Probability Distributions of Means of IA and IF for Gaussian Noise and Its Application to an Anomaly Detection

Abstract

The Hilbert–Huang transform (HHT) extracts the intrinsic oscillation modes of input data, and estimates instantaneous amplitude (IA) and frequency (IF) for each mode. The HHT is applied to detection of some anomaly structures of signals as well as to analysis of signals. However, only qualitative discussions have been conducted on the applications to the detections. To make more statistically-based arguments on the application of the HHT, we investigated the probability distribution of the means of IA and IF for white Gaussian noise and found that it fits the Pearson distribution rather than the normal distribution. We defined a feature value for an anomaly detection by using the probability density function estimated on the basis of the Pearson distribution. Our method does not require different models for different lengths of the segment over which the mean is calculated, and therefore it is useful especially for the case that the length cannot be fixed.