Add manuscript and bibliography files for shear-link beam dampers optimization study

Manuscript/Manuscript.tex

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 \articletype{Article Type}%
 
@@ -17,16 +24,16 @@
 
 \begin{document}
 
-\title{Fast design optimization of SLB dampers using FEM-calibrated surrogates: hysteresis prediction with LSTM and damage-constrained optimization}
+\title{Damage-aware surrogate-based optimization of shear-link beam dampers}
 
-\author[1]{Author One}
+\author[1]{Joaquín Irazábal González}
 
 \author[2,3]{Author Two}
 
 \author[3]{Author Three}
 
 \authormark{FIRST \textsc{et al.}}
-\titlemark{FAST DESIGN OPTIMIZATION OF SLB DAMPERS USING FEM-CALIBRATED SURROGATES: HYSTERESIS PREDICTION WITH LSTM AND DAMAGE-CONSTRAINED OPTIMIZATION}
+\titlemark{DAMAGE-AWARE SURROGATE-BASED OPTIMIZATION OF SHEAR-LINK BEAM DAMPERS}
 
 \address[1]{\orgdiv{Department Name}, \orgname{Institution Name}, \orgaddress{\state{State Name}, \country{Country Name}}}
 
@@ -34,16 +41,16 @@
 
 \address[3]{\orgdiv{Department Name}, \orgname{Institution Name}, \orgaddress{\state{State Name}, \country{Country Name}}}
 
-\corres{Corresponding author Author One, This is sample corresponding address. \email{authorone@gmail.com}}
+\corres{Joaquín Irazábal González. \email{jirazabal@cimne.upc.edu}}
 
-\presentaddress{This is sample for present address text this is sample for present address text.}
+% \presentaddress{This is sample for present address text this is sample for present address text.}
 
 %\fundingInfo{Text}
 %\JELinfo{ejlje}
 
-\abstract[Abstract]{The geometric optimization of shear-link beam (SLB) dampers under cyclic loading is challenged by strong nonlinear behavior and the need to control local damage mechanisms. High-fidelity finite element method (FEM) simulations provide detailed information on global response and internal damage, but their computational cost limits their use in design optimization. This work proposes a surrogate-assisted optimization framework based on FEM-generated datasets covering SLB configurations with varying geometric complexity. Supervised learning models and Radial Basis Function (RBF) approximations are used to approximate performance indicators and enable efficient exploration of the design space. The different surrogate approaches are systematically compared in terms of predictive accuracy and computational cost. An interpretability analysis based on SHapley Additive exPlanations (SHAP) is incorporated to quantify the influence of geometric variables. Results demonstrate an effective trade-off between accuracy and efficiency, and provide insight into key design drivers, enabling fast and reliable optimization of SLB dampers.}
+\abstract[Abstract]{The geometric optimization of \red{shear-link beam (SLB) dampers} under cyclic loading is challenged by strong nonlinear behavior and the need to control local damage mechanisms. High-fidelity finite element method (FEM) simulations provide detailed information on global response and internal damage, but their computational cost limits their use in design optimization. This work proposes a surrogate-assisted optimization framework based on FEM-generated datasets covering SLB configurations with varying geometric complexity. Supervised learning models and Radial Basis Function (RBF) approximations are used to evaluate the performance indicators and enable efficient exploration of the design space. The different surrogate approaches are \red{systematically compared in terms of predictive accuracy and computational cost}. An interpretability analysis based on SHapley Additive exPlanations (SHAP) is incorporated to quantify the influence of geometric variables in the response of the device. \red{Results demonstrate an effective trade-off between accuracy and efficiency, and provide insight into key design drivers, enabling fast and reliable optimization of SLB dampers.}}
 
-\keywords{Hysteresis, surrogate modeling, supervised learning, radial basis functions, structural optimization, FEM-calibrated models, shear-link dampers, model interpretability, SHAP}
+\keywords{\red{Shear-link dampers}, structural optimization, surrogate modeling, supervised learning, radial basis functions, FEM-calibrated models, model interpretability, SHAP}
 
 \jnlcitation{\cname{%
 \author{Taylor M.},
@@ -63,39 +70,38 @@
 
 \section{Introduction}\label{sec1}
 
-\subsection{Motivation and engineering problem}\label{sec1_1}
+\red{Shear-link beam (SLB) dampers} are widely used as passive energy dissipation devices in seismic-resistant structures due to their ability to undergo stable inelastic deformations while limiting damage to the primary structural system. Their design aims at maximizing energy dissipation capacity and ductility under cyclic loading, while simultaneously controlling local damage levels to ensure reliability, durability, and predictable failure mechanisms.
 
-Shear-link beam (SLB) dampers are widely used as passive energy dissipation devices in seismic-resistant structures due to their ability to undergo stable inelastic deformations while limiting damage to the primary structural system. Their design aims at maximizing energy dissipation capacity and ductility under cyclic loading, while simultaneously controlling local damage levels to ensure reliability, durability, and predictable failure mechanisms.
-
-Experimental testing plays a fundamental role in characterizing the global hysteretic response of SLB dampers. However, laboratory campaigns present inherent limitations when addressing design optimization problems. On the one hand, internal state variables such as local plastic strains, stress triaxiality, or damage indicators cannot be directly measured with sufficient spatial resolution. On the other hand, the high cost and logistical complexity of experimental programs severely restrict the number of geometric configurations that can be explored, making systematic optimization impractical.
+Experimental testing plays a fundamental role in characterizing the global hysteretic response of SLB dampers. However, laboratory campaigns present inherent limitations when addressing design optimization problems. Internal state variables such as local plastic strains, stress triaxiality, or damage indicators cannot be directly measured with sufficient spatial resolution. In addition, the high cost and logistical complexity of experimental programs severely restrict the number of geometric configurations that can be explored, making systematic optimization impractical.
 
 In this context, high-fidelity finite element method (FEM) simulations constitute a powerful alternative. Advanced nonlinear FEM models enable detailed representation of cyclic plasticity, geometric nonlinearity, and damage evolution, providing access to both global response quantities and local indicators governing failure mechanisms. Moreover, FEM simulations allow the systematic generation of data across a wide range of geometric parameters, making them particularly suitable as a foundation for data-driven optimization strategies.
 
-\subsection{Main challenges}\label{sec1_2}
-
-Despite their advantages, the direct use of FEM models within optimization loops remains computationally prohibitive. The cyclic response of SLB dampers is characterized by pronounced hysteresis and strong memory effects, where the force-displacement relationship depends not only on the instantaneous deformation but also on the full loading history. Accurately capturing such behavior requires fine temporal discretization and sophisticated constitutive models, resulting in simulation times that can span several hours per configuration.
-
-Furthermore, purely data-driven approaches face intrinsic limitations when applied to this class of problems. Models trained on limited datasets often exhibit poor extrapolation capabilities when queried outside the domain covered by the training data, which is particularly critical in design optimization scenarios. As a consequence, there is a clear need for surrogate modeling techniques that are both computationally efficient and sufficiently reliable to approximate complex nonlinear responses, while remaining consistent with the underlying physics captured by FEM simulations.
+Despite these advantages, the direct use of FEM models within optimization loops remains computationally prohibitive. The cyclic response of SLB dampers is characterized by pronounced hysteresis and strong memory effects, where the force–displacement relationship depends on the full loading history. Accurately capturing such behavior requires fine temporal discretization and sophisticated constitutive models, resulting in simulation times that can span several hours per configuration. At the same time, purely data-driven approaches face intrinsic limitations, particularly poor extrapolation capabilities outside the training domain. This creates the need for surrogate models that are both computationally efficient and sufficiently reliable, while remaining consistent with the underlying physics captured by FEM simulations. Furthermore, understanding the relative influence of geometric variables on performance indicators remains challenging, especially when surrogate models behave as black-box predictors.
 
-In addition, understanding the relative influence of geometric variables on performance indicators remains challenging, particularly when surrogate models behave as black-box predictors.
+Over the past decades, FEM has been widely used to study seismic energy dissipation devices, providing detailed insight into nonlinear cyclic response, stiffness degradation, and local inelastic mechanisms \cite{Deng2014a, Deng2015}. It has also supported the optimization of these devices by enabling systematic exploration of geometric configurations and performance criteria under prescribed loading \cite{Deng2014, Deng2015a}. Simplified analytical and semi-empirical models have been proposed to reduce computational cost in practice \cite{Deng2014b}, while more recent parametric and simulation-based studies have examined the influence of geometric and material variables on damper performance \cite{Kim2022}.
 
-\subsection{State of the art and related work}\label{sec1_3}
+FEM-based parametric analyses have been widely used to characterize the mechanical response of metallic dampers. Motamedi et al. \cite{Motamedi2018} investigated accordion metallic dampers through combined experimental and numerical analyses, assessing the influence of key geometric variables on stiffness, strength, and energy dissipation. Ghamari et al. \cite{Ghamari2021} studied I-shaped shear links in concentrically braced frames, and Xiong et al. \cite{Xiong2024} examined replaceable steel shear links with different short-length ratios, highlighting the strong influence of geometry on cyclic performance and failure modes.
 
-Over the past decades, the finite element method (FEM) has been widely used to study seismic energy dissipation devices, providing detailed insight into nonlinear cyclic response, stiffness degradation, and local inelastic mechanisms \cite{Deng2014a, Deng2015}. FEM has also supported the optimization of these devices by enabling systematic exploration of geometric configurations and performance criteria under prescribed loading \cite{Deng2014, Deng2015a}. Simplified analytical and semi-empirical models have been proposed to reduce computational cost in practical applications \cite{Deng2014b}, while more recent parametric and simulation-based studies have further examined the influence of geometric and material variables on damper performance \cite{Kim2022}. Nevertheless, computational efficiency and predictive fidelity remain difficult to reconcile when complex hysteretic behavior and local damage must be captured simultaneously.
+Geometric optimization has also been extensively explored. Zhang et al. \cite{Zhang2017} proposed a Kriging-assisted framework to maximize hysteretic energy in coupling beam dampers. Farzampour et al. \cite{Farzampour2019} optimized butterfly-shaped shear links by maximizing the ratio between dissipated energy and plastic strain, while Khatibinia et al. \cite{Khatibinia2019, Khatibinia2021} developed efficient strategies for U-shaped dampers using FEM and surrogate models. Shi et al. \cite{Shi2019} introduced a non-parametric shape optimization framework for shear panel dampers, and Saleh et al. \cite{Saleh2024, Saleh2026} extended this line through topology optimization of shear-link configurations. More recent contributions include the hybrid cellular automata approach by Mendoza-Cuy et al. \cite{MendozaCuy2025} and the statistical optimization framework by Rios et al. \cite{Rios2025}. While these approaches expand the design space, they remain strongly dependent on high-fidelity FEM simulations, which limits their efficiency in large-scale design exploration.
 
-Many studies have focused on the characterization of metallic dampers through FEM-supported parametric analyses. Motamedi et al. \cite{Motamedi2018} investigated accordion metallic dampers through combined experimental and numerical analyses, assessing the influence of key geometric variables on stiffness, strength, and energy dissipation. Ghamari et al. \cite{Ghamari2021} studied I-shaped shear links in concentrically braced frames, and Xiong et al. \cite{Xiong2024} examined replaceable steel shear links with different short-length ratios, both highlighting the strong influence of geometry on cyclic performance and failure modes.
+Data-driven approaches have mainly focused on response or property prediction. Chan et al. \cite{Chan2015} used nonlinear autoregressive exogenous (NARX) models to reproduce hysteretic behavior. Bae et al. \cite{Bae2020} developed models for low-cycle fatigue estimation, and Almasabha et al. \cite{Almasabha2022} predicted shear strength of short steel links using ML. Elgammal et al. \cite{Elgammal2024} modeled hysteretic restoring forces using data-driven approaches, while Hu et al. \cite{Hu2023} proposed explainable ML models for probabilistic prediction of buckling stress. Physics-informed approaches have also been explored, such as the PINN framework proposed by Hu et al. \cite{Hu2022}. Despite their potential, these methods remain primarily focused on prediction rather than on integration into geometry optimization frameworks.
 
-Geometric optimization has also been widely addressed. Zhang et al. \cite{Zhang2017} proposed a Kriging-assisted framework to maximize the hysteretic energy of coupling beam dampers. Farzampour et al. \cite{Farzampour2019} optimized butterfly-shaped shear links by maximizing the ratio between dissipated energy and plastic strain, whereas Khatibinia et al. \cite{Khatibinia2019, Khatibinia2021} developed efficient optimization strategies for U-shaped steel dampers using FEM and surrogate models. Shi et al. \cite{Shi2019} proposed a non-parametric shape optimization framework for elastic-plastic shear panel dampers, and Saleh et al. \cite{Saleh2024} extended this line through topology optimization of vertical shear-link dampers. More recently, Mendoza-Cuy et al. \cite{MendozaCuy2025} applied a hybrid cellular automata technique to the topology optimization of steel slotted dampers, while Rios et al. \cite{Rios2025} proposed a computational design framework for U-shaped seismic dampers based on statistical optimization. Saleh et al. \cite{Saleh2026} further investigated stiffened topology-optimized shear links for eccentrically braced frames. These studies expand the design space substantially, but they still rely heavily on high-fidelity FEM simulations, which limits their efficiency in large design searches.
+Overall, most existing studies address either response prediction or the maximization of energy dissipation. This leaves a critical aspect insufficiently explored: the need to control local damage while maintaining adequate dissipative capacity. In practice, excessive local damage may compromise structural integrity, reduce durability, and lead to premature failure even when global energy dissipation is improved.
 
-Data-driven approaches have mainly focused on response or property prediction. Chan et al. \cite{Chan2015} used nonlinear autoregressive exogenous (NARX) models to reproduce hysteretic response in passive control systems. Bae et al. \cite{Bae2020} developed machine learning models for low-cycle fatigue estimation in metallic dampers, and Almasabha et al. \cite{Almasabha2022} predicted the shear strength of short steel links using ML. Elgammal et al. \cite{Elgammal2024} modeled hysteretic restoring forces in shear-link dampers with machine learning, showing that complex cyclic behavior can be reproduced without explicit constitutive formulations. Hu et al. \cite{Hu2023} proposed explainable ML models for probabilistic prediction of buckling stress in steel shear panel dampers, while Hu et al. \cite{Hu2022} introduced a physics-informed neural network to model the cyclic behavior of S-shaped steel dampers. Although these works show the potential of ML, explainable ML, and PINNs for structural response modeling, they remain focused on prediction rather than on geometry optimization.
+The present work addresses this gap through a damage-aware optimization framework in which the objective is not only to maximize \red{distortion or energy} dissipation, but to balance dissipative performance and minimized damage indicators derived from FEM simulations. The proposed methodology combines high-fidelity FEM-generated datasets with multiple surrogate strategies, including supervised learning models and radial basis functions, to efficiently explore the design space of SLB dampers with different geometric complexities. The framework is physically grounded, as all models are trained on simulation data that capture both global response and local damage mechanisms.
 
-Despite these advances, most existing studies address either response prediction or the maximization of energy dissipation through geometric optimization. This leaves a critical aspect insufficiently explored: the need to control local damage while maintaining adequate dissipative capacity. In practice, excessive local damage can reduce durability, compromise reliability, and lead to premature failure even when global energy dissipation is improved.
+\red{In contrast to previous works focused on a single model or performance metric, this study provides a systematic comparison of surrogate techniques in terms of predictive accuracy and computational cost within the context of geometry optimization.} An interpretability analysis based on SHapley Additive exPlanations (SHAP) is also incorporated to quantify the influence of geometric variables on the predicted performance metrics, providing insight into the governing design drivers. In addition, the framework includes an adaptive validation and retraining loop in which selected optimal candidates are re-evaluated with FEM and iteratively incorporated into the training dataset.
 
-The present work addresses this gap through a damage-aware optimization framework in which the objective is not only to maximize distortion or energy dissipation, but to balance dissipative performance and minimized damage indicators derived from FEM simulations. The proposed methodology combines high-fidelity FEM-generated datasets with multiple surrogate strategies, including supervised learning models and radial basis functions, to explore the design space of SLB dampers with different geometric complexities. The framework is physically grounded because all models are trained on simulation data that capture both global response and local damage mechanisms.
+As a result, the main contribution of this work lies in the development of a robust, scalable, and physically informed design methodology that explicitly accounts for the trade-off between energy dissipation and damage, while enhancing model interpretability for engineering decision-making.
 
-Unlike previous studies focused on a single predictive model or a single optimization metric, this work provides a systematic comparison of surrogate techniques in terms of predictive accuracy and computational cost within the context of geometry optimization. In addition, an interpretability analysis based on SHapley Additive exPlanations (SHAP) is incorporated to quantify the influence of geometric variables on the predicted performance metrics, providing additional insight into the underlying design drivers. The framework also includes an adaptive validation and retraining loop in which selected optimal candidates are re-evaluated with FEM and iteratively added to the training set.
-
-The main contribution is therefore not only the acceleration of the optimization process, but the development of a robust and scalable design methodology that explicitly addresses the trade-off between energy dissipation and damage, while enhancing model interpretability for engineering decision-making.
+To summarize, the main contributions of this work are:
+\begin{itemize}
+\item Generation of high-fidelity FEM datasets for SLB dampers with increasing geometric complexity.
+\item Geometric optimization using surrogate models, including supervised learning techniques and radial basis functions.
+\item Systematic comparison of surrogate strategies in terms of accuracy and computational cost.
+\item Interpretability analysis using SHAP to assess the influence of geometric variables.
+\item Adaptive validation and retraining strategy based on additional FEM simulations.
+\end{itemize}
 
 \subsection{Contributions of this work}\label{sec1_4}