A Hybrid Estimation Scheme Based on the Sequential Importance Resampling Particle Filter and the Particle Swarm Optimization (PSO-SIR)

  • Wellington Betencurte da Silva
  • Julio Cesar Sampaio Dutra
  • José Mir Justino da Costa
  • Luiz Alberto da Silva Abreu
  • Diego Campos Knupp
  • Antônio José Silva Neto


Particle filters are recursive Bayesian estimators, which are being applied to many areas of engineering in recent years to estimate states and parameters, regarding fire spread, tumors, oil pipelines, heat transfer, chemical reactors, etc. The key idea behind particle filters is that they use an initial distribution (sample), based on the previous state estimate, to calculate the best estimate for the current state, relying only on the current available measurements and the knowledge about the system. The greatest advantage of these methods is the easy computational implementation. However, setting the standard deviation for the initial distribution is very important for the success of the method. For this reason, standard formulation of these methods may not provide good results in problems with large discontinuities (or irregular/abrupt changes). For example, this would be the case of estimating step changes in the heat flux on a plate. Although several solutions have been proposed to improve the estimation performance, they still suffer from the curse of discontinuity. This occurs because particle filters proposed in the literature are not adaptive methods. In the example mentioned above, particle filters can have both a priori information and sample satisfactory before the change. However, after the change begins, the available information could be not enough to draw a suitable sample for the estimation. At this point, it is necessary to modify the standard deviation to broaden the particle search field or to move the a priori information to a new region where a new sample should be drawn. In this regard, the aim of this chapter is to propose a hybrid estimation scheme based on Particle Swarm Optimization (PSO) built into the particle filter Sampling Importance Resampling (SIR) to project the a priori information to a new search region, according to the current observation. To demonstrate the proposal, the problem of estimating step changes on the heat flux on a plate is taken into account, considering experimental measurements. The results allow to state that the scheme combining PSO and SIR provides good performance for this type of problem.



The authors acknowledge the financial support provided by FAPERJ–Fundação Carlos Chagas Filho de Amparo à Pesquissa do Estado do Rio de Janeiro, CNPq–Conselho Nacional de Desenvolvimento Científico e Tecnológico, and CAPES–Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, research supporting agencies from Brazil.


  1. 1.
    Cappé, O., Moulines, E., Rydén, T.: Inference in Hidden Markov Models. Springer, New York (2005)zbMATHGoogle Scholar
  2. 2.
    Cheng, W.C.: PSO algorithm particle filters for improving the performance of lane detection and tracking systems in difficult roads. Sensors 12, 17168–17185 (2012)CrossRefGoogle Scholar
  3. 3.
    Colaço, M.J., Dulikravich, G.S.: A survey of basic deterministic, heuristic, and hybrid methods for single-objective optimization and response surface generation. In: Orlande, H.R.B., Fudym, O., Maillet, D., Cotta, R.M. (eds.) Thermal Measurements and Inverse Techniques, vol. 1, pp. 355–405. CRC Press, Boca Raton (2011)Google Scholar
  4. 4.
    Costa, J.M.J., Orlande, H.R.B., Campos Velho, H.F., Pinho, S.T.R., Dulikravich, G.S., Cotta, R.M., Cunha Neto, S.H.: Estimation of tumor size evolution using particle filters. J. Comput. Biol. 22(7), 1–17 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Cotta, R.M., Milkhailov, M.D.: Heat Conduction: Lumped Analysis, Integral Transforms, Symbolic Computation. Wiley, Chichester (1997)Google Scholar
  6. 6.
    Demuner, L.R., Rangel, F.D., Dutra, J.C.S., Silva, W.B.: Particle filter application for estimation of valve behavior in fault condition. J. Chem. Eng. Chem. 1, 73–87 (2015) (in Portuguese)CrossRefGoogle Scholar
  7. 7.
    Dias, C.S.R., Demuner, L.R., Rangel, F.D., Dutra, J.C.S., Silva, W.B.: Online state estimation through particle filter for feedback temperature control. In: XXI Brazilian Congress of Chemical Engineering, Fortaleza (2016)Google Scholar
  8. 8.
    Doucet, A., Freitas, N., Gordon, N.: Sequential Monte Carlo Methods in Practice. Springer, New York (2001)CrossRefGoogle Scholar
  9. 9.
    Gordon, N., Salmond, D., Smith, A.F.M.: Novel approach to nonlinear and non-Gaussian Bayesian state estimation. Proc. Inst. Elect. Eng. 140, 107–113 (1993)Google Scholar
  10. 10.
    Kaipio, J., Somersalo, E.: Statistical and Computational Inverse Problems, Applied Mathematical Sciences. Springer, New York (2004)Google Scholar
  11. 11.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of the 1995 IEEE International Conference on Neural Networks vol. 4, pp. 1942–1948 (1995)Google Scholar
  12. 12.
    Knupp, D.C., Naveira-Cotta, C.P., Ayres, J.V.C., Orlande, H.R.B., Cotta, R.M.: Space-variable thermophysical properties identification in nanocomposites via integral transforms, Bayesian inference and infrared thermography. Inverse Probl. Sci. Eng. 20(5), 609–637 (2012)CrossRefGoogle Scholar
  13. 13.
    Li, T., Sun, S., Sattar, T.P., Corchado, J.M.: Fight sample degeneracy and impoverishment in particle filters: a review of intelligent approaches. Expert Syst. Appl. 41, 3944–3954 (2014)CrossRefGoogle Scholar
  14. 14.
    MacKay, D.J.C.: A practical Bayesian framework for back-propagation networks. Neural Comput. 4, 448–472 (1992)CrossRefGoogle Scholar
  15. 15.
    Maybeck, P.: Stochastic Models, Estimation and Control. Academic, New York (1979)Google Scholar
  16. 16.
    Orlande, H.R.B., Colaço, M.J., Dulikravich, G.S., Vianna, F.L.V., Silva, W.B., Fonseca, H.M., Fudym, O.: Kalman and particle filters. In: METTI5 Advanced Spring School: Thermal Measurements & Inverse Techniques (2011)Google Scholar
  17. 17.
    Orlande, H.R.B., Colaço, M.J., Dulikravich, G.S., Vianna, F., Silva, W.B., Fonseca, H., Fudym, O.: State estimation problems in heat transfer. Int. J. Uncertain. Quantif. 2(3), 239–258 (2012)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Orlande, H.R.B., Dulikravich, G.S., Neumayer, M., Watzenig, D., Colaço, M.J.: Accelerated Bayesian inference for the estimation of spatially varying heat flux in a heat conduction problem. Numer. Heat Transf. A Appl. 65(1), 1–25 (2014)CrossRefGoogle Scholar
  19. 19.
    Pacheco, C.C., Orlande, H.R.B., Colaço, M.J., Dulikravich, G.S.: Estimation of a location-and time-dependent high-magnitude heat flux in a heat conduction problem using the Kalman filter and the approximation error model. Numer. Heat Transf. A Appl. 68(11), 1198–1219 (2015)CrossRefGoogle Scholar
  20. 20.
    Petris, G., Petrone, S., Campagnoli, P.: Dynamic Linear Models with R. Springer, New York (2009)CrossRefGoogle Scholar
  21. 21.
    Ristic, B., Arulampalam, S., Gordon, N.: Beyond the Kalman Filter. Artech House, Boston (2004)zbMATHGoogle Scholar
  22. 22.
    Silva, W.B., Orlande, H.R.B., Colaço, M.J.: Evaluation of Bayesian filters applied to heat conduction problems. In: 2nd International Conference on Engineering Optimization, Lisboa (2010)Google Scholar
  23. 23.
    Silva, W.B., Orlande, H.R.B., Colaço, M.J., Fudym, O.: Application of Bayesian filters to a one-dimensional solidification problem. In: 21st Brazilian Congress of Mechanical Engineering, Natal (2011)Google Scholar
  24. 24.
    Silva, W.B., Rochoux, M., Orlande, H.R.B., Colaço, M.J., Fudym, O., El Hafi, M., Cuenot B., Ricci, S.: Application of particle filters to regional-scale wildfire spread. High Temp. High Pressures 43, 415–440 (2014)Google Scholar
  25. 25.
    Silva, W.B., Dutra, J.C.S., Abreu, L.A.S., Knupp, D.C., Silva Neto, A.J.: Estimation of timewise varying boundary heat flux via Bayesian filters and Markov Chain Monte Carlo method. In: II Simposio de Modelación Matemática Aplicada a la Ingeniería, Havana (2016)Google Scholar
  26. 26.
    Wang, J., Zabaras, N.: A Bayesian inference approach to the inverse heat conduction problem. Int. J. Heat Mass Transf. 47(17), 3927–3941 (2004)CrossRefGoogle Scholar
  27. 27.
    Zhao, J., Li, Z.: Particle filter based on particle swarm optimization resampling for vision tracking. Expert Syst. Appl. 37, 8910–8914 (2010)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Wellington Betencurte da Silva
    • 1
  • Julio Cesar Sampaio Dutra
    • 1
  • José Mir Justino da Costa
    • 2
  • Luiz Alberto da Silva Abreu
    • 3
  • Diego Campos Knupp
    • 3
  • Antônio José Silva Neto
    • 3
  1. 1.Chemical Engineering Program, Center of Agrarian Sciences and EngineeringFederal University of Espírito SantoAlegreBrazil
  2. 2.Statistics DepartmentFederal University of AmazonasManausBrazil
  3. 3.Department of Mechanical Engineering and EnergyPolytechnic Institute, IPRJ-UERJNova FriburgoBrazil

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