Certified Model Order Reduction

Certified Model Order Reduction for Coupled Mechanical Systems

Principal investigators

Dr. Ashish Bhatt





This project aims at certified model order reduction of coupled mechanical systems. Coupled mechanical systems are generally high dimensional nonlinear models and therefore their repeated numerical simulation with varying parameters is prohibitively expansive. One therefore employs model order reduction (MOR) techniques to reduce the order of the mechanical system in order to reduce time complexity of numerical simulations. The process of model order reduction inevitably introduces additional simulation error and estimating this error is important in many applications.
For the simulation of mechanical subsystems in a multiphysics environment very frequently elastic multibody systems (EMBS), with their inherent modular fashion, are an appropriate modeling choice. EMBS represent a collection of coupled rigid and elastic bodies connected to the surrounding and one another. Mathematically they are a high dimensional nonlinear differential-algebraic system of equations. To simulate these high dimensional systems, it is necessary to reduce degrees of freedom (DOFs) of the systems.
The essence of MOR is the approximation of a large scale dynamical system (many DOFs) with a system of much smaller dimension while attempting to preserve the most dominant features, such as input-output behavior, passivity, stability, etc., of the system. The generation of the reduced model is typically only performed only once in a computationally expansive offline phase. Then the reduced model can be simulated rapidly and possibly repeatedly during the so-called online phase.

The MOR process results in undesirable but unavoidable approximation errors. For the safe and successful application and certification of reduced order models, knowledge regarding the error introduced by the model reduction process is of major importance. Therefore it is very important to estimate the error in the simulation.

This project aims to pursue the following objectives:

Coupling of subsystems and port reduction
Error estimation in model order reduction of EMBS
Efficient implementation of large scale dynamical systems and integration in third-party software.

Funding Source

German Research Foundation(DFG)

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