## 5 Integration of Pruning for Stream-Lined Control
### Pruning Methods with Periodic PSO-H Retraining  
While the error that incurred through the removal of weights was relatively small, it was next considered whether the control effectiveness could be improved by periodically retraining the weighted control matrix using the PSO-H algorithm during the three pruning processes. Each pruning method was re-executed with the modification that once groups of 10 weights have been removed, the weighted control matrix was retrained. The PSO-H-retraining algorithm continued to use 50 particles, with each particle also eliminating the weights that were identified through the pruning mechanism. At the start of each retraining session, \(\lambda\), the inertia weight from Equation (3), was reset to 1.0 to allow the search to start globally and move locally. The PSO-H algorithm iterates until the best fitness function does not change for 50 iterations. The retraining pruning algorithms were compared against the control effectiveness of the full-state network, each using the El Centro earthquake for seismic excitation. The resulting percent change from the full-state network is shown in Figure 9a for the three different pruning methods. For comparison, the pruning methods without retraining, extracted from Figure 8a, are also overlain on the figure. In general, all three pruning methods showed improvement over the full-state matrix when including periodic retraining. In contrast to the pruning without retraining, the OBS and minimal-value deletion methods now outperformed the minimum error method and were able to improve the control effectiveness when compared to the full-state matrix by over 6% in some cases. The pruned network produced the best results when using minimal-value deletion pruning to eliminate 170 weights, with a 6.28% improvement in control effectiveness. However, this only resulted in eliminating six filters, which did not streamline data communication. When 220 weights were removed using Minimal-value deletion pruning, this still maintained an improved control effectiveness, with 5.27% difference, and also eliminated 20 filters or an approximate reduction of 36.4% in the data transmission (=20 removed filters/55 total filters). Removing 230 weights is also attractive as it improves control effectiveness, though less with a 1.93% difference, and now eliminates 28 filters or an approximate reduction of 50.9% in the data transmission (Table 5). The OBS method performed similarly to the minimal-value deletion pruning method but was not able to achieve the same improvement in control effectiveness and therefore was not considered in more detail. The minimum error method was able to improve when integrated into periodic retraining but contrary to the results without retraining, its performance lagged behind the minimal-value deletion and OBS methods. To once again ensure that the pruned weighted control matrix was not over-trained to the El Centro earthquake, the matrices that were pruned using minimal-value deletion pruning for 220 weights and 230 weights were applied to control the structure when subject to the 1995 Kobe (NS JMA) and 1989 Loma Prieta (CORRALITOS) earthquake ground acceleration records (Table 5). When removing 220 weights, the remaining weights allowed for enough generality that effective control could still be achieved for these two earthquakes, as indicated by the negative percent change in the fitness function. When removing 230 weights, however, the remaining weights were less effective at controlling the structure and some degradation in the control began to be apparent, perhaps indicating overfitting. Therefore, removing 220 weights using the minimal-value deletion pruning method is chosen as the optimal scenario as it is effective at controlling the structure but still remains generalizable to multiple input earthquakes. The full results for all cost functions using the minimal-value deletion pruning for 220 weights are shown in Tables 2-4.