## 3 Experiment and Analysis Results
### Analysis Results
Based on this ratio, the initial thresholds of the different states of the online devices under the same working environment conditions can be derived, as listed in Table 7.  
The online monitoring data are input into the one-dimensional probabilistic neural network model, from which the probabilistic neural network can establish the probabilistic model of the running state of the equipment. According to the calculation method of the dynamic early warning value mentioned above, the data of each additional 10 cycles (i.e., 8000 sampling points) are input into the model for updating purposes, and each alarm value is linked to obtain dynamic early warning lines at all levels, as shown in Figure 8a. Selecting the normal state data as an example, Figure 9 shows the early warning method based on a fixed threshold [36] and the early warning line of the early warning method proposed in this paper. It is clear that the warning line obtained with the warning method based on the fixed threshold will clearly cause many over-limit alarms. However, the dynamic adaptive early warning line can adjust the threshold value fittingly according to the environment fluctuation when the data do not produce large anomalies, which can greatly reduce the number of false positives. From the dynamic warning diagram, it is evident that the dynamic warning lines at all levels can regulate the operation range of the equipment in the different health states. When the detection features exceed a certain range, the current equipment has deviated from its existing state. Field staff can further process the equipment according to its state, such as strengthening monitoring or directly shutting down for maintenance. When the detection features fluctuate above and below the threshold line or even drop, the equipment \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Equipment State** & **Normal Operation** & **Mild Anomaly** & **Moderate Anomaly** & **Severe Anomaly** \\ \hline RMS (mm/s) & 0.5834 & 2.3382 & 3.0751 & 6.2441 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The initial threshold of the online equipment in each state. Figure 8: Adaptive dynamic alarm line in each state of the equipment. is considered to be in the unstable state, which is the run-in period rather than a fault. When the detection features exceed the level-4 warning line and keep rising, the equipment is considered to be in the fault state and needs to be shut down for maintenance in this case. For the two methods, the result when the actual value exceeds the warning line is recorded as 1 at a certain time and as 0 below the warning line. The result is shown in Figure 10. Through comparative analysis of the two methods in Figure 10a,b, it can be seen that for the normal state data, both early warning methods exhibit over-limit behavior in the early stage, but the data quickly recede, indicating that at this time, only data fluctuation occurs within the normal range. The data after the 3000 th instance are considered to be developing toward the abnormal state, namely, it is regarded as the correct early warning behaviour for any method. Before the 3000 th instance, the method based on the fixed threshold issued 69 false alarms, while the method based on dynamic adaptive warning only issued 7 false alarms, indicating that the latter greatly reduced the number of false alarms in the online detection of equipment. Based on the dynamic adaptive early warning method, after the equipment leaves the abnormal state, it can make adaptive adjustments for the different abnormal states and issue early warnings for the more serious abnormal states or even complete faults in the next stage, providing more detailed guidance and maintenance strategies for the field staff. Figure 10: Warning results based on the different threshold methods. Figure 9: Comparison of the different threshold methods (normal state).