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2026_Article_RESILINK_ML
Commit f94d3488 by Joaquín Irazábal González
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Add RESILINK surrogate optimization manuscript and update references

- Created new manuscript file for RESILINK surrogate optimization. - Added PDF version of the manuscript. - Updated LaTeX file to reference the correct journal name and include necessary figures. - Adjusted figure paths to ensure correct referencing in the document. - Modified USG.cls to correctly handle page numbering for the manuscript. - Updated bibliography path in the manuscript for proper citation.
parent e27d5af6
Showing with 4269 additions and 352 deletions
Bibliography/CIMNE_docs/RESILINK_surrogate_optimization_manuscript_merged_intro.tex
......@@ -16,7 +16,7 @@
\received{Date Month Year}
\revised{Date Month Year}
\accepted{Date Month Year}
\journal{Journal}
\journal{Earthquake Engineering \& Structural Dynamics}
\volume{00}
\copyyear{2026}
\startpage{1}
......@@ -57,7 +57,7 @@
\author{Bozzo G.},
\author{Bozzo L.}, and
\author{Irazabal J.}}.
\ctitle{Adaptive FEM-validated surrogate optimization of buckling-delayed shear-link dampers for seismic damage mitigation.} \cjournal{\it Journal.} \cvol{2026;00(00):1--18}.}
\ctitle{Adaptive FEM-validated surrogate optimization of buckling-delayed shear-link dampers for seismic damage mitigation.} \cjournal{\it Earthquake Engineering \& Structural Dynamics.} \cvol{2026;00(00):1--18}.}
\maketitle
......
Manuscript/Optimal-Design-layout/RESILINK_surrogate_optimization_OptimalDesignLayout.aux
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Manuscript/Optimal-Design-layout/RESILINK_surrogate_optimization_OptimalDesignLayout.tex
......@@ -16,17 +16,52 @@
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\articletype{ORIGINAL ARTICLE}%
\subarticletype{Optimal Design and Surrogate Optimization}
\received{Date Month Year}
\revised{Date Month Year}
\accepted{Date Month Year}
\journal{Journal}
\journal{Earthquake Engineering \& Structural Dynamics}
\volume{00}
\copyyear{2026}
\startpage{1}
\articledoi{10.1002/0000}
\articledoi{10.1002/eqe.0000} % placeholder DOI
\raggedbottom
......@@ -64,7 +99,7 @@
\author{Rastellini F.},
\author{Bozzo G.}, and
\author{Bozzo L.}}.
\ctitle{Damage-aware surrogate optimization of buckling-delayed shear-link dampers with adaptive finite element validation.} \cjournal{\it Journal.} \cvol{2026;00(00):1--18}.}
\ctitle{Damage-aware surrogate optimization of buckling-delayed shear-link dampers with adaptive finite element validation.} \cjournal{\it Earthquake Engineering \& Structural Dynamics.} \cvol{2026;00(00):1--18}.}
\maketitle
......@@ -223,83 +258,10 @@ This work compares several supervised surrogate models for predicting FEM-derive
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.
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. Table~\ref{tab:cv_hyperparameter_settings} summarizes the hyperparameter search spaces considered.
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}.
The cross-validation strategy is adapted to the dataset size. Leave-One-Out validation is used for $N\leq20$, repeated four-fold cross-validation with five repetitions for $21\leq N\leq80$, and shuffled five-fold cross-validation for larger datasets. For small datasets, the search spaces of tree-based models are additionally restricted to reduce overfitting.
\begin{table*}[ht!]
\centering
\caption{Hyperparameter search spaces used for Bayesian optimization of the supervised surrogate models.}
\label{tab:cv_hyperparameter_settings}
\scriptsize
\setlength{\tabcolsep}{5pt}
\renewcommand{\arraystretch}{1.10}
\begin{tabular}{llll}
\toprule
Model & Preprocessing / kernel & Hyperparameter & Search space \\
\midrule
\multirow{5}{*}{RF}
& \multirow{5}{*}{--}
& $n_{\mathrm{estimators}}$ & $[200,2000]$ \\
& & max depth & $[5,40]$ \\
& & min samples split & $[2,10]$ \\
& & min samples leaf & $[1,6]$ \\
& & max features & $[0.5,1.0]$ \\
\midrule
\multirow{5}{*}{GBR}
& \multirow{5}{*}{--}
& $n_{\mathrm{estimators}}$ & $[200,3000]$ \\
& & learning rate & $[10^{-3},10^{-1}]$ \\
& & max depth & $[2,6]$ \\
& & subsample & $[0.6,1.0]$ \\
& & max features & $[0.5,1.0]$ \\
\midrule
\multirow{6}{*}{XGBoost}
& \multirow{6}{*}{--}
& $n_{\mathrm{estimators}}$ & $[200,2000]$ \\
& & max depth & $[3,8]$ \\
& & learning rate & $[10^{-3},0.3]$ \\
& & subsample & $[0.6,1.0]$ \\
& & colsample by tree & $[0.6,1.0]$ \\
& & min child weight & $[1,10]$ \\
\midrule
\multirow{3}{*}{SVR}
& \multirow{3}{*}{StandardScaler + RBF kernel}
& $C$ & $[10^{0},10^{4}]$ \\
& & $\gamma$ & $[10^{-4},10^{-1}]$ \\
& & $\epsilon$ & $[10^{-4},10^{-1}]$ \\
\midrule
\multirow{6}{*}{GPR}
& \multirow{6}{*}{StandardScaler}
& kernel & $\{\mathrm{RBF},\mathrm{Matern}_{3/2},\mathrm{Matern}_{5/2},\mathrm{RQ}\}$ \\
& & amplitude & $[10^{-2},10^{2}]$ \\
& & length scale & $[10^{-2},10^{2}]$ \\
& & $\alpha_{\mathrm{RQ}}$ & $[10^{-2},10^{2}]$ \\
& & noise & $[10^{-12},10^{-4}]$ \\
& & restarts & $[1,10]$ \\
\midrule
\multirow{5}{*}{MLP}
& \multirow{5}{*}{StandardScaler}
& hidden layers & $[1,5]$ \\
& & neurons per layer & $[64,512]$ \\
& & activation & $\{\mathrm{ReLU},\tanh\}$ \\
& & $\alpha$ & $[10^{-5},10^{-2}]$ \\
& & initial learning rate & $[10^{-4},10^{-2}]$ \\
\bottomrule
\end{tabular}
\vspace{2mm}
\parbox{0.95\textwidth}{\footnotesize \textit{Note:} For tree-based models, the search spaces are automatically restricted for small datasets to reduce overfitting.}
\end{table*}
Model selection is performed in two stages. First, for each candidate algorithm, Bayesian hyperparameter optimization is carried out using cross-validated Root Mean Squared Error (RMSE) as the refit criterion. The best hyperparameter configuration is therefore the one with the lowest mean RMSE. Then, the best configurations from all candidate algorithms are compared. The model with the lowest mean RMSE defines a competitive threshold and all models with an RMSE within 5\% of this value are retained. Among these competitive models, the final selection is based on the lowest relative RMSE dispersion, computed as the standard deviation of the fold-wise RMSE divided by the mean RMSE. If two models have the same dispersion, the one with the lower mean RMSE is preferred. This procedure, summarized in Figure \ref{fig:BayesianSearchCV}, favours surrogates that are both accurate and stable.
\begin{figure*}[htbp]
......@@ -400,7 +362,7 @@ The supervised-learning comparison shows a clear hierarchy among the candidate s
These results indicate that kernel-based models are particularly well suited to the present surrogate task. SVR provides the best compromise between accuracy and computational cost, while GPR is the second most competitive supervised strategy, especially in some higher-dimensional cases. Tree-based models, although robust, are less frequently selected and MLP models are not competitive in terms of computational efficiency for the dataset sizes considered here. As mentioned in previous sections, this behaviour motivated the additional evaluation of RBF interpolation as a simpler surrogate alternative. In contrast to the supervised models, RBF models were trained in less than one second per output, making them especially attractive for repeated surrogate updates within the adaptive optimization loop.
The FEM validation of the optimized geometries is summarized in Table~\ref{tab:final_surrogate_comparison}. For each geometry family and surrogate strategy, the table reports the final accepted adaptive iteration, the optimized window thicknesses $\mathbf{t}_w^{\star}$, the surrogate-predicted objective value ($J_{\mathrm{surr}}$), the corresponding FEM-recomputed objective value ($J_{\mathrm{FEM}}$) and the associated validation errors ($|e_J|$ and $e_{\max}$). The optimization process required between two and three adaptive iterations depending on the geometry family and surrogate type, with most cases converging after three iterations. No systematic difference in the number of iterations was observed between RBF and supervised ML surrogates. The maximum variable error, $e_{\max}$, is defined as the largest relative error among all quantities entering the objective function, namely ${\Exy}_i$, $\TFD_i$ and $\TFD_f$, whereas the objective-function error, $|e_J|$, is reported in absolute value.
The FEM validation of the optimized geometries is summarized in Table~\ref{tab:final_surrogate_comparison}, while the complete optimization results for all adaptive iterations are provided in Appendix~\ref{appendix:optimization_results}. For each geometry family and surrogate strategy, Table~\ref{tab:final_surrogate_comparison} reports the final accepted adaptive iteration, the optimized window thicknesses $\mathbf{t}_w^{\star}$, the surrogate-predicted objective value $J_{\mathrm{surr}}$, the corresponding FEM-recomputed objective value $J_{\mathrm{FEM}}$, and the associated validation errors, $|e_J|$ and $e_{\max}$. The maximum variable error, $e_{\max}$, is defined as the largest relative error among all quantities entering the objective function, namely ${\Exy}_i$, $\TFD_i$ and $\TFD_f$, whereas $|e_J|$ denotes the absolute objective-function error. The optimization required between two and three adaptive iterations depending on the geometry family and surrogate type, with most cases converging after three iterations. No systematic difference in the number of iterations was observed between RBF and supervised ML surrogates.
\begin{table*}[ht!]
\centering
......@@ -519,6 +481,342 @@ The authors declare no potential conflict of interests.
\bmsection*{Supporting information}
Additional supporting information may include the FEM database, trained surrogate models, optimization scripts and final FEM-validation simulations.
Additional information related to this study is available from the corresponding author upon reasonable request.
\appendix
\bmsection{Hyperparameter search spaces for supervised ML surrogate models}
\label{app:hyperparameter_search_spaces}
\vspace*{12pt}
Table~\ref{tab:cv_hyperparameter_settings} summarizes the hyperparameter search spaces used for the Bayesian optimization of the supervised surrogate models. The same ranges are used for kernel-based and neural-network models across all dataset sizes, whereas the search spaces of tree-based models are automatically restricted for small datasets to reduce overfitting. The cross-validation strategy is also adapted to the dataset size: Leave-One-Out validation is used for $N\leq20$, repeated four-fold cross-validation with five repetitions for $21\leq N\leq80$, and shuffled five-fold cross-validation for larger datasets.
\begin{table*}[htbp]
\centering
\caption{Hyperparameter search spaces used for Bayesian optimization of the supervised surrogate models.}
\label{tab:cv_hyperparameter_settings}
\scriptsize
\setlength{\tabcolsep}{5pt}
\renewcommand{\arraystretch}{1.10}
\begin{tabular}{llll}
\toprule
Model & Preprocessing / kernel & Hyperparameter & Search space \\
\midrule
\multirow{5}{*}{RF}
& \multirow{5}{*}{--}
& $n_{\mathrm{estimators}}$ & $[200,2000]$ \\
& & max depth & $[5,40]$ \\
& & min samples split & $[2,10]$ \\
& & min samples leaf & $[1,6]$ \\
& & max features & $[0.5,1.0]$ \\
\midrule
\multirow{5}{*}{GBR}
& \multirow{5}{*}{--}
& $n_{\mathrm{estimators}}$ & $[200,3000]$ \\
& & learning rate & $[10^{-3},10^{-1}]$ \\
& & max depth & $[2,6]$ \\
& & subsample & $[0.6,1.0]$ \\
& & max features & $[0.5,1.0]$ \\
\midrule
\multirow{6}{*}{XGBoost}
& \multirow{6}{*}{--}
& $n_{\mathrm{estimators}}$ & $[200,2000]$ \\
& & max depth & $[3,8]$ \\
& & learning rate & $[10^{-3},0.3]$ \\
& & subsample & $[0.6,1.0]$ \\
& & colsample by tree & $[0.6,1.0]$ \\
& & min child weight & $[1,10]$ \\
\midrule
\multirow{3}{*}{SVR}
& \multirow{3}{*}{StandardScaler + RBF kernel}
& $C$ & $[10^{0},10^{4}]$ \\
& & $\gamma$ & $[10^{-4},10^{-1}]$ \\
& & $\epsilon$ & $[10^{-4},10^{-1}]$ \\
\midrule
\multirow{6}{*}{GPR}
& \multirow{6}{*}{StandardScaler}
& kernel & $\{\mathrm{RBF},\mathrm{Matern}_{3/2},\mathrm{Matern}_{5/2},\mathrm{RQ}\}$ \\
& & amplitude & $[10^{-2},10^{2}]$ \\
& & length scale & $[10^{-2},10^{2}]$ \\
& & $\alpha_{\mathrm{RQ}}$ & $[10^{-2},10^{2}]$ \\
& & noise & $[10^{-12},10^{-4}]$ \\
& & restarts & $[1,10]$ \\
\midrule
\multirow{5}{*}{MLP}
& \multirow{5}{*}{StandardScaler}
& hidden layers & $[1,5]$ \\
& & neurons per layer & $[64,512]$ \\
& & activation & $\{\mathrm{ReLU},\tanh\}$ \\
& & $\alpha$ & $[10^{-5},10^{-2}]$ \\
& & initial learning rate & $[10^{-4},10^{-2}]$ \\
\bottomrule
\end{tabular}
\end{table*}
\bmsection{Summary of optimization results}
\label{appendix:optimization_results}
\vspace*{12pt}
This appendix summarizes the surrogate-predicted optimized configurations, the corresponding FEM validation values and the associated errors for all adaptive iterations. The source ``Surr.'' denotes the values predicted by the surrogate model during the optimization, whereas ``FEM'' denotes the values recomputed with the high-fidelity numerical model. Error rows report the relative error for the response variables and the absolute error for the objective function.
\begin{table*}[htbp]
\centering
\caption{Optimization results for the H30\_B29 family using Supervised ML surrogates.}
\label{tab:app_ml_h30_b29}
\scriptsize
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{1.08}
\begin{tabular}{llllllll}
\toprule
Iter. & Source & $\mathbf{t}_w$ [mm] & $\boldsymbol{\varepsilon}_{xy}$ & $\boldsymbol{\mathcal{D}}_w$ & $\mathcal{D}_f$ & $J$ \\
\midrule
1 & Surr. & $[12.60,\;14.64]$ & $[0.05048,\;0.06183]$ & $[90.00,\;90.00]$ & 89.65 & 0.00 \\
& FEM & $[12.60,\;14.64]$ & $[0.04501,\;0.0616]$ & $[88.25,\;91.19]$ & 87.17 & 3.16 \\
& Error & -- & $[12.15\%,\;0.37\%]$ & $[1.99\%,\;1.30\%]$ & 2.84\% & 3.16 \\
\addlinespace[1mm]
2 & Surr. & $[12.53,\;14.75]$ & $[0.04602,\;0.06061]$ & $[90.00,\;90.00]$ & 89.32 & 0.00 \\
& FEM & $[12.53,\;14.75]$ & $[0.04555,\;0.06053]$ & $[89.95,\;90.18]$ & 86.61 & 0.07947 \\
& Error & -- & $[1.03\%,\;0.12\%]$ & $[0.05\%,\;0.20\%]$ & 3.14\% & 0.0795 \\
\bottomrule
\end{tabular}
\end{table*}
\begin{table*}[htbp]
\centering
\caption{Optimization results for the H30\_B34 family using Supervised ML surrogates.}
\label{tab:app_ml_h30_b34}
\scriptsize
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{1.08}
\begin{tabular}{llllllll}
\toprule
Iter. & Source & $\mathbf{t}_w$ [mm] & $\boldsymbol{\varepsilon}_{xy}$ & $\boldsymbol{\mathcal{D}}_w$ & $\mathcal{D}_f$ & $J$ \\
\midrule
1 & Surr. & $[15.69,\;20.00]$ & $[0.05065,\;0.04732]$ & $[105.29,\;72.51]$ & 96.62 & 541.95 \\
& FEM & $[15.69,\;20.00]$ & $[0.05127,\;0.04603]$ & $[103.51,\;73.24]$ & 99.21 & 980.46 \\
& Error & -- & $[1.21\%,\;2.80\%]$ & $[1.72\%,\;0.99\%]$ & 2.61\% & 438.51 \\
\addlinespace[1mm]
2 & Surr. & $[15.14,\;20.00]$ & $[0.05444,\;0.04442]$ & $[110.55,\;71.35]$ & 97.30 & 830.19 \\
& FEM & $[15.14,\;20.00]$ & $[0.05413,\;0.04418]$ & $[110.40,\;71.84]$ & 97.12 & 795.11 \\
& Error & -- & $[0.58\%,\;0.53\%]$ & $[0.14\%,\;0.68\%]$ & 0.19\% & 35.08 \\
\addlinespace[1mm]
3 & Surr. & $[15.20,\;20.00]$ & $[0.05398,\;0.0441]$ & $[109.73,\;71.61]$ & 97.30 & 796.29 \\
& FEM & $[15.20,\;20.00]$ & $[0.05379,\;0.04439]$ & $[109.65,\;72.03]$ & 97.36 & 802.64 \\
& Error & -- & $[0.36\%,\;0.64\%]$ & $[0.07\%,\;0.59\%]$ & 0.06\% & 6.35 \\
\bottomrule
\end{tabular}
\end{table*}
\begin{table*}[htbp]
\centering
\caption{Optimization results for the H45\_B29 family using Supervised ML surrogates.}
\label{tab:app_ml_h45_b29}
\scriptsize
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{1.08}
\begin{tabular}{llllllll}
\toprule
Iter. & Source & $\mathbf{t}_w$ [mm] & $\boldsymbol{\varepsilon}_{xy}$ & $\boldsymbol{\mathcal{D}}_w$ & $\mathcal{D}_f$ & $J$ \\
\midrule
1 & Surr. & $[5.96,\;8.23,\;9.47]$ & $[0.05164,\;0.04547,\;0.04887]$ & $[90.00,\;90.00,\;90.00]$ & 71.00 & 0.00 \\
& FEM & $[5.96,\;8.23,\;9.47]$ & $[0.04637,\;0.04648,\;0.05136]$ & $[89.20,\;85.22,\;83.96]$ & 68.08 & 11.62 \\
& Error & -- & $[11.37\%,\;2.18\%,\;4.85\%]$ & $[0.90\%,\;5.61\%,\;7.19\%]$ & 4.28\% & 11.62 \\
\addlinespace[1mm]
2 & Surr. & $[5.70,\;7.90,\;9.02]$ & $[0.04801,\;0.0478,\;0.0493]$ & $[90.00,\;90.00,\;90.00]$ & 71.22 & 0.00 \\
& FEM & $[5.70,\;7.90,\;9.02]$ & $[0.04906,\;0.04815,\;0.05333]$ & $[93.70,\;89.65,\;88.89]$ & 68.18 & 15.15 \\
& Error & -- & $[2.14\%,\;0.73\%,\;7.55\%]$ & $[3.95\%,\;0.39\%,\;1.25\%]$ & 4.46\% & 15.15 \\
\addlinespace[1mm]
3 & Surr. & $[5.72,\;7.87,\;8.96]$ & $[0.04862,\;0.04822,\;0.05305]$ & $[90.00,\;90.00,\;90.00]$ & 68.58 & 0.00 \\
& FEM & $[5.72,\;7.87,\;8.96]$ & $[0.04846,\;0.04798,\;0.05389]$ & $[92.64,\;89.69,\;89.81]$ & 68.52 & 7.47 \\
& Error & -- & $[0.32\%,\;0.50\%,\;1.57\%]$ & $[2.85\%,\;0.34\%,\;0.21\%]$ & 0.09\% & 7.47 \\
\bottomrule
\end{tabular}
\end{table*}
\begin{table*}[htbp]
\centering
\caption{Optimization results for the H45\_B34 family using Supervised ML surrogates.}
\label{tab:app_ml_h45_b34}
\scriptsize
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{1.08}
\begin{tabular}{llllllll}
\toprule
Iter. & Source & $\mathbf{t}_w$ [mm] & $\boldsymbol{\varepsilon}_{xy}$ & $\boldsymbol{\mathcal{D}}_w$ & $\mathcal{D}_f$ & $J$ \\
\midrule
1 & Surr. & $[7.34,\;9.28,\;10.13]$ & $[0.03217,\;0.03708,\;0.05097]$ & $[90.00,\;90.00,\;90.00]$ & 71.57 & 0.00 \\
& FEM & $[7.34,\;9.28,\;10.13]$ & $[0.03834,\;0.04702,\;0.05298]$ & $[80.76,\;86.78,\;87.08]$ & 69.66 & 15.38 \\
& Error & -- & $[16.10\%,\;21.13\%,\;3.79\%]$ & $[11.44\%,\;3.71\%,\;3.35\%]$ & 2.75\% & 15.38 \\
\addlinespace[1mm]
2 & Surr. & $[6.87,\;9.08,\;9.86]$ & $[0.03612,\;0.05013,\;0.05362]$ & $[90.00,\;90.00,\;90.00]$ & 68.42 & 0.00 \\
& FEM & $[6.87,\;9.08,\;9.86]$ & $[0.04277,\;0.04322,\;0.05375]$ & $[90.40,\;89.46,\;88.14]$ & 68.49 & 2.56 \\
& Error & -- & $[15.56\%,\;15.99\%,\;0.24\%]$ & $[0.44\%,\;0.60\%,\;2.11\%]$ & 0.10\% & 2.56 \\
\addlinespace[1mm]
3 & Surr. & $[6.84,\;9.05,\;9.73]$ & $[0.04169,\;0.04354,\;0.05319]$ & $[90.00,\;90.00,\;90.00]$ & 68.81 & 0.00 \\
& FEM & $[6.84,\;9.05,\;9.73]$ & $[0.04271,\;0.04299,\;0.05478]$ & $[90.36,\;89.19,\;89.59]$ & 68.94 & 1.35 \\
& Error & -- & $[2.40\%,\;1.27\%,\;2.91\%]$ & $[0.40\%,\;0.90\%,\;0.46\%]$ & 0.19\% & 1.35 \\
\bottomrule
\end{tabular}
\end{table*}
\begin{table*}[htbp]
\centering
\caption{Optimization results for the H60\_B34 family using Supervised ML surrogates.}
\label{tab:app_ml_h60_b34}
\scriptsize
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{1.08}
\begin{tabular}{llllllll}
\toprule
Iter. & Source & $\mathbf{t}_w$ [mm] & $\boldsymbol{\varepsilon}_{xy}$ & $\boldsymbol{\mathcal{D}}_w$ & $\mathcal{D}_f$ & $J$ \\
\midrule
1 & Surr. & $[5.97,\;7.38,\;8.56,\;6.70,\;5.00]$ & $[0.05963,\;0.05258,\;0.06459,\;0.06971,\;0.05512]$ & $[90.00,\;90.00,\;90.00,\;90.00,\;79.42]$ & 74.65 & 10.58 \\
& FEM & $[5.97,\;7.38,\;8.56,\;6.70,\;5.00]$ & $[0.05635,\;0.05188,\;0.05966,\;0.07124,\;0.05824]$ & $[84.95,\;90.65,\;87.91,\;81.06,\;74.18]$ & 79.15 & 32.33 \\
& Error & -- & $[5.83\%,\;1.36\%,\;8.27\%,\;2.14\%,\;5.35\%]$ & $[5.94\%,\;0.72\%,\;2.38\%,\;11.03\%,\;7.07\%]$ & 5.69\% & 21.74 \\
\addlinespace[1mm]
2 & Surr. & $[5.76,\;7.37,\;8.46,\;6.67,\;5.00]$ & $[0.0615,\;0.05313,\;0.06014,\;0.07067,\;0.05734]$ & $[90.00,\;90.00,\;90.00,\;90.00,\;73.04]$ & 74.85 & 16.96 \\
& FEM & $[5.76,\;7.37,\;8.46,\;6.67,\;5.00]$ & $[0.06398,\;0.05679,\;0.06492,\;0.07844,\;0.06236]$ & $[95.56,\;95.92,\;92.86,\;85.17,\;71.37]$ & 75.19 & 97.55 \\
& Error & -- & $[3.88\%,\;6.45\%,\;7.36\%,\;9.90\%,\;8.05\%]$ & $[5.81\%,\;6.17\%,\;3.08\%,\;5.67\%,\;2.34\%]$ & 0.45\% & 80.59 \\
\addlinespace[1mm]
3 & Surr. & $[5.74,\;7.46,\;8.50,\;6.37,\;5.00]$ & $[0.06117,\;0.05325,\;0.0609,\;0.07548,\;0.05962]$ & $[90.00,\;90.00,\;90.00,\;90.00,\;73.10]$ & 75.62 & 16.90 \\
& FEM & $[5.74,\;7.46,\;8.50,\;6.37,\;5.00]$ & $[0.06082,\;0.05335,\;0.05924,\;0.07453,\;0.05842]$ & $[91.93,\;89.75,\;87.52,\;86.70,\;72.88]$ & 78.19 & 26.87 \\
& Error & -- & $[0.59\%,\;0.18\%,\;2.80\%,\;1.28\%,\;2.06\%]$ & $[2.10\%,\;0.28\%,\;2.83\%,\;3.81\%,\;0.30\%]$ & 3.29\% & 9.97 \\
\bottomrule
\end{tabular}
\end{table*}
\begin{table*}[htbp]
\centering
\caption{Optimization results for the H30\_B29 family using RBF surrogates.}
\label{tab:app_rbf_h30_b29}
\scriptsize
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{1.08}
\begin{tabular}{llllllll}
\toprule
Iter. & Source & $\mathbf{t}_w$ [mm] & $\boldsymbol{\varepsilon}_{xy}$ & $\boldsymbol{\mathcal{D}}_w$ & $\mathcal{D}_f$ & $J$ \\
\midrule
1 & Surr. & $[12.34,\;14.34]$ & $[0.04755,\;0.06219]$ & $[90.00,\;90.00]$ & 88.74 & 0.00 \\
& FEM & $[12.34,\;14.34]$ & $[0.04612,\;0.06351]$ & $[91.00,\;94.60]$ & 87.68 & 22.15 \\
& Error & -- & $[3.12\%,\;2.07\%]$ & $[1.10\%,\;4.86\%]$ & 1.20\% & 22.15 \\
\addlinespace[1mm]
2 & Surr. & $[12.68,\;14.91]$ & $[0.04531,\;0.06034]$ & $[90.00,\;90.00]$ & 87.53 & 0.00 \\
& FEM & $[12.68,\;14.91]$ & $[0.04499,\;0.0598]$ & $[88.74,\;88.84]$ & 86.81 & 2.42 \\
& Error & -- & $[0.73\%,\;0.91\%]$ & $[1.42\%,\;1.31\%]$ & 0.83\% & 2.42 \\
\addlinespace[1mm]
3 & Surr. & $[12.56,\;14.79]$ & $[0.04553,\;0.06042]$ & $[90.00,\;90.00]$ & 86.88 & 0.00 \\
& FEM & $[12.56,\;14.79]$ & $[0.04544,\;0.06033]$ & $[89.75,\;89.84]$ & 86.63 & 0.40514 \\
& Error & -- & $[0.19\%,\;0.15\%]$ & $[0.28\%,\;0.18\%]$ & 0.29\% & 0.4051 \\
\bottomrule
\end{tabular}
\end{table*}
\begin{table*}[htbp]
\centering
\caption{Optimization results for the H30\_B34 family using RBF surrogates.}
\label{tab:app_rbf_h30_b34}
\scriptsize
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{1.08}
\begin{tabular}{llllllll}
\toprule
Iter. & Source & $\mathbf{t}_w$ [mm] & $\boldsymbol{\varepsilon}_{xy}$ & $\boldsymbol{\mathcal{D}}_w$ & $\mathcal{D}_f$ & $J$ \\
\midrule
1 & Surr. & $[15.50,\;20.00]$ & $[0.05243,\;0.04593]$ & $[105.09,\;73.10]$ & 96.41 & 507.38 \\
& FEM & $[15.50,\;20.00]$ & $[0.05211,\;0.0454]$ & $[105.82,\;72.74]$ & 98.50 & 880.86 \\
& Error & -- & $[0.60\%,\;1.16\%]$ & $[0.69\%,\;0.50\%]$ & 2.12\% & 373.48 \\
\addlinespace[1mm]
2 & Surr. & $[14.80,\;18.93]$ & $[0.05458,\;0.04902]$ & $[109.57,\;78.18]$ & 96.74 & 700.74 \\
& FEM & $[14.80,\;18.93]$ & $[0.05377,\;0.04931]$ & $[109.14,\;78.71]$ & 96.78 & 689.16 \\
& Error & -- & $[1.52\%,\;0.59\%]$ & $[0.39\%,\;0.67\%]$ & 0.04\% & 11.58 \\
\addlinespace[1mm]
3 & Surr. & $[14.77,\;18.95]$ & $[0.05395,\;0.04908]$ & $[109.61,\;78.49]$ & 96.64 & 688.53 \\
& FEM & $[14.77,\;18.95]$ & $[0.054,\;0.04906]$ & $[109.69,\;78.51]$ & 96.63 & 691.06 \\
& Error & -- & $[0.10\%,\;0.05\%]$ & $[0.07\%,\;0.03\%]$ & 0.00\% & 2.53 \\
\bottomrule
\end{tabular}
\end{table*}
\begin{table*}[htbp]
\centering
\caption{Optimization results for the H45\_B29 family using RBF surrogates.}
\label{tab:app_rbf_h45_b29}
\scriptsize
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{1.08}
\begin{tabular}{llllllll}
\toprule
Iter. & Source & $\mathbf{t}_w$ [mm] & $\boldsymbol{\varepsilon}_{xy}$ & $\boldsymbol{\mathcal{D}}_w$ & $\mathcal{D}_f$ & $J$ \\
\midrule
1 & Surr. & $[5.94,\;8.38,\;9.28]$ & $[0.04571,\;0.05098,\;0.05057]$ & $[90.00,\;90.00,\;90.00]$ & 71.81 & 0.00 \\
& FEM & $[5.94,\;8.38,\;9.28]$ & $[0.04632,\;0.04484,\;0.05324]$ & $[89.24,\;82.01,\;85.72]$ & 69.82 & 13.04 \\
& Error & -- & $[1.32\%,\;13.70\%,\;5.00\%]$ & $[0.86\%,\;9.75\%,\;5.00\%]$ & 2.85\% & 13.04 \\
\addlinespace[1mm]
2 & Surr. & $[5.69,\;7.97,\;9.02]$ & $[0.04677,\;0.04855,\;0.05551]$ & $[90.00,\;90.00,\;90.00]$ & 70.49 & 0.00 \\
& FEM & $[5.69,\;7.97,\;9.02]$ & $[0.04928,\;0.04787,\;0.05344]$ & $[94.17,\;88.58,\;88.69]$ & 68.47 & 20.11 \\
& Error & -- & $[5.09\%,\;1.42\%,\;3.86\%]$ & $[4.43\%,\;1.60\%,\;1.47\%]$ & 2.95\% & 20.11 \\
\addlinespace[1mm]
3 & Surr. & $[5.81,\;7.88,\;8.98]$ & $[0.04722,\;0.04867,\;0.05416]$ & $[90.00,\;90.00,\;90.00]$ & 69.17 & 0.00 \\
& FEM & $[5.81,\;7.88,\;8.98]$ & $[0.04703,\;0.04785,\;0.05415]$ & $[90.02,\;89.07,\;90.02]$ & 68.85 & 0.93372 \\
& Error & -- & $[0.42\%,\;1.70\%,\;0.01\%]$ & $[0.02\%,\;1.05\%,\;0.02\%]$ & 0.46\% & 0.9337 \\
\bottomrule
\end{tabular}
\end{table*}
\begin{table*}[htbp]
\centering
\caption{Optimization results for the H45\_B34 family using RBF surrogates.}
\label{tab:app_rbf_h45_b34}
\scriptsize
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{1.08}
\begin{tabular}{llllllll}
\toprule
Iter. & Source & $\mathbf{t}_w$ [mm] & $\boldsymbol{\varepsilon}_{xy}$ & $\boldsymbol{\mathcal{D}}_w$ & $\mathcal{D}_f$ & $J$ \\
\midrule
1 & Surr. & $[7.21,\;9.27,\;9.82]$ & $[0.04351,\;0.04034,\;0.05378]$ & $[90.00,\;90.00,\;90.00]$ & 71.35 & 0.00 \\
& FEM & $[7.21,\;9.27,\;9.82]$ & $[0.03892,\;0.04601,\;0.05525]$ & $[82.20,\;85.06,\;90.33]$ & 70.86 & 12.85 \\
& Error & -- & $[11.80\%,\;12.31\%,\;2.66\%]$ & $[9.49\%,\;5.80\%,\;0.37\%]$ & 0.69\% & 12.85 \\
\addlinespace[1mm]
2 & Surr. & $[6.81,\;9.02,\;9.65]$ & $[0.0419,\;0.04824,\;0.05385]$ & $[90.00,\;90.00,\;90.00]$ & 69.63 & 0.00 \\
& FEM & $[6.81,\;9.02,\;9.65]$ & $[0.04228,\;0.04629,\;0.05421]$ & $[90.55,\;89.06,\;90.38]$ & 69.09 & 1.39 \\
& Error & -- & $[0.92\%,\;4.21\%,\;0.66\%]$ & $[0.61\%,\;1.05\%,\;0.42\%]$ & 0.78\% & 1.39 \\
\bottomrule
\end{tabular}
\end{table*}
\begin{table*}[htbp]
\centering
\caption{Optimization results for the H60\_B34 family using RBF surrogates.}
\label{tab:app_rbf_h60_b34}
\scriptsize
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{1.08}
\begin{tabular}{lllllll}
\toprule
Iter. & Source & $\mathbf{t}_w$ [mm] & $\boldsymbol{\varepsilon}_{xy}$ & $\boldsymbol{\mathcal{D}}_w$ & $\mathcal{D}_f$ & $J$ \\
\midrule
1 & Surr. & $[5.98,\;7.29,\;8.53,\;6.73,\;5.00]$ & $[0.06013,\;0.05438,\;0.05386,\;0.06869,\;0.05284]$ & $[90.00,\;90.00,\;90.00,\;90.00,\;74.98]$ & 70.51 & 15.02 \\
& FEM & $[5.98,\;7.29,\;8.53,\;6.73,\;5.00]$ & $[0.05632,\;0.0526,\;0.05986,\;0.07083,\;0.05884]$ & $[84.59,\;92.60,\;89.02,\;80.76,\;73.89]$ & 78.89 & 38.48 \\
& Error & -- & $[6.77\%,\;3.39\%,\;10.02\%,\;3.02\%,\;10.19\%]$ & $[6.40\%,\;2.80\%,\;1.10\%,\;11.44\%,\;1.48\%]$ & 10.62\% & 23.46 \\
\addlinespace[1mm]
2 & Surr. & $[5.71,\;7.44,\;8.51,\;6.15,\;5.00]$ & $[0.05915,\;0.05193,\;0.06105,\;0.07748,\;0.05922]$ & $[90.00,\;90.00,\;90.00,\;90.00,\;73.32]$ & 80.01 & 16.68 \\
& FEM & $[5.71,\;7.44,\;8.51,\;6.15,\;5.00]$ & $[0.05934,\;0.05266,\;0.05789,\;0.07678,\;0.05857]$ & $[92.17,\;89.57,\;86.36,\;90.05,\;72.42]$ & 77.82 & 26.36 \\
& Error & -- & $[0.32\%,\;1.38\%,\;5.47\%,\;0.91\%,\;1.11\%]$ & $[2.36\%,\;0.47\%,\;4.21\%,\;0.06\%,\;1.25\%]$ & 2.81\% & 9.69 \\
\addlinespace[1mm]
3 & Surr. & $[5.77,\;7.38,\;8.37,\;6.18,\;5.00]$ & $[0.05805,\;0.05275,\;0.05965,\;0.07628,\;0.05832]$ & $[90.00,\;90.00,\;90.00,\;90.00,\;72.26]$ & 77.60 & 17.74 \\
& FEM & $[5.77,\;7.38,\;8.37,\;6.18,\;5.00]$ & $[0.05914,\;0.05314,\;0.05986,\;0.07616,\;0.05681]$ & $[89.36,\;89.65,\;89.64,\;90.73,\;72.63]$ & 77.89 & 19.26 \\
& Error & -- & $[1.84\%,\;0.73\%,\;0.34\%,\;0.14\%,\;2.66\%]$ & $[0.72\%,\;0.39\%,\;0.41\%,\;0.80\%,\;0.51\%]$ & 0.37\% & 1.51 \\
\bottomrule
\end{tabular}
\end{table*}
\end{document}
Manuscript/Optimal-Design-layout/RESILINK_surrogate_optimization_manuscript.aux 0 → 100644
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Manuscript/Optimal-Design-layout/RESILINK_surrogate_optimization_manuscript.tex
\documentclass[AMA,Times1COL]{WileyNJDv5} %STIX1COL,STIX2COL,STIXSMALL
\documentclass[AMA,Times1COL]{../WileyNJDv5} %STIX1COL,STIX2COL,STIXSMALL
% Own definitions
\newcommand{\tb}[1]{\textbf{#1}}
......@@ -16,7 +16,7 @@
\received{Date Month Year}
\revised{Date Month Year}
\accepted{Date Month Year}
\journal{Journal}
\journal{Earthquake Engineering \& Structural Dynamics}
\volume{00}
\copyyear{2026}
\startpage{1}
......@@ -57,7 +57,7 @@
\author{Rastellini F.},
\author{Bozzo G.}, and
\author{Bozzo L.}}.
\ctitle{Damage-aware surrogate optimization of buckling-delayed shear-link dampers with adaptive finite element validation.} \cjournal{\it Journal.} \cvol{2026;00(00):1--18}.}
\ctitle{Damage-aware surrogate optimization of buckling-delayed shear-link dampers with adaptive finite element validation.} \cjournal{\it Earthquake Engineering \& Structural Dynamics.} \cvol{2026;00(00):1--18}.}
\maketitle
......@@ -87,7 +87,7 @@ Figure \ref{fig:MethodologyFlowChart} summarizes the proposed workflow. The diff
\begin{figure}[htbp]
\centering
\includegraphics[width=0.75\textwidth]{./Figures/MethodologyFlowChart.pdf}
\includegraphics[width=0.75\textwidth]{../Figures/MethodologyFlowChart.pdf}
\caption{Flow chart of the proposed adaptive surrogate-assisted optimization framework.}
\label{fig:MethodologyFlowChart}
\end{figure}
......@@ -98,7 +98,7 @@ The BDSL dampers analysed in this work, with one representative configuration sh
\begin{figure}[htbp]
\centering
\includegraphics[width=0.25\textwidth]{./Figures/Device.png}
\includegraphics[width=0.25\textwidth]{../Figures/Device.png}
\caption{Representative BDSL damper configuration considered in the optimization.}
\label{fig:Device}
\end{figure}
......@@ -114,11 +114,11 @@ where $W$ denotes the number of windows. The width and height identifiers of the
\begin{figure}[htbp]
\centering
\includegraphics[width=0.15\textwidth]{Figures/H30_B29.png}\label{fig:H30_B29}
\includegraphics[width=0.15\textwidth]{Figures/H30_B34.png}\label{fig:H30_B34}
\includegraphics[width=0.15\textwidth]{Figures/H45_B29.png}\label{fig:H45_B29}
\includegraphics[width=0.15\textwidth]{Figures/H45_B34.png}\label{fig:H45_B34}
\includegraphics[width=0.15\textwidth]{Figures/H60_B34.png}\label{fig:H60_B34}
\includegraphics[width=0.15\textwidth]{../Figures/H30_B29.png}\label{fig:H30_B29}
\includegraphics[width=0.15\textwidth]{../Figures/H30_B34.png}\label{fig:H30_B34}
\includegraphics[width=0.15\textwidth]{../Figures/H45_B29.png}\label{fig:H45_B29}
\includegraphics[width=0.15\textwidth]{../Figures/H45_B34.png}\label{fig:H45_B34}
\includegraphics[width=0.15\textwidth]{../Figures/H60_B34.png}\label{fig:H60_B34}
\caption{BDSL families considered for optimization in the current study. From left to right: H30\_B29, H30\_B34, H45\_B29, H45\_B34 and H60\_B34.}
\label{fig:GeometryFamilies}
\end{figure}
......@@ -152,7 +152,7 @@ The imposed displacement is applied through an actuator-like connector that tran
\begin{figure}[htbp]
\centering
\includegraphics[width=0.60\textwidth]{./Figures/FEMsetup.png}
\includegraphics[width=0.60\textwidth]{../Figures/FEMsetup.png}
\caption{FEM validation model of the BDSL device: mesh discretization, main components, boundary conditions and local/global buckling control.}
\label{fig:FEMsetup}
\end{figure}
......@@ -161,7 +161,7 @@ The model was calibrated and validated against cyclic experimental tests perform
\begin{figure}[htbp]
\centering
\includegraphics[width=0.80\textwidth]{./Figures/plot_FEM_validation/FEM_validation_comparison.png}
\includegraphics[width=0.80\textwidth]{../Figures/plot_FEM_validation/FEM_validation_comparison.png}
\caption{Experimental--numerical validation of the BDSL model: hysteretic response (left) and cumulative dissipated energy (right).}
\label{fig:FEM_validation_comparison}
\end{figure}
......@@ -201,7 +201,7 @@ For every sampled configuration, a FEM simulation is performed under a displacem
\begin{figure}[htbp]
\centering
\includegraphics[width=0.50\textwidth]{./Figures/LoadPatterns/LoadPatterns.png}
\includegraphics[width=0.50\textwidth]{../Figures/LoadPatterns/LoadPatterns.png}
\caption{Displacement-controlled cyclic loading patterns adopted for the different device heights considered in the FEM campaign.}
\label{fig:LoadPatterns}
\end{figure}
......@@ -297,7 +297,7 @@ Model selection is performed in two stages. First, for each candidate algorithm,
\begin{figure}[htbp]
\centering
\includegraphics[width=1.0\textwidth]{./Figures/BayesianSearchCV.pdf}
\includegraphics[width=1.0\textwidth]{../Figures/BayesianSearchCV.pdf}
\caption{Workflow of the supervised surrogate training and selection strategy. For each output variable, the cross-validation strategy is adapted to the dataset size, Bayesian optimization is used to tune each candidate model and the final surrogate is selected according to RMSE accuracy and fold-wise RMSE dispersion.}
\label{fig:BayesianSearchCV}
\end{figure}
......@@ -375,7 +375,7 @@ The surrogate-optimized geometry is not accepted directly. Instead, once an opti
\begin{figure}[htbp]
\centering
\includegraphics[width=1.0\textwidth]{./Figures/OptimizationFlowChart.pdf}
\includegraphics[width=1.0\textwidth]{../Figures/OptimizationFlowChart.pdf}
\caption{Surrogate-assisted optimization and FEM validation retraining loop.}
\label{fig:OptimizationFlowChart}
\end{figure}
......@@ -386,7 +386,7 @@ The supervised-learning comparison shows a clear hierarchy among the candidate s
\begin{figure}[htbp]
\centering
\includegraphics[width=1.0\textwidth]{./Figures/MLSurrogatesComparison/surrogate_selection_summary_barplot.png}
\includegraphics[width=1.0\textwidth]{../Figures/MLSurrogatesComparison/surrogate_selection_summary_barplot.png}
\caption{Summary of the supervised surrogate selection over all geometry families, adaptive iterations and target outputs. The training time corresponds to the median time required for one Bayesian hyperparameter search for a single output variable and, for visualization purposes, is in logarithmic scale.}
\label{fig:surrogate_selection_summary_barplot}
\end{figure}
......@@ -457,7 +457,7 @@ Figure~\ref{fig:optimized_window_thickness_evolution} shows the evolution of the
\begin{figure}[htbp]
\centering
\includegraphics[width=1.0\textwidth]{./Figures/OptimizedWindowThicknessEvolution/optimized_window_thickness_evolution.png}
\includegraphics[width=1.0\textwidth]{../Figures/OptimizedWindowThicknessEvolution/optimized_window_thickness_evolution.png}
\caption{Evolution of the optimized window thicknesses during the adaptive optimization process.}
\label{fig:optimized_window_thickness_evolution}
\end{figure}
......@@ -470,7 +470,7 @@ This behaviour is illustrated in Figure~\ref{fig:rbf_surface_evolution}, which s
\begin{figure}[htbp]
\centering
\includegraphics[width=1.0\textwidth]{./Figures/RBFOptimizationSurfaceEvolution/rbf_surface_evolution.png}
\includegraphics[width=1.0\textwidth]{../Figures/RBFOptimizationSurfaceEvolution/rbf_surface_evolution.png}
\caption{Evolution of the RBF objective surface during the adaptive optimization process for the two-window families. Left: H30\_B29. Right: H30\_B34.}
\label{fig:rbf_surface_evolution}
\end{figure}
......@@ -508,7 +508,7 @@ None reported.
The authors declare no potential conflict of interests.
\bibliography{wileyNJD-AMA}
\bibliography{../wileyNJD-AMA}
\bmsection*{Supporting information}
......
Manuscript/Optimal-Design-layout/USG.cls
......@@ -661,11 +661,12 @@
\newcounter{spagecounter}
\newcounter{lpagecounter}
%%\AtBeginDocument{\setcounter{spagecounter}{\c@page}}
\AtEndDocument{\setcounter{lpagecounter}{\c@page}%
\AtEndDocument{\clearpage%
\setcounter{lpagecounter}{\c@page}%
\addtocounter{lpagecounter}{-1}%
\immediate\write\@xmlpage{\string\FirstPg{\thespagecounter}\string\LastPg{\thelpagecounter}}%
\addtocounter{lpagecounter}{1}%
\immediate\write\@auxout{\string\FirstPg{\thespagecounter}\string\LastPg{\thelpagecounter}}%
\addtocounter{lpagecounter}{1}%
\immediate\closeout\@xmlpage%
}%
......
Manuscript/RESILINK_surrogate_optimization_manuscript.tex
......@@ -16,7 +16,7 @@
\received{Date Month Year}
\revised{Date Month Year}
\accepted{Date Month Year}
\journal{Journal}
\journal{Earthquake Engineering \& Structural Dynamics}
\volume{00}
\copyyear{2026}
\startpage{1}
......@@ -57,7 +57,7 @@
\author{Rastellini F.},
\author{Bozzo G.}, and
\author{Bozzo L.}}.
\ctitle{Damage-aware surrogate optimization of buckling-delayed shear-link dampers with adaptive finite element validation.} \cjournal{\it Journal.} \cvol{2026;00(00):1--18}.}
\ctitle{Damage-aware surrogate optimization of buckling-delayed shear-link dampers with adaptive finite element validation.} \cjournal{\it Earthquake Engineering \& Structural Dynamics.} \cvol{2026;00(00):1--18}.}
\maketitle
......
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