Several methods have been proposed for fault detection in mechanical systems based on sensor signals. It is preferable that the corresponding label for each sensor signal should be provided and analyzed via appropriate supervised classification methods. However, the label information about a system’s status often does not perfectly pair with the corresponding data. Therefore, we apply a semi-supervised classification for fault detection using pattern extraction of multivariate signals. This approach transforms continuous time series into a set of contiguous bins via multivariate discretization. Then, we identify informative patterns in the system states, by using a self-training method with limited label information.
To demonstrate the effectiveness of the proposed extraction method, five accelerometer signals are collected from a bearing-shaft system. The proposed method successfully reveals informative fault patterns that can be applied as references for fault detection. The method achieved a higher detection performance, regardless of the ratio of unlabeled inputs in datasets.
With the introduction of new technology and the divergence of customer preferences, mechanical systems have become more intelligent, more complex, and therefore more uncertain. Failure to adequately control a system leads to the occurrence of faults and system downtimes; these result in economic losses, such as high warranty costs, and social losses, including negative impacts on consumer confidence. Therefore, to reliably operate a system while preventing unexpected fault occurrences, appropriate strategies for fault detection and identification have been pursued.
Because it is difficult to obtain clear and quantitative information in advance about a mechanical system—such as the fault-related frequency band and the state-space representation —many researchers have tried to indirectly analyze the sensor signals related to faults in various mechanical systems. However, very few sensor signals can typically be obtained for fault detection in a mechanical element, and these signals are typically very short, nonlinear, and non-stationary. These signal characteristics can easily give rise to unclear relationships between the signal and the system’s operational states (e.g., no-fault state and fault state).
In such a case, the typical geometric similarity is not satisfied because of inconsistencies incorrectly identifying as statistical outliers those signal values or trends associated with fault states. To address this issue, pattern extraction with time series representations has been introduced to identify informative indicators of faults. Among such approaches, time series discretization has been widely used to analyze unexpected or anomalous signal changes by preserving meaningful signal changes while reducing the size of the dataset.
After transforming the original signals, the significant signal patterns are extracted from the target states of a system as motifs. For example, the transformation of the original signals to discretized state vectors (DSVs) is applied both in discrete wavelet transforms and in one of the time series discretization methods, namely, symbolic aggregate approximation (SAX).
By counting the number of occurrences of each DSV and using the k-nearest neighbor classifier, George et al. extracted meaningful patterns about rotor faults in induction motors. Duane et al. analyzed compressor transformation and bit map. After transforming the original vibration signals, they generated a meaningful bit map from each different fault state (e.g., spring faults, valve fracture, and valve wear). In addition, many researchers have used time series classification with a supervised learning classifier for the extraction of significant markers of faults. However, obtaining corresponding and correct labels for the entire time series data is very expensive and time-consuming, and mechanical systems are usually rife with unknown faults. In other words, in practice, the label information about a system’s status often fails to perfectly pair with the corresponding sensor data. For example, fully labeled datasets are often collected from in-lab experiments or test runs, whereas unlabeled datasets are collected using the identical system in practical environments.
Therefore, several semi-supervised learning approaches have been introduced in order to leverage the advantages of both supervised and unsupervised learning. Zhao et al. proposed a semi-supervised learning classifier for fault detection in solar photovoltaic arrays. They normalized and filtered measurements and then distinguished fault data from other data by using supervised and unsupervised classifiers together in a semi-supervised manner. This method showed good performance without labeling costs in continuously updating models.
For the extraction of meaningful vibration signals, a semi-supervised classifier was applied with Kernel marginal Fisher analysis. Those authors first reduced redundant information in order to highlight indicative signal behaviors related to system status change. They then extracted optimal low-dimensional features in order to improve the classification performance of various bearing fault types. In many studies, semi-supervised learning approaches showed improvement in fault detection with not fully labeled input datasets. However, it is not easy to apply a seem supervised classifier to DSVs, because time series discretization reduces the number of datasets, making the preprocessed dataset smaller than the original dataset. Jun et al. obtained a symbolic representation of time series with a semi-supervised classification. They transformed the time series data into a series of granules by applying a hidden Markov model, and then used both the hidden Markov model and a shallow neural network together with symbolic and original real-valued data, respectively. Also, a convolution neural network (CNN) was modified and used for semi-supervised learning in the time-series classification.
First, the investigators artificially increased the amount of training data to handle partially labeled inputs in the supervised classification problem. In addition, they conducted the pre-training of each layer in an unsupervised manner to find appropriate parameter settings for the classifier. Then, in a supervised manner, they applied convolution filters to discretize time-series data. A combination of SAX and neural networks was also used to distinguish gestures and actions. A 3D posed image was converted into a symbol matrix using SAX, and then a hierarchical-clustering method was used to assign symbol matrices to several 3D posed-image groups. After generating the groups in a semi-supervised manner, the investigators converted a symbol matrix into a feature vector using a CNN and predicted the current gesture by an extended short-term memory model in a supervised condition. However, during the time-series classification and fault detection, a decrease in the performance of semi-supervised learning approaches was observed compared with that of supervised learning.
In addition, several detection approaches provided high detection performance either with few labeled and many unlabeled input datasets or with few labeled and many unlabeled inputs. Because semi-supervised detection cannot be controlled in practical environments, it should not be susceptible to the number of unlabeled inputs in the entire dataset. Therefore, in this study, we propose adding the number of DSV occurrences in no-fault and fault patterns as input data in semi-supervised learning to re-weigh the extracted patterns and make up for the information loss from the discretization. The proposed occurrence information should enable dealing with severity as a fault marker. Subsequently, we analyzed the dependence of fault detection performance on the amount of data in training sets to compare the performance of our proposed method with the existing supervised or semi-supervised detection methods.
The remainder of the present study is organized as follows. Section 2 details the transformation of the original continuous signals into DSVs and describes the extraction of fault patterns using semi-supervised classification in consideration of the number of DSV occurrences. Section 3 describes the bearing-shaft system analyzed here, the collection of acceleration signals, and the control of abnormal states. The pattern extraction method is experimentally verified and validated for the detection of fault states in the bearing shaft. Finally, Section 4 presents concluding remarks and future directions following this work.
Causes of Bearing Failure
| Causes | The failure rate in % |
| Dirt | 45.4 |
| Improper assembly | 12.8 |
| Misalignment | 12.6 |
| Insufficient Lubrication | 11.4 |
| Overloading | 8.1 |
| Corrosion | 3.7 |
| Improper Finish | 3.2 |
