A non-parametric statistical technique for changepoint detection in cyber-physical systems

Cyber-physical systems generate multidimensional time series describing the state of the system. When the state of the system changes, it is necessary to detect the transition point in the time series. The article describes a new nonparametric method for detecting the transition point in multidimensional time series generated by components of cyber-system components, using the principal component analysis (PCA) as a dimensionality reduction method, and this dimensionality reduction is accompanied by the application of Petunin statistics to one-dimensional data sets. Numerical and quasi-real experiments demonstrate the high accuracy and stability of the proposed algorithm over a wide range of distributions and hypothetical examples of cyber-physical systems. The accuracy is measured by the number of steps after the transition point when it was detected. There is also a comparison with the already known methods — the Wilcoxon test and the KolmogorovSmirnov consistency test. Accuracy up to 20 steps from the transition point was achieved, and in most cases even less — no more than 10 steps. This method provides a clear and human-understandable interpretation of algorithms and their results.