ANOVA and other statistical tools for bearing damage detection

The aim of the paper is to exhaustively exploit and test some statistical tools, such as ANOVA and Linear Discriminant Analysis, to investigate a massive amounts of data collected over a rig available @DIRG Lab, specifically conceived to test high speed aeronautical bearings; the rig permits the control of rotational speed (6000 – 30000 RPM), radial load (0 to 1800 N) and temperature, and allows monitoring vibrations by means of 4 tri-axial accelerometers. Fifteen different damages have been realised on the bearing but, for simplicity, this papers only treats those cases where simple identification methods have failed or not demonstrated to be fully affordable. The damages have been inferred on rolls or on the internal ring, with different severities, which are reported as a function of their extension, i.e. 150, 250, 450 μm. A total number of 17 combinations of load and speed have been analysed per each damaged bearing. Although ANOVA rigorously applies when some conditions are respected on the probability distribution of the responses, such as Independence of observations, Normality (normal distribution of the residuals) and Homoscedasticity (homogeneity of variances – equal variances), the paper exploits the robustness of the technique even when data do not fully fall into the requisites. Analyses are focused on the best features to be taken into account, trying to seek for the most informative, but also trying to extract a “best choice” for the acceleration direction and the most informative point to be monitored over the simple structure. Wanting to focus on the classification of the single observation, Linear Discriminant Analysis has been tested, demonstrating to be quite effective as the number of misclassification is not very high, (at least considering the widest damages). All these classifications have unfortunately the limit of requiring labelled examples. Acquisitions in un- damaged and damaged conditions are in fact essential to guarantee their applicability, which is quite often impossible for real industrial plants. The target can be anyway reached by adopting distances from un-damaged conditions which, conversely, must be known as a reference. Advantages of the statistical methods are quickness, simplicity and full independence from human interaction.