Quantification of Bias Errors Influence in Frequency Based Substructuring Using Sensitivity Analysis

Abstract

The methodology to divide complex systems into several subsystems is a common practice in the field of structural dynamics. Structural dynamic analyses can be carried out more efficiently if subsystems are analysed separately and later coupled using dynamic substructuring techniques. However a reliable experimental application of frequency based substructuring (FBS) remains a challenge as it requires highly accurate acquisition of subsystems’ frequency response functions (FRFs). Even a small error from the measurement campaign can yield erroneous coupling results. The measurement errors can be either random or systematic, with the latter often referred to as bias. Impact excitation is popular in dynamic substructuring due to the fast FRF calculation for each impact location. However, deviations in the location of excitation as a typical example of measurement bias affect the FRFs throughout the whole frequency range. This paper proposes a novel methodology to characterize bias errors in FBS based on the small deviations in impact excitation from typical experimental measurements. The deviations are utilized to reconstruct a range of bias-affected FRFs. These are then used in the global sensitivity analysis in order to characterize how each impact location affects an arbitrary quality indicator, such as FRFs reciprocity or passivity. Therefore, the effect of bias can be evaluated directly from a single measurement campaign, without the need for a numerical model. The proposed approach is shown on a synthetic numerical example, where the advantages and limitations are outlined. Virtual point transformation is applied to obtain admittance matrix at the substructures’ interfaces. Hence, virtual point reciprocity is proposed as a criterion to quantify bias error influence. Finally, an application of frequency based substructuring on beam-like structure is depicted.