Real time parameter identification and solution reconstruction from experimental data using the Proper Generalized Decomposition

Abstract

Some industrial processes are modelled by parametric partial differential equations. Integrating computational modelling and data assimilation into the control process requires obtaining a solution of the numerical model at the characteristic frequency of the process (realtime). This paper introduces a computational strategy allowing to efficiently exploit measurements of those industrial processes, providing the solution of the model at the required frequency. This is particularly interesting in the framework of control algorithms that rely on a model involving a set of parameters. For instance, the curing process of a composite material is modelled as a thermo-mechanical problem whose corresponding parameters describe the thermal and mechanical 1 behaviours. In this context, the information available (measurements) is used to update the parameters of the model and to produce new values of the control variables (data assimilation). The methodology presented here is devised to ensure the possibility of having a response in real-time of the problem and therefore the capability of integrating it in the control scheme. The Proper Generalized Decomposition is used to describe the solution in the multi-parametric space. The realtime data assimilation requires a further simplification of the solution representation that better fits the data (reconstructed solution) and it provides an implicit parameter identification. Moreover, the analysis of the assimilated data sensibility with respect to the points where the measurements are taken suggests a criterion to locate of the sensors.

Parametric model for the simulation of the railway catenary system static equilibrium problem

“…When the just described separated representation constructor is used in nonsymmetric problems, the obtained solution contains more modes than those provided by the Singular Value Decomposition (SVD) (or its multidimensional counterpart, the High Order Singular Value Decomposition (HOSVD)) applied to the problem solution computed by using standard discretization techniques. Thus, the decomposition provided by the PGD constructor is not optimal [27]. This reveals that some modes do not make an important contribution to the solution reconstruction and are not necessary in the reduced basis.…”

Analysis of Uncertainty and Variability in Finite Element Computational Models for Biomedical Engineering: Characterization and Propagation

“…An upgrade of this technique is the proper generalized decomposition (Nadal et al, 2015), suitable to be used in any engineering and biomedical engineering problem. Another approach is the spectral representation method which similarly expands the random field as a sum of trigonometric functions with random phase angles and amplitudes (Eiermann et al, 2007; Stefanou, 2009).…”

POD-Based Constrained Sensor Placement and Field Reconstruction from Noisy Wind Measurements: A Perturbation Study

“…To avoid redundant measurements, the authors [25] suggested an approach without using the exclusion disk strategy. However, the approach therein only allows one sensor per mode.…”

“…We remark that there are many other ways to accommodate noise into models and predict the state space from reconstruction-for example, Kalman filtering [21], empirical interpolation method [22,23], and proper generalized decomposition [24,25]. The purpose of our paper is to understand the effect of noisy and bad measurements within the POD framework.…”