Add changes after suggestions from Wiley journal

ComparisonSurrogatesOptimizationBDSL.spl

+\g@addto@macro\@biboptions{,numbers}

Manuscript/wileyNJD-AMA.bib → Manuscript/ComparisonSurrogatesOptimizationBDSL.bib

@@ -807,4 +807,20 @@ steel from coupon test results available. First, the theory of metal plasticity
   language  = {en},
 }
 
+@InProceedings{Lundberg2017,
+  author    = {Lundberg, Scott M. and Lee, Su-In},
+  booktitle = {Proceedings of the 31st {International} {Conference} on {Neural} {Information} {Processing} {Systems}},
+  title     = {A unified approach to interpreting model predictions},
+  year      = {2017},
+  address   = {Red Hook, NY, USA},
+  month     = dec,
+  pages     = {4768--4777},
+  publisher = {Curran Associates Inc.},
+  series    = {{NIPS}'17},
+  abstract  = {Understanding why a model makes a certain prediction can be as crucial as the prediction's accuracy in many applications. However, the highest accuracy for large modern datasets is often achieved by complex models that even experts struggle to interpret, such as ensemble or deep learning models, creating a tension between accuracy and interpretability. In response, various methods have recently been proposed to help users interpret the predictions of complex models, but it is often unclear how these methods are related and when one method is preferable over another. To address this problem, we present a unified framework for interpreting predictions, SHAP (SHapley Additive exPlanations). SHAP assigns each feature an importance value for a particular prediction. Its novel components include: (1) the identification of a new class of additive feature importance measures, and (2) theoretical results showing there is a unique solution in this class with a set of desirable properties. The new class unifies six existing methods, notable because several recent methods in the class lack the proposed desirable properties. Based on insights from this unification, we present new methods that show improved computational performance and/or better consistency with human intuition than previous approaches.},
+  doi       = {10.5555/3295222.3295230},
+  isbn      = {978-1-5108-6096-4},
+  urldate   = {2026-04-21},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}

Manuscript/ComparisonSurrogatesOptimizationBDSL.tex

@@ -38,14 +38,14 @@
 
 \title{Comparison of surrogate strategies for damage-aware optimization of buckling-delayed shear-link dampers with adaptive finite element validation}
 
-\author[aff1,aff2]{J. Irazábal\corref{cor1}}
+\author[aff1,aff2]{Joaquín Irazábal\corref{cor1}}
 \ead{jirazabal@cimne.upc.edu}
-\author[aff1,aff3]{J. Ramírez}
-\author[aff1,aff3]{J. M. González}
-\author[aff1]{L. Lázaro}
-\author[aff1,aff3]{F. Rastellini}
-\author[aff3,aff4]{G. Bozzo}
-\author[aff5]{L. Bozzo}
+\author[aff1,aff3]{Junior Ramírez}
+\author[aff1,aff3]{José Manuel González}
+\author[aff1]{Lucy Lázaro}
+\author[aff1,aff3]{Fernando Rastellini}
+\author[aff3,aff4]{Guillermo Bozzo}
+\author[aff5]{Luis Bozzo}
 
 \cortext[cor1]{Corresponding author.}
 
@@ -112,7 +112,7 @@ Figure \ref{fig:MethodologyFlowChart} summarizes the proposed workflow. The diff
 
 \section{Buckling-delayed shear-link damper}\label{sec:device}
 
-The BDSL dampers analysed in this work, with one representative configuration shown in Figure~\ref{fig:Device}, are designed to concentrate energy dissipation in localized reduced-thickness zones, hereafter referred to as windows, while preserving the structural integrity of the surrounding frame. The dissipative element is connected to a load-transfer system through a mechanism that allows imposed in-plane displacement while preventing axial force transmission, thereby promoting a shear-dominated response. Under cyclic loading, plastic deformation is intended to concentrate in the windows, whereas the frame provides load transfer and stability.
+The BDSL dampers analysed in this work, with one representative configuration shown in Figure~\ref{fig:Device}, are steel devices designed to concentrate inelastic deformation and energy dissipation in localized reduced-thickness regions, hereafter referred to as windows, while preserving the structural integrity of the surrounding frame. The damper is connected to a load-transfer system through a mechanism that allows imposed in-plane displacement while preventing axial force transmission, thereby favouring a shear-dominated response. Under cyclic loading, the windows are expected to act as the primary dissipative regions, whereas the frame ensures load transfer and global stability.
 
 \begin{figure}[htbp]
   \centering
@@ -158,26 +158,52 @@ $F_5$ & 2.00 & 1.17 & 5 & $t_{w,1},\ldots,t_{w,5}$ & 5--12 mm \\
 
 \section{Validation of the FEM numerical model}\label{sec:fem}
 
-The surrogate models developed in this work were trained using data generated from three-dimensional FEM simulations. The numerical model is based on a previously calibrated and validated representation of the BDSL device, described in detail in Ramírez et al. \cite{RamirezMachado2025}. An example of the numerical setup is shown in Figure \ref{fig:FEMSetup}. The simulations were carried out using the COMPACK code, an explicit dynamic FEM solver for linear and nonlinear problems \cite{Martinez2011}. The model accounts for large displacements, material and geometric nonlinearities, contact interactions and the boundary conditions associated with the experimental configuration.
-
-The dissipative steel component is modelled as ASTM A36 steel, whose cyclic plastic behaviour is represented by the Yoshida--Uemori model \cite{Yoshida2002,Jia2014}. This constitutive law allows the model to reproduce cyclic hardening, softening and Bauschinger-type effects under large plastic deformation. The steel component is discretized using linear eight-node hexahedral solid elements, providing a structured three-dimensional mesh suitable for extracting local stress, strain and damage-related fields.
-
-The imposed displacement is applied through an actuator-like connector that transfers horizontal displacement while preventing axial load transmission, thereby reproducing the kinematic condition required to promote a shear-dominated response. Three experimental tests were performed following the loading protocols defined in the ANSI/AISC 341-16 \cite{American2002} and ASCE 7-22 \cite{American2017} qualification standards for seismic energy dissipation devices. Those protocols involve cyclic loading with progressively increasing amplitudes. Additional contact and confinement conditions are included to represent the experimental system to restrain buckling.
+The surrogate models developed in this work were trained using data generated from three-dimensional FEM simulations of the BDSL device under cyclic loading. The numerical model reproduces the geometry defined in Section~\ref{sec:device} and incorporates the boundary and loading conditions of the experimental setup. A schematic representation of the complete numerical model is shown in Figure~\ref{fig:FEMSetup}. The simulations were carried out using the COMPACK code, an explicit dynamic FEM solver based on an incremental formulation for linear and nonlinear problems~\cite{Martinez2011}. The model accounts for large displacements, material and geometric nonlinearities, contact interactions, support flexibility and the boundary conditions associated with the experimental configuration.
 
 \begin{figure}[htbp]
-  \centering
-  \includegraphics[width=0.495\textwidth]{./images/FEMSetup/FEMSetup.pdf}
-  \caption{FEM validation model of the BDSL device: mesh discretization, main components, boundary conditions and local/global buckling control.}
-  \label{fig:FEMSetup}
+\centering
+\includegraphics[width=0.495\textwidth]{./images/FEMSetup/FEMSetup.pdf}
+\caption{FEM validation model of the BDSL device: mesh discretization, main components, boundary conditions and local/global buckling control.}
+\label{fig:FEMSetup}
 \end{figure}
 
-The calibration involved the material parameters, assembled geometry, contact definitions, support flexibility and boundary conditions. The validated model accurately reproduces the main global experimental responses. Figure \ref{fig:FEM_validation_comparison} shows the comparison between experimental and numerical results, confirming the suitability of the FEM model as a numerical reference for configurations beyond those experimentally tested.
+The damper is supported by a flexible base, which allows the imposed differential displacement at the support to be represented. At the top of the device, the cyclic horizontal displacement is transmitted through an actuator--connector assembly consisting of a welded connector and an actuator-like component. This assembly imposes the prescribed in-plane motion while preventing axial force transmission, thereby reproducing the shear-dominated loading condition considered in the tests. The interaction between the actuator and the connector, as well as the local and global buckling constraints introduced for the windows and the frame, are simulated through contact surfaces using a penalty-based formulation. The contact parameters were calibrated to ensure accurate displacement transmission and a stable representation of the boundary conditions.
+
+The dissipative steel component is modelled as ASTM A36 steel, whose cyclic plastic behaviour is reproduced using the Yoshida--Uemori constitutive model~\cite{Yoshida2002,Jia2014}. This formulation accounts for material nonlinearity, cyclic hardening, softening and Bauschinger-type effects under large plastic deformation. The steel component is discretized using linear eight-node hexahedral solid elements, providing a structured three-dimensional mesh suitable for extracting local stress, strain and damage-related fields. The material parameters adopted for the Yoshida--Uemori model are summarized in Table~\ref{tab:steel_params}.
+
+\begin{table*}[htbp]
+\centering
+\caption{Material parameters for ASTM A36 steel in the Yoshida--Uemori model.}
+\label{tab:steel_params}
+\begin{tabular}{lllllll}
+\toprule
+$\sigma_{y0}$ [MPa] & $b$ [MPa] & $C$ [MPa] & $m$ & $B$ [MPa] & $R_{\mathrm{sat}}$ [MPa] & $h$ \\
+\midrule
+255.9 & 194.9 & 338.7 & 7.9 & 277.3 & 196.0 & 0.5 \\
+\bottomrule
+\end{tabular}
+\end{table*}
+
+In Table~\ref{tab:steel_params}, $\sigma_{y0}$ is the initial yield stress, $b$ is the saturated size of the backstress $\beta$, $C$ is the hardening rate of the kinematic hardening component, $m$ is the hardening rate of the isotropic hardening component $R$ and of the kinematic hardening component $\beta$, $B$ is the initial size of the bounding surface, $R_{\mathrm{sat}}$ is the saturated size of the isotropic hardening component and $h$ is the expansion rate of the memory surface.
+
+The adopted material parameters were taken from prior experimental and numerical studies on ASTM A36 steel~\cite{Jia2014a}, in which several specimens were tested and subsequently reproduced using the Yoshida--Uemori model. In the present work, two representative tests were used to verify the implementation of this constitutive model in COMPACK. The first one corresponds to a monotonic loading test, while the second one consists of a cyclic loading protocol with an initial cycle followed by progressively increasing displacement amplitudes until specimen failure. In both cases, the numerical response obtained with the Yoshida--Uemori formulation showed good agreement with the experimental results, as illustrated in Figure~\ref{fig:YoshidaUemoriValidation}.
 
 \begin{figure*}[htbp]
-  \centering
-  \includegraphics[width=0.80\textwidth]{./images/PlotFEMValidation/FEM_validation_comparison.pdf}
-  \caption{Experimental--numerical validation of the BDSL model: hysteretic response (left) and cumulative dissipated energy (right).}
-  \label{fig:FEM_validation_comparison}
+\centering
+\includegraphics[width=0.95\textwidth]{./images/YoshidaUemoriValidation/YoshidaUemoriValidation.pdf}
+\caption{FEM validation of ASTM A36 steel under monotonic and cyclic loading using Yoshida-Uemori model and experimental tests.}
+\label{fig:YoshidaUemoriValidation}
+\end{figure*}
+
+After the verification of the material model, the complete numerical model of the BDSL device was validated against three experimental tests performed according to the loading protocols defined in the ANSI/AISC 341-16~\cite{American2002} and ASCE 7-22~\cite{American2017} qualification standards for seismic energy dissipation devices. These protocols consist of cyclic loading histories with progressively increasing amplitudes. The calibration and validation procedure involved the material parameters, assembled geometry, contact definitions, support flexibility and boundary conditions of representative BDSL specimens. Further details on the numerical model and experimental campaign can be found in Ramírez et al.~\cite{RamirezMachado2025}.
+
+The validated model accurately reproduces the main global experimental responses, including the hysteretic behaviour and cumulative dissipated energy. Figure~\ref{fig:FEM_validation_comparison} compares the experimental and numerical results, confirming the suitability of the FEM model as a numerical reference for configurations beyond those experimentally tested.
+
+\begin{figure*}[htbp]
+\centering
+\includegraphics[width=0.80\textwidth]{./images/PlotFEMValidation/FEM_validation_comparison.pdf}
+\caption{Experimental--numerical validation of the BDSL model: hysteretic response (left) and cumulative dissipated energy (right).}
+\label{fig:FEM_validation_comparison}
 \end{figure*}
 
 \section{Dataset generation and surrogate modelling}\label{sec:surrogates}
@@ -415,7 +441,9 @@ The proposed methodology also has some limitations that should be acknowledged.
 
 Future work should extend the design space by including additional geometric and mechanical variables, such as window height, window spacing, frame thickness or global device proportions. This extension would increase the dimensionality and complexity of the surrogate task. In those cases, the performance of RBF interpolation should therefore be reassessed. While RBF models performed very well in the present study, their efficiency and accuracy may decrease as the input space becomes larger or the response surfaces develop stronger local nonlinearities. In such cases, supervised ML models or hybrid surrogate strategies may become more advantageous.
 
-Another relevant future direction is the incorporation of interpretability analyses, such as SHapley Additive exPlanations, to quantify the influence of each geometric variable on window damage, frame damage and dissipative activation. Although such analysis lies outside the main scope of the present study, it could provide valuable insight into the design drivers governing the behaviour of BDSL dampers and support more transparent engineering decision-making. Overall, the proposed methodology establishes a scalable basis for FEM-consistent, damage-aware optimization of seismic energy dissipation devices, while leaving room for broader design variables, richer surrogate strategies and experimental validation of the optimized configurations.
+A complementary line of future work is the consideration of non-symmetric cyclic loading histories or recorded seismic displacement demands. The present study focuses on symmetric cyclic protocols because they provide a standardized and industry-relevant basis for the qualification of seismic energy dissipation devices, which must satisfy prescribed cyclic testing requirements before being implemented in practice. Nevertheless, earthquake-induced demands may lead to non-symmetric deformation histories in structural components. Extending the proposed framework to asymmetric cyclic protocols or representative seismic displacement histories would therefore be an interesting step towards broader performance assessment conditions.
+
+Another future direction is the incorporation of interpretability analyses, such as SHapley Additive exPlanations \cite{Lundberg2017}, to quantify the influence of each geometric variable on window damage, frame damage and dissipative activation. Although such analysis lies outside the main scope of the present study, it could provide valuable insight into the design drivers governing the behaviour of BDSL dampers and support more transparent engineering decision-making. Overall, the proposed methodology establishes a scalable basis for FEM-consistent, damage-aware optimization of seismic energy dissipation devices, while leaving room for broader design variables, richer surrogate strategies and experimental validation of the optimized configurations.
 
 \appendix
 
@@ -797,6 +825,6 @@ During the preparation of this work the authors used OpenAI Codex to assist with
 The authors acknowledge the financial support of Project ACE100/23/000022, ``Edificacions resilients equipades amb dissipadores Shear Link'', funded by the Government of Catalonia through ACCIO and with the support of the Catalan Office for Climate Change, with the participation of Luis Bozzo Estructuras y Proyectos S.L. and the Centre Internacional de Metodes Numerics en Enginyeria (CIMNE).
 
 \bibliographystyle{elsarticle/elsarticle-num}
-\bibliography{wileyNJD-AMA}
+\bibliography{ComparisonSurrogatesOptimizationBDSL}
 
 \end{document}

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