Marc Rébillat

Sebastian Rodriguez, Borja Ferrandiz, Francisco Chinesta et al.

Structural Health Monitoring (SHM) aims at the real-time monitoring of the integrity of engineering structures, with Guided-waves (GWs) providing high sensitivity to damage presence and to ageing effects for thin-walled components. In conventional GW-based SHM, a bonded piezoelectric transducer (PZT) emits a short tone burst that produces an Initial Wave Packet (IWP) propagating through the structure. As this packet interacts with boundaries and potential damages, additional scattered wave packets are produced. A major limitation of such approaches lies in the simultaneous excitation of multiple dispersive GW modes by a single PZT, which significantly complicates signal interpretation and damage monitoring. In this context, this work proposes the Physics-Informed Single Atom Matching Pursuit (PISAMP) method, a signal decomposition method grounded in the physical principles governing wave propagation. In contrast with purely data-driven or numerically intensive techniques, the proposed approach embeds strong physical constraints into a low-dimensional and computationally efficient signal representation. This formulation enables the direct identification of key physically meaningful features, including modal wavenumber functions and propagation distances between actuator, damage and sensors. These extracted features, especially source-damage-sensor distances, allows to subsequently perform damage location using well established Elliptical Localization techniques. The principal novelty of this study lies in integrating wave propagation physics into a compact signal decomposition framework and developing an interpretable damage localization methodology for GW-SHM applications.

Shawn L. Kiser, Mikhail Guskov, Marc Rébillat et al.

Identification of nonlinear dynamical systems has been popularized by sparse identification of the nonlinear dynamics (SINDy) via the sequentially thresholded least squares (STLS) algorithm. Many extensions SINDy have emerged in the literature to deal with experimental data which are finite in length and noisy. Recently, the computationally intensive method of ensembling bootstrapped SINDy models (E-SINDy) was proposed for model identification, handling finite, highly noisy data. While the extensions of SINDy are numerous, their sparsity-promoting estimators occasionally provide sparse approximations of the dynamics as opposed to exact recovery. Furthermore, these estimators suffer under multicollinearity, e.g. the irrepresentable condition for the Lasso. In this paper, we demonstrate that the Trimmed Lasso for robust identification of models (TRIM) can provide exact recovery under more severe noise, finite data, and multicollinearity as opposed to E-SINDy. Additionally, the computational cost of TRIM is asymptotically equal to STLS since the sparsity parameter of the TRIM can be solved efficiently by convex solvers. We compare these methodologies on challenging nonlinear systems, specifically the Lorenz 63 system, the Bouc Wen oscillator from the nonlinear dynamics benchmark of Noël and Schoukens, 2016, and a time delay system describing tool cutting dynamics. This study emphasizes the comparisons between STLS, reweighted $\ell_1$ minimization, and Trimmed Lasso in identification with respect to problems faced by practitioners: the problem of finite and noisy data, the performance of the sparse regression of when the library grows in dimension (multicollinearity), and automatic methods for choice of regularization parameters.