International Journal of Optimization in Civil Engineering

PREDICTION OF NONLINEAR INTER-STORY DRIFTS IN STEEL MOMENT FRAMES UNDER SEISMIC LOADING USING CASCADE FORWARD NEURAL NETWORKS

S. Gholizadeh

This paper aims to predict the maximum inter-story drift ratios of steel moment-resisting frame (MRF) structures under seismic loading, corresponding to different performance levels, using cascade-forward back-propagation (CFBP) neural network models. To this end, CFBP networks with varying numbers of hidden layer neurons are trained on nonlinear time-history analysis results of 6- and 12-story planar steel MRFs subjected to a suite of earthquake ground motions. The predictive performance of the trained models is systematically compared. Numerical results demonstrate that CFBP networks with 15 neurons in the hidden layer consistently outperform other network architectures, yielding more accurate predictions of the maximum inter-story drift ratios at each seismic performance level for both frame heights. These findings highlight the potential of moderately sized CFBP networks as efficient surrogates for nonlinear dynamic analysis in performance-based seismic assessment.

A SURROGATE APPROACH FOR ACCURATE ESTIMATION OF STRUCTURAL RESPONSE IN STEEL FRAME OPTIMIZATION

H. Azizian

Structural design seeks to achieve optimal performance with minimum cost while meeting code requirements. Evaluating optimized designs usually depends on finite element analysis, which is computationally expensive. Recently, surrogate models have been developed to predict structural behavior more efficiently. Among these, Support Vector Machine (SVM) has become a reliable tool in civil engineering. However, the predictive power of SVM is highly dependent on proper parameter tuning. This study introduces the Improved Electric Eel Foraging Optimization Algorithm (I-EEFO) for training SVM to estimate the response of steel frames. Two benchmark structures, a 2‑story and a 7‑story steel frame, were analyzed, and the results were compared with other metaheuristic algorithms. The proposed method achieved very high accuracy: mean squared errors of 1.11E‑13 for the 2‑story frame and 2.99E‑07 meters for the 7‑story frame over 10 runs. The root mean square errors for displacement prediction on test data were 2.67E‑07 and 7.23E‑04 meters, respectively, confirming reliable estimates. Convergence curves demonstrated that I‑EEFO converges faster and more effectively than competing methods. These findings highlight the potential of the proposed approach as a robust and computationally efficient alternative to traditional simulations, offering engineers a practical tool to reduce costs in structural design without compromising accuracy.

STRUCTURAL RELIABILITY ASSESSMENT OF CONCRETE-FILLED STEEL FRAME BUILDINGS VIA A COMPLEX-VALUED DEEP SURROGATE MODEL

H. Rahami

This paper presents a novel framework for structural reliability assessment of buildings incorporating Concrete-Filled Steel Tubular columns, utilizing a deep surrogate model formulated in the complex number domain. High-fidelity numerical models are developed using SAP2000 software, with analysis outputs pre-processed in MATLAB. A hybrid deep learning architecture is implemented within the PyTorch framework, featuring complex-valued parameters and activation functions that enable superior representation of phase-dependent and oscillatory behaviors inherent in nonlinear limit state functions. Each complex parameter simultaneously encodes both real and imaginary influences, enhancing representational efficiency while requiring fewer parameters than conventional real-valued networks. Bidirectional communication between MATLAB and PyTorch is established through system-level execution protocols, enabling seamless integration with the SM Toolbox for parametric structural modeling. The surrogate model is trained on strategically sampled datasets, with architecture complexity and dataset size adaptively determined based on parameter counts. Reliability indices are computed using the Weighted Average Simulation Method applied separately to real and imaginary components, with final reliability estimated through weighted averaging. The proposed method is validated through three mathematical benchmark functions and three engineering case studies, including a three-span continuous beam, a roof truss, and a ten-story building with CFST columns. Results demonstrate minimum improvements of 79% in mathematical examples and up to 95% in engineering applications regarding required function evaluations, while maintaining essentially zero estimation error. For the ten-story building, computation time reduced from approximately 3.9 days using conventional simulation to 2.3 hours—a 98% improvement—demonstrating the framework's potential for efficient and accurate reliability assessment of complex structural systems.