A Physics-Informed Matching Pursuit Framework for Damage Detection in Pipes

B. Ferrándiz, Sebastian Rodriguez, R. Hodé, L. Dolbachian, N. Mechbal, F. Chinesta, Marc R'ebillat

Guided wave testing (GWT) is widely employed nowadays in the structural health monitoring (SHM) of plate-like and tubular components, offering long-range inspection capabilities and sensitivity to local geometric and material discontinuities. However, practical use remains challenged by the complexity of GW signals: multimodal propagation, dispersion, and multiple reflections from boundaries or attachments often mask the influence of small or closely spaced defects. Robust signal-decomposition tools are therefore essential to isolate relevant wave packets and extract interpretable features for reliable diagnostics. This work proposes a physics-informed matching pursuit (MP) framework [1,2] for damage detection in pipes. MP decomposes a measured waveform into a sparse expansion of propagated basis atoms—here referred to as initial wave packets (IWPs)—enabling the separation of overlapping components and filtering of noise. The incorporation of dispersion curves and mode shapes computed via the semi-analytical finite element (SAFE) method improves interpretability, enforces physical realism, and mitigates the selection of spurious, non-physical atoms [3]. The methodology is validated on a reference experimental setup consisting of a pipe instrumented with piezoelectric transducers. Signals are collected under pristine and damaged conditions, with defect size and number progressively increased to induce measurable perturbations in the received waveforms. SAFE simulations are used to construct the physics-informed model, after which MP is applied to extract wave packets and quantify variations in atom coefficients associated with damage. The approach also enables rapid switching between IWPs, as most information is retained across input cases, supporting efficient analysis. Results show that the proposed framework enhances defect detectability while maintaining high interpretability. Embedding modal information guides MP toward atoms that match expected guided-wave characteristics, resulting in cleaner decompositions, lower residual energy, and improved separation of overlapping reflections. The sparse representations make defect-induced changes more evident, supporting earlier and more reliable identification of damage signatures. Overall, this study demonstrates that incorporating wave physical constraints into sparse-decomposition algorithms provides a powerful means for fast, accurate, and interpretable processing of guided-wave signals in pipe inspection. The framework is general and can be extended to other geometries, sparse-representation techniques, and incorporated into machine-learning-based automated SHM methods. References [1] S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries”, IEEE Transactions on Signal Processing, vol. 41, pp. 3397–3415, 1993. [2] S. Rodriguez, M. Rébillat, S. Paunikar, P. Margerit, E. Monteiro, F. Chinesta, and N. Mechbal, “Single atom convolutional matching pursuit: Theoretical framework and application to Lamb waves based structural health monitoring”, Signal Processing, vol. 231, pp. 1650–1684, 2025. [3] J. Rostami, P.W.T Tse, and Z. Fang, "Sparse and Dispersion-Based Matching Pursuit for Minimizing the Dispersion Effect Occurring when Using Guided Wave for Pipe Inspection", Materials, vol. 10, pp. 622, 2017.