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arxiv: 2606.03933 · v1 · pith:6ATUQPFEnew · submitted 2026-06-02 · 💻 cs.CE

Physics-Informed Single Atom Matching Pursuit: Guided-Waves Wavenumbers and Propagation Distance Estimation for Damage Localization in Structural Health Monitoring

Sebastian Rodriguez , Borja Ferrandiz , Francisco Chinesta , Nazih Mechbal , Marc R\'ebillat This is my paper

Pith reviewed 2026-06-28 07:46 UTC · model grok-4.3

classification 💻 cs.CE
keywords guided wavesstructural health monitoringmatching pursuitdamage localizationphysics-informedsignal decompositionwavenumber estimationelliptical localization
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The pith

Physics-informed matching pursuit extracts modal wavenumbers and propagation distances to enable elliptical damage localization.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents PISAMP as a signal decomposition technique that incorporates the physical principles of guided-wave propagation into a low-dimensional matching pursuit framework. This embedding of constraints allows the method to separate multiple dispersive modes and directly identify modal wavenumber functions along with propagation distances between the actuator, damage, and sensors. These distances then support damage localization through established elliptical techniques. The approach offers an efficient and interpretable alternative to data-driven methods in structural health monitoring of thin-walled components.

Core claim

The PISAMP method embeds strong physical constraints into a low-dimensional and computationally efficient signal representation grounded in wave propagation physics. This enables the direct identification of modal wavenumber functions and propagation distances between actuator, damage and sensors, which subsequently allow damage location using elliptical localization techniques.

What carries the argument

The Physics-Informed Single Atom Matching Pursuit (PISAMP) representation, which incorporates wave propagation physics to decompose signals and extract physically meaningful features like wavenumbers and distances.

Load-bearing premise

Strong physical constraints embedded in the low-dimensional matching pursuit representation allow accurate separation of dispersive modes and reliable extraction of propagation distances without needing adjustments for interference.

What would settle it

Observation of extracted distances that produce damage location errors exceeding expected tolerances when applied to elliptical localization on structures with known damage positions.

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes the Physics-Informed Single Atom Matching Pursuit (PISAMP) algorithm for decomposing guided-wave signals in structural health monitoring. It embeds dispersion relations and propagation physics into a low-dimensional matching-pursuit dictionary so that a single atom per mode directly yields modal wavenumber functions k(f) and actuator-damage-sensor distances d; these distances are then fed into standard elliptical localization.

Significance. If the physics embedding succeeds in separating modes and recovering unique distances without post-processing, the method would supply an interpretable, computationally light alternative to purely data-driven or finite-element approaches for multi-mode dispersive signals. The explicit link from extracted d values to elliptical localization is a concrete, falsifiable output.

major comments (1)
  1. [Method / atom construction (implicit in abstract and § on dictionary design)] The guided-wave atom is constructed with phase factor exp(-j k(f) * d). Only the product k(f)*d appears in the observed phase; any pair (α k(f), d/α) produces an identical atom. The manuscript does not state how the single-atom parameterization, the chosen reference distances, or the multi-sensor consistency constraints explicitly break this scaling invariance. Without such a mechanism the extracted d values remain non-unique, undermining the subsequent elliptical localization claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful review and for identifying the scaling invariance issue in the atom parameterization. We address the major comment below and will revise the manuscript to explicitly clarify the resolution mechanism.

read point-by-point responses

  1. Referee: [Method / atom construction (implicit in abstract and § on dictionary design)] The guided-wave atom is constructed with phase factor exp(-j k(f) * d). Only the product k(f)*d appears in the observed phase; any pair (α k(f), d/α) produces an identical atom. The manuscript does not state how the single-atom parameterization, the chosen reference distances, or the multi-sensor consistency constraints explicitly break this scaling invariance. Without such a mechanism the extracted d values remain non-unique, undermining the subsequent elliptical localization claim.

    Authors: We agree that the scaling invariance must be explicitly addressed. In the PISAMP formulation the wavenumber function k(f) is constrained by the physics-informed dictionary to the dispersion relation determined by the plate thickness and material properties; this fixes the frequency dependence and prevents arbitrary rescaling of the function shape. The multi-sensor consistency constraints further enforce that the recovered distances d produce geometrically consistent source locations across all actuator-sensor pairs, which uniquely determines the absolute scale. Reference distances are taken from the known experimental geometry. We acknowledge that the manuscript does not spell out this mechanism in sufficient detail. We will add a dedicated paragraph in the revised Methods section explaining how the combination of physical dispersion constraints, reference distances, and cross-sensor consistency resolves the ambiguity and guarantees unique d values for the subsequent elliptical localization step. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The provided abstract and description frame the PISAMP method as embedding independent physical constraints from guided-wave propagation (dispersion relations, phase factors) into a low-dimensional matching pursuit dictionary to extract modal wavenumbers and distances. No quoted equations or steps show a quantity defined in terms of itself, a fitted parameter from the target data renamed as a prediction, or a central claim resting solely on self-citation chains. The derivation is presented as relying on external physical principles rather than tautological reduction to inputs, qualifying as self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review supplies no concrete free parameters, axioms, or invented entities; the central claim rests on the unstated premise that wave physics can be compactly encoded as atom constraints without loss of accuracy.

axioms (1)
  • domain assumption Wave propagation physics can be embedded as strong constraints in a low-dimensional signal representation
    Stated in abstract as the grounding of the PISAMP method.

pith-pipeline@v0.9.1-grok · 5802 in / 1113 out tokens · 19120 ms · 2026-06-28T07:46:19.853658+00:00 · methodology

discussion (0)

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Reference graph

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