Probabilistic bounds for model invalidation assessment

This paper is concerned with a mixed deterministic/probabilistic model invalidation problem, which amounts to determining the probability for a given model to reproduce some given experimental data. We consider an additive uncertain model, in which the modelling uncertainty is characterized in time domain by the l₁ induced system norm. The data available for invalidation are input-output time series and are assumed to have been corrupted by a random noise with Gaussian distribution. For a given uncertainty norm bound, our objective is to compute the probability for no uncertainty to exist that may satisfy the prescribed bound and match the input-output measurements. While the exact computation of this probability may pose a formidable task, we derive its upper and lower bounds.