fire zone (or its fragment) risk parameters are thus calculated across all floors specified in Apainter. The scenario is treated as a whole and there is no floor-division in poctprocessing.

Usual goal in risk assessment is to obtain probabilities of certain unfavorable effects. At this moment our software provides data about the probabilities of those effects in case of fire. So, we assume that the fire has already happened and we are looking into the course of events as it goes. Nevertheless, one can obtain [1/year] or [fatalities/year] values of risk by simply multiplying our risk indices by the probability of fire [1/year]. In the future an interface for fire probability assessment will be included in the software.

The reference where brief theoretical foundation can be found: S.N. Jonkman, P.H.A.J.M. van Gelder, J.K. Vrijling, An overview of quantitative risk measures for loss of life and economic damage, Journal of Hazardous Materials 99(1), pp.1-30, 2003

We define individual risk as the death probability of the typical user of the building due to fire. It is a specific case of the measure defined by the UK's health safety executive. Mathematical formula used to derive this number is as follows:

$$IR=\frac{N_{fatalities}}{N_{present}}$$

where $N_{fatalities}$ is the number of deaths due to fire and $N_{present}$ is the number of people present in the building during the fire.

Number of fatalities is derived with MonteCarlo sampling from the set of Bernoulli distributions of incapacitation for each agent.

There is variety of different measures to describe the level of societal risk. We have implemented some of them in our post-processing module. Some of them, however, contains

Weighted risk integral takes into account the risk aversion effect. It is integral over probability density function of deaths in fire multiplied by fatalities number to the risk aversion coefficient. We use $\alpha=1.4$ as a default value. In the future user will be able to change this value in advanced settings.

$$WRI = \int x^\alpha f_N(x) dx$$

where $x$ is fatalities number, $\alpha$ is risk aversion coefficient and $f_N(x)$ is PDF of fatalities in fire.

Aggregated weighted risk on the other hand is just a product of individual risk defined in previous subsection and number of people affected. In our simulations as affected we assume all the people present in building during the fire. No risk aversion effects are included in this value.

$$AWR=IR\times N_{present}$$

Scaled risk integral takes into account also the spatial and transitional factors. Remember that in our post-processing module time share is not included. User should multiply the value obtained form our model with $t$ on his/her own. This statistic may be more suitable for large areas than for small buildings. Nevertheless, it is available in postprocess section to provide user with more complete picture of risk.

$$SRI=\frac{P\cdot IR \cdot t}{A}$$

where $P=\frac{N_{present}+N_{present}^2}{2}$ is population factor, $t$ [1/year] is share of time the area $A$ is occupied by $N_{present}$ persons.

The intensity of $FED$ intakes is presented graphically on heatmaps. One can use those to identify liabilities of building's layout.

Heatmaps are plotted separately for each floor. Plane section of the floor is divided into structured square mesh with cells of 50 cm dimension. In each iteration $FED\times t$ products are assigned to the proper cell and summed accordingly to agent position. However to make the presented values independent on numbers of iterations matrix of $FED$ sum is divided by number of iterations.

Darker cells stands for spots where more $FED$ was absorbed by evacuees. (Perfectly white color of cell shows that no doses of toxines/asphyxiants where absorbed at this place through all iterations).

Post-processing module allows to compare multiply scenarios within one project. There are several plots available in this module - each scenario is shown in them as a separate data series:

• fatalities number probability density functions;
• frequency-fatalities number curves;
• ASET and RSET cumulative distribution functions (CDFs);
• maximum temperature CDFs;
• minimal visibility CDFs;
• minimal layer interface level CDFs.

Moreover, risk indices and multisimulation summary outputs are gathered across all compared scenarios. They are set together in separate columns in order to be easily cross-referenced.

Also detailed data and pictures downloads are available. Separate txt files and CSV databases for each scenario are compressed to ZIP archive as well as figures with multiple scenarios plotted.

Comparison is launched on-demand and involves executing post-processing command for each scenario, so the most actual results are gathered and imported to comparing module. Then all plots are created and archive prepared.