A Digital Twin Modeling Approach for Structural Heat Conduction Analysis Based on Stochastic Modeling and Bayesian Inference

The accurate prediction of structural heat transfer temperature fields under extreme thermal environments is a critical foundation for evaluating the thermo-mechanical performance of equipment. The digital twin technology enables high-precision dynamic reconstruction of temperature fields through the deep integration of observed data and simulation models. However, digital twin models for predicting structural heat transfer temperature fields with multi-source uncertainties, such as observation noise, model parameter uncertainty, and boundary condition disturbances, are still relatively scarce. Aimed to construct a heat conduction digital twin model with uncertainty quantification, a data-model fusion method combined with stochastic heat conduction analysis was proposed based on the Bayesian inference framework. First, a Gaussian random perturbation heat source term was introduced into the heat conduction equation to simulate uncertainty factors not quantified by the original model. Second, the stochastic heat conduction model was solved with the stochastic finite element method to obtain a prior distribution of the temperature field incorporating physical information. Finally, based on Bayes’ theorem, the noisy observation data was fused with the model-predicted prior distribution, and an analytical expression for the posterior distribution of the temperature field was derived for the Gaussian case. The results of 1D and 2D heat conduction examples demonstrate that, the proposed method not only achieves high-precision prediction of the temperature field but also effectively quantifies the uncertainty of the prediction results.