PSI - Issue 78

Marco Martino Rosso et al. / Procedia Structural Integrity 78 (2026) 301–308

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modal analysis provided the results reported in Table 2 and is visually inspected in Figure 2. The modal results are also in agreement with previous studies on the same un-retrofitted building conducted by Rebecchi et al (2023).

Fig. 2. STKO FEM model modal analysis mode shape visualization.

Mode [Hz] Mass-X [%]

Table 2. STKO FEM reference modal analysis results for Building 1: natural frequency and mass participating ratios.

Mass-Y [%]

Mass-Z [%]

Rot. Mass X [%]

Rot. Mass Y [%]

Rot. Mass Z [%]

Mode Description

1 2 3 4 5 6

1.83 5.43 5.84 7.68 8.31 8.35

0.00 0.00 0.00 0.00 0.00 86.5 86.50

83.73

0.00 0.00 0.00 0.00 0.00

14.83

0.00 0.00 0.00 0.00 0.00 10.7 10.66

0.00

1° Bend. Y 1° Torsion

0.00

0.00

85.59

11.33

60.30

0.00 0.00 0.00 0.00 85.6

2° Torsion + Bend. Y

0.00 1.65 0.00 96.7

0.00 6.02

1° Bend. X

Local 1° Story in phase

0.000015 0.00

Local 1° Story in counter-phase

Total

0.0

81.1

With reference provided by the modal properties of the FEM model, OMA have been conducted on the White Noise time histories collected from the two RC buildings considering only the six sensor per building directly attached to the RC frame as depicted in Figure 1. Modal parameters were extracted using frequency domain and time domain techniques implemented in pyOMA2 software, see Pasca et al. (2024). In the frequency domain, power spectral density matrices were estimated by Welch averaging and decomposed by Frequency Domain Decomposition (FDD). Candidate natural frequencies were taken at peaks of the first singular value, and the associated singular vectors provided initial mode shape estimates. In parallel, stochastic subspace identification (SSI) was applied to the resampled time histories over a range of model orders, and a stabilization diagram was constructed to identify poles that stabilized in frequency, damping, and mode shape. Mode identification and validation combined several independent checks (hard and soft stabilization criteria) to distinguish physical modes from numerical spurious ones. Stabilized poles in the SSI diagrams were accepted when relative changes in frequency were within approximately 1 – 2%, absolute changes in damping were within about 5 – 1.0%, and mode shape consistency across adjacent model orders exceeded a high MAC threshold (typically ≥ 0.85). Among the various White Noise conditions, decimation factors have been parametrically analyzed in order to provide the best results in agreement with the reference FEM model. Indeed, the decimation factors for White Noise from 2 to 7 were set respectively to 10, 15, 20, 15, 10, 15 both for Building 1 and 2, except for Building 2 in White Noise 4 where 35 was set, Building 2 in White Noise 5 with a factor of 10, and Building 2 in White Noise 7 with a decimation factor of 10. Moreover, the SSI-cov algorithm requires the definition of two governing parameters that can affect the resolution of the stabilization diagram and the quality of the modal estimates, i.e. maximum order and the number of