Ce diaporama a bien été signalé.
Nous utilisons votre profil LinkedIn et vos données d’activité pour vous proposer des publicités personnalisées et pertinentes. Vous pouvez changer vos préférences de publicités à tout moment.

Bayesian Inference for front-tracking problems - 2013 IPDO conference

733 vues

Publié le

This talk demonstrates the capability of particle filters to combine measurements to model simulation in a stochastic framework, in order to formulate some feedback information on the wildfire behavior. This is illustrated based on a reduced-scale controlled grassland fire experiment.

Sampling Importance Re-sampling (SIR) and Auxiliary Sampling Importance Re-sampling (ASIR) filters were built on top of a level-set based front-tracking simulator in order to assimilate the time-evolving positions of the fire front and thereby correct the input environmental parameters of the fire spread model (i.e. vegetation properties, surface wind conditions).

Reference published in October 2014
➞ da Silva, W.B., Rochoux, M.C., Orlande, H., Colaço, M., Fudym, O., El Hafi, M., Cuenot, B., and Ricci, S. (2014) Application of particle filters to regional-scale wildfire spread, High Temperatures-High Pressures, International Journal of Thermophysical Properties Research, 43, 415-440.

Publié dans : Sciences
  • DOWNLOAD FULL eBOOK INTO AVAILABLE FORMAT ......................................................................................................................... ......................................................................................................................... 1.DOWNLOAD FULL. PDF eBook here { https://tinyurl.com/y3nhqquc } ......................................................................................................................... 1.DOWNLOAD FULL. EPUB eBook here { https://tinyurl.com/y3nhqquc } ......................................................................................................................... 1.DOWNLOAD FULL. doc eBook here { https://tinyurl.com/y3nhqquc } ......................................................................................................................... 1.DOWNLOAD FULL. PDF eBook here { https://tinyurl.com/y3nhqquc } ......................................................................................................................... 1.DOWNLOAD FULL. EPUB eBook here { https://tinyurl.com/y3nhqquc } ......................................................................................................................... 1.DOWNLOAD FULL. doc eBook here { https://tinyurl.com/y3nhqquc } ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... .............. Browse by Genre Available eBooks ......................................................................................................................... Art, Biography, Business, Chick Lit, Children's, Christian, Classics, Comics, Contemporary, CookeBOOK Crime, eeBOOK Fantasy, Fiction, Graphic Novels, Historical Fiction, History, Horror, Humor And Comedy, Manga, Memoir, Music, Mystery, Non Fiction, Paranormal, Philosophy, Poetry, Psychology, Religion, Romance, Science, Science Fiction, Self Help, Suspense, Spirituality, Sports, Thriller, Travel, Young Adult,
       Répondre 
    Voulez-vous vraiment ?  Oui  Non
    Votre message apparaîtra ici
  • Soyez le premier à aimer ceci

Bayesian Inference for front-tracking problems - 2013 IPDO conference

  1. 1. Applications of particle filters in moving frontier problems: Wildfire spread forecasting W. Da Silva, M. Rochoux, H. Orlande, M. Colaço, O. Fudym, M. El Hafi, B. Cuenot & S. Ricci ©  Pauline  Crombe/e  ©  Domingo  Viegas  
  2. 2. 2  INTRODUCTION     Wildfire  modeling  challenges   2     Uncertain)es  in  large-­‐scale  fire  spread  predic)ons  due  to   ➔  large  range  of  length  scales  (pyrolysis  vegetaFon  scales  to  plume  dynamic  scales)   ➔  unknown  boundary  and  iniFal  condiFons   • non-­‐homogeneous  and  poorly  defined  vegetal  fuels   • atmospheric  external  forcing   ➔  difficult  validaFon  (lab-­‐scale  and  field-­‐scale  experiments)   cm   m   km   • Cost-­‐effecFve     • Front-­‐tracking  simulator   • Empirical  model  of  the   fire  front  spread-­‐rate   OperaFonally-­‐oriented   front-­‐tracking  simulator     ©  ANR-­‐IDEA  
  3. 3. 3  INTRODUCTION     Regional-­‐scale  wildfire  spread  modeling   3     ➔  ParameterizaFon  of  the  rate  of  spread  (ROS)  as  a   funcFon  of  the  local  condiFons:   Weather   •  Wind  velocity  and  direcFon   •  Air  temperature  and  humidity   •  Rainfall   Terrain     •  Terrain  slope   Vegetal  fuel   •  Moisture  content   •  Depth  of  the  vegetal  layer   •  Packing  raFo   •  Fuel  parFcles  (density,  size,  …)   Front  topology   ©  Cheney     (CSIRO)   ➔  ISSUE  -­‐  Need  to  quanFfy  and   reduce  uncertainFes  in   • Model  formulaFon   • Input  model  parameters   • External  forcing   R   R(x, y, t) = f(uw, αsl, Mf , δf , βf , Σf ...) FOCUS   ©  ANR-­‐IDEA  
  4. 4. INTRODUCTION     Why  parFcle  filters  for  tracking  wildfire  spread?   4     ➔  In  principle,  parFcle  filters  can  handle  the  non-­‐lineariFes  present  in  a  physical  system              (in  a  more  formal  way  than  the  Kalman  filter  and  its  extensions).   • Time-­‐varying  wind   • Highly  heterogeneous  vegetal  fuel   properFes  that  change  over  Fme   Normalizing  constant   ©  M.  Finney  (2011)   Skewed  fire  size   distribuFon  
  5. 5. 5  OUTLINE   Wildfire  spread  forecasFng  using  parFcle  filters   5     ©  Horus  (SDIS  66)   ①   Regional-­‐scale  wildfire  spread  simulaFon  capability   ②   ParFcle  filter  algorithms   ③   ApplicaFon  to  a  controlled  burning  experiment  
  6. 6. Focus:  surface  fire  spread   ➔  Build  a  simplified  model  that  gives  the  Fme-­‐evoluFon  of   the  flame  front  locaFon   • Front-­‐tracking  strategy   • 2-­‐D  propagaFon  within  the  vegetal  fuel  bed  (li/er)   PART.  1          PART.  2        PART.  3   InformaFon  at  regional-­‐scales:  model   6     ➔  Level-­‐set-­‐based  front  propagaFon  solver     • 2-­‐D  variable:  reacFon  progress  variable  c   • Flame  front  marker:  isoline  c  =  0.5   ∂c ∂t = R|∇c| FIREFLY:   c  =  1   c  =  0   ➔  Issue:  How  to  accurately   describe  uncertainFes  in   input  parameters  of  the   rate  of  spread  R?  
  7. 7. PART.  1          PART.  2        PART.  3   InformaFon  at  regional-­‐scales:  data   7     ➔  GeolocaFon  of  acFve  fire  areas   • Middle  InfraRed  (MIR)  camera  aboard   • FRP  (Fire  RadiaFve  Power)  measurements   sensiFve  to  acFve  fire  areas   Airborne-­‐based  thermal  infrared  imaging     ➔  Requirements  for  inverse  problems   • High-­‐spaFal  resoluFon  imagery  (<  30  m)   • Short  revisit  period   X (m) Y(m) 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4 ©  Ronan  Paugam   (King’s  College)   Assume  iso-­‐  temperature   for  fire  igniFon  (600K)   Temperature  field  [K]   ReconstrucFon  of  fire  front  posiFon   ©  D.  Viegas  
  8. 8. PART.  1          PART.  2        PART.  3   Inverse  problem  strategy   8     Why?      1-­‐  Uncertainty  on  inputs                        Uncertainty  on  outputs                              2-­‐  Find  best  esFmate  of  control  variables  given  available  observaFons   ➔  Which  input  model  parameters              are  criFcal  to  control?   • SensiFvity  analysis  of  Rothermel  spread-­‐rate  model   • IllustraFon  of  the  non-­‐lineariFes  present  in  the   wildfire  spread  model     R(x, y, t) = f(uw, Mf , δf , βf , Σf , ...) Mf [!] ![m/s] 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 R [m/s] Mf [-] Wind-­‐aided  fire   spread  (1  m/s)   Short  grass   Long  grass   Timber  li/er   Control  parameters   Simulated  fronts  Firefly  simulator   ¤  level-­‐set  simulator     ¤   moisture  content  Mf ¤   fuel  parFcle  surface/volume  Σf ¤   wind  speed  uw
  9. 9. PART.  1          PART.  2        PART.  3               Inverse  problem  strategy   9     Why?      1-­‐  Uncertainty  on  inputs                        Uncertainty  on  outputs                              2-­‐  Find  best  esFmate  of  control  variables  given  available  observaFons.   ➔  How  to  compare  simulated  fire  front   posiFons  and  observaFons?   Discrete  Fme-­‐evolving   fire  front  posiFons   Uncertainty   range  for  each   front  posiFon   x   y   Fme   Control  parameters   Simulated  fronts  Firefly  simulator   ¤  level-­‐set  simulator     ¤   moisture  content  Mf ¤   fuel  parFcle  surface/volume  Σf ¤   wind  speed  uw ObservaFons    prior  distribuFon   likelihood  DistribuFons  for  modeling   and  observaFon  errors   ¤  selecFon  of  the  front  at   the  assimilaFon  Fme   xk zk hkObserva)on  model  
  10. 10. PART.  1          PART.  2        PART.  3                 Inverse  problem  strategy   10     Why?      1-­‐  Uncertainty  on  inputs                        Uncertainty  on  outputs                              2-­‐  Find  best  esFmate  of  control  variables  given  available  observaFons.   Control  parameters   Simulated  fronts  Firefly  simulator   ¤  level-­‐set  simulator     ¤   moisture  content  Mf ¤   fuel  parFcle  surface/volume  Σf ¤   wind  speed  uw ObservaFons    prior  distribuFon   Bayesian  filtering   Data-­‐driven  feedback   Simulated  front   Observed  front   (xf , yf )1 (xf , yf )p (xf , yf )j (xo f , yo f )j (xo f , yo f )1 (xo f , yo f )p Posterior   distance   Extended  state  es)ma)on  
  11. 11. PART.  1          PART.  2        PART.  3   Inverse  problem  strategy   11     ➔  Bayesian  filtering  in  2  steps:   • PredicFon  of  the  physical  model   • Update  of  the  control  parameters  based  on  Bayes’  theorem   πposterior(xk) = π(xk|zk) = πprior(xk)π(zk|xk) π(zk) Likelihood     (measurement  model   including  uncertainFes)   Normalizing  constant   πprior(xk) = π(xk|xk−1) ➔  ISSUE:  How  to  describe  the  prior  model?   • Is  represented  as  a  transiFon  probability  density  from  Fme  (k-­‐1)  to  Fme  k   • Includes  a  random  walk  model  for  the  parameter  evoluFon   ➔  SOLUTION:  ParFcle  filters  to  obtain  the  posterior   • Monte-­‐Carlo  technique:  representaFon  of  the  posterior  by   a  set  of  random  samples  (parFcles)  with  associated  weights  
  12. 12. reality       model  predicFon   diagnosis             measurements   analysis   PART.  1          PART.  2        PART.  3   Inverse  problem  strategy   12     ➔  Bayesian  filtering  in  2  steps:   • PredicFon  of  the  physical  model   • Update  of  the  control  parameters  based  on  Bayes’  theorem   πposterior(xk) = π(xk|zk) = πprior(xk)π(zk|xk) π(zk) Likelihood     (measurement  model   including  uncertainFes)   predicFon   update   predicFon   ➔  SequenFal  esFmaFon   Normalizing  constant  
  13. 13. PART.  1          PART.  2        PART.  3   Inverse  problem  strategy   13     ➔  Sampling  Importance  Resampling  (SIR)  algorithm     1   i   N  parFcles   • Ref.  RisFc  et  al.  (2004),  Beyond  the  Kalman  filter   1)  PredicFon   π(xk|xi k−1) 2)  Likelihood   4)  Resampling   (avoid  parFcles  with   negligible  weight)   3)  Update   π(xk|zk)(xi k, wi k) (xi∗ k , 1/N) • LimitaFon  in  the  parallelizaFon   • Loss  of  diversity  (sample  impoverishment)   ISSUES   wi k = π(zk|xi k)
  14. 14. PART.  1          PART.  2        PART.  3   Inverse  problem  strategy   14     ➔  New  algorithm:  Auxiliary  Sampling  Importance  Resampling  (ASIR)   1   i   N  parFcles   • Ref.  W.  Da  Silva  et  al.,  ApplicaFon  to  one-­‐dimensional  solidificaFon  problem,  COBEM  2011   • Key  idea:  improve  the  prior  informaFon  based  on  some  point  esFmate  μi k  using  an  auxiliary   set  of  parFcles   1)  PredicFon   π(xk|xi k−1) 2)  Likelihood   4)  Resampling   (avoid  parFcles  with   negligible  weight)   3)  Update   π(xk|zk)(xi k, wi k) wi k = π(zk|µi k) wi k−1 wi k = π(zk|xi k) (xi∗ k , wi∗ k ) • more  realisFc  parFcles   • less  sensiFve  to  outliers  than  SIR   ADDED-­‐VALUES  FOR  ASIR  
  15. 15. 15  PART.  1          PART.  2        PART.  3       ApplicaFon  to  controlled  burning  experiment   15     Environmental  condi)ons   ➔  Reduced-­‐scale  fire:  4m  x  4m   ➔  Homogeneous  short  grass  vegetaFon   •  Fuel  bed  depth:  8  cm   •  Moisture  content:  22%   ➔  Mean  rate  of  spread:  1-­‐2  cm/s  (max.  5  cm/s)   ➔  ObservaFon:       •  Error  due  to  the  resoluFon  of  the  MIR  camera   •  Error  esFmaFon:  5  cm  (1%  burning  area)     2min14s   3min10s  2min42s  1min28s   1min46s   !          Mean  wind     1  m/s,  307°     Time  series  of  surface  temperature  field  (Ronan  Paugam,  King’s  College  of  London)   Time  
  16. 16. 16  PART.  1          PART.  2        PART.  3       ApplicaFon  to  controlled  burning  experiment   16     3  control  parameters   ➔  Wind  magnitude  (fluctuaFons  between  0-­‐2  m/s)   ➔  Fuel  moisture  content  (22%)   ➔  Fuel  parFcle  surface/volume  (11500  m-­‐1)     2min14s   3min10s  2min42s  1min28s   1min46s   !          Mean  wind     1  m/s,  307°     Time  series  of  surface  temperature  field  (Ronan  Paugam,  King’s  College  of  London)   Time   R(x, y, t) = f(uw, Mf , δf , βf , Σf , ...)
  17. 17. PART.  1          PART.  2        PART.  3       ApplicaFon  to  controlled  burning  experiment   17     ➔  Sequen)al  es)ma)on:  5  successive  esFmaFons  of  the  control  parameters   SIR  algorithm  (N  =  200)   ASIR  algorithm  (N  =  50)   Results:   •  Consistent  results  of  the  SIR  and  ASIR  algorithms   •  Good  tracking  of  the  observed  fire  front.  
  18. 18. PART.  1          PART.  2        PART.  3       ApplicaFon  to  controlled  burning  experiment   18     ➔  Sequen)al  es)ma)on:  5  successive  esFmaFons  of  the  control  parameters   SIR  algorithm  (N  =  200)   ASIR  algorithm  (N  =  50)   Moisture   content   Fuel  parFcle   surface/ volume   99%  Confidence  interval   Mean  value   EKF  result  
  19. 19. PART.  1          PART.  2        PART.  3       ApplicaFon  to  controlled  burning  experiment   19     ➔  Sequen)al  es)ma)on:  5  successive  esFmaFons  of  the  control  parameters   Wind   magnitude   (m/s)   SIR  algorithm  (N  =  200)   ASIR  algorithm  (N  =  50)   Results:   •  Same  level  accuracy  reached  by  the  SIR  and  ASIR  algorithms   •  ValidaFon  against  independent  measurements  of  the  wind  velocity  magnitude,  even   though  the  wind  is  subject  to  significant  fluctuaFons   In-­‐situ   measurements  of   the  wind  magnitude   In-­‐situ   measurements  of   the  wind  magnitude  
  20. 20. CONCLUSIONS   ApplicaFons  of  parFcle  filters  to  moving  fronFer  problems       •   SIR  and  ASIR  par)cle  filters  able  to     ➔  achieve  mulF-­‐parameter  esFmaFon     ➔  reduce  fire  modeling  uncertainFes   ➔  track  fire  front  for  a  controlled  burning  experiment     •   Valida)on  of  the  ASIR  algorithm:  shown  to  be  less   computaFonally  expensive  than  the  SIR  algorithm  in  a  wide   range  of  experiments   [W.  Da  Silva  et  al.,  ApplicaFon  to  one-­‐dimensional  solidificaFon   problem,  COBEM  2011]  
  21. 21.     •   Comparison  to  Ensemble  Kalman  filter  algorithm  (CERFACS-­‐University  of   Maryland,  M.  Rochoux’s  PhD  thesis)     •     Applica)ons  of  ASIR  par)cle  filters  to  new  fields  of  applica)ons  (Wellington)   ➔  temperature  field  predicFon  of  a  mulF-­‐layer  composite  pipeline   ➔  reservoir  history  matching  problem   PERSPECTIVES   ApplicaFons  of  parFcle  filters  to  moving  fronFer  problems   Parameter  esFmaFon   • CorrecFon  on  the  model  physics  (dynamic  learning)     • Surrogate  model  of  the  fire  spread  simulator  to   limit  computaFonal  cost        [Rochoux  et  al.  (2012),  CTR  Summer  Program]   Polynomial  Chaos  
  22. 22. Thank  you  for  your  a/enFon!      
  23. 23. Acknowledgments       •   FAPERJ,  CAPES  and  CNPq,  Brazilian  agencies  and  French  Ministry  of  foreign  affairs.   •   Centre  NaFonal  pour  la  Recherche  ScienFfique  (CNRS).   •   Project  «11STIC06-­‐I3PE-­‐Inverse  Problems  in  Physical  Property  EsFmaFon».   •   Project  «IDEA  ANR-­‐09-­‐COSI-­‐006-­‐06,  Wilfires:  From  PropagaFon  to  Atmospheric   Emissions»   •   Dept.  of  Geography,  King’s  College  of  London  (MarFn  Wooster  and  Ronan  Paugam   for  the  data  of  the  controlled  burning  experiment).    

×