BP neural network regularized by wall temperature characteristics to reduce the ill-posedness of two-dimensional inverse heat transfer problems in rotating disk cavities

In the two-dimensional heat transfer experiments of aero-engine rotating disk cavities, the inverse heat transfer problem method can be used to obtain the wall heat flux numerically, which uses the two-dimensional measured wall temperature to solve the rotating disk heat conduction equation. A back propagation (BP) neural network data approximation method is proposed to reduce the ill-posedness of the two-dimensional inverse heat transfer problems in rotating disk cavities in this paper. The priori knowledge of wall temperature characteristics expressed by two-dimensional wall temperature first-order radial partial derivative distribution is used for BP neural networks’ regularization. The distribution characteristics of the wall temperature first-order radial partial derivative in a typical preswirl rotating disk cavity were investigated by the flow-thermal coupling numerical simulation. Based on these characteristics, the BP neural network construction and training method with uncertain regularization coefficient is adopted. The numerical experiment results show that compared with the traditional polynomial fitting methods, the BP neural network approximation methods in this paper show significant advantages in data processing performance and stability; The fluctuation amplitude of the wall heat flux relative error on the disk surface can be reduced by 1–3 orders of magnitude, reducing the relative error of wall heat flux in most areas of the disk to within 20 % of the original value; The maximum wall heat flux relative error suppression area where |δq_r,cal/δq_r,mea × 100 %| < 100 % of BP neural network approximation method can reach 1.93 times that of the traditional fitting method, and 3.18 times for the area where |δq_r,cal/δq_r,mea × 100 %| < 30 % in the current study.