Ordinal Decision Tree Based Fault Level Detection

With the development of artificial intelligence, especially machine learning and pattern recognition, intelligent techniques in detecting of mechanical failure become popular. In practice, we should know not only whether a device is failure or not but also the severity of the failure. Machine systems should reach a certain level before shutdown: It will cause unnecessary waste if shutdown is too early, and will cause a serious accident if too late.In the field of pattern recognition, fault level detection can be seen as ordinal classification problem: the degree of failure can be represented by a group of integer n (n = 1, 2, 3, ...), means 'slight fault', 'medium failure', 'serious failure 'and so on. Compared with the classical classification, there exist ordinal relationships in decision class of ordinal classification (i.e. fault level). Due to this ordinal relationship, the design principle of classifier and evaluation criteria has to be reconsidered.Moreover, we consider a special task of fault level detection, in which when the value of a fault value increases(or decreases), fault level increases too. So there is a sort of monotonic constraint between fault features and fault levels. This type of fault features are named monotonic features, which can provide simple but useful information for detecting the level of mechanical failure.In this paper, we design two ordinal learning algorithms to deal with fault level detection, and the details are described as follows:Firstly, we give a systematic introduction to the field of ordinal classification. In literature, there are mainly 5 methods to solve this problem, that is ordinal classification, monotone classification, multiple criteria decision analyze, multi-objective optimize, and ordinal regression. We give a short introduction to each of these methods, and give some comments and cooperation between these methods.Secondly, we introduce monotonicity constraint between features and classes in ordinal classification. In literature, all learning algorithms can derivate monotonic models only if training samples are monotonic, which seldom happen in practice due to the presence of noise. To deal with this problem, we introduce a new constraint to describe the monotonicity between features and classes, namely, stochastic monotonicity constraint. We point out that features and classes are probabilistic monotone. Based on this idea, we introduce rank entropy model, which not only inherits the robustness of classical Shannon information entropy, but also reflects the probabilistic monotonicity between features and classes. Then we apply rank entropy to building decision tree, to deal with monotone classification and also give the theoretical proof of its properties.Thirdly, we recognize that not all features are monotonic. Some features have no such a monotonicity constraint. To solve this problem, Stochastic Hybrid Ordinal Tree (SHOT) is proposed. We conduct numerous experiment to test the performance of the two proposed methods on both artificial data and real-world data. One the one hand, compared with other classical classification algorithms, such as SVM, neural network, the proposed methods can be easy to understand by human beings, which helps us better understand the orderly classification of nature as well as the innate character of fault level detection. One the other hand, our methods are very competent among other ordinal and monotone methods. They are more robust, and produce low generalization error.Finally, we conduct the proposed methods on the practical application of the degree of gear crack fault monitoring experiments. The results show that our methods are very effective and efficient.