Refine objective function and penalties in optimization manuscript

Manuscript/Figures/LoadPatterns/LoadPatterns.csv

 Time (s),Displacement H30 (mm),Displacement H45 (mm),Displacement H60 (mm)
 0,0,0,0
-0.0625,12,16,20
+0.0625,12,16,25
 0.125,0,0,0
-0.1875,-12,-16,-16
+0.1875,-12,-16,-25
 0.25,0,0,0
-0.3125,12,16,16
+0.3125,12,16,25
 0.375,0,0,0
-0.4375,-12,-16,-16
+0.4375,-12,-16,-25
 0.5,0,0,0
-0.5625,25,32,32
+0.5625,25,32,50
 0.625,0,0,0
-0.6875,-25,-32,-32
+0.6875,-25,-32,-50
 0.75,0,0,0
-0.8125,25,32,32
+0.8125,25,32,50
 0.875,0,0,0
-0.9375,-25,-32,-32
+0.9375,-25,-32,-50
 1,0,0,0
-1.0625,38,48,48
+1.0625,38,48,75
 1.125,0,0,0
-1.1875,-38,-48,-48
+1.1875,-38,-48,-75
 1.25,0,0,0
-1.3125,38,48,48
+1.3125,38,48,75
 1.375,0,0,0
-1.4375,-38,-48,-48
+1.4375,-38,-48,-75
 1.5,0,0,0
-1.5625,50,64,64
+1.5625,50,64,100
 1.625,0,0,0
-1.6875,-50,-64,-64
+1.6875,-50,-64,-100
 1.75,0,0,0
-1.8125,50,64,64
+1.8125,50,64,100
 1.875,0,0,0
-1.9375,-50,-64,-64
+1.9375,-50,-64,-100
 2,0,0,0
-2.0625,60,75,75
-2.125,0,0,0
-2.1875,-60,-75,-75
-2.25,0,0,0
-2.3125,60,75,75
-2.375,0,0,0
-2.4375,-60,-75,-75
-2.5,0,0,0
-2.5625,70,85,85
-2.625,0,0,0
-2.6875,-70,-85,-85
-2.75,0,0,0
-2.8125,70,85,85
-2.875,0,0,0
-2.9375,-70,-85,-85
-3,0,0,0

Manuscript/RESILINK_surrogate_optimization_manuscript.tex

@@ -250,16 +250,16 @@ This validation strategy is particularly suitable for the present application be
 
 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.
 
-For each candidate geometry $\mathbf{x}$, the trained surrogate models predict the window distortions $\hat{\Exy}_i$, the window damage indicators $\widehat{\TFD}_i$ and the frame damage indicator $\widehat{\TFD}_f$. These quantities are combined into a scalar objective function designed to encode four mechanical criteria: damage must remain limited in all structural components; frame damage must be penalized more severely than window damage because frame failure would compromise the structural integrity of the damper; the windows should develop comparable damage levels to avoid concentration of the dissipative demand in a single region; and, among geometries with similar damage performance, the preferred solution should be the one with higher energy dissipation capacity.
+For each candidate geometry $\mathbf{x}$, the trained surrogate models predict the window distortions $\hat{\Exy}_i$, the window damage indicators $\widehat{\TFD}_i$ and the frame damage indicator $\widehat{\TFD}_f$. These predictions are combined into a scalar objective function that prioritizes damage control while using dissipative performance as a secondary selection criterion. In particular, damage is constrained in all regions of the device, frame damage is penalized more severely than window damage because it may compromise the structural integrity of the damper and the window penalties are formulated to promote comparable damage levels among them, avoiding configurations in which the dissipative demand is concentrated in a single region. The energy dissipation contribution, based on $\hat{\Exy}_i^2$, the window thickness and the area factor, is not scaled to have the same magnitude as the damage terms; instead, it acts as a tie-breaking term 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{\Exy}_i^2\, t_{w,i}\, V_i +
+J(\mathbf{x}) = - \sum_{i=1}^{W} \hat{\Exy}_i^2\, t_{w,i}\, A_i +
 \sum_{i=1}^{W} P_w\left(\widehat{\TFD}_i;\TFD_w^{\star}\right) +
 P_f\left(\widehat{\TFD}_f;\TFD_f^{\max}\right),
 \label{eq:objective}
 \end{equation}
-where $W$ is the number of windows, $t_{w,i}$ is the thickness of window $i$, $V_i$ is the corresponding volume factor, $\TFD_w^{\star}$ is the target damage level for the windows, and $\TFD_f^{\max}$ is the maximum admissible frame damage threshold. The first term is negative because the optimizer minimizes $J$; therefore, larger stable distortion contributions reduce the objective value and are favoured once the damage criteria are satisfied.
+where $W$ is the number of windows, $t_{w,i}$ is the thickness of window $i$, $A_i$ is the corresponding area factor, $\TFD_w^{\star}$ is the target damage level for the windows, and $\TFD_f^{\max}$ 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}
@@ -281,23 +281,23 @@ P_f\left(\widehat{\TFD}_f;\TFD_f^{\max}\right)=
 \end{cases}
 \label{eq:frame_penalty}
 \end{equation}
-The cubic penalty reflects the greater severity of frame damage compared with localized damage in a replaceable window. In the current implementation, $\TFD_f^{\max}=90$ is adopted, while the target window threshold $\TFD_w^{\star}$ is provided as an input parameter to the optimizer.
+The cubic penalty reflects the greater severity of frame damage compared with localized damage in a window. Since a damage value $\TFD=100$ represents complete failure, $\TFD_f^{\max}=90$ is adopted in the current implementation. The target window threshold is also set to $\TFD_w^{\star}=90$.
 
-The distortion contribution in Eq.~\eqref{eq:objective} is weighted by a geometric factor $V_i$ that accounts for the effective volume associated with each window. These factors depend on the geometry family because the windows differ in size and position. The values currently used in the optimization scripts are summarized in Table~\ref{tab:volume_factors}. If a geometry family is not explicitly covered, the implementation falls back to an unweighted contribution.
+The distortion contribution in Eq.~\eqref{eq:objective} is weighted by $t_{w,i}$ and the geometric factor $A_i$ that accounts for the effective area associated with each window. These factors, summarized in Table~\ref{tab:volume_factors}, depend on the geometry family because the windows differ in size.
 
 \begin{table}[ht!]
 \centering
-\caption{Window volume factors used to weight the distortion contribution in the objective function.}
+\caption{Window area factors used to weight the distortion contribution in the objective function.}
 \label{tab:volume_factors}
-\begin{tabular}{lll}
+\begin{tabular}{ll}
 \toprule
-Family & Width identifier $B$ & Volume factors $V_i$ \\
+Family & Area factors $A_i$ \\
 \midrule
-2 windows & 29 & 0.0208, 0.0185 \\
-2 windows & 34 & 0.0263, 0.0240 \\
-3 windows & 29 & 0.0229, 0.0210, 0.0185 \\
-3 windows & 34 & 0.0262, 0.0262, 0.0240 \\
-5 windows & -- & 0.0410, 0.0265, 0.0240, 0.0098, 0.0098 \\
+H30\_B29 & 0.0208, 0.0185 \\
+H30\_B34 & 0.0263, 0.0240 \\
+H30\_B29 & 0.0229, 0.0210, 0.0185 \\
+H30\_B34 & 0.0262, 0.0262, 0.0240 \\
+H30\_B34 & 0.0410, 0.0265, 0.0240, 0.0098, 0.0098 \\
 \bottomrule
 \end{tabular}
 \end{table}