A Hybrid Estimation Scheme Based on the Sequential Importance Resampling Particle Filter and the Particle Swarm Optimization (PSO-SIR)
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.
- 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
- 5.Cotta, R.M., Milkhailov, M.D.: Heat Conduction: Lumped Analysis, Integral Transforms, Symbolic Computation. Wiley, Chichester (1997)Google Scholar
- 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
- 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.Kaipio, J., Somersalo, E.: Statistical and Computational Inverse Problems, Applied Mathematical Sciences. Springer, New York (2004)Google Scholar
- 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
- 15.Maybeck, P.: Stochastic Models, Estimation and Control. Academic, New York (1979)Google Scholar
- 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
- 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.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.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.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