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Asymptotic Random Distortion Testing and Application to Change-in-Mean Detection

We introduce an extension of the Random Distortion Testing (RDT) framework which allows its use when the noise variance is estimated. This asymptotic extension, named AsympRDT, shows that we asymptotically retain the level of the RDT test as the estimate of the noise variance converges to its real value. The validity of this approach is justified through both theoretical and simulation results. We make use of AsympRDT to develop a change-in-mean detection method for time series. It features three parameters: the size of the processed blocks, the maximum desired false alarm rate and a tolerance. We then show a use-case for this method in cybersecurity for Industrial Control Systems (ICS) as part of an anomaly and cyberattack detection system, where it can be used for segmenting signals and learning normal behaviors.