Bayesian grey-box identification of nonlinear convection effects in heat transfer dynamics
This work addresses heat transfer modeling for engineering applications, but it is incremental as it builds on existing grey-box and Gaussian process methods.
The authors tackled the problem of identifying nonlinear convection effects in heat transfer dynamics by proposing a Bayesian grey-box identification method that combines known physics with a Gaussian process model, and validated it through simulation error on both simulated and physical data.
We propose a computational procedure for identifying convection in heat transfer dynamics. The procedure is based on a Gaussian process latent force model, consisting of a white-box component (i.e., known physics) for the conduction and linear convection effects and a Gaussian process that acts as a black-box component for the nonlinear convection effects. States are inferred through Bayesian smoothing and we obtain approximate posterior distributions for the kernel covariance function's hyperparameters using Laplace's method. The nonlinear convection function is recovered from the Gaussian process states using a Bayesian regression model. We validate the procedure by simulation error using the identified nonlinear convection function, on both data from a simulated system and measurements from a physical assembly.