This paper introduces a fully automated modal identification algorithm based on the Multivariate Variational Mode Decomposition (MVMD) of free vibration responses to determine structural modal parameters. Addressing the challenge of setting MVMD parameters, we introduce a fusion parameter combining power spectral cross-entropy with reconstruction error as an adaptive fitness function in the optimization algorithm, enabling optimal parameter selection. Then, modal frequencies, damping ratios, and shapes of structures can be extracted from autonomously decomposed Intrinsic Mode Functions by employing the principle of modal superposition and least squares fitting without manual parameter adjustments. Validated by a four-degree-offreedom numerical model, the method demonstrated accurate, automatic modal parameter identification. The method was further applied to a subway tunnel structure model experiment. Comprehensive modal identification was conducted on tunnel structures under varying degrees of damage. The results validate the proposed method's effectiveness and reveal the damaged segment structure's multimodal parameter variation patterns and surrounding soil.

Numerical models play a crucial role in the study and understanding of cultural heritage structures, serving as valuable tools for predicting their behavior under diverse and prospective scenarios. They are however affected by various uncertainties, which impact can be mitigated through the calibration of model parameters. For heritage structures, where testing is usually restricted to the use of non-destructive techniques, and often unable to directly assess the inherent heterogeneity of the materials, a calibration approach can prove particularly useful to obtain a working model. This work applies a Bayesian model updating procedure to material-related uncertainties affecting a recently developed finite element model of the Leaning Tower of Pisa also comprising the underlying soil layers. The procedure takes advantage of literature modal data of the Tower and uses a general Polynomial Chaos Expansion-based surrogation of the model to evaluate sensitivity and ease the computational burden that comes with the probabilistic framing of the updating problem. The results represent the first probabilistic model-based assessment of material uncertainties in a three-dimensional finite element model of the Leaning Tower of Pisa. They shed some light into the value of specific modal information, while the use of analytical surrogation paves the way for the future design of a real-time updating procedure for monitoring and damage detection.