Dynamic inversion in electrical capacitance tomography using the ensemble Kalman filter

IET Science, Measurement and Technology

Volumn 6, Issue 2, 2012, Pages 63-77

  Lei, J ^a   Liu, S ^a   Wang, X Y ^b  

^a NORTH CHINA ELECTRIC POWER UNIVERSITY   (China)

^b INSTITUTE OF ENGINEERING THERMOPHYSICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMIC INVERSION; DYNAMIC RECONSTRUCTION MODELS; DYNAMICS EQUATION; EFFICIENT ALGORITHM; ELECTRICAL CAPACITANCE TOMOGRAPHY; ENSEMBLE KALMAN FILTER; FILLED FUNCTION METHOD; GLOBAL OPTIMAL SOLUTIONS; HOMOTOPY METHOD; IMAGE RECONSTRUCTION ALGORITHM; M-ESTIMATION; MEASUREMENT INFORMATION; PROCESS TOMOGRAPHY; RECONSTRUCTED IMAGE; SPATIAL RESOLUTION;

ELECTRIC IMPEDANCE TOMOGRAPHY; IMAGE RECONSTRUCTION; INVERSE PROBLEMS; KALMAN FILTERS;

ALGORITHMS;

EID: 84863253029     PISSN: 17518822     EISSN: None     Source Type: Journal    
DOI: 10.1049/iet-smt.2011.0193     Document Type: Article

References (69)

1. Yang, W.Q., and Liu, S.: 'Role of tomography in gas/solids flow measurement', Flow Meas. Instrum., 2000, 11, p. 237-24410.1016/S0955-5986(00)00023-6 0955-5986
2. Bennett, M.A., West, R.M., Luke, S.P., and Williams, R.A.: 'The investigation of bubble column and foam processes using electrical capacitance tomography', Miner. Eng., 2002, 15, p. 225-23410.1016/S0892-6875(02)00005-5
3. Zhu, K., Madhusudana, R., Wang, C.H., and Sundaresan, S.: 'Electrical capacitance tomography measurements on vertical and inclined pneumatic conveying of granular solids', Chem. Eng. Sci., 2003, 58, p. 4225-424510.1016/S0009-2509(03)00306-3 0009-2509
4. Liu, S., Chen, Q., Wang, H.G., Jiang, F., Ismail, I., and Yang, W.Q.: 'Electrical capacitance tomography for gas-solids flow measurement for circulating fluidized beds', Flow Meas. Instrum., 2005, 16, p. 135-14410.1016/j.flowmeasinst.2005.02.013 0955-5986
5. Wiens, J., and Pugsley, T.: 'Tomographic imaging of a conical fluidized bed of dry pharmaceutical granule', Powder Technol., 2006, 169, p. 49-5910.1016/j.powtec.2006.07.022 0032-5910
6. Du, B., Warsito, W., and Fan, L.S.: 'Imaging the choking transition in gas-solid risers using electrical capacitance tomography', Ind. Eng. Chem. Res., 2006, 45, p. 5384-539510.1021/ie051401w 0888-5885
7. Liu, S., Chen, Q., Xiong, X., Zhang, Z., and Lei, J.: 'Preliminary study on ECT imaging of flames in porous media', Meas. Sci. Technol., 2008, 19, p. 1-710.1088/0957-0233/19/9/094017 0957-0233
8. Meng, S., Liu, S., Lei, J., and Li, Z.H.: 'Concentration and angular velocity measurement in a cyclone separator dipleg using electrical capacitance tomography', Chin. Sci. Bull., 2008, 53, p. 2724-272810.1007/s11434-008-0164-1 1001-6538
9. Wang, H.G., and Yang, W.Q.: 'Measurement of fluidised bed dryer by different frequency and different normalisation methods with electrical capacitance tomography', Powder Technol., 2010, 199, p. 60-6910.1016/j.powtec.2009.04.019 0032-5910
10. Zhao, T., Takei, M., and Doh, D.H.: 'ECT measurement and CFD-DEM simulation of particle distribution in a down-flow fluidized bed', Flow Meas. Instrum., 2010, 21, p. 212-21810.1016/j.flowmeasinst.2009.12.008 0955-5986
11. Xie, C.G., Huang, S.M., and Hoyle, B.S.: et al. 'Electrical capacitance for flow imaging: system model for development of image reconstruction algorithms and design of primary sensors', IEE Proc. G, 1992, 139, p. 89-9810.1049/ip-g-2.1992.0015
12. Tikhonov, A.N., and Arsenin, V.Y.: 'Solution of Ill-posed problems', (V.H. Winston & Sons, New York 1977)
13. Landweber, L.: 'An iteration formula for fredholm integral equations of the first kind', Am. J. Math., 1951, 73, p. 615-62410.2307/2372313
14. Yang, W.Q., Spink, D.M., York, T.A., and McCann, H.: 'An image reconstruction algorithm based on Landweber's iteration method for electrical capacitance tomography', Meas. Sci. Technol., 1999, 10, p. 1065-106910.1088/0957-0233/10/11/315 0957-0233
15. Yang, W.Q., and Peng, L.H.: 'Image reconstruction algorithms for electrical capacitance tomography', Meas. Sci. Technol., 2003, 14, p. L1-L1310.1088/0957-0233/14/1/201 0957-0233
16. Jang, J.D., Lee, S.H., Kim, K.Y., and Choi, B.Y.: 'Modified iterative Landweber method in electrical capacitance tomography', Meas. Sci. Technol., 2006, 17, p. 1909-191710.1088/0957-0233/17/7/032 0957-0233
17. Warsito, W., and Fan, L.S.: 'Neural network based multi-criterion optimization image reconstruction technique for imaging two and three-phase flow systems using electrical capacitance tomography', Meas. Sci. Technol., 2001, 12, p. 2198-221010.1088/0957-0233/12/12/323 0957-0233
18. Liu, S., Fu, L., Yang, W.Q., Wang, H.G., and Jiang, F.: 'Prior-online iteration for image reconstruction with electrical capacitance tomography', IEE Proc. Sci. Meas. Technol., 2004, 151, p. 195-20010.1049/ip-smt:20040246 1350-2344
19. Ortiz-Aleman, C., Martin, R., and Gamio, J.C.: 'Reconstruction of permittivity images from capacitance tomography data by using very fast simulated annealing', Meas. Sci. Technol., 2004, 15, p. 1382-139010.1088/0957-0233/15/7/022 0957-0233
20. Fang, W.F.: 'A nonlinear image reconstruction algorithm for electrical capacitance tomography', Meas. Sci. Technol., 2004, 15, p. 2124-213210.1088/0957-0233/15/10/023 0957-0233
21. Soleimani, M., and Lionheart, W.R.B.: 'Nonlinear image reconstruction for electrical capacitance tomography using experimental data', Meas. Sci. Technol., 2005, 16, p. 1987-199610.1088/0957-0233/16/10/014 0957-0233
22. Marashdeh, Q., Warsito, W., Fan, L.S., and Teixeira, F.L.: 'Non-linear image reconstruction technique for ECT using a combined neural network approach', Meas. Sci. Technol., 2006, 17, p. 2097-210310.1088/0957-0233/17/8/007 0957-0233
23. Mou, C.H., Peng, L.H., Yao, D.Y., and Xiao, D.Y.: 'Image reconstruction using a genetic algorithm for electrical capacitance tomography', Tsinghua Sci. Technol., 2005, 10, p. 587-59210.1016/S1007-0214(05)70123-1 1007-0214
24. Takei, M.: 'GVSPM image reconstruction for capacitance CT images of particles in a vertical pipe and comparison with the conventional method', Meas. Sci. Technol., 2006, 17, p. 2104-211210.1088/0957-0233/17/8/008 0957-0233
25. Wang, H.X., Tang, L., and Cao, Z.: 'An image reconstruction algorithm based on total variation with adaptive mesh refinement for ECT', Flow Meas. Instrum., 2007, 18, p. 262-26710.1016/j.flowmeasinst.2007.07.004 0955-5986
26. Banasiak, R., and Soleimani, M.: 'Shape based reconstruction of experimental data in 3D electrical capacitance tomography', NDT&E Int., 2010, 43, p. 241-24910.1016/j.ndteint.2009.12.001 0963-8695
27. Lei, J.: 'Research on image reconstruction algorithms of electrical capacitance tomography for the multiphase flow', 2008, PhD, Institute of Engineering Thermophysics Chinese Academy of Sciences
28. Watzenig, D., Brandner, M., and Steiner, G.: 'A particle filter approach for tomographic imaging based on different state-space representations', Meas. Sci. Technol., 2007, 18, p. 30-4010.1088/0957-0233/18/1/004 0957-0233
29. Soleimani, M., Vauhkonen, M., Yang, W.Q., Peyton, A., Kim, B.S., and Ma, X.D.: 'Dynamic imaging in electrical capacitance tomography and electromagnetic induction tomography using a Kalman filter', Meas. Sci. Technol., 2007, 18, p. 3287-329410.1088/0957-0233/18/11/004 0957-0233
30. Soleimani, M., Mitchell, C.N., Banasiak, R., Wajman, R., and Adler, A.: 'Four-dimensional electrical capacitance tomography imaging using experimental data', Prog. Electromagn. Res.-PIER, 2009, 90, p. 171-18610.2528/PIER09010202
31. Kaipio, J.P., Karjalainen, P.A., Somersalo, E., and Vauhkonen, M.: 'State estimation in time-varying electrical impedance tomography', Ann. New York Acad. Sci., 1999, 873, p. 430-43910.1111/j.1749-6632.1999.tb09492.x
32. Vauhkonen, P.J., Vauhkonen, M., Mäkinen, T., Karjalainen, P.A., and Kaipio, J.P.: 'Dynamic electrical impedance tomography-phantom studies', Inverse Probl. Eng., 2000, 8, p. 495-51010.1080/174159700088027743
33. Seppänen, A., Vauhkonen, M., Vauhkonen, P.J., Somersalo, E., and Kaipio, J.P.: 'State estimation with fluid dynamical evolution models in process tomography-an application to impedance tomography', Inverse Prob., 2001, 17, p. 467-48410.1088/0266-5611/17/3/307
34. Kim, K.Y., Kim, B.S., Kim, M.C., Lee, Y.J., and Vauhkonen, M.: 'Image reconstruction in time-varying electrical impedance tomography based on the extended Kalman filter', Meas. Sci. Technol., 2001, 12, p. 1032-103910.1088/0957-0233/12/8/307 0957-0233
35. Tossavainen, O.P., Vauhkonen, M., Kolehmainen, V., and Kim, K.Y.: 'Tracking of moving interfaces in sedimentation processes using electrical impedance tomography', Chem. Eng. Sci., 2006, 61, p. 7717-772910.1016/j.ces.2006.09.010 0009-2509
36. Khambampati, A.K., Rashid, A., Ijaz, U.Z., Kim, S., Soleimani, M., and Kim, K.Y.: 'Unscented Kalman filter approach to tracking a moving interfacial boundary in sedimentation processes using three-dimensional electrical impedance tomography', Philos. Trans. R. Soc., 2009, 367, p. 3095-312010.1098/rsta.2009.0081
37. Xie, C.G., Plaskowski, A., and Beck, M.S.: 'Eight-electrode capacitance system for two-component flow identification Part 1: tomographic flow imaging', IEE Proc., 1989, 136, p. 173-183
38. Butala, M.D., Hewett, R.J., Frazin, R.A., and Kamalabadi, F.: 'Dynamic three-dimensional tomography of the solar corona', Sol. Phy., 2010, 262, p. 495-50910.1007/s11207-010-9536-1
39. Kalman, R.E.: 'A new approach to linear filtering and prediction problems', Trans. ASME-J. Basic Eng., 1960, 82D, p. 35-4510.1115/1.3662552
40. Liu, S., and Zhang, H.M.: 'The optimal estimation theory', (Science Press, Beijing 2011)
41. Zhu, Z.Y.: 'Algorithms and applications in the particle filter', (Science Press, Beijing 2010)
42. Yang, Y.X.: 'Adaptive navigation and kinematic positioning', (Surveying and Mapping Press, Beijing 2006)
43. Yang, Y., He, H., and Xu, G.: 'Adaptively robust filtering for kinematic geodetic positioning', J. Geodesy, 2001, 75, p. 109-11610.1007/s001900000157
44. Yang, Y., and Gao, W.: 'An optimal adaptive Kalman filter', J. Geodesy, 2006, 80, p. 177-18310.1007/s00190-006-0041-0
45. Evensen, G.: 'Data assimilation: the ensemble Kalman filter', (Springer-Verlag, Berlin 2007)
46. Houtekamer, P.L., and Mitchell, H.: 'Data assimilation using an Ensemble Kalman filter technique', Mon. Weather Rev., 1998, 126, p. 796-81110.1175/1520-0493(1998)126<0796:DAUAEK>2.0.CO;2 0027-0644
47. Hamill, T.M., Whitaker, J.S., and Snyder, C.: 'Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter', Mon. Weather Rev., 2001, 129, p. 2776-279010.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2 0027-0644
48. Han, X., and Li, X.: 'An evaluation of the nonlinear/non-Gaussian filter for the sequential data assimilation', Remote Sens. Environ., 2008, 112, p. 1434-144910.1016/j.rse.2007.07.008 0034-4257
49. Evensen, G.: 'The Ensemble Kalman filter for combined state and parameter estimation', IEEE Control Syst. Mag., 2009, 29, (3), p. 83-10410.1109/MCS.2009.932223 0272-1708
50. Vachhani, P., Narasimhan, S., and Rengaswamy, R.: 'Robust and reliable estimation via unscented recursive nonlinear dynamic data reconciliation', J. Process Control, 2006, 16, p. 1075-108610.1016/j.jprocont.2006.07.002 0959-1524
51. Teixeira, B.O.S., Chandrasekar, J., Torres, L.A.B., Aguirre, L.A., and Bernstein, D.S.: 'State estimation for linear and non-linear equality-constrained systems', Int. J. Control, 2009, 82, p. 918-93610.1080/00207170802370033 0020-7179
52. Ishihara, S., and Yamakita, M.: 'Constrained state estimation for nonlinear systems with non-Gaussian noise', Joint 48th IEEE Conf. on Decision and Control and 28th Chinese Control Conf., Shanghai, P.R. China, December 16-18 2009, p. 1279-1284
53. Simon, D.: 'Kalamn filtering with state constraints: a survey of linear and nonlinear algorithms', IET Control Theory Appl., 2010, 4, p. 1303-131810.1049/iet-cta.2009.0032
54. Teixeira, B.O.S., Chandrasekar, J., Palanthandalam-Madapusi, H.J., Tôrres, L.A.B., Aguirre, L.A., and Bernstein, D.S.: 'Gain-constrained Kalman filtering for linear and nonlinear systems', IEEE Trans. Signal Proc., 2008, 56, p. 4113-412310.1109/TSP.2008.926101 1053-587X
55. Prakash, J., Patwardhan, C., and Shah, S.L.: 'Constrained state estimation using the ensemble Kalman filter', 2008 American Control Conf., Seattle, Washington, USA, June 11-13 2008, p. 3542-3547 Westin Seattle Hotel
56. Kolas, S., Foss, B.A., and Schei, T.S.: 'Constrained nonlinear state estimation based on the UKF approach', Comput. Chem. Eng., 2009, 33, p. 1386-140110.1016/j.compchemeng.2009.01.012 0098-1354
57. Prakash, J., Patwardhan, C., and Shah, S.L.: 'On the choice of importance distributions for unconstrained and constrained state estimation using particle filter', J. Process Control, 2010, 21, p. 3-1610.1016/j.jprocont.2010.08.001 0959-1524
58. Huber, P.J.: 'Robust statistics', (John Wiley & Sons, New York 1981)
59. Wang, T.: 'Methods on robust estimation and detection of multiple outliers in linear regression', 2000, PhD, The Fourth Military Medical University
60. Hebert, T., and Leahy, R.: 'A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors', IEEE Trans. Med. Imaging, 1989, 8, p. 194-20210.1109/42.24868 0278-0062
61. Acar, R., and Vogel, C.R.: 'Analysis of bounded variation penalty methods for ill posed problem', Inverse Probl., 1994, 10, p. 1217-122910.1088/0266-5611/10/6/003 0266-5611
62. Xiao, T.Y., Yu, S.G., and Wang, Y.F.: 'Numerical methods of the inverse problems', (Science Press, Beijing 2003)
63. Wang, Y.F.: 'Computational methods for inverse problems and their applications', (Higher Education Press, Beijing 2007)
64. Shen, P.P.: 'Global optimization methods', (Science Press, Beijing 2006)
65. Zhang, K.C., and Li, H.Q.: 'Engineering optimization methods and applications', (Xi'an Jiaotong University Press, Xi'an 2007)
66. Ge, R.P.: 'A filled function method for finding a global minimizer of a function of several variables', Math. Program., 1990, 46, p. 191-20410.1007/BF01585737 0025-5610
67. Ma, Z.H.: 'Handbook of modern applied mathematics', (Tsinghua University Press, Beijing 2005)
68. Li, Q.Y., Mo, Z.H., and Qi, L.Q.: 'Numerical methods for system of nonlinear equations', (Science Press, Beijing 1987)
69. Huang, X.D., Zeng, Z.G., and Ma, Y.N.: 'Theory and methods for nonlinear numerical analysis', (Wuhan University Press, Wuhan 2004)