Robust online updating of a digital twin with imprecise probability

Abstract

We present a method for the robust online updating of the parameters of a digital twin for engineering dynamics. The method is robust because it makes neither prior nor likelihood assumptions while rigorously quantifying the inferential uncertainty, which is useful in the context of scarce data. With the proposed updating strategy, the digital twin can update effectively instantaneously when presented with additional data. An algorithm for nonparametric inference with consonant random sets recently developed by the authors is applied. The method constructs a consonant joint structure of the updating parameters. This structure is composed of a sequence of nested sets, each of which is assigned a belief measure, i.e., a lower probability, a nominal level of confidence. This joint structure represents an outer approximation of the credal set where the target joint probability distribution resides. Thus, it can be regarded as a rigorous inferential model. The obtained joint structure has a possibilistic interpretation so that it can be seen as a joint fuzzy set and can be converted to a joint probability box using an established transformation. The method is arguably more efficient than traditional alternative Bayesian updating methods because it is intrinsically non-sequential thus parallelizable. The inference method can also be extended, with nearly no additional computational cost, to the case of interval measurement uncertainty. Because of its efficiency, the method can update the parameters of a digital twin model practically in real time, provided that (1) the data-generating mechanism is stationary, (2) the physical model has not changed, e.g. due to damage, and (3) input–output simulation data within the range of interest is available. We present an application to online updating of a digital twin of an aluminium three-storey structure subject to impact-hammer excitation.