Structural damage detection utilizing probabilistic divergence of FFT coefficient ratios and DBSCAN cluster algorithm

In structural health monitoring (SHM), uncertainties from environmental noise and modeling errors affect damage detection accuracy. This paper introduces a new concept: the Fast Fourier Transform Coefficient Ratio (FFTCR), which develops a damage indicator (DI) based on a probability model. The method involves calculating the probability density function (PDF) of the ratio and the Jensen-Shannon divergence (JSD) square root distance, which measures similarity between probability distributions. A baseline threshold is proposed using the Markov Chain Monte Carlo (MCMC) method and Monte Carlo discordancy test to handle uncertainties in statistical parameters. The robustness of the method is validated through the DBSCAN algorithm, which distinguishes damage states by applying a 1% exclusive threshold to the clustering results. The method requires no postprocessing of raw data, relying solely on response measurements. It is validated through two experiments, including laboratory ambient vibration tests and a field test on a bridge under forced vibration. Results show superior accuracy and broader applicability compared to the Mahalanobis Squared Distance (MSD) method.