  This paper proposes a novel fast online methodology for outlier detection
called the exception maximization outlier detection method(EMODM), which
employs probabilistic models and statistical algorithms to detect abnormal
patterns from the outputs of complex systems. The EMODM is based on a two-state
Gaussian mixture model and demonstrates strong performance in probability
anomaly detection working on real-time raw data rather than using special prior
distribution information. We confirm this using the synthetic data from two
numerical cases. For the real-world data, we have detected the short circuit
pattern of the circuit system using EMODM by the current and voltage output of
a three-phase inverter. The EMODM also found an abnormal period due to COVID-19
in the insured unemployment data of 53 regions in the United States from 2000
to 2024. The application of EMODM to these two real-life datasets demonstrated
the effectiveness and accuracy of our algorithm.
