FRF-based non-simultaneous real-time hybrid testing of multiple subsystems with moderate nonlinearities

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The existing cyber physical testing methods have been extended in a recent publication by non-simultaneous real-time hybrid testing, see Witteveen et al. [1]. There, an overall system is decomposed into two subsystems, one experimental and one numerical. The subsystems are loaded by certain inputs and simulated or tested separately in loops until compatibility conditions are fulfilled. If not, an input update based on the error of the kinematic compatibility in the frequency domain is computed for the next loop run. Each single test run is independent from the numerical model and therefore both is possible: Slow speed and real-time testing. In this work, the generalization to a systematic approach for an arbitrary number of subsystems is presented. The subsystems can be of numerical or experimental nature. While in the last publication the subsystems had to be tested one after the other within a loop run, they can be processed totally independently from each other in this generalized method. Further, both compatibility conditions (kinematic and cutting force) are considered for the update of the input signals. Finally, approximate models of the tested components can be considered in the numerical subsystems to improve convergence. The update for the inputs is again computed in the frequency domain based on FRFs of the isolated subsystems. The theory section is followed by two examples. The first one is of academic nature, and it is demonstrated that in case of convergence, all subsystems behave as they were part of one assembled overall system. The second one is a full vehicle hybrid testing where two shock absorbers are considered as real hardware while the vehicle is a multibody simulation model on a virtual four-poster test rig.

Original languageEnglish
Article number109944
JournalMechanical Systems and Signal Processing
Issue number188
Early online date2022
Publication statusPublished - 1 Apr 2023


  • Coupled simulation
  • Cyberphysical systems
  • Domain decomposition
  • Hardware in the loop (HIL)
  • Hybrid simulation
  • Hybrid substructuring


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