The use of correlation dimension in condition monitoring of systems with clearance

In this paper the application of embedding space and fractal dimension estimation to monitor the condition of a system with clearance is considered by examining the effect on the correlation dimension of variations of the gap clearance in a bearing system. The model analysed represents an elastically supported rotor and stator, subject to excitation by an imbalance, which is restricted to two-dimensional linear movement perpendicular to the axis of rotation. From full-phase space calculations it is found that as the clearance between the rotor and stator is increased, there is a discernible decrease in the value of the correlation dimension. Thus, it may be feasible to determine changing events such as gap clearance by monitoring the correlation dimension of the system. Employing the conventional method of delays results in substandard estimates for the correlation dimension. However, modifying the method of delays by incorporating values from an additional observable into the vectors used for reconstructing the phase space produce results in accordance with those from the full-phase space. (C) 2000 Academic Press.