基于EKF和UKF算法非均匀介质热物性参数重建

doi:10.11949/0438-1157.20191023

摘要/Abstract

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

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

中图分类号:

TK 124

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.

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.

图/表 6

图1 一维介质物理模型

Fig.1 Schematic of physical model

图2 EKF和UKF的线性化原理

Fig.2 Linearization principle of EKF and UKF technique

图3 热导率重建结果

Fig.3 Reconstructed results of thermal conductivity

图4 不同测量误差协方差下热导率重建结果

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

图5 不同测量误差下随位置变化的热导率重建结果

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

图6 测量信息量对随温度变化的热导率重建研究的影响

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

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