A machine includes at least one piston and a pump shaft. A method for detecting a leak in the machine includes receiving a vibration signal from a vibration sensor disposed on at least one of an upstream pipe and a downstream pipe of the machine, receiving a rotational speed signal and an angular shaft position signal from a speed and position sensor disposed on the machine, calculating a rotational speed and an angular shaft position of the pump shaft, calculating at least one complex harmonic Fourier amplitude of the received vibration signal, low pass filtering the at least one complex harmonic Fourier amplitude, calculating a deviation amplitude as a magnitude of a complex difference between the filtered amplitude and a base amplitude, and monitoring the deviation amplitude to detect a leakage.