Method for the monitoring of a machine with a rotating machine component, wherein in an automated manner - at successive measurement times parameter values ( P t) of operating parameters of the machine and in each case over a predefined measurement duration vibrations of the machine are recorded, - for each measurement duration a vibration spectrum ( Y t ( f)) of vibration amplitudes is determined depending on vibration frequencies ( f) of the vibrations recorded during the measurement duration, charcterised in that - a mean power density Φ t i of the vibration spectrum ( Y t ( f)) is in each case determined from the vibration spectrum ( Y t ( f)) for a multiplicity of frequency ranges, - during a learning phase comprising a multiplicity of measurement times, for each frequency range a model function ( Φ̂ to Φ̂) is determined from the mean power densities ( Φ t i) established for these measurement times and recorded parameter values ( P t) for an expected power density averaged over the frequency range as a linear function of the operating parameters, by a linear multiple regression model being trained for estimation of the model function (Φ̂ to Φ̂), - and during a monitoring phase for each measurement time and each frequency range a deviation measure is formed for a deviation of the mean power density Φ t i established from the recorded vibrations from an expected mean power density (Φ̂ ( i) ( P t)), - wherein for a measurement time and a frequency range the expected mean power density (Φ̂ ( i) ( P t)) is formed as a function value of the model function (Φ̂ to Φ̂) established in the learning phase for the frequency range at the point defined by the parameter values ( P t) recorded at the respective measurement time. - at successive measurement times parameter values ( P t) of operating parameters of the machine and in each case over a predefined measurement duration vibrations of the machine are recorded, - for each measurement duration a vibration spectrum ( Y t ( f)) of vibration amplitudes is determined depending on vibration frequencies ( f) of the vibrations recorded during the measurement duration, - a mean power density Φ t i of the vibration spectrum ( Y t ( f)) is in each case determined from the vibration spectrum ( Y t ( f)) for a multiplicity of frequency ranges, - during a learning phase comprising a multiplicity of measurement times, for each frequency range a model function ( Φ̂ to Φ̂) is determined from the mean power densities ( Φ t i) established for these measurement times and recorded parameter values ( P t) for an expected power density averaged over the frequency range as a linear function of the operating parameters, by a linear multiple regression model being trained for estimation of the model function (Φ̂ to Φ̂), - and during a monitoring phase for each measurement time and each frequency range a deviation measure is formed for a deviation of the mean power density Φ t i established from the recorded vibrations from an expected mean power density (Φ̂ ( i) ( P t)), - wherein for a measurement time and a frequency range the expected mean power density (Φ̂ ( i) ( P t)) is formed as a function value of the model function (Φ̂ to Φ̂) established in the learning phase for the frequency range at the point defined by the parameter values ( P t) recorded at the respective measurement time.