Geometric Phase Sensing Using Cross-Correlations for Structural Anomaly Detection Under Broadband and Stochastic Excitations

This study demonstrates a novel nondestructive evaluation (NDE) method that combines geometric phase sensing with cross-correlation processed acoustical responses, enabling the detection of structural anomalies even when the acoustic excitation is stochastic and the source characteristics are variable. Traditional ultrasonic techniques, which depend on impulse responses from known source locations to capture wave transmission behavior, often fail under stochastic excitations due to incoherent phase alignment and unpredictable wave paths. The proposed method applies cross-correlation between a fixed reference site and other sensor locations to refine the acoustic field representation, enabling physically meaningful geometric phase extraction through the dot product of two state vectors representative of the acoustic field in a high-dimensional complex Hilbert space. This allows detection of both excitation-induced field asymmetries and subtle nonlinearities. Experimental validation using laser Doppler vibrometry on a circular IN625 plate demonstrates that this approach preserves excitation-induced field asymmetries while remaining sensitive to structural perturbations such as mass defects. The cross-correlation geometric phase change (CC-Δφ) spectra reveal modal differences across excitation conditions, even under white noise, where geometric phase without cross-correlation (Δφ) remains centered near 90 deg, obscuring structural insights. The method also detects mass-induced effects, showing increased average CC-Δφ compared to the no-mass case under the same excitation condition. These results establish a foundation for a robust, non-contact, source-independent NDE technique, suitable for operation under variable and uncontrolled excitation scenarios.