Bayesian grey-box identification of nonlinear convection effects in heat transfer dynamics

TL;DR

This paper introduces a Bayesian grey-box modeling approach combining known physics and Gaussian processes to identify nonlinear convection effects in heat transfer, validated through simulations and physical experiments.

Contribution

It presents a novel Gaussian process latent force model integrating physics-based and black-box components for nonlinear heat transfer analysis.

Findings

Accurate identification of nonlinear convection effects.

Effective Bayesian smoothing and hyperparameter estimation.

Validated method on simulated and real data.

Abstract

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.