The HT method is applied to perform the transient time-frequency analysis so as to characterize different faults in this system. The five reconstructed results in Figure 8 are transformed by the HT method and shown in Figure 9, where each sharp peak corresponds to the moment of the pressure wave passing through the specific pipe fault. Based on Equation (7), the total number of pipe faults and the locations of the faults in the system can then be predicted and the results are given in Table 3. Meanwhile, the relative errors of the prediction, which is defined by the difference between the predicted and real values normalized by the real value, are calculated and also listed under the location results in Table 3.