A new generalised approach for health monitoring has been formulated. The generalised approach consists of using two new monitoring features simultaneously, which are based on the Fourier transform and which take into account the covariance between features. The generalisation of the approach improves the effectiveness of health monitoring. The monitoring effectiveness between the generalised approach and the power spectral density approach was compared for vibroacoustical monitoring. It was found that the power spectral density approach is not optimal, and represents only a particular case of the generalised approach. The power spectral density approach is optimal only if both: the correlation coefficient between new features is equal to zero, and the standard deviations of the features are equal. Use of the generalised approach provides an improvement in monitoring effectiveness as compared with the power spectral density approach. Application of the generalised approach was considered for the vibroacoustical diagnostics of damping.