Reconstruction of thermophysical parameters in inhomogeneous media using extended Kalman filter and unscented Kalman filter

doi:10.11949/0438-1157.20191023

Abstract

Abstract:

In this paper, the unscented Kalman filter (UKF) is used for the first time to solve the inverse problem of one-dimensional dielectric thermophysical properties. In addition, this paper also studies the inversion of thermal conductivity in one-dimensional media using extended Kalman filter (EKF). The forward model is introduced firstly. Basic principles of the EKF and UKF technique are also introduced in detail. In order to examine the feasibility of the proposed algorithms, the space-dependent and time-dependent thermal conductivities in media are reconstructed by the UKF and EKF techniques, respectively. All the reconstruction results indicate that thermal conductivities of media can be retrieved effectively by the EKF and UKF techniques. Moreover, the small measurement error covariance R should be selected to decrease the time lag of the reconstructed results.

Key words: extended Kalman filter, unscented Kalman filter, inverse heat conduction problem, thermal conductivities

摘要：

将无迹卡尔曼滤波技术(unscented Kalman filter, UKF)用于求解一维介质热物性参数反演问题；也对利用扩展卡尔曼滤波技术(extended Kalman filter, EKF)反演一维介质中热导率问题进行了研究。首先给出了正问题模型，然后详细介绍了EKF算法和UKF算法的基本原理。最后为了验证当前算法的可行性，采用UKF算法重建了介质内部随位置变化的热导率，并采用EKF算法重建了介质内部随时间变化的热导率。计算结果表明，UKF算法和EKF算法均能较为准确地反演介质的热导率。为了减小重建结果的时间滞后，建议使用较小的测量误差协方差R。

关键词: 扩展卡尔曼滤波, 无迹卡尔曼滤波, 导热反问题, 热导率

CLC Number:

TK 124

Shuang WEN, Hong QI, Shaobin LIU, Yatao REN, Liming RUAN. Reconstruction of thermophysical parameters in inhomogeneous media using extended Kalman filter and unscented Kalman filter[J]. CIESC Journal, 2020, 71(4): 1432-1439.

文爽, 齐宏, 刘少斌, 任亚涛, 阮立明. 基于EKF和UKF算法非均匀介质热物性参数重建[J]. 化工学报, 2020, 71(4): 1432-1439.

Figures/Tables 6

Fig.1 Schematic of physical model

Fig.2 Linearization principle of EKF and UKF technique

Fig.3 Reconstructed results of thermal conductivity

Fig.4 Retrieval results of thermal conductivity with different measurement error covariance

Fig.5 Reconstructed results of space-dependent thermal conductivity with different measurement errors

Fig.6 Retrieval results of thermal conductivity with different quantities of measurement signals

References 29

1	Sawaf B, Özisik M N. An inverse analysis to estimate linearly temperature dependent thermal conductivity components and heat capacity of an orthotropic medium[J]. International Journal of Heat and Mass Transfer, 1995, 38(16): 3005-3010.
2	Ukrainczyk N. Thermal diffusivity estimation using numerical inverse solution for 1D heat conduction[J]. International Journal of Heat and Mass Transfer, 2009, 52(25/26): 5675-5681.
3	Huang C H, Yan J Y. An inverse problem in simultaneously measuring temperature-dependent thermal conductivity and heat capacity[J]. International Journal of Heat and Mass Transfer, 1995, 38(18): 3433-3441.
4	Huang C H, Yan J Y, Chen H T. Function estimation in predicting temperature-dependent thermal conductivity without internal measurements[J]. Journal of Thermophys and Heat Transfer, 1995, 9(4): 667-673.
5	Huang C H, Yan J Y. An inverse problem in predicting temperature dependent heat capacity per unit volume without internal measurements[J]. International Journal for Numerical Methods in Engineering, 1996, 39(4): 605-618.
6	Huang C H, Chin S C. A two-dimensional inverse problem in imaging the thermal conductivity of a non-homogeneous medium[J]. International Journal of Heat and Mass Transfer, 2000, 43(22): 4061-4071.
7	Wang F Q, Tan J Y, Wang Z Q. Heat transfer analysis of porous media receiver with different transport and thermophysical models using mixture as feeding gas[J]. Energy Conversion and Management, 2014, 83: 159-166.
8	Kosaka M, Monde M. Simultaneous measurement of thermal diffusivity and thermal conductivity by means of inverse solution for one-dimensional heat conduction (anisotropic thermal properties of CFRP for FCEV)[J]. International Journal of Thermophysics, 2015, 36(10/11): 2590-2598.
9	Cui M, Duan W W, Gao X W. A new inverse analysis method based on a relaxation factor optimization technique for solving transient nonlinear inverse heat conduction problems[J]. International Journal of Heat and Mass Transfer, 2015, 90: 491-498.
10	Zhao S Y, Zhang B M, Du S Y, et al. Inverse identification of thermal properties of fibrous insulation from transient temperature measurements[J]. International Journal of Thermophysics, 2009, 30(6): 2020-2035.
11	Cui M, Gao X W, Zhang J B. A new approach for the estimation of temperature-dependent thermal properties by solving transient inverse heat conduction problems[J]. International Journal of Thermal Sciences, 2012, 58: 113-119.
12	Zhang B, Xu C L, Wang S M. An inverse method for flue gas shielded metal surface temperature measurement based on infrared radiation[J]. Measurement Science & Technology, 2016, 27(7): 74002-74012.
13	Zmywaczyk J, Koniorczyk P. Numerical solution of inverse radiative-conductive transient heat transfer problem in a grey participating medium[J]. International Journal of Thermophysics, 2009, 30(4): 1438-1451.
14	Tang G H, Xu C L, Shao L T, et al. Improve algorithms of differential optical absorption spectroscopy for monitoring SO₂, NO₂ from flue gas[J]. Measurement Science & Technology, 2009, 20(1): 015601.
15	Raudenský M, Horský J, Krejsa J, et al. Usage of artificial intelligence methods in inverse problems for estimation of material parameters[J]. International Journal of Numerical Methods for Heat & Fluid Flow, 1996, 6(8): 19-29.
16	Ardakani M D, Khodadad M. Identification of thermal conductivity and the shape of an inclusion using the boundary elements method and the particle swarm optimization algorithm[J]. Inverse Problems in Science & Engineering, 2009, 17(7): 855-870.
17	Vakili S, Gadala M S. Effectiveness and efficiency of particle swarm optimization technique in inverse heat conduction analysis[J]. Numerical Heat Transfer Part B-Fundamentals, 2009, 56(2): 119-141.
18	Kalman R E. A new approach to linear filtering and prediction problems[J]. Transactions of the ASME-Journal of Basic Engineering, 1960, 82D (1): 35-45.
19	Scarpa F, Bartolini R, Milano G. State space (Kalman) estimator in the reconstruction of thermal diffusivity from noisy temperature measurements[J]. High Temperatures-High Pressure, 1991, 23: 633-642.
20	Ji C C, Tuan P C, Jang H Y. A recursive least-squares algorithm for on-line 1-D inverse heat conduction estimation[J]. International Journal of Heat and Mass Transfer, 1997, 40(9): 2081-2096.
21	Noh J H, Cha K U, Ahn S T, et al. Prediction of time-varying heat flux along a hollow cylindrical tube wall using recursive input estimation algorithm and thermal resistance network method[J]. International Journal of Heat and Mass Transfer, 2016, 97: 232-241.
22	Chen T C, Cheng C H, Jang H Y, et al. Using input estimation to estimate heat source in nonlinear heat conduction problem[J]. International Journal of Thermophysics, 2007, 21(1): 166-172.
23	Deng S, Hwang Y. Solution of inverse heat conduction problems using Kalman filter-enhanced Bayesian back propagation neural network data fusion[J]. International Journal of Heat and Mass Transfer, 2007, 50: 2089-2100.
24	LeBreux M, Désilets M, Lacroix M. Control of the ledge thickness in high temperature metallurgical reactor using a virtual sensor[J]. Inverse Problems in Science & Engineering, 2012, 20(8): 1215-1238.
25	LeBreux M, Désilets M, Lacroix M. Fast inverse prediction of phase change banks in high temperature furnaces with a Kalman filter coupled with a recursive least-square estimator[J]. International Journal of Heat and Mass Transfer, 2010, 53(23/24): 5250-5260.
26	LeBreux M, Désilets M, Lacroix M. An unscented Kalman filter inverse heat transfer method for the prediction of the ledge thickness inside high-temperature metallurgical reactors[J]. International Journal of Heat and Mass Transfer, 2013, 57(1): 265-273.
27	郝晓静, 李国新, 李明珠, 等. 无迹卡尔曼滤波算法在目标跟踪中的研究[J].电子设计工程, 2012, 20(13): 161-164.
	Hao X J, Li G X, Li M Z, et al. Research of UKF in the target tracking[J]. Electronic Design Engineering, 2012, 20(13): 161-164.
28	王磊, 李宏, 武明珠, 等. 基于扩展卡尔曼滤波的永磁同步电动机参数辨识[J]. 微特电机, 2012, 40(7): 19-22.
	Wang L， Li H，Wu M Z, et al. Parameters identification of PMSM based on extended Kalman filter[J]. Small & Special Electrical Machines, 2012, 40(7): 19-22.
29	Julier S J, Ulhmann J K, Durrant-Whyte H F. A new method for the nonlinear transformation of means and covariances in filters and estimators[J]. IEEE Transactions on Automatic Control, 2000,45 (3): 477-482.

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