Machine learning prediction of fundamental time periods of regular RC bare frame buildings: A comparative study with empirical code formulations for seismic disaster risk reduction

Aniket  N Bhalkikar; Jacob Alex Kollerathu

doi:10.64866/j.ijdscr.2026.10026

Authors

Aniket N Bhalkikar Civil Engineering Department, CHRIST (Deemed to be University), Bangalore, India Author
Jacob Alex Kollerathu Civil Engineering Department, CHRIST (Deemed to be University), Bangalore, India Author https://orcid.org/0000-0002-7057-2720

DOI:

https://doi.org/10.64866/j.ijdscr.2026.10026

Keywords:

Fundamental time period, Machine Learning (ML), Reinforced concrete frames, Ensemble boosting algorithms, ETABS API, Empirical period formula, Risk Reduction

Abstract

This study investigates the prediction of fundamental time periods of reinforced concrete (RC) bare-frame buildings using machine learning (ML) techniques as an alternative to empirical height-based code formulas. A synthetic dataset consisting of 292 RC frame configurations was generated through parametric modelling using the ETABS API, varying key structural parameters including building height, base width, height-to-base ratio, mass, and stiffness. Seven supervised ML regression algorithms—Linear Regression, Support Vector Regression, Decision Tree Regressor, Random Forest Regressor, Adaptive Boosting, Gradient Boosting, and XGBoost—were trained using 80% of the dataset and validated with 10-fold cross-validation. Model performance was evaluated using R², RMSE, MAE, and the a20 index and results compared against empirical formulations from IS 1893:2016 and prominent literature-based models. Ensemble boosting models exhibited superior accuracy, with AdaBoost achieving the highest predictive performance (R² = 0.969, MAE = 0.050s, a20 = 0.90). SHapley Additive exPlanations (SHAP) analysis revealed mass and stiffness as the most influential parameters controlling the time period, unlike code formulations dependent solely on height. Comparative analysis demonstrated that empirical models significantly overestimate or underestimate period values with large scatter, whereas ML-based predictions closely match calculated values with minimal deviation. The findings confirm the capability of ML models, particularly AdaBoost, to improve reliability in seismic design and risk assessment of existing RC frames. Future extensions may include neural network architectures and irregular structural configurations.

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References

Ahmad, F., Alasskar, A., Samui, P., Asteris, P., 2025. Machine learning-based graphical user interface for predicting high-performance concrete compressive strength: Comparative analysis of Gradient Boosting Machine, Random Forest, and Deep Neural Network Models. Frontiers of Structural and Civil Engineering 19, 1075–1090. https://doi.org/10.1007/s11709-025-1201-8.

Ajay Kumar, S., Pradeep Kumar, R., 2013. Earthquake behavior of reinforced concrete framed buildings on hill slopes, in: International Symposium on New Technologies for Urban Safety of Mega Cities in Asia (USMCA 2013), Hanoi, Vietnam.

Ali, D., Mahmood, R., Ahmed, M., 2025. Effect of steel bracing on seismic performance of reinforced concrete structures. SSRG International Journal of Civil Engineering 12, 96–104. https://doi.org/10.14445/23488352/IJCE-V12I7P108.

Arlekar, J.N., Murty, C.V., 2000. Ambient vibration survey of RC-frame buildings having brick masonry infill walls. Indian Concrete Journal 74, 581–588.

ASCE7-22, 2022. Minimum Design Loads and Associated Criteria for Buildings and Other Structures. American Society of Civil Engineers (ASCE), Washington, USA.

Badkoubeh, A., Massumi, A., 2017. Fundamental period of vibration for seismic design of concrete shear wall buildings. Scientia Iranica 24, 1010–1016. https://doi.org/10.24200/sci.2017.4084.

Balendra, T., Ma, Z., Tan, C., 2003. Design of tall residential buildings in Singapore for wind effects. Wind and Structures 6, 221–248. https://doi.org/10.12989/was.2003.6.3.221.

Banik, A., Chakma, T., Debbarma, P., Das, B., Sapu, R., Nath, J., Tripura, B., 2025. Effect of floor area ratio reduction on the fundamental period of RC buildings on flat and sloped terrains. Procedia Structural Integrity 70, 604–610. https://doi.org/10.1016/j.prostr.2025.07.096.

Bioud, N.-I., Oulad Laid, I., Benbouras, M., 2023. Estimating the fundamental period of infilled RC frames structures via deep learning. Urbanism. Architecture. Constructions 14, 59–80.

Breiman, L., 1996. Bagging predictors. Machine Learning 24, 123–140. https://doi.org/10.1007/BF00058655.

Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.J., 1984. Classification and Regression Trees. Wadsworth & Brooks/Cole, Monterey, CA.

Calitz, D., Markou, G., Bakas, N., Papadrakakis, M., 2023. Developing fundamental period formulae for steel framed structures through machine learning and automated algorithms, in: COMPDYN Proceedings. https://doi.org/10.7712/120123.10468.20613.

Chen, T., Guestrin, C., 2016. XGBoost: A scalable tree boosting system, in: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, p. 785–794. https://doi.org/10.1145/2939672.2939785.

Chengsheng, T., Huacheng, L., Bing, X., 2017. AdaBoost typical algorithm and its application research. MATEC Web of Conferences 139, 00222. https://doi.org/10.1051/matecconf/201713900222.

Cinar, O.F., Aldemir, A., Zervent, A., Yucel, O.B., Erberik, M.A., Anil, O., Askan, A., 2024. Fundamental period estimation of RC buildings by considering structural and nonstructural damage distributions through neural network. Neural Computing and Applications 24, 1329–1350. https://doi.org/10.1007/s00521-023-09107-6.

Cortes, C., Vapnik, V., 1995. Support-vector networks. Machine Learning 20, 273–297. https://doi.org/10.1007/BF00994018.

Di Sarno, D., Amiri, S., 2019. Period elongation of deteriorating structures under mainshock-aftershock sequences. Engineering Structures, 196https://doi.org/10.1016/j.engstruct.2019.109341.

Dietterich, T.G., 2000. Ensemble methods in machine learning, in: International Workshop on Multiple Classifier Systems, Lecture Notes in Computer Science, 1857, p. 1–15. https://doi.org/10.1007/3-540-45014-9_1.

Dilmaç, H., 2020. Influence of openings of infill wall on seismic vulnerability of existing RC structures. Structural Engineering and Mechanics 75, 211–227. https://doi.org/10.12989/sem.2020.75.2.211.

Ditommaso, R., Vona, M., Gallipoli, M., Mucciarelli, M., 2013. Evaluation and considerations about fundamental periods of damaged reinforced concrete buildings. Natural Hazards and Earth System Science 13, 1903–1912. https://doi.org/10.5194/nhess-13-1903-2013.

Elgohary, H.A., 2025. A comprehensive review and ANN analysis of empirical formulae for determining the fundamental period of multi-story RC moment resisting frames. Journal of Umm Al-Qura University for Engineering and Architecture https://doi.org/10.1007/s43995-025-00192-3.

Eurocode 8, 2004. Design of Structures for Earthquake Resistance – Part 1: General Rules, Seismic Actions and Rules for Buildings. European Committee for Standardization (CEN), Brussels, Belgium.

Gallipoli, M.R., Petrovic, B., Calamita, G., Tragni, N., Scaini, C., Barnaba, C., Parolai, S., 2023. Towards specific T–H relationships: FRIBAS database for better characterization of RC and URM buildings. Bulletin of Earthquake Engineering 21, 2281–2307. https://doi.org/10.1007/s10518-022-01594-7.

Giri, P., Bhatt, A., Gautam, D., Chaulagain, H., 2019. Comparison between the seismic codes of Nepal, India, Japan and EU. Asian Journal of Civil Engineering 20, 301–312. https://doi.org/10.1007/s42107-018-0102-8.

Goel, R.K., Chopra, A.K., 1997. Period formulas for moment resisting frame buildings. Journal of Structural Engineering 123, 1454–1461. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:11(1454).

Guo, J., Enokida, R., Li, D., Ikago, K., 2023. Combination of physics-based and data-driven modeling for nonlinear structural seismic response prediction through deep residual learning. Earthquake Engineering & Structural Dynamics 52, 2295–2571. https://doi.org/10.1002/eqe.3863.

Hadzima-Nyarko, M., Morić, D., Draganić, H., Štefić, T., 2015. Comparison of fundamental periods of reinforced shear wall dominant building models with empirical expressions. Tehnički Vjesnik 22, 685–694. https://doi.org/10.17559/TV-20140228124615.

Inel, M., Ozmen, H.B., Cayci, B.T., 2019. Determination of period of RC buildings by the ambient vibration method. Advances in Civil Engineering, 1213078https://doi.org/10.1155/2019/1213078.

IS 1893:2016, 2016. Criteria for Earthquake Resistant Design of Structures – Part 1: General Provisions and Buildings. Bureau of Indian Standards (BIS), New Delhi, India.

Jitteh, K., Song, Y., Wang, Z., Li, Y., Chen, J., 2025. A robust automated machine learning predictive model for natural period of buildings. Structural Engineering and Mechanics 94, 351–362. https://doi.org/10.12989/sem.2025.94.5.351.

Jose, A., Mishra, N., 2021. Seismic analysis of multistorey RC building with vertical setback and its retrofit strategies. Lecture Notes in Civil Engineering, 143https://doi.org/10.1007/978-981-33-6969-6_42.

Joseph, H., Quaranta, G., Carboni, B., Lacarbonara, W., 2024. Deep learning architectures for data-driven damage detection in nonlinear dynamic systems under random vibrations. Nonlinear Dynamics 112, 20611–20636. https://doi.org/10.1007/s11071-024-10270-1.

Kewate, S., Murudi, M., 2018. A critical study on empirical period–height relationship for reinforced concrete moment resisting frame buildings. Indian Concrete Journal 92, 89–94. https://doi.org/10.1088/1757-899X/481/1/012018.

Li, S., Jin, X., Laima, S., Li, H., 2024. Efficient data-driven nonlinear system identification for structural health monitoring: A proof-of-principle study. Advances in Structural Engineering 27, 2950–2961. https://doi.org/10.1177/13694332241281529.

Ma, G., Wang, Y., 2023. Prediction of deformation capacity of rectangular RC shear walls subjected to bending damage based on symbolic regression. Earthquake Engineering and Engineering Dynamics 43, 139–149. https://doi.org/10.13197/j.eeed.2023.0615.

Masi, A., Vona, M., 2010. Experimental and numerical evaluation of the fundamental period of undamaged and damaged RC framed buildings. Bulletin of Earthquake Engineering 8, 643–656. https://doi.org/10.1007/s10518-009-9136-3.

Mohamed, A., El Kashif, K., Salem, H., 2019. An investigation of the fundamental period of vibration for moment resisting concrete frames. Civil Engineering Journal (Iran) 5. https://doi.org/10.28991/cej-2019-03091438.

Narkhede, J., 2024. Comparative evaluation of post-hoc explainability methods in AI: LIME, SHAP, and Grad-CAM, in: 4th International Conference on Sustainable Expert Systems, ICSES 2024 Proceedings, p. 826–830. https://doi.org/10.1109/ICSES63445.2024.10762963.

Nguyen, D., Choo, Y., Nguyen, P., Kim, D., 2025. Nonlinear seismic soil-structure interaction analysis of shallow-founded structure: centrifuge test, numerical analysis, and deep learning approach. Computers and Geotechnics, 186https://doi.org/10.1016/j.compgeo.2025.107382.

Nguyen, H., Kim, C., Lee, K., Shin, M., 2024. Development of data-driven models to predict seismic drift response of RC wall structures: An application of deep neural networks. Soil Dynamics and Earthquake Engineering, 186https://doi.org/10.1016/j.soildyn.2024.108952.

Panzera, F., Lombardo, G., Muzzetta, I., 2013. Evaluation of building dynamic properties through in situ experimental techniques and 1D modeling: The example of Catania, Italy. Physics and Chemistry of the Earth, Parts A/B/C 63, 136–146. https://doi.org/10.1016/j.pce.2013.04.008.

Rahman, T., Momin, M., Provasha, A., 2025. Comprehensive analysis of structural parameters influencing the fundamental period of steel-braced RC buildings using machine learning interpretability. AI in Civil Engineering 4. https://doi.org/10.1007/s43503-025-00051-z.

Ron, K., 1995. A study of cross validation and bootstrap for accuracy estimation and model selection, in: International Joint Conference on Artificial Intelligence (IJCAI), Montreal, Quebec.

Sarma, S., Sundar Das, T., Bora, A., Bharadwaj, K., 2022. Parametric study on the variation of time period of RC MRF buildings. Lecture Notes in Civil Engineering 175, 415–426. https://doi.org/10.1007/978-981-16-4617-1_33.

Schapire, R., 2013. Explaining AdaBoost, in: Schölkopf, B., Luo, Z., Vovk, V. (Eds.), Empirical Inference. Springer, p. 37–52. https://doi.org/10.1007/978-3-642-41136-6_5.

Shan, J., Huang, C., Wang, L., Loong, C., 2024. Data-driven prediction of natural period for existing RC high-rise buildings using probabilistic machine learning methods. Journal of Building Engineering, 90https://doi.org/10.1016/j.jobe.2024.109394.

Sharma, N., Dasgupta, K., Dey, A., 2023. Soil-structure interaction induced modification on the natural period of reinforced concrete buildings. Lecture Notes in Civil Engineering 326, 352–361. https://doi.org/10.1007/978-3-031-30125-4_32.

Shendkar, M., Beiraghi, H., Mandal, S., 2021. Effect of irregularity on seismic design parameters of RC-infilled structures. Magazine of Civil Engineering 108. https://doi.org/10.34910/MCE.108.7.

Ukwaththa, U., Liyanarachchi, T., Kulasooriya, W., Ranasinghe, R., 2024. Use of interpretable machine learning methods to predict the fundamental period of masonry infilled reinforced concrete frame structures. Moratuwa Engineering Research Conference (MERCon) , 127–132 https://doi.org/10.1109/MERCon63886.2024.10688600.

Velani, P., Ramancharla, P.K., 2023. Approximate natural period expression for reinforced concrete tall buildings in India. Current Science 124, 1412–1421. https://doi.org/10.18520/cs/v124/i12/1412-1421.

Xiong, W., Jiang, L.-Z., Li, Y.-Z., 2016. Influence of soil structure interaction (structure-to-soil relative stiffness and mass ratio) on the fundamental period of buildings: Experimental observation and analytical verification. Bulletin of Earthquake Engineering 14, 139–160. https://doi.org/10.1007/s10518-015-9814-2.

Zhang, H., Cheng, X., Li, Y., He, D., Du, X., 2023. Rapid seismic damage state assessment of RC frames using machine learning methods. Journal of Building Engineering, 65 https://doi.org/10.1016/j.jobe.2022.105797.