PSI - Issue 78

Akshay Rai et al. / Procedia Structural Integrity 78 (2026) 891–898

894

The SCR is defined as the ratio of spectral centroids between real ( SC real ) and generated ( SC gen ) distributions: SCR = SC real / SC gen . An SCR value close to 1 indicates strong spectral alignment, while deviations suggest frequency shifts in the reconstructed signals. 2. Spectral Bandwidth Ratio (SBR): This metric indicates the spread of energy around the spectral centroid. The spectral bandwidth (SB) is defined as: SB = F i = 1 ( f i − SC ) 2 · S ( f i ) F i = 1 S ( f i ) (4) The SBR compares the spread of frequency components in real ( SB real ) and generated signals ( SB gen ): SBR = SB real / SB gen . An SBR value close to unity means the generative model accurately replicates the variability observed in real data. At the same time, deviations may indicate frequency spread mismatches, signalling possible anomalies or signal degradation. 3. Spectral Entropy Ratio (SER): measures the randomness in spectral distribution, defined by the normalised spectral power P ( f i ):

F i = 1

SE = −

P ( f i ) log( P ( f i ) + ϵ )

(5)

where ( P ( f i ) = S ( f i ) / F j = 1 S ( f j ) and ϵ ensures numerical stability. The SER is calculated as: SER = SE real / SE gen . A SER close to 1 indicates consistent entropy, while significant deviations suggest structural issues or a loss of spectral richness. These metrics, which incorporate thermal history and frequency-domain errors, enhance the diagnostic e ffi cacy in post-earthquake assessments.

3. The Consoli Palace SHM system

The Consoli Palace in Gubbio, Italy, a 14th-century monument that lies in a seismically active area, serves as a testbed for the proposed framework. An SHM system was installed in July 2017, featuring 12 uniaxial piezoelectric accelerometers (PCB393B12 A1-A12) and six K-type thermocouple temperature sensors, with data collected every 30 minutes from specific sensors. For the current problem, only nine accelerometers (A1-A6, A10-A12) and two thermocouples ( T 0 internal and T 1 external), which are specifically monitoring the ambient temperature, were used. The sensor placements are shown in Figure 1. On May 15, 2021, a low-intensity seismic event (Mw 3.9) occurred, causing minimal structural damage but resulting in a small decline (up to 2%) in the palace’s average resonant frequencies.

3.1. Description of training and testing datasets

For this study, two datasets were meticulously curated. The Training Dataset comprised exclusively of ”healthy” structural responses from the Consoli Palace, collected over the week leading up to the May 15, 2021, earthquake (from May 2nd to May 8th, 2021). This established a baseline of 336 samples, evenly split into training data and a proxy for unseen healthy conditions. The Testing Dataset featured post-earthquake recordings from May 15, 16, and 30, 2021, representing “damaged” samples to evaluate immediate and longer-term structural changes. This dataset also included unseen healthy samples from February to early May 2021, allowing for an assessment of the model’s robustness against varying seasonal environmental conditions. The total number of post-earthquake samples was 122. Each sample consisted of multivariate sensor recordings from nine accelerometers and two thermocouples ( T 0 and T 1 ). The raw signals underwent a series of preprocessing steps: they were filtered, transformed into Cross Spectral Density (CSD) matrices, and finally, Singular Value Decomposition (SVD) was applied to extract 257 dominant singular values per sample. These dominant SVs, along with normalised internal and external temper ature readings, were used as inputs for the anomaly detection model. This multi-step preprocessing ensures nu merical stability, computational e ffi ciency, and e ff ective model training by transforming high-dimensional, noisy time-domain signals and temperature data into a structured, lower-dimensional representation suitable for the CAE. The final input for each CAE sample is a multivariate vector of shape (257, 3), combining the 257-bin dominant SV distribution with the two temperature channels. The steps to calculate the temperature-compensated metrics for a reconstructed signal is explained in Figure 2