Bearings are fundamental mechanical components in rotary machines (engines, gearboxes, generators, radars, tur- bines, etc) that have been identified as one of the primary causes of failure in these machines. This make bearing fault diagnosis (detection, classification and prognosis) an economic very relevant topic, as well as a technically challenging one as evaluated by the extensive research literature on the subject. This paper employs a systematic methodology to identify, summarize, analyze, and interpret the primary literature on fuzzy formalisms for bearing fault diagnosis from 2000 to 2017 (March). The main contribution is an updated, unbiased and (to a higher extend) repeatable search, review and analysis (summary, classification, and critique) of the available approaches resorting to fuzzy formalisms in this trendy topic. A discussion on a new promising future research direction is provided. A comprehensive list of references is also included.

Fuzzy clustering has emerged as a fundamental technique of information granulation. In this study, we introduce and discuss multivariable encoding and decoding mechanisms (referred altogether as a reconstruction problem) expressed in the language of fuzzy sets and fuzzy relations. The underlying performance index associated with the problem helps quantify a reconstruction error that arises when transforming a numeric datum through fuzzy sets (relations) and then reconstructing it into an original numeric format. The clustering platform considered in this study concerns the well-known algorithm of Fuzzy C-Means (FCM). The main design aspects deal with the relationships between the number of clusters versus the reconstruction properties and the resulting reconstruction error. The impact of the fuzzification coefficient on the reconstruction quality is investigated. This finding is of interest, given the fact that predominantly all applications involving FCM use the value of the fuzzification coefficient equal to 2. In light of the completed experiments, we demonstrate that this selection may not be experimentally legitimate. We also carry out a comparative analysis of the reconstruction properties of the Boolean decoding that is induced by the fuzzy partition. Experimental investigations involve selected machine learning data.

Bearings are one of the most omnipresent and vulnerable components in rotary machinery such as motors, generators, gearboxes, or wind turbines. The consequences of a bearing fault range from production losses to critical safety issues. To mitigate these consequences condition based maintenance is gaining momentum. This is based on a variety of fault diagnosis techniques where fuzzy clustering plays an important role as it can be used in fault detection, classification, and prognosis. A variety of clustering algorithms have been proposed and applied in this context. However, when the extensive literature on this topic is investigated, it is not clear which clustering algorithm is the most suitable, if any. In an attempt to bridge this gap, in this study four representative fuzzy clustering algorithms are compared under the same experimental realistic conditions: fuzzy c-means (FCM), the Gustafson-Kessel algorithm, FN-DBSCAN, and FCMFP. The study considers only real-world bearing vibration data coming from both a benchmark data set (CWRU) and from a lab setup where interference between bearing faults can be studied. The comparison takes into account the quality of the generated partitions measured by the external quality (Rand and Adjusted Rand) indexes. The conclusions of the study are grounded in statistical tests of hypotheses.