Physics‐Informed Machine Learning–Assisted Assessment of Multiple Incipient Cracks Using Broadband Modal Frequencies From Piezoelectric Wafers Bonded on a Beam

Conventional crack evaluation techniques that utilize the first few narrowband modal frequencies often suffer from limited accuracy and robustness, particularly when assessing multiple incipient cracks in a beam (i.e., crack–depth ratio < 0.2). To overcome these limitations, this study proposes a crack assessment method that leverages broadband modal frequencies measured from surface‐bonded piezoelectric wafers up to the beam’s cut‐off frequency. The proposed approach employs a closed‐form frequency equation derived from the phase‐closure principle, which accurately predicts the fractional reduction in modal frequencies caused by incipient cracks. This equation enables the construction of a large database of fractional reduction in modal frequencies for various multiple incipient crack scenarios with minimal computational cost. Using this database, we constructed a physics‐informed machine learning model to identify the number of incipient cracks. Next, we estimated the locations and depths of the cracks by minimizing the least‐squares error between the measured and calculated fractional reductions using the closed‐form frequency equation. In addition, the optimal grid resolution was determined using a bilinear fitting method to reduce the computation time required to solve the minimization problem. The proposed method is evaluated through blind tests using numerical simulation datasets from finite element analysis and experimental datasets from piezoelectric wafers bonded on beams with various multiple‐crack scenarios. The blind‐test results provide insight into the diagnostic capability and robustness of the proposed approach, demonstrating its practical applicability for reliable crack‐number prediction under experimental measurement uncertainty and supporting its potential use in structural health monitoring of beam‐like structures.