A Fast Maximum Likelihood-Based Estimation of a Modal Model

Abstract

In this paper, the ML-MM estimator, a multivariable frequency-domain maximum likelihood estimator based on a modal model formulation, will be represented and improved in terms of the computational speed and the memory requirements. Basically, the design requirements to be met in the ML-MM estimator were to have accurate estimate for both of the modal parameters and their confidence limits and, meanwhile, having a clear stabilization chart which enables the user to easily select the physical modes within the selected frequency band. The ML-MM method estimates the modal parameters by directly identifying the modal model instead of identifying a rational fraction polynomial model. In the ML-MM estimator, the confidence bounds on the estimated modal parameters (i.e., frequency, damping ratios, mode shapes, etc.) are derived directly by inverting the so-called Fisher information matrix and without using many linearization formulas that are normally used when identifying rational fraction polynomial-based models. Another advantage of the ML-MM estimator lies in its potential to overcome the difficulties that the classical modal parameter estimation methods face when fitting an FRF matrix that consists of many (i.e., 4 or more) columns, i.e., in cases where many input excitation locations have to be used in the modal testing. For instance, the high damping level in acoustic modal analysis requires many excitation locations to get sufficient excitation of the modes. In this contribution, the improved ML-MM estimator will be validated and compared with some other classical modal parameter estimation methods using simulated datasets and real industrial applications.