Real‐time updating of structural mechanics models using Kalman filtering, modified constitutive relation error, and proper generalized decomposition

Abstract

Summary The paper aims at proposing a new strategy for real‐time identification or updating of structural mechanics models defined as dynamical systems. The main idea is to introduce the modified constitutive relation error concept, which is a practical tool that enables to efficiently solve identification problems with highly corrupted data, into the Kalman filtering, which is a classical framework for data assimilation. Furthermore, a PGD‐based model reduction method is performed in order to optimize capabilities of the online updating strategy. Performances of the proposed approach, in terms of robustness gain and computational cost reduction, are illustrated on several unsteady thermal applications. Copyright © 2015 John Wiley & Sons, Ltd.

Fast model updating coupling Bayesian inference and PGD model reduction

“…Since [19], this method was used in many fields: model verification and validation [18], virtual charts for the engineering [20] [21] etc. PGD is also used for identification problems in a deterministic framework [25] [10] [3] and the great possible number of parameters types to use in those models [8] seems to be well suited for Bayesian inference. A first PGD-Bayesian inference approach is given in [6] where a PGD model is used in a Monte Carlo Markov Chain framework.…”

Synergies between the constitutive relation error concept and PGD model reduction for simplified V&V procedures

“…In this section, we implement a PGD meta-model to find, in an offline phase, parameterized solutions u, λ to (41). Defining σ r = r 1−r σ ∈ r (single parameter gathering scaling and weighting effects in mCRE) and assuming that P = ⊗ P j=1 P j , these are searched of the form:…”

“…In other cases such as data assimilation on time-dependent problems, they can be considered as extra-parameters in the PGD decomposition as performed in [40,41].…”

“…This involves about 40 sub-iterations, each of them corresponding to the solution of a linear system with the size of the problem in space [resulting from (41)]. Considering 10 iterations in the mCRE identification process thus leads to the solution of about 400 linear systems of the space problem size; • Considering PGD-mCRE, the offline computational cost is due to the use of a greedy algorithm to compute 15 PGD modes.…”

“…On the other hand, in the context of model validation, PGD was used for model updating within classical procedures with least square minimization [39]. It was also recently used in particular applications involving robust model updating with the CRE concept [40,41]. Here, the goal is to give a general framework on the effective use of PGD for model updating with CRE.…”