Damped SVD for operational transfer path analysis

Transfer path analysis (TPA) is a method to identify energy transfer paths based on experiment and principle of linear superposition, which is widely used to identify the source of main faults based on vibration and noise signals, thus benefiting the works of PHM. However, load identification and transfer function measurement make it complex and slow to carry out. Operational transfer path analysis (OTPA) gets rid of the load identification and transfer function measurement, has attracted more attention due to simple and fast modeling. From a theoretical perspective, OTPA belongs to an inverse problem. Conventional OTPA use truncated singular value decomposition (TSVD) to identify transmissibility function matrix, which has two main shortages. Firstly, TSVD uses 0 and 1 as filter factors, without considering smoothness of filter factors, the sudden change of filter factors will result in large rounding errors, thus aggravating the ill-conditioned degree and approximate solution distortion. Secondly, the truncating parameter is usually chosen from experience, which is one of the most important parameters in TSVD, it's obviously not precise enough to meet the requirements. DSVD uses smooth filter factors to overcome the shortage of sudden change of filter factors in TSVD. Moreover, the regularization parameter is used to calculate the filter factors, which is easy to figure out by L-curve, overcoming the shortage of choosing from experience. A simulation experiment is adopted to test the proposed OTPA which proves that the proposed OTPA is correct and effective to solve vibration and noise problems. The proposed OTPA is also compared with the conventional OTPA which proves that precision of the proposed OTPA is much higher than that of the conventional OTPA.