Data-based Reduced Order Modeling (ROM): sensitivity analysis and approximation with FMOP

ROMs are of great importance for system simulation and also become a key technology for digital twins. In order to optimize the maintenance and operation of a system, a detailed product simulation must be linked to sensor data for an accurate prediction of the characteristic values (e.g. the service life of turbine blades). The requirements for the response time of digital twins can only be met if the detailed simulation models are simplified. The classical "physics-based" approach of ROMs uses a matrix condensation whose formula still contains the physical influences of the input variation on the response variables. However, this type of reduction is often only suitable for linear systems. A data-based ROM is the better alternative for simulating nonlinear systems. The method uses function models for approximating the response surfaces, taking into account the influence of input variations on the response variation depending on the given parameter set. For the field data of the input or response variables, SoS uses the Field Metamodel of Optimal Prognosis (FMOP) to approximate signals, FEM solutions or geometric deviations.

SoS offers the possibility to visualize FMOPs interactively via slider. The evaluation of an FMOP can be binary coupled with a DLL, so that the metamodels can be evaluated directly in C++, Python, Matlab or as a background process on a website. Using SoS nodes, the evaluation of an FMOP can also be carried out in an optimization in optiSLang. The field prediction measure F-CoP provides information at which points of the FEM network the FMOP has a high or low prediction quality.

The quality of the FMOP can also be used to identify global sensitivity measures for the input parameters. Therefore the sensitivity of the input parameters can be assigned to the different positions on the FEM mesh.

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