Issue 74

E. Sharaf et alii, Fracture and Structural Integrity, 74 (2025) 262-293; DOI: 10.3221/IGF-ESIS.74.17

S UMMARY OF RECENT STUDIES ON FUNDAMENTAL PERIOD ESTIMATION AND THEIR METHODOLOGICAL CHARACTERISTICS n addition to the comparison with empirical code-based formulas and FEM results, it is important to situate the proposed analytical model within the context of recent research. Tab.10 is an overview of recent advances in fundamental period prediction methods, comparing structural scope, methodologies, parameters treated, and main findings across selected studies. The development of research provides a clear trend toward the integration of data-driven approaches, namely machine learning (ML), with traditional analytical models both to enhance accuracy and enable interpretability. Kumar et al. [25] explored RC moment-resisting frames via comparative analysis of ML algorithms (ANN, GP, RT), where ANN was most accurate. Their results emphasize the requirement for geometric parameters such as number of bays and bay length to influence period predictions. Rahman et al. [26] extended their scope to steel-braced, RC structures and employed ML models that were enhanced with SHAP-based interpretability. Shan et al. [27] addressed the issue of prediction of existing high-rise RC buildings by integrating probabilistic ML with explicit accounting for material deterioration and structural aging. Karampinis et al. [28] bridged analytical and ML approaches, explaining the influence of plan irregularities and stiffness ratios through SHAP values, while also producing analytical equations with comparable performance to ML models. Relative to recent advances in fundamental period predictive techniques (Tab.10), the deterministic analytical model developed herein offers a novel compromise between predictability, computational efficiency, and transparency. While several recent studies have applied machine learning (ML) techniques either alone or in combinations to enhance predictability, these approaches are often require large amount of data (with high-quality data sets), model-intensive (with sophisticated training), and may be infested with interpretability challenges in the lack of specific explainability tools (e.g., SHAP) [25, 26, 27, 28]. Compared to the previous, the new model is an analytical model based on merely the basic structural parameters of mass, height, and stiffness distribution and therefore can be applied without the computational overhead or data dependence of ML-based methods. Moreover, unlike probabilistic or data-driven methods, the present approach gives closed-form solutions that are inherently interpretable and therefore can be applied directly in early design and code development. I

Study & year

Structural Scope

Methodology

Key Parameters Considered

Main Findings

Kumar et al. [25]

RC moment resisting frames RC buildings with steel bracing RC high-rise buildings

Algorithms for comparative machine learning (ANN, GP, RT) Interpretable machine learning (SHAP values)

Height, length of the bays, number of bays, and material Height, bracing arrangement, and stiffness distribution building height, and material deterioration

The influence of geometric irregularities was highlighted by ANN, which achieved the highest accuracy Period was greatly shortened by bracing; important stiffness variables were identified by ML interpretability For older structures, probabilistic machine learning captured uncertainty and enhanced prediction. Created comprehensible analytical formulas with precision on par with the ML Easy to understand, transparent, and computationally efficient; similar accuracy for a standard configuration

Rahman et al. [26]

Shan et al. [27]

Probabilistic machine learning

Karampinis et al. [28]

Structures with frames

ML + Analytical hybrid with SHAP

Height, stiffness ratios, and plan irregularities

Deterministic Analytical Model

Height, mass and stiffness distribution,

Proposed Model

RC moment resisting frames

Table 10 . Summary of recent studies on fundamental period prediction, highlighting structural scope, methodology, key parameters, and main findings, with emphasis on the positioning of the proposed deterministic analytical model relative to contemporary machine learning and hybrid approaches.

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