Optimal Modal Parameter Estimation for Highly Challenging Industrial Cases

Abstract

In this paper, the recently-developed MLMM method (Maximum Likelihood estimation of a Modal Model) will be introduced and applied to challenging industrial cases. Specific about the method is that the well-established statistical concept of maximum likelihood estimation is applied to estimate directly a modal model based on measured Frequency Response Functions (FRFs). Due to the nature of this model, the optimal modal parameters are estimated using an iterative Gauss-Newton minimization scheme. The method is able to tackle some of the remaining challenges in modal analysis. For instance, in highly-damped cases (e.g. acoustic cavity modal analysis, trimmed body modal analysis) where it is needed to use a large amount of excitation locations to sufficiently excite the modes and to obtain a reliable modal model, the more classical modal parameter estimation methods sometimes fail to achieve a high-quality curve-fit of the measured FRF data. Due to the iterative minimization of the cost function, MLMM is able to estimate a model that very closely represents the measurements. Another benefit of the method is that additional constraints can be imposed to the model. For instance, it is possible to impose that real modes and participation factors are estimated and/or to impose that the estimated modal model is reciprocal (as prescribed by the modal theory). More classical modal parameter estimation methods have rarely the possibly to fully integrate these constraints and the obtained modal parameters are typically altered in a subsequent step to satisfy the desired realness and reciprocity constraints. It is obvious that this may lead to sub-optimal results, as for instance evidenced by a degradation of the quality of the fit between the identified modal model and the measurements. The applicability of MLMM to estimate a constrained modal model will be demonstrated using challenging industrial applications.