Digital twinning of self-sensing structures using the statistical finite element method

Abstract

The monitoring of infrastructure assets using sensor networks is becoming increasingly prevalent. A digital twin in the form of a finite element model, as used in design and construction, can help in making sense of the copious amount of collected sensor data. This study demonstrates the application of the statistical finite element method (statFEM), which provides a consistent and principled means for synthesising data and physics-based models, in developing a digital twin of an instrumented railway bridge. The considered structure is a steel skewed half-through bridge of 27.34 m length located along the West Coast Mainline near Staffordshire in the UK. Using strain data captured from fibre Bragg grating (FBG) sensors at 108 locations along the bridge superstructure, statFEM can predict the 'true' system response while taking into account the uncertainties in sensor readings, applied loading and finite element model misspecification errors. Longitudinal strain distributions along the two main I-beams are both measured and modelled during the passage of a passenger train. The digital twin, because of its physics-based component, is able to generate reasonable strain distribution predictions at locations where no measurement data is available, including at several points along the main I-beams and on structural elements on which sensors are not even installed. The implications for long-term structural health monitoring and assessment include optimization of sensor placement, and performing more reliable what-if analyses at locations and under loading scenarios for which no measurement data is available.

Error analysis for a statistical finite element method

“…Consequently, the response of the actual engineering product and the inevitably misspecified mathematical model often bear little resemblance to each other, resulting in inefficient designs and overtly cautious operational decisions. Fortunately, more and more engineering products are equipped with sensor networks providing operational measurement data (e.g., Febrianto et al, 2021). The recently proposed statistical finite element method (statFEM) allows us to infer the true system response by synthesising limited measurement data with the misspecified the finite element model (Girolami et al, 2021).…”

Statistical Finite Elements via Langevin Dynamics

“…Examples [11,12,15] have demonstrated the usefulness of this approach, with the computed posterior distribution providing a statistically coherent synthesis of physics and data, with an interpretable UQ. Yet to provide UQ, uncertainty associated with θ must be taken into account in order to compute the statFEM prior and posterior distributions.…”