Unified Framework for Probabilistic Modeling and Uncertainty Quantification of Aerospace Structures via Stochastic Latent Space Representations

Structural Health Monitoring (SHM) is a critical area for ensuring the reliability of engineering systems, with ultrasonic waves emerging as a preferred tool due to their ability to propagate over long distances and their sensitivity to structural changes. However, the inherent complexities of guided wave propagation, including frequency-dependent velocities, multimodal dispersion, and overlapping reflections, necessitate advanced feature extraction techniques to enable accurate damage detection. Conventional methods, such as Damage Index (DI), are effective for identifying anomalies but struggle to maintain sensitivity and stability under varying environmental and operational conditions (EOCs). Recent advancements in computational power have significantly advanced the adoption of machine learning techniques, particularly convolutional neural networks (CNNs) and autoencoders (AEs), in Structural Health Monitoring (SHM) applications. Convolutional autoencoders (CAEs), which leverage the strengths of both CNNs and AEs, are particularly effective for efficiently compressing and reconstructing data in system identification tasks. Alternatively, nonlinear data compression techniques, such as diffusion maps (DMaps), can also be utilized within state estimation schemes to address nonlinearity and high-dimensionality challenges. This study proposes an innovative framework that integrates these two distinct approaches - CAEs and DMaps - for data compression and reconstruction in SHM, particularly under varying EOCs. Stochastic signals are compressed into a low-dimensional latent space, significantly reducing computational costs. The first approach leverages diffusion maps for nonlinear dimensionality reduction, followed by polynomial chaos expansion (PCE) and Laplacian pyramids for signal reconstruction. The second approach employs an encoder-decoder architecture for signal processing. By comparing the performance and robustness of these methods across two distinct datasets, this work demonstrates their potential for achieving reliable state prediction and signal reconstruction, thereby advancing SHM capabilities under complex operational conditions.