## 4 Laboratory Experiments
### Signal Processing for Leakage Location  
The leakage location procedure for the MLPNN locator is shown in Figure 10, and the MLPNN locator operates in two different modes:  
1. In the learning mode, the training sets of the MLPNN contain the input vectors and the output vectors. The input vectors are the energy ratios of two impulse response signals in corresponding frequency bands. Since the impulse response signals are non-stationary signals, and the wavelet packet analysis is suitable for processing the non-stationary signals, then the impulse response signals were processed by the wavelet packet transform in this study. The output vectors are the distances between one sensor and each impact location. The learning procedure for the MLPNN is as follows:  
1. Since the energy of a leakage-induced signal at frequency band from 100 to 150 kHz is higher than at other frequency bands, and three-level decomposition can extract the signal in this frequency range, so all the impulse response signals are decomposed into three layers of wavelet packet coefficients, and the signals are reconstructed in eight frequency bands by wavelet packet coefficients. The Haar wavelet is used in this study.
2. Calculate the energies of the decomposed signals in step 1 by Equation (13); then calculate the energy ratios of two impulse response signals in the corresponding frequency band.
3. Train the MLPNN with the input and output vectors. The input vectors are the energy ratios in step 2, and the output vectors are the distances between one sensor and each impact location, and the epochs in the training method is set to 0.01.  
2. In the application mode, the trained MLPNN locator can locate the leakage by using the energy ratios of the leakage-induced signals in the frequency bands with greater power spectral density. The leakage location procedures for the MLPNN locator are described as follows:  
1. Measure the leakage-induced signals by using the two AE sensors.
2. Determine the peak frequency of the leakage-induced signals by using the power spectral density.
3. Estimate the group speed of the leakage-induced signals by using the peak frequency in step 2 and the known group speed dispersive curve of the fundamental flexural mode.
4. Calculate the CCC by using the CCF method and the modified GCC method.
5. Compare the maximum peak amplitudes of the two CCCs obtained in step 4. \(\rho_{x1 xz}c\) and \(\rho_{x1 xz}s\) are the maximum peak amplitudes of the CCCs obtained by using the CCF method and the modified GCC method, respectively. If \(\rho_{x1 xz}s\) is greater than \(\rho_{x1 xz}c\), it implies that compared to the CCC obtained by using CCF method, the CCC obtained by using modified GCC method is more reliable; then perform step 6, otherwise perform step 7.
6. Calculate the distance between the leakage and sensor 1 by Equation (9). The group speed of the leakage-induced signal was determined in step 3, and the time delay was determined by the sampling frequency and the offset of the CCC maximum peak obtained by the modified GCC method in step 4.  
7. Decompose the leakage-induced signals into three layers wavelet packet coefficients, reconstruct the signals in eight frequency bands by using the wavelet packet coefficients.
8. Calculate the energy ratios of the decomposed signals in the frequency bands with the greater power spectral density.
9. Locate the leakage by using the energy ratios in step 8 and the trained MLPNN locator.