Robust online updating of a digital twin with imprecise probability

de Angelis, Marco and Gray, Ander and Ferson, Scott and Patelli, Edoardo (2023) Robust online updating of a digital twin with imprecise probability. Mechanical Systems and Signal Processing, 186. 109877. ISSN 0888-3270 (

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We present a method for the robust online updating of the parameters of a digital twin for engineering dynamics. The method is robust because 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 and nearly 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. Such structure is composed of a sequence of nested sets, each of which is assigned a belief measure, i.e. a lower probability, with the desired level of confidence. This joint structure represents an outer approximation of the credal set where the target joint probability distribution resides, thus can be regarded as a rigorous inferential model. The obtained joint structure can be given a possibilistic interpretation thus seen as a joint fuzzy set, and can be converted to a joint probability box using established transformation. The method is arguably more efficient than traditional competitive Bayesian updating methods because 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 the online updating of a digital twin of an aluminium three-storey structure subject to impact-hammer excitation.


de Angelis, Marco ORCID logoORCID:, Gray, Ander, Ferson, Scott and Patelli, Edoardo ORCID logoORCID:;