Statistical evidence of central moment as fault indicators in ball bearing diagnostics

This paper deals with post processing of vibration data coming from a experimental tests. An AC motor running at constant speed is provided with a faulted ball bearing, tests are done changing the type of fault (outer race, inner race and balls) and the stage of the fault (three levels of severity: from early to late stage). A healthy bearing is also measured for the aim of comparison. The post processing simply consists in the computation of scalar quantities that are used in condition monitoring of mechanical systems: variance, skewness and kurtosis. These are the second, the third and the fourth central moment of a real-valued function respectively. The variance is the expectation of the squared deviation of a random variable from its mean, the skewness is the measure of the lopsidedness of the distribution, while the kurtosis is a measure of the heaviness of the tail of the distribution, compared to the normal distribution of the same variance. Most of the papers in the last decades use them with excellent results. This paper does not propose a new fault detection technique, but it focuses on the informative content of those three quantities in ball bearing diagnostics from a statistical point of view. In this paper, a discriminant function analysis is used, to determine which central moment has a high discrimination power in the diagnostics of ball bearing in stationary conditions.