Prediction of discontinuous surface heat flux based on the calibration integral equation method with Bayesian regularization

This paper investigates the reconstruction of surface heat fluxes with discontinuity, which is of significant importance in engineering applications. Based on the underlying mechanism of heat conduction, a calibration integral equation is proposed, which formulates the inverse problem into a Volterra integral equation. Combined with Bayesian regularization, this approach can effectively predict surface heat flux with sudden changes or discontinuities in the thermal data. Results demonstrate that Bayesian regularization outperforms traditional methods, such as Tikhonov regularization, in reconstructing both smooth and abrupt heat flux variations. It accurately captures sudden changes, even in the presence of noise and rapid thermal fluctuations. In contrast, classical regularization methods are only effective for smooth heat flux predictions. The contributions of this study include: (1) demonstrating the effectiveness of CIEM for dynamic and abrupt boundary conditions, (2) introducing Bayesian regularization to mitigate over-smoothing. These advancements provide critical insights for optimizing thermal protection systems and improving safety in high-speed flight applications.