Cross-moment reduction in multi-moment matching

This thesis discusses the realisation of cross-moment reduction respectively multi-moment vector reduction in multimoment matching model order reduction against the background of a generic vibroacoustic model to enhance the method’s computational efficiency. In order to reduce the number of multi-moment vectors, which is connected to the number of model parameters, non-influential model parameters are identified via sensitivity analysis by Morris screening and Sobol analysis. The sensitivity analysis enables multi-moment vector reduction based on two working principles: general multi-moment vector reduction and specific multi-moment vector reduction. In the case of general multi-moment vector reduction, the expansion points describing the non-influential parameters’ variation are deleted, and, therefore, also the respective local projection matrices. Then, during the construction of the global reduced-order model by concatenating the local reduced-order models’ projection matrices, fewer local projection matrices are summarised into the global projection matrix; reducing the size of the global reduced order model and, thus increasing the method’s computational efficiency. Specific multi-moment vector reduction deletes the non-sensitive parmeters’ multi-moments from the Taylor series expansion at an expansion point, reducing the size of the local reduced-order models’ projection matrices, which are then concatenated into the global reduced order models’ projection matrix; again, enhancing the method’s computational efficiency due to the smaller size of the global reduced order model. Nonetheless, specific multi-moment vector reduction can only be applied to additive models, where a physical parameter equals a respective affine parameter in the affine decomposition of the system matrix. As the vibroacoustic system is non-additive, this thesis only examines the efficiency of general multi-moment vector reduction in multi-moment matching model order reduction for an undamped and damped vibroacoustic model. Finally, applying sensitivity analysis-based multi-moment matching model order reduction yields accurate parametric reduced order models that allow time-efficient computations. In the case of the undamped vibroacoustic model, the parametric reduced order model is competitive to this derived by standard multi-moment matching. For the application to the damped vibroacoustic model, the parametric reduced order models of the here-proposed method are superior to these computed with standard multi-moment matching as the standard method is unable to find an accurate parametric reduced order model that additionally allows time-efficient computations.