Abstract
Since the iron-making process is performed in complicated environments and controlled by operators, observation labeling is difficult and time-consuming. Therefore, unsupervised fault detection methods are a promising research topic. Recently, an unsupervised graph-based change point detection method has been introduced, and the graph of observations is constructed by the minimum spanning tree. In this paper, a novel fault detection method based on the graph for an iron-making process is proposed, and a weight calculation method for constructing the minimum spanning tree is introduced. The Euclidean distance and Mahalanobis distance are combined to calculate the weights in the minimum spanning tree, which contain important relations of variables. The distance calculation method is determined by the correlation coefficients of variables. Each testing observation is set as a change point candidate, and a change point candidate divides the observations into two groups. The number of a special type of edge in the minimum spanning tree is used as a fault detection statistic. That special edge connects two observations from two different groups. The minimum number of that type of edge corresponding to the change point candidate is a true change point. Finally, numerical simulation is used to test the power of the proposed method, and a real iron-making process including low stock, cooling, and slip faults is implemented to illustrate the effectiveness of fault detection in industrial processes.
Highlights
In recent decades, industrial processes have become increasingly complicated, and a large quantity of data has been collected
Since the covariance matrix of some observations without change points needs to be calculated for the Mahalanobis distance, the graph-based change point detection method introduced in the above section is used to obtain observations with the same distribution, defined by yi, i = 1, 2, . . . , 10
Step 7: Statistic calculation The number of the edges connecting two observations obtained from different groups is regarded as the fault detection statistic, and the groups are divided by a change point candidate
Summary
Industrial processes have become increasingly complicated, and a large quantity of data has been collected. Compared with the above unsupervised process monitoring methods in the industrial processes, the graph-based method can be used to handle various types of data, such as non-Gaussian data and nonlinear data, and accords to the characteristics of observations collected from iron-making processes. The goal of fault detection in iron-making processes is to find the abnormal events from the collected data matrix, which can be regarded as the change points in the observations. In this paper, the graph-based change point detection method is used for fault detection in the iron-making processes. To the best of our knowledge, the graph-based change point detection method has barely been applied for fault detection in the iron-making process. The graph-based change point detection method uses the Euclidean minimum spanning tree to build the graph.
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