Bayesian waveform inversion for structural parameter estimation using narrow spectral characteristics of guided waves

The non-destructive mechanical evaluation of engineering materials and structural components is essential for modern structural health monitoring. However, conventional ultrasonic-based parameter identification methods rely on wave propagation characteristics over a wide frequency range, typically requiring comprehensive data acquisition systems, multi-frequency measurements, and associated complex multi-domain processing. To simplify practical deployment, this study develops an innovative waveform-inversion framework that operates on narrow spectral characteristics at a single operating frequency, enabling quantitative identification of dimensional and material parameters from a single pitch-catch measurement. The framework combines signal representation and parameter identification in a unified probabilistic scheme, enabling an interpretable mapping between measured waveforms and structural properties. In the forward wavefield modeling, sparse Bayesian regularization is employed to select relevant sub-waves from a candidate waveform dictionary and weight them to synthesize the predicted waveform. In the backward optimization process, an adaptive sequential Monte Carlo (ASMC) scheme performs Bayesian misfit minimization between the predicted and measured waveforms to infer structural properties and their posterior uncertainties. Numerical and experimental studies on homogeneous plate-like structures are conducted to validate the practicality and effectiveness of the proposed methodology, treating thickness and Young’s modulus as the unknown structural parameters. The results confirm that independent structural parameters, along with their uncertainties, can be reliably identified from fast and cost-effective experimental measurements acquired using only a single pair of piezoelectric transducers. Moreover, the waveform inversion-based framework provides an intuitive validation of the inversion outcome through direct visual comparison between reconstructed and experimental waveforms.