Convex Hull-Based Pattern Recognition Technique And Its Applications To Fault Diagnosis For Roller Bearings

Roller bearings are widely used as key components in rotating mechanical equipments. The operational performance of a rotating mechanical equipment is closely related to the operating condition of roller bearings. Therefore, the fault diagnosis technique for roller bearings has always been an important research topic in the field of mechanical fault diagnosis. With the increasingly high degree of automation in mechanical equipments, it is particularly necessary to perform the research on intelligent fault diagnosis in order to detect and recognize roller bearing faults timely and accurately.Fault diagnosis for roller bearings includes two aspects: fault detection and fault type recognition. Intrinsically, the former is a one-class classification problem, and the latter is a multi-class classification problem. Therefore, the key to intelligent fault diagnosis for roller bearings lies in pattern recognition. In recent years, some pattern recognition techniques such as probability and statistics-based techniques, clustering algorithms, neural networks and kernel-based techniques have been introduced to fault diagnosis for roller bearings, and many fruitful achievements have been obtained. Among these methods, kernel-based techniques are of particular interest to relevant scholars. From geometrical point of view, some typical kernel-based techniques, including support vector machines, support vector data description and maximum margin classification based on affine hulls, estimate the class distribution of each sample set with a kind of geometric model and then built the classification model based on certain decision rule. Inspired by this idea, the convex hull is used as the estimation model for the class distribution. Accordingly, the convex hull-based pattern recognition technique is proposed in this dissertation, which can provide new ideas and new techniques for intelligent fault diagnosis of roller bearings. This dissertation is supported by the National Natural Science Foundation of China(Grant no. 51075131) and the Hunan Provincial Innovation Foundation for Postgraduate(Grant no. CX2014B146).The main research contents of this dissertation are listed as follows:(1) Concerning fault detection for roller bearings, a novel method called one-class classification based on the convex hull(OCCCH) is proposed, and then a generalized Gilbert algorithm is further proposed to solve the minimum norm problem involved in OCCCH. The relationship between OCCCH and one-class support vector machine(OCSVM) is investigated theoretically. The classification accuracy and the computational efficiency of the two one-class classification methods are compared through the experiments conducted on several benchmark datasets. Experimental results show that OCCCH with generalized Gilbert algorithm performs more efficiently than OCSVM with sequential minimal optimization(SMO) algorithm. At the same time, the two methods can always obtain comparable classification accuracies.(2) Aimed at the kernel parameter selection of OCCCH, an improved MIES(IMIES) is developed for selecting the Gaussian kernel parameter. Numerical experiments are conducted to compare the performance of IMIES and other two kernel parameter selection methods based on the tightness of decision boundaries(i.e., MIES and DTL). Experimental results show that the proposed IMIES is able to select more suitable Gaussian kernel parameters compared to MIES and DTL. After selecting the Gaussian kernel parameter by IMIES and training the model by generalized Gilbert algorithm, OCCCH is applied to construct monitoring models for bearing fault detection. Monitoring results demonstrate that the proposed method can detect the bearing fault successfully.(3) To solve the problem of generalized Gilbert algorithm that it may work slowly as it approaches the final solution, a generalized Mitchell-Dem’yanov-Malozemov(MDM) algorithm is proposed to solve the minimum norm problem involved in OCCCH. The comparison between generalized MDM algorithm and generalized Gilbert algorithm is analyzed theoretically on the iteration strategy and the algorithm complexity. Comparative numerical experiments show that generalized MDM algorithm presents great computational superiority over generalized Gilbert algorithm.(4) To identify fault types for roller bearings, a maximum margin classification based on flexible convex hulls(MMC-FCH) is proposed based on defining the flexible convex hull. Numerical experiments on several datasets verify the effectiveness of MMC-FCH. Comparisons among MMC-FCH and other two maximum margin classification methods are also investigated. MMC-FCH is applied to identify bearing fault types. Experimental results demonstrate that MMC-FCH can reliably identify not only fault locations but also fault severities.(5) Another multi-class classification method based on convex hulls is proposed, i.e., nearest neighbor convex hull classification(NNCHC). NNCHC is a pattern recognition approach which combines the convex hull estimation and the nearest neighbor classification rule. Generalized MDM algorithm with slight modification can be also employed to solve the optimization problem involved in NNCHC. A fault diagnosis approach combining NNCHC with local characteristic-scale decomposition(LCD) is proposed for roller bearings. Experimental results show that NNCHC can recognize fault locations accurately and obtain high classification accuracies even in the case of a limited number of samples.