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.

ENHANCING THE SEISMIC PERFORMANCE OF STEEL MOMENT FRAME STRUCTURES THROUGH THE OPTIMAL TUNING OF A PASSIVE INERTER-TUNED MASS DAMPER

R. Kamgar

A new type of seismic control device is introduced—the elastoplastic inerter-tuned mass damper—which omits the conventional viscous damping element and instead incorporates stiffness with elastoplastic behavior. The key objective is to benchmark its earthquake performance against alternative vibration mitigation strategies, including the standard tuned mass damper, the elastoplastic tuned mass damper, and the inerter-tuned mass damper. For each configuration, the design variables are optimized by minimizing the Park–Ang damage index, thereby maximizing the structure’s seismic resilience. A nine-story moment-resisting frame is employed and is modeled with the OpenSees software nonlinearly. Simulation results reveal that the proposed elastoplastic inerter-tuned mass damper surpasses all other examined systems. Specifically, it delivers up to a 38% drop in the global damage index and a 50% damage reduction in the lower stories.

AN INTEGRATED GRAPH-BASED IFC DECISION SUPPORT FRAMEWORK FOR SUSTAINABLE BUILDING COMPONENT SELECTION

M. Rastegar Moghaddam

Decision-making in the selection of sustainable building components remains one of the most persistent challenges in the construction industry. Projects involve numerous conflicting objectives and highly interdependent variables, yet the rich semantic and relational data embedded in IFC-based BIM models is rarely fully exploited for advanced analytical support. Existing approaches typically suffer from fragmented workflows, inefficient data extraction, and poor integration between modelling, optimisation, and decision-making processes. This study proposes a comprehensive, integrated data-driven decision-support framework that directly addresses these limitations. The framework transforms IFC-based BIM data into a scalable graph database using Neo4j and connects it seamlessly with multi-objective optimisation, Data Envelopment Analysis (DEA), and multi-criteria decision-making (MCDM) within a single coherent pipeline. The framework was implemented and validated on a residential building case study, considering four key sustainability objectives. Results demonstrate that the graph-based representation improves data accessibility and efficient retrieval, while the integrated pipeline effectively reduces the solution space and delivers transparent, high-quality recommendations that balance technical performance with stakeholder preferences. Compared with conventional fragmented methods, the proposed framework offers a more coherent, practical, and potentially scalable solution for complex multi-criteria decision-making problems across the Architecture, Engineering, and Construction (AEC) industry.

THERMOMECHANICAL TOPOLOGY OPTIMIZATION BASED ON MOVING MORPHABLE COMPONENTS WITH DESIGN-DEPENDENT STEADY-STATE HEAT CONDUCTION

S. A. Latifi Rostami

In thermomechanical topology optimization, variations in material distribution influence not only the structural stiffness but also the temperature field and thermal loads induced by constrained thermal expansion. In this study, a moving morphable component (MMC)-based framework is proposed for thermomechanical topology optimization, in which the density-based representation of the SIMP method is replaced with an explicit geometry description using an MMC. In the proposed approach, steady-state heat conduction analysis, equivalent thermomechanical load formulation, and structural mechanical analysis are retained, whereas compliance minimization subject to a volume constraint is adopted as the optimization objective. The elemental density field is derived from the topology description and Heaviside functions, and the sensitivity of the objective function with respect to the geometric parameters of the MMC is evaluated using the chain rule. Numerical examples demonstrate that the proposed method achieves satisfactory thermomechanical performance while producing smoother boundaries and a more explicit geometric representation than the conventional SIMP method.

PREDICTION OF BRIDGE ACCELERATION RESPONSES USING AN ADAPTIVE AWAN FRAMEWORK

G. Ghodrati Amiri

Bridge Health Monitoring (BHM) plays a vital role in ensuring the safety, reliability, and long-term performance of bridge infrastructure. This study proposes an ARMA–Wavelet–Artificial Neural Network (AWAN) framework for predicting unmeasured bridge deck acceleration responses from limited sensor measurements. The proposed methodology integrates Auto-Regressive Moving Average (ARMA) modeling for temporal feature extraction, Continuous Wavelet Transform (CWT) for signal denoising, and a feed-forward Artificial Neural Network (ANN) for nonlinear response prediction. The combined framework exploits both spatial and short-term temporal correlations to achieve accurate response reconstruction while maintaining computational efficiency. The proposed framework was validated using three bridge models, including a simply supported beam, a two-span steel grid benchmark, and a scaled single-plane cable-stayed bridge. Prediction performance was evaluated using different statistical metrics under multiple loading scenarios. The results demonstrated excellent agreement between the predicted and measured acceleration responses, with higher prediction accuracy generally achieved at mid-span locations than near the supports, reflecting differences in local structural dynamics. In addition, the framework maintained stable performance under moderate temperature variation, demonstrating its robustness for practical bridge health monitoring applications. The proposed AWAN framework provides an efficient and reliable approach for reconstructing unmeasured structural responses while reducing sensor requirements. Its combination of prediction accuracy, computational efficiency, and robustness makes it a promising tool for data-driven bridge health monitoring and response reconstruction.

UNCERTAINTY QUANTIFICATION IN APPROXIMATING DYNAMIC RESPONSES OF STRUCTURES USING REDUCED ORDER MODELS

M. Ilchi Ghazaan

Reduced order models (ROMs) are widely used to approximate the dynamic response of large-scale structural systems while substantially reducing computational cost. Inherent uncertainties necessitate the assessment of ROMs within an uncertainty quantification (UQ) framework. Although the deterministic accuracy of reduction techniques has been extensively investigated, their capability for UQ remains insufficiently understood. This study presents a systematic UQ-based assessment of four condensation techniques: Guyan reduction, dynamic condensation, Improved Reduced System (IRS), and the System Equivalent Reduction Expansion Process (SEREP). A shear frame and a plane truss are used to evaluate the combined influence of the reduction technique, master degree of freedom (DOF) selection, and structural dynamic complexity on ROM predictive capability. Polynomial Chaos Expansion (PCE) is employed for UQ, and variance-based Sobol' indices are adopted for global sensitivity analysis (GSA). SEREP consistently provides the closest approximation to the full order model, whereas IRS also maintains high accuracy over most vibration modes. The accuracy of the Guyan and dynamic condensation methods decreases as higher-order dynamics become increasingly important.