https://hal-utt.archives-ouvertes.fr/hal-02353877Nikiforov, IgorIgorNikiforovLM2S - Laboratoire Modélisation et Sûreté des Systèmes - ICD - Institut Charles Delaunay - UTT - Université de Technologie de Troyes - CNRS - Centre National de la Recherche ScientifiqueOn a class of quadratic tests for detection of abrupt changes in signals and systemsHAL CCSD1998[INFO.INFO-SY] Computer Science [cs]/Systems and Control [cs.SY][MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]VU VAN, Jean-Baptiste2019-11-07 14:52:372023-03-24 14:53:132019-11-07 14:52:37enConference papers10.1109/ACC.1998.7035081We 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 /spl chi//sup 2/ statistic (/spl chi//sup 2/-CUSUM, /spl chi//sup 2/-GLR and /spl chi//sup 2/-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 /spl chi//sup 2/-CUSUM and /spl chi//sup 2/-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.