Efficient identification of random fields coupling Bayesian inference and PGD reduced order model for damage localization

Abstract

One of the main challenges regarding our civil infrastructure is the efficient operation over their complete design lifetime while complying with standards and safety regulations. Thus, costs for maintenance or replacements must be optimized while still ensuring specified safety levels. This requires an accurate estimate of the current state as well as a prognosis for the remaining useful life. Currently, this is often done by regular manual or visual inspections within constant intervals. However, the critical sections are often not directly accessible or impossible to be instrumented at all. Model-based approaches can be used where a digital twin of the structure is set up. For these approaches, a key challenge is the calibration and validation of the numerical model based on uncertain measurement data. The aim of this contribution is to increase the efficiency of model updating by using the advantage of model reduction (Proper Generalized Decomposition, PGD) and applying the derived method for efficient model identification of a random stiffness field of a real bridge.

Bayesian inference for random field parameters with a goal-oriented quality control of the PGD forward model’s accuracy

“…The inference method of choice is the variational Bayesian approach after [3], allowing a very efficient calculation of the two convergence criteria. Although the proposed procedure makes use of these two methods [4], it is certainly not limited to them. The problem of selecting a sufficiently accurate reduced-order model is presented in the context of identifying a spatially-varying Young's modulus field which can account for variations in stiffness, e.g.…”

“…It is important to emphasize the ability of the PGD surrogate to speed-up the inference runs: for example, one identification run with the PGD reduced models M 4,8 PG D is more than 4000 times faster than the corresponding run with the full order finite element model. A complete inference with the PGD model is performed in a fraction of seconds (0.03 seconds).…”