The local approach to change detection, diagnosis, and model validation: application to vibration mechanics∗

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 1/ √ 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.