## 5 Experimental Data Analysis
### Analysis of Test and Simulation Results
#### 5.3.2 Error Analysis of Test Simulation Experiment Results  
Three typical acoustic signals were selected from the test data set for a comparative analysis. 'Signal a' and 'Signal b' were signals when the upper layer was seriously flooded, and 'Signal c' was the test signal when the column was in normal operation at the same position. The time-frequency domain characteristics comparison diagram of three test signals is shown in Figure 5. Figure 5a is composed of three subgraphs showing the waveform, linear prediction and spectrum of the 'Signal a' original acoustic signal from left to right; Figure 5b shows the waveform, linear prediction and spectrum diagram of the 'Signal b' original acoustic signal; and Figure 5c shows the waveform, linear prediction and spectrum of the 'Signal c' original acoustic signal. The time domain characteristic parameter used in the experiment was the sectional energy ratio, and the frequency domain characteristic parameter was the sixth-order LPC. The characteristic parameters of the three test signals are shown in Table 4. The actual experimental result shows that 'Signal b' was judged as flooding, which is correct; however, 'Signal a' was incorrectly judged to be in a normal operation state. \begin{table}
\begin{tabular}{c c c c} \hline
**Characteristic Vector** & **Normal Operation of the** & **Flooding of the** & & \\
**Parameters** & **Upper Layer** & **Upper Layer** & **Flooding of the Lower Layer** \\ \hline \multirow{3}{*}{Sectional energy ratio} & 0.3403 & 0.1252 & 0.5526 \\  & 0.3362 & 0.5126 & 0.2338 \\  & 0.3234 & 0.3622 & 0.2137 \\ \hline \multirow{6}{*}{Sixth-order LPC} & \(-\)0.0109 & \(-\)0.1563 & \(-\)0.2805 \\  & \(-\)0.1616 & \(-\)0.0894 & \(-\)0.0781 \\ \cline{1-1}  & \(-\)0.1427 & \(-\)0.0249 & 0.4036 \\ \cline{1-1}  & 0.1167 & \(-\)0.0671 & 0.0163 \\ \cline{1-1}  & 0.0752 & 0.0792 & 0.2537 \\ \cline{1-1}  & \(-\)0.0706 & \(-\)0.0881 & 0.1217 \\ \hline \end{tabular}
\end{table} 
Table 2: The characteristic vector parameters of acoustic signal of tray column under different operating conditions. \begin{table}
\begin{tabular}{c c c} \hline
**Prediction Outcomes** & **Normal** & **Abnormal** \\ \hline Abnormal data & 5 & 35 \\ Normal data & 27 & 3 \\ \hline \end{tabular}
\end{table} 
Table 3: Prediction result of acoustic signal to be measured. Figure 4: The waveform of the original acoustic signal and the spectrum of linear prediction: (**a**) normal operation of the upper layer; (**b**) flooding of the upper layer; (**c**) flooding of the lower part. In Table 4, the sectional energy ratio of 'Signal a' decreases in turn, and the gap is very small, which is highly similar to the 'Signal c' sectional energy ratio, while the sectional energy ratio of 'Signal b' is larger at both ends and smaller in the middle, which is the first reason for miscalculation. In Figure 5, the linear prediction spectrum of 'Signal a' has \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Characteristic Vector Parameters** & **Signal a** & **Signal b** & **Signal c** \\ \hline \multirow{4}{*}{Sectional energy ratio} & 0.3528 & 0.3511 & 0.3403 \\  & 0.3256 & 0.2978 & 0.3362 \\  & 0.3216 & 0.3511 & 0.3234 \\ \hline \multirow{4}{*}{Sixth-order LPC} & 0.2286 & \(-\)0.0179 & \(-\)0.0109 \\  & 0.0070 & \(-\)0.3010 & \(-\)0.1616 \\ \cline{1-1}  & \(-\)0.1259 & \(-\)0.3978 & \(-\)0.1427 \\ \cline{1-1}  & 0.3901 & 0.3375 & 0.1167 \\ \cline{1-1}  & 0.1045 & 0.0704 & 0.0752 \\ \cline{1-1}  & 0.2355 & 0.2038 & \(-\)0.0706 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Characteristic vector of ‘Signal a’, ‘Signal b’ and ‘Signal c’. Figure 5: The waveform, linear prediction and spectrogram of the acoustic signal: (**a**) ‘Signal a’; (**b**) ‘Signal b’; (**c**) ‘Signal c’. two peaks (4.5, 1.60) (17.4, 2.69), while the linear prediction spectrum of 'Signal b' has two peaks (3.1, 2.31) (17.1, 2.43), and the peak value of 'Signal c' is (15.2, 1.30), which is the second reason for miscalculation.