The local approach to change detection, diagnosis, and model
validation: application to vibration mechanics
Albert Benveniste, Michèle Basseville, Maurice Goursat, and
Laurent Mével
In this paper we survey our results on model validation, change
detection, and diagnosis, based on the local approach. We see this
work as a counterpart of the central contribution by Lennart Ljung to a
systematic approach to system identification. We reuse concepts brought
by Lennart such as: model set, true system model, identification
method, and we enrich this set of concepts by considering also the
nominal model. The local approach consists in assuming that nominal and
true models differ by a factor of order one over the square root of N, where N is the sample length. This
allows deriving Gaussian approximations for the (generalized)
likelihood ratio statistics relating these two models. This allows
designing systematically criteria and test statistics for model
validation, change detection, and diagnosis. We report our experience
in using these techniques in the area of vibrations monitoring in
mechanical engineering, where they have proven very useful and
effective.