Fast and Simultaneous Estimation of Thermophysical and Geometric Parameters for Thermal Barrier Coating Systems in High-Temperature Environments via a PCA-Optimized ANN-PSO-Based Accelerated Inverse Model

In this article, an inverse mathematical model was developed to achieve fast and simultaneous estimation of thermophysical and geometric parameters for thermal barrier coating (TBC) systems in high-temperature environments with measurement errors. First, considering the convective and radiative heat transfer between the TBC system and the external environment, a one-dimensional unsteady conduction–radiation coupled heat transfer model was originally developed in high-temperature environments. Subsequently, this forward model was solved using the finite volume method (FVM), and the grid independence as well as the accuracy were validated. Thereafter, an accelerated inverse model, which adopts a principal component analysis (PCA)-optimized artificial neural network (ANN) to fit and substitute the forward model and employs the particle swarm optimization (PSO) algorithm for estimation, was developed based on the inverse method. Finally, under three different noise conditions, two situations were used to perform simultaneous estimation studies: a two-parameter case (top coat thermal conductivity and thermally grown oxide (TGO) layer thickness) and a three-parameter case (adding the thickness of an additional existing debonding defect layer). The results show that the PCA-optimized ANN-PSO-based accelerated inverse model is approximately 111–130 times faster than the traditional PSO-based inverse model, and the maximum relative errors of the arithmetic means of 20 estimations for two-parameter and three-parameter situations under three noise cases are on the order of 2.4% to 4.3%. Overall, the proposed accelerated inverse model achieves a favorable balance between speed and accuracy in multi-type parameter simultaneous estimation for TBC systems at high temperature, providing a methodological basis for addressing parameter estimation in more complex situations in future research.