Author: QuentinJULLIEN

jullien/presentation/jullien-presentation.mdk

@@ -2,7 +2,7 @@
 Title         : Stochastic analysis of egress simulations
 Sub Title     : 
 Author        : Quentin Jullien
-Affiliation   : Centre Scientifique et Technique du Bâtiment ![logo2]
+Affiliation   : Centre Scientifique et Technique du Bâtiment - France ![logo2]
 Email         : [email protected] 
 Reveal Theme  : sky
 Beamer Theme  : singapore
@@ -26,13 +26,16 @@ Toc Depth     : 1
 # Context 
 The use of egress simulation models in performance-based analysis relies on the confidence in the input data and the output data.
 
-* But data strongly depend on a large number of parameters.
-* So the results are prone to be scattered.
+But, data strongly depend on a large number of parameters.
+
+These parameters model human behavior and are scattered.
+
+→ The results are prone to be scattered.
 
 
 
 ## Aim of the study
-Propose a method to analyze the statistical aspects of an egress simulation model.
+Realization of a method to analyze the stochastic aspects of an egress simulation model.
 
 * The method is based on statistical estimations of the distribution quantiles of the output parameters.
 The key result is Required Safe Egress Time (RSET).
@@ -47,13 +50,13 @@ Benefits of the method:
 
 ~ Begin Vertical { data-background:Gainsbor }
 
-# Presentation of the method of statistical analysis {#vertical}
+# Statistical analysis method {#vertical}
 
 Example: 
 
-* Take a sample of n realizations of a random variable that follows a normal law distribution.
-* Build a confidence interval Ip for each order quantile α.
-* Choose a level of confidence p: here 90%.
+* A sample of n realizations of a random variable that follows a normal law distribution.
+* A confidence interval Ip for each quantile α.
+* A level of confidence p: here 90%.
 
 ~ Math { #eq-alignment; caption:"Alignment example" }
 \begin{aligned} 
@@ -64,7 +67,7 @@ Example:
 c equals to 1.645 for p=90%. 
 
 
-## Build the empirical distribution function
+## Calculating the empirical distribution function
 → Random realizations ranked in ascending order constitute the 
 empirical distribution function.
 
@@ -80,14 +83,14 @@ empirical distribution function.
 ~ Align-Left
 * A random variable can not show a theoretical maximum.
 * Even if there is a maximum value, the finite size of 
-the samples didn't allow to access to this maximum value.
+the samples prevent from calculating this maximum value.
 
 → Only percentiles are available.
 
-* Percentiles increases with the growth of the sample size.
-* Confidence interval decreases with the growth of the sample size.
+* Available percentiles increases with the growth of the sample size.
+* Confidence interval width decreases with the growth of the sample size.
 
-→ So, the required number of draws is set by:
+→ So, the required number of simulations is set by:
 
 * the desired precision,
 * the order of the desired quantile.
@@ -127,7 +130,6 @@ Reminder:
 ~ Align-Left
 Occupants:
 
-* are men,
 * have same leaderships,
 * have same patience,
 * are valid,
@@ -136,7 +138,7 @@ Occupants:
 * act independently of each other.
 
 The identical leaderships imply a conflict resolution time included between 0.8 s and 1.5 s.
- During this study the fixed value of 1.15 s will be use too.
+ The fixed value of 1.15 s will be use too.
 
 The draws are realized with an uniform law.
 ~
@@ -150,66 +152,51 @@ The draws are realized with an uniform law.
 ~ Begin Vertical { data-background:Gainsbor }
 # Reference study case
 
-Occupants are randomly positioned in the room and drawn between 1 and 1,000.
+Occupants are randomly located in the room and drawn between 1 and 1,000.
 
 ~ Begin Columns
 ~ Column { width:50% }
-100 draws
+100 simulations
 
 ![fig5_1]
-[fig5_1]: images/fig5_1.PNG "fig5_1" { width:auto; max-width:80%; border:solid 1px black}
+[fig5_1]: images/fig5_1.PNG "fig5_1" { width:auto; max-width:100%; border:solid 1px black}
 ~
 ~ Column
-1,000 draws
+1,000 simulations
 
 ![fig5_2]
-[fig5_2]: images/fig5_2.PNG "fig5_2" { width:auto; max-width:80%; border:solid 1px black}
+[fig5_2]: images/fig5_2.PNG "fig5_2" { width:auto; max-width:100%; border:solid 1px black}
 ~
 ~ End Columns
 
 
 
 ## Observations (1)
 
-It is impossible to determine statistically a RSET maximum.
+It is impossible to statistically determine a RSET maximum.
 ~ Align-Left
 * Extreme percentiles have a confidence interval with infinite bounds.
-~
+
 
 In any case, a RSET max is bound to a catastrophic scenario.
 
-→ It seems preferable to retain the associated RSET 95^th^ percentile.
+→ It seems preferable to retain a high order percentile.
 
+* This study used the 95^th^ percentile.
+~
 ~ Align-Left
-* The value of 95^th^ percentile is arbitrary.
+* The value of this parameter is essential to an egress study conclusions and has to be discussed.
 ~
 
 ## Observations (2)
-The confidence interval decreases with the increase of the number of draws.
-
-~ Center
-![fig5_3]
-[fig5_3]: images/fig5_3.PNG "fig5_3" { width:auto; max-width:60%; border:solid 1px black}
-~
-
-## Observations (3)
-There are at least 3 separate evacuation schemes according to the number of occupants.
+The confidence interval decreases with the increase of the number of simulations. &bcheckmark;
 
-~ Center
-![fig_tab3]
-[fig_tab3]: images/fig_tab3.PNG "fig_tab3" { width:auto; max-width:50%; border:solid 1px black}
-~
-~ Begin Columns
-~ Column { width:50% }
-![fig5_2]
-[fig5_2]: images/fig5_2.PNG "fig5_2" { width:auto; max-width:80%; border:solid 1px black}
-~
-~ Column
-![fig5_4]
-[fig5_4]: images/fig5_4.PNG "fig5_4" { width:auto; max-width:85%; border:solid 1px black}
+There are at least 3 separate evacuation patterns according to the number of occupants.
+~ Align-left
 
+* Three parameters sets are based on this three patterns and used in this study to get rid of the occupant density influence.These patterns are used in this study to see the influence of others parameters more independently of the density of people.
 ~
-~ End Columns
+→ The method provides additional elements to understand evacuation behaviors even in this simplistic case.
 
 ~ End Vertical
 
@@ -227,22 +214,31 @@ There are at least 3 separate evacuation schemes according to the number of occu
 
 Parameters tested: conflict resolution time, position of the occupants and response time (RT).
 
-~ Center
-![fig_tab4]
-[fig_tab4]: images/fig_tab4.PNG "fig_tab4" { width:auto; max-width:55%; border:solid 1px black}
-~
-3 schemes to free from influence of occupant density.
-~ Center
-![fig_tab5]
-[fig_tab5]: images/fig_tab5.PNG "fig_tab5" { width:auto; max-width:55%; border:solid 1px black}
-~
+1,000 simulations for each patterns.
+
+
+
+|-----------|---------------------|---------------|----------|
+| Test case | Conflict resolution | Position of   | RT (s)   |
+|           | time (s)            | the occupants |          |
++:---------:+:-------------------:+:-------------:+:--------:+
+| 1         | [0.8 ; 1.5]         | Fixed         | 15       |
+| 2         | 1.15                | Fixed         | 15       |
+| 3         | [0.8 ; 1.5]         | Random        | 15       |
+| 4         | [0.8 ; 1.5]         | Random        | [0 ; 30] |
+|-----------|---------------------|---------------|----------|
+|           |                     |               |          |
+{ text-align:center }
+
+
+
 
 
 ## Test case 1
 
-The empirical distribution function is not linear.
+The empirical distribution function is not uniform.
 
-→ linked to the variability of the conflict resolution time and to the effect of history.
+→ linked to the variability of the conflict resolution time and to the history effect.
 
 ~ Center
 ![fig6_3]
@@ -280,54 +276,39 @@ Notations used to make quantitative comparisons:
 Reminder:
 Conflict resolution time, position, RT fixed. 
 
-~ Begin Columns
-~ Column { width:55% }
+~ Center
 ![fig6_5]
-[fig6_5]: images/fig6_5.PNG "fig6_5" { width:auto; max-width:85%; border:solid 1px black}
-~
-~ Column
-![fig_tab7]
-[fig_tab7]: images/fig_tab7.PNG "fig_tab7" { width:auto; max-width:100%; border:solid 1px black}
+[fig6_5]: images/fig6_5.PNG "fig6_5" { width:auto; max-width:50%; border:solid 1px black}
 ~
-~ End Columns
+
 
 
 ~ left-align
-→ Most of the variability comes from the effect of history.
+→ Most of the variability comes from the history effect.
 
-→ Width of confidence intervals can increase or decrease whereas the parameters are less variable.
+→ Confidence intervals width variations are not intuitive.
 ~
 
 ## Test case 3
 Reminder: 
 Conflict resolution time and position vary, RT is fixed.
-~ Begin Columns
-~ Column { width:55% }
+~ Center
 ![fig6_6]
-[fig6_6]: images/fig6_6.PNG "fig6_6" { width:auto; max-width:85%; border:solid 1px black}
+[fig6_6]: images/fig6_6.PNG "fig6_6" { width:auto; max-width:50%; border:solid 1px black}
 ~
-~ Column
-![fig_tab8]
-[fig_tab8]: images/fig_tab8.PNG "fig_tab8" { width:auto; max-width:100%; border:solid 1px black}
-~
-~ End Columns
 → Position has more influence on low and average densities.
 
 
 
 ## Test case 4
 Reminder:
 Resolution conflict time, position and RT vary.
-~ Begin Columns
-~ Column { width:50% }
+
+~ Center
+
 ![fig6_7]
-[fig6_7]: images/fig6_7.PNG "fig6_7" { width:auto; max-width:100%; border:solid 1px black}
+[fig6_7]: images/fig6_7.PNG "fig6_7" { width:auto; max-width:50%; border:solid 1px black}
 ~
-~ Column
-![fig_tab9]
-[fig_tab9]: images/fig_tab9.PNG "fig_tab9" { width:auto; max-width:100%; border:solid 1px black}
-~
-~ End Columns
 
 → the variability of output parameters increases with the one of the input parameters &bcheckmark;
 
@@ -340,11 +321,29 @@ Resolution conflict time, position and RT vary.
 ~ Begin Vertical { data-background:Gainsbor }
 # Synthesis of results
 
+|--------------------------|-----------------------------------------------------|-----------------------|
+| Studied parameters       | Variation range of the input parameter              | Qualitative influence |
++:------------------------:+:---------------------------------------------------:+:---------------------:+
+| Occupant number          | From 1 to 1,000 persons or 187, 610 and 927 persons | Very important        |
+|--------------------------|-----------------------------------------------------|-----------------------|
+| Occupant position        | Fixed or random                                     | Important             |
+|--------------------------|-----------------------------------------------------|-----------------------|
+| Conflict resolution time | From 0.8 s to 1.5 s or 1.15 s                       | Negligible            |
+|--------------------------|-----------------------------------------------------|-----------------------|
+| Response time            | From 0 s to 30 s or 15 s                            | Important             |
+|--------------------------|-----------------------------------------------------|-----------------------|
+|                          |                                                     |                       |
+{  }
+
+
+
+
+
 
-~ center
-![fig_tab10]
-[fig_tab10]: images/fig_tab10.PNG "fig_tab10" { width:auto; max-width:70%; border:solid 1px black}
-~
+
+
+
+# Synthesis of results (2)
 
 Advantage of the method:
 
@@ -355,10 +354,17 @@ Advantage of the method:
 * Estimate quantitatively the influence on the RSET of the input parameters dispersion.
 ~
 
-~ End Vertical
+# Synthesis of results (3)
+
 
 
 
+
+
+~ End Vertical
+
+
+~ Begin Vertical { data-background:Gainsbor }
 # Conclusion
 
 
@@ -369,22 +375,30 @@ Advantage of the method:
 
 → There is still a lot of work.
 
+Pas les données 
+la méthode à améliorer
+
+
+# Conclusion (2)
+
 Prospects:
 
 ~ Align-Left
-* Test more complex geometry.
+* Test more realistic case.
 * Test cross interactions thoroughly (experiment plans).
 * Compare to some evacuation trials.
 * Need for a bibliography work.
 * Industrialize the method on tools dedicated to stochastic analysis.
 * Compare different simulations tools.
 ~
 
+~ End Vertical
+
+
 
 
 
 
-# Thank you for your attention