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Computational and Applied Mathematics

, Volume 37, Supplement 1, pp 220–236 | Cite as

Sequential state inference of engineering systems through the particle move-reweighting algorithm

  • R. MarquesEmail author
  • W. da Silva
  • R. Hoffmann
  • J. Dutra
  • F. Coral
Article
  • 62 Downloads

Abstract

Intractable sequential inference arises in several applications in the physical engineering process. One of the most successful and efficient stochastic simulation techniques that is appropriate to perform the Bayesian inference (inversion decision) in complex dynamic models is the sequential Monte Carlo (SMC) methods. Although, these methods have become widely accepted among researchers and practitioners, in practice the manifestation of the path degeneracy implies a poor approximation of the target measures. This is an unavoidable deep problem when approximating sequence target models, and it becomes evident when strong non-linearity is presented. To deal with this drawback of the SMC methods, a promise mechanism is used to create particle diversity to move the particle according some kernel perturbation. In this article, we apply in three non-linear engineering dynamical systems (reservoir dynamics, van de Vusse reaction and pipe-in-pipe), a class of move algorithms, without the need to change the computational complexity called the move-regweighting scheme proposed by Marques and Storvik [(Particle move-reweighting strategies for online inference. Preprint series. Statistical Research Report (1), 2013]. Numerical simulations with different number of particles are performed to demonstrate the accuracy of the algorithm.

Keywords

Bayesian inference Engineering system Particle move-regweighting filter Sequential Monte Carlo methods State space models 

Mathematics Subject Classification

60J05 60J22 62F15 65C05 65C60 

Notes

Acknowledgements

We gratefully acknowledge financial support from CAPES-Brazil and Statistics for Innovation Center.

References

  1. An C, Su J (2015) Lumped models for transient thermal analysis of multilayered composite pipeline with active heating. Appl Therm Eng 87:749–759CrossRefGoogle Scholar
  2. Andrieu C, de Freitas JFG, Doucet A (1999) Sequential Bayesian estimation and model selection applied to neural networks. Technical Report CUED/F-INFENG/TR 341, Cambridge University Engineering DepartmentGoogle Scholar
  3. Andrieu C, Doucet A, Holenstein R (2010) Particle Markov chain Monte Carlo methods. J R Stat Soc Ser B (Stat Methodology) 72(3):269–342MathSciNetCrossRefGoogle Scholar
  4. Arulampalam MS, Maskell S, Gordon N, Clapp T (2002) A tutorial on particle filters for online nonlinear/non-gaussian bayesian tracking. IEEE Trans Signal process 50(2):174–188CrossRefGoogle Scholar
  5. Berzuini C, Gilks W (2003) Particle filtering methods for dynamic and static Bayesian problems. In: Green PJ, Hjort N L, Richardson S(eds) Models and inference in HSSS: recent developments and perspectives. Oxford University Press, pp 207–227Google Scholar
  6. Buckley SE, Leverett M et al (1942) Mechanism of fluid displacement in sands. Trans AIME 146(01):107–116CrossRefGoogle Scholar
  7. Candy J (2009) Bayesian signal processing: classical, modern, and particle filtering methods, vol 54. Wiley-Interscience, HobokenCrossRefGoogle Scholar
  8. Cappé O, Godsill S, Moulines E (2007) An overview of existing methods and recent advances in sequential Monte Carlo. Proc IEEE 95(5):899–924CrossRefGoogle Scholar
  9. Cappé O, Moulines E, Rydén T (2005) Inference in hidden Markov models. Springer, BerlinzbMATHGoogle Scholar
  10. Chen H, Kremling A, Allgöwer F (1995) Nonlinear predictive control of a benchmark CSTR. In: Proceedings of 3rd European control conference, pp 3247–3252Google Scholar
  11. Chopin N (2002) A sequential particle filter method for static models. Biometrika 89(3):539–552MathSciNetCrossRefGoogle Scholar
  12. Chopin N (2004) Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. Ann Stat 32(6):2385–2411MathSciNetCrossRefGoogle Scholar
  13. Chopin N, Jacob PE, Papaspiliopoulos O (2013) Smc\(^{2}\): an efficient algorithm for sequential analysis of state space models. J R Stat Soc Ser B (Stat Methodol) 75(3):397–426MathSciNetCrossRefGoogle Scholar
  14. Colaco MJ, Orlande HR, da Silva WB, Dulikravich GS (2011) Application of a bayesian filter to estimate unknown heat fluxes in a natural convection problem. In: ASME 2011 international design engineering technical conferences and computers and information in engineering conference, pp 425–434. American Society of Mechanical EngineersGoogle Scholar
  15. da Silva W, Orlande H, Colaço M, Fudym O (2011) Application of bayesian filters to a one-dimensional solidification problem. In: Proceedings of 21st Brazilian congress of mechanical engineering, pp 24–28Google Scholar
  16. Dahlin J, Lindsten F, Schön TB (2013) Particle metropolis Hastings using Langevin dynamics. In: Acoustics, speech and signal processing (ICASSP), 2013 IEEE international conference on. pp 6308–6312. IEEEGoogle Scholar
  17. Del Moral P (2004) Feynman–Kac formulae, genealogical and interacting particle systems with applications. Springer-Verlag, New YorkCrossRefGoogle Scholar
  18. Del Moral P, Doucet A, Jasra A (2006) Sequential Monte Carlo samplers. J R Stat Soc Ser B (Stat Methodol) 68(3):411–436MathSciNetCrossRefGoogle Scholar
  19. Douc R, Cappé O (2005) Comparison of resampling schemes for particle filtering. In: Image and signal processing and analysis, 2005. ISPA 2005. Proceedings of the 4th international symposium on. pp 64–69. IEEEGoogle Scholar
  20. Douc R, Moulines E, Stoffer D (2014) Nonlinear time series: theory, methods and applications with R examples. CRC Press, Boca RatonCrossRefGoogle Scholar
  21. Doucet A, de Freitas N, Gordon N (2001) Sequential Monte Carlo methods. Springer, BerlinCrossRefGoogle Scholar
  22. Doucet A, Godsill S, Andrieu C (2000) On sequential Monte Carlo sampling methods for Bayesian filtering. Stat Comput 10(3):197–208CrossRefGoogle Scholar
  23. Doucet A, Johansen AM (2009) A tutorial on particle filtering and smoothing: fifteen years later. In: Crisan D, Rozovskii B (eds) The Oxford handbook of nonlinear filtering, vol 12. pp 656–704, Oxford University PressGoogle Scholar
  24. Engell S, Klatt K-U (1993) Nonlinear control of a non-minimum-phase CSTR. In: American control conference, 1993, pp 2941–2945. IEEEGoogle Scholar
  25. Fearnhead P (2008) Computational methods for complex stochastic systems: a review of some alternatives to MCMC. Stat Comput 18:151–171MathSciNetCrossRefGoogle Scholar
  26. Freitas A, Gaspari E, Vitullo L, Carvalho et al P (2005) Formation and removal of a hydrate plug formed in the annulus between coiled tubing and drill string. In: Offshore technology conferenceGoogle Scholar
  27. Gilks W, Berzuini C (2001) Following a moving target Monte Carlo inference for dynamic Bayesian models. J R Stat Soc Ser B (Stat Methodol) 63(1):127–146MathSciNetCrossRefGoogle Scholar
  28. Gordon N, Salmond D, Smith A (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation. Radar Signal Process IEE Proc F 140(2):107–113CrossRefGoogle Scholar
  29. Green P, Hjort N, Richardson S (2003) Highly structured stochastic systems, vol 10. Oxford University Press, OxfordzbMATHGoogle Scholar
  30. Gustafsson F (2010) Particle filter theory and practice with positioning applications. IEEE Aerosp Electron Syst Mag 25(7):53–82CrossRefGoogle Scholar
  31. Hamilton FC, Colaço MJ, Carvalho RN, Leiroz AJ (2014) Heat transfer coefficient estimation of an internal combustion engine using particle filters. Inverse Probl Sci Eng 22(3):483–506CrossRefGoogle Scholar
  32. Hanea A, Gheorghe M (2011) Parameter estimation in a reservoir engineering application. Adv Saf Reliab Risk Manag ESREL 2011:19Google Scholar
  33. Kantas N, Doucet A, Singh S, Maciejowski J (2009) An overview of sequential Monte Carlo methods for parameter estimation in general state-space models. In: Proceedings of the IFAC symposium on system identification (SYSID)Google Scholar
  34. Kashou S, Subramanian S, Matthews P, Thummel L, Faucheaux E, Subik D, Qualls D, Akey R, Carter et al. J (2004) GOM export gas pipeline, hydrate plug detection and removal. In: Offshore Technology ConferenceGoogle Scholar
  35. Kevin M (2012) Machine learning: a probabilistic perspective. The MIT Press, CambridgezbMATHGoogle Scholar
  36. Kuntanapreeda S, Marusak PM (2012) Nonlinear extended output feedback control for cstrs with van de Vusse reaction. Comput Chem Eng 41:10–23CrossRefGoogle Scholar
  37. Lee A (2012) On the choice of MCMC kernels for approximate Bayesian computation with SMC samplers. In: Simulation conference (WSC), Proceedings of the 2012 winter, pp 1–12. IEEEGoogle Scholar
  38. LeVeque RJ (2002) Finite volume methods for hyperbolic problems, vol 31. Cambridge university Press, CambridgeCrossRefGoogle Scholar
  39. Liu JS (2001) Monte Carlo strategies in scientific computing. Springer, BerlinzbMATHGoogle Scholar
  40. Liu JS, Chen R (1995) Blind deconvolution via sequential imputations. J Am Stat Assoc 90(430):567–576MathSciNetCrossRefGoogle Scholar
  41. Luo X, Hoteit I, Duan L, Wang W (2011) Review of nonlinear Kalman, ensemble and particle filtering with application to the reservoir history matching problem. In: Nonlinear Estimation and Applications to Industrial Systems Control. Nova PublishersGoogle Scholar
  42. Marques R, Storvik G (2013) Particle move-reweighting strategies for online inference. Preprint series. Statistical Research Report (1)Google Scholar
  43. Okuma K, Taleghani, A, De Freitas N, Little JJ, Lowe DG (2004) A boosted particle filter: multitarget detection and tracking. In: European conference on computer vision, Springer. pp 28–39Google Scholar
  44. Pitt MK, Shephard N (1999) Filtering via simulation: auxiliary particle filters. J Am Stat Assoc 94(446):590–599MathSciNetCrossRefGoogle Scholar
  45. Prado R, West M (2010) Time series: modeling, computation, and inference. Chapman & Hall, Chapel HillCrossRefGoogle Scholar
  46. Prakash J, Patwardhan SC, Shah SL (2011) On the choice of importance distributions for unconstrained and constrained state estimation using particle filter. J Process Control 21(1):3–16CrossRefGoogle Scholar
  47. Septier F, Peters GW (2016) Langevin and Hamiltonian based sequential MCMC for efficient bayesian filtering in high-dimensional spaces. IEEE J Select Top Signal Process 10(2):312–327CrossRefGoogle Scholar
  48. Stone H et al (1970) Probability model for estimating three-phase relative permeability. J Petrol Technol 22(02):214–218CrossRefGoogle Scholar
  49. Storvik G (2011) On the flexibility of Metropolis–Hastings acceptance probabilities in auxiliary variable proposal generation. Scand J Stat 38(2):342–358MathSciNetCrossRefGoogle Scholar
  50. Van de Vusse J (1964) Plug-flow type reactor versus tank reactor. Chem Eng Sci 19(12):994–996CrossRefGoogle Scholar
  51. Vianna FL, Orlande HR, Dulikravich GS (2013) Pipeline heating method based on optimal control and state estimation. In: 20th International congress of mechanical engineering. COBEMGoogle Scholar
  52. Vo B-N., Singh S, Doucet A (2003) Sequential Monte Carlo implementation of the PHD filter for multi-target tracking. In: Proc. int conf. on information fusion, pp 792–799Google Scholar
  53. West M, Harrison J (1997) Bayesian forecasting and dynamic models. Springer series in statistics. Springer, BerlinGoogle Scholar
  54. Whiteley N, Johansen AM (2011) Auxiliary particle filtering: recent developments In: Barber D, Cemgil T, Chiappa S (eds) Bayesian time series models. Cambridge University Press. doi: 10.1017/CBO9780511984679.004

Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  • R. Marques
    • 1
    Email author
  • W. da Silva
    • 2
  • R. Hoffmann
    • 2
  • J. Dutra
    • 2
  • F. Coral
    • 3
  1. 1.University of Oslo and Statistics for Innovation CentreOsloNorway
  2. 2.Federal University of Espírito SantoVitoriaBrazil
  3. 3.Kongsberg Oil & Gas TechnologiesOsloNorway

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