## 5 Integration of Pruning for Stream-Lined Control  
As previously noted, the weighted control matrix has high dimensionality (\(W\in\mathbb{R}^{55\times 5}\)) and can assume a large range of values (Figure 7). It is hypothesized that due to the high connectivity, not all weight values within the matrix are necessary and some can be removed. This hypothesis is based on experiences with artificial neural networks (ANNs), which share a similar architecture to the proposed weighted-control algorithm. Similar to the structure of the weighted-control algorithm, ANNs typically need to predefine the network architecture, which can cause over-fitting if too many weights are defined or under-fitting if not enough weights are defined. Numerous methods exist for eliminating or pruning the weights in ANNs, such as minimal-value deletion [39], ref [40] that focus only on the magnitude or other methods that develop criteria to assess the importance of the weight [41; 42; 43; 44]. The architecture of the proposed control method is more basic than a traditional ANN, only having a single layer of weights and, as a result, some of the elimination criteria in these studies is overly complex. As such, three methods are explored: (1) minimal-value deletion [39], (2) optimal brain surgeon (OBS) [41], and (3) a brute force method, termed minimum error pruning. With each method, the effect of the minimized weighted control matrix is evaluated using the percent change in the fitness function,  
\[C=\frac{O_{2,1}-O_{2,0}}{O_{2,0}}*100\%, \tag{18}\]  
where \(C\) is the percent difference, \(O_{2,1}\) is the fitness function after implementing a pruning method, and \(O_{2,0}\) is the original fitness function from the PSO-H optimization using the El Centro earthquake record, both of which use a modified fitness function (Equation (19)). As the weighted control matrix becomes sparse, it is possible for all connections to be eliminated to an actuator. When this occurs, elements of the \(J_{5}\) cost function become zero while the displacement or acceleration of the structure may be undesirably increasing. As a \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **El Centro EQ** & **Kobe EQ** & **Loma Prieta EQ** \\ \hline Minimal-value deletion pruning–220 & \(-5.27\%\) & \(-3.85\%\) & \(-5.71\%\) \\ \hline Minimal-value deletion pruning–230 & \(-1.93\%\) & \(3.27\%\) & \(0.15\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Percent difference in the fitness function, O2, from the full-state weight matrix for three difference earthquakes. Figure 7: Pictorial representation of values of the weighted control matrix, \(W\in\mathbb{R}^{55\times 5}\). Note: bandpass filter numbers \(11\times l-10\) to \(11\times l\) correspond to the filters on the \(l\)th floor. result, a modified fitness function is used for the assessment of the effectiveness of the pruning method that omits the control force cost function (i.e., \(J_{5}\)),  
\[O_{2}=\sum_{l=1}^{m}J_{1,l}+J_{2,l}+J_{3,l}+J_{4,l}. \tag{19}\]  
The effectiveness of the pruning algorithms was also evaluated using the number of removed weights and the number of removed filters. A filter is removed when it is no longer connected to any of the five controllers, indicating that its information is not required for any of the control force calculations. It is the removal of a filter, rather than just a weight, that is most beneficial to the network as it results in less information exchange across the network, which translates to power savings and also a more streamlined control-force calculation at the controller. The first pruning method that was considered is a minimal-value deletion algorithm that eliminates a single weight with each iteration of the algorithm based on its magnitude [39]. For this algorithm, the weight with the smallest absolute magnitude is eliminated and the fitness function is evaluated for the reduced weighted control matrix. The process is repeated for the weight with the second smallest absolute magnitude.