## 3 Model Verification
Furthermore, a throttle valve located within an end rigid mass block supplies impedance loading for the pipeline. The primary advantage offered by this fluid noise generator lies in its ability to precisely adjust sinusoidal excitation frequencies via an upper computer to attain the desired frequencies of fluid pulsation while minimizing motor pump group-generated noise through the implementation of both pulsation attenuators and a long flexible hose. This configuration effectively decouples both the noise source and the flow source, thereby ensuring the acquisition of high signal-to-noise ratio (SNR) fluid noise across the entire frequency spectrum. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Pipeline (Stainless Steel)** & \\ \hline Density: 7985 kg/m\({}^{3}\) & L1: 1.5 m & R: 0.038 m \\ Young’s modulus: 206 GPa & L2: 1.5 m & Inner radius: 0.0125 m \\ Poisson’s ratio: 0.29 & L3: 1.1 m & Wall thickness: 0.0045 m \\ \hline Fluid (Hydraulic oil) & \\ \hline Density: 876 kg/m\({}^{3}\) & Bulk modulus: 1.68 GPa & Kinematic viscosity: 46 mm\({}^{2}\)/s \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The parameters of the pipeline and fluid. Figure 8: A schematic diagram of the fluid noise generator. Figure 7: The configuration of the measured pipeline. The experiment platform, illustrated in Figure 9, primarily comprised three components: the flow source and noise source, the data acquisition equipment, and the measured pipeline. Both ends of the pipeline were connected to a rigid mass block with sufficient weight, which can be considered as providing fixed constraints. During the experiment, the throttle valve was closed off while the system pressure was regulated via the relief valve located at the pump outlet. At this juncture, the impedance at the fluid's end approached infinity, effectively simulating a rigid boundary condition. Prior to the initiating test, the system operated under constant conditions for half an hour to mitigate any interference caused by bubbles within the pipeline. Throughout the experiment procedures, the temperature was maintained at 24 \({}^{\circ}\)C, with a flow rate of 36 L/min and a pressure of 10 MPa. The fluid noise generator delivered wide-band fluid excitation ranging from 100 Hz to 1 kHz for the measured pipeline; sweeping occured in increments of 5 Hz with each single-frequency line spectrum held for a duration of 1.5 s. The time-frequency waterfall diagram recorded at point P1 is presented in Figure 10. It reveals that amplitude fluctuations in pressure occur periodically across various frequencies--this phenomenon correlates with specific distribution parameter characteristics inherent to the pipeline structure. Overall, it can be concluded that the fluid noise generator produces relatively high SNR fluid noise within the frequency band of 100 Hz to 1 kHz, thus serving as an effective excitation source for evaluating pipeline systems. In order to evaluate the advantages of this method regarding computational stability, the two transfer functions defined in Table 5 were utilized as verification indicators. The pipeline was modeled using commercial finite element software. Both ends of the pipeline were subjected to fixed constraints, with the fluid end configured as a closed port. The input excitation applied was a unit of sound pressure. A comparison of the calculation results from the classical TMM, the MVTMM proposed in this paper, and the FEM is presented in Figure 11. As illustrated in Figure 11a, for the indicator H-P2/P1, the TMM exhibits instability within a frequency range above 600 Hz, rendering it incapable of accurately predicting the vibration characteristics of fluid dynamics in that frequency domain. In contrast, the MVTMM maintains stability across all frequencies and aligns closely with the FEM results. This observation underscores the MVTMM's advantage in enhancing result stability.