# Anomaly Monitoring of Process Based on Recurrent Timeliness Rules (AMP-RTR)
## 4 Experimental Results
### Model Testing in Synthetic Datasets
The number of times greater than 1 is recorded with \(R(A)\) and the value of \(R(A)\) is monitored to reach the set threshold \(N(A)\) (i.e., Formula (10): \(N(A)=100\times fall(A)\times\frac{1}{\alpha}\times\frac{1}{t-1}\)). Under different parameter configurations, the threshold value to be met for the number of times the evaluation value reaches 1 is shown in Table 2.  
Through the comparison between Tables 1 and 2, it can be seen that under the same parameter configuration, the time to deviate from the set cycle is the same, and the threshold value \(N(A)\) set earlier than the set cycle update has a greater correlation with the number of iterations required to update the model convergence later than the set cycle. For example, the number of iterations (55 times) of the \(04^{\#}\) experiments (\(t=09,\ t-T=2\)) is close to the threshold \(N(A)=50\) set by the parameters of group \(D\) (\(t=5,\ T-3=2\)). In order to test the effectiveness of the model in the case of abnormal fluctuation data (that is, whether the degree of deviation from the set value is the same), the synthetic datasets are input to the model. Table 3 shows the number of iterations required for model convergence under different parameters when the data update time fluctuates before and after the set cycle. Table 3 describes the number of iterations required to change the timeliness score from the initial value of \(f_{1}=0.5\) to \(f_{n}=1\) or \(f_{n}=0\) when the data update time fluctuates around the set period. It clearly explains the influence of the time difference between the data update time and the set cycle on the convergence speed of the recurrent timeliness score. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Value** & **Setting of \(N(A)\)** \\ \hline \(A\): \(\alpha=0.05,\ fall=0.2,\ t=5\) & 200 \\ \(B\): \(\alpha=0.05,\ fall=0.2,\ t=3\) & 100 \\ \(C\): \(\alpha=0.05,\ fall=0.1,\ t=3\) & 50 \\ \(D\): \(\alpha=0.10,\ fall=0.1,\ t=5\) & 50 \\ \(E\): \(\alpha=0.20,\ fall=0.1,\ t=5\) & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The number of iterations required for the convergence of the model when the data update time is always earlier than the set period (\(T=7\)). Figure 4: Convergence trend of the model when the data are updated later. It can be seen from Table 3 that the model can effectively monitor the fluctuating data. Through the statistical analysis of the periodically generated data, it is found that the distribution of the time series basically obeys the Gaussian distribution. According to the data update period of \(T=7\) and characteristics of Gaussian distribution, \(t=6|8\) and \(t=5|9\) groups of data close to period \(T=7\) are selected for testing. Through the comparison of \(06^{\#}\) and \(07^{\#}\), it can be seen that under the same parameter configuration, the greater the fluctuation range, the faster the model converges. Through the comparison of \(07^{\#}\) and \(08^{\#}\), it can be seen that the smaller the \(fall(A)\) value is, the faster the convergence speed of the model is under the same fluctuation amplitude. Abnormal data of symmetric fluctuations were used in the above three groups of experiments. It can be concluded that inputting symmetrical time series to the model will increase or decrease the timeliness score, as shown in Figure 5a. Abnormal data of asymmetric fluctuations were used in the \(09^{\#}\) and \(10^{\#}\) experiments. Through the comparison of \(09^{\#}\) groups and \(10^{\#}\) groups of experiments, two conclusions can be drawn. First, if the time series is later than the cycle, the timeliness score will decrease. Second, if the time series is earlier than the cycle, the timeliness score will rise. The change trend of the experimental timeliness score values of groups \(09^{\#}\) and \(10^{\#}\) with the number of iterations is shown in Figure 5b. Figure 5 show that in the case of symmetric data (Figure 5a) and asymmetric data (Figure 5b), respectively, the score of data timeliness changes roughly linearly with the number of iterations.