CHAPTER 5 FAULT PATTERN EXTRACTION
5.4 D ISCUSSION
5.4.3 Performance improvement plan through conventional machine learning models
Since this study follows a quite stick crisp set theory, less considering the uncertainty, or generalization or estimation to the not discovered parts, there are several rooms for applying the conventional machine learning algorithms to improve the either computational costs or inferring the unknowns from the already known information, as follows:
๏ฌ Cut-point determination using SVM: Originally, we determine the cut-points using the estimated optimal PDFs of the given sensor data, in forms of unsupervised problem. As shown in Figure 5.21-(a) the original cut-point determination is one of the Boolean reasoning methods without class information. However, we have a class information on normal, symptom and fault states of the system, and thus we can employ the SVM so that the measurements form the three differential states being to as many different bins as possible. In addition, the research conducts the cut-point determination for each sensor signal individually, but it is possible to partition the multivariate sensor signals at the
Figure 5.21 Cut-point determination: (a) the original method explained in Section 5.2, and (b) the proposed SVM-based method
same time by applying SVM.
For example, one-against-SVM will partition the cut-points of two sensor signals, as illustrated in Figure 5.21-(b). Due to the class information, they will split the bins so that the measurements from different classes belong to the different bins as much as possible. This concept consequently helps to extract significant pattern in the fault pattern extraction.
๏ฌ Similarity measure for the event codes by ANN or clustering algorithm: The research uses arbitrary contiguous integers, such as coded value of the representative the quantity of sensor data in each bin, in order to adopt a Euclidean distance-based similarity measure between event codes. However, it is not always guaranteed that Euclidean distance is appropriate to measure the similarities of event codes. For example, suppose that b is 3, linearT = true, and the corresponding cut-points are computed as ๐ถ๐๐ = [๐๐๐1 ๐๐๐2]๐, then a set of nine labels for the ith sensor ๐ฟ๐ is made. Here, ๐๐7 indicate the relatively large magnitude with negative slope, then we cannot easy answer which one is more similar to this ๐๐7, between ๐๐4 (i.e., a negative slope but medium magnitude), ๐๐6 (i.e., medium magnitude with positive slope, but the most close code number). In addition, it is also hard to compare the event codes which have different number of columns.
Therefore, ANN can be adopted as a mapping function to calculate a distance between two event codes by considering DSVs in event codes, from the perspective of multi-feature and multi-sensor fusion. If we train the ANN with DSVs and arbitrary assigned event codes, then it gives an approximated event code number of the new event codes, and we can consider to be the similar number be similar signalsโ behavior. In the case of clustering algorithm, they will make several clusters using the label information, not the arbitrary code number. If an unknown event code is found, then the clustering algorithms will tell you which cluster it belongs to.
๏ฌ Online monitoring by NB classifier: When we monitoring the sensor signal in real time, we search an exactly identical event code to the extracted pattern. However, we can consider uncertainty to the extracted pattern by adopting NB classifier. After obtaining event codes, NB classifier can be trained using the fault pattern and symptom pattern with their severities, and DSVs which are found in the normal states, and the posterior probability of a fault state and a normal state will be calculated. When the posterior
probability exceeds the predefined threshold, the it is considered to be fault detected or predicted. We can use posterior probability of either normal states, fault state, or ratio of them. As shown in Figure 5.22, we conducted this concept to detect defective weldment (S. Baek et al., 2015b), and automotive gasoline engine knocking (S. Baek & D.-Y. Kim, 2013), and it showed reasonable classification/detection results.
For detecting weld defects, DSVs which have 12 columns were only analyzed, whereas individual DSVs were only applied. As illustrated in Figure 5.23, we transformed the given monitoring sensor signals into a matrix of DSVs, assigned arbitrary number for each DSV, and then train NB classifier. The performance was
Figure 5.22 The multivariate discretization and the Naive Bayes classifier for fault detection
Figure 5.23 An example of multivariate discretization using laser welding monitoring sensor signals:
(a) three original sensor signals, and (b) the corrsponding matrix of DSVs
compared with a set of three univariate SPC models and a set of PCA-based Hotellingโs T2 and Q statistics with regard of sensitivity and specificity. Sensitivity (also called the true positive rate or the recall) measures the proportion of positives that are correctly identified, whereas specificity (also called the true negative rate) measures the proportion of negatives that are correctly identified. As a result summarized in Table 5.15, fault pattern extraction via multivariate discretization and NB classifier showed better performance in detecting defects and not providing any false alarm.
In this case, we can use DSVs from the normal states by differentiating them whether it is found in the normal states only or not. Then, the DSVs which are found any systemโs states can be considered as less informative since it has a large uncertainty than others, when training the NB classifier. It is also possible to adopt other supervised machine learning algorithms for systemโs state classification.
Table 5.15 Comparison of the pattern extraction performance in weld defect detection among univariate SPC charts, multivariate statistical projection, and the proposed fault pattern extraction
Detection method Sensitivity* Specificity**
Three univariate SPC models 0.60 0.84
PCA-based Hotellingโs T2 and Q statistics 1.00 0.13 Multivariate discretization and NB classifier 1.00 0.98
* Sensitivity (also called the true positive rate, the recall) measures the proportion of positives that are correctly identified
** Specificity (also called the true negative rate) measures the proportion of negatives that are correctly identified