Deep Operator Learning-based Surrogate Models with Uncertainty Quantification for Optimizing Internal Cooling Channel Rib Profiles

TL;DR

This paper introduces a Bayesian DeepONet surrogate model with uncertainty quantification for optimizing internal cooling channel rib profiles, trained on simulated data with variable geometries to improve thermal performance predictions.

Contribution

It develops a novel Bayesian DeepONet framework with uncertainty quantification for surrogate modeling of rib geometries in cooling channels, using stochastic gradient replica-exchange MCMC for training.

Findings

The surrogate accurately predicts pressure and heat transfer distributions.

Uncertainty quantification enhances the reliability of the predictions.

The model effectively handles arbitrary rib geometries.

Abstract

This paper designs surrogate models with uncertainty quantification capabilities to improve the thermal performance of rib-turbulated internal cooling channels effectively. To construct the surrogate, we use the deep operator network (DeepONet) framework, a novel class of neural networks designed to approximate mappings between infinite-dimensional spaces using relatively small datasets. The proposed DeepONet takes an arbitrary continuous rib geometry with control points as input and outputs continuous detailed information about the distribution of pressure and heat transfer around the profiled ribs. The datasets needed to train and test the proposed DeepONet framework were obtained by simulating a 2D rib-roughened internal cooling channel. To accomplish this, we continuously modified the input rib geometry by adjusting the control points according to a simple random distribution with constraints, rather than following a predefined path or sampling method. The studied channel has a hydraulic diameter, Dh, of 66.7 mm, and a length-to-hydraulic diameter ratio, L/Dh, of 10. The ratio of rib center height to hydraulic diameter (e/Dh), which was not changed during the rib profile update, was maintained at a constant value of 0.048. The ribs were placed in the channel with a pitch-to-height ratio (P/e) of 10. In addition, we provide the proposed surrogates with effective uncertainty quantification capabilities. This is achieved by converting the DeepONet framework into a Bayesian DeepONet (B-DeepONet). B-DeepONet samples from the posterior distribution of DeepONet parameters using the novel framework of stochastic gradient replica-exchange MCMC.