PSI - Issue 78

Shahin Sayyad et al. / Procedia Structural Integrity 78 (2026) 277–284

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supports the suitability of GA for parameters that are more sensitive or difficult to identify. In the case of unit weights (γ 1 to γ 5 ), a wider variation in error is observed. Notably, γ 4 and γ 5 have the highest estimation errors, particularly for GA under F 1 . GA with F 2 demonstrates a marked improvement in estimating γ 5 , reducing the error by nearly half compared to PSO. Overall, GA shows more consistent and lower errors across all unit weight parameters under F 2 . In conclusion, GA relatively outperformed PSO in most cases and showed greater reliability, particularly for challenging parameters such as Poisson’s ratios and unit weights. Additionally, the use of mode shapes (as in 2 ) particularly enhanced calibration accuracy, though fewer frequencies were used. In the following table, the results of model calibration using both GA and PSO are presented, considering only the natural frequencies of the first three modes due to a lack of highly reliable experimental data for higher modes. Based on the results of the first phase, it is concluded that these results can be improved by incorporating the MAC term into the objective function, along with the frequencies of higher modes.

Table. 3 Values of updated parameters using PSO and GA under different objective functions, considering the first three modes.

N Mechanical Parameters ParameterBounds [L b , U b ]

PSO - F1 - SS: 50, MI: 200 GA - F 1 - PS: 10, NG: 20 Unit

1 2 3 4 5 6 7 8 9

E 1 (Bell Chamber)

[1000, 3000] [1000, 3000] [1000, 3000] [1000, 3000] [1000, 3000] [0.1, 0.2]

1000.00 2000.00 2000.00 2000.00 1827.71

1136.25 2040.18 2053.57 2236.22 1879.03

MPa MPa MPa MPa MPa

E 2 (Shaft)

E 3 (Base/Battered Wall)

E 4 (Vault/Arch) E 5 (Stair Ramps) ν 1 (Bell Chamber)

0.20 0.20 0.20 0.16 0.15

0.14 0.19 0.15 0.14 0.20

- - - - -

ν 2 (Shaft)

[0.1, 0.2] [0.1, 0.2] [0.1, 0.2] [0.1, 0.2]

ν 3 (Base/Battered Wall)

ν 4 (Vault/Arch) ν 5 (Stair Ramps) γ 1 (Bell Chamber)

10 11 12 13 14 15

[10000, 20000] [10000, 20000] [10000, 20000] [10000, 20000] [10000, 20000]

10439.44 19620.00 17301.42 17404.45 17057.77

12003.52 17385.38 12933.21 15823.33 13793.74

N/m N/m N/m N/m N/m

3 3 3 3 3

γ 2 (Shaft)

γ 3 (Base/Battered Wall)

γ 4 (Vault/Arch) γ 5 (Stair Ramps)

This study demonstrated that although OpenSeesPy is primarily recognized for its nonlinear modeling and simulation of the seismic response of structural and geotechnical systems, it also offers a lesser-known but valuable capability: its suitability for automated finite element model calibration and integration with optimization algorithms. Future improvements will include modeling the masonry bell tower with orthotropic material properties to enhance calibration accuracy. To accelerate finite element analyses, enable real-time calibration, and ultimately achieve a digital twin of the structure, the development of a surrogate model is identified as the next goal of this research. References Altunişik, A. C., Karahasan, O. Ş., Okur, . Y., Kalkan, E., & Ozgan, K. (2019). inite element model updating and dynamic an alysis of a restored historical timber mosque based on ambient vibration tests. Journal of Testing and Evaluation, 47(5), 3533-3562. Ereiz, S., Duvnjak, I., & Jiménez-Alonso, J. F. (2022). Review of finite element model updating methods for structural applications. Structures, Eskew, E. L., & Jang, S. (2017). Remaining stiffness estimation of buildings using incomplete measurements. Structural Control and Health Monitoring, 24(4), e1899. Gad, A. F. (2024). Pygad: An intuitive genetic algorithm python library. Multimedia tools and applications, 83(20), 58029-58042. Kennedy, J., & Eberhart, R. (1995, 27 Nov.-1 Dec. 1995). Particle swarm optimization. Proceedings of ICNN'95 - International Conference on Neural Networks, Li Rosi, D., Contrafatto, L., & Varum, H. (2024). 3D FE modelling strategies for ancient masonry bell towers. Updating of mechanical parameters and boundary conditions. 18th World Conference on Earthquake Engineering (WCEE2024), Miranda, L. J. (2018). PySwarms: a research toolkit for Particle Swarm Optimization in Python. Journal of Open Source Software, 3(21), 433. Nozari, A., Behmanesh, I., Yousefianmoghadam, S., Moaveni, B., & Stavridis, A. (2017). Effects of variability in ambient vibration data on model updating and damage identification of a 10-story building. Engineering Structures, 151, 540-553. Zhu, M., McKenna, F., & Scott, M. H. (2018). OpenSeesPy: Python library for the OpenSees finite element framework. SoftwareX, 7, 6-11. https://doi.org/https://doi.org/10.1016/j.softx.2017.10.009