Purpose <p>Early micro-crack detection in plate structures using linear ultrasonics is limited by low sensitivity and strong dependence on historical baselines. This study aims to develop a baseline-free nonlinear indicator for quantitative micro-crack sizing by combining Lamb-wave mixing with a Four-State Phase-Cycling Isolation (SPI-4) protocol.</p> Methods <p>A baseline-free nonlinear response coefficient (NLRC) was defined as ,where is the SPI-4-isolated mixing component and and are the two fundamentals obtained from a shared-settings dual-spectrum readout under identical gate, window, zero-padding, and front-end gain. Finite-element simulations and experiments were conducted on 1.6-mm aluminium plates. Modal – analysis was used to verify the intended excitation at and and the predominant reception at . Probability-of-detection (POD) analysis was further performed to assess reliability.</p> Results <p>Under matched readout settings and within a narrow operating band, multiplicative path-gain factors largely canceled in the NLRC ratio, making the indicator effectively baseline-free. Simulations showed that NLRC remained nearly invariant over wide drive-level variations, while experiments demonstrated a monotonic increase in NLRC with crack length across five propagation paths. The crack-length dependence was well described by , enabling path-aware quantitative sizing with light calibration. The modal analysis confirmed small wavenumber mismatch and coherent accumulation of the mixed component. The pooled POD analysis yielded an threshold, indicating high sensitivity at a low false-alarm level.</p> Conclusion <p>The proposed NLRC/SPI-4 framework provides a practical and quantitatively reliable structural health monitoring approach for early micro-crack detection and sizing in plates. By reducing sensitivity to multiplicative drift and minimizing reliance on pristine historical baselines, it offers improved robustness and deployment potential for baseline-free nonlinear Lamb-wave inspection.</p>

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Baseline-Free Nonlinear Response Coefficient for Quantitative Micro-Crack Sizing in Plates via SPI-4 Lamb-Wave Mixing

  • Peijiang Li,
  • Ting You

摘要

Purpose

Early micro-crack detection in plate structures using linear ultrasonics is limited by low sensitivity and strong dependence on historical baselines. This study aims to develop a baseline-free nonlinear indicator for quantitative micro-crack sizing by combining Lamb-wave mixing with a Four-State Phase-Cycling Isolation (SPI-4) protocol.

Methods

A baseline-free nonlinear response coefficient (NLRC) was defined as ,where is the SPI-4-isolated mixing component and and are the two fundamentals obtained from a shared-settings dual-spectrum readout under identical gate, window, zero-padding, and front-end gain. Finite-element simulations and experiments were conducted on 1.6-mm aluminium plates. Modal – analysis was used to verify the intended excitation at and and the predominant reception at . Probability-of-detection (POD) analysis was further performed to assess reliability.

Results

Under matched readout settings and within a narrow operating band, multiplicative path-gain factors largely canceled in the NLRC ratio, making the indicator effectively baseline-free. Simulations showed that NLRC remained nearly invariant over wide drive-level variations, while experiments demonstrated a monotonic increase in NLRC with crack length across five propagation paths. The crack-length dependence was well described by , enabling path-aware quantitative sizing with light calibration. The modal analysis confirmed small wavenumber mismatch and coherent accumulation of the mixed component. The pooled POD analysis yielded an threshold, indicating high sensitivity at a low false-alarm level.

Conclusion

The proposed NLRC/SPI-4 framework provides a practical and quantitatively reliable structural health monitoring approach for early micro-crack detection and sizing in plates. By reducing sensitivity to multiplicative drift and minimizing reliance on pristine historical baselines, it offers improved robustness and deployment potential for baseline-free nonlinear Lamb-wave inspection.