Fast maximum-likelihood identification of modal parameters with uncertainty intervals: A modal model formulation with enhanced residual term

• In this article, the modal model-based maximum likelihood estimator is improved.
• The improvement lies in introducing a new lower and upper residuals term.
• The logarithmic formulation of the estimator is also introduced.
• The results show that the new residuals term improves the estimated modal model.
• The logarithmic formulation seems better when the FRFs variance is lacked.

Recently, a new maximum likelihood modal model-based (ML-MM) modal parameter estimator has been proposed [1] and [2]. One major drawback of this estimator is the modeling error, which can be caused by the effects of out-of-band modes (i.e. lower and upper residual effects). The ML-MM estimator uses the modal model as a parameterization form. This modal model includes so-called lower and upper residual terms, which have been included to cope for the effects of the out-of-band modes. However, those classical lower and upper residual terms are found to be not sufficient to properly compensate for the effects coming from the out-of-band modes. This leads to high modeling errors. In this paper, a new residual term will be introduced to better cope for the effects of these out-of-band modes. In this contribution, the ML-MM estimator [1] and [2] will be reformulated taking into account the new residual term. The ML-MM estimator with the new residual term will be compared to the one with the classical residual terms. Moreover, the logarithmic implementation of this estimator will be introduced and compared with the linear implementation. The validation will be done using simulated data and real data.