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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. [ABSTRACT FROM AUTHOR]

In this study, a combined method of Kalman filter (KF) and fuzzy logic is presented to solve the inverse problem of heat transfer in a R920K brake disc. The proposed algorithm uses the temperature data from a set of sensors for real-time reconstruction of the temperature field and the time-varying boundary heat flux for 10 different locomotive braking scenarios. The results show that the adaptive fuzzy type 2 Kalman filter (AFT2KF) algorithm is accurate and stable in estimating the temperature field and boundary heat flux. The use of adaptive fuzzy type 1 Kalman filter (AFT1KF) also significantly reduces the estimation error compared to the KF algorithm. The results show that the use of adaptive methods increases the time for parameter estimation compared to the KF algorithm, however can still be considered as real-time estimation. The performance of the AFT2KF method in parameter estimation is better than that of KF and AFT1KF, so it reduces the error in heat flux estimation by more than 80% compared to KF. [ABSTRACT FROM AUTHOR]