Maximum likelihood estimator of operational modal analysis for linear time-varying structures in time–frequency domain

• A time–frequency-domain parametric model of LTV structures.
• An orthogonal polynomial and z-domain mapping hybrid time–frequency basis function.
• To adapt the frequency-domain identification methods to time–frequency domain.
• A time–frequency-domain parametric maximum likelihood estimator of LTV structures.
• Numerical and experimental validation of the proposed estimator.

This paper investigates the problem of modal parameter estimation of time-varying structures under unknown excitation. A time–frequency-domain maximum likelihood estimator of modal parameters for linear time-varying structures is presented by adapting the frequency-domain maximum likelihood estimator to the time–frequency domain. The proposed estimator is parametric, that is, the linear time-varying structures are represented by a time-dependent common-denominator model. To adapt the existing frequency-domain estimator for time-invariant structures to the time–frequency methods for time-varying cases, an orthogonal polynomial and z-domain mapping hybrid basis function is presented, which has the advantageous numerical condition and with which it is convenient to calculate the modal parameters. A series of numerical examples have evaluated and illustrated the performance of the proposed maximum likelihood estimator, and a group of laboratory experiments has further validated the proposed estimator.