Propagation of mode shape errors in structural identification

It is of interest to the modal testing and health monitoring community to quantify how an error in any identified mode shape propagates to the identified flexibility matrix. Here this problem is investigated in a probabilistic framework. The approach followed involves deriving analytical expressions to track how errors, due to random deviations between identified and “true” mode shapes, propagate to the Modal Assurance Criterion (MAC) and the Coordinate Modal Assurance Criterion (COMAC) values as well as the estimated flexibility matrix. The comparison of the expected values and variances of these errors identifies the inconsistency between the magnitude of errors in the MAC and COMAC values and the identified flexibility matrix. The analytical results are further validated via Monte Carlo simulations. Finally, two mode shape comparison criteria, termed as the Flexibility Proportional Modal Assurance Criterion (FPMAC) and the Flexibility Proportional Coordinate Modal Assurance Criterion (FPCOMAC), are proposed. These new criteria aim to mimic the expected error in the predicted flexibility matrix in a direct comparison of the identified and “true” mode shapes, and hence they can be used to complement MAC and COMAC in interpreting the analysis results.