The system configurations in Figure 1(b) and 1(c) are firstly used for numerical validations of the proposed TFR-based leak detection method, with the system parameter settings and information given in Table 1. Different leakage cases (location and size) are considered for each test system and shown in Table 2, with tests no. 1 to no. 3 for the branched pipe system and tests no. 4 to no. 7 for the simple looped pipe system. For clarity, the relative leak effective area, A_L^* = C_dA_L/A_p with C_dA_L being leaking area and A_p the cross-sectional area of leaking pipe, for each test case is also listed in the table for reference. The system transient responses are obtained by the 1D numerical simulations in the time domain (i.e. Equations (1) and (2)). The transient pressure head at the just upstream of the inline valve are collected and then converted by Fourier transform into the frequency domain for the analysis. The results of leakage detection based on the proposed method and procedure in this study are obtained and listed in Table 2. The accuracy of the method is evaluated by the difference between the real and predicted values of the leakage information, which is defined as the relative error (ɛ) by: