Add Methodology Flow Chart and enhance manuscript content

Manuscript/RESILINK_surrogate_optimization_manuscript.tex

@@ -81,20 +81,14 @@ Data-driven approaches have mainly focused on response or property prediction. C
 
 All these works demonstrate the increasing interest in applying FEM-based and data-driven approaches, as well as in combining both, to analyse, understand and optimize seismic energy dissipation devices. However, most of these studies focus either on the prediction of the hysteretic response or on maximizing energy dissipation, leaving 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.
 
-The present work addresses this gap through a damage-aware surrogate-assisted optimization framework in which the objective is not only to maximize distortion or energy dissipation, but to balance dissipative performance with damage indicators derived from FEM simulations. The proposed methodology combines: (i) experimentally calibrated nonlinear FEM models used as ground truth; (ii) supervised surrogate models trained to predict local damage and distortion indicators; (iii) a Differential Evolution (DE) optimizer; and (iv) an adaptive FEM validation and retraining loop. The framework remains consistent with the underlying physics, as all surrogate models are trained on FEM-generated data that capture both global response and local damage mechanisms.
+The present work addresses this gap through a damage-aware surrogate-assisted optimization framework in which the objective is not only to maximize distortion or energy dissipation, but to balance dissipative performance with damage indicators derived from FEM simulations. The proposed methodology combines: (i) experimentally calibrated nonlinear FEM models used as ground truth; (ii) supervised surrogate models trained to predict local damage and distortion indicators; (iii) a Differential Evolution (DE) optimizer; and (iv) an adaptive FEM validation and retraining loop. The framework remains consistent with the underlying physics, as all surrogate models are trained on FEM-generated data that capture both global response and local damage mechanisms. Figure \ref{fig:MethodologyFlowChart} illustrates the proposed framework. The methods applied in each stage of the methodology the results obtained and the conclusions drawn are described in detail in the following sections.
 
-% 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. The supervised surrogate set includes Random Forest (RF), Gradient Boosting Regression (GBR), XGBoost, Support Vector Regression (SVR), Multilayer Perceptron (MLP) and Gaussian Process Regression (GPR). Since preliminary calculations indicated that SVR and GPR often dominate the high-accuracy regime, RBF interpolants are also assessed as a computationally efficient alternative for fast optimization. The novelty is not the development of a new constitutive model, but the integration of FEM-calibrated damage indicators into an optimization workflow that explicitly distinguishes between damage in the windows and damage in the frame, encourages balanced window activation and verifies the optimized geometry with a high-fidelity FEM simulation before accepting it.
-
-% The adaptive validation stage is a central component of the proposed framework. Once an optimal geometry is identified by the surrogate-assisted optimizer, it is re-evaluated with FEM to verify that the surrogate remains accurate in the region of the design space where the optimum lies. The candidate geometry is accepted only if: (i) the prediction error of all damage and distortion variables remains below the prescribed tolerance; (ii) the absolute error of the objective function remains within the admissible limit; and (iii) the optimized window thicknesses remain stable between consecutive optimization iterations, with variations smaller than a prescribed percentage of the full design range. If any of these criteria is not satisfied, the new FEM result is incorporated into the training dataset and the surrogate models are retrained.
-
-% 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. To summarize, the main contributions of this work are:
-% \begin{itemize}
-%     \item generation of high-fidelity FEM datasets for BDSL dampers with increasing geometric complexity and different numbers of dissipative windows;
-%     \item geometric optimization using surrogate models, including supervised ML techniques and RBF interpolants;
-%     \item systematic comparison of surrogate strategies in terms of predictive accuracy, computational cost and practical suitability for optimization;
-%     \item a damage-aware objective function that combines window damage control, severe frame-damage penalization, window-to-window damage balancing and dissipated-energy maximization;
-%     \item an adaptive FEM validation and retraining strategy based on explicit tolerances for surrogate error, objective-function error and stability of the optimized geometry between successive iterations.
-% \end{itemize}
+\begin{figure}[!ht]
+  \centering
+  \includegraphics[width=1.0\textwidth]{./Figures/MethodologyFlowChart.png}
+  \caption{Flow chart of the proposed adaptive surrogate-assisted optimization framework.}
+  \label{fig:MethodologyFlowChart}
+\end{figure}
 
 \section{Buckling-delayed shear-link damper}\label{sec:device}
 
@@ -186,6 +180,8 @@ Family & Height identifier $H$ & Design variables & Bounds in current scripts \\
 
 \subsection{Supervised ML surrogate models}\label{subsec:ml_models}
 
+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. The supervised surrogate set includes Random Forest (RF), Gradient Boosting Regression (GBR), XGBoost, Support Vector Regression (SVR), Multilayer Perceptron (MLP) and Gaussian Process Regression (GPR). Since preliminary calculations indicated that SVR and GPR often dominate the high-accuracy regime, RBF interpolants are also assessed as a computationally efficient alternative for fast optimization. The novelty is not the development of a new constitutive model, but the integration of FEM-calibrated damage indicators into an optimization workflow that explicitly distinguishes between damage in the windows and damage in the frame, encourages balanced window activation and verifies the optimized geometry with a high-fidelity FEM simulation before accepting it.
+
 A set of supervised regression models is trained independently for each output variable. The considered algorithms are RF, GBR, XGBoost, SVR, MLP and GPR. The input vector is composed only of the window thicknesses of the corresponding device family. For each output, the model-selection routine evaluates all candidate algorithms and stores the best model as a serialized \texttt{joblib} file.
 
 Hyperparameters are optimized using Bayesian search with 40 iterations. The scoring metrics are root mean squared error (RMSE), mean absolute error (MAE) and $R^2$. Since the available dataset size changes between geometry families and between adaptive iterations, the cross-validation strategy is selected automatically. Leave-One-Out validation is used for datasets with $N\leq 20$, repeated five-fold cross-validation with five repetitions is used for $21\leq N\leq 80$ and standard shuffled five-fold cross-validation is used for larger datasets. For small datasets, the hyperparameter search spaces of tree-based models are reduced to mitigate overfitting.
@@ -282,6 +278,17 @@ Family & Width identifier $B$ & Volume factors $V_i$ \\
 
 \section{Adaptive FEM validation and retraining}\label{sec:adaptive}
 
+The adaptive validation stage is a central component of the proposed framework. Once an optimal geometry is identified by the surrogate-assisted optimizer, it is re-evaluated with FEM to verify that the surrogate remains accurate in the region of the design space where the optimum lies. The candidate geometry is accepted only if: (i) the prediction error of all damage and distortion variables remains below the prescribed tolerance; (ii) the absolute error of the objective function remains within the admissible limit; and (iii) the optimized window thicknesses remain stable between consecutive optimization iterations, with variations smaller than a prescribed percentage of the full design range. If any of these criteria is not satisfied, the new FEM result is incorporated into the training dataset and the surrogate models are retrained.
+
+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. To summarize, the main contributions of this work are:
+\begin{itemize}
+    \item generation of high-fidelity FEM datasets for BDSL dampers with increasing geometric complexity and different numbers of dissipative windows;
+    \item geometric optimization using surrogate models, including supervised ML techniques and RBF interpolants;
+    \item systematic comparison of surrogate strategies in terms of predictive accuracy, computational cost and practical suitability for optimization;
+    \item a damage-aware objective function that combines window damage control, severe frame-damage penalization, window-to-window damage balancing and dissipated-energy maximization;
+    \item an adaptive FEM validation and retraining strategy based on explicit tolerances for surrogate error, objective-function error and stability of the optimized geometry between successive iterations.
+\end{itemize}
+
 The surrogate-optimized geometry is not accepted directly. Instead, the optimal candidate proposed by the surrogate-assisted DE process is evaluated with the high-fidelity FEM model. This validation step checks whether the surrogate has remained reliable in the region of the design space selected by the optimizer.
 
 Three acceptance criteria are used. First, the prediction error of all variables entering the optimization process, including damage and distortion indicators, must be lower than 5\%. Second, the absolute error in the objective function must be lower than 10. Third, the optimized window thicknesses must be stable between consecutive optimization iterations: no thickness is allowed to change by more than 2\% of the total admissible range. For example, if a thickness is optimized within the interval 10--20 mm, the total range is 10 mm and the maximum admissible variation between iterations is 0.2 mm.