# Pipeline Leakage localization Based on FBG Hoop Strain Sensors Combined with BP Neural Network
## 4 Leakage Localization Based on BP Neural Network
### Method Validation
The localization results using the pressure gauges are presented in Figure 8. It can be seen from the figure that although the predicted leak values are around the fitted line of the actual leak points, the errors are extremely large in many locations. Therefore the BPNN-based pipeline leakage localization method cannot be established when using traditional pressure gauges. Then, we replace the pressure gauge signals with the five FBG hoop strain sensing signals. It is worth mentioning that, compared with the traditional pressure gauge method, the FBG hoop strain sensor is a kind of nondestructive evaluation approach since it can be installed at any point along the pipeline. Thus, more information from the pipeline mid-side can be acquired besides the inlet and outlet pressure variation when multi-hoop strain sensing points are set along the pipeline. In this case study, five hoop strain sensing signals are chosen as the input neurons for the BPNN-based leakage localization approach. However, the pressure gauge-based method cannot be improved since it is impossible to install extra pressure gauges after the pipeline is constructed or even in operation status. The neural network prediction result of the non-noise case is shown in Figure 9. The horizontal axis in the graph represents the assumed leak point number ranging from 2-49 and the vertical axis represents the neural network prediction result of the leak point. The regression coefficient R value in non-noise situation is nearly 0.999, which is very close to one. This means that the predicted values of the neural network and actual leak points are very close. Figure 7: The BP neural network structure for leakage localization. The network's performance is quantified using the mean of squared errors, or the RMS errors, which is the deviation between the predicted and the actual value with the predictive number \(n\). The RMS error is used to evaluate the deviation degree of the calculated values from the true values. Besides the RMS error, the standard deviation and the regression coefficient are adopted to evaluate the influence of different hidden node numbers. From Table 2, it can be seen when there are 15 hidden neurons. The standard deviation and the RMS error are smaller than the others. Thus, the number of hidden layer neurons is set as 15 in order to train the neural network for noise cases. Measurement noise always influences the localization accuracy for real pipeline monitoring. In the above validation, the hoop strain variation is calculated based on MOC; thus, it is a numerical solution with no signal noise. For the actual application, the measurement noise will influence the localization effect. On the one hand, the measurement noise is generated from the FBG sensing system, like the FBG interrogator. On the other hand, the external disturbance or vibration will induce extra noise on all of the sensing points. Besides, the novel developed FBG hop strain sensor has enhanced strain sensitivity, which means the noise level will also be enlarged in the measurement. Thus, it is important to consider the signal noise for different levels for the real application. To demonstrate the robustness of the neural network, the calculated hoop strain variations are randomly added with Gaussian noises and sent as test samples for the trained neural network. Figure 10 shows the prediction results under different level noises. The noise levels are 1%, 2%, 5% and 10%, respectively. The error analysis of several noise levels is presented in Table 3. It can be seen that the neural network for leakage localization has a very good anti-noise capacity. The RMS error is as low as 1.7473% even  
Figure 8: Localization results based on two pressure gauges and BPNN. Figure 9: Contrast of the prediction result with real leak point. The results of the case study in this paper are from an ideal pipeline, without considering any external disturbance. Thus, this is a preliminary investigation with scope for further research.