This paper compares Krylov-subspace-based model order reduction (KSM) and the modal truncation method (MTM) of projection-based model order reduction in terms of their numerical accuracy and efficiency for frequency response analysis. The numerical results were compared to determine the superior method in terms of accuracy and efficiency. This paper reveals whether a reduced order can be determined automatically. It also discusses the convergence behavior of reduced models in cases of damping.
The evaluation standards for the accuracy are the frequency responses in the reduced order models of KSM and MTM, their frequency-dependent relative errors, and their reduced-order-dependent relative errors. The evaluation standards for the efficiency are the calculation time for the projection matrix and the frequency response analysis. A shaking table, sphere tank, and car suspension were considered as numerical examples.
As for the relative errors of the frequency response analysis, it was verified that they decreased with the increase in the reduced order. Because of the moment matching property of KSM, it was verified that the relative errors in the frequency response analysis decreased with the increase in the reduced order. Such decrease was more significant than the decrease in MTM. Therefore, it was verified that KSM is more accurate than MTM. The analysis of the convergence behavior of the relative errors showed that KSM’s relative errors converged in the lower reduced order, unlike those of MTM. Moreover, MTM did not show the same convergence behavior as KSM. In terms of efficiency, it was verified that both methods are very efficient. However, KSM’s computation time was relatively faster than that of MTM.
In conclusion, it was verified that KSM is a better projection-based model order reduction method than MTM in terms of accuracy and efficiency for frequency response analysis.