Exploring Compressed Sensing Approaches for ToA Estimation in Thin Composite Plates

Guided Wave-based Structural Health Monitoring (GWSHM) systems make a promising technique for monitoring and evaluating the integrity of many industrial structures like pipelines, aircraft, and civil structures. Composite structures used in aircraft must continue in flight-safe conditions when subjected to various levels of damage and operating conditions, such as stress, load, temperature, humidity, during manufacturing and operational usage. Even though the GWSHM system has the capability to observe the structure integrity continuously, it requires a significantly high sampling rates that become a burden while recording and transmitting the data for continuous monitoring. Recording data with a high sampling rate results in high energy consumption during transmitting/uploading, resulting in a bottleneck issue for modern embedded SHM systems that may be battery-operated and/or have a wireless connection. One possible solution is applying compression during the acquisition stage, thereby keeping only the relevant information. This article proposes a compressed sensingbased framework for estimating the time of arrival (ToA), which is a key parameter in signal recovery, damage detection, localization, and imaging applications. In this framework, the ToA is estimated by solving a sparse deconvolution problem with Orthogonal Matching Pursuit (OMP), investigating different sparsity-providing bases such as Discrete Fourier Transform (DFT), Discrete Wavelet Transform (DWT), and Discrete Cosine Transform (DCT). These bases can be combined with subsampling strategies for compression. For recovery, several grid-free techniques such as the Atomic Norm Minimization (ANM) and parametric high-resolution ToA estimators such as Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT), are explored. The methods are tested on synthetically generated data as well as experimental measurements on composite plates. The results are compared to traditional methods for ToA estimation using the maximum peak of the envelope of the Hilbert transform of the received signal, providing a complete framework for resource-efficient ToA estimation in SHM applications.