Sas Institute Inc.

Zohreh Asgharzadeh Talebi

Kai Shen

Carol Wagih Sadek

Kyungduck Cha

Steven Guanxing Xu

Sudipta Kolay

Chengpeng Zeng

Functions representing sequences of values of a time-series dataset measured within a particular time period are accessed. For a current time window of the time period, a first discretized covariance function is computed that represents a relationship between each value measured within the current time window. Eigenanalysis of the first covariance function is performed to estimate first eigenfunctions. The current time window is incremented to obtain a subsequent time window that overlaps a majority of the current time window at a shared window region. A second discretized covariance function is computed for the subsequent time window and eigenanalysis is performed to estimate second normalized eigenfunctions. An angle change is computed between a portion of the first normalized eigenfunctions and a corresponding portion of the second normalized eigenfunctions located within the shared window region. Based on the angle change, an anomaly detection output is generated.

Real-time anomaly detection and mitigation for streaming functional data

A computing device identifies an anomaly among a plurality of observation vectors. An observation vector is projected using a predefined orthogonal complement matrix. The predefined orthogonal complement matrix is determined from a decomposition of a low-rank matrix. The low-rank matrix is computed using a robust principal component analysis algorithm. The projected observation vector is multiplied by a predefined demixing matrix to define a demixed observation vector. The predefined demixing matrix is computed using an independent component analysis algorithm and the predefined orthogonal complement matrix. A detection statistic value is computed from the defined, demixed observation vector. When the computed detection statistic value is greater than or equal to a predefined anomaly threshold value, an indicator is output that the observation vector is an anomaly.

Anomaly detection using RPCA and ICA

Physical-device anomalies and degradation can be mitigated by implementing some aspects described herein. For example, a system can determine a first data window and a second data window by applying a window function to streaming data. The system can determine a first principal eigenvector of the first data window and a first principal eigenvector of the second data window. The system can determine an angle change between the first principal eigenvectors of the two data windows. The system can then detect an anomaly based on determining that the angle change exceeds a predefined angle-change threshold. Additionally or alternatively, the system may compare the first principal eigenvector for the second data window to a baseline value to determine an absolute angle associated with the second data window. The system can then detect a degradation based on determining that the absolute angle exceeds a predefined absolute-angle threshold.

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Zohreh Asgharzadeh Talebi