## Signal Features

Signal features provide general signal-based statistical metrics that can be applied to any kind of signal, including a time-synchronized average (TSA) vibration signal. Changes in these features can indicate changes in the health status of your system. Diagnostic Feature Designer provides a set of feature options .

### Statistical Features

The statistical features include basic mean, standard deviation, and root mean square (RMS) metrics. In addition, the feature set includes shape factor and the higher order kurtosis and skewness statistics. All these statistics can be expected to change as a deteriorating fault signature intrudes upon the nominal signal.

Shape factor — RMS divided by the mean of the absolute value. Shape factor is dependent on the signal shape while being independent of the signal dimensions.

`${x}_{SF}=\frac{{x}_{rms}}{\frac{1}{N}\sum _{i=1}^{N}|{x}_{i}|}$`

The higher-order statistics provide insight to system behavior through the fourth moment (kurtosis) and third moment (skewness) of the vibration signal.

• Kurtosis — Length of the tails of a signal distribution, or equivalently, how outlier prone the signal is. Developing faults can increase the number of outliers, and therefore increase the value of the kurtosis metric. The kurtosis has a value of 3 for a normal distribution. For more information, see `kurtosis`.

`${x}_{kurt}=\frac{\frac{1}{N}\sum _{i=1}^{N}{\left({x}_{i}-\overline{x}\right)}^{4}}{{\left[\frac{1}{N}\sum _{i=1}^{N}{\left({x}_{i}-\overline{x}\right)}^{2}\right]}^{2}}$`

• Skewness — Asymmetry of a signal distribution. Faults can impact distribution symmetry and therefore increase the level of skewness.

`${x}_{skew}=\frac{\frac{1}{N}\sum _{i=1}^{N}{\left({x}_{i}-\overline{x}\right)}^{3}}{{\left[\frac{1}{N}\sum _{i=1}^{N}{\left({x}_{i}-\overline{x}\right)}^{2}\right]}^{3/2}}$`

For more information, see `skewness`.

### Impulsive Metrics

• Impulsive Metrics are properties related to the peaks of the signal.

• Peak value — Maximum absolute value of the signal. Used to compute the other impulse metrics.

`${x}_{p}=\underset{i}{\mathrm{max}}|{x}_{i}|$`

• Impulse Factor — Compare the height of a peak to the mean level of the signal.

`${x}_{IF}=\frac{{x}_{p}}{\frac{1}{N}\sum _{i=1}^{N}|{x}_{i}|}$`

• Crest Factor — Peak value divided by the RMS. Faults often first manifest themselves in changes in the peakiness of a signal before they manifest in the energy represented by the signal root mean squared. The crest factor can provide an early warning for faults when they first develop. For more information, see `peak2rms`.

`${x}_{crest}=\frac{{x}_{p}}{\sqrt{\frac{1}{N}\sum _{i=1}^{N}{x}_{i}{}^{2}}}$`

• Clearance Factor — Peak value divided by the squared mean value of the square roots of the absolute amplitudes. For rotating machinery, this feature is maximum for healthy bearings and goes on decreasing for defective ball, defective outer race, and defective inner race respectively. The clearance factor has the highest separation ability for defective inner race faults.

`${x}_{clear}=\frac{{x}_{p}}{{}^{\left(\frac{1}{N}\sum _{i=1}^{N}{\sqrt{|{x}_{i}|\right)}}^{2}}}$`

### Signal Processing Metrics

The signal processing metrics consist of distortion measurement functions. System degradation can cause an increase in noise, a change in a harmonic relative to the fundamental, or both.

• Signal-to-Noise Ratio (SNR) —Ratio of signal power to noise power

• Total Harmonic Distortion (THD) — Ratio of total harmonic component power to fundamental power

• Signal to Noise and Distortion Ratio (SINAD) — Ratio of total signal power to total noise-plus-distortion power

For more information on these metrics, see `snr`, `thd`, and `sinad`.

The software stores the results of the computation in new features. The new feature names include the source signal name with the suffix `stats`.