To deal with inverse nonlinear heat transfer problems in a two-dimensional heat conduction problem, this paper presents a hybrid approach combining fuzzy logic and the extended Kalman filter (EKF). The proposed algorithm has been applied to the real-time reconstruction of the temperature field, time-varying convective heat transfer coefficient, and time-varying boundary heat flux using temperature data from a set of sensors. The effects of the covariance of the initial estimation error, the time step of data acquisition by the sensors, and the number of installed sensors on the precision and stability of the estimation results has been investigated by numerical experiments. To compare and validate the results, all these parameters were investigated using the EKF method. The results show that the adaptive fuzzy extended Kalman filter (FEKF) method for estimating temperature, convection coefficient, and heat flux at the boundaries is precise and stable. The comparison shows that the performance of the FEKF method in parameter estimation is better than the EKF method, and the highest increase in precision and stability of the results is related to the convective heat transfer coefficient.

中文翻译：

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应用自适应方法确定扩展卡尔曼滤波器中的过程噪声来估计二维传热逆问题的参数

为了处理二维热传导问题中的逆非线性传热问题，本文提出了一种结合模糊逻辑和扩展卡尔曼滤波器（EKF）的混合方法。该算法已应用于使用一组传感器的温度数据实时重建温度场、时变对流换热系数和时变边界热通量。通过数值实验研究了初始估计误差的协方差、传感器数据采集的时间步长以及安装的传感器数量对估计结果精度和稳定性的影响。为了比较和验证结果，使用 EKF 方法研究了所有这些参数。结果表明，自适应模糊扩展卡尔曼滤波器（FEKF）估算边界温度、对流系数和热通量的方法精确且稳定。对比表明，FEKF方法在参数估计方面的性能优于EKF方法，并且结果的精度和稳定性提升幅度最高与对流换热系数有关。