## 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 .

### Basic Statistics

The basic statistics include mean, standard deviation, root mean square (RMS), and shape factor. 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.

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

### Higher-Order Statistics

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`.

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

• Excess Kurtosis — Kurtosis value shifted by 3 so that the feature value is 0 for a normal distribution.

• Bias-corrected — Correct systematic bias that occurs when a sample represents a larger population. For ensemble signals, this representation applies when taking or using signal measurements for one portion of the operating interval that the measurements represent. For example, if you track machinery telemetry health for one hour per week while the machinery runs continuously, the difference between one hour and one week imposes a bias on the kurtosis estimate.

Bias correction is most effective with normal distributions. Consider using bias correction especially when you are using segmented rather than continuous data.

For more information, see `kurtosis`

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

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

• Bias-corrected — Correct systematic bias that occurs when a sample represents a larger population. For ensemble signals, this representation applies when taking or using signal measurements for one portion of the operating interval that the measurements represent. For example, if you track machinery telemetry health for one hour per week while the machinery runs continuously, the difference between one hour and one week imposes a bias on the skewness estimate.

Bias correction is most effective with normal distributions. Consider using bias correction especially when you are using segmented data (frames).

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`.

For information on interpreting feature histograms, see Interpret Feature Histograms in Diagnostic Feature Designer.