KurtosisInTime

Arguments

Description

The calculation of the kurtosis is used, e.g. for the evaluation and analysis of oscillations. It serves to determine the number of outliers within an oscillation 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 oscillations. 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 oscillation components. In the event of damage, individual pulse signals interfere with this signal, altering the distribution function. An evaluation of the system's condition can be carried out through the formation of suitable statistical values, such as the crest factor or the kurtosis factor.

If regularly measured, these methods offer an overview of the machine status. However, the disadvantage is that after they have increased, the characteristic values decrease again. The reason for this is that the number of pulse signals increases with progressive damage. Whereas in turn this has influence on the effective value but barely no effect on the peak value.

Modifications of the time signal caused by shock pulses induce a change in the resulting distribution function. Distinctively discrete damage can cause an increase of the kurtosis factor. Its absolute value thus allows statements on a damage.