Application of enhanced least square to component synthesis using FRF for analyzing dynamic interaction of coupled body-subframe system

The component response synthesis approach utilizing frequency response function (FRF) has been used to analyze the dynamic interaction of two or more vehicle components coupled at discrete interface points. This method is somewhat suitable for computing higher frequency response because experimental component FRFs can be incorporated into the formulation directly. However its calculations are quite sensitive to measurement errors in the FRFs due to the several matrix inversion steps involved. In the past, researchers have essentially used a combined direct inverse and truncated singular valued decomposition (TSVD) technique to ensure a stable calculation, which is typically applied semi-empirically due to the lack of understanding of the influence of measurement error. In this study, we applied an enhanced Least Square (LS) method based on TSVD to obtain the solution of an equivalent set of over-determined linear algebraic equations, which has been transformed from the classical direct matrix inverse problem. The numerical solution here provides a means to evaluate the dynamic response of an n-component system. A typical automotive body-subframe example for n=2 is analyzed to demonstrate the feasibility of studying vehicle-type NVH problems using this method.