PSI - Issue 78

Livia Fabbretti et al. / Procedia Structural Integrity 78 (2026) 823–830

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Fig. 2. (a) Force-displacement behavior law of FPS isolators; (b) Schematic representation of the simplified 6DOF model; (c) Simplified 6DOF model in SAP2000.

Due to the impossibility of identifying the key isolator parameters using real data, there is the need to implement a dynamic identification methodology based on the use of simulated data as a surrogate for experimentaldata. This consists of an automatic optimization procedure that enables the calibration of the isolators’ parameters by minimizing the discrepancy between simulated outputs and reference targets. In the future, with the availability of real monitoring data from seismic events that have activated isolator sliding, this procedure will allow immediate identification of new optimal parameter values by simply updating the input and output data. Model calibration through real data will then allow the model to be used during seismic events: by comparing simulated and measured outputs, significant variations in isolator parameters potentially due to damage, structural modifications, or isolator degradation can be identified.

3. Dynamic identification methodology 3.1. Simplified six-degree-of-freedom model

The dynamic identification methodology can be mainly addressed with two strategies: an analytical approach through the equations of motion or an approach based on artificial intelligence algorithms, i.e., self-optimizing routines implemented in software such as Python or MATLAB. In this research, the second method was chosen for its simplicity and efficiency. The simplified structural model allows describing the dynamic behavior of the isolated system while keeping the computational complexity within manageable limits. It consists of two lumped masses, M 2 and M 3 , which respectively represent the aggregated mass of levels 1-2 and levels 3-4 of the building (Fig. 2b). The masses are evaluated according to a load analysis on the complete finite element model, following the criteria of the 2018 Italian Building Code, considering all permanent loads and, as variable loads, only the live loads. The equivalent superstructure stiffness, K 23 , is calculated by performing static analyses again on the complete model, applying known forces and measuring the resulting displacements so as to derive K = F/δx . The stiffness of the pilotis, K 01 , is determined as the parallel sum of the individual stiffnesses of the columns. Regarding the stiffness of the isolators, K is , this has been determined considering the target values of the isolator parameters reported in Table 1. This includes the vertical stiffness K V and the initial stiffness K 1 , both calculated as the sum of the individual stiffnesses of the thirty-eight isolators, and the effective stiffness K eff , calculated through an iterative procedure similar to that used in Fabbretti et al. (2025), considering the a priori uncertainty on d max . In the resulting model, the structure thus corresponds to a segmented composite beam, with a single fixed-base constraint and a nonlinear link (NL link) representing the isolator (Fig. 2c). The system is considered to have six degrees of freedom, corresponding to the quantities that the monitoring system will be able to record: acceleration over time, 3̈ (t), at point 3 on the roof (in both horizontal directions); acceleration over time, 2̈ (t), at point 2 at the first slab level (in x and y directions); and isolator deformation over time, 2 − 1 (t), also in x and y directions. Additionally, the three components of ground acceleration, 0̈ (t), including the vertical one, are also considered known.