Operational transfer path analysis with regularized total least-squares method

Abstract

Operational transfer path analysis (OTPA) uses only operational responses to characterize the paths, so it is efficient and widely used in various engineering fields. However, the operational responses are inevitably contaminated by errors, which seriously reduce the accuracy of OTPA. To reduce the influence of errors and improve the accuracy of OTPA, a Tikhonov regularized total least-squares method (RTLSM) which is based on the Tikhonov regularized least-squares method (RLSM) is used to estimate the transmissibility matrix, and then the individual contributions are calculated. The total least-squares method takes into account not only the influence of the errors in the target point responses but also the influence of the errors in the indicator point responses. Tikhonov regularization is introduced to regularize the total least-squares method to improve the ill-conditioning of the indicator point response matrix in the process of estimating the transmissibility matrix. An OTPA simulation on a lumped mass model and an OTPA experiment on an aluminum plate are studied to test the performance of the RLSM and RTLSM. Both simulation and experimental results show that the RTLSM is better than the RLSM in OTPA, and improved the accuracy of OTPA effectively.