1. A method of monitoring vibration amplitude and frequency in a rotary machine, comprising: receiving measurements of vibration amplitude and rotation speed of the machine from at least one sensor; recording as a data point each amplitude measurement as a function of vibration frequency and rotational speed; storing a plurality of different amplitude thresholds each representing a noise floor for a respective one of a first set of sub-ranges of vibration frequency and rotational speed, wherein each sub-range includes a sub-range of speeds and a sub-range of frequencies, wherein the different amplitude thresholds are set in a training process using training data points comprising vibration data from a run of the rotary machine deemed to be normal, and wherein the different amplitude thresholds are set by fitting an amplitude distribution to the training data points in each sub-range of vibration frequency and rotational speed; comparing each amplitude measurement to the amplitude threshold for a corresponding sub-range of vibration frequency and rotational speed for the data points within which the amplitude measurement falls; determining the amplitude measurement to represent noise if it falls below the amplitude threshold and as significant spectral content if it is above the amplitude threshold; using the amplitude measurement determined to be significant spectral content, assessing abnormalities of at least a component of the rotary machine; and when an abnormality is assessed, generating a signal configured to indicate the abnormality of at least a component of the rotary machine.