Bearing condition diagnosis and prognosis using applied nonlinear dynamical analysis of machine vibration signal

In this paper, we introduce a modified form of the correlation integral developed by Grassberger and Procaccia referred to as the partial correlation integral, which can be computed in real time. The partial correlation integral algorithm is then used to analyze machine vibration data obtained throughout a life test of a rolling element bearing. From the experimental results, the dimensional exponent (an approximation of the correlation dimension) as computed from the partial correlation integral algorithm tends to increase as time progresses and the useful remaining life of the bearing is decreasing. The dimensional exponents of a healthy bearing and a bearing close to failure are statistically different. We also propose a computational scheme for bearing condition monitoring (diagnosis and prognosis) using the dimensional exponent integrated with a surrogate data testing technique. As a result, we can characterize the condition of the bearing from the results of the surrogate data test and furthermore, we provide some preliminary evidence that the dimensional exponent can be used to predict the failure of rolling element bearings in rotating machinery from real-time vibration data.