A double decentralized fuzzy inference method for estimating the time and space-dependent thermal boundary condition

For the inverse heat conduction problem to estimate the time and space-dependent thermal boundary condition, a double decentralized fuzzy inference (DDFI) method with a temporal-spatial decoupling characteristic is proposed. A set of decentralized fuzzy inference modules (DFIMs) corresponding to the temperature measurement points are established. Each DFIM contains a set of decentralized fuzzy inference units (DFIUs), and each DFIM performs the fuzzy inference process from the vector of time series of temperature measurements at the corresponding temperature measurement points. The inference results of DFIUs in the time domain are weighed and synthesized by dynamic response coefficients to obtain the time adjustment vector of the thermal boundary condition. In the space domain, the inference results of DFIMs are weighed and synthesized by the normal distribution function to obtain the space adjustment vector. Numerical experiments are performed to study the effects of the number of measurement points, measurement errors and the buried depth of thermocouples on the inversion results. Comparison with the existing dynamic matrix control inverse method is also conducted, and it shows the validity of the inverse method established in this paper.