The calculation of the kurtosis is used, for example, for the evaluation and analysis of vibrations. It serves to determine the number of outliers within an vibration signal.

In mathematical terms, the kurtosis is a measure for the relative "flatness" of a distribution (compared to the normal distribution which has a kurtosis of zero). A positive kurtosis indicates a tapering distribution (a leptokurtic distribution), whereas a negative kurtosis indicates a flat distribution (platykurtic distribution).

This statistical method is particularly suitable for analyzing random or stochastic signals, e.g., in terms of condition-based maintenance (condition monitoring) when analyzing vibrations.

For characterizing the signal curve, methods of probability density or frequency are used. It is assumed that a noise signal with a Gaussian amplitude distribution can be measured in machines in good order after filtering out, e.g., rotational frequency vibration components. In the event of damage, individual pulse signals interfere with this signal, altering the distribution function. By choosing suitable characteristic values such as the crest factor or the kurtosis factor, the condition of the machine can be evaluated.

If regularly measured, these methods offer an overview of the machine status. However, the disadvantage is that after they increase, the characteristic values decrease again. The reason for this is that the number of pulse signals increases with progressive damage. This in turn influences the effective value but barely effects the peak value.

Modifications of the time signal caused by shock pulses induce a change in the resulting distribution function. Thus, damages with a distinctly discrete nature can cause the kurtosis factor to increase sharply. Its absolute value thus allows statements on a damage.

The calculation of the kurtosis is similar to the calculation of the standard deviation StdDev. ibaAnalyzer uses the following formula:

n: Number of measured values s: Standard deviation

Kurtosis

Kurtosis('Expression')

Description

This operation returns the kurtosis of the selected time signal.

KurtosisInTime

KurtosisInTime('Expression','Interval')

Arguments

'Expression'	Signal or expression for which to form the kurtosis
'Interval'	Length of the interval over which to calculate the kurtosis

Description

With this operation, the selected expression is divided into equal-duration intervals of the length 'Interval'. For these intervals, the kurtosis is subsequently calculated.

KurtosisValid

KurtosisValid('Expression','Valid')

Arguments

'Expression'	Signal or expression for which to form the kurtosis
'Valid'	Control signal

Description

This operation describes the kurtosis for those intervals in which a related control signal is TRUE.

MKurtosis

MKurtosis('Expression','Interval')

Arguments

'Expression'	Signal or expression for which to form the kurtosis
'Interval'	Length of the interval over which to form the kurtosis (in seconds)

Description

This operation calculates the kurtosis of 'Expression' over a floating X-axis interval of fixed length 'Interval'.