The use of Numerical Optimisation Techniques in Computational ...

The use of Numerical Optimisation Techniques in Computational Fire Engineering Models: a study through Evacuation Modelling Analysis by Rodrigo Machado Tavares

Supervisors: Prof. Ed. Galea (1st supervisor) Dr. J. Ewer (2nd supervisor)

Acknowledgements I would like to acknowledge the assistance provided by: Dr. Stoyan Stoyanov; Professor Vitaly Strusevich; Professor Chris Bailey and Mr. João Marcelo Lopes I would like also to thank CMS, Professor Ram and Professor Galea Author: RODRIGO MACHADO TAVARES

Acknowledgements And clearly, I am very grateful to:

Mrs. Sara Lynne Machado-Jones; Philip Richard Machado-Jones; Samuel George Machado-Jones. I

Author: RODRIGO MACHADO TAVARES

Contents • 1) Introduction;

• 2) General Objectives; • 3) The problem; • 4) Methodology; • 5) The Thesis – Discussion; • 6) Conclusions and further work. Author: RODRIGO MACHADO TAVARES

1) Introduction What is a safe design? - comfort; - functionality;

Design

- maintenance; - esthetic; - costs/benefits;

Safe Design (Fire Safety)‫‏‬

- safety Safe Design – a design which could provide a safe egress for its occupants RSET (required safe egress time) < ASET (available safe egress time)‫‏‬


1) Introduction RSET (required safe egress time) < ASET (available safe egress time)‫‏‬

CFE – Computational Fire Engineering SAFE DESIGN

COMFORT

MAINTENANCE FUNCTIONALITY

DESIGN 1

DESIGN 2

COSTS/BENEFITS

DESIGN 3

ESTHETICAL

DESIGN 4

SAFETY OF THE OCCUPANTS

DESIGN N


1) Introduction

Evacuation Analysis

CFE – Computational Fire Engineering

(“the‫‏‬optimal‫‏‬positioning of exits within an arbitrarily complex structure”)‫‏‬


1) Introduction

ETT1 T2

ET T1

– Time spent during the movement

T2

– Time spent towards the exit

– Evacuation Time


2) General Objectives

• To develop an analytical methodology which could provide an optimised analysis of designs in terms of fire safety of the occupants;

•To simulate evacuation processes, analysing some important relations, such as: building-people, peoplepeople, building-fire. Author: RODRIGO MACHADO TAVARES

2) General Objectives

• A) To develop an analytical methodology which could provide an optimised analysis of designs in terms of fire safety of the occupants;

• B) To investigate the manner in which the core variables interact to control evacuation efficiency.


3) The Problem •In addition to investigating the use of optimisation theory for evacuation applications, we are also interested in investigating the manner in which the core variables interact to control evacuation efficiency. •There is no clear guidance regarding for example: • where to place a door in order to produce minimum evacuation times? • is it better to have two doors of X m or one door of 2X m? • if we have two doors, what is the optimal relative positioning of these doors?

•Our project is concerned with: • investigating these fundamental questions, and • developing an optimisation methodology for use with Fire Safety Engineering applications.


3) The problem Evacuation Time (dependent variable/response) = objective function Independent variables (design variables/factors): - Exit Width (EW); - Exit Location (EL); - Number of Exits (NE); - Relative distance between the exits (RDBE); - Number of People (NP); - Response Time (RT); - Shape of the room (SR); - Type of Fire (TF); - Location of the Fire (LF); . . . - etc. Evacuation‫‏‬Time‫‏=‏‬f‫(‏‬EW,‫‏‬EL,‫‏‬NE,‫‏‬NP,‫‏‬SR,‫‏‬RT,‫‏‬TF,‫‏‬LF…)‫‏‬


3) The problem Maximize (or minimize):

OBJ (X ,Y ,Z ... n )

g j ( X)  0 Subject to:

hk (X)  0

( j 1, m) (k 1, L)

X L  X  XU OBJ(X )

Objective function (ET)‫‏‬

gj (X) 0

Equality constraints

hk (X)  0

In-equality constraints

m L X L XU

Number of equality constraints Number of in-equality constraints Lower and Upper bounds of the design variables


4) Methodology


5.1) The Thesis – Discussion

1) 2) 3) 4) 5)

This Ph.D. thesis is divided into 12 chapters: Introduction; Overview of Evacuation Modelling; Mathematical and Statistical Review; The Problem: The Evacuation Process as a Multi-variable Optimisation Problem; Identifying Optimal Solutions to Unconstrained and Constrained Problems Through “Brute Force Method”; Author: RODRIGO MACHADO TAVARES

5.1) The Thesis – Discussion 6) Identifying Optimal Solutions to Unconstrained and Constrained Problems Using Numerical Optimisation Techniques; 7) More Complex Geometries: Case Study 1 – “LShaped Room”; 8) More Complex Geometries: Case Study 2 Multiple Connected Compartments;


5.1) The Thesis – Discussion 9) More Complex Geometries: Case Study 3 – Multiple Exits of Varying Sizes; 10) Proposal of a Generic Method for picking up Design Points for Constrained Problems; 11) Guidelines and Recommendations on the Use of Numerical Optimisation Techniques for Evacuation Modelling Analyses; 12) Conclusion. Author: RODRIGO MACHADO TAVARES

5.1) The Thesis – Discussion Chapter 2) Overview of Evacuation Modelling 4 Journal Papers + 1 Book Chapter + 1 Magazine Article + 1 Project + 1 Company Report + some paragraphs in the PAS 911 (published by BSI) -Tavares, R.M. and Galea, E.R., Collection and Analysis of Pre-Evacuation Time Data Collected from Evacuation Trials Conducted in Library Facilities in Brazil , Journal of Applied Fire Science, Volume 15, Issue 1, p.23-40, (2006); - Tavares, R.M., Prescriptive codes vs. performance-based codes: which one is the best fire safety code for the Brazilian context?, Safety Science Monitor, Volume 12, Issue 1, (2008); Author: RODRIGO MACHADO TAVARES

5.1) The Thesis – Discussion Chapter 2) Overview of Evacuation Modelling -Tavares, R.M, An Analysis of the Fire Safety Codes in Brazil: Is the Performance-Based Approach the Best Practice?, Fire Safety Journal, 07/2009, Volume 44, Issue 5, p.749-755 , (2009); -Tavares, R.M, Evacuation Processes Versus Evacuation Models: “Quo Vadimus”?, Fire Technology, 12/2009, Volume 45, Issue 4, p.419-430, (2009);


5.1) The Thesis – Discussion Chapter 4) The Problem: The Evacuation Process as a Multi-variable Optimisation Problem 2 Journal Papers + 1 Conference Paper + 1 whole Chapter in the new CIBSE Guide E: Fire Engineering -Tavares, R.M., Tavares, J.M.L. and Parry-Jones, S.L., The use of a mathematical multicriteria decision-making model for selecting the fire origin room, Building and Environment, 12/2008, Volume 43, Issue 12, p.2090-2100, (2008); -Tavares, R.M. and Galea, E.R., Evacuation Modeling Analysis within the Operational Research Context: a Combined Approach for Improving Enclosure Designs, Building and Environment, 05/2009, Volume 44, Issue 5, p.1005-1016, (2009); Author: RODRIGO MACHADO TAVARES

5.1) The Thesis – Discussion Chapter 4) The Problem: The Evacuation Process as a Multi-variable Optimisation Problem -Tavares, R.M. and Galea, E.R., Numerical Optimisation Techniques Applied to Evacuation Analysis, PED 2008 4th International Conference on Pedestrian Dynamics, Wuppertal, Germany , p.555-561, (2008).




Author: Author:RODRIGO RODRIGOMACHADO MACHADOTAVARES TAVARES


5.1) The Thesis – Discussion Chapter 5) Identifying Optimal Solutions to Unconstrained and Constrained Problems Through “Brute Force Method”;



5.1) The Thesis – Discussion Chapter 5)

evacuation times (sec)

Evacuation Time X Exit locations (1 door - 1.0m) 168 167.5 167 166.5

Evacuation Time (sec)

166 165.5 165 0

2

4

6

8

exit locations

Curve Evacuation Time X Exit Location for the squared room with one exit of 1.00m


5.1) The Thesis – Discussion Chapter 5) Normalized Curves Evacuation Time X Exit Locations for all the squared rooms with one exit Normalized Evacuation Times

1.014 1.012 1.01 1.008

EW = 1.0m

1.006

EW = 1.5m EW = 2.0m

1.004

EW = 2.5m

1.002 1 0.998 Exit Locations

Normalized Curve Evacuation Time X Exit Locations for all the squared rooms with one exit







AA~ ET

AA  C  FR  ET  Author: RODRIGO MACHADO TAVARES

Flow Rates X Scenarios (the use of barries in barriers the exits) Evacuation Time X Scenarios (the use of in the exit)

(sec) Times(p/s) Evacuation Flow Rates

2.37

0.5m barrier

2.0m barrier 172.5 no barrier 2.36 172 1.0m barrier 2.35 171.5 Average 2.34 171 Evacuation Time Average Flow 2.33 170.5 Scenario (sec)‫‏‬ Average Flow Rate Rate (p/s)‫‏‬ Average Evacuation (p/s) 2.32 170 Time (sec) 0.5m 2.0m barrier 169.5 2.31 barrier 167.9 2.36 169 2.3 1.0m 168.5 1.0m barrier 2.29 barrier 168 2.36 no barrier 168 0.5m barrier 2.28 2.0m 167.5

barrier

no barrier

169.8 Scenarios Scenarios 172

2.36

2.29



Normalized Evacuation Times

Normalized Curves Evacuation Time X Exit Positions for all the squared rooms with two exits 1.18 1.16 1.14 1.12 1.1 1.08 1.06 1.04 1.02 1 0.98

EW EW EW EW

= = = =

1.0m 1.5m 2.0m 2.5m

Exit Positions

Normalized Curve Evacuation Time X Exit Positions for all the squared room with two exits cases



5.1) The Thesis – Discussion Chapter 5) Evacuation Times X Exit Configurations (two doors of 1.5m)

Evacuation Times (sec)

66

8

65 64 63

2

Symmetrical

5

62

Asymmetrical

61 6

59 58 57

Adjacent

4

60 3

7

9

11

12

10

1 Exit Configurations

Curve Evacuation Time X Symmetry (of the exit positions in relation with the room lay-out) – two doors 1.5m cases


5.1) The Thesis – Discussion parei aqui Chapter 6) Identifying Optimal Solutions to Unconstrained and Constrained Problems Using Numerical Optimisation Techniques Using all the design points (4 x 13 = 52 design points)‫‏‬ Optimum Solution (3 - 4; 2.5; 36.9)‫‏‬

Response Surface Model Polynomial of higher order (R2 = 0.98)‫‏‬ Response Surface Regression (R2 = 0.99)‫‏‬

Numerical Optimisation Technique Fletcher-Reeves

PSO – Particle Swarm Optimisation

(6; 2.5; 37.3)‫‏‬

(3.8; 2.5; 35.6)‫‏‬

(3.5; 2.5; 36.6)‫‏‬

(3.5; 2.5; 36.6)‫‏‬

Using DoE techniques to pick up the design points Optimum = (3 - 4; 2.5; 36.9)‫‏‬ Response Surface Model Full-quadratic (R2 = 0.99)

Numerical Optimisation Technique

DoE Technique

Fletcher-Reeves


CCD – 9 points

(4.4; 2.5; 38.64)

(4.2; 2.5; 37.76)

5.2) Application of the methodology A) First study case – L shaped room (case 2 – populated by 116 people)‫‏‬

Z  f (X;Y) ET f (EL1; EL2) 0 EL1 48 48 EL20

108m2

Area = ρ‫‏=‏‬1.07‫‏‬p/m2

DoE technique used: CCD (Central Composite Design)‫‏‬ Numerical Optimisation Techniques used: Fletcher-Reeves and PSO

5.2) Application of the methodology Z=51.566+0.091X-0.46Y-0.003X2+0.001XY-0.009Y2 (where: ET=Z; EL1=X; EL2=Y)‫‏‬


5.2) Application of the methodology Numerical Optimisation Technique Fletcher-Reeves


(0; - 42.0 ; 52.96)‫‏‬

(48.0 ; - 48.0; 48.056)‫‏‬


6) Conclusions and further work - An understanding of the optimal positioning of exits within arbitrarily simple enclosures was developed; - Some hypothesis regarding to the interaction between the design variables were also established; - The response surfaces generated by the design points present highly non-linear behaviour and polynomial higher order approximations proved to model them satisfactorily; - The numerical optimisation techniques (i.e., Fletcher-Reeves and PSO methods) achieved the best results (i.e., the global minima region and/or the closest to this region, avoiding the local minima region); - The CCD DoE technique seem to be suitable for most of this study.


6) Conclusions and further work

T1

ETT1 T2

– (Time spent during the movement): is influenced, mainly, by: the lay-out of the enclosure, the travel distance, the number of the people (ρ- population density) and the enclosure features. – (Time spent towards the exit): is 2 influenced, mainly, by: the exit location, exit width, the number of people (ρpopulation density).

T










Summary – aircraft geometry Scenarios

TET (sec)‫‏‬

Flow Rate (door 1)‫‏‬ p/min



Flow Flow Flow Rate Rate Rate (door 4)‫( ‏‬door 5)‫( ‏‬door 6)‫‏‬ p/min p/min p/min

Scenario 1

74.25

43.25

71.00

31.65

42.58

26.39

31.71

Best Scenario

44.75

39.21

43.25

34.39

38.50

43.04

42.25


6) Conclusions and further work -To incorporate non-physical variables in future studies; -To continue the application of this methodology to more complex structures (i.e., a whole multi-storey building);

- To perform real scale experiments and/or small scale experiments in order‫‏‬to‫‏‬observe‫‏‬the‫‏‬interaction‫‏‬between‫‏‬the‫“‏‬occupants”‫‏‬and‫‏‬the‫‏‬ enclosure and how this affect the flow dynamics and the whole evacuation efficiency; - Given the features of evacuation processes in enclosures (i.e., highnon linear behaviour; dynamic; continuum; non-periodic; dependent to the initial conditions), to study the crowd dynamics in assemblies under the Chaos Theory perspective.


Thank you very much! Muito Obrigado!


The use of Numerical Optimisation Techniques in Computational ...

The use of Numerical Optimisation Techniques in Computational ...

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