Project Details
Projekt
Certified Model Order Reduction for Coupled Mechanical Systems
Subject Area
Mechanics
Term
from 2016 to 2024
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 314733389
In the first phase of the project, efficient model reduction techniques and error estimators have been developed and implemented for elastic multi-body systems.In particular, a first version of a software package, CCMOR, containing the reduction and error estimation routines was set up. Furthermore, the project leaders have organized within the scope of the present project a workshop "Model Reduction of Coupled Systems MORCOS 2018" in the series of the renowned IUTAM symposia; a corresponding conference proceedings volume will be published in August 2019. In the second phase of this project requested with the current proposal, we want to extend certified model reduction to coupled multiphysics systems and for the approximation of of output variables, e.g. indicators for the system status.This is an essential step towards the reliable real-time simulation of complex technical systems. Real-time capable simulation models will enable to develop control concepts, system optimization, or "digital twins" of systems.Based on the experience gained in the first project phase, we will put an essential focus on structure preservation in all steps of modeling, integration, reduction, basis generation, and error estimation in order to maintain conservative properties and thus guarantee implicitly improved accuracy and stability.To this end, it is necessary to address the following central sub-problems:1. Identification and establishment of suitable system formulations (geometry) for the multiphysics systems: These should reflect conservation properties such as energy conservation through (Port) Hamiltonian system structure.2. Development of efficient structure-preserving integrators, reduction, and basis generation methods for these structured systems: Each of these steps must be carried out individually and adapted to the system structure.3. Exploit the structure preservation for improved error estimation of the system state and output quantities: Especially ideal effectivity by minimal overestimation of the error and fast calculation of stability constants are crucial requirements. Newer approaches of hierarchical estimators and the "auxiliary linear problem" (ALP) based error estimators developed by us are transferred to structure-preserving model reduction.4. Efficient implementation of all algorithms: The new error estimators and reduction techniques have to be implemented and incorporated in multi-body simulators. For this purpose, the joint CCMOR software package will be extended by the corresponding functionalities.The approaches will be validated on two exemplary multiphysics models. First, a model of the human inner ear will be considered which is based on a coupling of elasticity and acoustics. Further, a thermomechanical system will be addressed which represents the brake of a vehicle. The thermal properties influence the braking process with regard to noise and braking performance.
DFG Programme
Research Grants
