Component-Based Transfer Path Analysis and Hybrid Substructuring at high frequencies : A treatise on error modelling in Transfer Path Analysis

Abstract: The field of modal testing and analysis is currently facing a surge of interest in error modelling. Several errors which occur during testing campaigns are modelled analytically or numerically and propagated to various system coupling and interface reduction routines effectively. This study aims to propagate human errors, like position measurement errors and orientation measurement errors, and random noise-based errors in the measured Frequency Response Functions(FRFs) to the interface reduction algorithm called Virtual Point Transformation(VPT) and later to a substructure coupling method called Frequency-Based Substructuring(FBS). These methods form the cornerstone for Transfer Path Analsysis (TPA). Furthermore, common sources of error like sensor mass loading effect and sensor misalignment have also been investigated. Lastly, a new method to calculate the sensor positions and orientations after a measurement has been devised based on rigid body properties of the system and from the applied force characteristics. The error propagation was performed using a computationally efficient, moment method of the first order and later validated using Monte-Carlo simulations. The results show that the orientation measurement error is the most significant followed by FRF error and position measurement error. The mass loading effect is compensated using the Structural Modification Using Response Functions (SMURF) method and the sensor misalignment is corrected using coordinate transformation. The sensor positions and orientations are accurately estimated from rigid body properties and applied force characteristics; individually using matrix algebra and simultaneously using an optimization-based non-linear least squares solver.