This paper introduces a novel method called extended phase space topology (EPST) for machinery diagnostics and pattern recognition. In particular, the research focuses on fault detection and diagnostics of rolling element bearings. The proposed method is based on mapping the vibrational response onto the density space and approximating the density using orthogonal functions. The method has been applied to vibration data of a rotating machine where the data were measured by proximity probes. The method was applied to two operating conditions: constant operating speed and variable operating speed. As will be shown, the proposed feature extraction method has an outstanding capability in characterizing the system response and diagnosing the system. The method is evidently robust to noise, does not depend on expert knowledge about the system, requires no feature ranking or selection, and can easily be applied in an automated process. Finally, a comparison with utilization of statistical features is performed for each operating condition, which demonstrates that the proposed method performs better than the traditional statistical methods.

This article presents the application of phase space topology and time-domain statistical features for rolling element bearing diagnostics in rotating machines under variable operating conditions. The results indicate very promising performance in identifying various faults with virtually perfect accuracy, recall, and precision. A comparison with the envelope analysis method is performed to show the superior performance of the proposed approach. In addition, the results demonstrate an outstanding prediction rate for the fault diameter of bearing defects.

This paper presents the application of recurrence plots (RPs) and recurrence quantification analysis (RQA) in the diagnostics of various faults in a gear-train system. For this study, multiple test gears with different health conditions (such as a healthy gear, and defective gears with a root crack on one tooth, multiple cracks on five teeth and missing tooth) are studied. The vibration data of a gear-train is measured by a triaxial accelerometer installed on the test. Two different support vector machine classifiers are trained and compared. Mutual information is used to rank the extracted features in order to select an optimal subset that provides as much information as possible about the intrinsic dynamics of the system. Results indicate that our approach is quite efficient in diagnosing the status of the health of the gear system and characterizing the dynamic behavior.

This study investigates the use of the mapped density of time response using orthogonal functions to detect single and multiple faults in rolling element bearings. The method is based on constructing the density of a single time response of the system by using orthogonal functions. The coefficients of the orthogonal functions create the feature vector in order to discriminate between different rolling element bearing faults. The method does not require preprocessing of the data, noise reduction, or feature selection. This method has been applied to vibration data of different bearing conditions at rotational speeds ranging from 300 rpm to 3000 rpm. These conditions include a healthy bearing, and bearings with defects in inner race, outer race, combination of inner race and outer race and rolling element. The results have shown remarkable detection efficiency in the case of a single and two bearing fault configurations. In general, for all bearing configurations, the approach has high performance in detecting defective conditions. These results indicate that using the mapped density to characterize the system under different conditions has considerable potential in bearing diagnostics.