Anomaly detection and section estimation methods using multiplexed fiber Bragg gratings (FBGs) have been developed to identify propellant supply anomalies rapidly and autonomously in spacecraft propulsion systems. FBGs were used to measure the external strain of the pipe due to internal pressure fluctuations in the pipe during the pressure response caused by a water hammer. The measured strain was substituted into the constructed conversion formula to obtain the differential pressure through the FBGs. As a result, compared with the differential pressure measured by a conventional pressure sensor at the same position, the error was 2% for the maximum pressure of the water hammer and 1% for the natural frequency, indicating high applicability as a differential pressure sensor in piping with FBG simply wrapped around the outside of the pipe. Since the peak intensity and frequency of the measured values in the frequency domain change during flow anomaly and bubble localization, the frequency response function (FRF) between response data of the section to be detected was calculated, and the least-squares error of the FRF was used as the degree of anomaly. As a result, flow anomalies and bubble localization became detectable and sectional estimation was possible.