Full-field expansion and damage detection from sparse measurements using physics-informed variational autoencoders

Recent advancements in machine learning and artificial neural network algorithms have created new opportunities for expanding sparse measurements to full-field representations. However, these methods often face accuracy challenges when used for condition monitoring of physical systems. For example, traditional autoencoders can capture complex phenomena and their underlying physics in the latent space, but due to their frequentist nature, they lack generative and damage detection capabilities. To address these challenges, a novel physics-informed variational autoencoder (PI-VAE) network is proposed for expanding sparse measurements to full-field representations while also detecting damage. The effectiveness of the proposed PI-VAE network is evaluated through analytical and experimental studies on a metal plate under thermal excitation with embedded defects of various sizes and types. In the analytical studies using finite-element model data, the PI-VAE accurately expanded full-field temperature distributions and identified the dimensions of cracks, spalling, and hole-like defects with errors smaller than 5%. When tested with experimental data, the PI-VAE network maintained robust performance, detecting damage with errors smaller than 6%, despite being trained on undamaged data only. These findings demonstrate the PI-VAE’s potential as a reliable tool for full-field expansion and damage detection in structural health monitoring and nondestructive evaluation, even when limited sensors and datasets are available.