On a class of quadratic tests for detection of abrupt changes in signals and systems

We address the problem of detecting changes (faults) in systems and signals. We establish new results on a class of quadratic change detection algorithms which are based on the χ² statistic (χ²-CUSUM, χ²-GLR and χ²-FSS algorithms). We compare optimal sequential and nonsequential (fixed-size sample) strategies in the problem of abrupt change detection in multivariate Gaussian signals. However, the optimal sequential algorithms lead to a burdensome number of arithmetical operations. In order to reduce the computational burden we examine the recursive versions of the χ²-CUSUM and χ²-GLR algorithms. It is shown that these recursive algorithms have statistical performances which are similar to the original algorithms. We also propose a very simple heuristic solution to the case of unknown magnitude of change. This solution is a competitor for the window-limited GLR algorithm