# Simulation-assisted multimodal deep learning (Sim-MDL) fusion models for the evaluation of thermal barrier coatings using infrared thermography and Terahertz imaging

## TL;DR

This paper introduces a new deep learning framework that combines infrared and terahertz data to accurately evaluate thermal barrier coatings.

## Contribution

The novel Sim-MDL framework uses simulation and experimental data to improve TBC evaluation accuracy and robustness.

## Key findings

- The Sim-MDL framework achieved high prediction accuracy with MAPE values under 5% for thermal conductivity and heat capacity.
- The attention-based LSTM model outperformed single-modality and conventional methods in evaluating TBC properties.
- The framework successfully predicted topcoat thickness and refractive index with high precision.

## Abstract

Thermal Barrier Coatings (TBCs) are critical for high-temperature applications, such as gas turbines and aerospace engines, protecting metallic substrates from extreme thermal stress and degradation. Accurate evaluation of TBCs is essential to improve operational efficiency, optimize predictive maintenance strategies, and extend component life. Conventional non-destructive evaluation (NDE) techniques such as infrared thermography (IRT) and terahertz (THz) imaging have been widely used for TBC inspection with limitations when used independently, including sensitivity to surface conditions, limited penetration depth mainly in multi-layer coatings. This study proposes a novel framework called simulation-assisted multimodal deep learning (Sim-MDL) that combines IRT and THz data for a comprehensive evaluation of TBCs. To generalize the study to varying thermophysical properties of TBCs, the study uses simulation-generated data along with experimental data for training deep learning models. Two deep learning frameworks based on a 1D convolutional neural networks (CNN) and a long short-term memory (LSTM) with attention were developed for the multimodal feature fusion. The IR-THz fused frameworks enable simultaneous prediction of key TBC topcoat properties including thermal conductivity, heat capacity, topcoat thickness and refractive index. Experiments were conducted on four newly coated samples topcoat thicknesses ranging from 24 to 120 μm. An attention-based LSTM model trained on both simulation and experimental data shows high prediction accuracy with MAPE values ranging from 2.06% to 4.43% for thermal conductivity, 2.05% to 3.57% for heat capacity, 11.53% to 1.75% for topcoat thickness, and 0.27% to 1.05% for refractive index, respectively, for the topcoat layers of four samples. The proposed Sim-MDL framework outperformed single-modality and conventional parameter estimation methods in accuracy and robustness, highlighting the potential of multimodal data for automated analysis of TBC in industrial settings.