## 6 Conclusions  
In this paper, we propose a novel incremental learning model named BOA-GNG for online anomaly detection of streaming data. The proposed approach adopts our previous model [22] as a baseline model, of which the learning rate, neuron insertion strategy, and  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Datasets**} & \multicolumn{2}{c}{**GNG [1]**} & \multicolumn{2}{c}{**GWR [24]**} & \multicolumn{2}{c}{**GNG-I [20]**} & \multicolumn{2}{c}{**Proposed Method**} \\ \cline{2-9}  & \(\mathbf{v_{1}}\) & \(\mathbf{v_{2}}\) & \(\mathbf{v_{1}}\) & \(\mathbf{v_{2}}\) & \(\mathbf{v_{1}}\) & \(\mathbf{v_{2}}\) & \(\mathbf{v_{1}}\) & \(\mathbf{v_{2}}\) \\  & **(dot/s)** & **(dot/s)** & **(dot/s)** & **(dot/s)** & **(dot/s)** & **(dot/s)** & **(dot/s)** & **(dot/s)** & **(dot/s)** \\ \hline Shuttle & 497.40 & 19,772.57 & 357.49 & 15,303.42 & 3796.60 & 186,191.67 & **3822.58** & **203,118.18** \\ KDD-CUP99 & 453.26 & 21,276.60 & **1079.77** & 6467.26 & 479.47 & **22,727.27** & 459.61 & 22,222.22 \\ Satellite & 2204.30 & 9761.90 & 334.97 & 3504.27 & 1822.22 & 9318.18 & **2469.88** & **12,058.82** \\ SMAP & 2987.62 & 4888.26 & 315.71 & 3564.15 & 2687.14 & 5728.31 & **3111.11** & **5988.02** \\ MSL & 2504.17 & **4213.48** & 304.63 & 3170.53 & 2008.03 & 4065.04 & **2369.67** & 4043.13 \\ Payload dataset & 276.72 & 2002.50 & 143.63 & 1714.53 & 482.83 & 4212.74 & **535.98** & **4364.43** \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of online learning rates on each dataset.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithms** & \(\mathbf{p}\) & \(\mathbf{r}\) & \(\mathbf{f}\) \\ \hline BOA-GNG\({}_{\text{FLR}}\) & 0.8159 & 0.9951 & 0.8966 \\ BOA-GNG\({}_{\text{SLR}}\) & 0.8667 & 0.9951 & 0.9264 \\ BOA-GNG\({}_{\text{FIS}}\) & **0.9997** & 0.9834 & 0.9915 \\ BOA-GNG & **0.9997** & **0.9949** & **0.9973** \\ \hline \hline \end{tabular}
\end{table}
Table 7: Results of ablation experiments on the payload dataset.  
network optimization strategy are made for better dynamic data learning ability and online detection performance.  
We demonstrate that the adaptive learning rate can obtain faster convergence ability compared to the previous linear learning rate. Then, the new neuron insertion method can improve the model's adaptability for evolving data streams and make it more flexible to adapt to changes in data distributions. Finally, Bayesian optimization is introduced for fast and fine-grained hyperparameter setting instead of grid search.  
Five open datasets and a real engineering dataset from the aerospace satellite are taken as experimental cases to verify the effectiveness and superiority of the proposed model. Results indicate that BOA-GNG can improve precision, recall, F1 score, and computing efficiency of online anomaly detection compared with classical GNG-based models, and both the precision and recall of BOA-GNG reach more than 95% on six datasets. Additionally, the lowest learning and detecting velocity can reach nearly 500 dot/s and 4000 dot/s. Further studies demonstrate that an adaptive learning rate and new neuron insertion strategy are effective in improving the baseline model.  
Methodology, J.Z., L.S. and S.G.; writing--original draft, J.Z. and L.S.; software, S.G. and M.L.; supervision, X.L. and L.G.; investigation, C.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Prospective Foundation of Technology and Engineering Center for Space utilization, Chinese Academy of Sciences of funder grant number No. T303271.  
Not applicable.  
The data that support the findings of this study can be obtained by contacting [EMAIL_ADDRESS].  
The authors declare no conflict of interest.