## 5 Simulation Experiments  
### Experimental Facilities  
The outside diameter of the pipeline is 160 mm, the wall thickness of the pipeline is 6 mm and the length of the pipeline is 25 m. The pipeline is filled with a high pressure gas and the pressure is 0.2 Mpa. The leak process is simulated by a leak valve. There are five nodes with the same spacing placed near the leak point. The coordinates of nodes and leak point are 0, 5 m, 10 m, 15 m, 20 m and  
Figure 8: Signal decomposition of node 2. Figure 7: Signal decomposition of node 1. Figure 10: Signal decomposition of node 4. Figure 9: Signal decomposition of node 3. Figure 11: Signal decomposition of node 5. Figure 12: Single mode signals extracted from five original signals. Then, characteristic parameters are calculated according to the single mode signals. As characteristic input vectors, they are sent to SVM multiple classifiers for initial recognition. In this paper, 120 groups of data are selected independently as the sample set, which contains 40 groups of large leak state sample, 40 groups of small leak state sample and 40 groups of normal state sample. Among the sample set, 20 groups of each type of pipeline state (60 groups in total) are randomly chosen as the training sample set and the others make up the testing sample set. Table 1 gives the signal examples of three sorts of states: groups 1 and 2 are signals in normal state; groups 3 and 4 are signals in small leak state; groups 5 and 6 are signals in large leak state. We use SVM toolbox in Matlab to train classifiers. Then test samples are sent to multiple classifiers for pipeline state recognition. Output results are normalized finally. When there is a small leak happening along the pipeline, basic probability assignments determined by SVM multiple classifiers as the initial recognition results are shown in Table 2. From Table 2, uncertainty degrees in leak detection become increasingly large with the increase of distances between sensor nodes and leak point. In addition, the initial recognition result of Node 4 disagrees with that of others so that it is difficult to make a decision according to Equation (13). There are two factors contributing to the phenomenon. One is that sensor nodes have self problems which may lead to the error in characteristic input vectors of SVM multiple classifiers. The other is that the number of samples is so small that the samples could not include all the possible situations and this can cause recognition error of classifiers. To resolve evidence conflict problems, we use an improved evidence combination rule for the final decision. It can be seen from Table 3 that after evidence combination, the degree of support of proposition \(A_{2}\) rises to 0.4638. Comparing with the result of single node, the support degree has increased by 37%. In the meantime, the uncertainty degree declines to 0.044, which meets the requirement of Equation (13). Therefore, the diagnosis result supports proposition \(A_{2}\), which is \"small leak\". \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Peak** & **Average** & **Wariance** & **Root** & **Peak** & **Pulse** & **Margin** & **Skewness** & **Kurtosis** \\
**value** & **amplitude** & **amplitude** & **factor** & **factor** & **factor** & **factor** & **factor** & **factor** \\ \hline
0.04729 & 0.01272 & 0.00025 & 0.01077 & 2.96782 & 0.41931 & 3.71730 & \(-1.4047\) & 2.69521 \\
0.04496 & 0.01395 & 0.00029 & 0.01195 & 2.62446 & 0.38066 & 3.22298 & \(-1.4020\) & 2.53662 \\
0.07940 & 0.01381 & 0.00033 & 0.01126 & 4.33524 & 0.67553 & 5.74708 & \(-1.3712\) & 3.26362 \\
0.07187 & 0.01295 & 0.00028 & 0.01077 & 4.28256 & 0.63152 & 5.54897 & \(-1.4185\) & 3.13221 \\
0.11165 & 0.01607 & 0.00046 & 0.01320 & 5.17711 & 0.88072 & 6.94743 & \(-1.2839\) & 3.71906 \\
0.12724 & 0.01649 & 0.00055 & 0.01307 & 5.41933 & 0.99074 & 7.71438 & \(-1.5390\) & 4.92900 \\ \hline \end{tabular}
\end{table} 
Table 1: Signal sample.