Asymptotic analysis of subspace-based data-driven residual for fault detection with uncertain reference

Eva Viefhues (1) , Michael Dohler (2) , Falk Hille (1) , Laurent Mevel (2)

1 BAM Federal Institute for Materials Research and Testing
2 I4S - Statistical Inference for Structural Health Monitoring

The local asymptotic approach is promising for vibration-based fault diagnosis when associated to a subspace-based residual function and efficient hypothesis testing tools. It has the ability of detecting small changes in some chosen system parameters. In the residual function, the left null space of the observability matrix associated to a reference model is confronted to the Hankel matrix of output covariances estimated from test data. When this left null space is not perfectly known from a model, it should be replaced by an estimate from data to avoid model errors in the residual computation. In this paper, the asymptotic distribution of the resulting data-driven residual is analyzed and its covariance is estimated, which includes also the covariance related to the reference null space estimate. The importance of including the covariance of the reference null space estimate is shown in a numerical study.

Mots clés: FAULT DETECTION; UNCERTAINTY IN REFERENCE; RESIDUAL EVALUATION; STATISTICAL TESTS; VIBRATION MEASUREMENT

Mots clés: VIBRATION; ANALYSE STATISTIQUE; MESURE

Domaines: Dynamique, vibrations; Applications [stat.AP]

Eva Viefhues, Michael Dohler, Falk Hille, Laurent Mevel. Asymptotic analysis of subspace-based data-driven residual for fault detection with uncertain reference. SAFEPROCESS 2018, 10th IFAC Symposium on Fault Detection, Diagnosis and Safety of Technical Processes, Aug 2018, Varsovie, Poland. 6 p, ⟨10.1016/j.ifacol.2018.09.610⟩. ⟨hal-01886626⟩