A Fault Diagnosis Method Based on EEMD and Statistical Distance Analysis

Serious vibration or wear with large friction usually appear when faults occur, which leads to more serious faults such as the destruction of the oil film, bringing great damages to both the society and economic sector. Therefore, the accurate diagnosis of a fault in the early stage is important for the safety operation of machinery. To effectively extract the fault features for diagnosis, EMD-based methods are widely used. However, these methods spend lots of efforts diagnosing faults and require plenty of professional knowledge of diagnosis. Although many intelligent classifiers can be used to automatically diagnose faults such as wear, a broken tooth and imbalance, the combing EMD-based method, the scarcity of samplings with labels hinder the application of these methods to engineering. It is because the model of the intelligent classifier must be constructed based on sufficient samplings with a label. To solve this problem, we propose a novel fault diagnosis method, which is performed based on the EEMD and statistical distance analysis. In this method, the EEMD is used to decompose one original signal into several IMFs and then the probability density distribution of each IMF is calculated. To diagnose the fault of the machinery, the Euclidean distance between the signal acquired under an unknown fault with the other referenced signals acquired previously under various fault types is calculated. At last, the fault of the signal is the same with the referenced signal when the distance is the smallest. To verify the effectiveness of our proposed method, a dataset of bearings with different faults, and a dataset of 2009 Prognostics and Health Management (PHM) data challenge, including gear, bearing and shaft faults are used. The result shows that the proposed method can not only automatically diagnose faults effectively, but also fewer samplings with a label are used compared with the intelligent methods.

Statistical Distance-Based Travel-Time Reliability Measurement for Freeway Bottleneck Identification and Ranking

Freeway bottleneck identification is an essential component in the process of deploying mitigation strategies to reduce congestion at freeway bottlenecks. Most previous studies on bottleneck identification focus on recurrent bottlenecks, and limited work has been conducted to identify the locations of non-recurrent bottlenecks. Therefore, in this study, we propose a new travel time reliability (TTR) measurement and develop a freeway bottleneck identification method based on this measurement, which can identify with high probability not only recurrent bottlenecks but also the locations of non-recurrent bottlenecks. The TTR measurement is developed based on statistical distance between travel time distributions. Three statistical distance measurements, Jensen–Shannon divergence, Wasserstein distance, and Hellinger distance, are applied in the TTR measurement. The bottleneck identification method is evaluated in a case study on I-15 freeway corridor in Salt Lake City, Utah. The three statistical distance measurements show good consistency in ranking locations by the impacts of recurrent and non-recurrent congestion, especially for extreme cases with very high or low variation between travel time distributions. The recurrent bottlenecks identified in this study show their clustering characteristics, which is similar to the generating and dismissing process of recurrent congestion. The locations with high probability of non-recurrent bottlenecks scatter both spatially and temporally, which agrees with the random characteristic of non-recurrent congestion.

Modified Energy Statistic for Unsupervised Anomaly Detection

For prognostics in industrial applications, the degree of anomaly of a test point from a baseline cluster is estimated using a statistical distance metric. Among different statistical distance metrics, energy distance is an interesting concept based on Newton’s Law of Gravitation, promising simpler computation than classical distance metrics. In this paper, we review the state of the art formulations of energy distance and point out several reasons why they are not directly applicable to the anomaly-detection problem. Thereby, we propose a new energy-based metric called the P-statistic which addresses these issues, is applicable to anomaly detection and retains the computational simplicity of the energy distance. We also demonstrate its effectiveness on a real-life data-set.

Information Mandala: Statistical Distance Matrix with Clustering

<p>In machine learning, observation features are measured in a metric space to obtain their distance function for optimization. Given similar features that are statistically sufficient as a population, a statistical distance between two probability distributions can be calculated for more precise learning. Provided the observed features are multi-valued, the statistical distance function is still efficient. However, due to its scalar output, it cannot be applied to represent detailed distances between feature elements. To resolve this problem, this paper extends the traditional statistical distance to a matrix form, called a statistical distance matrix. The proposed approach performs well in object recognition tasks and clearly and intuitively represents the dissimilarities between cat and dog images in the CIFAR dataset, even when directly calculated using the image pixels. By using the hierarchical clustering of the statistical distance matrix, the image pixels can be separated into several clusters that are geometrically arranged around a center like a Mandala pattern. The statistical distance matrix with clustering is called the Information Mandala.</p><p><br></p><p>(This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible)<br></p>

Information Mandala: Statistical Distance Matrix with Clustering

<p>In machine learning, observation features are measured in a metric space to obtain their distance function for optimization. Given similar features that are statistically sufficient as a population, a statistical distance between two probability distributions can be calculated for more precise learning. Provided the observed features are multi-valued, the statistical distance function is still efficient. However, due to its scalar output, it cannot be applied to represent detailed distances between feature elements. To resolve this problem, this paper extends the traditional statistical distance to a matrix form, called a statistical distance matrix. The proposed approach performs well in object recognition tasks and clearly and intuitively represents the dissimilarities between cat and dog images in the CIFAR dataset, even when directly calculated using the image pixels. By using the hierarchical clustering of the statistical distance matrix, the image pixels can be separated into several clusters that are geometrically arranged around a center like a Mandala pattern. The statistical distance matrix with clustering is called the Information Mandala.</p><p><br></p><p>(This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible)<br></p>

Anonymous Vs. Attributed: Cluster Analysis of Tolstovskiĭ Sbornik Texts and Its Interpretation in Terms of Cultural Heritage

In the article, the quantitative analysis revealed lexical and semantic dominants and markers that distinguish the medieval anthology texts from each other. To verify whether three anonymous homilies in the thirteenth-century Tolstovskiĭ Sbornik might be attributed to Cyril of Turov, the authors examined the statistical distance between anonymous and already attributed texts. Using the clustering method based on the ranks of the most frequent tokens and the corresponding ranks of other texts, they constructed dendrograms that showed the text grouping. This technique allowed demonstrating the statistical proximity of six Cyril of Turov’s texts, their contrast to seven Cyril of Jerusalem’s texts, and the formation of the third cluster from texts of other authors. Cluster analysis made it possible to identify in Cyril of Turov’s homilies several crucial thematic keys, as well as to establish such a feature of his preaching discourse as the widespread use of role deixis. The analysis confirmed the sharp difference between the anonymous Parable of Wisdom and Cyril of Turov’s homilies. Separate convergences of two anonymous sermons with Cyril of Turov’s homilies were discovered. However, the level of convergence in this case, as analysis has shown, contrasts sharply with the level of convergence among Cyril of Turov’s homilies. It suggests that the causes of individual convergences are not associated with one person’s authorship