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2026_Article_RESILINK_ML
Commit 195076f5 by Joaquín Irazábal González
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Enhance manuscript with updated optimization framework and new references

- Revised the abstract and introduction sections of the manuscript to clarify the optimization framework for buckling-delayed shear-link dampers. - Updated design variables and parameters in the manuscript to improve clarity and accuracy. - Enhanced the validation section with additional details on the FEM model and experimental setup. - Improved the damage-aware optimization methodology, emphasizing the balance between damage control and energy dissipation. - Added a new reference for a conference paper on nonlinear dynamic analysis of structures equipped with shear links. - Introduced a new PDF document related to the optimization layout.
parent 7abfa26f
Showing with 1496 additions and 1146 deletions
Manuscript/Figures/FEMsetup.png
Manuscript/Figures/FEMsetup.png

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Manuscript/Figures/FEMsetup.png

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Manuscript/Figures/FEMsetup.png
Manuscript/Figures/FEMsetup.png
Manuscript/Figures/FEMsetup.png
Manuscript/Figures/FEMsetup.png
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Manuscript/Figures/FEMsetup.svg
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......
Manuscript/Figures/LoadPatterns/plot_load_patterns.py
......@@ -33,7 +33,7 @@ COLOR_GRID = "#d8d8d8"
X_LABEL = "Time (s)"
Y_LABEL = "Displacement (mm)"
SERIES_LABELS = ["H30", "H45", "H60"]
SERIES_LABELS = [r"$F_1$ and $F_2$", r"$F_3$ and $F_4$", r"$F_5$"]
def load_loading_patterns(path):
......
Manuscript/Figures/MLSurrogatesComparison/plot_surrogate_selection_summary.py
......@@ -11,8 +11,8 @@ Edit ``CSV_PATH`` and ``FIG_PATH`` if needed.
from pathlib import Path
import pandas as pd
import matplotlib.pyplot as plt
import pandas as pd
plt.rcParams.update(
{
......@@ -40,6 +40,11 @@ FIG_PATH = BASE_DIR / "surrogate_selection_summary_barplot"
MODEL_ORDER = ["SVR", "GPR", "GBR", "XGBoost", "MLP", "RF"]
WINDOW_ORDER = ["2W", "3W", "5W"]
TIME_WINDOW_ORDER = ["2W", "3W", "5W"]
WINDOW_LABELS = {
"2W": r"$N_w=2$",
"3W": r"$N_w=3$",
"5W": r"$N_w=5$",
}
VARIABLE_TYPE_ORDER = ["Distortion", "Damage"]
SUBGROUP_ORDER = [
("2W", "Distortion"),
......@@ -192,7 +197,7 @@ def main() -> None:
ax.text(
(distortion_x + damage_x) / 2,
-0.105,
window_group,
WINDOW_LABELS.get(window_group, window_group),
transform=ax.get_xaxis_transform(),
ha="center",
va="top",
......@@ -204,9 +209,7 @@ def main() -> None:
model_rows[[f"selected_{window}" for window in WINDOW_ORDER]].sum().sum()
)
total_lowest_rmse = int(
model_rows[[f"lowest_rmse_{window}" for window in WINDOW_ORDER]]
.sum()
.sum()
model_rows[[f"lowest_rmse_{window}" for window in WINDOW_ORDER]].sum().sum()
)
ax.text(
model_centers[MODEL_ORDER.index(model)],
......
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Napolitano C, Vaiana N, Monsalve JML, Rosati L. Nonlinear {Dynamic} {Analysis} of {Structures} {Equipped} with {Shear} {Links} by {NextFEM} {Designer}®. In: Mazzolani FM, Piluso V, Nastri E, Formisano A. \kern-2pt, eds. {\it Proceedings of the 11th {International} {Conference} on {Behaviour} of {Steel} {Structures} in {Seismic} {Areas}}International Conference on Behaviour of Steel Structures in Seismic Areas. Springer Nature Switzerland 2024; Cham\string:276--285
\bibitem{Malley1984}
Malley JO, Popov EP. Shear {Links} in {Eccentrically} {Braced} {Frames}. {\it Journal of Structural Engineering.} 1984\string;110(9)\string:2275--2295.
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Manuscript/Optimal-Design-layout/RESILINK_surrogate_optimization_OptimalDesignLayout.tex
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\corres{J. Irazábal. \email{jirazabal@cimne.upc.edu}}
\abstract[Abstract]{Buckling-delayed shear-link dampers are used in seismic-resistant structures as passive devices that concentrate energy dissipation while limiting damage to the primary system. Their geometric optimization requires balancing high energy dissipation with strict control of local damage. Finite element models can accurately reproduce the nonlinear cyclic response of these devices and provide internal quantities such as damage indicators and local distortion, but their computational cost prevents their direct use within iterative optimization loops. This work proposes an adaptive surrogate-assisted optimization framework for buckling-delayed shear-link dampers. First, experimentally calibrated nonlinear finite element models are used to generate reference datasets for dampers with different geometric and mechanical configurations. Supervised learning models are initially evaluated, with support vector regression and Gaussian process regression consistently providing high predictive accuracy. This suggests that kernel-based, distance-dependent approximations are well suited to the problem, motivating the introduction of radial basis function surrogates as a computationally efficient alternative. The surrogate predictions are coupled with a differential evolution algorithm through a damage-aware objective function that controls local damage and uses dissipated energy as a performance criterion. Optimized geometries are finally re-evaluated with finite element simulations. When the surrogate error exceeds the adopted tolerances, the new simulation result is added to the dataset and the surrogate models are retrained. The proposed framework provides an efficient damage-aware optimization of seismic energy dissipation devices.}
\abstract[Abstract]{Buckling-delayed shear-link dampers are used in seismic-resistant structures as passive devices that concentrate energy dissipation while limiting damage to the primary system. Their geometric optimization requires balancing high energy dissipation with strict control of local damage. Finite element models can accurately reproduce the nonlinear response of these devices under cyclic load and provide useful internal quantities for the optimization such as damage indicators and local distortion. However, their computational cost prevents their direct use within iterative optimization loops. This work proposes an adaptive surrogate-assisted optimization framework for buckling-delayed shear-link dampers. First, experimentally calibrated nonlinear finite element models are used to generate reference datasets for dampers with different geometric and mechanical configurations. Supervised learning models are initially evaluated, with support vector regression and Gaussian process regression consistently providing high predictive accuracy. This suggests that kernel-based, distance-dependent approximations are well suited to the problem, motivating the introduction of radial basis function surrogates as a computationally efficient alternative. The surrogate predictions are coupled with a differential evolution algorithm through a damage-aware objective function that controls local damage and uses dissipated energy as a performance criterion. Optimized geometries are finally re-evaluated with finite element simulations. When the surrogate error exceeds the adopted tolerances, the new simulation result is added to the dataset and the surrogate models are retrained. The proposed framework provides an efficient damage-aware optimization of seismic energy dissipation devices.}
\keywords{Buckling-delayed shear link, seismic energy dissipation, FEM validation, surrogate modelling, machine learning, radial basis functions, Differential Evolution.}
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\section{Introduction}\label{sec:introduction}
Shear-link beam (SLB) dampers are passive energy dissipation devices widely used in seismic-resistant structures, designed to undergo stable inelastic deformations while limiting damage to the primary system. Their configuration concentrates inelastic demand in replaceable components, enabling high energy dissipation, ductile response and stable hysteretic behavior under severe cyclic loading \cite{Malley1984,Okazaki2007}. Within this family, buckling-delayed shear-link (BDSL) dampers incorporate a mechanical configuration that promotes shear-dominated behaviour while delaying local and global buckling.
Shear-link metallic dampers are passive energy dissipation systems used in seismic-resistant structures, designed to undergo stable inelastic deformations while limiting damage to the primary system \cite{Napolitano2024}. Their configuration concentrates inelastic demand in replaceable components, enabling high energy dissipation, ductile response and stable hysteretic behavior under severe cyclic loading \cite{Malley1984,Okazaki2007}. Within this family, buckling-delayed shear-link (BDSL) dampers incorporate a mechanical configuration that promotes shear-dominated behaviour while delaying local and global buckling.
The global hysteretic response of BDSL dampers can be characterized through experimental testing. However, laboratory campaigns present important limitations when addressing design optimization problems: internal state variables such as local plastic strains, stress triaxiality or damage indicators cannot be directly measured and the high cost and logistical complexity of experimental programs restrict the number of geometric configurations that can be explored. These limitations become even more critical when the design objective is not only to increase global energy dissipation and maximum displacement supported by the device, but also to control where and how damage develops within the device, making systematic optimization impractical.
......@@ -149,10 +149,10 @@ This separation of functions leads to a non-trivial design problem. Thin windows
The design variables considered in this work are the window thicknesses,
\begin{equation}
\mathbf{x}=\left[t_{w,1},t_{w,2},\ldots,t_{w,W}\right],
\mathbf{x}=\left[t_{w,1},t_{w,2},\ldots,t_{w,N_w}\right],
\label{eq:design_vector}
\end{equation}
where $W$ denotes the number of windows. The device width and height are identified by $B$ and $H$, respectively. Five geometry families are analysed, defined by different combinations of height, width and number of windows. Due to confidentiality constraints, the main dimensions are reported in normalized form with respect to reference values, $H_{\text{ref}}$ and $B_{\text{ref}}$. Figure~\ref{fig:DeviceGeom} shows the geometric scheme of one representative BDSL configuration. The example corresponds to a two-window device; throughout the paper, windows are numbered from top to bottom.
where $N_w$ denotes the number of windows. The device width and height are identified by $B$ and $H$, respectively. Five geometry families are analysed, defined by different combinations of height, width and number of windows. Due to confidentiality constraints, the main dimensions are reported in normalized form with respect to reference values, $H_{\text{ref}}$ and $B_{\text{ref}}$. Figure~\ref{fig:DeviceGeom} shows the geometric scheme of one representative BDSL configuration. The example corresponds to a two-window device; throughout the paper, windows are numbered from top to bottom.
\begin{figure}[htbp]
\centering
......@@ -169,7 +169,7 @@ The admissible thickness ranges are defined for each geometry family according t
\label{tab:families}
\begin{tabular}{llllll}
\toprule
Family & $H/H_{\text{ref}}$ & $B/B_{\text{ref}}$ & $W$ & Design variables & Thickness bounds \\
Family & $H/H_{\text{ref}}$ & $B/B_{\text{ref}}$ & $N_w$ & Design variables & Thickness bounds \\
\midrule
$F_1$ & 1.00 & 1.00 & 2 & $t_{w,1},t_{w,2}$ & 10--20 mm \\
$F_2$ & 1.00 & 1.17 & 2 & $t_{w,1},t_{w,2}$ & 10--20 mm \\
......@@ -182,18 +182,18 @@ $F_5$ & 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 Ramirez 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 based on an incremental formulation \cite{Martinez2011}. The model accounts for large displacements, material and geometric nonlinearities, contact interactions and the boundary conditions associated with the experimental configuration.
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 Ramirez 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 anti-buckling system and to control local and global instability.
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.
\begin{figure*}[htbp]
\begin{figure}[htbp]
\centering
\includegraphics[width=0.60\textwidth]{../Figures/FEMsetup.png}
\includegraphics[width=0.495\textwidth]{../Figures/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*}
\end{figure}
The model was calibrated and validated against cyclic experimental tests performed on representative BDSL specimens. 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.
......@@ -208,11 +208,11 @@ The model was calibrated and validated against cyclic experimental tests perform
Once validated, the FEM model is used to generate the datasets required for surrogate training and optimization. The optimization strategy relies on local damage indicators in the dissipative windows and surrounding frame, together with local distortion measures associated with the activation of the dissipative mechanism. Since these quantities are difficult to measure experimentally, the use of a high-fidelity FEM model provides valuable access to the internal state variables and local fields governing damage evolution and energy dissipation.
The damage indicator adopted in this work is the Triaxial Failure Damage Map (TFDMap) \cite{Rastellini2016}. This stress-triaxiality-based indicator evaluates the proximity of each material point to ductile failure by comparing its stress triaxiality and accumulated equivalent plastic strain with a reference failure envelope \cite{Rice1969,Bao2004,Wierzbicki2005,Bai2008}. In this study, the TFDMap is used as a post-processing damage-screening indicator, not as a constitutive fracture criterion. Its purpose is therefore not to explicitly predict crack initiation, but to compare geometrical configurations and ensure that optimized designs remain within acceptable damage levels.
The damage indicator adopted in this work is the Triaxial Failure Damage Map (TFDMap) \cite{Rastellini2016}. This stress-triaxiality-based indicator evaluates the proximity of each material point to ductile failure by comparing, for a given triaxiality, the accumulated equivalent plastic strain with a reference failure envelope \cite{Rice1969,Bao2004,Wierzbicki2005,Bai2008}. In this study, the TFDMap is used as a post-processing damage-screening indicator, not as a constitutive fracture criterion. Its purpose is therefore not to explicitly predict crack initiation, but to compare geometrical configurations and ensure that optimized designs remain within acceptable damage levels.
\subsection{Design of experiments}\label{subsec:doe}
The FEM campaign is planned to cover the admissible parameter domain of each device family while ensuring a homogeneous exploration of the multidimensional space. The design variables are the window thicknesses $t_{w,i}$, whose combinations are generated through a Design of Experiments (DoE) strategy based on Latin Hypercube Sampling (LHS) optimized with the maximin criterion \cite{Joseph2008}. This approach provides a near-random yet space-filling distribution of samples, reducing clustering and improving the representation of the admissible domain.
The FEM campaign is planned to cover an admissible range of values for the geometric parameters of each device family while ensuring a homogeneous exploration of the multidimensional space. The design variables are the window thicknesses $t_{w,i}$, whose combinations are generated through a Design of Experiments (DoE) strategy based on Latin Hypercube Sampling (LHS) optimized with the \textit{maximin} criterion \cite{Joseph2008}. This approach provides a near-random yet space-filling distribution of samples, reducing clustering and improving the representation of the admissible range.
For each geometry family, the optimization cycle starts from an initial set of FEM simulations selected to provide reasonable coverage of the design space while keeping the computational cost as low as possible. The number of initial samples is defined according to the dimensionality of each family: 8 samples for two-window devices, 16 samples for three-window devices and 64 samples for five-window devices. In all cases, the number of samples is selected as a power of two, which facilitates the potential use of Progressive Latin Hypercube Sampling (PLHS) \cite{Sheikholeslami2017} in future iterations. This would allow the DoE to be expanded while preserving its space-filling properties and avoiding the need to repeat previously computed simulations.
......@@ -224,7 +224,7 @@ To improve surrogate robustness near the admissible limits, the sampling domain
\label{tab:families_doe}
\begin{tabular}{lllllll}
\toprule
Family & $H/H_{\text{ref}}$ & $B/B_{\text{ref}}$ & $W$ & Design variables & Thickness bounds & Simulations (DoE) \\
Family & $H/H_{\text{ref}}$ & $B/B_{\text{ref}}$ & $N_w$ & Design variables & Thickness bounds & Simulations (DoE) \\
\midrule
$F_1$ & 1.00 & 1.00 & 2 & $t_{w,1},t_{w,2}$ & 8--22 mm & 8 \\
$F_2$ & 1.00 & 1.17 & 2 & $t_{w,1},t_{w,2}$ & 8--22 mm & 8 \\
......@@ -252,7 +252,7 @@ The maximum local shear distortion in each window is denoted by $\varepsilon_{xy
This work compares several supervised surrogate models for predicting FEM-derived damage and distortion indicators. The considered models cover three families: tree-based methods, including Random Forest (RF) \cite{Breiman2001}, Gradient Boosting Regression (GBR) \cite{Friedman2001} and XGBoost \cite{Chen2016}; kernel-based methods, including Support Vector Regression (SVR) \cite{Drucker1996} and Gaussian Process Regression (GPR) \cite{Williams1995}; and neural-network models, represented by the Multilayer Perceptron (MLP) \cite{Rosenblatt1958,Rumelhart1986}. RF relies on bootstrap aggregation of decision trees, GBR and XGBoost are sequential boosting approaches, SVR and GPR exploit kernel functions to model nonlinear relationships and MLP approximates nonlinear input--output mappings through interconnected layers.
For every geometry family, a separate regression model is trained for each target output. The input vector contains the window thicknesses of the corresponding device, while the outputs are the local distortion indicators in each window, $\varepsilon_{xy,i}$, the window damage indicators, $\TFD_i$, and the frame damage indicator, $\TFD_f$. Therefore, for a geometry family with $W$ windows, $2W+1$ surrogate models are trained: $W$ models for window distortion, $W$ models for window damage and one model for frame damage. For each output, all candidate algorithms are evaluated independently and the selected model is retained for the optimization stage.
For every geometry family, a separate regression model is trained for each target output. The input vector contains the window thicknesses of the corresponding device, while the outputs are the local distortion indicators in each window, $\varepsilon_{xy,i}$, the window damage indicators, $\TFD_i$, and the frame damage indicator, $\TFD_f$. Therefore, for a geometry family with $N_w$ windows, $2N_w+1$ surrogate models are trained: $N_w$ models for window distortion, $N_w$ models for window damage and one model for frame damage. For each output, all candidate algorithms are evaluated independently and the selected model is retained for the optimization stage.
Hyperparameters are optimized using Bayesian optimization \cite{Snoek2012}, with 40 evaluations per model and RMSE as the refit criterion. The first 10 evaluations are randomly sampled to explore the search space, while the remaining 30 are guided by the Bayesian surrogate model. This strategy provides a more efficient alternative to exhaustive grid search, particularly considering the number of geometry families, target outputs and candidate algorithms analysed. It also allows a broader exploration of continuous hyperparameter ranges. The hyperparameter search spaces considered are summarized in Appendix \ref{app:hyperparameter_search_spaces}.
......@@ -284,18 +284,18 @@ For each output variable, a final RBF surrogate is trained using all available F
\section{Damage-aware surrogate-assisted optimization}\label{sec:optimization}
The proposed methodology seeks to minimize local damage in both the dissipative windows and the surrounding frame, while promoting a balanced contribution of all windows to the energy dissipation process. The geometric optimization is carried out using DE \cite{Storn1997}, a population-based global optimizer that does not require gradient information and is therefore suitable for nonlinear and non-convex surrogate response surfaces. In the current implementation, DE is run with a maximum of 500 iterations, a population size factor of 25 and a convergence tolerance of $10^{-6}$. Once an optimal candidate is obtained, an adaptive FEM validation loop is applied to verify the predicted geometry before acceptance.
The proposed methodology seeks to balance damage among the dissipative windows while keeping it below a prescribed threshold. At the same time, it limits damage in the surrounding frame and promotes the highest possible energy dissipation through the activation of the windows. The geometric optimization is carried out using DE \cite{Storn1997}, a population-based global optimizer that does not require gradient information and is therefore suitable for nonlinear and non-convex surrogate response surfaces. In the current implementation, DE is run with a maximum of 500 iterations, a population size factor of 25 and a convergence tolerance of $10^{-6}$. Once an optimal candidate is obtained, an adaptive FEM validation loop is applied to verify the predicted geometry before acceptance.
For each candidate geometry $\mathbf{x}$, the trained surrogate models predict the window distortions $\hat{\varepsilon}_{xy,i}$, the window damage indicators $\hat{\mathcal{D}}_i$, and the frame damage indicator $\hat{\mathcal{D}}_f$. Damage is therefore controlled in all regions of the device, but with different mechanical relevance: frame damage is penalized more severely because it may compromise the structural integrity of the damper, whereas the window penalties are formulated to promote comparable damage levels among windows and avoid concentrating the dissipative demand in a single region. The dissipative contribution is estimated from $\hat{\varepsilon}_{xy,i}^2$, the window thickness and the corresponding area of the window, since the energy dissipated by each window depends not only on the distortion level but also on the amount of material involved. This term is several orders of magnitude smaller than the damage penalties and is intentionally left unscaled. As a result, damage control remains the dominant criterion, while the dissipative term acts as a tie-breaker among geometries with similar damage performance, favouring those with higher distortion and, consequently, greater energy dissipation capacity.
For each candidate geometry $\mathbf{x}$, the trained surrogate models predict the window distortions $\hat{\varepsilon}_{xy,i}$, the window damage indicators $\hat{\mathcal{D}}_i$, and the frame damage indicator $\hat{\mathcal{D}}_f$. Damage is therefore controlled in all regions of the device, but with different mechanical relevance: frame damage is penalized more severely because it may compromise the structural integrity of the damper, whereas the window damage penalties are formulated to promote comparable damage levels among windows and avoid concentrating the dissipative demand in a single region. The dissipative contribution is estimated from $\hat{\varepsilon}_{xy,i}^2$, the window thickness and the corresponding area of the window, since the energy dissipated by each window depends not only on the distortion level but also on the amount of material involved. This term is several orders of magnitude smaller than the damage penalties and is intentionally left unscaled. As a result, damage control remains the dominant criterion, while the dissipative term acts as a tie-breaker among geometries with similar damage performance, favouring those with higher distortion and, consequently, greater energy dissipation capacity.
The implemented objective function to be minimized is
\begin{equation}
J(\mathbf{x}) = - \sum_{i=1}^{W} \hat{\varepsilon}_{xy,i}^2\, t_{w,i}\, A_i +
\sum_{i=1}^{W} P_w\left(\hat{\mathcal{D}}_i;\mathcal{D}_w^{\star}\right) +
J(\mathbf{x}) = - \sum_{i=1}^{N_w} \hat{\varepsilon}_{xy,i}^2\, t_{w,i}\, A_i +
\sum_{i=1}^{N_w} P_w\left(\hat{\mathcal{D}}_i;\mathcal{D}_w^{\star}\right) +
P_f\left(\hat{\mathcal{D}}_f;\mathcal{D}_f^{\max}\right),
\label{eq:objective}
\end{equation}
where $W$ is the number of windows, $t_{w,i}$ is the thickness of window $i$, $A_i$ is the corresponding area factor, $\mathcal{D}_w^{\star}$ is the target damage level for the windows and $\mathcal{D}_f^{\max}$ is the maximum admissible frame damage threshold. The first term is negative because the optimizer minimizes $J$; therefore, larger energy dissipation contributions reduce the objective value and are favoured once the damage criteria are satisfied.
where $N_w$ is the number of windows, $t_{w,i}$ is the thickness of window $i$, $A_i$ is the corresponding area factor, $\mathcal{D}_w^{\star}$ is the target damage level for the windows and $\mathcal{D}_f^{\max}$ is the maximum admissible frame damage threshold. The first term is negative because the optimizer minimizes $J$; therefore, larger energy dissipation contributions reduce the objective value and are favoured once the damage criteria are satisfied.
The window penalty is defined as
\begin{equation}
......@@ -330,7 +330,7 @@ The surrogate-optimized geometry is not accepted directly. Instead, once an opti
\section{Numerical results and discussion}\label{sec:results}
The supervised-learning comparison shows a clear hierarchy among the candidate surrogate models. A total of 100 output-specific training problems were considered, corresponding to the $2W+1$ target variables required for each geometry family and adaptive iteration. The $F_1$ family required two optimization iterations, whereas the remaining families required three. Across all geometry families, iterations and output variables, SVR was the most frequently selected model and also the model that most often achieved the lowest cross-validated RMSE. As summarized in Figure~\ref{fig:surrogate_selection_summary_barplot}, SVR was selected in 71 cases, followed by GPR, GBR, XGBoost and MLP, while Random Forest was not selected in any case. This dominance was particularly clear for the two-window families, where only one output was assigned to a GPR model and for the damage-related outputs, for which SVR was selected in 47 out of 57 cases. For more complex devices, those with three and five windows, and for distortion-related outputs, the model selection became more heterogeneous, although SVR still provided the best overall performance. From the computational point of view, SVR also offered the lowest median training times among the supervised models, whereas MLP required substantially longer training times without providing gain in accuracy.
The supervised-learning comparison shows a clear hierarchy among the candidate surrogate models. A total of 100 output-specific training problems were considered, corresponding to the $2N_w+1$ target variables required for each geometry family and adaptive iteration. The $F_1$ family required two optimization iterations, whereas the remaining families required three. Across all geometry families, iterations and output variables, SVR was the most frequently selected model and also the model that most often achieved the lowest cross-validated RMSE. As summarized in Figure~\ref{fig:surrogate_selection_summary_barplot}, SVR was selected in 71 cases, followed by GPR, GBR, XGBoost and MLP, while Random Forest was not selected in any case. This dominance was particularly clear for the two-window families, where only one output was assigned to a GPR model and for the damage-related outputs, for which SVR was selected in 47 out of 57 cases. For more complex devices, those with three and five windows, and for distortion-related outputs, the model selection became more heterogeneous, although SVR still provided the best overall performance. From the computational point of view, SVR also offered the lowest median training times among the supervised models, whereas MLP required substantially longer training times without providing gain in accuracy.
\begin{figure*}[htbp]
\centering
......@@ -425,7 +425,7 @@ This behaviour is illustrated in Figure~\ref{fig:rbf_surface_evolution}, which s
\section{Conclusions and future work}\label{sec:conclusions}
This work presented an adaptive surrogate-assisted optimization framework for buckling-delayed shear-link dampers subjected to cyclic seismic loading. The proposed methodology addresses the main limitation of direct FEM-based optimization, the high computational cost associated with repeatedly evaluating nonlinear cyclic simulations. By training surrogate models on FEM-generated datasets and validating the optimized candidates through additional FEM analyses, the optimizer can efficiently explore the design domain while remaining consistent with the mechanical response captured by the calibrated numerical model.
This work presents an adaptive surrogate-assisted optimization framework for buckling-delayed shear-link dampers subjected to cyclic seismic loading. The proposed methodology addresses the main limitation of direct FEM-based optimization, the high computational cost associated with repeatedly evaluating nonlinear cyclic simulations. By training surrogate models on FEM-generated datasets and validating the optimized candidates through additional FEM analyses, the optimizer can efficiently explore the design domain while remaining consistent with the mechanical response captured by the calibrated numerical model.
One of the key features of the proposed optimization framework, compared to approaches focused primarily on energy maximization, is the formulation of an objective function that takes damage into account. The aim is to prioritise local damage control in both the dissipative windows and the surrounding frame, whilst promoting a balanced contribution from all windows to the energy dissipation process. Thus, damage to the windows is permitted and expected, as they are intended to act as dissipative regions, provided that it remains controlled and reasonably distributed; conversely, damage to the frame is penalised more severely because it can compromise the structural integrity of the damper. Therefore, rather than merely maximizing the energy dissipated, the proposed formulation favours geometries that concentrate dissipative activation in the windows, prevent excessive damage localization in a single region and protect the frame from critical damage.
......
Manuscript/wileyNJD-AMA.bib
......@@ -792,4 +792,21 @@ steel from coupon test results available. First, the theory of metal plasticity
urldate = {2026-05-13},
}
@InProceedings{Napolitano2024,
author = {Napolitano, Ciro and Vaiana, Nicolò and Monsalve, Julian Mauricio Londono and Rosati, Luciano},
booktitle = {Proceedings of the 11th {International} {Conference} on {Behaviour} of {Steel} {Structures} in {Seismic} {Areas}},
title = {Nonlinear {Dynamic} {Analysis} of {Structures} {Equipped} with {Shear} {Links} by {NextFEM} {Designer}®},
year = {2024},
address = {Cham},
editor = {Mazzolani, Federico M. and Piluso, Vincenzo and Nastri, Elide and Formisano, Antonio},
organization = {International Conference on Behaviour of Steel Structures in Seismic Areas},
pages = {276--285},
publisher = {Springer Nature Switzerland},
abstract = {Shear link devices are metallic dampers that can be adopted to control structural vibrations induced by seismic and wind loads due to their typical rate-independent hysteretic behavior. To allow for an accurate and computationally efficient nonlinear dynamic analysis of structures equipped with shear links, we briefly present both the analytical and differential formulations of the Vaiana-Rosati model of hysteresis. Such a phenomenological model has been recently implemented in NextFEM Designer, a computer program for finite element analysis. To simplify the hysteresis model calibration, some preliminary details on a parameter identification procedure are provided. Finally, nonlinear time history analyses are carried out, by using NextFEM Designer, on a structure subjected to earthquake excitation.},
doi = {10.1007/978-3-031-62888-7_25},
isbn = {978-3-031-62888-7},
keywords = {Nonlinear Dynamic Analysis, Rate-Independent Hysteresis, Shear Link, Vaiana-Rosati Model},
language = {en},
}
@Comment{jabref-meta: databaseType:bibtex;}
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