Guided Wave-Based Structural Awareness Under Varying Operating States via Manifold Representations

Guided wave-based structural health monitoring (SHM) remains a powerful strategy for identifying early-stage defects and safeguarding vital aerospace structures. Yet, its practical use is often hindered by the enormous, high-dimensional data streams produced by sensor arrays operating at megahertz sampling rates, coupled with the added complexity of shifts in environmental and operational conditions (EOCs). Studies have explored various data-compression approaches that retain critical diagnostic details in a lower-dimensional latent space. While conventional techniques can streamline dimensionality to some extent, they do not always capture the nonlinear interactions typical of guided waves. Manifold learning, as illustrated by Diffusion Maps, tackles these nonlinearities by deriving low-dimensional embeddings directly from wave signals, minimizing the need for manual feature extraction. In parallel, developments in deep learning -- particularly autoencoders -- provide an encoder-decoder model for both data compression and reconstruction. Convolutional autoencoders (CAEs) and variational autoencoders (VAEs) have been particularly effective for guided wave applications. However, current methods can still struggle to maintain accurate state estimation under changing EOCs, and they are often limited to a single task. In response, the proposed framework adopts a two-fold strategy: it compresses high-dimensional signals into lower-dimensional representations and then leverages those representations to both estimate structural states and reconstruct the original data, even as conditions vary. Applied to two real-world SHM use-cases, this integrated method has proven its ability to preserve and retrieve key damage signatures under noise, shifting operational parameters, and other complicating factors.